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[[File:500kV 3-Phase Transmission Lines.png|thumb|500 kV [[三相電]] Transmission Lines at [[大古力水坝]]; four circuits are shown; two additional circuits are obscured by trees on the right; the entire 7079 MW generation capacity of the dam is accommodated by these six circuits.]]
{{NoteTA|G1=物理學}}
{{other uses|Electric transmission (disambiguation)}}
{{infobox| title = 光速
'''輸電系統'''是指由[[發電廠]]至次級本地負載中心之間的極高壓大電能輸送過程,由負載中心轉換電壓至中高壓再輸送至客戶則為[[配電系統]],兩者相加則為[[輸電網路]],又稱為電網。自電流戰爭起,電力系統由大量獨立小型電力網絡整合為一個大型的電力輸送網絡,而發電能力亦集中至遠離民居的大型發電廠。輸電系統着重於可靠且低損耗地將大量電力作遠距離輸送
| image = -{zh-hant:[[File:Sun to Earth-zh-hk.jpg|300px]];zh-hans:[[File:Sun to Earth-zh-hans.jpg|300px]]}-
| caption = [[太陽光]]平均只要8分19秒即可到達[[地球]]。
| header1 = 準確數字
|labelstyle = font-weight:normal
| label2 = [[米每秒]]
| data2 = {{val|299792458}}
| label3 = [[普朗克單位制|普朗克]]
| data3 = 1
| header4 = 大約數字 <!--3 s.f.-->
| label5 = [[公里每小時|公里每秒]]
| data5 = 300,000
| label6 = [[公里每小時]]
| data6 = 1,080,000,000
| label7 = [[英里每小時|英里每秒]]
| data7 = 186,000
| label8 = [[英里每小時]]
| data8 = 671,000,000
| label9 = [[天文單位]]每日
| data9 = 173
| header10 = 前進某一距離所需時間
| label11 = '''距離'''
| data11 = '''時間'''
| label12 = 1[[英尺]]
| data12 = 1.0[[納秒]]
| label13 = 1[[米]]
| data13 = 3.3納秒
| label16 = 從[[地球靜止軌道]]到地面
| data16 = 119[[毫秒]]
| label17 = [[赤道]]長度
| data17 = 134毫秒
| label18 = 從[[月球]]到地球
| data18 = 1.3[[秒]]
| label19 = 從[[太陽]]到地球(1[[天文單位]])
| data19 = 8.3[[分鐘]]
| label21 = 從[[毗鄰星]]到太陽(1.3[[秒差距]])
| data21 = 4.2[[年]]
| label23 = 從[[大犬座矮星系]]到地球
| data23 = 25,000年
| label24 = 橫越[[銀河系]]
| data24 = 100,000年
| label25 = 從[[仙女座星系]]到地球
| data25 = 2,500,000年
}}
'''光速''',通常指[[光波]]傳播的速度<ref>{{cite book|title=现代汉语词典|edition=第五版|year=2005|publisher=[[商务印书馆]]|isbn=9787100043854}}</ref>。光在真空中傳播的速度,又名{{Smallmath|f=c}},是一個於[[物理學]]中極為重要的[[物理常數]]。此值為299,792,458[[米每秒]]。其為一實數,因為[[秒]]為國際單位,而[[米]]的長度亦由光速定義<ref name="penrose">{{Cite book|last=Penrose|first=R|year=2004|title=The Road to Reality: A Complete Guide to the Laws of the Universe|pages=410–1|publisher=[[Vintage Books]]|isbn=978-0-679-77631-4|quote=...the most accurate standard for the metre is conveniently ''defined'' so that there are exactly 299,792,458 of them to the distance travelled by light in a standard second, giving a value for the metre that very accurately matches the now inadequately precise standard metre rule in Paris.}}</ref>。以英制單位來說,此值約為186,282尺每秒。


A {{tsl|en|wide area synchronous grid|}}, also known as an "interconnection" in North America, directly connects many generators delivering AC power with the same relative ''frequency'' to many consumers. For example, there are four major interconnections in North America (the {{tsl|en|Western Interconnection|}}, the {{tsl|en|Eastern Interconnection|}}, the {{tsl|en|Quebec Interconnection|}} and the {{tsl|en|Electric Reliability Council of Texas|}} (ERCOT) grid). In Europe {{tsl|en|Synchronous grid of Continental Europe||one large grid connects most of continental Europe}}.
跟據[[狹義相對論]],{{Smallmath|f=c}}是宇宙中所有能量、物質或[[資訊 (物理學)|資訊]]所能達至的最高速度。{{Smallmath|f=c}}也是[[無質量粒子]]<!--massless particle,無誤?-->及相關的[[場 (物理)|場]](包括[[電磁波]],如[[光]])於真空中前進的速度。其亦是現時理論中預測[[重力波 (相對論)|重力波]]的[[重力速度|傳遞速度]]。上述的粒子或波皆以{{Smallmath|f=c}}傳遞,不論來源有否[[運動 (物理學)|運動]]或觀察者的[[慣性參考系]]。[[相對論]]中,{{Smallmath|f=c}}與[[時空]]相關連,亦出現於[[質能等價]]公式{{Smallmath|f=E=mc^2}}之中<ref name=LeClerq>{{Cite book|last=Uzan|first=J-P|last2=Leclercq|first2=B|year=2008|title=The Natural Laws of the Universe:Understanding Fundamental Constants| url=http://books.google.com/?id=dSAWX8TNpScC&pg=PA43 | pages=43–4 | publisher=Springer (publisher)|Springer|isbn=0-387-73454-6}}</ref>。


Historically, transmission and distribution lines were owned by the same company, but starting in the 1990s, many countries have [[電力自由化|liberalized]] the regulation of the [[電力市場]] in ways that have led to the separation of the electricity transmission business from the distribution business.<ref name=femp01>{{cite journal|url=https://www.pnnl.gov/main/publications/external/technical_reports/PNNL-13906.pdf|title=A Primer on Electric Utilities, Deregulation, and Restructuring of U.S. Electricity Markets|publisher=[[美國能源部]] {{tsl|en|Federal Energy Management Program|}} (FEMP)|date=May 2002|format=PDF|accessdate=October 30, 2018}}</ref>
光線傳播時若通過[[透明]]的物質,如空氣或水,則其速度會低於{{Smallmath|f=c}},而該速度{{Smallmath|f=v}}與{{Smallmath|f=c}}的比例為[[折射率]]-{{Smallmath|f=n}}({{Smallmath|f=n=\tfrac{c}{v} }})。例如[[可見光]]於[[玻璃]]的折射率通常約為1.5,即光於玻璃中傳播時的速度為{{nowrap|{{Smallmath|f=\tfrac{c}{1.5} \thickapprox 200,000}} }}公里每秒;空氣的折射率約為1.0003,即光於空氣中的速度比{{Smallmath|f=c}}慢約90公里每秒<!--TODO:REF-->。


== 系統 ==
大部分情況下,光都可以被理解為「瞬間到達」<!--我知道應用主語,但想不出-->,但當距離較長或要求非常精準時光的速度就顯得非常重要。當與遙遠的[[太空探測器]]溝通時,其需要數分鐘甚至以小時計<!--TODO:CLEANUP-->來傳遞訊息。由於星系之間的距離極長,所以我們看到的星光實際上由恆星於很多年前發出,使我們能借此研究宇宙的歷史<!--TODO:CLEANUP-->。光線有限的速度也限制了[[電腦]]於理論上的最高速度,因為電腦中的信息需於[[集成電路]]之間傳遞。最後,光速亦能用於精確測量長距離的飛行。
Most transmission lines are high-voltage [[三相電|three-phase]] [[交流電]] (AC), although [[單相電|single phase]] AC is sometimes used in [[電氣化鐵路]]s. [[高壓直流輸電|High-voltage direct-current]] (HVDC) technology is used for greater efficiency over very long distances (typically hundreds of miles). HVDC technology is also used in {{tsl|en|submarine power cable|}}s (typically longer than 30 miles (50&nbsp;km)), and in the interchange of power between grids that are not mutually synchronized. HVDC links are used to stabilize large power distribution networks where sudden new loads, or blackouts, in one part of a network can result in synchronization problems and {{tsl|en|cascading failure|}}s.


[[File:Electricity grid simple- North America.svg|thumb|400px|left|Diagram of an electric power system; transmission system is in blue]]
[[奧勒·羅默]]於1676年首次以[[木衛一]]與[[木星]]之間的掩食演示了光的速度有限。1865年,[[詹姆斯·克拉克·馬克士威]]提出光是一種電磁波,因此在他的理論中為光速予以{{Smallmath|f=c}}<ref>{{cite web|title=How is the speed of light measured?|url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html}}</ref>。1905年,[[阿爾伯特·愛因斯坦]]假設光速對於任何慣性系來說都是獨立於其光源<ref name="stachel">{{cite book |title=Einstein from "B" to "Z" – Volume 9 of Einstein studies |first1=JJ |last1=Stachel |publisher=Springer |year=2002 |isbn=0-8176-4143-2 |page=226 |url=http://books.google.com/books?id=OAsQ_hFjhrAC&pg=PA226}}</ref>,並根據[[狹義相對論]]探討了一些推論,並由此顯示{{Smallmath|f=c}}不只在光和電磁方面的相關性。經過百多年來越來越精確的測量,1975年測出為約為{{val|299792458}}米每秒。1983年,[[國際單位制]]將[[米]]按光速重新定義,改為每秒的299,792,458分之1<ref name="SIbrochure">{{SIbrochure}}</ref>{{rp|112}}。


Electricity is transmitted at [[高壓電]]s (66&nbsp;kV or above) to reduce the energy loss which occurs in long-distance transmission. Power is usually transmitted through [[高压电线]]s. {{tsl|en|Undergrounding||Underground power transmission}} has a significantly higher installation cost and greater operational limitations, but reduced maintenance costs. Underground transmission is sometimes used in urban areas or environmentally sensitive locations.
{{TOC limit}}


A lack of electrical energy storage facilities in transmission systems leads to a key limitation. Electrical energy must be generated at the same rate at which it is consumed. A sophisticated control system is required to ensure that the [[發電]] very closely matches the demand. If the demand for power exceeds supply, the imbalance can cause generation plant(s) and transmission equipment to automatically disconnect or shut down to prevent damage. In the worst case, this may lead to a cascading series of shut downs and a major regional [[停電|blackout]]. Examples include the US Northeast blackouts of [[1965年北美大停电|1965]], {{tsl|en|New York City blackout of 1977||1977}}, [[2003年美加大停电|2003]], and major blackouts in other US regions in {{tsl|en|1996 Western North America blackouts||1996}} and {{tsl|en|2011 Southwest blackout||2011}}. Electric transmission networks are interconnected into regional, national, and even continent wide networks to reduce the risk of such a failure by providing multiple [[冗餘|redundant]], alternative routes for power to flow should such shut downs occur. Transmission companies determine the maximum reliable capacity of each line (ordinarily less than its physical or thermal limit) to ensure that spare capacity is available in the event of a failure in another part of the network.
==數值、符號和單位==
光在真空中傳播的速度通常以{{Smallmath|f=c}}代表,而{{Smallmath|f=c}}則意為{{lang|en|constant}}(常數)或拉丁文{{lang|la|celeritas}}(迅捷)。一開始使用的符號為[[詹姆斯·克拉克·馬克士威]]於1865年發明的{{Smallmath|f=V}}。而{{Smallmath|f=c}}原本,由1856開始,[[魯道夫·科爾勞施]]與[[威廉·韋伯]]皆用之於真空中光速的{{Smallmath|f=\sqrt{2} }}倍。1894年,[[保羅·德汝德]]將其重新定義至現有意思。[[阿爾伯特·愛因斯坦|愛因斯坦]]於1905年的[[奇蹟年論文]]使用{{Smallmath|f=V}},到1907時則轉用{{Smallmath|f=c}},其後{{Smallmath|f=c}}更成為了一標準符號<ref name=Yc>{{cite web|last=Gibbs|first=P|year=2004|origyear=1997|title=Why is ''c'' the symbol for the speed of light?|url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html|work=Usenet Physics FAQ|publisher=University of California, Riverside|accessdate=2009-11-16|archiveurl=http://www.webcitation.org/5lLMPPN4L|archivedate=2009-11-17}}</ref><ref>{{cite journal|last=Mendelson|first=KS|year=2006|title=The story of ''c''|journal=American Journal of Physics|volume=74|issue=11|pages=995–997|doi=10.1119/1.2238887|bibcode = 2006AmJPh..74..995M }}</ref>。


== 架空電䌫 ==
有時{{Smallmath|f=c}}用作光於任何材質中的速度,而{{Smallmath|f=c}}<sub>{{Smallmath|f=_0}}</sub>則用於真空中的光速<ref name=handbook>
{{Main|架空電䌫}}
*{{Cite book|last=Lide|first=DR|year=2004|title=CRC Handbook of Chemistry and Physics|url=http://books.google.com/?id=WDll8hA006AC&pg=PT76&dq=speed+of+light+%22c0+OR+%22|pages=2–9|publisher=CRC Press|isbn=0-8493-0485-7}}
[[File:High Voltage Lines in Washington State.tif|thumb|upright=0.75|left|3-phase high-voltage lines in Washington State, "Bundled" 3-ways]]
*{{Cite book|last=Harris|first=JW|coauthors=''et al.''|year=2002|title=Handbook of Physics|url=http://books.google.com/?id=c60mCxGRMR8C&pg=PA499&dq=speed+of+light+%22c0+OR+%22+date:2000-2009|page=499|publisher=Springer|isbn=0-387-95269-1

}}
{{multiple image
*{{Cite book|last=Whitaker|first=JC|year=2005|title=The Electronics Handbook|url=http://books.google.com/?id=FdSQSAC3_EwC&pg=PA235&dq=speed+of+light+c0+handbook|page=235|publisher=CRC Press|isbn=0-8493-1889-0
|direction = vertical
|align = right
|width = 225
|image1=Electric power transmission line.JPG
|image2=Sample cross-section of high tension power (pylon) line.jpg
|caption1=Four-circuit, two-voltage power transmission line; "Bundled" 2-ways
|caption2=A typical [[鋼芯鋁纜|ACSR]]. The conductor consists of seven strands of steel surrounded by four layers of aluminium.
}}
}}
*{{Cite book|last=Cohen|first=ER|coauthors=''et al.''|year=2007|title=Quantities, Units and Symbols in Physical Chemistry |url=http://books.google.com/?id=TElmhULQoeIC&pg=PA143&dq=speed+of+light+c0+handbook|page=184|edition=3rd|publisher=[[Royal Society of Chemistry]]|isbn=0-85404-433-7}}</ref>。此法受國際單位制官方文章認可<ref name="SIbrochure"/>{{rp|112}},而同時亦存在於相關的常數,如{{Smallmath|f=\mu}}<sub>{{Smallmath|f=0}}</sub>為[[真空磁導率]]、{{Smallmath|f=\epsilon}}<sub>{{Smallmath|f=0}}</sub>為[[真空電容率]]、{{Smallmath|f=\Zeta}}<sub>{{Smallmath|f=0}}</sub>為[[自由空間阻抗]]。此條目使用{{Smallmath|f=c}}代表真空中的光速。


High-voltage overhead conductors are not covered by insulation. The conductor material is nearly always an [[铝]] alloy, made into several strands and possibly reinforced with steel strands. Copper was sometimes used for overhead transmission, but aluminum is lighter, yields only marginally reduced performance and costs much less. Overhead conductors are a commodity supplied by several companies worldwide. Improved conductor material and shapes are regularly used to allow increased capacity and modernize transmission circuits. Conductor sizes range from 12&nbsp;mm<sup>2</sup> (#6 [[美国线规]]) to 750&nbsp;mm<sup>2</sup> (1,590,000&nbsp;[[圓密耳]]s area), with varying resistance and {{tsl|en|current-carrying capacity|}}. For large conductors (more than a few centimetres in diameter) at power frequency, much of the current flow is concentrated near the surface due to the [[集膚效應]]. The center part of the conductor carries little current, but contributes weight and cost to the conductor. Because of this current limitation, multiple parallel cables (called [[高压电线]]s) are used when higher capacity is needed. Bundle conductors are also used at high voltages to reduce energy loss caused by [[电晕放电]].
[[國際單位制]]中,米定義為{{Smallmath|f=c}}的{{val|299792458}}分之1秒,因此{{Smallmath|f=c}}也倒過來固定於{{val|299792458}}米每秒<ref name=Boyes>{{Cite book|last=Sydenham|first=PH|year=2003|chapter=Measurement of length|chapterurl=http://books.google.com/books?id=sarHIbCVOUAC&pg=PA56|editor=Boyes, W|title=Instrumentation Reference Book|edition=3rd|page=56|publisher=Butterworth–Heinemann|isbn=0-7506-7123-8|quote=... if the speed of light is defined as a fixed number then, in principle, the time standard will serve as the length standard ...}}</ref><ref name="Fundamental Physical Constants">{{cite web|title=CODATA value: Speed of Light in Vacuum|url=http://physics.nist.gov/cgi-bin/cuu/Value?c|work=The NIST reference on Constants, Units, and Uncertainty
|publisher=National Institute of Standards and Technology|accessdate=2009-08-21}}</ref><ref name=Jespersen>{{Cite book |last=Jespersen|first=J|last2=Fitz-Randolph|first2=J|last3=Robb|first3=J|year=1999|title=From Sundials to Atomic Clocks: Understanding Time and Frequency|url=http://books.google.com/?id=Z7chuo4ebUAC&pg=PA280|page=280|edition=Reprint of National Bureau of Standards 1977, 2nd|publisher=Courier Dover|isbn=0-486-40913-9}}</ref>。{{Smallmath|f=c}}的數值於不同系統也有不同數值,如[[英制單位|英制]]及[[美制單位]]中,若按每寸等於2.54厘米則{{Smallmath|f=c}}為186,282英里,698碼,2呎及{{frac|5|21|127}}吋每秒<ref>
{{cite web|last=Savard|first=J|title=From Gold Coins to Cadmium Light|url=http://www.quadibloc.com/other/cnv03.htm|work=[http://www.quadibloc.com/ John Savard's Home Page]|accessdate=2009-11-14|archiveurl=http://www.webcitation.org/5lHYVsp5E |archivedate=2009-11-14}}</ref>。[[自然單位制]]中,{{Smallmath|f=c}}[[歸一化]]成為{{nowrap|{{Smallmath|f=c=1}}}}<ref name=Lawrie>{{Cite book|last=Lawrie|first=ID|year=2002|chapter=Appendix C: Natural units|chapterurl=http://books.google.com/books?id=9HZStxmfi3UC&pg=PA540|title=A Unified Grand Tour of Theoretical Physics|edition=2nd|publisher=CRC Press |isbn=0-7503-0604-1}}</ref>{{rp|540}}<ref name=Hsu>{{Cite book|last=Hsu|first=L|year=2006|chapter=Appendix A: Systems of units and the development of relativity theories|chapterurl=http://books.google.com/books?id=amLqckyrvUwC&pg=PA428|title=A Broader View of Relativity: General Implications of Lorentz and Poincaré Invariance|edition=2nd|publisher=World Scientific|isbn=981-256-651-1}}</ref>{{rp|427-8}}。


Today, transmission-level voltages are usually considered to be 110&nbsp;kV and above. Lower voltages, such as 66&nbsp;kV and 33&nbsp;kV, are usually considered {{tsl|en|||subtransmission}} voltages, but are occasionally used on long lines with light loads. Voltages less than 33&nbsp;kV are usually used for [[配電系統|distribution]]. Voltages above 765&nbsp;kV are considered [[高壓電|extra high voltage]] and require different designs compared to equipment used at lower voltages.
==物理學中的基本作用==
{{See also|狹義相對論}}
光於真空中傳播的速度獨立於其來源的運動模式及觀察者的慣性參考系,但同時,光的[[頻率]]可以因[[多普勒效應]]而改變。受到[[以太]]缺乏證據的刺激及[[詹姆斯·克拉克·馬克士威]]的[[電磁學|電磁理論]]所激勵<ref>{{cite journal|last=Einstein|first=A|year=1905|title=Zur Elektrodynamik bewegter Körper|journal=Annalen der Physik|volume=171|doi=10.1002/andp.19053221004|language=German}}英文翻譯:{{cite web|last=Perrett|first=W|last2=Jeffery|first2=GB (tr.)|last3=Walker|first3=J (ed.)|title=On the Electrodynamics of Moving Bodies|url=http://www.fourmilab.ch/etexts/einstein/specrel/www/|work=Fourmilab|accessdate=2009-11-27}}</ref>{{rp|890-2}},愛因斯坦於1905年發表光速不變性的假設<ref name="stachel"/>,其後各項實驗亦證明此理論。另外,實驗只能證明光的雙程速度,如從光源到鏡子再反射回來,因為[[單程光線速度]]無法量度。<!--TODO:RECHECK-->其原因為沒有方法為兩邊的時鐘<!--間 TO:RECHECK-->同步。然而,若使用[[愛因斯坦同步]]則可顯示單程光線速度等於雙程光線速度<ref name=Hsu>{{Cite book|last=Hsu|first=J-P|last2=Zhang|first2=YZ|year=2001|title=Lorentz and Poincaré Invariance|url=http://books.google.com/?id=jryk42J8oQIC&pg=RA1-PA541#v=onepage&q=|publisher=World Scientific|series=Advanced Series on Theoretical Physical Science|volume=8|isbn=981-02-4721-4}}</ref>{{rp|543''ff''}}<ref name=Zhang>{{Cite book|last=Zhang|first=YZ|year=1997|title=Special Relativity and Its Experimental Foundations |url=http://www.worldscibooks.com/physics/3180.html|publisher=World Scientific|series=Advanced Series on Theoretical Physical Science|volume=4|isbn=981-02-2749-3}}</ref>{{rp|172-3}}。狹義相對論利用了「各慣性參考系的物理定律相同」探討了{{Smallmath|f=c}}不變的結果<ref>{{Cite book|last=d'Inverno|first=R|year=1992|title=Introducing Einstein's Relativity|publisher=Oxford University Press |isbn=0-19-859686-3}}</ref>{{rp|19-20}}<ref>{{Cite book|last=Sriranjan|first=B|year=2004|chapter=Postulates of the special theory of relativity and their consequences|chapterurl=http://books.google.com/books?id=FsRfMvyudlAC&pg=PA20#v=onepage&q=&f=false |title=The Special Theory to Relativity|publisher=PHI Learning|isbn=81-203-1963-X}}</ref>{{rp|20 ''ff''}}。其中之一個結果就是所有無質量粒子於太空中前進的速度固定為{{Smallmath|f=c}}。


Since overhead transmission wires depend on air for insulation, the design of these lines requires minimum clearances to be observed to maintain safety. Adverse weather conditions, such as high winds and low temperatures, can lead to power outages. Wind speeds as low as {{convert|23|kn|km/h}} can permit conductors to encroach operating clearances, resulting in a [[电弧|flashover]] and loss of supply.<ref>Hans Dieter Betz, Ulrich Schumann, Pierre Laroche (2009). [https://books.google.com/books?id=U6lCL0CIolYC&pg=PA187&lpg=PA187&dq=Spatial+Distribution+and+Frequency+of+Thunderstorms+and+Lightning+in+Australia+wind+gust&source=bl&ots=93Eto3OuyQ&sig=nB7VACqDBK7xJDGHijfCdny7Ylw&hl=en&ei=DFkLSt2lKJCdlQeTyPjtCw&sa=X&oi=book_result&ct=result&resnum=3#PPA203,M1 Lightning: Principles, Instruments and Applications.] Springer, pp.&nbsp;202–203. {{ISBN|978-1-4020-9078-3}}. Retrieved on 13&nbsp;May 2009.</ref>
[[File:Lorentz factor.svg|thumb|left|upright|勞侖茲因子{{Smallmath|f=\gamma}}是一個速度的函數。其由1開始,並於{{Smallmath|f=v}}接近{{Smallmath|f=v}}時接近無限。]]
Oscillatory motion of the physical line can be termed {{tsl|en|conductor gallop||conductor gallop or flutter}} depending on the frequency and amplitude of oscillation.
狹義相對論有許多與直覺相反的影響<ref>{{cite web|last=Roberts|first=T|last2=Schleif|first2=S|last3=Dlugosz|first3=JM (ed.)|year=2007|title=What is the experimental basis of Special Relativity?|url=http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html|work=Usenet Physics FAQ|publisher=University of California, Riverside|accessdate=2009-11-27}}</ref>,包括[[質能等價]]({{Smallmath|f=E=mc^3}})、[[長度收縮]](當運動中的物件「測量」為較短時,他們「看來」在旋轉,亦即[[特勒爾旋轉]]<ref>{{cite journal|last=Terrell|first=J|year=1959|title=Invisibility of the Lorentz Contraction|journal=Physical Review|volume=116|issue=4|doi=10.1103/PhysRev.116.1041|bibcode = 1959PhRv..116.1041T }}</ref>{{rp|1041-5}}<ref>{{cite journal|last=Penrose|first=R|year=1959|title=The Apparent Shape of a Relativistically Moving Sphere|journal=Proceedings of the Cambridge Philosophical Society|volume=55|issue=01|doi=10.1017/S0305004100033776|bibcode = 1959PCPS...55..137P}}</ref>{{rp|137-9}})及[[時間膨脹]]。代表長度收縮和時間膨脹的函數{{Smallmath|f=\gamma}}稱為[[勞侖茲因子]],並由{{Smallmath|f=\gamma = \frac{1}{\sqrt{1-v^2/c^2} } \,}}產生,其中{{Smallmath|f=v}}是速度。當速度比{{Smallmath|f=c}}低很多時,例如日常速度,{{Smallmath|f=\gamma}}數值接近1,因此可以忽略。此時的{{Smallmath|f=\gamma}}與[[伽利略不变性]]<!--CHECK-NAME-->相似,但其將於{{Smallmath|f=v}}接近{{Smallmath|f=c}}時逼近無限。


== Underground transmission ==
狹義相對論可以視時間及空間為一個統一結構-[[時空]],並需要一個名為[[勞侖茲協變性]]的理論來達至[[對稱性 (物理學)|對稱性]],而勞侖茲協變性中又包含{{Smallmath|f=c}}<ref name="Hartle">{{Cite book|last=Hartle|first=JB|year=2003|title=Gravity: An Introduction to Einstein's General Relativity|publisher=Addison-Wesley|isbn=9780805386622}}</ref>{{rp|52-9}}勞侖茲協變性以往是現代物理學中的必要假設,如[[量子電動力學]]、[[量子色動力學]]、[[粒子物理學]]的[[標準模型]]、[[廣義相對論]]等。{{Smallmath|f=c}}於現代物理學中看似無處不在,然而大部分理論,卻與光無關。其中如廣義相對論預測{{Smallmath|f=c}}是[[重力波 (相對論)|重力波]]或重力的速度<ref name="Hartle"/>{{rp|332}} <ref name="Brügmann">參見{{Cite book|last1=Schäfer|first1=G|first2=MH|last2=Brügmann|editor1-first=H|editor1-last=Dittus|editor2-first=C|editor2-last=Lämmerzahl|editor3-first=SG|editor3-last=Turyshev|chapter=Propagation of light in the gravitational filed of binary systems to quadratic order in Newton's gravitational constant: Part 3: ‘On the speed-of-gravity controversy’|url=http://books.google.com/?id=QYnfdXOI8-QC&pg=PA111|title=Lasers, clocks and drag-free control: Exploration of relativistic gravity in space|isbn=3-540-34376-8|year=2008|publisher=Springer}}</ref>。於[[非慣性參考系]]中,本地的光速是一個等於{{Smallmath|f=c}}的定量,而沿著一條有限長度的軌跡的光的速度<!--CLEANUP-->卻可以按定義了的時間及空間而與{{Smallmath|f=c}}有所不同<ref name="Gibbs1997">{{cite web|last=Gibbs|first=P|year=1997|origyear=1996|title=Is The Speed of Light Constant? |url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html|editor-last=Carlip|editor-first=S |work=Usenet Physics FAQ|publisher=University of California, Riverside|accessdate=2009-11-26|archiveurl=http://www.webcitation.org/5lLQD61qh|archivedate=2009-11-17}}</ref>。
{{Main|Undergrounding}}


Electric power can also be transmitted by {{tsl|en|high-voltage cable||underground power cables}} instead of overhead power lines. Underground cables take up less right-of-way than overhead lines, have lower visibility, and are less affected by bad weather. However, costs of insulated cable and excavation are much higher than overhead construction. Faults in buried transmission lines take longer to locate and repair.
通常來說,認知中{{Smallmath|f=c}}於整個時空都應為同一數值,即光的速度不依賴地點或時間。然而,有一些理論卻認為[[光速可變理論|光速可以改變]]<ref name=Ellis_Uzan>{{cite journal|last=Ellis|first=GFR|last2=Uzan|first2=J-P|year=2005|title=‘c’ is the speed of light, isn’t it?|journal=American Journal of Physics|volume=73|issue=3|doi=10.1119/1.1819929|arxiv=gr-qc/0305099|quote=The possibility that the fundamental constants may vary during the evolution of the universe offers an exceptional window onto higher dimensional theories and is probably linked with the nature of the dark energy that makes the universe accelerate today.|bibcode = 2005AmJPh..73..240E }}</ref>{{rp|240-7}}<ref name=Mota>{{cite arxiv|last=Mota|first=DF|year=2006|title=Variations of the fine structure constant in space and time|class=astro-ph|eprint=astro-ph/0401631}}</ref>。雖然沒有證據指光速確會改變,但這個是最近熱門的研究<ref name=Uzan>{{cite journal|last=Uzan|first=J-P|year=2003|title=The fundamental constants and their variation: observational status and theoretical motivations|journal=Reviews of Modern Physics|volume=75|issue=2|doi=10.1103/RevModPhys.75.403|arxiv=hep-ph/0205340
|bibcode=2003RvMP...75..403U}}</ref>{{rp|403}}<ref name=Camelia>{{cite arxiv|last=Amelino-Camelia|first=G|year=2008|title=Quantum Gravity Phenomenology|class=gr-qc|eprint=0806.0339}}</ref>。


