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=== 損耗 ===
=== 損耗 ===
雖然輸電系統的電壓皆已大幅提高,長距離輸送電力之時仍會有一定程度的損耗,例如一條{{convert|100|mile|abbr=on}}的763千伏特架空電纜在輸送1吉瓦時有約0.5%至1.1%的損耗,但若改用345千伏特則會有4.2%的損耗<ref>{{cite web |author1=American Electric Power |title=Transmission Facts |url=https://www.aep.com/about/transmission/docs/transmission-facts.pdf |archiveurl=https://web.archive.org/web/20110604181007/https://www.aep.com/about/transmission/docs/transmission-facts.pdf|archiveurl=2011-06-04}}</ref>。假設負載中心用電量不變,即輸電系統須輸送相同能量時,由於電能損失與電流的大小的平方成正比,以中電的輸電網絡為例從380伏特提升至400千伏特共提升約1053倍,輸電過程的電力損耗減少達111萬倍,由始可見輸電系統提升電壓的重要性。即使因應電流減少而相應縮減電纜的橫切面積,以上述例子仍可見損耗減少達1053倍,而輸電電纜的成本則可以大幅下降。長距離輸電的電壓一般可達115千伏特至1,200千伏特。若電壓繼續提高則[[电晕放电]]效應亦會隨之增加,如對地達2,000千伏特時电晕放电的損耗將抵消降低電流的好處。將同一相電力分組(bundle)輸送或直接加大電纜導體皆可降低电晕放电效應<ref>{{cite web |author1=California Public Utilties Commission |title=CORONA AND INDUCED CURRENT EFFECTS |url=https://www.cpuc.ca.gov/environment/info/aspen/deltasub/pea/16_corona_and_induced_currents.pdf |accessdate=2020-08-04 |date=2005-08}}</ref>
雖然輸電系統的電壓皆已大幅提高,長距離輸送電力之時仍會有一定程度的損耗,例如一條{{convert|100|mile|abbr=on}}的763千伏特架空電纜在輸送1吉瓦時有約0.5%至1.1%的損耗,但若改用345千伏特則會有4.2%的損耗<ref>{{cite web |author1=American Electric Power |title=Transmission Facts |url=https://www.aep.com/about/transmission/docs/transmission-facts.pdf |archiveurl=https://web.archive.org/web/20110604181007/https://www.aep.com/about/transmission/docs/transmission-facts.pdf|archivedate=2011-06-04}}</ref>。假設負載中心用電量不變,即輸電系統須輸送相同能量時,由於電能損失與電流的大小的平方成正比,以中電的輸電網絡為例從380伏特提升至400千伏特共提升約1053倍,輸電過程的電力損耗減少達111萬倍,由始可見輸電系統提升電壓的重要性。即使因應電流減少而相應縮減電纜的橫切面積,以上述例子仍可見損耗減少達1053倍,而輸電電纜的成本則可以大幅下降。長距離輸電的電壓一般可達115千伏特至1,200千伏特。若電壓繼續提高則[[电晕放电]]效應亦會隨之增加,如對地達2,000千伏特時电晕放电的損耗將抵消降低電流的好處。將同一相電力分組(bundle)輸送或直接加大電纜導體皆可降低电晕放电效應<ref>{{cite web |author1=California Public Utilties Commission |title=CORONA AND INDUCED CURRENT EFFECTS |url=https://www.cpuc.ca.gov/environment/info/aspen/deltasub/pea/16_corona_and_induced_currents.pdf |accessdate=2020-08-04 |date=2005-08}}</ref>


