Automatika

Frequency Transient Response Control Strategy of Distributed Generations

in Low voltage microgrid

LI Tan , YANG Honggeng, WEN Ke (School of Electrical Engineering and Information, Sichuan University, Chengdu 610065, Sichuan Province, China) Abstract: This paper investigates the problem of frequency fast change after mutations of load disturbance and proposes a novel controller for inverters to improve the frequency response of microgrid under disturbances involving large frequency deviations. On the basis of virtual synchronous generator model, Δω and D are regulation parameters of P/ω droop control under microgrid islanding operation. It could adopt different droop coefficient under the condition of different frequency deviation while reducing the impact of inverter transient response to the system after disturbance and slowing the rate of frequency change. A secondary frequency regulation module with Q-ω and Q/T coordination control has been used to realize no difference frequency regulation, to provide reference voltage inverter control and to suppress power oscillation. Index Terms: microgrid，frequency control ，virtual synchronous generator，coordination control，secondary frequency regulation I INTRODUCTION Due to fast development of distributed generation(DG) in recent years, the concept of distributed generation (DG) is gaining an important role in current microgrid situation.[1-5] DG is responsible for the microgrid frequency regulation, voltage adjustment and power factor correction. While the main goal of a microgrid control is to meet the requirements of the system load on voltage and frequency by accurate power distribution[6-7] ,So the research of DG frequency control in the microgrid after disturbance is of great significance . The large-scale penetration of DG in microgrid, which makes the traditional power system frequency modulation control strategy not satisfy the frequency adjustment of microgrid under disturbance. Aimming at the islanded running condition of microgrid, traditionally P/f droop control method is used to realize frequency regulating function , the strategy simulates primary frequency modulation characteristics of traditional power system and realize accurate power allocation without communication link. For synchronous generator，Droop characteristics and large inertia characteristics of synchronous generator are conducive to the stable operation of the generator unit. Synchronous generator could reach a new equilibrium by adjusting the rotor speed with the action of speed governor under Power gaps. Different from traditional power system, most of DGs in microgrid are power electronic inverter type interface which lack the rotation characteristics of synchronous generator and lack inertia in traditional grid. Therefore, if the microgrid has energy storage unit equivalent to the synchronous generator, it can increase inertia and reduce the differences between microgrid and the traditional power system appropriately. By simulating the traditional principle of synchronous generator in the power system , the virtual synchronous generator (VSG)algorithm can be used to regulate micro power grid frequency and voltage and relieves the system disturbance after mutation process[9-10].But VSG is easy to cause power oscillation problem, which could influence the stability of the system. Using virtual frequency inertial system frequency modulation, which can make the DGs have synchronous generator rotor characteristics and can reduce power oscillation by the optimization of controller parameters[11-12].However this method is only consider the primary frequency control that may can’t realizes no difference frequency . VSG transient mathematical model has been proposed and realizes no difference adjusting frequency which references traditional frequency regulation tuner and governor principle in the process of power system to makes the inverter output power by scheduling command. The method uses concentration of secondary frequency modulation control structure[13], but there is no change frequency transient response to adjust to the impact of the inverter, it is difficult to improve frequency transient response process. Frequency peak variation as the parameters of adjustment index has been explored in [15]. The method reduces the frequency of instantaneous change, but frequency peak instantaneous response change is has the problem of low rate and in the process of parameter selection, the method does not take the VSG virtual damping coefficient in the model into account. The damping coefficient affects the system stability directly. Based on the traditional power system secondary frequency modulation which introduces proportional integral (PI) controller in the secondary frequency modulation is analyzed in [16] .But the secondary frequency regulation link system inertia is small still need to join the inertial link, complex control structure. To override the aforementioned problems, a control strategy of improving the transient response frequency using VSG model is presented in this paper. The strategy is combined with the electrical angular velocity deviation Δω and virtual damping coefficient D as indicators of P/ω droop control regulation. Unlike conventional droop controllers，the proposed control which just can use different microgrid frequency deviation coefficient under different frequency prolapse conditions; therefore, low impact of the load mutation disturbance conditions such as instantaneous frequency response of the system and improvement of the system frequency stability can be obtained. The Q-ω and Q/T coordinated control of the secondary frequency modulation module restrain power oscillation and provide reference voltage inverter control. Simulation and hardware experiment verify the effectiveness of the proposed control strategy. This paper is organized as follows. The original VSG is reviewed in Section II. The improved control in Section III, with simulation and experimental results presented in Sections IV respectively . The conclusions and discussions are in Section V. II OVERVIEW OF THE VIRTUAL SYNCHRONOUS GENERATOR (VSG) TECHNOLOGY