In some metropolitan areas, underground transmission cables are enclosed by metal pipe and insulated with dielectric fluid (usually an oil) that is either static or circulated via pumps. If an electric fault damages the pipe and produces a dielectric leak into the surrounding soil, liquid nitrogen trucks are mobilized to freeze portions of the pipe to enable the draining and repair of the damaged pipe location. This type of underground transmission cable can prolong the repair period and increase repair costs. The temperature of the pipe and soil are usually monitored constantly throughout the repair period.<ref>{{cite news|url=https://www.nytimes.com/2001/09/16/us/after-attacks-workers-con-edison-crews-improvise-they-rewire-truncated-system.html|title=AFTER THE ATTACKS: THE WORKERS; Con Edison Crews Improvise as They Rewire a Truncated System|first=Neela|last=Banerjee|date=September 16, 2001|via=NYTimes.com}}</ref><ref>{{cite web|url=http://documents.dps.ny.gov/public/Common/ViewDoc.aspx?DocRefId={5B2369A6-97FC-4613-AD8B-91E23D41AC05} |title=INVESTIGATION OF THE SEPTEMBER 2013 ELECTRIC OUTAGE OF A PORTION OF METRO-NORTH RAILROAD’S NEW HAVEN LINE |publisher=documents.dps.ny.gov |date=2014 |accessdate=2019-12-29}}</ref><ref>NYSPSC case no. 13-E-0529</ref>
通常情況下亦會假定光速具有[[各向同性]],即其於各方位測量的速度既一樣。但核[[能階]]發放的過程卻顯示其可能為[[各向異性]]<!--REVIEW--><ref name=Herrmann>{{cite journal|last1=Herrmann|first1=S|last2=Senger|first2=A|last3=Möhle|first3=K|last4=Nagel|first4=M|last5=Kovalchuk|first5=EV|last6=Peters|first6=A|display-authors=1|title=Rotating optical cavity experiment testing Lorentz invariance at the 10<sup>−17</sup> level |journal=Physical Review D|volume=80|issue=100|year=2009|doi=10.1103/PhysRevD.80.105011|arxiv=1002.1284|bibcode=2009PhRvD..80j5011H }}</ref>{{rp|105011}}<ref name=Lang>{{Cite book|title=Astrophysical formulae|first=KR|last=Lang|url=http://books.google.com/?id=OvTjLcQ4MCQC&pg=PA152|isbn=3-540-29692-1|publisher=Birkhäuser|edition=3rd |year=1999}}</ref>{{rp|152}}。


Underground lines are strictly limited by their thermal capacity, which permits less overload or re-rating than overhead lines. Long underground AC cables have significant [[電容]], which may reduce their ability to provide useful power to loads beyond {{convert|50|mi|abbr=off}}. DC cables are not limited in length by their capacitance, however, they do require {{tsl|en|HVDC converter station|}}s at both ends of the line to convert from DC to AC before being interconnected with the transmission network.
===<!--光的-->速度<!--的-->上限===
根據狹義相對論所說,某物件與其[[不變質量]]{{smallmath|f=m}}及速度{{smallmath|f=v}}由{{smallmath|f=\gamma mc^2}}給出<!--CHECK-->,{{smallmath|f=\gamma}}則是上方的勞侖茲因子。當速度為0,{{smallmath|f=\gamma}}為1,引出{{smallmath|f=E=mc^2}}。由於{{smallmath|f=\gamma}}於速度接近{{smallmath|f=c}}時會逼近無限,故該物件將需要無限能量來加速至光速。亦因此,光速的上限為光速。此理論亦為許多[[相對能量和動量測試|測試]]所證實<ref>{{cite web|last=Fowler|first=M|date=March 2008|title=Notes on Special Relativity |url=http://galileo.phys.virginia.edu/classes/252/SpecRelNotes.pdf|publisher=University of Virginia|accessdate=2010-05-07}}</ref>{{rp|56}}。


== History ==
[[File:Relativity of Simultaneity Animation.gif|thumb|right|綠色格網發生傾斜時,將出現三種可能性:先於、慢於、同步。請點擊圖片查看動畫。]]
{{Main|History of electric power transmission}}
更普遍來說,信息或能量的速度不可能超過{{smallmath|f=c}}。而其又引申出一個違反直覺的論點-[[同時性的相對性]]。如果事件A與B之間的距離大於時間的間距乘事件C<!--CHECK-->,那麼參照系將有三種<!--CHECK-->:A先於B,B先於A或同步。因此,當一物件相對一慣性參考系來說比C快、其將於另一個參考系顯得向後移動,而[[因果關係 (物理學)|因果關係]]也將會顛倒<ref name="Wheeler">{{Cite book|last=Taylor|first=EF|last2=Wheeler|first2=JA|year=1992 |title=Spacetime Physics: Introduction to Special Relativity|url=http://books.google.com/?id=PDA8YcvMc_QC&pg=PA59#v=onepage&q=|edition=2nd |publisher=Macmillan|isbn=0-7167-2327-1}}</ref>{{rp|74-5}}。亦因此,於此參照系中,結果可能比起因更早,因而做成如[[快子電話]]的[[悖論]]<ref>{{Cite book|last=Tolman|first=RC|year=2009|origyear=1917|chapter=Velocities greater than that of light|title=The Theory of the Relativity of Motion|edition=Reprint|publisher=BiblioLife|isbn=978-1-103-17233-7}}</ref>{{rp|54}}。但這種違反因果關係的事件卻從未被記錄過<ref name=Zhang/>。另外,一般認為[[沙恩霍斯特效應]]容許信息以比{{smallmath|f=c}}稍快的速度傳播,但其所需的特殊條件使得無法使用此效應來說反因果定律<ref>{{cite journal|last=Liberati|first=S|last2=Sonego|first2=S|last3=Visser|first3=M|year=2002 |title=Faster-than-c signals, special relativity, and causality|journal=Annals of Physics|volume=298|issue=1|doi=10.1006/aphy.2002.6233 |arxiv=gr-qc/0107091|bibcode = 2002AnPhy.298..167L }}</ref>{{rp|167-85}}。
[[File:New York utility lines in 1890.jpg|thumb|New York City streets in 1890. Besides telegraph lines, multiple electric lines were required for each class of device requiring different voltages]]


In the early days of commercial electric power, transmission of electric power at the same voltage as used by lighting and mechanical loads restricted the distance between generating plant and consumers. In 1882, generation was with [[直流電]] (DC), which could not easily be increased in voltage for long-distance transmission. Different classes of loads (for example, lighting, fixed motors, and traction/railway systems) required different voltages, and so used different generators and circuits.<ref name=hughes>{{cite book |url=https://books.google.com/?id=g07Q9M4agp4C&pg=PA122&lpg=PA122&dq=westinghouse+%22universal+system%22|pages=119–122|author=Thomas P. Hughes|title=Networks of Power: Electrification in Western Society, 1880–1930|publisher=Johns Hopkins University Press|location=Baltimore|isbn=0-8018-4614-5 |year=1993|authorlink=Thomas P. Hughes}}</ref><ref name="guarnieri 7-1">{{Cite journal|last=Guarnieri|first=M.|year=2013|title=The Beginning of Electric Energy Transmission: Part One|journal=IEEE Industrial Electronics Magazine|volume=7|issue=1|pages=57–60|doi=10.1109/MIE.2012.2236484|ref=harv}}</ref>
==超光速觀察和實驗==
{{Main|超光速}}
有一些情況下,物質、能量甚至信息似乎可以以比{{smallmath|f=c}}更快的速度傳播,但實際上它們不能。例如不少波的速度比{{smallmath|f=c}}快;又例如[[X射線]]於玻璃中的[[相速度]]經常超過{{smallmath|f=c}}<ref>{{Cite book|last=Hecht|first=E|year=1987|title=Optics|edition=2nd|publisher=Addison-Wesley|isbn=0-201-11609-X}}</ref>{{rp|62}},但這些波不能傳達任何訊號<ref>{{cite book|last=Quimby|first=RS|title=Photonics and lasers: an introduction|publisher=John Wiley and Sons|year=2006 |isbn=978-0-471-71974-8|url=http://books.google.com/books?id=yWeDVfaVGxsC&lpg=PA9&pg=PA9#v=onepage}}</ref>{{rp|9}},亦即[[訊號速度]]不會超越{{smallmath|f=c}}。


Due to this specialization of lines and because transmission was inefficient for low-voltage high-current circuits, generators needed to be near their loads. It seemed, at the time, that the industry would develop into what is now known as a [[分散式發電]] system with large numbers of small generators located near their loads.<ref name=ncep1>{{cite journal|url=https://www.energy.gov/sites/prod/files/oeprod/DocumentsandMedia/primer.pdf|title=Electricity Transmission: A primer|author=National Council on Electricity Policy|format=PDF|journal=|access-date=September 17, 2019}}</ref>
當激光束快速掃過遙遠物體時,光點可以移動得比{{smallmath|f=c}}快,而光點一開始則因光束需時傳播而延遲移動<!--RECHECK-->。然而,由於只有光束本身帶有物理信息,而其移動速度為{{smallmath|f=c}}。陰影亦能因類似理論而超越光速<ref>{{cite news|last=Wertheim|first=M |title=The Shadow Goes|url=http://www.nytimes.com/2007/06/20/opinion/20wertheim.html?_r=1&scp=1&sq=%27the%20shadow%20goes%27&st=cse&oref=slogin |work=The New York Times|accessdate=2009-08-21|date=2007-06-20}}</ref>。在以上兩種情況下,訊號速度仍然沒有超越{{smallmath|f=c}}<ref name=Gibbs>{{cite web|last=Gibbs|first=P |year=1997|title=Is Faster-Than-Light Travel or Communication Possible?|url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html |publisher=University of California, Riverside|work=Usenet Physics FAQ|accessdate=2008-08-20|archivedate=2009-11-17|archiveurl=http://www.webcitation.org/5lLRguF0I}}</ref>。


The transmission of electric power with [[交流電]] (AC) became possible after {{tsl|en|Lucien Gaulard|}} and {{tsl|en|John Dixon Gibbs|}} built what they called the secondary generator, an early transformer provided with 1:1 turn ratio and open magnetic circuit, in 1881.
當兩件物體互相飛離時,它們之間的距離可以增長得比{{smallmath|f=c}}快,然而,仍然沒有任何一樣物體於單一慣性參考系中能超越光速<ref name="Gibbs"/>。


The first long distance AC line was {{convert|34|km|abbr=off}} long, built for the 1884 International Exhibition of [[都灵]]. It was powered by a 2 kV, 130&nbsp;Hz {{tsl|en|Siemens & Halske|}} alternator and featured several Gaulard secondary generators with their primary windings connected in series, which fed incandescent lamps. The system proved the feasibility of AC electric power transmission on long distances.<ref name="guarnieri 7-1"/>
某些量子特質,例如[[愛因斯坦-波多爾斯基-羅森悖論]]中所顯示的,往往顯得快於光速<!--CHECK-->。其中的一個例子<!--CHECK-->顯示<!--CHECK-->涉及<!--CHECK-->了兩個粒子的[[量子態]]可以[[量子糾纏|糾纏]]一起。直至觀察到其中一個的顆粒之前,它們會存在於一個[[態疊加原理|量子疊加]]狀態<!--CHECK-->。當粒子分離而其中一個粒子的量子態被觀察了<!--CHECK-->,另一顆也會立刻決定出其量子態。但由於無法控制觀察第一顆粒子的量子態,故亦不能傳達信息<ref name=Gibbs /><ref>{{Cite book |last=Sakurai|first=JJ|year=1994|editor-last=T|editor-first=S|title=Modern Quantum Mechanics|edition=Revised|publisher=Addison-Wesley|isbn=0-201-53929-2}}</ref>{{rp|231-232}}。


The very first AC system to operate was in service in 1885 in via dei Cerchi, [[罗马]], for public lighting. It was powered by two Siemens & Halske alternators rated 30&nbsp;hp (22&nbsp;kW), 2 kV at 120&nbsp;Hz and used 19&nbsp;km of cables and 200&nbsp;parallel-connected 2 kV to 20&nbsp;V step-down transformers provided with a closed magnetic circuit, one for each lamp. A few months later it was followed by the first British AC system, which was put into service at the {{tsl|en|Grosvenor Gallery|}}, London. It also featured Siemens alternators and 2.4 kV to 100&nbsp;V step-down transformers &ndash; one per user &ndash; with shunt-connected primaries.<ref name="guarnieri 7-2">{{Cite journal|last=Guarnieri|first=M.|year=2013|title=The Beginning of Electric Energy Transmission: Part Two|journal=IEEE Industrial Electronics Magazine|volume=7|issue=2|pages=52–59|doi=10.1109/MIE.2013.2256297|ref=harv}}</ref>
另一個帶有超光速特性的量子特質為{{tsl|en|Hartman effect|哈特曼效應}}。在某些情況下,一顆[[虛粒子]][[量子穿隧效應|穿隧]]時無視阻擋層的厚度,所需時間為一常數<ref name=Muga>{{Cite book|last=Muga|first=JG|last2=Mayato|first2=RS|last3=Egusquiza|first3=IL, eds|year=2007|title=Time in Quantum Mechanics |url=http://books.google.com/?id=InKru6zHQWgC&pg=PA48|publisher=Springer|isbn=3-540-73472-4}}</ref>{{rp|48}}<ref name=Recami>{{Cite book|last=Hernández-Figueroa|first=HE|last2=Zamboni-Rached|first2=M|last3=Recami|first3=E|year=2007|title=Localized Waves|url=http://books.google.com/?id=xxbXgL967PwC&pg=PA26 |publisher=Wiley Interscience|isbn=0-470-10885-1}}</ref>{{rp|26}}。此可導致虛粒子能以超光速穿越一大間隙。然而,同樣沒有信息能以此方法傳達<ref name=Wynne>{{cite journal|last=Wynne|first=K|year=2002|title=Causality and the nature of information|url=http://144.206.159.178/ft/809/64567/1101504.pdf |journal=Optics Communications|volume=209|issue=1–3|doi=10.1016/S0030-4018(02)01638-3|bibcode=2002OptCo.209...85W}}</ref>{{rp|84-100}}。


[[File:William-Stanley jr.jpg|thumbnail|left|Working for Westinghouse, William Stanley Jr. spent his time recovering from illness in Great Barrington installing what is considered the world's first practical AC transformer system.]]
So-called 某些天文物體中也有出現[[超光速運動]]現象<ref>{{cite journal|last=Rees|first=M|year=1966|title=The Appearance of Relativistically Expanding Radio Sources |journal=Nature|volume=211|issue=5048|doi=10.1038/211468a0|bibcode = 1966Natur.211..468R }}</ref>{{rp|468}},例如[[電波星系]]或[[類星體]]的[[相對論性噴流]]。但是,這些噴流並沒有超越光速,其只是因物體以接近光速的速度<!--CHECK-->並以一個小角度接近地球時造成的{{tsl|en|Graphical projection|圖像投影|投影}}效應使其看似超越光速。原因為當噴流起距離較遠的位置發出光線時,該光速需要更長時間來到達觀察者,亦即地球<ref>{{cite web|last=Chase|first=IP |title=Apparent Superluminal Velocity of Galaxies|url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/Superluminal/superluminal.html |publisher=[[加州大學河濱分校]]|work=Usenet Physics FAQ|accessdate=2009-11-26}}</ref>。
Working from what he considered an impractical Gaulard-Gibbs design, electrical engineer [[威廉·史坦雷 (物理學家)]] developed what is considered the first practical series AC transformer in 1885.<ref name="edisontechcenter.org">{{cite web|url=http://edisontechcenter.org/GreatBarrington.html|title=Great Barrington Experiment|website=edisontechcenter.org}}</ref> Working with the support of [[乔治·威斯汀豪斯]], in 1886 he demonstrated a transformer based alternating current lighting system in {{tsl|en|Great Barrington, Massachusetts|}}. Powered by a steam engine driven 500&nbsp;V Siemens generator, voltage was stepped down to 100&nbsp;Volts using the new Stanley transformer to power incandescent lamps at 23&nbsp;businesses along main street with very little power loss over {{convert|4000|ft|m}}.<ref>{{cite web|url=https://ethw.org/William_Stanley|title=William Stanley - Engineering and Technology History Wiki|website=ethw.org}}</ref> This practical demonstration of a transformer and alternating current lighting system would lead Westinghouse to begin installing AC based systems later that year.<ref name="edisontechcenter.org"/>


1888 saw designs for a functional [[交流电动机]], something these systems had lacked up till then. These were [[异步电动机]]s running on [[多相系統|polyphase]] current, independently invented by [[加利莱奥·费拉里斯]] and [[尼古拉·特斯拉]] (with Tesla's design being licensed by Westinghouse in the US). This design was further developed into the modern practical [[三相電|three-phase]] form by {{tsl|en|Mikhail Dolivo-Dobrovolsky|}} and {{tsl|en|Charles Eugene Lancelot Brown|}}.<ref name="books.google.com">{{tsl|en|Arnold Heertje|}}, Mark Perlman [https://books.google.com/books?id=qQMOPjUgWHsC&pg=PA138&lpg=PA138&dq=tesla+motors+sparked+induction+motor&source=bl&ots=d0d_SjX8YX&sig=sA8LhTkGdQtgByBPD_ZDalCBwQA&hl=en&sa=X&ei=XoVSUPnfJo7A9gSwiICYCQ&ved=0CEYQ6AEwBA#v=onepage&q=tesla%20motors%20sparked%20induction%20motor&f=false Evolving Technology and Market Structure: Studies in Schumpeterian Economics], page 138</ref> Practical use of these types of motors would be delayed many years by development problems and the scarcity of poly-phase power systems needed to power them.<ref>Carlson, W. Bernard (2013). Tesla: Inventor of the Electrical Age. Princeton University Press. {{ISBN|1-4008-4655-2}}, page 130</ref><ref>Jonnes, Jill (2004). Empires of Light: Edison, Tesla, Westinghouse, and the Race to Electrify the World. Random House Trade Paperbacks. {{ISBN|978-0-375-75884-3}}, page 161.</ref>
在膨脹宇宙模型中,彼此越遠的星系,他們分離的速度越快。但這並不因空間上的移動,而是{{tsl|en|Metric expansion of space|空間的度規膨脹|空間的膨脹}}<ref name="Gibbs"/>。例如,星系遠離地球的速度與距離成正比。當星球越過[[哈柏體積|哈柏極限]]時,其速度將超越光速<ref name=Harrison>{{Cite book|last= Harrison|first=ER|year=2003|title=Masks of the Universe|url=http://books.google.com/?id=tSowGCP0kMIC&pg=PA206|publisher=Cambridge University Press |isbn=0-521-77351-2}}</ref>{{rp|206}}。


The late 1880s and early 1890s would see the financial merger of smaller electric companies into a few larger corporations such as [[冈茨公司|Ganz]] and [[AEG]] in Europe and [[通用电气]] and [[西屋电气|Westinghouse Electric]] in the US. These companies continued to develop AC systems but the technical difference between direct and alternating current systems would follow a much longer technical merger.<ref name="Thomas Parke Hughes 1930, pages 120-121"/> Due to innovation in the US and Europe, alternating current's economy of scale with very large generating plants linked to loads via long-distance transmission was slowly being combined with the ability to link it up with all of the existing systems that needed to be supplied. These included single phase AC systems, poly-phase AC systems, low voltage incandescent lighting, high voltage arc lighting, and existing DC motors in factories and street cars. In what was becoming a ''universal system'', these technological differences were temporarily being bridged via the development of [[回轉變流機]]s and [[電動發電機]]s that would allow the large number of legacy systems to be connected to the AC grid.<ref name="Thomas Parke Hughes 1930, pages 120-121">{{cite book|first=Thomas |last=Parke Hughes|title=Networks of Power: Electrification in Western Society, 1880-1930|publisher=JHU Press|year=1993|pages=120–121}}</ref><ref name="Raghu Garud 2009, page 249">{{cite book|first1=Raghu|last1=Garud|first2=Arun|last2=Kumaraswamy|first3= Richard|last3= Langlois|title= Managing in the Modular Age: Architectures, Networks, and Organizations|url=https://archive.org/details/managingmodulara00garu|url-access=limited|publisher= John Wiley & Sons |year=2009| page=[https://archive.org/details/managingmodulara00garu/page/n256 249]}}</ref> These stopgaps would slowly be replaced as older systems were retired or upgraded.
2011年9月,[[OPERA實驗]]指[[微中子]]由[[歐洲核子研究組織]]飛至{{tsl|en|Laboratori_Nazionali_del_Gran_Sasso|格蘭沙索國家實驗室}}比光速更快<ref name="OPERA">{{cite arxiv|title=Measurement of the neutrino velocity with the OPERA detector in the CNGS beam|author=OPERA Collaboration|author-link=OPERA experiment |eprint=1109.4897 |class=hep-ex|year=2011}}</ref>。此發現常稱為{{tsl|en|Faster-than-light neutrino anomaly|超光速微中子異常}},到最後確定為測量錯誤<ref>{{cite news|title= BREAKING NEWS: Error Undoes Faster-Than-Light Neutrino Results|first=Edwin|last=Cartlidge|url=http://news.sciencemag.org/scienceinsider/2012/02/breaking-news-error-undoes-faster.html|newspaper=Science| accessdate=2012-02-22|date=2012-02-22}}</ref>。


[[File:Tesla polyphase AC 500hp generator at 1893 exposition.jpg|thumb|right|Westinghouse alternating current [[多相系統|polyphase]] generators on display at the 1893 [[芝加哥哥伦布纪念博览会|World's Fair in Chicago]], part of their "Tesla Poly-phase System". Such polyphase innovations revolutionized transmission]]
==光的傳播==
[[古典物理學]]中,光是一種[[電磁波]]。以[[麥克斯韋方程組]]描述的[[電磁場]]古典行為預測{{Smallmath|f=c}}和電磁波於真空中傳播的速度皆按{{nowrap|''c''{{=}}1/{{radic|''ε''<sub>0</sub>''μ''<sub>0</sub>}}}}而與[[真空電容率]]''ε''<sub>0</sub>及[[真空磁導率]]''μ''<sub>0</sub><ref>{{Cite book |last=Panofsky |first=WKH |last2=Phillips |first2=M |year=1962 |title=Classical Electricity and Magnetism |publisher=Addison-Wesley |isbn=978-0-201-05702-7}}</ref>{{rp|182}}相連。現代[[量子力學]]中電磁場由[[量子電動力學]]理論所描述。此理論中,光由[[光子]]所組成。量子電動力學中,光子為無質量粒子,亦因此,跟據狹義相對論,光子於真空中以光速運行。


The first transmission of single-phase alternating current using high voltage took place in Oregon in 1890 when power was delivered from a hydroelectric plant at Willamette Falls to the city of Portland {{convert|14|mi|km}} downriver.<ref>{{Cite journal|last=Argersinger|first=R.E.|date=1915|title=Electric Transmission of Power|url=|journal=General Electric Review|volume=XVIII|page=454|via=}}</ref> The first three-phase alternating current using high voltage took place in 1891 during the {{tsl|en|International Electro-Technical Exhibition – 1891||international electricity exhibition}} in [[美因河畔法兰克福]]. A 15 kV transmission line, approximately 175&nbsp;km long, connected [[内卡河畔劳芬|Lauffen on the Neckar]] and Frankfurt.<ref name="guarnieri 7-2"/><ref>Kiessling F, Nefzger P, Nolasco JF, Kaintzyk U. (2003). ''Overhead power lines''. Springer, Berlin, Heidelberg, New York, p.&nbsp;5</ref>
量子電動力學中有伸延部分<!--RECHECK-->考慮到光子帶有重量的情況。這種理論中,其速度將取決於其頻率,而狹義相對論中的{{smallmath|f=c}}則成為光於真空中的最高速度<ref name="Gibbs1997"/>。在嚴謹的測試中沒有觀察到同一頻率的光有不同的速度<ref name=Schaefer>{{cite journal |last=Schaefer|first=BE|year=1999|title=Severe limits on variations of the speed of light with frequency|journal=Physical Review Letters|volume=82 |issue=25|pages=4964–6 |doi=10.1103/PhysRevLett.82.4964|arxiv=astro-ph/9810479|bibcode=1999PhRvL..82.4964S}}</ref><ref name=Sakharov>{{cite journal |last=Ellis |first=J |last2=Mavromatos |first2=NE |last3=Nanopoulos |first3=DV |last4=Sakharov |first4=AS |year=2003 |title=Quantum-Gravity Analysis of Gamma-Ray Bursts using Wavelets |journal=Astronomy & Astrophysics|volume=402|issue=2|pages=409–24|doi=10.1051/0004-6361:20030263|arxiv=astro-ph/0210124 |bibcode=2003A&A...402..409E}}</ref><ref name="Füllekrug">{{cite journal|last=Füllekrug |first=M|year=2004|title=Probing the Speed of Light with Radio Waves at Extremely Low Frequencies|journal=Physical Review Letters|volume=93|issue=4 |page=043901| doi=10.1103/PhysRevLett.93.043901| bibcode=2004PhRvL..93d3901F}}</ref>,因此光子的重量有著嚴格的限制。該限制取決於所使用的模型:若光子由{{tsl|en|Proca action|普羅卡理論}}產生<ref name="adelberger">{{cite journal |last=Adelberger |first=E |last2=Dvali |first2=G |last3=Gruzinov |first3=A |year=2007 |title=Photon Mass Bound Destroyed by Vortices |journal=Physical Review Letters |volume=98 |issue=1 |page=010402 |doi=10.1103/PhysRevLett.98.010402 |arxiv=hep-ph/0306245 |pmid=17358459 |bibcode=2007PhRvL..98a0402A}}</ref>,其質量的實驗上限約為10<sup>−57</sup>克<ref name=Sidharth>{{Cite book |last=Sidharth |first=BG |year=2008 |title=The Thermodynamic Universe |url=http://books.google.com/?id=OUfHR36wSfAC&pg=PA134 |page=134 |publisher=[[World Scientific]] |isbn=981-281-234-2}}</ref>;若是由[[希格斯機制]]所產生,其質量之實驗上限則沒有那麼準確:{{nowrap|''m'' ≤ 10<sup>−14</sup> [[電子伏特#電子伏特與質量|eV/c<sup>2</sup>]]}}<ref name="adelberger"/>。


Voltages used for electric power transmission increased throughout the 20th&nbsp;century. By 1914, fifty-five transmission systems each operating at more than 70 kV were in service. The highest voltage then used was 150 kV.<ref>Bureau of Census data reprinted in Hughes, pp.&nbsp;282–283</ref>
另一個光速因其頻率而相異的原因是[[量子重力]]的一些理論中認為[[狹義相對論]]無法應用於任意的較小比例<!--RECHECK-->。2009年一項對[[伽瑪射線暴]]光譜的觀測沒有發現不同能量的光子速度有任何分別,確認了普朗克長度除以1.2下的勞侖茲協變性<ref>{{cite journal|last=Amelino-Camelia |first=G|year=2009|title=Astrophysics: Burst of support for relativity|journal=[[Nature (journal)|Nature]]|volume=462 |pages=291–292|doi=10.1038/462291a|laysummary=http://www.nature.com/nature/journal/v462/n7271/edsumm/e091119-06.html|laysource=Nature |laydate=19&nbsp;November 2009|pmid=19924200|issue=7271|bibcode = 2009Natur.462..291A }}</ref>。
By allowing multiple generating plants to be interconnected over a wide area, electricity production cost was reduced. The most efficient available plants could be used to supply the varying loads during the day. Reliability was improved and capital investment cost was reduced, since stand-by generating capacity could be shared over many more customers and a wider geographic area. Remote and low-cost sources of energy, such as [[水力發電|hydroelectric]] power or mine-mouth coal, could be exploited to lower energy production cost.<ref name="hughes" /><ref name="guarnieri 7-2"/>


The rapid industrialization in the 20th&nbsp;century made electrical transmission lines and grids [[維生管線]] items in most industrialized nations. The interconnection of local generation plants and small distribution networks was spurred by the requirements of [[第一次世界大战]], with large electrical generating plants built by governments to provide power to munitions factories. Later these generating plants were connected to supply civil loads through long-distance transmission.<ref>Hughes, pp.&nbsp;293–295</ref>{{clear left}}
===介質中===
{{See also|折射率}}
於介質中,光通常不以''c''前進,In a medium, light usually does not propagate at a speed equal to ; further, different types of light wave will travel at different speeds. The speed at which the individual crests and troughs of a [[plane wave]] (a wave filling the whole space, with only one [[frequency]]) propagate is called the [[phase velocity]]&nbsp;''v''<sub>p</sub>. An actual physical signal with a finite extent (a pulse of light) travels at a different speed. The largest part of the pulse travels at the [[group velocity]]&nbsp;''v''<sub>g</sub>, and its earliest part travels at the [[front velocity]]&nbsp;''v''<sub>f</sub>.