焦耳第一定律中電力的損耗除與電流有關外,亦與電纜本身所帶有的電阻成正比關系。電纜的材質、温度、卷扎方法、[[集膚效應]]等皆會影響電阻。當電纜温度上升時,其電阻亦[[電阻#溫度對電阻的影響|隨之增加]]。集膚效應使較高頻率的交流電有更高損耗。這些電阻皆可使用數學模型估計<ref>{{cite web |title=AC Transmission Line Losses |author=Curt Harting |date=2010-10-24 |publisher=[[史丹佛大學]] |url=http://large.stanford.edu/courses/2010/ph240/harting1/ |accessdate=2019-06-10}}</ref>。
焦耳第一定律中電力的損耗除與電流有關外,亦與電纜本身所帶有的電阻成正比關系。電纜的材質、温度、卷扎方法、[[集膚效應]]等皆會影響電阻。當電纜温度上升時,其電阻亦[[電阻#溫度對電阻的影響|隨之增加]]。集膚效應使較高頻率的交流電有更高損耗。這些電阻皆可使用數學模型估計<ref>{{cite web |title=AC Transmission Line Losses |author=Curt Harting |date=2010-10-24 |publisher=[[史丹佛大學]] |url=http://large.stanford.edu/courses/2010/ph240/harting1/ |accessdate=2019-06-10}}</ref>。
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=== 轉置相位 ===
=== 轉置相位 ===
當電流流經輸電線時將產生感應磁場並影響附近電線的電感。電線導體的互感與導體之間的相互位置有關系。一般輸電塔上的三相電線會分別置於不同的高度,使位於中間的導體所得的互感與另外兩相有顯着的分別,再加上三條導體與大地的距離不一致而各有不同電容,最終引致三相的輸送電力不平衡。故此,輸電線須定期於{{tsl|en|transposition tower|轉置塔}}轉置相位使三相所受的互感和對地電容大致相等。
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}}.


=== Subtransmission ===
=== 次輸電系統 ===
[[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]]]]
[[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]]]]
[[File:Wood Pole Structure.JPG|thumb|173px|115 kV H-frame transmission tower]]


'''次輸電系統'''為輸電系統中使用較低電壓的一部分。由於極高壓的設備較為大型且昂貴,一般情況下不會將所有變電站連接至輸電系統中,而是將較低電壓的變電站連接至配電系統。在一些較大型的極高壓輸電系統中,將輸電系統直接連接至配電系統亦有同樣問題,故就需要使用次輸電系統作為兩者之間的連接。次輸電系統通常為環狀連接以避免單一線路故障時影響大量客戶,環狀連接亦可作常閉連接以提供無間斷供電。較低電壓的次輸電系統的建築結構亦較為簡單且佔地較少,亦使地下輸電成本較低。
'''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.


次輸電系統與輸電系統或配電系統之間沒有固定邊界,亦不能單靠電壓判斷。港燈的輸電系統中包含132千伏特及275千伏特的輸電線路,但並沒有區分次輸電系統與輸電系統,兩者皆會直接連接至配電系統<ref name="HKE T&D">{{Cite magazine|origyear=2014|access-date=2020-07-30|title=Transmission & Distribution System|publisher=[[香港電燈有限公司]]}}</ref>。北美的次輸電系統通常為69千伏特、115千伏特或138千伏特。部份次輸電系統為輸電網絡因應發展而擴張及提高電壓後由輸電系統轉換而成。次輸電系統既帶有輸電系統輸送大量電力的特徵,亦有配電系統為地區供電的特點<ref>{{cite book |author1=Donald G. Fink |author2=H. Wayne Beaty |title=Standard Handbook for Electrical Engineers |date=2007 |isbn=978-0-07-144146-9 |edition=15 |chapter=18.5}}</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>


=== Transmission grid exit ===
=== 配電側 ===
於輸電系統的分支變電站會將高壓電轉換為較低電壓並轉至配電系統。
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]]).


== 輸電系統的數學理論 ==
== Advantage of high-voltage power transmission ==
=== 高壓輸電系統的好處 ===
{{See also|ideal transformer}}
高壓輸電系統令遠距離輸送電力的損耗較少,從而減低發電及操作成本。
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.