The core idea of VSG control model is simulating the dynamic process of the rotor dynamic response rate to improve the DG control rate, so damping coefficient is used to cut frequency oscillation. Virtual synchronous generator mathematical model is as follows[11-13]
 	(1)

(2) (3) (4) where P is the electromagnetic power, T and Ti are the VSG mechanical torque and electromagnetic torque of the model (N.m)，Respectively. J is the moment of inertia of the rotor （kg.m2）and ω* is the electrical angular velocity for reference. ωs is the actual electrical angular velocity, D is For the constant damping coefficient, e is for induced electromotive force. Mf is the biggest mutual inductance between excitation winding and field winding. ie is for exciting current and is the electric Angle. A virtual synchronous generator control block diagram is shown in Figure 1..

Fig.1 Based on virtual synchronous motor control block diagram

VSG Mechanical model has damping inertia of synchronous generator and electric characteristics of stator. By eqn. (1), it can be seen that the VSG rotor motion equation of the model has droop characteristics under steady state. The characteristics can be seen as P/ω or T/ω droop control which can realize power distribution between DGs under islanded state . According to(1) -(4), the equations of the VSG model , the damping coefficient is constant. Then according to different size of frequency disturbance, the model control cannot be reasonable regulation and VSG start time is long .What’s more , the stator voltage equation of synchronous reactance options is restricted by system disturbance and microgrid mode switch III PROPOSED CONTROLLER TOPOLOGY AND DESIGN PROCESS A .The primary frequency regulation control stragety

Microgrid frequency under the islanded state is more susceptible to disturbance and VSG model regulate active power to achieve the purpose of power distribution between DGs by T/ω droop control. T/ω prolapse function which implement active power distribution under the microgrid islanded state is achieved according to eqn. (1) [14] :
 	(5) 

where m is droop control coefficient of T/ω The islanded microgrid disturbance may result in frequency mutation and transient deviation may overstep the normal operation standard. If the system damping coefficient is big enough ,it can simulate the process that the speed of generator rotor slow down and the energy is released slowly , extend frequency dynamic transition time and avoid frequency transient impact caused by large frequency offset, during the system power shortage. No matter what condition the system ioperation is, System is not stable when the damping coefficient is less than zero. So this article research's damping coefficient D > 0 [18]. In order to achieve the damping coefficient and frequency coordinated control, this paper puts forward the frequency modulation strategy that is shown in the following equation: (6) in which, Δω=ωs-ω，km and kn are droop gain of T-ω during disturbance, Virtual damping coefficient D is obtained by the system maximum electromagnetic torque ΔTmax and system frequency deviation Δωmax.

 	(7)

(8) According to the microgrid design and operational standards, parameters Δωmax is designed to meet the stipulations in [17]. Fig. 2 is the improved frequency modulation control flow chart which shows T/ω Droop coefficient using two modes, can use different droop coefficient under different frequency deviation in microrgrid . It can solve frequency offset significantly that caused by a large droop coefficient during large disturbance[8]. At the same time, the method can reduce the impact of the frequency transient response to microgrid. (9)

Fig.2 Flow chart of improvement frequency control

Fig.3 Primary frequency modulation control block B. Characteristic analysis of the primary frequency regulation When microgrid is under the disturibance of large load change or big disturbance such as state switch, the control Coefficient need to select a larger prolapse to realize balance of power rapidly that Results large frequency offset[8]. Fig. 4 shows the method of a frequency modulation droop in this paper.