== Bulk power transmission ==
[[File:frontgroupphase.gif|thumb|left|The blue dot moves at the speed of the ripples, the phase velocity; the green dot moves with the speed of the envelope, the group velocity; and the red dot moves with the speed of the foremost part of the pulse, the front velocity|alt=A modulated wave moves from left to right. There are three points marked with a dot: A blue dot at a node of the carrier wave, a green dot at the maximum of the envelope, and a red dot at the front of the envelope.]]
[[File:Transmissionsubstation.jpg|thumb|A [[變電所|transmission substation]] decreases the voltage of incoming electricity, allowing it to connect from long-distance high voltage transmission, to local lower voltage distribution. It also reroutes power to other transmission lines that serve local markets. This is the {{tsl|en|PacifiCorp|}} Hale Substation, [[奥勒姆 (犹他州)]], USA]]
The phase velocity is important in determining how a light wave travels through a material or from one material to another. It is often represented in terms of a ''refractive index''. The refractive index of a material is defined as the ratio of ''c'' to the phase velocity&nbsp;''v''<sub>p</sub> in the material: larger indices of refraction indicate lower speeds. The refractive index of a material may depend on the light's frequency, intensity, [[polarization (waves)|polarization]], or direction of propagation; in many cases, though, it can be treated as a material-dependent constant. The [[refractive index of air]] is approximately 1.0003.<ref name=Podesta>{{Cite book
|last=de Podesta |first=M
|year=2002
|title=Understanding the Properties of Matter
|url=http://books.google.com/?id=h8BNvnR050cC&pg=PA131&lpg=PA131
|page=131
|publisher=CRC Press
|isbn=0-415-25788-3
}}</ref> Denser media, such as [[Optical properties of water and ice|water]],<ref>{{cite web
|title=Refractive index of Water, H20 [Liquids]
|url=http://refractiveindex.info/?group=LIQUIDS&material=Water
|publisher=Mikhail Polyanskiy
|work=refractiveindex.info
|accessdate =2010-03-14
}}</ref> glass,<ref>{{cite web
|title=Refractive index of Fused Silica [Glasses]
|url=http://refractiveindex.info/?group=GLASSES&material=F_SILICA
|publisher=Mikhail Polyanskiy
|work=refractiveindex.info
|accessdate =2010-03-14
}}</ref> and [[Material properties of diamond#Optical properties|diamond]],<!--there must be a way to make it clearer where these links go--><ref>
{{cite web
|title=Refractive index of C [Crystals etc.]
|url=http://refractiveindex.info/?group=CRYSTALS&material=C
|publisher=Mikhail Polyanskiy
|work=refractiveindex.info
|accessdate =2010-03-14
}}</ref> have refractive indexes of around 1.3, 1.5 and 2.4, respectively, for visible light. In exotic materials like Bose-Einstein condensates near absolute zero, the effective speed of light may be only a few meters per second. However, this represents absorption and re-radiation delay between atoms, as does all slower-than-c speeds in material substances. As an extreme example of this, light "slowing" in matter, two independent teams of physicists claimed to bring light to a "complete standstill" by passing it through a [[Bose-Einstein Condensate]] of the element [[rubidium]], one team at [[Harvard University]] and the [[Rowland Institute for Science]] in Cambridge, Mass., and the other at the [[Harvard-Smithsonian Center for Astrophysics]], also in Cambridge. However, the popular description of light being "stopped" in these experiments refers only to light being stored in the excited states of atoms, then re-emitted at an arbitrarily later time, as stimulated by a second laser pulse. During the time it had "stopped," it had ceased to be light. This type of behaviour is generally microscopically true of all transparent media which "slow" the speed of light.<ref>{{cite web|author=Harvard News Office |url=http://www.news.harvard.edu/gazette/2001/01.24/01-stoplight.html |title=Harvard Gazette: Researchers now able to stop, restart light |publisher=News.harvard.edu |date=2001-01-24 |accessdate=2011-11-08}}</ref>
In transparent materials, the refractive index generally is greater than 1, meaning that the phase velocity is less than ''c''. In other materials, it is possible for the refractive index to become smaller than 1 for some frequencies; in some exotic materials it is even possible for the index of refraction to become negative.<ref name="Milonni">{{Cite book
|title=Fast light, slow light and left-handed light
|last=Milonni |first=PW
|url=http://books.google.com/?id=kE8OUCvt7ecC&pg=PA25
|isbn=0-7503-0926-1
|year=2004
|publisher=CRC Press
}}</ref>{{rp|25}} The requirement that causality is not violated implies that the [[real and imaginary parts]] of the [[dielectric constant]] of any material, corresponding respectively to the index of refraction and to the [[attenuation coefficient]], are linked by the [[Kramers–Kronig relation]]s.<ref>{{cite journal
|last=Toll |first=JS
|year=1956
|title=Causality and the Dispersion Relation: Logical Foundations
|journal=[[Physical Review]]
|volume=104
|issue=6 |pages=1760–1770
|doi=10.1103/PhysRev.104.1760
|bibcode = 1956PhRv..104.1760T }}</ref> In practical terms, this means that in a material with refractive index less than 1, the absorption of the wave is so quick that no signal can be sent faster than ''c''.


Engineers design transmission networks to transport the energy as efficiently as possible, while at the same time taking into account the economic factors, network safety and redundancy. These networks use components such as power lines, cables, [[斷路器]]s, switches and [[变压器]]s. The transmission network is usually administered on a regional basis by an entity such as a {{tsl|en|regional transmission organization|}} or {{tsl|en|transmission system operator|}}.
A pulse with different group and phase velocities (which occurs if the phase velocity is not the same for all the frequencies of the pulse) smears out over time, a process known as [[Dispersion (optics)|dispersion]]. Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called [[slow light]], which has been confirmed in various experiments.<ref>{{cite journal
|last=Hau |first=LV
|last2=Harris |first2=SE
|last3=Dutton |first3=Z
|last4=Behroozi |first4=CH
|year=1999
|title=Light speed reduction to 17 metres per second in an ultracold atomic gas
|url=http://www.nature.com/nature/journal/v397/n6720/pdf/397594a0.pdf
|journal=Nature
|volume=397
|issue=6720 |pages=594–598
|doi=10.1038/17561
|bibcode = 1999Natur.397..594V }}</ref><ref>
{{cite journal
|last=Liu |first=C |last2=Dutton |first2=Z |last3=Behroozi |first3=CH |last4=Hau |first4=LV
|year=2001
|title=Observation of coherent optical information storage in an atomic medium using halted light pulses
|url=http://www.nature.com/nature/journal/v409/n6819/pdf/409490a0.pdf
|journal=Nature
|volume=409 |issue=6819 |pages=490–493
|doi=10.1038/35054017
|pmid=11206540
|bibcode = 2001Natur.409..490L }}</ref><ref>
{{cite journal
|last=Bajcsy |first=M |last2=Zibrov |first2=AS |last3=Lukin |first3=MD
|year=2003
|title=Stationary pulses of light in an atomic medium
|journal=Nature
|volume=426 |issue=6967 |pages=638–41
|doi=10.1038/nature02176
|pmid=14668857
|arxiv = quant-ph/0311092 |bibcode = 2003Natur.426..638B }}</ref><ref>
{{cite web
|last=Dumé |first=B
|year=2003
|title=Switching light on and off
|url=http://physicsworld.com/cws/article/news/18724
|work=[[Physics World]]
|publisher=Institute of Physics
|accessdate=2008-12-08
}}</ref>
The opposite, group velocities exceeding ''c'', has also been shown in experiment.<ref>
{{cite news
|last=Whitehouse |first=D
|date=19 July 2000
|title=Beam Smashes Light Barrier
|url=http://news.bbc.co.uk/2/hi/science/nature/841690.stm
|publisher=BBC News
|accessdate=2008-12-08
}}</ref> It should even be possible for the group velocity to become infinite or negative, with pulses travelling instantaneously or backwards in time.<ref name="Milonni"/>{{rp|Ch2}}


Transmission efficiency is greatly improved by devices that increase the voltage (and thereby proportionately reduce the current), in the line conductors, thus allowing power to be transmitted with acceptable losses. The reduced current flowing through the line reduces the heating losses in the conductors. According to [[焦耳加热|Joule's Law]], energy losses are directly proportional to the square of the current. Thus, reducing the current by a factor of two will lower the energy lost to conductor resistance by a factor of four for any given size of conductor.
None of these options, however, allow information to be transmitted faster than ''c''. It is impossible to transmit information with a light pulse any faster than the speed of the earliest part of the pulse (the [[front velocity]]). It can be shown that this is (under certain assumptions) always equal to ''c''.<ref name="Milonni"/>{{rp|Ch2}} {{clr}}


The optimum size of a conductor for a given voltage and current can be estimated by [[Kelvin's law for conductor size]], which states that the size is at its optimum when the annual cost of energy wasted in the resistance is equal to the annual capital charges of providing the conductor. At times of lower interest rates, Kelvin's law indicates that thicker wires are optimal; while, when metals are expensive, thinner conductors are indicated: however, power lines are designed for long-term use, so Kelvin's law has to be used in conjunction with long-term estimates of the price of copper and aluminum as well as interest rates for capital.
It is possible for a particle to travel through a medium faster than the phase velocity of light in that medium (but still slower than ''c''). When a [[charged particle]] does that in a [[dielectric]] material, the electromagnetic equivalent of a [[shock wave]], known as [[Cherenkov radiation]], is emitted.<ref>{{cite journal| last=Cherenkov | first=Pavel A. | authorlink=Pavel Alekseyevich Cherenkov | year=1934 |title=Видимое свечение чистых жидкостей под действием γ-радиации| trans_title=Visible emission of clean liquids by action of γ radiation | journal=[[Doklady Akademii Nauk SSSR]] | volume=2 | page=451}} Reprinted in [http://ufn.ru/ru/articles/1967/10/n/ ''Usp. Fiz. Nauk'' 93 (1967) 385], and in "Pavel Alekseyevich Čerenkov: Chelovek i Otkrytie" A. N. Gorbunov, E. P. Čerenkova (eds.), Moscow, Nauka (1999) pp. 149–153.</ref>


The increase in voltage is achieved in AC circuits by using a ''step-up [[变压器]]''. [[高壓直流輸電|HVDC]] systems require relatively costly conversion equipment which may be economically justified for particular projects such as submarine cables and longer distance high capacity point-to-point transmission. HVDC is necessary for the import and export of energy between grid systems that are not synchronized with each other.
==Practical effects of finiteness==
The speed of light is of relevance to [[telecommunication|communications]]: the one-way and [[round-trip delay time]] are greater than zero. This applies from small to astronomical scales. On the other hand, some techniques depend on the finite speed of light, for example in distance measurements.


A transmission grid is a network of [[發電廠]]s, transmission lines, and [[變電所|substations]]. Energy is usually transmitted within a grid with [[三相電|three-phase]] [[交流電|AC]]. Single-phase AC is used only for distribution to end users since it is not usable for large polyphase [[异步电动机]]s. In the 19th&nbsp;century, two-phase transmission was used but required either four wires or three wires with unequal currents. Higher order phase systems require more than three wires, but deliver little or no benefit.
===Small scales===
In [[supercomputer]]s, the speed of light imposes a limit on how quickly data can be sent between [[central processing unit|processor]]s. If a processor operates at 1 [[gigahertz]], a signal can only travel a maximum of about {{convert|30|cm|ft|0}} in a single cycle. Processors must therefore be placed close to each other to minimize communication latencies; this can cause difficulty with cooling. If clock frequencies continue to increase, the speed of light will eventually become a limiting factor for the internal design of single [[integrated circuit|chips]].<ref name="processorlimit">{{Cite book
|last=Parhami |first=B
|year=1999
|title=Introduction to parallel processing: algorithms and architectures
|url=http://books.google.com/?id=ekBsZkIYfUgC&printsec=frontcover&q=
|page=5
|publisher=[[Plenum Press]]
|isbn=978-0-306-45970-2
}} and {{cite conference
|url=http://books.google.com/books?id=sona_r6dPyQC&lpg=PA26&dq=%22speed%20of%20light%22%20processor%20limit&pg=PA26#v=onepage&q=%22speed%20of%20light%22%20processor%20limit&f=false
|title=Software Transactional Memories: An Approach for Multicore Programming
|first1=D |last1=Imbs
|first2=Michel |last2=Raynal
|year=2009
|conference=10th International Conference, PaCT 2009, Novosibirsk, Russia, August 31 – September 4, 2009
|editor=Malyshkin, V
|booktitle=Parallel Computing Technologies
|publisher=Springer
|isbn=978-3-642-03274-5
|page=26
}}</ref>


[[File:ElectricityUCTE.svg|thumb|left|The {{tsl|en|wide area synchronous grid||synchronous grids}} of the [[欧洲联盟]]]]
===Large distances on Earth===
For example, given the equatorial circumference of the Earth is about {{nowrap|40,075 km}} and ''c'' about {{nowrap|300,000 km/s}}, the theoretical shortest time for a piece of information to travel half the globe along the surface is about 67 milliseconds. When light is travelling around the globe in an [[optical fibre]], the actual transit time is longer, in part because the speed of light is slower by about 35% in an optical fibre, depending on its refractive index ''n''.<ref name=Midwinter>A typical value for the refractive index of optical fibre is between 1.518 and 1.538: {{Cite book
| last = Midwinter |first=JE
| year = 1991
| title = Optical Fibers for Transmission
| edition = 2nd
| publisher = [[Krieger Publishing Company]]
| isbn = 0-89464-595-1
}}</ref> Furthermore, straight lines rarely occur in global communications situations, and delays are created when the signal passes through an electronic switch or signal regenerator.<ref>{{cite web
|date=June 2007
|title=Theoretical vs real-world speed limit of Ping
|url=http://royal.pingdom.com/2007/06/01/theoretical-vs-real-world-speed-limit-of-ping/
|work=Royal Pingdom
|publisher=[[Pingdom]]
|accessdate=2010-05-05
}}</ref>


The price of electric power station capacity is high, and electric demand is variable, so it is often cheaper to import some portion of the needed power than to generate it locally. Because loads are often regionally correlated (hot weather in the Southwest portion of the US might cause many people to use air conditioners), electric power often comes from distant sources. Because of the economic benefits of load sharing between regions, {{tsl|en|wide area synchronous grid||wide area transmission grids}} now span countries and even continents. The web of interconnections between power producers and consumers should enable power to flow, even if some links are inoperative.
===Spaceflights and astronomy===
[[File:Speed of light from Earth to Moon.gif|thumb|right|upright=1.6|alt=The diameter of the moon is about one quarter of that of Earth, and their distance is about thirty times the diameter of Earth. A beam of light starts from the Earth and reaches the Moon in about a second and a quarter.|A beam of light is depicted travelling between the Earth and the Moon in the time it takes a light pulse to move between them: 1.255 seconds at their mean orbital (surface-to-surface) distance. The relative sizes and separation of the Earth–Moon system are shown to scale.]]
Similarly, communications between the Earth and spacecraft are not instantaneous. There is a brief delay from the source to the receiver, which becomes more noticeable as distances increase. This delay was significant for communications between [[Mission Control Center|ground control]] and [[Apollo 8]] when it became the first manned spacecraft to orbit the Moon: for every question, the ground control station had to wait at least three&nbsp;seconds for the answer to arrive.<ref>{{cite web
|url=http://history.nasa.gov/ap08fj/15day4_orbits789.htm
|title=Day 4: Lunar Orbits 7, 8 and 9
|work=The Apollo 8 Flight Journal
|publisher=NASA
|accessdate=2010-12-16
}}</ref> The communications delay between Earth and [[Mars (planet)|Mars]] can vary between five and twenty minutes depending upon the relative positions of the two planets. As a consequence of this, if a robot on the surface of Mars were to encounter a problem, its human controllers would not be aware of it until at least five minutes later, and possibly up to twenty minutes later; it would then take a further five to twenty minutes for instructions to travel from Earth to Mars.


The unvarying (or slowly varying over many hours) portion of the electric demand is known as the ''[[基本負載發電廠|base load]]'' and is generally served by large facilities (which are more efficient due to economies of scale) with fixed costs for fuel and operation. Such facilities are nuclear, coal-fired or hydroelectric, while other energy sources such as [[太陽熱能|concentrated solar thermal]] and [[地熱能發電]] have the potential to provide base load power. Renewable energy sources, such as solar photovoltaics, wind, wave, and tidal, are, due to their intermittency, not considered as supplying "base load" but will still add power to the grid. The remaining or 'peak' power demand, is supplied by [[尖峰負載發電廠]]s, which are typically smaller, faster-responding, and higher cost sources, such as combined cycle or combustion turbine plants fueled by natural gas.
NASA must wait several hours for information from a probe orbiting Jupiter, and if it needs to correct a navigation error, the fix will not arrive at the spacecraft for an equal amount of time, creating a risk of the correction not arriving in time.


Long-distance transmission of electricity (hundreds of kilometers) is cheap and efficient, with costs of US$0.005–0.02 per kWh (compared to annual averaged large producer costs of US$0.01–0.025 per kWh, retail rates upwards of US$0.10 per kWh, and multiples of retail for instantaneous suppliers at unpredicted highest demand moments).<ref name="limits-of-very-long-distance"/> Thus distant suppliers can be cheaper than local sources (e.g., New York often buys over 1000&nbsp;MW of electricity from Canada).<ref>{{cite web|title=NYISO Zone Maps|url=http://www.nyiso.com/public/markets_operations/market_data/maps/index.jsp|publisher=New York Independent System Operator|accessdate=10 January 2014}}</ref> Multiple '''local sources''' (even if more expensive and infrequently used) can make the transmission grid more fault tolerant to weather and other disasters that can disconnect distant suppliers.
Receiving light and other signals from distant astronomical sources can even take much longer. For example, it has taken 13&nbsp;billion (13{{e|9}}) years for light to travel to Earth from the faraway galaxies viewed in the [[Hubble Ultra Deep Field]] images.<ref name=Hubble>{{cite press
|date=5 January 2010
|title=Hubble Reaches the "Undiscovered Country" of Primeval Galaxies
|url=http://hubblesite.org/newscenter/archive/releases/2010/02/full/
|publisher=[[Space Telescope Science Institute]]
}}</ref><ref>
{{cite web
|title=The Hubble Ultra Deep Field Lithograph
|url=http://www.nasa.gov/pdf/283957main_Hubble_Deep_Field_Lithograph.pdf
|format=PDF
|publisher=[[NASA]]
|accessdate=2010-02-04
}}</ref> Those photographs, taken today, capture images of the galaxies as they appeared 13&nbsp;billion years ago, when the universe was less than a billion years old.<ref name=Hubble/> The fact that more distant objects appear to be younger, due to the finite speed of light, allows astronomers to infer the [[evolution of stars]], [[Galaxy formation and evolution|of galaxies]], and [[history of the universe|of the universe]] itself.


[[File:Electicaltransmissionlines3800ppx.JPG|thumb|A high-power electrical transmission tower, 230&nbsp;kV, double-circuit, also double-bundled]]
Astronomical distances are sometimes expressed in [[light-year]]s, especially in [[popular science]] publications and media.<ref>{{cite web
|title=The IAU and astronomical units
|url=http://www.iau.org/public/measuring/
|publisher=[[International Astronomical Union]]
|accessdate=2010-10-11
}}</ref> A light-year is the distance light travels in one year, around 9461&nbsp;billion kilometres, 5879&nbsp;billion miles, or 0.3066 [[parsec]]s. [[Proxima Centauri]], the closest star to Earth after the Sun, is around 4.2 light-years away.<ref name=starchild>Further discussion can be found at {{cite web
|year=2000
|title=StarChild Question of the Month for March 2000
|url=http://starchild.gsfc.nasa.gov/docs/StarChild/questions/question19.html
|work=StarChild
|publisher=[[NASA]]
|accessdate=2009-08-22
}}</ref>


Long-distance transmission allows remote renewable energy resources to be used to displace fossil fuel consumption. Hydro and wind sources cannot be moved closer to populous cities, and solar costs are lowest in remote areas where local power needs are minimal. Connection costs alone can determine whether any particular renewable alternative is economically sensible. Costs can be prohibitive for transmission lines, but various proposals for massive infrastructure investment in high capacity, very long distance [[超級電網]] transmission networks could be recovered with modest usage fees.
===Distance measurement===
[[Radar]] systems measure the distance to a target by the time it takes a radio-wave pulse to return to the radar antenna after being reflected by the target: the distance to the target is half the round-trip [[Radar#Transit time|transit time]] multiplied by the speed of light. A [[Global Positioning System]] (GPS) receiver measures its distance to GPS satellites based on how long it takes for a radio signal to arrive from each satellite, and from these distances calculates the receiver's position. Because light travels about 300,000 kilometres (186,000 miles) in one second, these measurements of small fractions of a second must be very precise. The [[Lunar Laser Ranging Experiment]], [[radar astronomy]] and the [[Deep Space Network]] determine distances to the Moon,<ref name=science265_5171_482>{{cite journal
|last=Dickey |first=JO
|coauthors=''et al.''
|title=Lunar Laser Ranging: A Continuing Legacy of the Apollo Program
|journal=Science | volume=265 | issue=5171
|pages=482–490 | month=July | year=1994
|doi=10.1126/science.265.5171.482
|bibcode=1994Sci...265..482D | pmid=17781305}}</ref> planets<ref name=cm26_181>{{cite journal
|last=Standish |first=EM
|title=The JPL planetary ephemerides
|journal=Celestial Mechanics |volume=26 |month=February
|issue=2
|year=1982 |pages=181–186 |doi=10.1007/BF01230883
|bibcode=1982CeMec..26..181S }}</ref> and spacecraft,<ref name=pieee95_11_2202>{{cite journal
|last1=Berner |first1=JB
|last2=Bryant |first2=SH
|last3=Kinman |first3=PW
|title=Range Measurement as Practiced in the Deep Space Network
|journal=Proceedings of the IEEE |month=November
|year=2007 |volume=95 |issue=11 |pages=2202–2214
|doi=10.1109/JPROC.2007.905128 }}</ref> respectively, by measuring round-trip transit times.


==Measurement==
=== Grid input ===
At the [[發電廠]]s, the power is produced at a relatively low voltage between about 2.3&nbsp;kV and 30&nbsp;kV, depending on the size of the unit. The generator terminal voltage is then stepped up by the power station [[变压器]] to a higher [[電壓]] (115&nbsp;kV to 765&nbsp;kV AC, varying by the transmission system and by the country) for transmission over long distances.
<!--- The article Galileo Galileo links to this section. Please do not change the title of the section without amending the articles which link to it. --->
There are different ways to determine the value of ''c''. One way is to measure the actual speed at which light waves propagate, which can be done in various astronomical and earth-based setups. However, it is also possible to determine ''c'' from other physical laws where it appears, for example, by determining the values of the electromagnetic constants ''ε''<sub>0</sub> and ''μ''<sub>0</sub> and using their relation to ''c''. Historically, the most accurate results have been obtained by separately determining the frequency and wavelength of a light beam, with their product equalling ''c''.


In the United States, power transmission is, variously, 230&nbsp;kV to 500&nbsp;kV, with less than 230&nbsp;kV or more than 500&nbsp;kV being local exceptions.
In 1983 the metre was defined as "the length of the path travelled by light in vacuum during a time interval of 1⁄299,792,458 of a second",<ref name=Resolution_1/> fixing the value of the speed of light at {{val|299792458|u=m/s}} by definition, as [[#Increased accuracy of c and redefinition of the metre|described below]]. Consequently, accurate measurements of the speed of light yield an accurate realization of the metre rather than an accurate value of ''c''.


For example, the Western System has two primary interchange voltages: 500&nbsp;kV AC at 60&nbsp;Hz, and ±500&nbsp;kV (1,000&nbsp;kV net) DC from North to South ([[哥倫比亞河]] to [[南加利福尼亞州]]) and Northeast to Southwest (Utah to Southern California). The 287.5&nbsp;kV ([[胡佛水壩|Hoover]] to [[洛杉矶]] line, via [[维克多维尔 (加利福尼亚州)]]) and 345&nbsp;kV ({{tsl|en|Arizona Public Service||APS}} line) being local standards, both of which were implemented before 500&nbsp;kV became practical, and thereafter the Western System standard for long distance AC power transmission.
===Astronomical measurements===
[[Outer space]] is a natural setting for measuring the speed of light because of its large scale and nearly perfect [[vacuum]]. Typically, one measures the time needed for light to traverse some reference distance in the [[solar system]], such as the [[radius]] of the Earth's orbit. Historically, such measurements could be made fairly accurately, compared to how accurately the length of the reference distance is known in Earth-based units. It is customary to express the results in [[astronomical unit]]s (AU) per day. An astronomical unit is approximately the average distance between the Earth and Sun; it is not based on the [[International System of Units]].{{#tag:ref|The astronomical unit is defined as the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with an [[angular frequency]] of {{gaps|0.017|202|098|95}} [[radian]]s (approximately {{frac|{{val|365.256898}}}} of a revolution) per day.<ref name="SIbrochure"/>{{rp|126}}.
It may be noted that the astronomical unit increases at a rate of about (15 ± 4) cm/yr, probably due to the changing mass of the Sun.<ref name=Nieto>{{cite journal
|arxiv=0907.2469
|title=Astrometric solar-system anomalies
|author=John D. Anderson and Michael Martin Nieto
|journal=Proceedings of the International Astronomical Union
|year=2009 |volume=5
|issue=S261 |pages=189–197
|publisher=Cambridge University Press
|doi=10.1017/S1743921309990378 }}</ref> This unit has the advantage that the [[gravitational constant]] multiplied by the Sun's mass has a fixed, exact value in cubic astronomical units per day squared.|group=Note}} Because the AU determines an actual length, and is not based upon time-of-flight like the SI units, modern measurements of the speed of light in astronomical units per day can be compared with the defined value of ''c'' in the International System of Units.


=== Losses ===
[[Ole Christensen Rømer]] used an astronomical measurement to make [[Rømer's determination of the speed of light|the first quantitative estimate of the speed of light]].<ref name=cohen>{{cite journal
Transmitting electricity at high voltage reduces the fraction of energy lost to [[焦耳加热|resistance]], which varies depending on the specific conductors, the current flowing, and the length of the transmission line. For example, a {{convert|100|mile|abbr=on}} span at 765&nbsp;kV carrying 1000&nbsp;MW of power can have losses of 1.1% to 0.5%. A 345&nbsp;kV line carrying the same load across the same distance has losses of 4.2%.<ref>American Electric Power, Transmission Facts, page&nbsp;4: https://web.archive.org/web/20110604181007/https://www.aep.com/about/transmission/docs/transmission-facts.pdf</ref> For a given amount of power, a higher voltage reduces the current and thus the [[焦耳加热]]es in the conductor. For example, raising the voltage by a factor of 10 reduces the current by a corresponding factor of 10 and therefore the <math>I^2 R</math> losses by a factor of 100, provided the same sized conductors are used in both cases. Even if the conductor size (cross-sectional area) is decreased ten-fold to match the lower current, the <math>I^2 R</math> losses are still reduced ten-fold. Long-distance transmission is typically done with overhead lines at voltages of 115 to 1,200&nbsp;kV. At extremely high voltages, more than 2,000&nbsp;kV exists between conductor and ground, [[电晕放电]] losses are so large that they can offset the lower resistive losses in the line conductors. Measures to reduce corona losses include conductors having larger diameters; often hollow to save weight,<ref>[http://www.cpuc.ca.gov/environment/info/aspen/deltasub/pea/16_corona_and_induced_currents.pdf California Public Utilities Commission] Corona and induced currents</ref> or bundles of two or more conductors.
|last=Cohen |first=IB
|year=1940
|title=Roemer and the first determination of the velocity of light (1676)
|journal=[[Isis (journal)|Isis]]
|volume=31 |issue=2 |pages=327–79
|doi=10.1086/347594
|ref=cohen-1940
}}</ref><ref name=roemer>
{{cite journal
|year=1676
|title=Touchant le mouvement de la lumiere trouvé par M. Rŏmer de l'Académie Royale des Sciences
|language=French
|url=http://www-obs.univ-lyon1.fr/labo/fc/ama09/pages_jdsc/pages/jdsc_1676_lumiere.pdf
|journal=[[Journal des sçavans]]
|pages=233–36
|ref=roemer-1676
}}<br/>Translated in {{cite journal
|doi=10.1098/rstl.1677.0024
|year=1677
|title=On the Motion of Light by M. Romer
|url=http://www.archive.org/stream/philosophicaltra02royarich#page/397/mode/1up
|journal=[[Philosophical Transactions of the Royal Society]]
|volume=12 |issue=136 |pages=893–95
|ref=roemer-1676-EnglishTrans
}} (As reproduced in {{Cite book
|last1=Hutton |first1=C
|last2=Shaw |first2=G
|last3=Pearson |first3=R eds.
|year=1809
|title=The Philosophical Transactions of the Royal Society of London, from Their Commencement in 1665, in the Year 1800: Abridged
|chapter=On the Motion of Light by M. Romer
|chapterurl=http://www.archive.org/stream/philosophicaltra02royarich#page/397/mode/1up
|location=London |publisher=C. & R. Baldwin
|volume= 2| pages=397–98
}})<br>
The account published in ''Journal des sçavans'' was based on a report that Rømer read to the [[French Academy of Sciences]] in November 1676 [[#cohen-1940|(Cohen, 1940, p.&nbsp;346)]].</ref> When measured from Earth, the periods of moons orbiting a distant planet are shorter when the Earth is approaching the planet than when the Earth is receding from it. The distance travelled by light from the planet (or its moon) to Earth is shorter when the Earth is at the point in its orbit that is closest to its planet than when the Earth is at the farthest point in its orbit, the difference in distance being the [[diameter]] of the Earth's orbit around the Sun. The observed change in the moon's orbital period is actually the difference in the time it takes light to traverse the shorter or longer distance. Rømer observed this effect for [[Jupiter (planet)|Jupiter]]'s innermost moon [[Io (moon)|Io]] and deduced that light takes 22 minutes to cross the diameter of the Earth's orbit.