{{multiple image
[[File:Power split two resistances.svg|thumb|Electrical grid without a transformer.]]
|direction = vertical
[[File:Transformer power split.svg|thumb|Electrical grid with a transformer.]]
|align = right
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>.
|width = 200
|image1=Power split two resistances.svg
|image2=Transformer power split.svg
|caption1=沒有變壓器的輸電線路模型
|caption2=帶有變壓器的輸電線路模型
}}
在極為簡單的數學模型中可以假設[[輸電網路]]由單一發電機輸送電力至單一負載,由交流電源和純電阻表示,而輸電線僅有電阻。


由於線路為[[串聯]]且沒有變壓器,則輸電線的電阻與負載的電阻則為[[電壓分配定則|分壓器]]。串聯中所有零件皆有同樣電流流通,為<math>I=\frac{V}{R+R_C}</math>。故此,負載的所收到的可用功為:
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:
:<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>
:<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>
現在輸電線路中加上變壓器,於供電最後階段變壓為低電壓高電流。理想變壓器僅將輸入的能量轉換,使電壓按比例<math>a</math>減少時,電流則以<math>a</math>增加。同樣按分壓器方法計算,輸電線路的電阻經過變壓器後僅為<math>R_C/a^2</math>,而可用功則為:
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:
:<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>
:<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>


如<math>a>1</math>,即電壓於負載則由高壓降至低壓,從上述算式可見輸電網絡的損耗將有所減少。
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]].


=== 輸電系統模型及矩陣 ===
== Modeling and the transmission matrix ==
{{Main|交流電輸電的效能與模型}}
{{Main|Performance and modelling of AC transmission}}
[[File:Transmission Line Black Box.JPG|thumb|upright=1.6|輸電系統的「黑盒」數學模型]]


大多數時候,輸送系統的模型只會關注輸電線兩端的特性,包括傳送及接收兩端的電壓和電流。輸電網則可以化為一個2x2矩陣的「黑盒」:
[[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>
:<math>
第125行: 第132行:
</math>
</math>


輸電線一般假設為對稱的網絡,一次側與二次側相互對調時對輸送電力沒有影響。輸電矩陣'''T'''會有以下特性:
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>\det(T) = AD - BC = 1</math>
* <math>A = D</math>
* <math>A = D</math>


當中四個參數A、B、C及D由輸電網絡的電阻(R)、电感(L)、電容(C)、並聯電導(G)按照不同模型所組成。模型中的大寫字母皆為整條輸電線該參數的總和。
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===
==== 無損輸電線 ====
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]]
[[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.


無損輸電線為最不準確的模型,一般只用於極短的輸電線上。這種模型中一次側與二次側的電壓與電流相同。
===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:
==== 短線模型 ====
短線模型主要用於約{{Convert|50|mi|km}}長的輸電線。短線模型中電容和並聯電導數值較少而可以忽略而只須計算由電阻和串聯電感組成的[[阻抗]](Z)。最終參數為<math>A = D = 1</math>、<math>B = Z</math>及<math>C = 0</math>,故矩陣則為:
:<math>
:<math>
\begin{bmatrix}
\begin{bmatrix}
第154行: 第161行:
</math>
</math>


===Medium line===
==== 中線模型 ====
中線模型主要用於約{{Convert|80-250|mi|km}}長的輸電線。此模型中由於輸電線路延長,不可再忽略輸電線所帶有的電容及並聯電導。此模型將所有電容和並聯電導加起,然後於輸電線兩側各置一半。模型可見上方一條串聯阻抗,頭尾各有電容連至大地,故又可按其形狀稱之為「π模型」。中線模型的矩陣為:
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>
:<math>
\begin{bmatrix}
V_\mathrm{S}\\
I_\mathrm{S}\\
\end{bmatrix}
=
\begin{bmatrix}
1 + \frac{G Z}{2} & Z\\
G \Big( 1 + \frac{G Z}{4}\Big)S & 1 + \frac{G Z}{2}\\
\end{bmatrix}
\begin{bmatrix}
V_\mathrm{R}\\
I_\mathrm{R}\\
\end{bmatrix}
\begin{align}
\begin{align}
A &= D = 1 + \frac{G Z}{2} \text{ per unit}\\
A &= D = 1 + \frac{G Z}{2} \text{ per unit}\\
第165行: 第185行:
</math>
</math>