Fig.4 Droop characteristic figure Eq. (6) and (8) and Fig. 4 shows that: the Selection of km depends on virtual damping coefficient, the maximum electrical angular velocity deviation and the maximum electromagnetic torque that is to say the largest active power system. Eq. (9) shows the introduction of the km makes droop gain coefficient smaller,Fig.4 shows that the smaller kn is, the smaller droop gain is which can expand the DG output power range and reduce the output power fluctuations caused by microgrid frequency deviation. The introduction of virtual synchronous generator inertia of the system increases the kn .The system become more easily to run beyond the peak of frequency with kn becoming smaller. Conversely, the bigger kn is, the more easily frequency oscillation occur, So it needs to find the right coefficient of kn. From Eq. (9) ,the mdroop is less than traditional droop coefficient that is helpful to prevent inverter operating over the maximum power . In this section, the detail of primary frequency regulation is introduced. Fig. 2 shows that △ωmax is the limit of frequency under the system normal operation . When the system is under normal operation of the system , frequency is lower than the threshold △ωmax.Then mdroop is the coefficient of traditional droop control and Inverter works in traditional droop control mode. Frequency saltation happens after System disturbance. When the system frequency runs beyond the limit of △ωmax , mdroop is revised according to eq. (9). This method adopts different droop coefficient under different operation mode which makes the droop coefficient decreases thus reducing the frequency deviation. When the system is under large disturbance, The virtual synchronous generator model increases system inertia then kn is reduced under scheduled time step. It makes the system inertia decreases to zero and the system frequency gradually returns to normal operation. C. The secondary frequency regulation control strategy Traditional secondary frequency modulation in power system uses frequency modulator which makes the frequency characteristic of the generator set in parallel moving and makes the frequency deviation within the allowed range. Supposing there is a generator to supply the load power supply in the system, the initial point is point A, the system frequency is f1and the characteristic curves of Generator and load is PG(f) and PD(f)respectively. The traditional secondary frequency regulation process is shown in Fig. 5. When the system load increases byΔPD0 , before secondary adjustment, the operating point moves to B, and the frequency of the system reduces to the f2 . The static generator units moves Up to the point of B ' and the frequency of the system is f2’ under the effect of frequency modulator .The traditional electric power system secondary frequency modulation power balance equation is shown in eq.(10)[18]  :

Fig. 5 Traditional secondary power system frequency adjustment

 	(10)

where ΔPload is the load increase, ΔPG is active increase output and K is unit adjustment power of the traditional secondary frequency modulation. The secondary frequency modulation is to increase DG output, When the required power and DG power system become same to each other, there is no difference adjusting frequency. Secondary frequency modulation in microgrid usually introduces the proportional integral (PI) controller on the basis of secondary frequency modulation in traditional power system. But the controller inertia is small and still need to join inertial link which complex control structure. There is error in the system device and error accumulation is formed by integrated controller which can affect DG output. If the controller add the PI control to the VSG model of inverter, There is a difference between the frequency calculated by eq.(1) to (4) and the reference frequency. Therefore, PI regulation may change the input mechanical power of VSG model, then output electromagnetic power of inverter may be changed. There exists power flows between parallel operation inverters, then the output of other inverters’ electromagnetic power may also be affected. And each inverter is adjusted respectively which makes the system drop into the infinite loop regulation. In this paper, the Q-ω and Q/T droop control coordination of secondary frequency modulation, introducing variable torque ΔT, is proposed in this part. This module can not only generate a reference voltage but also can control output power of inverter. Then it can achieve the purpose of the secondary frequency modulation.

Fig.6 Secondary frequency regulation block diagram Eq.(11) is derived from Eq. (2), (3), (4) and (10) : (11) secondary frequency modulation control block diagram is shown in Fig. 6, U is the reference voltage of inverter, k is the gain coefficient of reactive power control, then:

 	(12)

Δω1 and Δω2 is electrical angular velocity of the primary and secondary frequency regulation. The secondary frequency modulation control process is shown in Fig.7. At the initial time, assuming that deviation between the frequency after the primary frequency regulation and the target frequency isΔf1 . DG1 and DG2 runs at A1 and B1 respectively. Δf2 is the deviation between the frequency after the secondary frequency regulation and the target frequency. Then the deviation between the primary and secondary frequency regulation is (Δf1-Δf2). After the primary frequency control,the Q-ω droop control makes initial secondary frequency regulation and econdary electrical angular velocity ΔωT is detected automatically after initial frequency modulation. Then the control start the Q/T droop control and increase the the mechanical torque, of VSG inverter model based on primary frequency control and initial secondary frequency regulation. The process of the secondary frequency control is equivalent to move the frequency characteristics curve of DG1 and DG2 upward（Δf1-Δf2）on the parallel. Eventually DG1 and DG2 is running at A2 and B2 and increase energy output achieving no difference frequency regulation. In addition this controller takes place of the voltage current inner loop control in traditional droop control which is for generating inverter modulation signal quickly and effectively. This control uses torque deviation ΔT and the deviation of the angular velocity Δω as input to generate the reference voltage inverter which simplifies the selection of control parameters.