Factors that affect the resistance, and thus loss, of conductors used in transmission and distribution lines include temperature, spiraling, and the [[集膚效應]]. The resistance of a conductor increases with its temperature. Temperature changes in electric power lines can have a significant effect on power losses in the line. Spiraling, which refers to the way stranded conductors spiral about the center, also contributes to increases in conductor resistance. The skin effect causes the effective resistance of a conductor to increase at higher alternating current frequencies. Corona and resistive losses can be estimated using a mathematical model.<ref>{{cite web |title=AC Transmission Line Losses |author=Curt Harting |date=October 24, 2010 |publisher=[[史丹佛大學]] |url=http://large.stanford.edu/courses/2010/ph240/harting1/ |accessdate=June 10, 2019}}</ref>
[[File:SoL Aberration.svg|thumb|right|Aberration of light: light from a distant source appears to be from a different location for a moving telescope due to the finite speed of light.|alt=A star emits a light ray which hits the objective of a telescope. While the light travels down the telescope to its eyepiece, the telescope moves to the right. For the light to stay inside the telescope, the telescope must be tilted to the right, causing the distant source to appear at a different location to the right.]]
Another method is to use the [[aberration of light]], discovered and explained by [[James Bradley]] in the 18th century.<ref name="Bradley1729">{{Cite journal
|last=Bradley |first=J
|year=1729
|title=Account of a new discoved Motion of the Fix'd Stars
|url=http://gallica.bnf.fr/ark:/12148/bpt6k55840n.image.f375.langEN
|journal=[[Philosophical Transactions]]
|volume=35 |pages=637–660
|doi=
}}</ref> This effect results from the [[vector addition]] of the velocity of light arriving from a distant source (such as a star) and the velocity of its observer (see diagram on the right). A moving observer thus sees the light coming from a slightly different direction and consequently sees the source at a position shifted from its original position. Since the direction of the Earth's velocity changes continuously as the Earth orbits the Sun, this effect causes the apparent position of stars to move around. From the angular difference in the position of stars (maximally 20.5 [[arcsecond]]s)<ref>
{{Cite book
|last=Duffett-Smith
|first=P
|year=1988
|title=[[Practical Astronomy with your Calculator]]
|url=http://books.google.com/?id=DwJfCtzaVvYC
|page=62
|publisher=[[Cambridge University Press]]
|isbn=0-521-35699-7}}, [http://books.google.com/books?id=DwJfCtzaVvYC&pg=PA62 Extract of page 62]</ref> it is possible to express the speed of light in terms of the Earth's velocity around the Sun, which with the known length of a year can be easily converted to the time needed to travel from the Sun to the Earth. In 1729, Bradley used this method to derive that light travelled 10,210 times faster than the Earth in its orbit (the modern figure is 10,066 times faster) or, equivalently, that it would take light 8&nbsp;minutes 12&nbsp;seconds to travel from the Sun to the Earth.<ref name="Bradley1729"/>


Transmission and distribution losses in the USA were estimated at 6.6% in 1997,<ref name="tonto.eia.doe.gov">{{cite web |url=http://tonto.eia.doe.gov/tools/faqs/faq.cfm?id=105&t=3 |title=Where can I find data on electricity transmission and distribution losses? |date=19 November 2009 |work=Frequently Asked Questions – Electricity |publisher=[[美国能源信息署]] |accessdate=29 March 2011 }}{{Dead link|date=August 2019 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> 6.5% in 2007<ref name="tonto.eia.doe.gov"/> and 5% from 2013 to 2019.<ref name="eia.gov">{{cite web |url=https://www.eia.gov/tools/faqs/faq.php?id=105&t=3|title=How much electricity is lost in electricity transmission and distribution in the United States? |date=9 January 2019 |work=Frequently Asked Questions – Electricity |publisher=[[美国能源信息署]] |accessdate=27 February 2019}}</ref> In general, losses are estimated from the discrepancy between power produced (as reported by power plants) and power sold to the end customers; the difference between what is produced and what is consumed constitute transmission and distribution losses, assuming no utility theft occurs.
Nowadays, the "light time for unit distance"—the inverse of&nbsp;''c'', expressed in seconds per astronomical unit—is measured by comparing the time for radio signals to reach different spacecraft in the Solar System, with their position calculated from the gravitational effects of the Sun and various planets. By combining many such measurements, a [[best fit]] value for the light time per unit distance is obtained. {{As of|2009}}, the best estimate, as approved by the [[International Astronomical Union]] (IAU), is:<ref name="Pitjeva09">
{{cite journal
|last1=Pitjeva |first1=EV
|last2=Standish |first2=EM
|year=2009
|title=Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit
|journal=[[Celestial Mechanics and Dynamical Astronomy]]
|volume=103 |issue=4 |pages=365–372
|doi=10.1007/s10569-009-9203-8
|bibcode = 2009CeMDA.103..365P }}</ref><ref name="IAU">
{{cite web
|author=IAU Working Group on Numerical Standards for Fundamental Astronomy
|title=IAU WG on NSFA Current Best Estimates
|url=http://maia.usno.navy.mil/NSFA/CBE.html
|publisher=[[US Naval Observatory]]
|accessdate=2009-09-25
}}</ref>
:light time for unit distance: {{val|499.004783836|(10)|u=s}}
:''c''&nbsp;=&nbsp;{{val|0.00200398880410|(4)|u=AU/s}}&nbsp;=&nbsp;{{val|173.144632674|(3)|u=AU/day.}}
The relative uncertainty in these measurements is 0.02 parts per billion (2{{e|-11}}), equivalent to the uncertainty in Earth-based measurements of length by interferometry.<ref>
{{cite web
|title=NPL's Beginner's Guide to Length
|url=http://www.npl.co.uk/educate-explore/posters/length/length-%28poster%29
|publisher=[[National Physical Laboratory (United Kingdom)|UK National Physical Laboratory]]
|accessdate=2009-10-28
}}</ref>{{#tag:ref|The value of the speed of light in [[Astronomical system of units|astronomical units]] has a measurement uncertainty, unlike the value in SI units, because of the different definitions of the unit of length.|group=Note}} Since the metre is defined to be the length travelled by light in a certain time interval, the measurement of the light time for unit distance can also be interpreted as measuring the length of an AU in metres.{{#tag:ref|Nevertheless, at this degree of precision, the effects of [[general relativity]] must be taken into consideration when interpreting the length. The metre is considered to be a unit of [[proper length]], whereas the AU is usually used as a unit of observed length in a given frame of reference. The values cited here follow the latter convention, and are [[Barycentric Dynamical Time|TDB]]-compatible.<ref name="IAU"/>|group=Note}}


As of 1980, the longest cost-effective distance for [[直流電|direct-current]] transmission was determined to be {{convert|7000|km|mi|abbr=off}}. For [[交流電]] it was {{convert|4000|km|mi|abbr=off}}, though all transmission lines in use today are substantially shorter than this.<ref name="limits-of-very-long-distance">{{cite web |url=http://www.geni.org/globalenergy/library/technical-articles/transmission/cigre/present-limits-of-very-long-distance-transmission-systems/index.shtml |title=Present Limits of Very Long Distance Transmission Systems | first1 = L. | last1 = Paris | first2 = G. | last2 = Zini | first3 = M. | last3 = Valtorta | first4 = G. | last4 = Manzoni | first5 = A. | last5 = Invernizzi | first6 = N. | last6 = De Franco | first7 = A. | last7 = Vian |year=1984 |work={{tsl|en|CIGRE|}} International Conference on Large High Voltage Electric Systems, 1984 Session, 29&nbsp;August &ndash; 6&nbsp;September |publisher={{tsl|en|Global Energy Network Institute|}} |accessdate=29 March 2011 |format=PDF}} 4.98&nbsp;MB</ref>
===Time of flight techniques===
A method of measuring the speed of light is to measure the time needed for light to travel to a mirror at a known distance and back. This is the working principle behind the [[Fizeau–Foucault apparatus]] developed by [[Hippolyte Fizeau]] and [[Léon Foucault]].


In any alternating current transmission line, the [[电感]] and capacitance of the conductors can be significant. Currents that flow solely in ‘reaction’ to these properties of the circuit, (which together with the [[电阻|resistance]] define the [[阻抗|impedance]]) constitute [[交流电功率]] flow, which transmits no ‘real’ power to the load. These reactive currents, however, are very real and cause extra heating losses in the transmission circuit. The ratio of 'real' power (transmitted to the load) to 'apparent' power (the product of a circuit's voltage and current, without reference to phase angle) is the [[功率因数]]. As reactive current increases, the reactive power increases and the power factor decreases. For transmission systems with low power factor, losses are higher than for systems with high power factor. Utilities add capacitor banks, reactors and other components (such as {{tsl|en|phase-shifting transformer|}}s; {{tsl|en|static VAR compensator|}}s; and {{tsl|en|flexible AC transmission system|}}s, FACTS) throughout the system help to compensate for the reactive power flow, reduce the losses in power transmission and stabilize system voltages. These measures are collectively called 'reactive support'.
[[File:Fizeau.JPG|thumb|right|Diagram of the [[Fizeau–Foucault apparatus|Fizeau apparatus]]|alt=A light ray passes horizontally through a half-mirror and a rotating cog wheel, is reflected back by a mirror, passes through the cog wheel, and is reflected by the half-mirror into a monocular.]]
The setup as used by Fizeau consists of a beam of light directed at a mirror {{convert|8|km|mi|0}} away. On the way from the source to the mirror, the beam passes through a rotating cogwheel. At a certain rate of rotation, the beam passes through one gap on the way out and another on the way back, but at slightly higher or lower rates, the beam strikes a tooth and does not pass through the wheel. Knowing the distance between the wheel and the mirror, the number of teeth on the wheel, and the rate of rotation, the speed of light can be calculated.<ref name=How>{{cite web
|last=Gibbs |first=P
|year=1997
|title=How is the speed of light measured?
|url=http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html
|work=Usenet Physics FAQ
|publisher=University of California, Riverside
|accessdate=2010-01-13
}}</ref>


=== Transposition ===
The method of Foucault replaces the cogwheel by a rotating mirror. Because the mirror keeps rotating while the light travels to the distant mirror and back, the light is reflected from the rotating mirror at a different angle on its way out than it is on its way back. From this difference in angle, the known speed of rotation and the distance to the distant mirror the speed of light may be calculated.<ref>{{cite web
Current flowing through transmission lines induces a magnetic field that surrounds the lines of each phase and affects the [[电感]] of the surrounding conductors of other phases. The mutual inductance of the conductors is partially dependent on the physical orientation of the lines with respect to each other. Three-phase power transmission lines are conventionally strung with phases separated on different vertical levels. The mutual inductance seen by a conductor of the phase in the middle of the other two phases will be different than the inductance seen by the conductors on the top or bottom. An imbalanced inductance among the three conductors is problematic because it may result in the middle line carrying a disproportionate amount of the total power transmitted. Similarly, an imbalanced load may occur if one line is consistently closest to the ground and operating at a lower impedance. Because of this phenomenon, conductors must be periodically transposed along the length of the transmission line so that each phase sees equal time in each relative position to balance out the mutual inductance seen by all three phases. To accomplish this, line position is swapped at specially designed {{tsl|en|transposition tower|}}s at regular intervals along the length of the transmission line in various {{tsl|en|Transposition (telecommunications)||transposition schemes}}.
|last=Fowler |first=M
|date=
|title=The Speed of Light
|url=http://galileoandeinstein.physics.virginia.edu/lectures/spedlite.html
|publisher=[[University of Virginia]]
|accessdate=2010-04-21
}}</ref>


=== Subtransmission ===
Nowadays, using [[oscilloscopes]] with time resolutions of less than one nanosecond, the speed of light can be directly measured by timing the delay of a light pulse from a laser or an LED reflected from a mirror. This method is less precise (with errors of the order of 1%) than other modern techniques, but it is sometimes used as a laboratory experiment in college physics classes.<ref>
[[File:Cavite, Batangas jf0557 11.jpg|thumb|175px|A 115&nbsp;kV subtransmission line in the [[菲律宾]], along with 20&nbsp;kV [[配電系統|distribution]] lines and a [[街燈]], all mounted in a wood [[电线杆|subtransmission pole]]]]
{{cite journal
[[File:Wood Pole Structure.JPG|thumb|173px|115 kV H-frame transmission tower]]
|last=Cooke |first=J
|last2=Martin |first2=M
|last3=McCartney |first3=H
|last4=Wilf |first4=B
|year=1968
|title=Direct determination of the speed of light as a general physics laboratory experiment
|journal=[[American Journal of Physics]]
|volume=36 |issue=9 |page=847
|doi=10.1119/1.1975166
|bibcode = 1968AmJPh..36..847C }}</ref><ref>
{{cite journal
|last=Aoki |first=K |last2=Mitsui |first2=T
|year=2008
|title=A small tabletop experiment for a direct measurement of the speed of light
|journal=[[American Journal of Physics]]
|volume=76 |issue=9 |pages=812–815
|doi=10.1119/1.2919743
|arxiv=0705.3996
|bibcode = 2008AmJPh..76..812A }}</ref><ref>
{{cite journal
|last=James |first=MB |last2=Ormond |first2=RB |last3=Stasch |first3=AJ
|year=1999
|title=Speed of light measurement for the myriad
|journal=[[American Journal of Physics]]
|volume=67 |issue=8 |pages=681–714
|doi=10.1119/1.19352
|bibcode = 1999AmJPh..67..681J }}</ref>{{clr}}


'''Subtransmission''' is part of an electric power transmission system that runs at relatively lower voltages. It is uneconomical to connect all [[變電所|distribution substation]]s to the high main transmission voltage, because the equipment is larger and more expensive. Typically, only larger substations connect with this high voltage. It is stepped down and sent to smaller substations in towns and neighborhoods. Subtransmission circuits are usually arranged in loops so that a single line failure does not cut off service to many customers for more than a short time. Loops can be "normally closed", where loss of one circuit should result in no interruption, or "normally open" where substations can switch to a backup supply. While subtransmission circuits are usually carried on [[高压电线|overhead lines]], in urban areas buried cable may be used. The lower-voltage subtransmission lines use less right-of-way and simpler structures; it is much more feasible to put them underground where needed. Higher-voltage lines require more space and are usually above-ground since putting them underground is very expensive.
===Electromagnetic constants===
An option for deriving ''c'' that does not directly depend on a measurement of the propagation of electromagnetic waves is to use the relation between ''c'' and the [[vacuum permittivity]] ''ε''<sub>0</sub> and [[vacuum permeability]] ''μ''<sub>0</sub> established by Maxwell's theory: ''c''<sup>2</sup>&nbsp;=&nbsp;1/(''ε''<sub>0</sub>''μ''<sub>0</sub>). The vacuum permittivity may be determined by measuring the [[capacitance]] and dimensions of a [[capacitor]], whereas the value of the [[vacuum permeability]] is fixed at exactly {{val|4|end=π|e=-7|u=H*m-1}} through the definition of the [[ampere (unit)|ampere]]. Rosa and Dorsey used this method in 1907 to find a value of {{val|299710|22|u=km/s}}.<ref name="Essen1948"/><ref name="RosaDorsey">{{cite journal
|last=Rosa |first=EB |last2=Dorsey |first2=NE
|year=1907
|title=The Ratio of the Electromagnetic and Electrostatic Units|journal=[[Bulletin of the Bureau of Standards]]
|volume=3
|issue=6 |page=433
|doi=10.1103/PhysRevSeriesI.22.367
|bibcode = 1906PhRvI..22..367R }}</ref>


There is no fixed cutoff between subtransmission and transmission, or subtransmission and [[配電系統|distribution]]. The voltage ranges overlap somewhat. Voltages of 69&nbsp;kV, 115&nbsp;kV, and 138&nbsp;kV are often used for subtransmission in North America. As power systems evolved, voltages formerly used for transmission were used for subtransmission, and subtransmission voltages became distribution voltages. Like transmission, subtransmission moves relatively large amounts of power, and like distribution, subtransmission covers an area instead of just point-to-point.<ref>Donald G. Fink and H. Wayne Beaty. (2007), ''Standard Handbook for Electrical Engineers (15th&nbsp;Edition)''. McGraw-Hill. {{ISBN|978-0-07-144146-9}} section&nbsp;18.5</ref>
===Cavity resonance===
[[File:Waves in Box.svg|thumb|right|Electromagnetic [[standing waves]] in a cavity.|alt=A box with three waves in it; there are one and a half wavelength of the top wave, one of the middle one, and a half of the bottom one.]]


=== Transmission grid exit ===
Another way to measure the speed of light is to independently measure the frequency ''f'' and wavelength ''λ'' of an electromagnetic wave in vacuum. The value of ''c'' can then be found by using the relation ''c''&nbsp;=&nbsp;''fλ''. One option is to measure the resonance frequency of a [[cavity resonator]]. If the dimensions of the resonance cavity are also known, these can be used determine the wavelength of the wave. In 1946, [[Louis Essen]] and A.C. Gordon-Smith establish the frequency for a variety of [[normal mode]]s of microwaves of a [[microwave cavity]] of precisely known dimensions. The dimensions were established to an accuracy of about ±0.8&nbsp;μm using gauges calibrated by interferometry.<ref name="Essen1948"/> As the wavelength of the modes was known from the geometry of the cavity and from [[electromagnetic theory]], knowledge of the associated frequencies enabled a calculation of the speed of light.<ref name="Essen1948">{{cite journal
At the [[變電所|substations]], transformers reduce the voltage to a lower level for [[配電系統|distribution]] to commercial and residential users. This distribution is accomplished with a combination of sub-transmission (33 to 132&nbsp;kV) and distribution (3.3 to 25&nbsp;kV). Finally, at the point of use, the energy is transformed to low voltage (varying by country and customer requirements &ndash; see [[家用電源列表]]).
|last=Essen |first=L
|last2=Gordon-Smith |first2=AC
|year=1948
|title=The Velocity of Propagation of Electromagnetic Waves Derived from the Resonant Frequencies of a Cylindrical Cavity Resonator
|journal=[[Proceedings of the Royal Society of London A]]
|volume=194 |issue=1038 |pages=348–361
|doi=10.1098/rspa.1948.0085
|bibcode=1948RSPSA.194..348E
|jstor=98293
}}</ref><ref>
{{cite journal
|last=Essen |first=L
|year=1947
|title=Velocity of Electromagnetic Waves
|journal=Nature
|volume=159 |issue=4044 |pages=611–612
|doi=10.1038/159611a0
|bibcode=1947Natur.159..611E
}}</ref>


== Advantage of high-voltage power transmission ==
The Essen–Gordon-Smith result, {{val|299792|9|u=km/s}}, was substantially more precise than those found by optical techniques.<ref name="Essen1948" /> By 1950, repeated measurements by Essen established a result of {{val|299792.5|3.0|u=km/s}}.<ref name="Essen1950">
{{See also|ideal transformer}}
{{cite journal
High-voltage power transmission allows for lesser resistive losses over long distances in the wiring. This efficiency of high voltage transmission allows for the transmission of a larger proportion of the generated power to the substations and in turn to the loads, translating to operational cost savings.
|last=Essen |first=L
|year=1950
|title=The Velocity of Propagation of Electromagnetic Waves Derived from the Resonant Frequencies of a Cylindrical Cavity Resonator
|journal=[[Proceedings of the Royal Society of London A]]
|volume=204 |issue=1077 |pages=260–277
|doi=10.1098/rspa.1950.0172
|bibcode=1950RSPSA.204..260E
|jstor=98433
}}</ref>


[[File:Power split two resistances.svg|thumb|Electrical grid without a transformer.]]
A household demonstration of this technique is possible, using a [[microwave oven]] and food such as marshmallows or margarine: if the turntable is removed so that the food does not move, it will cook the fastest at the [[antinode]]s (the points at which the wave amplitude is the greatest), where it will begin to melt. The distance between two such spots is half the wavelength of the microwaves; by measuring this distance and multiplying the wavelength by the microwave frequency (usually displayed on the back of the oven, typically 2450&nbsp;MHz), the value of ''c'' can be calculated, "often with less than 5% error".<ref>
[[File:Transformer power split.svg|thumb|Electrical grid with a transformer.]]
{{cite journal
In a very simplified model, assume the [[輸電網路]] delivers electricity from a generator (modelled as an [[电压源]] with voltage <math>V</math>, delivering a power <math>P_V</math>) to a single point of consumption, modelled by a pure resistance <math>R</math>, when the wires are long enough to have a significant resistance <math>R_C</math>.
| last = Stauffer | first = RH
| year = 1997 | month = April
| title = Finding the Speed of Light with Marshmallows
| journal = [[The Physics Teacher]]
| volume = 35
| page = 231
| publisher = American Association of Physics Teachers
| url = http://www.physics.umd.edu/icpe/newsletters/n34/marshmal.htm
| accessdate = 2010-02-15
|bibcode = 1997PhTea..35..231S |doi = 10.1119/1.2344657
| issue = 4 }}</ref><ref>{{cite web
| url =http://www.bbc.co.uk/norfolk/features/ba_festival/bafestival_speedoflight_experiment_feature.shtml
| title = BBC Look East at the speed of light
| work = BBC Norfolk website
|publisher=BBC
| accessdate = 2010-02-15
}}</ref>


If the resistance are simply {{tsl|en|in series|}} without any transformer between them, the circuit acts as a [[電壓分配定則]], because the same current <math>I=\frac{V}{R+R_C}</math> runs through the wire resistance and the powered device. As a consequence, the useful power (used at the point of consumption) is:
===Interferometry===
:<math>P_R= V_2\times I = V\frac{R}{R+R_C}\times\frac{V}{R+R_C} = \frac{R}{R+R_C}\times\frac{V^2}{R+R_C} = \frac{R}{R+R_C} P_V</math>
[[File:Interferometer sol.svg|thumb|upright=1.4|An interferometric determination of length. Left: [[constructive interference]]; Right: [[destructive interference]].|alt=Schematic of the working of a Michelson interferometer.]]
Assume now that a transformer converts high-voltage, low-current electricity transported by the wires into low-voltage, high-current electricity for use at the consumption point. If we suppose it is an [[变压器]] with a voltage ratio of <math>a</math> (i.e., the voltage is divided by <math>a</math> and the current is multiplied by <math>a</math> in the secondary branch, compared to the primary branch), then the circuit is again equivalent to a voltage divider, but the transmission wires now have apparent resistance of only <math>R_C/a^2</math>. The useful power is then:
[[Interferometry]] is another method to find the wavelength of electromagnetic radiation for determining the speed of light.<ref name=Vaughan>
:<math>P_R= V_2\times I_2 = \frac{a^2R\times V^2}{(a^2 R+R_C)^2} = \frac{a^2 R}{a^2 R+R_C} P_V = \frac{R}{R+R_C/a^2} P_V</math>
A detailed discussion of the interferometer and its use for determining the speed of light can be found in {{Cite book
|last=Vaughan |first=JM
|year=1989
|title=The Fabry-Perot interferometer
|url=http://books.google.com/?id=mMLuISueDKYC&printsec=frontcover#PPA47,M1
|page=47, pp.&nbsp;384–391
|publisher=CRC Press
|isbn=0-85274-138-3
}}</ref> A [[Coherence (physics)|coherent]] beam of light (e.g. from a [[laser]]), with a known frequency (''f''), is split to follow two paths and then recombined. By adjusting the path length while observing the [[interference (wave propagation)|interference pattern]] and carefully measuring the change in path length, the wavelength of the light (''λ'') can be determined. The speed of light is then calculated using the equation&nbsp;''c''&nbsp;=&nbsp;''λf''.


For <math>a>1</math> (i.e. conversion of high voltage to low voltage near the consumption point), a larger fraction of the generator's power is transmitted to the consumption point and a lesser fraction is lost to [[焦耳加热]].
Before the advent of laser technology, coherent [[radiowave|radio]] sources were used for interferometry measurements of the speed of light.<ref name=Froome1858>
{{cite journal
|doi=10.1098/rspa.1958.0172
|title=A New Determination of the Free-Space Velocity of Electromagnetic Waves
|first=KD
|last=Froome
|journal=Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences,
|volume=247
|year=1958
|pages=109–122
|issue=1248
|publisher=The Royal Society
|bibcode = 1958RSPSA.247..109F
|jstor=100591 }}</ref> However interferometric determination of wavelength becomes less precise with wavelength and the experiments were thus limited in precision by the long wavelength (~0.4&nbsp;cm) of the radiowaves. The precision can be improved by using light with a shorter wavelength, but then it becomes difficult to directly measure the frequency of the light. One way around this problem is to start with a low frequency signal of which the frequency can be precisely measured, and from this signal progressively synthesize higher frequency signals whose frequency can then be linked to the original signal. A laser can then be locked to the frequency, and its wavelength can be determined using interferometry.<ref name="NIST_pub">
{{Cite book
|title=A Century of Excellence in Measurements, Standards, and Technology
|editor-last=Lide |editor-first=DR
|contribution=Speed of Light from Direct Frequency and Wavelength Measurements
|last=Sullivan |first=DB
|year=2001
|pages=191–193
|publisher=CRC Press
|isbn=0-8493-1247-7
|url=http://nvl.nist.gov/pub/nistpubs/sp958-lide/191-193.pdf
}}</ref> This technique was due to a group at the National Bureau of Standards (NBS) (which later became [[National Institute of Standards and Technology|NIST]]). They used it in 1972 to measure the speed of light in vacuum with a [[Measurement uncertainty|fractional uncertainty]] of {{val|3.5|e=-9}}.<ref name="NIST_pub"/><ref name="NIST heterodyne">
{{cite journal
|last1=Evenson |first1=KM |coauthors=''et al.''
|year=1972
|title=Speed of Light from Direct Frequency and Wavelength Measurements of the Methane-Stabilized Laser
|journal=Physical Review Letters
|volume=29
|issue=19 |pages=1346–49
|doi=10.1103/PhysRevLett.29.1346
|bibcode=1972PhRvL..29.1346E
}}</ref>


== Modeling and the transmission matrix ==
==History==
{{Main|Performance and modelling of AC transmission}}
{| class="infobox wikitable" style="width:40%; margin:0 0 0.5em 1em; text-align:left;"

|+History&nbsp;of&nbsp;measurements&nbsp;of&nbsp;''c'' (in km/s)
[[File:Transmission Line Black Box.JPG|thumb|upright=1.6|"Black box" model for transmission line]]Oftentimes, we are only interested in the terminal characteristics of the transmission line, which are the voltage and current at the sending and receiving ends. The transmission line itself is then modeled as a "black box" and a 2&nbsp;by&nbsp;2 transmission matrix is used to model its behavior, as follows:

:<math>
\begin{bmatrix}
V_\mathrm{S}\\
I_\mathrm{S}\\
\end{bmatrix}
=
\begin{bmatrix}
A & B\\
C & D\\
\end{bmatrix}
\begin{bmatrix}
V_\mathrm{R}\\
I_\mathrm{R}\\
\end{bmatrix}
</math>

The line is assumed to be a reciprocal, symmetrical network, meaning that the receiving and sending labels can be switched with no consequence. The transmission matrix '''T''' also has the following properties:
* <math>\det(T) = AD - BC = 1</math>
* <math>A = D</math>

The parameters ''A'', ''B'', ''C'', and ''D'' differ depending on how the desired model handles the line's [[Electrical resistance and conductance|resistance]] (''R''), [[电感]] (''L''), [[電容]] (''C''), and shunt (parallel, leak) [[电阻|conductance]] ''G''. The four main models are the short line approximation, the medium line approximation, the long line approximation (with distributed parameters), and the lossless line. In all models described, a capital letter such as ''R'' refers to the total quantity summed over the line and a lowercase letter such as ''c'' refers to the per-unit-length quantity.

===Lossless line===
The '''lossless line''' approximation is the least accurate model; it is often used on short lines when the inductance of the line is much greater than its resistance. For this approximation, the voltage and current are identical at the sending and receiving ends.
[[File:Losslessline.jpg|thumb|Voltage on sending and receiving ends for lossless line]]
The characteristic impedance is pure real, which means resistive for that impedance, and it is often called '''surge impedance''' for a lossless line. When lossless line is terminated by surge impedance, there is no voltage drop. Though the phase angles of voltage and current are rotated, the magnitudes of voltage and current remain constant along the length of the line. For load&nbsp;>&nbsp;SIL, the voltage will drop from sending end and the line will “consume” VARs. For load&nbsp;<&nbsp;SIL, the voltage will increase from sending end, and the line will “generate” VARs.

===Short line===
The '''short line''' approximation is normally used for lines less than 80 km (50&nbsp;mi) long. For a short line, only a series impedance ''Z'' is considered, while ''C'' and ''G'' are ignored. The final result is that '''A&nbsp;=&nbsp;D&nbsp;=&nbsp;1 per unit''', '''B&nbsp;=&nbsp;Z&nbsp;Ohms''', and '''C&nbsp;=&nbsp;0'''. The associated transition matrix for this approximation is therefore:
:<math>
\begin{bmatrix}
V_\mathrm{S}\\
I_\mathrm{S}\\
\end{bmatrix}
=
\begin{bmatrix}
1 & Z\\
0 & 1\\
\end{bmatrix}
\begin{bmatrix}
V_\mathrm{R}\\
I_\mathrm{R}\\
\end{bmatrix}
</math>

===Medium line===
The '''medium line''' approximation is used for lines between 80-250 km (50-150 mi) long. In this model, the series impedance and the shunt (current leak) conductance are considered, with half of the shunt conductance being placed at each end of the line. This circuit is often referred to as a “nominal {{tsl|en|Π||''π'' (pi)}}” circuit because of the shape (''π'') that is taken on when leak conductance is placed on both sides of the circuit diagram. The analysis of the medium line brings one to the following result:

:<math>
\begin{align}
A &= D = 1 + \frac{G Z}{2} \text{ per unit}\\
B &= Z\Omega\\
C &= G \Big( 1 + \frac{G Z}{4}\Big)S
\end{align}
</math>

Counterintuitive behaviors of medium-length transmission lines:

* voltage rise at no load or small current ({{tsl|en|Ferranti effect|}})
* receiving-end current can exceed sending-end current

===Long line===
The '''long line''' model is used when a higher degree of accuracy is needed or when the line under consideration is more than 250 km (150&nbsp;mi) long. Series resistance and shunt conductance are considered as distributed parameters, meaning each differential length of the line has a corresponding differential resistance and shunt admittance. The following result can be applied at any point along the transmission line, where <math>\gamma</math> is the {{tsl|en|propagation constant|}}.
:<math>
\begin{align}
A &= D = \cosh(\gamma x) \text{ per unit}\\[3mm]
B &= Z_c \sinh(\gamma x) \Omega\\[2mm]
C &= \frac{1}{Z_c} \sinh(\gamma x) S
\end{align}
</math>

To find the voltage and current at the end of the long line, <math>x</math> should be replaced with <math>l</math> (the line length) in all parameters of the transmission matrix.