由此輸電線會有以下特性:
Counterintuitive behaviors of medium-length transmission lines:


* voltage rise at no load or small current ({{tsl|en|Ferranti effect|}})
* 電壓會於低負載時上升({{tsl|en|Ferranti effect|費冉倜效應}}
* 接收側(二次側)電流可高於輸送側(一次側)
* receiving-end current can exceed sending-end current


===Long line===
==== 長線模型 ====
長線模型由[[电报员方程]]推論而得出,主要用於{{Convert|150|mi|km}}或以上的輸電線。長線模型與中線模型的主要分別為電容和並聯電導不再位於輸電線的兩端,而是分配於整條輸電線,使其有多於兩條並聯線。此舉能提高模型的準碓性,但需要作較為複雜且多次的計算。下為長線模型的參數,而<math>\gamma</math>為{{tsl|en|propagation constant|傳播常數}}.
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>
:<math>
\begin{align}
\begin{align}
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</math>
</math>


長線模型可以用於計算輸電線上任何一點的電流和電壓,如須計算接收端的電流和電壓則須把<math>x</math>替換為<math>l</math>,即輸電線的總長度。
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]].)


== 高壓直流輸電 ==
== High-voltage direct current ==
{{Main|High-voltage direct current}}
{{Main|高壓直流輸電}}


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.
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.
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(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]].
(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 ==
== 容量 ==
<!-- Linked from wind power. -->
<!-- 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.
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.
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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.
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 ==
== 控制 ==
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.
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 ===
=== 負載平衡 ===
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 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.


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| publisher = EnPowered | date = 2016-03-28}}</ref>
| publisher = EnPowered | date = 2016-03-28}}</ref>


=== Failure protection ===
=== 故障保護 ===
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.
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.
{{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 ==
== 通訊 ==
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:
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
* [[微波]]s
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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.
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.


== 電力市場改革 ==
== Electricity market reform ==
{{Main|Electricity market}}
{{Main|Electricity market}}


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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|}}.
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|}}.


== 輸電系統成本 ==
== 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>
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>



2020年8月5日 (三) 06:40的版本

大古力水坝的500千伏特三相輸電線,每座電塔左右方各有一組線路,圖右方樹後亦有另外兩組。全電廠發出的7079百萬瓦電力全部經由此六組輸電網路輸送

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,亦需要為各電網、發電與供電之間的連接作平衡。例如在大範圍同步電力網絡英语wide area synchronous grid之中,為增加電力傳送的效率同時降低發電與輸電的成本,電力或需要跨國傳送,將輸電網絡連結亦能提升輸電系統的穩定性。

通常而言,輸電網絡與配電網絡同屬一間公司,但自1990年代起不少國家發起電力自由化,使部分電力市場之中輸電網絡與配電網絡未必屬於同一公司[1]

歷史

1890年紐約街頭,除電報線外亦有各種不同電壓的電線

商業供電的早期,直流電會以單一電壓輸送予客戶使用,其後為改進電動機及其他設備的工作效率則改為輸送多種電壓以適應如照明、電動機或鐵路等不同的應用[2][3]。由於直流電於低壓高電流的輸送時效率甚低,故需於負載中心附近設置小型發電機供電,類似現今的分散式發電[4]

威廉·史坦雷安裝了世界第一組應用變壓器

首條長距離交流電纜為1884年都灵國際展覽中使用,約34公里(21英里)長,展示了交流電長距離輸電的能力[3]。首個商用交流電系統1885年於羅馬誕生,主要用於街燈照明,輸電距離共19公里長。數月後倫敦亦首次使用了交流電系統[5]威廉·史坦雷於1885年設計了首個實際可用的交流電變壓器[6]。他在乔治·威斯汀豪斯的支援下於1886年於麻省展示了一套基於變壓器的交流電照明系統。該系統由500伏西門子發電機推動,並以新設計的史坦雷變壓器降至100伏來供應予大街上23所商店,4,000英尺(1,200米)的輸電過程中僅有極少電力損失[7],由此推動威斯汀豪斯於該電其後開始安裝交流電系統[6]