Fig.7 Secondary frequency modulation process IV SIMULATION AND EXPERIMENT A. Energy Simulation Model In order to validate the proposed control strategy, a microgrid shown in Fig. 8 is considered for simulation. The system consists of loads (L1toL3)and DGs based with an inverter as the front end (DG1, DG2). The details of rating of machines, loads, droop constants of inverters, and synchronous machines are given in Tables I–V.

Fig.8 Simulation model of power grid Tab.1 The main parameters of the system Parameter DG1 DG2 Capacity（kvar） 50 25 DC Voltage (V) 800 800 Filter Inductance L (mh) 0.6 1.2 Filter Capacitance (μF) 1500 800 Tab. 2 Load Parameters Load P/kW Q/kvar L1 20 15 L2 10 7.5 L3 20 15 Tab. 3 Line parameters Line Impedance R/Ω Line Reactance x/Ω

          0.097                              0.213
          0.097                              0.213

Tab. 4 Primary frequency parameters Parameters DG1 DG2 D 5500 3750 km (rad/s)/(N.m) 1.35×10-5 0.625×10-5 kn (rad/s)/(N.m) 0.5 0.85

  J （kg.m2）         700                    400 

Tab. 5 Secondary frequency regulation parameters Control Parameters DG1 DG2

  k (rad/s)/kvar             12                  8.5
kT (N.m)/kvar        30                  19

k1 (rad/s)/kvar 0.5 0.25 k2 (rad/s)/kvar 20 15

Fig.9 Overall system control block diagram Overall control block diagram is shown in Fig. 9. Vdc is the inverter dc voltage and xi，Li and Ci (i=a,b,c) are line impedance, the filter inductance and capacitance respectively. 28. In this paper, the proposed technique is tested in three different scenarios when the microgrid is islanded (unintentional) from the main grid. A. Case A: Microgrid Islanded While Exporting Power In this case, the microgrid is islanded at 1 s while DG1 and DG2 exporting 30KWand 20kw power to the grid and L1,L2 is running in the system. The frequency and voltage of microgrid follow grid values before islanding. After islanding, the sources in the island must reduce their power quickly to cater to the remaining load. The simulation of two active power reference value of DG is every DG’s active rated capacity and the reference frequency is 50 HZ.

Fig.10 Frequency regulation of Example 1 case

Fig.11 DG output active power of Example 1

 As shown in Fig. 10, when the microgrid is islanded, the traditional droop control leads the frequency to increase up to 50.45Hz before it slowly reaches a new steady state  at 50 Hz. The sharing of loads by various generators is shown in Fig. 11(a),(b) . DG1and DG2 reduce more power transiently with the modified droop control compared to traditional droop control.  It can be seen that the output active power of DG1 and DG2 is 25 kW and 12.5 kW respectively and  it that can be carried out that DGs output the reasonable distribution of power in accordance with the capacity .Virtual inertia of the system is reduced slowly to zero by decreasing k1in four

steps at predefined instants (t=3,4.3,6.2and7.7s) so that the frequency slowly reaches a new steady state value. B. Case B: Disturbance in Islanded Microgrid In order to validate the proposed scheme in an islanded microgrid, a large disturbance is created by add L3 into the microgrid at 1s. DG1 supplies 20KW of power and DG2 supplIes 10KW to the microgrid prior to 1s. Before 1s, L1 and L2 are running in the system. Fig. 12 shows the improvement in frequency profile (during the transient state) at PCC terminals using modified droop control for the DGs. Subsequent to disturbance, the traditional droop control Leads microgrid frequency from 50Hz fallup to 49.6HZ before it acquires the new steady state value of 49.98 Hz. The microgrid is operating at 50 Hz before the disturbance. the response time is 4.5 s . This may result in less load shedding and unwanted triggering of synchronous generators. By using modified droop control, the frequency peak under-shoot is now limited to 49.35 Hz before it reaches its steady-state value of 50 Hz. frequency adjustment time is 7.8 s; The sharing of loads by DGs is shown in Figs. 11(a)(b). Post DG1 islanding, DG2 contributes more power transiently, with modified droop control compared to traditional droop control. In all three cases, inverters contribute more to load change transiently with reduced frequency deviation. As a result, they contribute toward better transient response of the microgrid. Virtual inertia of the system is reduced slowly to zero by decreasing at predefined instants, so that frequency slowly reaches the new steady-state value.