(For the full development of this model, see the [[电报员方程]].)

== High-voltage direct current ==
{{Main|High-voltage direct current}}

High-voltage direct current (HVDC) is used to transmit large amounts of power over long distances or for interconnections between asynchronous grids. When electrical energy is to be transmitted over very long distances, the power lost in AC transmission becomes appreciable and it is less expensive to use [[直流電]] instead of [[交流電]]. For a very long transmission line, these lower losses (and reduced construction cost of a DC line) can offset the additional cost of the required converter stations at each end.

[[高壓直流輸電|HVDC]] is also used for long {{tsl|en|Submarine power cable||submarine cables}} where AC cannot be used because of the cable capacitance.<ref>Donald G. Fink, H. Wayne Beatty, ''Standard Handbook for Electrical Engineers 11th Edition'', McGraw Hill, 1978, {{ISBN|0-07-020974-X}}, pages 15-57 and 15-58</ref> In these cases special {{tsl|en|high-voltage cable|}}s for DC are used. Submarine HVDC systems are often used to connect the electricity grids of islands, for example, between [[大不列顛島]] and [[歐洲大陸]], between Great Britain and [[爱尔兰岛]], between [[塔斯馬尼亞州]] and the [[澳大利亚]]n mainland, between the North and South Islands of [[新西兰]], between [[新泽西州]] and [[纽约]], and between New Jersey and [[長島]]. Submarine connections up to {{convert|600|km}} in length are presently in use.<ref name="guarnieri 7-3">{{Cite journal|last=Guarnieri|first=M.|year=2013|title=The Alternating Evolution of DC Power Transmission|journal=IEEE Industrial Electronics Magazine|volume=7|issue=3|pages=60–63|doi=10.1109/MIE.2013.2272238|ref=harv}}</ref>

HVDC links can be used to control problems in the grid with AC electricity flow. The power transmitted by an AC line increases as the [[電力|phase angle]] between source end voltage and destination ends increases, but too large a phase angle will allow the systems at either end of the line to fall out of step. Since the power flow in a DC link is controlled independently of the phases of the AC networks at either end of the link, this phase angle limit does not exist, and a DC link is always able to transfer its full rated power. A DC link therefore stabilizes the AC grid at either end, since power flow and phase angle can then be controlled independently.

As an example, to adjust the flow of AC power on a hypothetical line between [[西雅圖]] and [[波士顿]] would require adjustment of the relative phase of the two regional electrical grids. This is an everyday occurrence in AC systems, but one that can become disrupted when AC system components fail and place unexpected loads on the remaining working grid system. With an HVDC line instead, such an interconnection would:
# Convert AC in Seattle into HVDC;
# Use HVDC for the {{convert|3000|mi|km}} of cross-country transmission; and
# Convert the HVDC to locally synchronized AC in Boston,
(and possibly in other cooperating cities along the transmission route). Such a system could be less prone to failure if parts of it were suddenly shut down. One example of a long DC transmission line is the {{tsl|en|Pacific DC Intertie|}} located in the Western [[美国]].

== Capacity ==
<!-- Linked from wind power. -->
The amount of power that can be sent over a transmission line is limited. The origins of the limits vary depending on the length of the line. For a short line, the heating of conductors due to line losses sets a thermal limit. If too much current is drawn, conductors may sag too close to the ground, or conductors and equipment may be damaged by overheating. For intermediate-length lines on the order of {{convert|100|km|mi|abbr=off}}, the limit is set by the {{tsl|en|voltage drop|}} in the line. For longer AC lines, [[工频|system stability]] sets the limit to the power that can be transferred. Approximately, the power flowing over an AC line is proportional to the cosine of the phase angle of the voltage and current at the receiving and transmitting ends. This angle varies depending on system loading and generation. It is undesirable for the angle to approach 90 degrees, as the power flowing decreases but the resistive losses remain. Very approximately, the allowable product of line length and maximum load is proportional to the square of the system voltage. Series capacitors or phase-shifting transformers are used on long lines to improve stability. [[輸電系統|High-voltage direct current]] lines are restricted only by thermal and voltage drop limits, since the phase angle is not material to their operation.

Up to now, it has been almost impossible to foresee the temperature distribution along the cable route, so that the maximum applicable current load was usually set as a compromise between understanding of operation conditions and risk minimization. The availability of industrial {{tsl|en|distributed temperature sensing|}} (DTS) systems that measure in real time temperatures all along the cable is a first step in monitoring the transmission system capacity. This monitoring solution is based on using passive optical fibers as temperature sensors, either integrated directly inside a high voltage cable or mounted externally on the cable insulation. A solution for overhead lines is also available. In this case the optical fiber is integrated into the core of a phase wire of overhead transmission lines (OPPC). The integrated Dynamic Cable Rating (DCR) or also called Real Time Thermal Rating (RTTR) solution enables not only to continuously monitor the temperature of a high voltage cable circuit in real time, but to safely utilize the existing network capacity to its maximum. Furthermore, it provides the ability to the operator to predict the behavior of the transmission system upon major changes made to its initial operating conditions.

== Control ==
To ensure safe and predictable operation, the components of the transmission system are controlled with generators, switches, circuit breakers and loads. The voltage, power, frequency, load factor, and reliability capabilities of the transmission system are designed to provide cost effective performance for the customers.

=== Load balancing ===
The transmission system provides for base load and [[尖峰負載發電廠|peak load capability]], with safety and fault tolerance margins. The peak load times vary by region largely due to the industry mix. In very hot and very cold climates home air conditioning and heating loads have an effect on the overall load. They are typically highest in the late afternoon in the hottest part of the year and in mid-mornings and mid-evenings in the coldest part of the year. This makes the power requirements vary by the season and the time of day. Distribution system designs always take the base load and the peak load into consideration.

The transmission system usually does not have a large buffering capability to match the loads with the generation. Thus generation has to be kept matched to the load, to prevent overloading failures of the generation equipment.

Multiple sources and loads can be connected to the transmission system and they must be controlled to provide orderly transfer of power. In centralized power generation, only local control of generation is necessary, and it involves {{tsl|en|alternator synchronization||synchronization of the generation units}}, to prevent large transients and overload conditions.

In [[分散式發電|distributed power generation]] the generators are geographically distributed and the process to bring them online and offline must be carefully controlled. The load control signals can either be sent on separate lines or on the power lines themselves. Voltage and frequency can be used as signalling mechanisms to balance the loads.

In voltage signaling, the variation of voltage is used to increase generation. The power added by any system increases as the line voltage decreases. This arrangement is stable in principle. Voltage-based regulation is complex to use in mesh networks, since the individual components and setpoints would need to be reconfigured every time a new generator is added to the mesh.

In frequency signaling, the generating units match the frequency of the power transmission system. In [[下垂速度控制]], if the frequency decreases, the power is increased. (The drop in line frequency is an indication that the increased load is causing the generators to slow down.)

[[風力發動機]]s, [[V2G]] and other locally distributed storage and generation systems can be connected to the power grid, and interact with it to improve system operation. Internationally, the trend has been a slow move from a heavily centralized power system to a decentralized power system. The main draw of locally distributed generation systems which involve a number of new and innovative solutions is that they reduce transmission losses by leading to consumption of electricity closer to where it was produced.<ref>{{cite web
| url = https://www.en-powered.com/blog/the-bumpy-road-to-energy-deregulation | title = The Bumpy Road to Energy Deregulation
| publisher = EnPowered | date = 2016-03-28}}</ref>

=== Failure protection ===
Under excess load conditions, the system can be designed to fail gracefully rather than all at once. {{tsl|en|Brownout (electricity)||Brownouts}} occur when the supply power drops below the demand. [[停電|Blackouts]] occur when the supply fails completely.

{{tsl|en|Rolling blackout|}}s (also called load shedding) are intentionally engineered electrical power outages, used to distribute insufficient power when the demand for electricity exceeds the supply.

== Communications ==
Operators of long transmission lines require reliable communications for [[数据采集与监控系统|control]] of the power grid and, often, associated generation and distribution facilities. Fault-sensing [[保护继电器]]s at each end of the line must communicate to monitor the flow of power into and out of the protected line section so that faulted conductors or equipment can be quickly de-energized and the balance of the system restored. Protection of the transmission line from [[短路]]s and other faults is usually so critical that {{tsl|en|common carrier|}} telecommunications are insufficiently reliable, and in remote areas a common carrier may not be available. Communication systems associated with a transmission project may use:
* [[微波]]s
* [[電力線通信]]
* [[光導纖維]]s
Rarely, and for short distances, a utility will use pilot-wires strung along the transmission line path. Leased circuits from common carriers are not preferred since availability is not under control of the electric power transmission organization.

Transmission lines can also be used to carry data: this is called power-line carrier, or [[電力線通信|PLC]]. PLC signals can be easily received with a radio for the long wave range.
[[File:High Voltage Pylons carrying additional fibre cable in Kenya.jpg|thumb|High Voltage Pylons carrying additional optical fibre cable in Kenya]]
Optical fibers can be included in the stranded conductors of a transmission line, in the overhead shield wires. These cables are known as [[複合光纜地線]] (''OPGW''). Sometimes a standalone cable is used, all-dielectric self-supporting (''ADSS'') cable, attached to the transmission line cross arms.

Some jurisdictions, such as [[明尼蘇達州]], prohibit energy transmission companies from selling surplus communication bandwidth or acting as a telecommunications {{tsl|en|common carrier|}}. Where the regulatory structure permits, the utility can sell capacity in extra {{tsl|en|dark fiber|}}s to a common carrier, providing another revenue stream.

== Electricity market reform ==
{{Main|Electricity market}}

Some regulators regard electric transmission to be a [[自然垄断]]<ref>{{cite web
| url = http://www.thehindubusinessline.com/iw/2004/08/15/stories/2004081501201300.htm
| title = Power transmission business is a natural monopoly
| author = Raghuvir Srinivasan
| publisher = The Hindu
| work = The Hindu Business Line
| date = August 15, 2004
| accessdate = January 31, 2008
}}</ref><ref>{{cite web
| url = http://www.reason.org/commentaries/kiesling_20030818b.shtml
| title = Rethink the Natural Monopoly Justification of Electricity Regulation
| author = Lynne Kiesling
| publisher = Reason Foundation
| date = 18 August 2003
| accessdate = 31 January 2008
| archive-url = https://web.archive.org/web/20080213034400/http://www.reason.org/commentaries/kiesling_20030818b.shtml
| archive-date = February 13, 2008
| url-status = dead
}}</ref> and there are moves in many countries to separately regulate transmission (see [[電力市場]]).

[[西班牙]] was the first country to establish a {{tsl|en|regional transmission organization|}}. In that country, transmission operations and market operations are controlled by separate companies. The transmission system operator is [[西班牙電網公司]] (REE) and the wholesale electricity market operator is Operador del Mercado Ibérico de Energía – Polo Español, S.A. (OMEL) [https://web.archive.org/web/20040906064835/http://www.omel.es/ OMEL Holding | Omel Holding]. Spain's transmission system is interconnected with those of France, Portugal, and Morocco.

The establishment of RTOs in the United States was spurred by the {{tsl|en|FERC|}}'s Order 888, ''Promoting Wholesale Competition Through Open Access Non-discriminatory Transmission Services by Public Utilities; Recovery of Stranded Costs by Public Utilities and Transmitting Utilities'', issued in 1996.<ref>{{cite web|url=https://www.ferc.gov/legal/maj-ord-reg/land-docs/order888.asp|title=FERC: Landmark Orders - Order No. 888|website=www.ferc.gov|access-date=December 7, 2016|archive-url=https://web.archive.org/web/20161219014712/https://www.ferc.gov/legal/maj-ord-reg/land-docs/order888.asp|archive-date=December 19, 2016|url-status=dead}}</ref>
In the United States and parts of Canada, several electric transmission companies operate independently of generation companies, but there are still regions - the Southern United States - where vertical integration of the electric system is intact. In regions of separation, transmission owners and generation owners continue to interact with each other as market participants with voting rights within their RTO. RTOs in the United States are regulated by the {{tsl|en|Federal Energy Regulatory Commission|}}.

== Cost of electric power transmission ==
The cost of high voltage electricity transmission (as opposed to the costs of [[配電系統]]) is comparatively low, compared to all other costs arising in a consumer's electricity bill. In the UK, transmission costs are about 0.2&nbsp;p per kWh compared to a delivered domestic price of around 10&nbsp;p per kWh.<ref>[http://www.claverton-energy.com/what-is-the-cost-per-kwh-of-bulk-transmission-national-grid-in-the-uk-note-this-excludes-distribution-costs.html What is the cost per kWh of bulk transmission] / National Grid in the UK (note this excludes distribution costs)</ref>

Research evaluates the level of capital expenditure in the electric power T&D equipment market will be worth $128.9&nbsp;bn in 2011.<ref>{{cite web |url=http://www.visiongain.com/Report/626/The-Electric-Power-Transmission-and-Distribution-(T-D)-Equipment-Market-2011-2021 |title=The Electric Power Transmission & Distribution (T&D) Equipment Market 2011–2021 |access-date=June 4, 2011 |archive-url=https://web.archive.org/web/20110618143614/http://www.visiongain.com/Report/626/The-Electric-Power-Transmission-and-Distribution-(T-D)-Equipment-Market-2011-2021 |archive-date=June 18, 2011 |url-status=dead }}</ref>

== Merchant transmission ==
Merchant transmission is an arrangement where a third party constructs and operates electric transmission lines through the franchise area of an unrelated incumbent utility.

Operating merchant transmission projects in the [[美国]] include the {{tsl|en|Cross Sound Cable|}} from {{tsl|en|Shoreham, New York|}} to [[纽黑文]], Neptune RTS Transmission Line from {{tsl|en|Sayreville, New Jersey|}} to [[New Bridge, New York]], and {{tsl|en|Path 15|}} in California. Additional projects are in development or have been proposed throughout the United States, including the Lake Erie Connector, an underwater transmission line proposed by ITC Holdings Corp., connecting Ontario to load serving entities in the PJM Interconnection region.<ref>How ITC Holdings plans to connect PJM demand with Ontario's rich renewables, Utility Dive, 8&nbsp;Dec 2014, http://www.utilitydive.com/news/how-itc-holdings-plans-to-connect-pjm-demand-with-ontarios-rich-renewables/341524/</ref>

There is only one unregulated or market interconnector in [[澳大利亚]]: {{tsl|en|Basslink|}} between [[塔斯馬尼亞州]] and [[維多利亞州|Victoria]]. Two DC links originally implemented as market interconnectors, {{tsl|en|Directlink|}} and {{tsl|en|Murraylink|}}, have been converted to regulated interconnectors. [https://web.archive.org/web/20080718211829/http://www.nemmco.com.au/psplanning/psplanning.html#interconnect NEMMCO]

A major barrier to wider adoption of merchant transmission is the difficulty in identifying who benefits from the facility so that the beneficiaries will pay the toll. Also, it is difficult for a merchant transmission line to compete when the alternative transmission lines are subsidized by incumbent utility businesses with a monopolized and regulated rate base.<ref>{{cite book
| author = Fiona Woolf
| title = Global Transmission Expansion
| publisher = Pennwell Books
|date=February 2003
| pages = 226, 247
| isbn = 0-87814-862-0
}}</ref> In the United States, the {{tsl|en|FERC|}}'s Order 1000, issued in 2010, attempts to reduce barriers to third party investment and creation of merchant transmission lines where a public policy need is found.<ref>{{cite web|url=https://www.ferc.gov/industries/electric/indus-act/trans-plan.asp|title=FERC: Industries - Order No. 1000 - Transmission Planning and Cost Allocation|website=www.ferc.gov|access-date=October 30, 2018|archive-url=https://web.archive.org/web/20181030205910/https://www.ferc.gov/industries/electric/indus-act/trans-plan.asp|archive-date=October 30, 2018|url-status=dead}}</ref>

== Health concerns ==
{{Main|Electromagnetic radiation and health}}

Some large studies, including a large study in the United States, have failed to find any link between living near power lines and developing any sickness or diseases, such as cancer. A 1997 study found that it did not matter how close one was to a power line or a sub-station, there was no increased risk of cancer or illness.<ref>[http://www.abc.net.au/rn/talks/8.30/helthrpt/stories/s175.htm Power Lines and Cancer] {{Webarchive|url=https://web.archive.org/web/20110417202936/http://www.abc.net.au/rn/talks/8.30/helthrpt/stories/s175.htm |date=April 17, 2011 }}, The Health Report / ABC Science - Broadcast on 7&nbsp;June 1997 (Australian Broadcasting Corporation)</ref>

The mainstream scientific evidence suggests that low-power, low-frequency, electromagnetic radiation associated with household currents and high transmission power lines does not constitute a short or long-term health hazard. Some studies, however, have found [[相关]]s between various diseases and living or working near power lines. No adverse health effects have been substantiated for people not living close to powerlines.<ref>[http://www.who.int/mediacentre/factsheets/fs322/en/ Electromagnetic fields and public health], [[世界卫生组织]]</ref>

The {{tsl|en|New York State Public Service Commission|}} conducted a study, documented in ''Opinion No. 78-13'' (issued June 19, 1978), to evaluate potential health effects of electric fields. The study's case number is too old to be listed as a case number in the commission's online database, DMM, and so the original study can be difficult to find. The study chose to utilize the electric field strength that was measured at the edge of an existing (but newly built) right-of-way on a 765 kV transmission line from New York to Canada, 1.6 kV/m, as the interim standard maximum electric field at the edge of any new transmission line right-of-way built in New York State after issuance of the order. The opinion also limited the voltage of all new transmission lines built in New York to 345 kV. On September 11, 1990, after a similar study of magnetic field strengths, the NYSPSC issued their ''Interim Policy Statement on Magnetic Fields''. This study established a magnetic field interim standard of 200 mG at the edge of the right-of-way using the winter-normal conductor rating. This later document can also be difficult to find on the NYSPSC's online database, since it predates the online database system. As a comparison with everyday items, a hair dryer or electric blanket produces a 100 mG - 500 mG magnetic field. An electric razor can produce 2.6 kV/m. Whereas electric fields can be shielded, magnetic fields cannot be shielded, but are usually minimized by optimizing the location of each phase of a circuit in cross-section.<ref>{{cite web|url=http://documents.dps.ny.gov/public/Common/ViewDoc.aspx?DocRefId=%7BED95C2A2-2DEA-4FFC-A8DA-CD9C39F5D361%7D|title=EMF Report for the CHPE|pp=1–4|publisher=TRC|date=March 2010|accessdate=November 9, 2018}}</ref><ref>{{cite web|url=https://www.transpower.co.nz/sites/default/files/publications/resources/EMF-fact-sheet-3-2009.pdf|title=Electric and Magnetic Field Strengths|publisher=Transpower New Zealand Ltd|p=2|accessdate=November 9, 2018}}</ref>

When a new transmission line is proposed, within the application to the applicable regulatory body (usually a public utility commission), there is often an analysis of electric and magnetic field levels at the edge of rights-of-way. These analyses are performed by a utility or by an electrical engineering consultant using modelling software. At least one state public utility commission has access to software developed by an engineer or engineers at the {{tsl|en|Bonneville Power Administration|}} to analyze electric and magnetic fields at edge of rights-of-way for proposed transmission lines. Often, public utility commissions will not comment on any health impacts due to electric and magnetic fields and will refer information seekers to the state's affiliated department of health.

There are established biological effects for {{tsl|en|Acute toxicity||acute}} ''high'' level exposure to magnetic fields well above 100&nbsp;[[特斯拉|µT]] (1&nbsp;[[高斯 (单位)|G]]) (1,000 mG). In a residential setting, there is "limited evidence of [[致癌物質]]icity in humans and less than sufficient evidence for carcinogenicity in experimental animals", in particular, childhood leukemia, ''associated with'' average exposure to residential power-frequency magnetic field above 0.3&nbsp;µT (3&nbsp;mG) to 0.4&nbsp;µT (4&nbsp;mG). These levels exceed average residential power-frequency magnetic fields in homes, which are about 0.07&nbsp;µT (0.7&nbsp;mG) in Europe and 0.11&nbsp;µT (1.1&nbsp;mG) in North America.<ref name="WHOFactsheet322">{{cite web |url=http://www.who.int/mediacentre/factsheets/fs322/en/index.html|title= Electromagnetic fields and public health|accessdate=23 January 2008 |date=June 2007|work= Fact sheet No.&nbsp;322|publisher=[[世界卫生组织]]}}</ref><ref name="NIEHS">{{cite web|url=http://www.niehs.nih.gov/health/docs/emf-02.pdf |title=Electric and Magnetic Fields Associated with the Use of Power |accessdate=29 January 2008 |date=June 2002 |format=PDF |publisher={{tsl|en|National Institute of Environmental Health Sciences|}} }}</ref>

The Earth's natural geomagnetic field strength varies over the surface of the planet between 0.035&nbsp;mT and 0.07&nbsp;mT (35&nbsp;µT - 70&nbsp;µT or 350 mG - 700 mG) while the International Standard for the continuous exposure limit is set at 40&nbsp;mT (400,000 mG or 400&nbsp;G) for the general public.<ref name="WHOFactsheet322"/>

Tree Growth Regulator and Herbicide Control Methods may be used in transmission line right of ways<ref>Transmission Vegetation Management NERC Standard FAC-003-2 Technical Reference Page 14/50. http://www.nerc.com/docs/standards/sar/FAC-003-2_White_Paper_2009Sept9.pdf</ref> which may have [[除草剂|health effects]].

== Policy by country ==
===United States===
The {{tsl|en|Federal Energy Regulatory Commission|}} (FERC) is the primary regulatory agency of electric power transmission and wholesale electricity sales within the United States. It was originally established by Congress in 1920 as the Federal Power Commission and has since undergone multiple name and responsibility modifications. That which is not regulated by FERC, primarily electric power distribution and the retail sale of power, is under the jurisdiction of state authority.

Two of the more notable U.S. energy policies impacting electricity transmission are [[Order No. 888]] and the [[2005年能源政策法案]].

Order No.&nbsp;888 adopted by FERC on 24&nbsp;April 1996, was “designed to remove impediments to competition in the wholesale bulk power marketplace and to bring more efficient, lower cost power to the Nation’s electricity consumers. The legal and policy cornerstone of these rules is to remedy undue discrimination in access to the monopoly owned transmission wires that control whether and to whom electricity can be transported in interstate commerce.”<ref name="Docket No. RM95-8-000">{{cite web|title=Order No. 888|url=https://www.ferc.gov/legal/maj-ord-reg/land-docs/rm95-8-00w.txt|publisher=United States of America Federal Energy Regulatory Commission}}</ref> Order No.&nbsp;888 required all public utilities that own, control, or operate facilities used for transmitting electric energy in interstate commerce, to have open access non-discriminatory transmission tariffs. These tariffs allow any electricity generator to utilize the already existing power lines for the transmission of the power that they generate. Order No.&nbsp;888 also permits public utilities to recover the costs associated with providing their power lines as an open access service.<ref name="Docket No. RM95-8-000"/><ref name="Order No. 888">{{cite web|last1=Order No. 888|title=Promoting Wholesale Competition Through Open Access Non-discriminatory Transmission Services by Public Utilities; Recovery of Stranded Costs by Public Utilities and Transmitting Utilities|first1=FERC|url=https://www.ferc.gov/legal/maj-ord-reg/land-docs/order888.asp|access-date=December 7, 2016|archive-url=https://web.archive.org/web/20161219014712/https://www.ferc.gov/legal/maj-ord-reg/land-docs/order888.asp|archive-date=December 19, 2016|url-status=dead}}</ref>

The Energy Policy Act of 2005 (EPAct) signed into law by congress on 8&nbsp;August 2005, further expanded the federal authority of regulating power transmission. EPAct gave FERC significant new responsibilities including but not limited to the enforcement of electric transmission reliability standards and the establishment of rate incentives to encourage investment in electric transmission.<ref>{{cite book|title=Energy Policy Act of 2005 Fact Sheet|date=8 August 2006|publisher=FERC Washington, D.C.|url=https://www.ferc.gov/legal/fed-sta/epact-fact-sheet.pdf|access-date=December 7, 2016|archive-url=https://web.archive.org/web/20161220231111/https://ferc.gov/legal/fed-sta/epact-fact-sheet.pdf|archive-date=December 20, 2016|url-status=dead}}</ref>

Historically, local governments have exercised authority over the grid and have significant disincentives to encourage actions that would benefit states other than their own. Localities with cheap electricity have a disincentive to encourage making {{tsl|en|interstate commerce|}} in electricity trading easier, since other regions will be able to compete for local energy and drive up rates. For example, some regulators in Maine do not wish to address congestion problems because the congestion serves to keep Maine rates low.<ref name=ncep2>{{cite journal|url=http://www.oe.energy.gov/DocumentsandMedia/primer.pdf|title=Electricity Transmission: A primer|author=National Council on Electricity Policy|page=32 (page&nbsp;41 in .pdf)|format=PDF|journal=|access-date=December 28, 2008|archive-url=https://web.archive.org/web/20081201222708/http://www.oe.energy.gov/DocumentsandMedia/primer.pdf|archive-date=December 1, 2008|url-status=dead}}</ref> Further, vocal local constituencies can block or slow permitting by pointing to visual impact, environmental, and perceived health concerns. In the US, generation is growing four times faster than transmission, but big transmission upgrades require the coordination of multiple states, a multitude of interlocking permits, and cooperation between a significant portion of the 500 companies that own the grid. From a policy perspective, the control of the grid is [[巴尔干化]], and even former [[美國能源部長|energy secretary]] [[比尔·理查森]] refers to it as a ''third world grid''. There have been efforts in the EU and US to confront the problem. The US national security interest in significantly growing transmission capacity drove passage of the [[2005年能源政策法案|2005 energy act]] giving the Department of Energy the authority to approve transmission if states refuse to act. However, soon after the Department of Energy used its power to designate two {{tsl|en|National Interest Electric Transmission Corridor|}}s, 14&nbsp;senators signed a letter stating the DOE was being too aggressive.<ref>{{cite journal | last = Wald | first = Matthew | title = Wind Energy Bumps into Power Grid’s Limits | date=27 August 2008 | page=A1 | accessdate=12 December 2008 | work=[[纽约时报]] | url = https://www.nytimes.com/2008/08/27/business/27grid.html?_r=2&ref=business&oref=slogin}}</ref>

== Special transmission ==

=== Grids for railways ===
{{Main|Traction power network}}

In some countries where [[電力機車]]s or [[電聯車]]s run on low frequency AC power, there are separate single phase {{tsl|en|traction power network|}}s operated by the railways. Prime examples are countries in Europe (including [[奥地利]], [[德国]] and [[瑞士]]) which utilize the older AC technology based on 16&nbsp;<sup>2</sup>''/''<sub>3</sub>&nbsp;Hz (Norway and Sweden also use this frequency but use conversion from the 50&nbsp;Hz public supply; Sweden has a 16&nbsp;<sup>2</sup>''/''<sub>3</sub>&nbsp;Hz traction grid but only for part of the system).

=== Superconducting cables ===
[[高溫超導]]s (HTS) promise to revolutionize power distribution by providing lossless transmission of electrical power. The development of superconductors with transition temperatures higher than the boiling point of [[液氮]] has made the concept of superconducting power lines commercially feasible, at least for high-load applications.<ref>{{cite journal |doi=10.1109/77.920339 |author=Jacob Oestergaard |journal=IEEE Transactions on Applied Superconductivity |title=Energy losses of superconducting power transmission cables in the grid |year=2001 |volume=11 |page=2375|display-authors=etal|url=http://orbit.dtu.dk/files/4280307/%C3%B8stergaard.pdf }}</ref> It has been estimated that the waste would be halved using this method, since the necessary refrigeration equipment would consume about half the power saved by the elimination of the majority of resistive losses. Some companies such as [[聯合愛迪生]] and {{tsl|en|American Superconductor|}} have already begun commercial production of such systems.<ref>{{cite web|url=https://www.newscientist.com/article/dn11907-superconducting-power-line-to-shore-up-new-york-grid/|title=Superconducting power line to shore up New York grid|first=New Scientist Tech and|last=Reuters|website=New Scientist}}</ref> In one hypothetical future system called a {{tsl|en|SuperGrid|}}, the cost of cooling would be eliminated by coupling the transmission line with a liquid hydrogen pipeline.