1888年交流电动机誕生,為基於多相系統异步电动机,分別由加利莱奥·费拉里斯尼古拉·特斯拉獨立研發。該設計其後由米哈伊·多利和-多布羅斯基英语Mikhail Dolivo-Dobrovolsky查理·尤金·蘭斯洛特·布朗英语Charles Eugene Lancelot Brown發展為現今的三相電[8]。然而,由於電力供應未能支援而未有即時使用[9][10]。1880年代後期,小型電力公司開始合併至較大型公司,例如歐洲成立了冈茨公司AEG,美國則為通用电气西屋电气,這些公司則有繼續發展交流電系統但因技術問題未能立刻將各種電力系統合併[11]。隨着交流電技術的進步,各種舊有的用電系統,例如單相交流電、多相交流電、高低壓照明和直流電機等可以利用回轉變流機電動發電機等設備連接至一通用網絡,從而達致交流電大規模發電及輸電所帶來的規模經濟[11][12]

首條單相高壓交流電輸電網於1890年啟用,為威拉米特瀑布的水力發電廠輸送電力至俄勒岡州波特蘭,總長約14英里(23公里)[13]。首條三相高壓輸電線則在美因河畔法兰克福於1891年為1891年國際電能技術展覽英语International Electro-Technical Exhibition – 1891而興建。內卡河畔勞芬法兰克福之間則建於一條175公里長的15千伏特輸電線[5][14]

20世紀期間,輸電系統的電壓一直上升。至1914年共有55套輸電系統使用70千伏特以上的電壓,最高則為150千伏特[15]。輸電系統連接後使各發電機可以相連,從而減低了發電成本。電力網絡的穩定性亦因此而增加而資本投入則有所減少。輸電系統的發展亦容許設立水力發電等較遙遠的發電設備[2][5]。直至今天,輸電網絡的範圍亦因上述理由而合併越加擴展。

大規模輸送電力

整個電力系統,輸電系統以藍色標示

如前所述,輸電系統的作用為可靠且高效地輸送電力。其外亦需要將經濟因素、安全性及冗餘等計算在內。

根據焦耳第一定律,電能損失與電流的大小的平方成正比,故輸電系統會大幅提高電壓,從而減少輸電線路中所流通的電流,繼而減少輸電過程中的電力損失。另一方面,電壓越高,則兩端變壓站所需成本亦會有所上升,線路之間的絕緣能力亦需要搞高。所以電壓不能無限制地提高,而需與成本、用電量之間作相應配合。交流電使用變壓器作為提高和降低電壓的工具,而高壓直流輸電技術雖可繼續減少電力損失卻則需要更為複雜的電力電子設備,故通常僅用於長距離大規模輸電之上。高壓直流輸電技術亦用於超越50公里長的海底電䌫英语submarine power cable以及連接不同步的電力網絡,例如60赫茲與50赫茲之間的連接。大多數輸電系統皆使用三相交流電,而電氣化鐵路中則或會使用單相電

歐盟大範圍同步電網英语wide area synchronous grid
變電站將電壓改變以適應發電及輸配電系統的電壓。圖為美國奥勒姆的一座變電站

除了輸送電力期間有電力損失的考慮,輸電系統在連接之後亦能同時提高系統的可靠性並降低發電成本和資本投入。電力公司需要為客戶於任何時候提供電力,但電力需求並非固定,例如日間的電力需求比深夜時為高,而發電廠則須在滿足頂峰需求英语Peak demand之外提供額外的發電容量以作冗餘。當輸電系統連接後即可減少整體所需的冗餘發電容量,從而減低整套電力系統的資本投入,而因單一發電機在發電量越高時成本亦隨之增加,故亦能減少發電的平均成本。當輸電系統擴大之後,因電網或會跨越不同地區,則電網亦能將各地需求平均分配至各發電廠,從而進一步降低冗餘發電容量。例如一個大型電網的南方於夏季天氣炎熱而需要冷氣,北方則於冬季天氣寒冷供暖,電網整體則不需要為兩方各自建設按年計算的冗餘發電容量。另外,當輸電系統以網狀連結時,當某一輸電線路受損又或修理之時,亦能使用其他線路繼續輸電。輸電系統亦使發電廠可各自分工,例如整天不變的基本電力需求可由基本負載發電廠供應,而基礎需求與頂峰需求之間則可由快速啟動的尖峰負載發電廠負責。