        Fig.12 Frequency regulation in Example 2 cases

Fig.13 Output active power of Example 2 .C. Case C: Secondary Frequency Regulation transient adjustment

   In order to reflect the secondary frequency modulation control process of this paper more clearly, case3 is proposed. The disturbance is created by cutting L3 out of the microgrid at 1s.Before 1s L1, L2 and L3 are all running in the system. The secondary frequency regulation uses the proposed method and the traditional secondary frequency modulation method respectively.

Fig.14 Secondary frequency regulation simulation comparison

As shown in Fig.14: the method use the primary frequency control from 1s to 3s . After 3s, the secondary frequency regulation  joins in the system. The method of secondary frequency regulation is divided into two stages. The response time is 2.5 s and the steady state frequency is 50 hz. The steady state frequency is 49.7 Hz which use traditional secondary frequency regulation. VSG use Q/ω to coordinate with Q/T in the proposed secondary frequency regulation.  After the instantaneous frequency reducing, the frequency after primary frequency regulation is 46.69 Hz, secondary frequency regulation increases gradually adjust the DG output power and   superimposed on output power of primary frequency regulation. It can be seen that, secondary frequency regulation divide the frequency adjustment process into five primary frequency response phase which makes the    grid frequency adjustment level off.

B. EXPERIMENT The hardware prototype of Fig. 9 has been implemented for experimental verification. The control algorithms have been programmed using a universal DSP control board developed in laboratory. The system was tested under the following conditions to experimentally verify the simulation results: 1) switching frequency f:10kHz; 2) output frequency: 50 Hz; 3) dead time: 3 μs; 4) filter inductor Li: 2 mH; 5) filter capacitorCf:5 μF; 6) output capacity: 6 KW

The experiment uses the inverter output active power and output to verify  the control method after the microgrid disturbance because the frequency offset observation is not obvious in the experiment,

Fig.15 Hardware experiment waveform Fig. 15 shows inverter output frequency, active power and current changes after the disturbance. It can be seen from Fig.15(a) that the frequency is 49.97 Hz after frequency regulation of the proposed control and the inverter output frequency is 48.85 Hz after the frequency regulation of traditional P/f droop control. From Fig15(b) : we can know that the disturbance has almost no impact on the system during the process of the proposed control and the output instantaneous active power of the inverter is 560 W. While the output active power of the inverter is decreased to 450 w during the process of the traditional P/f control. Fig.15 (c) shows that : the inverter output current in the proposed control strategy has smaller ripple than traditional P/f control. Experimental results show that proposed strategy has a robust performance where destabilizing interaction dynamics can be mitigated at different loading conditions of the VSR. V. CONCLUSION

 A new control technique to improve the transient response in microgrid in islanded conditions is proposed in this paper. The proposed control technique is applied to inverter-based DGs. The droop gain of the inverter is modified based on the observed by the inverter during transition. The results show that by employing modified droop control in inverters allows them to take the bulk of the power change transiently, at reduced frequency deviations. By adding virtual inertia as a function of , it is possible to reduce unwanted triggering of sources out of synchronism and to reduce load shedding in an islanded microgrid. The control can be designed to ensure microgrid operation within prescribed frequency limits, also making sure that the inverter is not overloaded.

The proof of stability in Sections II–IV that result in the generalized equation of ( 9) has been based on several assumptions. The assumptions will be summarized next with a brief justification of their validity for microgrid in general. 1) On the basis of the VSG model, the electrical angular velocity deviation Δω and virtual damping coefficient D is the frequency modulation control parameters which reduce the impact of the instantaneous frequency modulation on the microgrid and delay the frequency variation. The proposed strategy guarantee the stability of the microgrid frequency, make the microgrid use different deviation factor under different frequency deviation.. 2) The Q-ω and Q/T control coordinate together as the secondary frequency regulation and the secondary frequency modulation can be divided into two stages, and its principle is analyzed. And this module replaces the voltage current inner loop control link in the traditional P/f control that simplifies the control module. 3) Simulation results have been presented to show the stability of the microgrid for varying droop control gains. Experimental results have been presented to show the stable operation of the microgrid.