Superconducting cables are particularly suited to high load density areas such as the business district of large cities, where purchase of an [[地役权]] for cables would be very costly.<ref>{{cite web |url=http://www.futureenergies.com/modules.php?name=News&file=article&sid=237 |title=Superconducting cables will be used to supply electricity to consumers |access-date=June 12, 2014 |archive-url=https://web.archive.org/web/20140714161200/http://www.futureenergies.com/modules.php?name=News&file=article&sid=237 |archive-date=July 14, 2014 |url-status=dead }}</ref>

{| class="wikitable sortable"
|+HTS transmission lines<ref>{{cite web |url=https://spectrum.ieee.org/biomedical/imaging/superconductivitys-first-century/3 |title=Superconductivity's First Century |access-date=August 9, 2012 |archive-url=https://web.archive.org/web/20120812011121/https://spectrum.ieee.org/biomedical/imaging/superconductivitys-first-century/3 |archive-date=August 12, 2012 |url-status=dead }}</ref>
|-
|-
! Location !! Length (km) !! Voltage (kV) !! Capacity (GW) !! Date
|1675||[[Ole&nbsp;Rømer|Rømer]]&nbsp;and&nbsp;[[Christiaan&nbsp;Huygens|Huygens]], moons&nbsp;of&nbsp;Jupiter||{{val|220000}}<ref name=roemer/><ref name="Huygens 1690 8–9"/>
|-
|-
|Carrollton, Georgia || || || || 2000
|1729||[[James&nbsp;Bradley]], aberration&nbsp;of&nbsp;light||{{val|301000}}<ref name=How/>
|-
|-
|align=left|Albany, New York<ref>{{cite web|url=http://www.superpower-inc.com/content/hts-transmission-cable|title=HTS Transmission Cable|website=www.superpower-inc.com}}</ref>|| 0.35 || 34.5 || 0.048 ||2006
|1849||[[Hippolyte&nbsp;Fizeau]], toothed&nbsp;wheel||{{val|315000}}<ref name=How/>
|-
|-
|{{tsl|en|Holbrook Superconductor Project||Holbrook, Long Island}}<ref>{{cite web|url=http://www-03.ibm.com/ibm/history/ibm100/us/en/icons/hightempsuperconductors/|title=IBM100 - High-Temperature Superconductors|date=August 10, 2017|website=www-03.ibm.com}}</ref>|| 0.6 || 138 || 0.574 || 2008
|1862||[[Léon&nbsp;Foucault]], rotating&nbsp;mirror||{{val|298000|500}}<ref name=How/>
|-
|-
|align=left|{{tsl|en|Tres Amigas SuperStation||Tres Amigas}}|| || || 5 || Proposed 2013
|1907||Rosa&nbsp;and&nbsp;Dorsey, <abbr title="electromagnetic">EM</abbr>&nbsp;constants||{{val|299710|30}}<ref name="Essen1948"/><ref name="RosaDorsey"/>
|-
|-
|align=left|Manhattan: Project Hydra|| || || || Proposed 2014
|1926||[[Albert&nbsp;Michelson]], rotating&nbsp;mirror||{{val|299796|4}}<ref>{{cite journal|journal=The Astrophysical Journal|volume=65|language=en|issn=0004-637X|date=1927-01|pages=1|doi=10.1086/143021|url=http://adsabs.harvard.edu/doi/10.1086/143021|title=Measurement of the Velocity of Light Between Mount Wilson and Mount San Antonio|accessdate=2019-06-25|author=A. A. Michelson}}</ref>
|-
|-
|align=left|Essen, Germany<ref>{{cite web|url=https://www.powermag.com/high-temperature-superconductor-technology-stepped-up/|title=High-Temperature Superconductor Technology Stepped Up|first=03/01/2012 &#124; Sonal|last=Patel|date=March 1, 2012|website=POWER Magazine}}</ref><ref>{{cite web|url=https://phys.org/news/2014-05-longest-superconducting-cable-worldwide.html|title=Operation of longest superconducting cable worldwide started|website=phys.org}}</ref>|| 1 || 10 || 0.04 || 2014
|1950||{{nowrap|Essen and Gordon-Smith}}, cavity&nbsp;resonator||{{val|299792.5|3.0}}<ref name="Essen1950"/>
|-
|1958||K.D.&nbsp;Froome, radio&nbsp;interferometry||{{val|299792.50|0.10}}<ref name="Froome1858"/>
|-
|1972||Evenson&nbsp;''et&nbsp;al.'', laser&nbsp;interferometry||{{val|299792.4562|0.0011}}<ref name="NIST heterodyne"/>
|-
|1983||17th&nbsp;CGPM, definition&nbsp;of&nbsp;the&nbsp;metre||{{val|299792.458}}&nbsp;(exact)<ref name=Resolution_1/>
|}
|}
Until the [[early modern period]], it was not known whether light travelled instantaneously or at a very fast finite speed. The first extant recorded examination of this subject was in [[ancient Greece]]. The ancient Greeks, Muslim scholars and classical European scientists long debated this until Rømer provided the first calculation of the speed of light. Einstein's Theory of Special Relativity concluded that the speed of light is constant regardless of one's frame of reference. Since then, scientists have provided increasingly accurate measurements.


=== Single wire earth return ===
===Early history===
{{Main|Single-wire earth return}}
[[Empedocles]] was the first to claim that light has a finite speed.<ref>
{{Cite book
|last=Sarton |first=G
|year=1993
|title=Ancient science through the golden age of Greece
|url=http://books.google.com/?id=VcoGIKlHuZcC&pg=PA248
|page=248
|publisher=[[Courier Dover]]
|isbn=0-486-27495-0
}}</ref> He maintained that light was something in motion, and therefore must take some time to travel. [[Aristotle]] argued, to the contrary, that "light is due to the presence of something, but it is not a movement".<ref name=Statistics>
{{cite journal
|last=MacKay |first=RH |last2=Oldford |first2=RW
|year=2000
|title=Scientific Method, Statistical Method and the Speed of Light
|url=http://sas.uwaterloo.ca/~rwoldfor/papers/sci-method/paperrev/
|journal=[[Statistical Science (journal)|Statistical Science]]
|volume=15 |issue=3 |pages=254–78
|doi=10.1214/ss/1009212817
}} (click on "Historical background" in the table of contents)</ref> [[Euclid]] and [[Ptolemy]] advanced the [[Emission theory (vision)|emission theory]] of vision, where light is emitted from the eye, thus enabling sight. Based on that theory, [[Heron of Alexandria]] argued that the speed of light must be [[infinite]] because distant objects such as stars appear immediately upon opening the eyes.


Single-wire earth return (SWER) or single wire ground return is a single-wire transmission line for supplying single-phase electrical power for an electrical grid to remote areas at low cost. It is principally used for rural electrification, but also finds use for larger isolated loads such as water pumps. Single wire earth return is also used for HVDC over submarine power cables.
[[Early Islamic philosophy|Early Islamic philosophers]] initially agreed with the [[Aristotelian physics|Aristotelian view]] that light had no speed of travel. In 1021, [[Alhazen]] (Ibn al-Haytham) published the ''[[Book of Optics]]'', in which he presented a series of arguments dismissing the emission theory in favour of the now accepted intromission theory of [[Visual perception|vision]], in which light moves from an object into the eye.<ref>{{cite journal|journal=The Neuroscientist|volume=5|issue=1|language=en|issn=1073-8584|date=1999-01|pages=58–64|doi=10.1177/107385849900500108|url=http://journals.sagepub.com/doi/10.1177/107385849900500108|title=The Fire That Comes from the Eye|accessdate=2019-06-25|author=Charles G. Gross}}</ref>{{verify source|date=January 2012}} This led Alhazen to propose that light must have a finite speed,<ref name=Statistics/><ref name=Hamarneh>
{{cite journal
|last=Hamarneh |first=S
|year=1972
|title=Review: Hakim Mohammed Said, ''Ibn al-Haitham''
|journal=[[Isis (journal)|Isis]]
|volume=63 |issue=1 |page=119
|doi=10.1086/350861
}}</ref><ref name=Lester>
{{Cite book
|last=Lester |first=PM
|year=2005
|title=Visual Communication: Images With Messages
|pages=10–11
|publisher=[[Thomson Wadsworth]]
|isbn=0-534-63720-5
}}</ref> and that the speed of light is variable, decreasing in denser bodies.<ref name=Lester/><ref>
{{cite web
|first1=JJ
|last1=O'Connor
|authorlink1=John J. O'Connor (mathematician)
|first2=EF
|last2=Robertson
|authorlink2=Edmund F. Robertson
|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Haytham.html
|title=Abu Ali al-Hasan ibn al-Haytham
|work=[[MacTutor History of Mathematics archive]]
|publisher=[[University of St Andrews]]
|accessdate=2010-01-12
}}</ref> He argued that light is substantial matter, the propagation of which requires time, even if this is hidden from our senses.<ref>
{{cite conference
|last=Lauginie |first=P
|year=2005
|title=Measuring: Why? How? What?
|url=http://www.ihpst2005.leeds.ac.uk/papers/Lauginie.pdf
|booktitle=Proceedings of the 8th International History, Philosophy, Sociology & Science Teaching Conference
|accessdate=2008-07-18
}}</ref> Also in the 11th century, [[Abū Rayhān al-Bīrūnī]] agreed that light has a finite speed, and observed that the speed of light is much faster than the speed of sound.<ref>
{{cite web
|first1=JJ
|last1=O'Connor
|first2=EF
|last2=Robertson
|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Biruni.html
|title=Abu han Muhammad ibn Ahmad al-Biruni
|work=MacTutor History of Mathematics archive
|publisher=University of St Andrews
|accessdate=2010-01-12
}}</ref>


=== Wireless power transmission ===
In the 13th century, [[Roger Bacon]] argued that the speed of light in air was not infinite, using philosophical arguments backed by the writing of Alhazen and Aristotle.<ref name=Lindberg>
{{Main|Wireless energy transfer}}
{{Cite book
|last=Lindberg |first=DC
|year=1996
|title=Roger Bacon and the origins of Perspectiva in the Middle Ages: a critical edition and English translation of Bacon's Perspectiva, with introduction and notes
|url=http://books.google.com/?id=jSPHMKbjYkQC&pg=PA143
|page=143
|isbn=0-19-823992-0
|publisher=[[Oxford University Press]]
}}</ref><ref>
{{Cite book
|last=Lindberg |first=DC
|year=1974
|chapter=Late Thirteenth-Century Synthesis in Optics
|editor=Edward Grant
|title=A source book in medieval science
|url=http://books.google.com/?id=fAPN_3w4hAUC&pg=RA1-PA395&dq=roger-bacon+speed-of-light&q=roger-bacon%20speed-of-light
|page=396
|publisher=[[Harvard University Press]]
|isbn=978-0-674-82360-0
}}</ref> In the 1270s, [[Witelo]] considered the possibility of light travelling at infinite speed in vacuum, but slowing down in denser bodies.<ref name=Marshall>
{{cite journal
|last=Marshall |first=P
|year=1981
|title=Nicole Oresme on the Nature, Reflection, and Speed of Light
|journal=[[Isis (journal)|Isis]]
|volume=72 |issue=3 |pages=357–74 [367–74]
|doi=10.1086/352787
}}</ref>


Both [[尼古拉·特斯拉]] and {{tsl|en|Hidetsugu Yagi|}} attempted to devise systems for large scale wireless power transmission in the late 1800s and early 1900s, with no commercial success.
In the early 17th century, [[Johannes Kepler]] believed that the speed of light was infinite, since empty space presents no obstacle to it. [[René Descartes]] argued that if the speed of light were finite, the Sun, Earth, and Moon would be noticeably out of alignment during a [[lunar eclipse]]. Since such misalignment had not been observed, Descartes concluded the speed of light was infinite. Descartes speculated that if the speed of light were found to be finite, his whole system of philosophy might be demolished.<ref name=Statistics />


In November 2009, LaserMotive won the NASA 2009 Power Beaming Challenge by powering a cable climber 1&nbsp;km vertically using a ground-based laser transmitter. The system produced up to 1&nbsp;kW of power at the receiver end. In August 2010, NASA contracted with private companies to pursue the design of laser power beaming systems to power low earth orbit satellites and to launch rockets using laser power beams.
===First measurement attempts===


Wireless power transmission has been studied for transmission of power from [[太空太陽能]]s to the earth. A high power array of [[微波]] or laser transmitters would beam power to a {{tsl|en|rectenna|}}. Major engineering and economic challenges face any solar power satellite project.
In 1629, [[Isaac Beeckman]] proposed an experiment in which a person observes the flash of a cannon reflecting off a mirror about one mile (1.6&nbsp;km) away. In 1638, [[Galileo Galilei]] proposed an experiment, with an apparent claim to having performed it some years earlier, to measure the speed of light by observing the delay between uncovering a lantern and its perception some distance away. He was unable to distinguish whether light travel was instantaneous or not, but concluded that if it were not, it must nevertheless be extraordinarily rapid.<ref name=boyer>
{{cite journal
|last=Boyer |first=CB
|year=1941
|title=Early Estimates of the Velocity of Light
|journal=[[Isis (journal)|Isis]]
|volume=33 |issue=1 |page=24
|doi=10.1086/358523
|ref=boyer-1941
}}</ref><ref name=2newsciences>
{{Cite book
|last=Galilei |first=G
|year=1954 |origyear=1638
|title=Dialogues Concerning Two New Sciences
|url=http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=753&layout=html#a_2288356
|page=43
|others=Crew, H; de Salvio A (trans.)
|publisher=[[Dover Publications]]
|isbn=0-486-60099-8
|ref=Reference-Galileo-1954
}}</ref> Galileo's experiment was carried out by the [[Accademia del Cimento]] of Florence, Italy, in 1667, with the lanterns separated by about one&nbsp;mile, but no delay was observed. The actual delay in this experiment would have been about 11 [[microsecond]]s.


== Security of control systems ==
[[File:Illustration from 1676 article on Ole Rømer's measurement of the speed of light.jpg|thumb|left|upright=0.8|Rømer's observations of the occultations of Io from Earth|alt=A diagram of a planet's orbit around the Sun and of a moon's orbit around another planet. The shadow of the latter planet is shaded.]]
The [[美國聯邦政府]] admits that the power grid is susceptible to [[網絡戰]].<ref>{{cite news|url=http://news.bbc.co.uk/2/hi/technology/7990997.stm|title=Spies 'infiltrate US power grid'|date=April 9, 2009|via=news.bbc.co.uk}}</ref><ref>{{cite news|url=http://www.cnn.com/2009/TECH/04/08/grid.threat/index.html?iref=newssearch#cnnSTCVideo|title=Hackers reportedly have embedded code in power grid - CNN.com|website=www.cnn.com}}</ref> The [[美國國土安全部]] works with industry to identify vulnerabilities and to help industry enhance the security of control system networks, the federal government is also working to ensure that security is built in as the U.S. develops the next generation of 'smart grid' networks.<ref>{{cite web|url=https://in.reuters.com/article/cyberattack-usa-idINN0853911920090408|title=UPDATE 2-US concerned power grid vulnerable to cyber-attack|date=April 8, 2009|via=in.reuters.com}}</ref>
The first quantitative estimate of the speed of light was made in 1676 by Rømer (see [[Rømer's determination of the speed of light]]).<ref name="cohen"/><ref name="roemer"/> From the observation that the periods of Jupiter's innermost moon [[Io (moon)|Io]] appeared to be shorter when the Earth was approaching Jupiter than when receding from it, he concluded that light travels at a finite speed, and estimated that it takes light 22 minutes to cross the diameter of Earth's orbit. [[Christiaan Huygens]] combined this estimate with an estimate for the diameter of the Earth's orbit to obtain an estimate of speed of light of {{val|220000|u=km/s}}, 26% lower than the actual value.<ref name="Huygens 1690 8–9">{{Cite book
|last=Huygens |first=C
|year=1690
|title=Traitée de la Lumière |language=French
|url=http://books.google.com/?id=No8PAAAAQAAJ&pg=PA9
|pages=8–9
|publisher=[[Pierre van der Aa]]
}}</ref>


In June 2019, [[俄罗斯]] has conceded that it is "possible" its {{tsl|en|Electricity sector in Russia||electrical grid}} is under cyber-attack by the United States.<ref>{{cite news |title=US and Russia clash over power grid 'hack attacks |url=https://www.bbc.com/news/technology-48675203 |work=BBC News |date=18 June 2019}}</ref> ''The New York Times'' reported that American hackers from the [[美國網戰司令部]] planted malware potentially capable of disrupting the Russian electrical grid.<ref>{{cite news |title=How Not To Prevent a Cyberwar With Russia |url=https://www.wired.com/story/russia-cyberwar-escalation-power-grid/ |work=[[连线|Wired]] |date=18 June 2019}}</ref>
In his 1704 book ''[[Opticks]]'', [[Isaac Newton]] reported Rømer's calculations of the finite speed of light and gave a value of "seven or eight minutes" for the time taken for light to travel from the Sun to the Earth (the modern value is 8&nbsp;minutes 19&nbsp;seconds).<ref>
{{Cite book
|last=Newton |first=I
|year=1704
|contribution=Prop. XI
|title=Optiks
|url=http://gallica.bnf.fr/ark:/12148/bpt6k3362k.image.f235.vignettesnaviguer
}} The text of Prop.&nbsp;XI is identical between the first (1704) and second (1719) editions.</ref> Newton queried whether Rømer's eclipse shadows were coloured; hearing that they were not, he concluded the different colours travelled at the same speed. In 1729, [[James Bradley]] discovered the [[aberration of light]].<ref name="Bradley1729"/> From this effect he determined that light must travel 10,210 times faster than the Earth in its orbit (the modern figure is 10,066 times faster) or, equivalently, that it would take light 8&nbsp;minutes 12&nbsp;seconds to travel from the Sun to the Earth.<ref name="Bradley1729"/>


== 記錄 ==
===Connections with electromagnetism===
* Highest capacity system: 12 GW Zhundong–Wannan(准东-皖南)±1100&nbsp;kV HVDC.<ref>{{cite web|url=https://www.e-fermat.org/files/communication/Li-COMM-ASIAEM2015-2017-Vol21-May-Jun.-017.pdf|title=Development of UHV Transmission and Insulation Technology in China|last=|first=|date=|website=|url-status=live|archive-url=|archive-date=|access-date=}}</ref><ref>{{cite web|url=http://www.xj.xinhuanet.com/2019-09/27/c_1125048315.htm|title=准东-皖南±1100千伏特高压直流输电工程竣工投运|last=|first=|date=|website=|url-status=live|archive-url=|archive-date=|access-date=}}</ref>
{{See also|History of electromagnetic theory|History of special relativity}}
* Highest transmission voltage (AC):
In the 19th century [[Hippolyte Fizeau]] developed a method to determine the speed of light based on time-of-flight measurements on Earth and reported a value of {{val|315000|u=km/s}}. His method was improved upon by [[Léon Foucault]] who obtained a value of {{val|298000|u=km/s}} in 1862.<ref name="How"/> In the year 1856, [[Wilhelm Eduard Weber]] and [[Rudolf Kohlrausch]] measured the ratio of the electromagnetic and electrostatic units of charge, 1/√''ε''<sub>0</sub>''μ''<sub>0</sub>, by discharging a [[Leyden jar]], and found that its numerical value was very close to the speed of light as measured directly by Fizeau. The following year [[Gustav Kirchhoff]] calculated that an electric signal in a [[electrical resistance|resistanceless]] wire travels along the wire at this speed.<ref>{{cite journal
**planned: 1.20&nbsp;MV (Ultra High Voltage) on Wardha-Aurangabad line ([[印度]]) - under construction. Initially will operate at 400 kV.<ref>{{cite journal |url=http://tdworld.com/overhead_transmission/powergrid-research-development-201301/ |title=India Steps It Up |journal=Transmission & Distribution World | date=January 2013}}</ref>
|last1=Graneau |first1=P
**worldwide: 1.15&nbsp;MV (Ultra High Voltage) on {{tsl|en|Powerline Ekibastuz-Kokshetau||Ekibastuz-Kokshetau line}} ([[哈萨克斯坦]])
|last2=Assis |first2=AKT
* Largest double-circuit transmission, {{tsl|en|Kita-Iwaki Powerline|}} ([[日本]]).
|title=Kirchhoff on the motion of electricity in conductors
* Highest {{tsl|en|Transmission tower||towers}}: {{tsl|en|Yangtze River Crossing|}} ([[中华人民共和国]]) (height: {{convert|345|m|ft|0|abbr=on|disp=or}})
|journal=[[Apeiron (physics journal)|Apeiron]]
* Longest power line: {{tsl|en|Inga-Shaba|}} ([[刚果民主共和国]]) (length: {{convert|1700|km|mi|0|disp=or}})
|volume=19
* Longest span of power line: {{convert|5376|m|ft|0|abbr=on}} at {{tsl|en|Ameralik Span|}} ([[格陵兰]], [[丹麦]])
|year=1994
* Longest submarine cables:
|pages=19–25
**{{tsl|en|NorNed|}}, [[北海 (大西洋)]] ([[挪威]]/[[荷兰]]) – (length of submarine cable: {{convert|580|km|mi|0|disp=or}})
|url=http://www.physics.princeton.edu/~mcdonald/examples/EM/kirchhoff_apc_102_529_57_english.pdf
**{{tsl|en|Basslink|}}, [[巴斯海峡]], ([[澳大利亚]]) – (length of submarine cable: {{convert|290|km|mi|0|disp=or}}, total length: {{convert|370.1|km|mi|0|disp=or}})
|accessdate=2010-10-21
**{{tsl|en|Baltic Cable|}}, [[波罗的海]] ([[德国]]/[[瑞典]]) – (length of submarine cable: {{convert|238|km|mi|0|disp=or}}, [[高壓直流輸電|HVDC]] length: {{convert|250|km|mi|0|disp=or}}, total length: {{convert|262|km|mi|0|disp=or}})
}}</ref> In the early 1860s, Maxwell showed that according to the theory of electromagnetism which he was working on, that electromagnetic waves propagate in empty space<ref>{{cite book
* Longest underground cables:
|title=College physics: reasoning and relationships
**{{tsl|en|Murraylink|}}, {{tsl|en|Riverland|}}/{{tsl|en|Sunraysia|}} (Australia) – (length of underground cable: {{convert|170|km|mi|0|disp=or}})
|first1=Nicholas J.
|last1=Giordano
|publisher=Cengage Learning
|year=2009
|isbn=0-534-42471-6
|page=787
|url=http://books.google.com/books?id=BwistUlpZ7cC}}, [http://books.google.com/books?id=BwistUlpZ7cC&pg=PA787 Extract of page 787]
</ref><ref>{{cite book
|title=The riddle of gravitation
|first1=Peter Gabriel
|last1=Bergmann
|publisher=Courier Dover Publications
|year=1992
|isbn=0-486-27378-4
|page=17
|url=http://books.google.com/books?id=WYxkrwMidp0C}}, [http://books.google.com/books?id=WYxkrwMidp0C&pg=PA17 Extract of page 17]
</ref><ref>{{cite book
|title=The equations: icons of knowledge
|first1=Sander
|last1=Bais
|publisher=Harvard University Press
|year=2005
|isbn=0-674-01967-9
|page=40
|url=http://books.google.com/books?id=jKbVuMSlJPoC}}, [http://books.google.com/books?id=jKbVuMSlJPoC&pg=PA40 Extract of page 40]
</ref> at a speed equal to the above Weber/Kohrausch ratio, and drawing attention to the numerical proximity of this value to the speed of light as measured by Fizeau, he proposed that light is in fact an electromagnetic wave.<ref name=maxwellbio>
{{cite web
|last1=O'Connor |first1=JJ |last2=Robertson |first2=EF
|date=November 1997
|title= James Clerk Maxwell
|url= http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Maxwell.html
|publisher=School of Mathematics and Statistics, [[University of St Andrews]]
|accessdate=2010-10-13
}}</ref>


== 參見 ==
==="Luminiferous aether"===
{{Portal|Energy}}
[[File:Einstein en Lorentz.jpg|thumb|150px|Hendrik Lorentz with Albert Einstein.]]
{{div col|colwidth=30em}}
It was thought at the time that empty space was filled with a background medium called the [[luminiferous aether]] in which the electromagnetic field existed. Some physicists thought that this aether acted as a [[preferred frame]] of reference for the propagation of light and therefore it should be possible to measure the motion of the Earth with respect to this medium, by measuring the isotropy of the speed of light. Beginning in the 1880s several experiments were performed to try to detect this motion, the most famous of which is [[Michelson–Morley experiment|the experiment]] performed by [[Albert Michelson]] and [[Edward Morley]] in 1887.<ref>
* {{tsl|en|Dynamic demand (electric power)|}}
{{Cite journal
* {{tsl|en|Demand response|}}
|last1=Michelson |first1=AA |last2=Morley |first2=EW
* {{tsl|en|List of energy storage projects|}}
|year=1887
* {{tsl|en|Traction power network|}}
|title=[[s:On the Relative Motion of the Earth and the Luminiferous Ether|On the Relative Motion of the Earth and the Luminiferous Ether]]
* {{tsl|en|Backfeeding|}}
|journal=[[American Journal of Science]]
* {{tsl|en|Conductor marking lights|}}
|volume=34 |pages=333–345
* [[高压电线]]
|doi=
* {{tsl|en|Emtp||Electromagnetic Transients Program}} (EMTP)
}}</ref> The detected motion was always less than the observational error. Modern experiments indicate that the two-way speed of light is [[isotropic]] (the same in every direction) to within 6 nanometres per second.<ref>
* {{tsl|en|Flexible AC transmission system|}} (FACTS)
{{Cite book
* {{tsl|en|Geomagnetically induced current|}}, (GIC)
| last = French | first = AP
* {{tsl|en|Grid-tied electrical system|}}
| year = 1983
* {{tsl|en|List of high voltage underground and submarine cables|}}
| title = Special relativity
* {{tsl|en|Load profile|}}
| pages = 51–57 | publisher = Van Nostrand Reinhold
* {{tsl|en|National Grid (disambiguation)|}}
| isbn = 0-442-30782-9
* [[電力線通信]]s (PLC)
}}</ref>
* {{tsl|en|Power system simulation|}}
Because of this experiment [[Hendrik Lorentz]] proposed that the motion of the apparatus through the aether may cause the apparatus to [[Lorentz contraction|contract]] along its length in the direction of motion, and he further assumed, that the time variable for moving systems must also be changed accordingly ("local time"), which led to the formulation of the [[Lorentz transformation]]. Based on [[Lorentz ether theory|Lorentz's aether theory]], [[Henri Poincaré]] (1900) showed that this local time (to first order in v/c) is indicated by clocks moving in the aether, which are synchronized under the assumption of constant light speed. In 1904, he speculated that the speed of light could be a limiting velocity in dynamics, provided that the assumptions of Lorentz's theory are all confirmed. In 1905, Poincaré brought Lorentz's aether theory into full observational agreement with the [[principle of relativity]].<ref>
* {{tsl|en|Radio frequency power transmission|}}
{{Cite book
* {{tsl|en|Wheeling (electric power transmission)|}}
|last=Darrigol |first=O
{{div col end}}
|year=2000
|title= Electrodynamics from Ampére to Einstein
|publisher=Clarendon Press
|isbn=0-19-850594-9}}</ref><ref>{{Cite book
|last=Galison |first=P
|authorlink=Peter Galison
|year=2003
|title= Einstein's Clocks, Poincaré's Maps: Empires of Time
|publisher=W.W. Norton
|isbn=0-393-32604-7}}</ref>


== 參考資料 ==
===Special relativity===
{{reflist}}
In 1905 Einstein postulated from the outset that the speed of light in vacuum, measured by a non-accelerating observer, is independent of the motion of the source or observer. Using this and the principle of relativity as a basis he derived the [[special theory of relativity]], in which the speed of light in vacuum ''c'' featured as a fundamental constant, also appearing in contexts unrelated to light. This made the concept of the stationary aether (to which Lorentz and Poincaré still adhered) useless and revolutionized the concepts of space and time.<ref>{{Cite book
|last=Miller |first=AI
|year=1981
|title= Albert Einstein's special theory of relativity. Emergence (1905) and early interpretation (1905–1911)
|publisher=Addison–Wesley
|isbn=0-201-04679-2}}</ref><ref>
{{Cite book
|last=Pais |first=A
|authorlink=Abraham Pais
|year=1982
|title= Subtle is the Lord: The Science and the Life of Albert Einstein
|publisher=Oxford University Press
|isbn=0-19-520438-7}}</ref>


== 伸延閱讀 ==
===Increased accuracy of ''c'' and redefinition of the metre===
* Grigsby, L. L., et al. ''The Electric Power Engineering Handbook''. USA: CRC Press. (2001). {{ISBN|0-8493-8578-4}}
{{See also|History of the metre}}
* {{tsl|en|Thomas P. Hughes||Hughes, Thomas P.}}, ''Networks of Power: Electrification in Western Society 1880–1930'', The Johns Hopkins University Press, Baltimore 1983 {{ISBN|0-8018-2873-2}}, an excellent overview of development during the first 50 years of commercial electric power
In the second half of the 20th century much progress was made in increasing the accuracy of measurements of the speed of light, first by cavity resonance techniques and later by laser interferometer techniques. In 1972, using the latter method and the [[history of the metre#Krypton standard|1960 definition of the metre]] in terms of a particular spectral line of krypton-86, a group at [[National Institute of Standards and Technology|NBS]] in [[Boulder, Colorado]] determined the speed of light in vacuum to be ''c''&nbsp;=&nbsp;{{val|299792456.2|1.1|u=m/s}}. This was 100 times less [[Measurement uncertainty|uncertain]] than the previously accepted value. The remaining uncertainty was mainly related to the definition of the metre.{{#tag:ref|Since 1960 the metre was defined as: "The metre is the length equal to {{val|1650763.73}} wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p<sub>10</sub> and 5d<sub><sub>5</sub></sub> of the krypton 86 atom."<ref name="11thCGPM">
* {{cite book | author=Reilly, Helen | title= Connecting the Country – New Zealand’s National Grid 1886–2007| location=Wellington| publisher= Steele Roberts| year=2008| pages = 376 pages. | isbn=978-1-877448-40-9}}
{{cite web
* Pansini, Anthony J, E.E., P.E. ''undergrounding electric lines''. USA Hayden Book Co, 1978. {{ISBN|0-8104-0827-9}}
|year=1967
* Westinghouse Electric Corporation, "''Electric power transmission patents; Tesla polyphase system''". (Transmission of power; polyphase system; {{tsl|en|Tesla patents|}})
|title=Resolution 6 of the 15th CGPM
* [http://www.bsharp.org/physics/transmission The Physics of Everyday Stuff - Transmission Lines]
|url=http://www.bipm.org/en/CGPM/db/11/6/
|publisher=[[International Bureau of Weights and Measures|BIPM]]
|accessdate=2010-10-13
}}</ref> It was later discovered that this spectral line was not symmetric, which put a limit on the precision with which the definition could be realized in interferometry experiments.<ref>{{cite journal|journal=Applied Physics Letters|volume=22|issue=4|language=en|issn=0003-6951|date=1973-02-15|pages=196–199|doi=10.1063/1.1654608|url=http://aip.scitation.org/doi/10.1063/1.1654608|title=Wavelength of the 3.39‐μm laser‐saturated absorption line of methane|accessdate=2019-06-25|author=R.L. Barger, J.L. Hall}}
</ref>|group="Note"}}<ref name="NIST heterodyne"/> Since similar experiments found comparable results for ''c'', the 15th&nbsp;[[Conférence Générale des Poids et Mesures]] (CGPM) in 1975 recommended using the value {{val|299792458|u=m/s}} for the speed of light.<ref name="15thCGPM">
{{cite web
|year=1975
|title=Resolution 2 of the 15th CGPM
|url=http://www.bipm.org/en/CGPM/db/15/2/
|publisher=BIPM
|accessdate=2009-09-09
}}</ref>