長距離電力輸送的成本非常低,於美國最低僅為每度電0.005美元[16],使距離較遠的電力供應商亦能便宜地提供電力[17]。長距離電力輸送亦使偏遠可再生能源能納入至電力系統之中,包括太陽能電廠風力發電場海上風力發電場等一般與負載中心距離甚遠的發電方法非常依靠輸電系統來減低電力損失。

發電側

發電機的總端電壓(發電電壓)對比輸配電力系統通常較低,視乎其額定容量約為2.3千伏特至30千伏特之間。發電機不遠處即連接着變壓器以提高電壓至輸電電壓,發電廠內或有變電站或開關站將發出的電力導至不同的輸電線路。

架空電纜

美國華盛頓州的三相高壓架空電纜,可見每相各自再分為三組
鋼芯鋁纜的橫切面,可見內含七條鋼芯,外面再覆上四層鋁芯

高壓架空電纜僅使用空氣作絕緣使其成本相對地底電纜大為下降。導體絕大多數為铝合金,多股導體再繞成一條電纜,電纜中間亦可能加入鋼纜以強化該電纜。鋁合金導體相對銅導體可以於略低效能的情況下大幅降低成本,鋁合金重量較低亦能減少輸電塔所需支撐的拉力,從而降低輸電塔需要的結構強度,亦能降低土木工程相關的成本。導體面積由12mm2至750mm2不等,視乎該輸電線路所需的載流容量英语current-carrying capacity。較大的導體會因集膚效應使電流集中於電纜的外圍,從而降低內部導體的成本效益。故此,高壓架空電纜會分組而非合為一組大電纜以避開集膚效應,這種做法同時亦能減少因电晕放电而導致的能量損失。另外,架空電纜三相的三組電纜亦需要按距離如雙絞線般交換位置以減少外界環境做成三相不平衡,稱之為轉置相位

現時,輸電系統的高壓架空電纜大多為110千伏特或以上。部分僅有33或66千伏特的電力輸送線路則稱之為次輸電系統,在某些情況下會以較長距離供應輕負載。而電壓為765千伏特以上的特高電壓輸電系統會有其他特殊設計,但一般仍會使用架空電纜。

架空電纜僅依靠空氣作絕緣,故電纜之間需要留有最小安全距離。強風或低温等惡劣天氣下則有可能導致電纜隨風漂動而使電纜之間的距離低於最小安全距離,使三相之間或對地發生电弧,引致設備故障或停電[18]。風亦能把架空電纜吹動而造成大波幅低頻率的震動,稱之為電線跳動英语conductor gallop又或導體跳動。

地底輸電

電力輸送亦可利用地下高壓電纜進行。地底電纜佔地需求較少,對景觀影響亦較低,受天氣干擾的機會亦較少。然而,地底電纜本體成本較高,挖掘及鋪設電纜的工程費用更是架空電纜的數倍之多。雖然自然發生故障的機會稍低,因路面工程而誤傷電纜的機會卻因而增加,發生故障後確認位置與維修所需的時間亦是更長。

地底電纜有非常多種類,常見的為充油電纜和XLPE電纜,前者使用油、紙等材質來絕緣和散熱,後者則使用特製塑膠絕緣。電纜亦會外覆蓋上防水層。如果地底電纜直接置於地底(Direct Burial),則更會在外層加上金屬枝作保護,否則應將電纜置於石槽或鐵管內。有些輸電線路會把這些槽管充油,並於故障發生時使用液態氮將該段電纜凍結以供維修,唯這種方法會延長維修需時,亦會提高維修費用[19][20][21]