In 1983 the 17th&nbsp;CGPM redefined the metre thus, "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299&nbsp;792&nbsp;458 of a second."<ref name=Resolution_1>
{{cite web
|year=1983
|title=Resolution 1 of the 17th CGPM
|url=http://www.bipm.org/en/CGPM/db/17/1/
|publisher=BIPM
|accessdate=2009-08-23
}}</ref> As a result of this definition, the value of the speed of light in vacuum is exactly {{val|299792458|u=m/s}}<ref name="Wheeler"/><ref name=timeline>
{{cite web
|last=Penzes |first=WB
|year=2009
|title=Time Line for the Definition of the Meter
|url=http://www.nist.gov/pml/div683/upload/museum-timeline.pdf
|publisher=[[National Institute of Standards and Technology|NIST]]
|accessdate=2010-01-11
}}</ref> and has become a defined constant in the SI system of units.<ref name="Jespersen"/> Improved experimental techniques do not affect the value of the speed of light in SI units, but instead allow for a more precise realization of the definition of the metre.<ref name=Adams>
{{Cite book
|last=Adams |first=S
|year=1997
|title=Relativity: An Introduction to Space-Time Physics
|url=http://books.google.com/?id=1RV0AysEN4oC&pg=PA140
|page=140
|publisher=CRC Press
|isbn=0-7484-0621-2
|quote=One peculiar consequence of this system of definitions is that any future refinement in our ability to measure&nbsp;''c'' will not change the speed of light (which is a defined number), but will change the length of the meter!
}}</ref><ref name=W_Rindler>
{{Cite book
|last=Rindler |first=W
|year=2006
|title=Relativity: Special, General, and Cosmological
|url=http://books.google.com/?id=MuuaG5HXOGEC&pg=PT41
|page=41
|edition=2nd
|publisher=[[Oxford University Press]]
|isbn=0-19-856731-6
|quote=Note that [...] improvements in experimental accuracy will modify the meter relative to atomic wavelengths, but not the value of the speed of light!
}}</ref>

==See also==
*[[Light-second]]

==Notes==
{{reflist|group="Note"|3}}

==References==
{{Reflist|3}}

==Further reading==
===Historical references===
{{Refbegin}}
*{{Cite journal
|first=O |last=Rømer |author-link=Ole Rømer
|year=1676
|title=Démonstration touchant le mouvement de la lumière trouvé par M. Römer de l'Academie Royale des Sciences
|url=http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Roemer-1677/Roemer-1677.html
|journal=[[Journal des sçavans]]
|pages=223–36
|language=French
|archiveurl=http://web.archive.org/web/20070729214326/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Roemer-1677/Roemer-1677.html
|archivedate=2007-07-29
}}
** Translated as {{cite journal
|year=1677
|title=A Demonstration concerning the Motion of Light
|url=http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Roemer-1677/Roemer-1677.html
|journal=[[Philosophical Transactions of the Royal Society]]
|issue=136 |pages=893–4
|archiveurl = http://web.archive.org/web/20070729214326/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Roemer-1677/Roemer-1677.html
|archivedate = 2007-07-29
}}
*{{Cite journal
|first=E |last=Halley |author-link=Edmond Halley
|year=1694
|title=Monsieur Cassini, his New and Exact Tables for the Eclipses of the First Satellite of Jupiter, reduced to the Julian Stile and Meridian of London
|journal=[[Philosophical Transactions of the Royal Society]]
|volume=18 |issue=214 |pages=237–56
|doi=10.1098/rstl.1694.0048
}}
*{{Cite journal
|first=HL |last=Fizeau |author-link=Hippolyte Fizeau
|year=1849
|title=Sur une expérience relative à la vitesse de propagation de la lumière
|url=http://web.archive.org/web/20110613224002/http://www.academie-sciences.fr/membres/in_memoriam/Fizeau/Fizeau_pdf/CR1849_p90.pdf
|journal=[[Comptes rendus de l'Académie des sciences]]
|volume=29 |pages=90–92, 132
|language=French
}}
*{{Cite journal
|first=JL |last=Foucault |author-link=Léon Foucault
|year=1862
|title=Détermination expérimentale de la vitesse de la lumière: parallaxe du Soleil
|url=http://books.google.ca/books?id=yYIIAAAAMAAJ&pg=PA216&lpg=PA216&dq
|journal=[[Comptes rendus de l'Académie des sciences]]
|volume=55 |pages=501–503, 792–796
|language=French
}}
*{{Cite journal
|first=AA |last=Michelson |author-link=Albert Abraham Michelson
|year=1878
|title=Experimental Determination of the Velocity of Light
|url=http://www.gutenberg.org/ebooks/11753
|journal=[[Proceedings of the American Association of Advanced Science]]
|volume=27 |pages=71–77
}}
*{{Cite journal
|first1=AA |last1=Michelson
|first2=FG |last2=Pease |author2-link=Francis Gladheim Pease
|first3=F |last3=Pearson |author3-link=F. Pearson
|title=Measurement of the Velocity of Light in a Partial Vacuum
|journal=[[Astrophysical Journal]]
|volume=82 |pages=26–61 |year=1935
|doi=10.1086/143655 |bibcode=1935ApJ....82...26M
}}
*{{Cite journal
|first=S |last=Newcomb |author-link=Simon Newcomb
|year=1886
|title=The Velocity of Light
|journal=[[Nature (journal)|Nature]]
|volume=34
|issue=863 |pages=29–32
|doi=10.1038/034029c0
|bibcode = 1886Natur..34...29. }}
*{{Cite journal
|first=J |last=Perrotin |author-link=Henri Joseph Anastase Perrotin
|year=1900
|title=Sur la vitesse de la lumière
|journal=[[Comptes rendus de l'Académie des sciences]]
|volume=131 |pages=731–4
|language=French
}}
{{Refend}}

===Modern references===

{{Refbegin}}
*{{Cite book
|first=L |last=Brillouin |author-link=Léon Brillouin
|year=1960
|title=Wave propagation and group velocity
|publisher=[[Academic Press]]
|isbn=
}}
*{{Cite book
|first=JD |last=Jackson |author-link=J. D. Jackson
|year=1975
|title=Classical Electrodynamics
|edition=2nd
|publisher=[[John Wiley & Sons]]
|isbn=0-471-30932-X
}}
*{{Cite book
|first=G |last=Keiser
|year=2000
|title=Optical Fiber Communications
|page=32 |edition=3rd
|publisher=[[McGraw-Hill]]
|isbn=0-07-232101-6
}}
*{{Cite book
|last=Ng |first=YJ
|year=2004
|chapter=Quantum Foam and Quantum Gravity Phenomenology
|url=http://books.google.com/?id=RntpN7OesBsC
|editor=Amelino-Camelia, G; Kowalski-Glikman, J
|title=Planck Scale Effects in Astrophysics and Cosmology
|pages=321''ff''
|publisher=[[Springer (publisher)|Springer]]
|isbn=3-540-25263-0
}}
*{{Cite book
|last=Helmcke |first=J |last2=Riehle |first2=F
|year=2001
|chapter=Physics behind the definition of the meter
|url=http://books.google.com/?id=WE22Fez60EcC&pg=PA453
|editor=Quinn, TJ; Leschiutta, S; Tavella, P
|title=Recent advances in metrology and fundamental constants
|page=453
|publisher=[[IOS Press]]
|isbn=1-58603-167-8
}}
*{{cite arxiv
|last=Duff |first=MJ |author-link=Michael James Duff
|year=2004
|title=Comment on time-variation of fundamental constants
|class=hep-th
|eprint=hep-th/0208093
}}
{{Refend}}


{{Commons category|Electric power transmission}}
==External links==
{{Wiktionary|grid electricity}}
*[http://physics.nist.gov/cgi-bin/cuu/Value?c Speed of light in vacuum] (National Institute of Standards and Technology, NIST)
*[http://www.bipm.org/en/si/si_brochure/chapter2/2-1/metre.html Definition of the metre] (International Bureau of Weights and Measures, BIPM)
*[http://www.itl.nist.gov/div898/bayesian/datagall/michelso.htm Data Gallery: Michelson Speed of Light (Univariate Location Estimation)] (download data gathered by [[Albert Abraham Michelson|A.A. Michelson]])
*[http://gregegan.customer.netspace.net.au/APPLETS/20/20.html Subluminal] (Java applet demonstrating group velocity information limits)
*[http://www.mathpages.com/rr/s3-03/3-03.htm De Mora Luminis] at MathPages
*[http://www.ertin.com/sloan_on_speed_of_light.html Light discussion on adding velocities]
*[http://www.colorado.edu/physics/2000/waves_particles/lightspeed-1.html Speed of Light] (University of Colorado Department of Physics)
*[http://sixtysymbols.com/videos/light.htm c: Speed of Light] (Sixty Symbols, University of Nottingham Department of Physics [video])
*[http://math.ucr.edu/home/baez/physics/ Usenet Physics FAQ]
*[http://njsas.org/projects/speed_of_light/fizeau/ The Fizeau "Rapidly Rotating Toothed Wheel" Method]
<!-- en-GB-oed, -ize -->
{{extreme motion}}


{{Electricity generation}}
{{DEFAULTSORT:Speed Of Light}}
{{Authority control}}
[[Category:Fundamental constants]]
[[Category:Fundamental physics concepts]]
[[Category:Light]]
[[Category:Special relativity]]
[[Category:Units of velocity]]


[[Category:输电]]
[[als:Lichtgeschwindigkeit]]
[[Category:電機工程]]
[[am:የብርሃን ፍጥነት]]
[[Category:壟斷]]
[[ar:سرعة الضوء]]
[[Category:电气安全]]
[[an:Velocidat d'a luz]]
[[as:পোহৰৰ বেগ]]
[[ast:Velocidá de la lluz]]
[[az:İşıq sürəti]]
[[bn:আলোর দ্রুতি]]
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[[be-x-old:Хуткасьць сьвятла]]
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[[cs:Rychlost světla]]
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[[de:Lichtgeschwindigkeit]]
[[et:Valguse kiirus]]
[[el:Ταχύτητα του φωτός]]
[[es:Velocidad de la luz]]
[[eo:Lumrapido]]
[[ext:Velociá de la lus]]
[[eu:Argiaren abiadura]]
[[fa:سرعت نور]]
[[fr:Vitesse de la lumière]]
[[fur:Velocitât de lûs]]
[[ga:Luas an tsolais]]
[[gl:Velocidade da luz]]
[[ko:빛의 속력]]
[[hi:प्रकाश का वेग]]
[[hr:Brzina svjetlosti]]
[[id:Laju cahaya]]
[[ia:Rapiditate de lumine]]
[[is:Ljóshraði]]
[[it:Velocità della luce]]
[[he:מהירות האור]]
[[ka:სინათლის სიჩქარე]]
[[kk:Жарық жылдамдығы]]
[[sw:Kasi ya nuru]]
[[la:Celeritas lucis]]
[[lv:Gaismas ātrums]]
[[lb:Liichtgeschwënnegkeet]]
[[lt:Šviesos greitis]]
[[jbo:nilsutra lo gusni]]
[[hu:Fénysebesség]]
[[mk:Брзина на светлината]]
[[ml:പ്രകാശവേഗം]]
[[arz:سرعة النور]]
[[ms:Kelajuan cahaya]]
[[mn:Гэрлийн хурд]]
[[nl:Lichtsnelheid]]
[[ja:光速]]
[[frr:Faard faan't laacht]]
[[no:Lysets hastighet]]
[[nn:Ljosfarten]]
[[oc:Velocitat de la lutz]]
[[uz:Yorugʻlik tezligi]]
[[pnb:چانن دی دوڑ]]
[[pl:Prędkość światła]]
[[pt:Velocidade da luz]]
[[ro:Viteza luminii]]
[[rue:Швыдкость світла]]
[[ru:Скорость света]]
[[sco:Speed o licht]]
[[stq:Luchtgauegaid]]
[[sq:Shpejtësia e dritës]]
[[simple:Speed of light]]
[[sk:Rýchlosť svetla]]
[[sl:Hitrost svetlobe]]
[[ckb:خێرایی ڕووناکی]]
[[sr:Брзина светлости]]
[[sh:Brzina svjetlosti]]
[[su:Laju cahaya]]
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[[tr:Işık hızı]]
[[uk:Швидкість світла]]
[[vi:Tốc độ ánh sáng]]
[[zh-classical:光速]]
[[war:Kalaksi han lamrag]]
[[zh-yue:光速]]
[[zh:光速]]

2020年8月3日 (一) 06:10的版本

500 kV 三相電 Transmission Lines at 大古力水坝; four circuits are shown; two additional circuits are obscured by trees on the right; the entire 7079 MW generation capacity of the dam is accommodated by these six circuits.

輸電系統是指由發電廠至次級本地負載中心之間的極高壓大電能輸送過程,由負載中心轉換電壓至中高壓再輸送至客戶則為配電系統,兩者相加則為輸電網路,又稱為電網。自電流戰爭起,電力系統由大量獨立小型電力網絡整合為一個大型的電力輸送網絡,而發電能力亦集中至遠離民居的大型發電廠。輸電系統着重於可靠且低損耗地將大量電力作遠距離輸送

A wide area synchronous grid英语wide area synchronous grid, also known as an "interconnection" in North America, directly connects many generators delivering AC power with the same relative frequency to many consumers. For example, there are four major interconnections in North America (the Western Interconnection英语Western Interconnection, the Eastern Interconnection英语Eastern Interconnection, the Quebec Interconnection英语Quebec Interconnection and the Electric Reliability Council of Texas英语Electric Reliability Council of Texas (ERCOT) grid). In Europe one large grid connects most of continental Europe英语Synchronous grid of Continental Europe.

Historically, transmission and distribution lines were owned by the same company, but starting in the 1990s, many countries have liberalized the regulation of the 電力市場 in ways that have led to the separation of the electricity transmission business from the distribution business.[1]

系統

Most transmission lines are high-voltage three-phase 交流電 (AC), although single phase AC is sometimes used in 電氣化鐵路s. High-voltage direct-current (HVDC) technology is used for greater efficiency over very long distances (typically hundreds of miles). HVDC technology is also used in submarine power cable英语submarine power cables (typically longer than 30 miles (50 km)), and in the interchange of power between grids that are not mutually synchronized. HVDC links are used to stabilize large power distribution networks where sudden new loads, or blackouts, in one part of a network can result in synchronization problems and cascading failure英语cascading failures.

Diagram of an electric power system; transmission system is in blue

Electricity is transmitted at 高壓電s (66 kV or above) to reduce the energy loss which occurs in long-distance transmission. Power is usually transmitted through 高压电线s. Underground power transmission英语Undergrounding has a significantly higher installation cost and greater operational limitations, but reduced maintenance costs. Underground transmission is sometimes used in urban areas or environmentally sensitive locations.

A lack of electrical energy storage facilities in transmission systems leads to a key limitation. Electrical energy must be generated at the same rate at which it is consumed. A sophisticated control system is required to ensure that the 發電 very closely matches the demand. If the demand for power exceeds supply, the imbalance can cause generation plant(s) and transmission equipment to automatically disconnect or shut down to prevent damage. In the worst case, this may lead to a cascading series of shut downs and a major regional blackout. Examples include the US Northeast blackouts of 1965, 1977英语New York City blackout of 1977, 2003, and major blackouts in other US regions in 1996英语1996 Western North America blackouts and 2011英语2011 Southwest blackout. Electric transmission networks are interconnected into regional, national, and even continent wide networks to reduce the risk of such a failure by providing multiple redundant, alternative routes for power to flow should such shut downs occur. Transmission companies determine the maximum reliable capacity of each line (ordinarily less than its physical or thermal limit) to ensure that spare capacity is available in the event of a failure in another part of the network.

架空電䌫

3-phase high-voltage lines in Washington State, "Bundled" 3-ways
Four-circuit, two-voltage power transmission line; "Bundled" 2-ways
A typical ACSR. The conductor consists of seven strands of steel surrounded by four layers of aluminium.

High-voltage overhead conductors are not covered by insulation. The conductor material is nearly always an alloy, made into several strands and possibly reinforced with steel strands. Copper was sometimes used for overhead transmission, but aluminum is lighter, yields only marginally reduced performance and costs much less. Overhead conductors are a commodity supplied by several companies worldwide. Improved conductor material and shapes are regularly used to allow increased capacity and modernize transmission circuits. Conductor sizes range from 12 mm2 (#6 美国线规) to 750 mm2 (1,590,000 圓密耳s area), with varying resistance and current-carrying capacity英语current-carrying capacity. For large conductors (more than a few centimetres in diameter) at power frequency, much of the current flow is concentrated near the surface due to the 集膚效應. The center part of the conductor carries little current, but contributes weight and cost to the conductor. Because of this current limitation, multiple parallel cables (called 高压电线s) are used when higher capacity is needed. Bundle conductors are also used at high voltages to reduce energy loss caused by 电晕放电.

Today, transmission-level voltages are usually considered to be 110 kV and above. Lower voltages, such as 66 kV and 33 kV, are usually considered subtransmission voltages, but are occasionally used on long lines with light loads. Voltages less than 33 kV are usually used for distribution. Voltages above 765 kV are considered extra high voltage and require different designs compared to equipment used at lower voltages.

Since overhead transmission wires depend on air for insulation, the design of these lines requires minimum clearances to be observed to maintain safety. Adverse weather conditions, such as high winds and low temperatures, can lead to power outages. Wind speeds as low as 23節(43公里每小時) can permit conductors to encroach operating clearances, resulting in a flashover and loss of supply.[2] Oscillatory motion of the physical line can be termed conductor gallop or flutter英语conductor gallop depending on the frequency and amplitude of oscillation.

Underground transmission

Electric power can also be transmitted by underground power cables英语high-voltage cable instead of overhead power lines. Underground cables take up less right-of-way than overhead lines, have lower visibility, and are less affected by bad weather. However, costs of insulated cable and excavation are much higher than overhead construction. Faults in buried transmission lines take longer to locate and repair.

In some metropolitan areas, underground transmission cables are enclosed by metal pipe and insulated with dielectric fluid (usually an oil) that is either static or circulated via pumps. If an electric fault damages the pipe and produces a dielectric leak into the surrounding soil, liquid nitrogen trucks are mobilized to freeze portions of the pipe to enable the draining and repair of the damaged pipe location. This type of underground transmission cable can prolong the repair period and increase repair costs. The temperature of the pipe and soil are usually monitored constantly throughout the repair period.[3][4][5]

Underground lines are strictly limited by their thermal capacity, which permits less overload or re-rating than overhead lines. Long underground AC cables have significant 電容, which may reduce their ability to provide useful power to loads beyond 50英里(80公里). DC cables are not limited in length by their capacitance, however, they do require HVDC converter station英语HVDC converter stations at both ends of the line to convert from DC to AC before being interconnected with the transmission network.

History

New York City streets in 1890. Besides telegraph lines, multiple electric lines were required for each class of device requiring different voltages

In the early days of commercial electric power, transmission of electric power at the same voltage as used by lighting and mechanical loads restricted the distance between generating plant and consumers. In 1882, generation was with 直流電 (DC), which could not easily be increased in voltage for long-distance transmission. Different classes of loads (for example, lighting, fixed motors, and traction/railway systems) required different voltages, and so used different generators and circuits.[6][7]

Due to this specialization of lines and because transmission was inefficient for low-voltage high-current circuits, generators needed to be near their loads. It seemed, at the time, that the industry would develop into what is now known as a 分散式發電 system with large numbers of small generators located near their loads.[8]

The transmission of electric power with 交流電 (AC) became possible after Lucien Gaulard英语Lucien Gaulard and John Dixon Gibbs英语John Dixon Gibbs built what they called the secondary generator, an early transformer provided with 1:1 turn ratio and open magnetic circuit, in 1881.

The first long distance AC line was 34公里(21英里) long, built for the 1884 International Exhibition of 都灵. It was powered by a 2 kV, 130 Hz Siemens & Halske英语Siemens & Halske alternator and featured several Gaulard secondary generators with their primary windings connected in series, which fed incandescent lamps. The system proved the feasibility of AC electric power transmission on long distances.[7]

The very first AC system to operate was in service in 1885 in via dei Cerchi, 罗马, for public lighting. It was powered by two Siemens & Halske alternators rated 30 hp (22 kW), 2 kV at 120 Hz and used 19 km of cables and 200 parallel-connected 2 kV to 20 V step-down transformers provided with a closed magnetic circuit, one for each lamp. A few months later it was followed by the first British AC system, which was put into service at the Grosvenor Gallery英语Grosvenor Gallery, London. It also featured Siemens alternators and 2.4 kV to 100 V step-down transformers – one per user – with shunt-connected primaries.[9]

Working for Westinghouse, William Stanley Jr. spent his time recovering from illness in Great Barrington installing what is considered the world's first practical AC transformer system.

Working from what he considered an impractical Gaulard-Gibbs design, electrical engineer 威廉·史坦雷 (物理學家) developed what is considered the first practical series AC transformer in 1885.[10] Working with the support of 乔治·威斯汀豪斯, in 1886 he demonstrated a transformer based alternating current lighting system in Great Barrington, Massachusetts英语Great Barrington, Massachusetts. Powered by a steam engine driven 500 V Siemens generator, voltage was stepped down to 100 Volts using the new Stanley transformer to power incandescent lamps at 23 businesses along main street with very little power loss over 4,000英尺(1,200米).[11] This practical demonstration of a transformer and alternating current lighting system would lead Westinghouse to begin installing AC based systems later that year.[10]

1888 saw designs for a functional 交流电动机, something these systems had lacked up till then. These were 异步电动机s running on polyphase current, independently invented by 加利莱奥·费拉里斯 and 尼古拉·特斯拉 (with Tesla's design being licensed by Westinghouse in the US). This design was further developed into the modern practical three-phase form by Mikhail Dolivo-Dobrovolsky英语Mikhail Dolivo-Dobrovolsky and Charles Eugene Lancelot Brown英语Charles Eugene Lancelot Brown.[12] Practical use of these types of motors would be delayed many years by development problems and the scarcity of poly-phase power systems needed to power them.[13][14]

The late 1880s and early 1890s would see the financial merger of smaller electric companies into a few larger corporations such as Ganz and AEG in Europe and 通用电气 and Westinghouse Electric in the US. These companies continued to develop AC systems but the technical difference between direct and alternating current systems would follow a much longer technical merger.[15] Due to innovation in the US and Europe, alternating current's economy of scale with very large generating plants linked to loads via long-distance transmission was slowly being combined with the ability to link it up with all of the existing systems that needed to be supplied. These included single phase AC systems, poly-phase AC systems, low voltage incandescent lighting, high voltage arc lighting, and existing DC motors in factories and street cars. In what was becoming a universal system, these technological differences were temporarily being bridged via the development of 回轉變流機s and 電動發電機s that would allow the large number of legacy systems to be connected to the AC grid.[15][16] These stopgaps would slowly be replaced as older systems were retired or upgraded.

Westinghouse alternating current polyphase generators on display at the 1893 World's Fair in Chicago, part of their "Tesla Poly-phase System". Such polyphase innovations revolutionized transmission

The first transmission of single-phase alternating current using high voltage took place in Oregon in 1890 when power was delivered from a hydroelectric plant at Willamette Falls to the city of Portland 14英里(23公里) downriver.[17] The first three-phase alternating current using high voltage took place in 1891 during the international electricity exhibition英语International Electro-Technical Exhibition – 1891 in 美因河畔法兰克福. A 15 kV transmission line, approximately 175 km long, connected Lauffen on the Neckar and Frankfurt.[9][18]

Voltages used for electric power transmission increased throughout the 20th century. By 1914, fifty-five transmission systems each operating at more than 70 kV were in service. The highest voltage then used was 150 kV.[19] By allowing multiple generating plants to be interconnected over a wide area, electricity production cost was reduced. The most efficient available plants could be used to supply the varying loads during the day. Reliability was improved and capital investment cost was reduced, since stand-by generating capacity could be shared over many more customers and a wider geographic area. Remote and low-cost sources of energy, such as hydroelectric power or mine-mouth coal, could be exploited to lower energy production cost.[6][9]

The rapid industrialization in the 20th century made electrical transmission lines and grids 維生管線 items in most industrialized nations. The interconnection of local generation plants and small distribution networks was spurred by the requirements of 第一次世界大战, with large electrical generating plants built by governments to provide power to munitions factories. Later these generating plants were connected to supply civil loads through long-distance transmission.[20]

Bulk power transmission

A transmission substation decreases the voltage of incoming electricity, allowing it to connect from long-distance high voltage transmission, to local lower voltage distribution. It also reroutes power to other transmission lines that serve local markets. This is the PacifiCorp Hale Substation, 奥勒姆 (犹他州), USA

Engineers design transmission networks to transport the energy as efficiently as possible, while at the same time taking into account the economic factors, network safety and redundancy. These networks use components such as power lines, cables, 斷路器s, switches and 变压器s. The transmission network is usually administered on a regional basis by an entity such as a regional transmission organization英语regional transmission organization or transmission system operator英语transmission system operator.

Transmission efficiency is greatly improved by devices that increase the voltage (and thereby proportionately reduce the current), in the line conductors, thus allowing power to be transmitted with acceptable losses. The reduced current flowing through the line reduces the heating losses in the conductors. According to Joule's Law, energy losses are directly proportional to the square of the current. Thus, reducing the current by a factor of two will lower the energy lost to conductor resistance by a factor of four for any given size of conductor.

The optimum size of a conductor for a given voltage and current can be estimated by Kelvin's law for conductor size, which states that the size is at its optimum when the annual cost of energy wasted in the resistance is equal to the annual capital charges of providing the conductor. At times of lower interest rates, Kelvin's law indicates that thicker wires are optimal; while, when metals are expensive, thinner conductors are indicated: however, power lines are designed for long-term use, so Kelvin's law has to be used in conjunction with long-term estimates of the price of copper and aluminum as well as interest rates for capital.

The increase in voltage is achieved in AC circuits by using a step-up 变压器. HVDC systems require relatively costly conversion equipment which may be economically justified for particular projects such as submarine cables and longer distance high capacity point-to-point transmission. HVDC is necessary for the import and export of energy between grid systems that are not synchronized with each other.

A transmission grid is a network of 發電廠s, transmission lines, and substations. Energy is usually transmitted within a grid with three-phase AC. Single-phase AC is used only for distribution to end users since it is not usable for large polyphase 异步电动机s. In the 19th century, two-phase transmission was used but required either four wires or three wires with unequal currents. Higher order phase systems require more than three wires, but deliver little or no benefit.

The synchronous grids英语wide area synchronous grid of the 欧洲联盟

The price of electric power station capacity is high, and electric demand is variable, so it is often cheaper to import some portion of the needed power than to generate it locally. Because loads are often regionally correlated (hot weather in the Southwest portion of the US might cause many people to use air conditioners), electric power often comes from distant sources. Because of the economic benefits of load sharing between regions, wide area transmission grids英语wide area synchronous grid now span countries and even continents. The web of interconnections between power producers and consumers should enable power to flow, even if some links are inoperative.

The unvarying (or slowly varying over many hours) portion of the electric demand is known as the base load and is generally served by large facilities (which are more efficient due to economies of scale) with fixed costs for fuel and operation. Such facilities are nuclear, coal-fired or hydroelectric, while other energy sources such as concentrated solar thermal and 地熱能發電 have the potential to provide base load power. Renewable energy sources, such as solar photovoltaics, wind, wave, and tidal, are, due to their intermittency, not considered as supplying "base load" but will still add power to the grid. The remaining or 'peak' power demand, is supplied by 尖峰負載發電廠s, which are typically smaller, faster-responding, and higher cost sources, such as combined cycle or combustion turbine plants fueled by natural gas.

Long-distance transmission of electricity (hundreds of kilometers) is cheap and efficient, with costs of US$0.005–0.02 per kWh (compared to annual averaged large producer costs of US$0.01–0.025 per kWh, retail rates upwards of US$0.10 per kWh, and multiples of retail for instantaneous suppliers at unpredicted highest demand moments).[21] Thus distant suppliers can be cheaper than local sources (e.g., New York often buys over 1000 MW of electricity from Canada).[22] Multiple local sources (even if more expensive and infrequently used) can make the transmission grid more fault tolerant to weather and other disasters that can disconnect distant suppliers.

A high-power electrical transmission tower, 230 kV, double-circuit, also double-bundled

Long-distance transmission allows remote renewable energy resources to be used to displace fossil fuel consumption. Hydro and wind sources cannot be moved closer to populous cities, and solar costs are lowest in remote areas where local power needs are minimal. Connection costs alone can determine whether any particular renewable alternative is economically sensible. Costs can be prohibitive for transmission lines, but various proposals for massive infrastructure investment in high capacity, very long distance 超級電網 transmission networks could be recovered with modest usage fees.

Grid input

At the 發電廠s, the power is produced at a relatively low voltage between about 2.3 kV and 30 kV, depending on the size of the unit. The generator terminal voltage is then stepped up by the power station 变压器 to a higher 電壓 (115 kV to 765 kV AC, varying by the transmission system and by the country) for transmission over long distances.

In the United States, power transmission is, variously, 230 kV to 500 kV, with less than 230 kV or more than 500 kV being local exceptions.