地底電纜的主要限制為其温度限制,故載流容量通常不如架空電纜。長距離的交流地底電纜亦會產生顯着的電容,使其必須作功率修正。直流地底電纜沒有電容限制,但就需要於變電站設置轉換器。

損耗

雖然輸電系統的電壓皆已大幅提高,長距離輸送電力之時仍會有一定程度的損耗,例如一條100 mi(160 km)的763千伏特架空電纜在輸送1吉瓦時有約0.5%至1.1%的損耗,但若改用345千伏特則會有4.2%的損耗[22]。假設負載中心用電量不變,即輸電系統須輸送相同能量時,由於電能損失與電流的大小的平方成正比,以中電的輸電網絡為例從380伏特提升至400千伏特共提升約1053倍,輸電過程的電力損耗減少達111萬倍,由始可見輸電系統提升電壓的重要性。即使因應電流減少而相應縮減電纜的橫切面積,以上述例子仍可見損耗減少達1053倍,而輸電電纜的成本則可以大幅下降。長距離輸電的電壓一般可達115千伏特至1,200千伏特。若電壓繼續提高則电晕放电效應亦會隨之增加,如對地達2,000千伏特時电晕放电的損耗將抵消降低電流的好處。將同一相電力分組(bundle)輸送或直接加大電纜導體皆可降低电晕放电效應[23]

焦耳第一定律中電力的損耗除與電流有關外,亦與電纜本身所帶有的電阻成正比關系。電纜的材質、温度、卷扎方法、集膚效應等皆會影響電阻。當電纜温度上升時,其電阻亦隨之增加。集膚效應使較高頻率的交流電有更高損耗。這些電阻皆可使用數學模型估計[24]

輸配電損耗為發電量與客戶用電量之間的差異,主要可以歸於輸電和配電系統的損耗。美國的輸配電損耗於1997年估計為6.6%[25],2007年為6.5%[25],2013年至2019年則為5%[26]

1980年時估計直流電輸電符合成本效益的最長距離為7,000公里,而交流電則為4,000公里,但現今世上所有輸電線路遠遠短於此上限[16]

交流電輸電系統中,輸電的效能受電纜的电感與電容顯著的影響。電纜自身為電阻與電感的集合,而電纜與大地之間自然會產生電容。因這些特性而產生的電流為無功功率,僅會在輸電網絡間儲存及輸送,無法為負載提供實際功率。然而電流不論有否做功,依然會因電阻而產生損耗,故設計輸電系統時亦須減少系統當中的電容和電感,提升功率因数,減低因無功電流而做成的損耗。由於電感和電容是輸電網絡與電纜的固有特性無法直接消除,故只可依靠加入反向的電感和電容以抵消其效果。例如電容器組可與電纜串聯以抵消電纜自身的电感。連同電抗器、相移變壓器英语phase-shifting transformer靜止無功補償器等以補償輸電系統的無功功率。

轉置相位

當電流流經輸電線時將產生感應磁場並影響附近電線的電感。電線導體的互感與導體之間的相互位置有關系。一般輸電塔上的三相電線會分別置於不同的高度,使位於中間的導體所得的互感與另外兩相有顯着的分別,再加上三條導體與大地的距離不一致而各有不同電容,最終引致三相的輸送電力不平衡。故此,輸電線須定期於轉置塔英语transposition tower轉置相位使三相所受的互感和對地電容大致相等。

次輸電系統

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

次輸電系統為輸電系統中使用較低電壓的一部分。由於極高壓的設備較為大型且昂貴,一般情況下不會將所有變電站連接至輸電系統中,而是將較低電壓的變電站連接至配電系統。在一些較大型的極高壓輸電系統中,將輸電系統直接連接至配電系統亦有同樣問題,故就需要使用次輸電系統作為兩者之間的連接。次輸電系統通常為環狀連接以避免單一線路故障時影響大量客戶,環狀連接亦可作常閉連接以提供無間斷供電。較低電壓的次輸電系統的建築結構亦較為簡單且佔地較少,亦使地下輸電成本較低。