For example, the Western System has two primary interchange voltages: 500 kV AC at 60 Hz, and ±500 kV (1,000 kV net) DC from North to South (哥倫比亞河 to 南加利福尼亞州) and Northeast to Southwest (Utah to Southern California). The 287.5 kV (Hoover to 洛杉矶 line, via 维克多维尔 (加利福尼亚州)) and 345 kV (APS英语Arizona Public Service line) being local standards, both of which were implemented before 500 kV became practical, and thereafter the Western System standard for long distance AC power transmission.

Losses

Transmitting electricity at high voltage reduces the fraction of energy lost to resistance, which varies depending on the specific conductors, the current flowing, and the length of the transmission line. For example, a 100 mi(160 km) span at 765 kV carrying 1000 MW of power can have losses of 1.1% to 0.5%. A 345 kV line carrying the same load across the same distance has losses of 4.2%.[23] For a given amount of power, a higher voltage reduces the current and thus the 焦耳加热es in the conductor. For example, raising the voltage by a factor of 10 reduces the current by a corresponding factor of 10 and therefore the losses by a factor of 100, provided the same sized conductors are used in both cases. Even if the conductor size (cross-sectional area) is decreased ten-fold to match the lower current, the losses are still reduced ten-fold. Long-distance transmission is typically done with overhead lines at voltages of 115 to 1,200 kV. At extremely high voltages, more than 2,000 kV exists between conductor and ground, 电晕放电 losses are so large that they can offset the lower resistive losses in the line conductors. Measures to reduce corona losses include conductors having larger diameters; often hollow to save weight,[24] or bundles of two or more conductors.

Factors that affect the resistance, and thus loss, of conductors used in transmission and distribution lines include temperature, spiraling, and the 集膚效應. The resistance of a conductor increases with its temperature. Temperature changes in electric power lines can have a significant effect on power losses in the line. Spiraling, which refers to the way stranded conductors spiral about the center, also contributes to increases in conductor resistance. The skin effect causes the effective resistance of a conductor to increase at higher alternating current frequencies. Corona and resistive losses can be estimated using a mathematical model.[25]

Transmission and distribution losses in the USA were estimated at 6.6% in 1997,[26] 6.5% in 2007[26] and 5% from 2013 to 2019.[27] In general, losses are estimated from the discrepancy between power produced (as reported by power plants) and power sold to the end customers; the difference between what is produced and what is consumed constitute transmission and distribution losses, assuming no utility theft occurs.

As of 1980, the longest cost-effective distance for direct-current transmission was determined to be 7,000公里(4,300英里). For 交流電 it was 4,000公里(2,500英里), though all transmission lines in use today are substantially shorter than this.[21]

In any alternating current transmission line, the 电感 and capacitance of the conductors can be significant. Currents that flow solely in ‘reaction’ to these properties of the circuit, (which together with the resistance define the impedance) constitute 交流电功率 flow, which transmits no ‘real’ power to the load. These reactive currents, however, are very real and cause extra heating losses in the transmission circuit. The ratio of 'real' power (transmitted to the load) to 'apparent' power (the product of a circuit's voltage and current, without reference to phase angle) is the 功率因数. As reactive current increases, the reactive power increases and the power factor decreases. For transmission systems with low power factor, losses are higher than for systems with high power factor. Utilities add capacitor banks, reactors and other components (such as phase-shifting transformer英语phase-shifting transformers; static VAR compensator英语static VAR compensators; and flexible AC transmission system英语flexible AC transmission systems, FACTS) throughout the system help to compensate for the reactive power flow, reduce the losses in power transmission and stabilize system voltages. These measures are collectively called 'reactive support'.

Transposition

Current flowing through transmission lines induces a magnetic field that surrounds the lines of each phase and affects the 电感 of the surrounding conductors of other phases. The mutual inductance of the conductors is partially dependent on the physical orientation of the lines with respect to each other. Three-phase power transmission lines are conventionally strung with phases separated on different vertical levels. The mutual inductance seen by a conductor of the phase in the middle of the other two phases will be different than the inductance seen by the conductors on the top or bottom. An imbalanced inductance among the three conductors is problematic because it may result in the middle line carrying a disproportionate amount of the total power transmitted. Similarly, an imbalanced load may occur if one line is consistently closest to the ground and operating at a lower impedance. Because of this phenomenon, conductors must be periodically transposed along the length of the transmission line so that each phase sees equal time in each relative position to balance out the mutual inductance seen by all three phases. To accomplish this, line position is swapped at specially designed transposition tower英语transposition towers at regular intervals along the length of the transmission line in various transposition schemes英语Transposition (telecommunications).

Subtransmission

A 115 kV subtransmission line in the 菲律宾, along with 20 kV distribution lines and a 街燈, all mounted in a wood subtransmission pole
115 kV H-frame transmission tower

Subtransmission is part of an electric power transmission system that runs at relatively lower voltages. It is uneconomical to connect all distribution substations to the high main transmission voltage, because the equipment is larger and more expensive. Typically, only larger substations connect with this high voltage. It is stepped down and sent to smaller substations in towns and neighborhoods. Subtransmission circuits are usually arranged in loops so that a single line failure does not cut off service to many customers for more than a short time. Loops can be "normally closed", where loss of one circuit should result in no interruption, or "normally open" where substations can switch to a backup supply. While subtransmission circuits are usually carried on overhead lines, in urban areas buried cable may be used. The lower-voltage subtransmission lines use less right-of-way and simpler structures; it is much more feasible to put them underground where needed. Higher-voltage lines require more space and are usually above-ground since putting them underground is very expensive.

There is no fixed cutoff between subtransmission and transmission, or subtransmission and distribution. The voltage ranges overlap somewhat. Voltages of 69 kV, 115 kV, and 138 kV are often used for subtransmission in North America. As power systems evolved, voltages formerly used for transmission were used for subtransmission, and subtransmission voltages became distribution voltages. Like transmission, subtransmission moves relatively large amounts of power, and like distribution, subtransmission covers an area instead of just point-to-point.[28]

Transmission grid exit

At the substations, transformers reduce the voltage to a lower level for distribution to commercial and residential users. This distribution is accomplished with a combination of sub-transmission (33 to 132 kV) and distribution (3.3 to 25 kV). Finally, at the point of use, the energy is transformed to low voltage (varying by country and customer requirements – see 家用電源列表).

Advantage of high-voltage power transmission

High-voltage power transmission allows for lesser resistive losses over long distances in the wiring. This efficiency of high voltage transmission allows for the transmission of a larger proportion of the generated power to the substations and in turn to the loads, translating to operational cost savings.

Electrical grid without a transformer.
Electrical grid with a transformer.

In a very simplified model, assume the 輸電網路 delivers electricity from a generator (modelled as an 电压源 with voltage , delivering a power ) to a single point of consumption, modelled by a pure resistance , when the wires are long enough to have a significant resistance .

If the resistance are simply in series英语in series without any transformer between them, the circuit acts as a 電壓分配定則, because the same current runs through the wire resistance and the powered device. As a consequence, the useful power (used at the point of consumption) is:

Assume now that a transformer converts high-voltage, low-current electricity transported by the wires into low-voltage, high-current electricity for use at the consumption point. If we suppose it is an 变压器 with a voltage ratio of (i.e., the voltage is divided by and the current is multiplied by in the secondary branch, compared to the primary branch), then the circuit is again equivalent to a voltage divider, but the transmission wires now have apparent resistance of only . The useful power is then:

For (i.e. conversion of high voltage to low voltage near the consumption point), a larger fraction of the generator's power is transmitted to the consumption point and a lesser fraction is lost to 焦耳加热.

Modeling and the transmission matrix

"Black box" model for transmission line

Oftentimes, we are only interested in the terminal characteristics of the transmission line, which are the voltage and current at the sending and receiving ends. The transmission line itself is then modeled as a "black box" and a 2 by 2 transmission matrix is used to model its behavior, as follows:

The line is assumed to be a reciprocal, symmetrical network, meaning that the receiving and sending labels can be switched with no consequence. The transmission matrix T also has the following properties:

The parameters A, B, C, and D differ depending on how the desired model handles the line's resistance (R), 电感 (L), 電容 (C), and shunt (parallel, leak) conductance G. The four main models are the short line approximation, the medium line approximation, the long line approximation (with distributed parameters), and the lossless line. In all models described, a capital letter such as R refers to the total quantity summed over the line and a lowercase letter such as c refers to the per-unit-length quantity.

Lossless line

The lossless line approximation is the least accurate model; it is often used on short lines when the inductance of the line is much greater than its resistance. For this approximation, the voltage and current are identical at the sending and receiving ends.

Voltage on sending and receiving ends for lossless line

The characteristic impedance is pure real, which means resistive for that impedance, and it is often called surge impedance for a lossless line. When lossless line is terminated by surge impedance, there is no voltage drop. Though the phase angles of voltage and current are rotated, the magnitudes of voltage and current remain constant along the length of the line. For load > SIL, the voltage will drop from sending end and the line will “consume” VARs. For load < SIL, the voltage will increase from sending end, and the line will “generate” VARs.

Short line

The short line approximation is normally used for lines less than 80 km (50 mi) long. For a short line, only a series impedance Z is considered, while C and G are ignored. The final result is that A = D = 1 per unit, B = Z Ohms, and C = 0. The associated transition matrix for this approximation is therefore:

Medium line

The medium line approximation is used for lines between 80-250 km (50-150 mi) long. In this model, the series impedance and the shunt (current leak) conductance are considered, with half of the shunt conductance being placed at each end of the line. This circuit is often referred to as a “nominal π (pi)” circuit because of the shape (π) that is taken on when leak conductance is placed on both sides of the circuit diagram. The analysis of the medium line brings one to the following result:

Counterintuitive behaviors of medium-length transmission lines:

Long line

The long line model is used when a higher degree of accuracy is needed or when the line under consideration is more than 250 km (150 mi) long. Series resistance and shunt conductance are considered as distributed parameters, meaning each differential length of the line has a corresponding differential resistance and shunt admittance. The following result can be applied at any point along the transmission line, where is the propagation constant英语propagation constant.

To find the voltage and current at the end of the long line, should be replaced with (the line length) in all parameters of the transmission matrix.

(For the full development of this model, see the 电报员方程.)

High-voltage direct current

High-voltage direct current (HVDC) is used to transmit large amounts of power over long distances or for interconnections between asynchronous grids. When electrical energy is to be transmitted over very long distances, the power lost in AC transmission becomes appreciable and it is less expensive to use 直流電 instead of 交流電. For a very long transmission line, these lower losses (and reduced construction cost of a DC line) can offset the additional cost of the required converter stations at each end.

HVDC is also used for long submarine cables英语Submarine power cable where AC cannot be used because of the cable capacitance.[29] In these cases special high-voltage cable英语high-voltage cables for DC are used. Submarine HVDC systems are often used to connect the electricity grids of islands, for example, between 大不列顛島 and 歐洲大陸, between Great Britain and 爱尔兰岛, between 塔斯馬尼亞州 and the 澳大利亚n mainland, between the North and South Islands of 新西兰, between 新泽西州 and 纽约, and between New Jersey and 長島. Submarine connections up to 600公里(370英里) in length are presently in use.[30]

HVDC links can be used to control problems in the grid with AC electricity flow. The power transmitted by an AC line increases as the phase angle between source end voltage and destination ends increases, but too large a phase angle will allow the systems at either end of the line to fall out of step. Since the power flow in a DC link is controlled independently of the phases of the AC networks at either end of the link, this phase angle limit does not exist, and a DC link is always able to transfer its full rated power. A DC link therefore stabilizes the AC grid at either end, since power flow and phase angle can then be controlled independently.

As an example, to adjust the flow of AC power on a hypothetical line between 西雅圖 and 波士顿 would require adjustment of the relative phase of the two regional electrical grids. This is an everyday occurrence in AC systems, but one that can become disrupted when AC system components fail and place unexpected loads on the remaining working grid system. With an HVDC line instead, such an interconnection would:

  1. Convert AC in Seattle into HVDC;
  2. Use HVDC for the 3,000英里(4,800公里) of cross-country transmission; and
  3. Convert the HVDC to locally synchronized AC in Boston,

(and possibly in other cooperating cities along the transmission route). Such a system could be less prone to failure if parts of it were suddenly shut down. One example of a long DC transmission line is the Pacific DC Intertie英语Pacific DC Intertie located in the Western 美国.

Capacity

The amount of power that can be sent over a transmission line is limited. The origins of the limits vary depending on the length of the line. For a short line, the heating of conductors due to line losses sets a thermal limit. If too much current is drawn, conductors may sag too close to the ground, or conductors and equipment may be damaged by overheating. For intermediate-length lines on the order of 100公里(62英里), the limit is set by the voltage drop英语voltage drop in the line. For longer AC lines, system stability sets the limit to the power that can be transferred. Approximately, the power flowing over an AC line is proportional to the cosine of the phase angle of the voltage and current at the receiving and transmitting ends. This angle varies depending on system loading and generation. It is undesirable for the angle to approach 90 degrees, as the power flowing decreases but the resistive losses remain. Very approximately, the allowable product of line length and maximum load is proportional to the square of the system voltage. Series capacitors or phase-shifting transformers are used on long lines to improve stability. High-voltage direct current lines are restricted only by thermal and voltage drop limits, since the phase angle is not material to their operation.

Up to now, it has been almost impossible to foresee the temperature distribution along the cable route, so that the maximum applicable current load was usually set as a compromise between understanding of operation conditions and risk minimization. The availability of industrial distributed temperature sensing英语distributed temperature sensing (DTS) systems that measure in real time temperatures all along the cable is a first step in monitoring the transmission system capacity. This monitoring solution is based on using passive optical fibers as temperature sensors, either integrated directly inside a high voltage cable or mounted externally on the cable insulation. A solution for overhead lines is also available. In this case the optical fiber is integrated into the core of a phase wire of overhead transmission lines (OPPC). The integrated Dynamic Cable Rating (DCR) or also called Real Time Thermal Rating (RTTR) solution enables not only to continuously monitor the temperature of a high voltage cable circuit in real time, but to safely utilize the existing network capacity to its maximum. Furthermore, it provides the ability to the operator to predict the behavior of the transmission system upon major changes made to its initial operating conditions.

Control

To ensure safe and predictable operation, the components of the transmission system are controlled with generators, switches, circuit breakers and loads. The voltage, power, frequency, load factor, and reliability capabilities of the transmission system are designed to provide cost effective performance for the customers.

Load balancing

The transmission system provides for base load and peak load capability, with safety and fault tolerance margins. The peak load times vary by region largely due to the industry mix. In very hot and very cold climates home air conditioning and heating loads have an effect on the overall load. They are typically highest in the late afternoon in the hottest part of the year and in mid-mornings and mid-evenings in the coldest part of the year. This makes the power requirements vary by the season and the time of day. Distribution system designs always take the base load and the peak load into consideration.

The transmission system usually does not have a large buffering capability to match the loads with the generation. Thus generation has to be kept matched to the load, to prevent overloading failures of the generation equipment.

Multiple sources and loads can be connected to the transmission system and they must be controlled to provide orderly transfer of power. In centralized power generation, only local control of generation is necessary, and it involves synchronization of the generation units英语alternator synchronization, to prevent large transients and overload conditions.

In distributed power generation the generators are geographically distributed and the process to bring them online and offline must be carefully controlled. The load control signals can either be sent on separate lines or on the power lines themselves. Voltage and frequency can be used as signalling mechanisms to balance the loads.

In voltage signaling, the variation of voltage is used to increase generation. The power added by any system increases as the line voltage decreases. This arrangement is stable in principle. Voltage-based regulation is complex to use in mesh networks, since the individual components and setpoints would need to be reconfigured every time a new generator is added to the mesh.

In frequency signaling, the generating units match the frequency of the power transmission system. In 下垂速度控制, if the frequency decreases, the power is increased. (The drop in line frequency is an indication that the increased load is causing the generators to slow down.)

風力發動機s, V2G and other locally distributed storage and generation systems can be connected to the power grid, and interact with it to improve system operation. Internationally, the trend has been a slow move from a heavily centralized power system to a decentralized power system. The main draw of locally distributed generation systems which involve a number of new and innovative solutions is that they reduce transmission losses by leading to consumption of electricity closer to where it was produced.[31]

Failure protection

Under excess load conditions, the system can be designed to fail gracefully rather than all at once. Brownouts英语Brownout (electricity) occur when the supply power drops below the demand. Blackouts occur when the supply fails completely.

Rolling blackout英语Rolling blackouts (also called load shedding) are intentionally engineered electrical power outages, used to distribute insufficient power when the demand for electricity exceeds the supply.

Communications

Operators of long transmission lines require reliable communications for control of the power grid and, often, associated generation and distribution facilities. Fault-sensing 保护继电器s at each end of the line must communicate to monitor the flow of power into and out of the protected line section so that faulted conductors or equipment can be quickly de-energized and the balance of the system restored. Protection of the transmission line from 短路s and other faults is usually so critical that common carrier英语common carrier telecommunications are insufficiently reliable, and in remote areas a common carrier may not be available. Communication systems associated with a transmission project may use:

Rarely, and for short distances, a utility will use pilot-wires strung along the transmission line path. Leased circuits from common carriers are not preferred since availability is not under control of the electric power transmission organization.

Transmission lines can also be used to carry data: this is called power-line carrier, or PLC. PLC signals can be easily received with a radio for the long wave range.

High Voltage Pylons carrying additional optical fibre cable in Kenya

Optical fibers can be included in the stranded conductors of a transmission line, in the overhead shield wires. These cables are known as 複合光纜地線 (OPGW). Sometimes a standalone cable is used, all-dielectric self-supporting (ADSS) cable, attached to the transmission line cross arms.

Some jurisdictions, such as 明尼蘇達州, prohibit energy transmission companies from selling surplus communication bandwidth or acting as a telecommunications common carrier英语common carrier. Where the regulatory structure permits, the utility can sell capacity in extra dark fiber英语dark fibers to a common carrier, providing another revenue stream.

Electricity market reform

Some regulators regard electric transmission to be a 自然垄断[32][33] and there are moves in many countries to separately regulate transmission (see 電力市場).

西班牙 was the first country to establish a regional transmission organization英语regional transmission organization. In that country, transmission operations and market operations are controlled by separate companies. The transmission system operator is 西班牙電網公司 (REE) and the wholesale electricity market operator is Operador del Mercado Ibérico de Energía – Polo Español, S.A. (OMEL) OMEL Holding | Omel Holding. Spain's transmission system is interconnected with those of France, Portugal, and Morocco.

The establishment of RTOs in the United States was spurred by the FERC英语FERC's Order 888, Promoting Wholesale Competition Through Open Access Non-discriminatory Transmission Services by Public Utilities; Recovery of Stranded Costs by Public Utilities and Transmitting Utilities, issued in 1996.[34] In the United States and parts of Canada, several electric transmission companies operate independently of generation companies, but there are still regions - the Southern United States - where vertical integration of the electric system is intact. In regions of separation, transmission owners and generation owners continue to interact with each other as market participants with voting rights within their RTO. RTOs in the United States are regulated by the Federal Energy Regulatory Commission英语Federal Energy Regulatory Commission.

Cost of electric power transmission

The cost of high voltage electricity transmission (as opposed to the costs of 配電系統) is comparatively low, compared to all other costs arising in a consumer's electricity bill. In the UK, transmission costs are about 0.2 p per kWh compared to a delivered domestic price of around 10 p per kWh.[35]

Research evaluates the level of capital expenditure in the electric power T&D equipment market will be worth $128.9 bn in 2011.[36]

Merchant transmission

Merchant transmission is an arrangement where a third party constructs and operates electric transmission lines through the franchise area of an unrelated incumbent utility.

Operating merchant transmission projects in the 美国 include the Cross Sound Cable英语Cross Sound Cable from Shoreham, New York英语Shoreham, New York to 纽黑文, Neptune RTS Transmission Line from Sayreville, New Jersey英语Sayreville, New Jersey to New Bridge, New York, and Path 15英语Path 15 in California. Additional projects are in development or have been proposed throughout the United States, including the Lake Erie Connector, an underwater transmission line proposed by ITC Holdings Corp., connecting Ontario to load serving entities in the PJM Interconnection region.[37]

There is only one unregulated or market interconnector in 澳大利亚: Basslink英语Basslink between 塔斯馬尼亞州 and Victoria. Two DC links originally implemented as market interconnectors, Directlink英语Directlink and Murraylink英语Murraylink, have been converted to regulated interconnectors. NEMMCO

A major barrier to wider adoption of merchant transmission is the difficulty in identifying who benefits from the facility so that the beneficiaries will pay the toll. Also, it is difficult for a merchant transmission line to compete when the alternative transmission lines are subsidized by incumbent utility businesses with a monopolized and regulated rate base.[38] In the United States, the FERC英语FERC's Order 1000, issued in 2010, attempts to reduce barriers to third party investment and creation of merchant transmission lines where a public policy need is found.[39]

Health concerns

Some large studies, including a large study in the United States, have failed to find any link between living near power lines and developing any sickness or diseases, such as cancer. A 1997 study found that it did not matter how close one was to a power line or a sub-station, there was no increased risk of cancer or illness.[40]

The mainstream scientific evidence suggests that low-power, low-frequency, electromagnetic radiation associated with household currents and high transmission power lines does not constitute a short or long-term health hazard. Some studies, however, have found 相关s between various diseases and living or working near power lines. No adverse health effects have been substantiated for people not living close to powerlines.[41]

The New York State Public Service Commission英语New York State Public Service Commission conducted a study, documented in Opinion No. 78-13 (issued June 19, 1978), to evaluate potential health effects of electric fields. The study's case number is too old to be listed as a case number in the commission's online database, DMM, and so the original study can be difficult to find. The study chose to utilize the electric field strength that was measured at the edge of an existing (but newly built) right-of-way on a 765 kV transmission line from New York to Canada, 1.6 kV/m, as the interim standard maximum electric field at the edge of any new transmission line right-of-way built in New York State after issuance of the order. The opinion also limited the voltage of all new transmission lines built in New York to 345 kV. On September 11, 1990, after a similar study of magnetic field strengths, the NYSPSC issued their Interim Policy Statement on Magnetic Fields. This study established a magnetic field interim standard of 200 mG at the edge of the right-of-way using the winter-normal conductor rating. This later document can also be difficult to find on the NYSPSC's online database, since it predates the online database system. As a comparison with everyday items, a hair dryer or electric blanket produces a 100 mG - 500 mG magnetic field. An electric razor can produce 2.6 kV/m. Whereas electric fields can be shielded, magnetic fields cannot be shielded, but are usually minimized by optimizing the location of each phase of a circuit in cross-section.[42][43]

When a new transmission line is proposed, within the application to the applicable regulatory body (usually a public utility commission), there is often an analysis of electric and magnetic field levels at the edge of rights-of-way. These analyses are performed by a utility or by an electrical engineering consultant using modelling software. At least one state public utility commission has access to software developed by an engineer or engineers at the Bonneville Power Administration英语Bonneville Power Administration to analyze electric and magnetic fields at edge of rights-of-way for proposed transmission lines. Often, public utility commissions will not comment on any health impacts due to electric and magnetic fields and will refer information seekers to the state's affiliated department of health.

There are established biological effects for acute英语Acute toxicity high level exposure to magnetic fields well above 100 µT (1 G) (1,000 mG). In a residential setting, there is "limited evidence of 致癌物質icity in humans and less than sufficient evidence for carcinogenicity in experimental animals", in particular, childhood leukemia, associated with average exposure to residential power-frequency magnetic field above 0.3 µT (3 mG) to 0.4 µT (4 mG). These levels exceed average residential power-frequency magnetic fields in homes, which are about 0.07 µT (0.7 mG) in Europe and 0.11 µT (1.1 mG) in North America.[44][45]

The Earth's natural geomagnetic field strength varies over the surface of the planet between 0.035 mT and 0.07 mT (35 µT - 70 µT or 350 mG - 700 mG) while the International Standard for the continuous exposure limit is set at 40 mT (400,000 mG or 400 G) for the general public.[44]

Tree Growth Regulator and Herbicide Control Methods may be used in transmission line right of ways[46] which may have health effects.

Policy by country

United States

The Federal Energy Regulatory Commission英语Federal Energy Regulatory Commission (FERC) is the primary regulatory agency of electric power transmission and wholesale electricity sales within the United States. It was originally established by Congress in 1920 as the Federal Power Commission and has since undergone multiple name and responsibility modifications. That which is not regulated by FERC, primarily electric power distribution and the retail sale of power, is under the jurisdiction of state authority.

Two of the more notable U.S. energy policies impacting electricity transmission are Order No. 888 and the 2005年能源政策法案.

Order No. 888 adopted by FERC on 24 April 1996, was “designed to remove impediments to competition in the wholesale bulk power marketplace and to bring more efficient, lower cost power to the Nation’s electricity consumers. The legal and policy cornerstone of these rules is to remedy undue discrimination in access to the monopoly owned transmission wires that control whether and to whom electricity can be transported in interstate commerce.”[47] Order No. 888 required all public utilities that own, control, or operate facilities used for transmitting electric energy in interstate commerce, to have open access non-discriminatory transmission tariffs. These tariffs allow any electricity generator to utilize the already existing power lines for the transmission of the power that they generate. Order No. 888 also permits public utilities to recover the costs associated with providing their power lines as an open access service.[47][48]

The Energy Policy Act of 2005 (EPAct) signed into law by congress on 8 August 2005, further expanded the federal authority of regulating power transmission. EPAct gave FERC significant new responsibilities including but not limited to the enforcement of electric transmission reliability standards and the establishment of rate incentives to encourage investment in electric transmission.[49]

Historically, local governments have exercised authority over the grid and have significant disincentives to encourage actions that would benefit states other than their own. Localities with cheap electricity have a disincentive to encourage making interstate commerce英语interstate commerce in electricity trading easier, since other regions will be able to compete for local energy and drive up rates. For example, some regulators in Maine do not wish to address congestion problems because the congestion serves to keep Maine rates low.[50] Further, vocal local constituencies can block or slow permitting by pointing to visual impact, environmental, and perceived health concerns. In the US, generation is growing four times faster than transmission, but big transmission upgrades require the coordination of multiple states, a multitude of interlocking permits, and cooperation between a significant portion of the 500 companies that own the grid. From a policy perspective, the control of the grid is 巴尔干化, and even former energy secretary 比尔·理查森 refers to it as a third world grid. There have been efforts in the EU and US to confront the problem. The US national security interest in significantly growing transmission capacity drove passage of the 2005 energy act giving the Department of Energy the authority to approve transmission if states refuse to act. However, soon after the Department of Energy used its power to designate two National Interest Electric Transmission Corridor英语National Interest Electric Transmission Corridors, 14 senators signed a letter stating the DOE was being too aggressive.[51]

Special transmission

Grids for railways

In some countries where 電力機車s or 電聯車s run on low frequency AC power, there are separate single phase traction power network英语traction power networks operated by the railways. Prime examples are countries in Europe (including 奥地利, 德国 and 瑞士) which utilize the older AC technology based on 16 2/3 Hz (Norway and Sweden also use this frequency but use conversion from the 50 Hz public supply; Sweden has a 16 2/3 Hz traction grid but only for part of the system).

Superconducting cables

高溫超導s (HTS) promise to revolutionize power distribution by providing lossless transmission of electrical power. The development of superconductors with transition temperatures higher than the boiling point of 液氮 has made the concept of superconducting power lines commercially feasible, at least for high-load applications.[52] It has been estimated that the waste would be halved using this method, since the necessary refrigeration equipment would consume about half the power saved by the elimination of the majority of resistive losses. Some companies such as 聯合愛迪生 and American Superconductor英语American Superconductor have already begun commercial production of such systems.[53] In one hypothetical future system called a SuperGrid英语SuperGrid, the cost of cooling would be eliminated by coupling the transmission line with a liquid hydrogen pipeline.

Superconducting cables are particularly suited to high load density areas such as the business district of large cities, where purchase of an 地役权 for cables would be very costly.[54]

HTS transmission lines[55]
Location Length (km) Voltage (kV) Capacity (GW) Date
Carrollton, Georgia 2000
Albany, New York[56] 0.35 34.5 0.048 2006
Holbrook, Long Island英语Holbrook Superconductor Project[57] 0.6 138 0.574 2008
Tres Amigas英语Tres Amigas SuperStation 5 Proposed 2013
Manhattan: Project Hydra Proposed 2014
Essen, Germany[58][59] 1 10 0.04 2014

Single wire earth return

Single-wire earth return (SWER) or single wire ground return is a single-wire transmission line for supplying single-phase electrical power for an electrical grid to remote areas at low cost. It is principally used for rural electrification, but also finds use for larger isolated loads such as water pumps. Single wire earth return is also used for HVDC over submarine power cables.

Wireless power transmission

Both 尼古拉·特斯拉 and Hidetsugu Yagi英语Hidetsugu Yagi attempted to devise systems for large scale wireless power transmission in the late 1800s and early 1900s, with no commercial success.

In November 2009, LaserMotive won the NASA 2009 Power Beaming Challenge by powering a cable climber 1 km vertically using a ground-based laser transmitter. The system produced up to 1 kW of power at the receiver end. In August 2010, NASA contracted with private companies to pursue the design of laser power beaming systems to power low earth orbit satellites and to launch rockets using laser power beams.

Wireless power transmission has been studied for transmission of power from 太空太陽能s to the earth. A high power array of 微波 or laser transmitters would beam power to a rectenna英语rectenna. Major engineering and economic challenges face any solar power satellite project.

Security of control systems

The 美國聯邦政府 admits that the power grid is susceptible to 網絡戰.[60][61] The 美國國土安全部 works with industry to identify vulnerabilities and to help industry enhance the security of control system networks, the federal government is also working to ensure that security is built in as the U.S. develops the next generation of 'smart grid' networks.[62]

In June 2019, 俄罗斯 has conceded that it is "possible" its electrical grid英语Electricity sector in Russia is under cyber-attack by the United States.[63] The New York Times reported that American hackers from the 美國網戰司令部 planted malware potentially capable of disrupting the Russian electrical grid.[64]

記錄

參見

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