次輸電系統與輸電系統或配電系統之間沒有固定邊界,亦不能單靠電壓判斷。港燈的輸電系統中包含132千伏特及275千伏特的輸電線路,但並沒有區分次輸電系統與輸電系統,兩者皆會直接連接至配電系統[27]。北美的次輸電系統通常為69千伏特、115千伏特或138千伏特。部份次輸電系統為輸電網絡因應發展而擴張及提高電壓後由輸電系統轉換而成。次輸電系統既帶有輸電系統輸送大量電力的特徵,亦有配電系統為地區供電的特點[28]

配電側

於輸電系統的分支變電站會將高壓電轉換為較低電壓並轉至配電系統。

輸電系統的數學理論

高壓輸電系統的好處

高壓輸電系統令遠距離輸送電力的損耗較少,從而減低發電及操作成本。

沒有變壓器的輸電線路模型
帶有變壓器的輸電線路模型

在極為簡單的數學模型中可以假設輸電網路由單一發電機輸送電力至單一負載,由交流電源和純電阻表示,而輸電線僅有電阻。

由於線路為串聯且沒有變壓器,則輸電線的電阻與負載的電阻則為分壓器。串聯中所有零件皆有同樣電流流通,為。故此,負載的所收到的可用功為:

現在輸電線路中加上變壓器,於供電最後階段變壓為低電壓高電流。理想變壓器僅將輸入的能量轉換,使電壓按比例減少時,電流則以增加。同樣按分壓器方法計算,輸電線路的電阻經過變壓器後僅為,而可用功則為:

,即電壓於負載則由高壓降至低壓,從上述算式可見輸電網絡的損耗將有所減少。

輸電系統模型及矩陣

輸電系統的「黑盒」數學模型

大多數時候,輸送系統的模型只會關注輸電線兩端的特性,包括傳送及接收兩端的電壓和電流。輸電網則可以化為一個2x2矩陣的「黑盒」:

輸電線一般假設為對稱的網絡,一次側與二次側相互對調時對輸送電力沒有影響。輸電矩陣T會有以下特性:

當中四個參數A、B、C及D由輸電網絡的電阻(R)、电感(L)、電容(C)、並聯電導(G)按照不同模型所組成。模型中的大寫字母皆為整條輸電線該參數的總和。

無損輸電線

Voltage on sending and receiving ends for lossless line

無損輸電線為最不準確的模型,一般只用於極短的輸電線上。這種模型中一次側與二次側的電壓與電流相同。

短線模型

短線模型主要用於約50英里(80公里)長的輸電線。短線模型中電容和並聯電導數值較少而可以忽略而只須計算由電阻和串聯電感組成的阻抗(Z)。最終參數為,故矩陣則為:

中線模型

中線模型主要用於約80—250英里(130—400公里)長的輸電線。此模型中由於輸電線路延長,不可再忽略輸電線所帶有的電容及並聯電導。此模型將所有電容和並聯電導加起,然後於輸電線兩側各置一半。模型可見上方一條串聯阻抗,頭尾各有電容連至大地,故又可按其形狀稱之為「π模型」。中線模型的矩陣為:

由此輸電線會有以下特性:

長線模型

長線模型由电报员方程推論而得出,主要用於150英里(240公里)或以上的輸電線。長線模型與中線模型的主要分別為電容和並聯電導不再位於輸電線的兩端,而是分配於整條輸電線,使其有多於兩條並聯線。此舉能提高模型的準碓性,但需要作較為複雜且多次的計算。下為長線模型的參數,而傳播常數英语propagation constant.

長線模型可以用於計算輸電線上任何一點的電流和電壓,如須計算接收端的電流和電壓則須把替換為,即輸電線的總長度。

高壓直流輸電

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.

容量

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.

控制

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.

負載平衡

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]

故障保護

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.

通訊

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.

電力市場改革

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.

輸電系統成本

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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