Transient power equalization control strategy of virtual synchronous generator in isolated island microgrid with heterogeneous power supply

In the parallel supply system of synchronous generator and virtual synchronous generator, the physical structure and control structure of the two kinds of power supply are quite different, and it is difficult to distribute the transient power of the two kinds of power supply evenly when the load changes abruptly. Especially in the case of sudden load increase, virtual synchronous generator bears too much load in the transient process because of its fast adjustment speed, and even causes short-term overload, which makes the capacity of virtual synchronous generator can not be fully utilized. In view of this problem, firstly, the mechanism of transient power uneven distribution of two heterogeneous power sources is explained from the differences of frequency modulation, voltage regulation and output impedance. Secondly, virtual speed regulation, virtual excitation and dynamic virtual impedance are added to the traditional virtual synchronous generator control to simulate the speed regulation characteristics and electromagnetic transient characteristics of the synchronous generator, so as to realize the transient and steady-state power equalization between heterogeneous power supplies when the virtual synchronous generator and the synchronous generator run in parallel. Thirdly, in order to ensure the fast dynamic response characteristics of the virtual synchronous generator in independent operation mode, the traditional virtual synchronous generator control algorithm is still maintained in independent operation mode, and the mode switching control link based on state tracking is designed to realize smooth switching between the two working modes. Finally, the hardware in loop experiment results based on RT-LAB show that the proposed control method can realize the transient and steady-state power equalization when the virtual synchronous generator and the synchronous generator operate in parallel, it can keep the fast voltage regulation and frequency modulation ability when the virtual synchronous generator operates independently, and can realize smooth switching between independent and parallel operation modes.

Parallel power supply of synchronous generator (SG) and inverter is widely used in various independent power systems 1,2 , such as island and remote mountain power supply system, ship power system and so on.Constant power control, constant voltage/frequency control, droop control, virtual synchronous generator (VSG) control are commonly used in inverters.Among them, constant power control does not participate in the voltage adjustment and frequency adjustment of the system, and is only suitable for the grid-connected operation of inverters 3 .Constant voltage/frequency inverter is usually used as the main control power supply of constant voltage and constant frequency in microgrid 4 , providing voltage reference and frequency support for independent microgrid.By simulating the primary frequency modulation and primary voltage regulation characteristics of SG, sag control can realize the active and reactive power equalization of multiple parallel inverters without interconnection lines [5][6][7][8] .VSG control is based on droop control, and the simulation of SG mechanical motion and electromagnetic relationship is added, which can solve the problem of insufficient inertia and damping of distributed generation.Since it was put forward, it has been widely concerned by scholars at home and abroad [9][10][11] .

Description of transient power inequality between VSG and SG
Introduction of VSG control principle.The VSG topology and control block diagram are shown in Fig. 1, where C, L and R are filter capacitor, bridge arm filter inductor and internal resistance respectively, L 1 and R 1 are the load side filter inductance and internal resistance, respectively.
In Fig. 1, ignoring the filter capacitor, the frequency domain transfer function of the VSG main circuit can be expressed as: According to the design principle of filter circuit, the filter circuit parameters in VSG main circuit are selected as L = 0.6mH, C = 80μF and R = 6 mΩ.The Bird diagram of impedance gain G z (s) and voltage gain G u (s) is shown in Fig. 2. As shown in Fig. 2a, the output impedance of VSG shows inductive characteristics in the fundamental and low-order harmonic frequency bands.Near the resonant frequency, the output impedance amplitude is amplified.It shows capacitive characteristics in high frequency band.As shown in Fig. 2b, the voltage gain of VSG is 1 in fundamental and low harmonic frequency bands.Near the resonant frequency, the amplitude of harmonic voltage is seriously amplified.In high frequency band, the amplitude of harmonic voltage decays rapidly.
Based on above analysis, the relationship between the fundamental component of VSG output voltage u o and its modulated signal e is described as follows: (1) where E ref is the amplitude of the modulated signal, and X is the equivalent reactance value of VSG output impedance G z (s) in fundamental frequency band.In summary, VSG equates the bridge arm voltage of grid-connected inverter to the excitation induced electromotive force of traditional synchronous generator stator winding.The impedance of filter circuit is equivalent to synchronous reactance of synchronous generator, and the filtered output voltage is equivalent to stator winding terminal voltage.
VSG control uses inverter to simulate the running characteristics of synchronous generator to provide the moment of inertia and damping needed for stable operation of the system, and has the functions of primary frequency modulation and voltage regulation, which is mainly composed of active power-frequency and reactive power-voltage control links.Active power-frequency link is used to simulate the primary frequency modulation (2)  and rotor motion equation of synchronous generator.In the standard value system, the rated capacity and rated voltage of inverter are taken as reference values, active power frequency droop characteristics and rotor motion equation are shown in (3).
where P n is the rated active power of VSG, K p is the active-frequency sag coefficient, P m and P e are the virtual mechanical power and the output active power of the virtual synchronous generator.When the number of pole pairs is 1, the electrical angular velocity ω of synchronous generator is its mechanical angular velocity.ω n is the rated angular velocity, ω b is the reference value of angular velocity.θ is the virtual rotor angle, H is the time constant of virtual inertia, D is the virtual damping coefficient.The reactive power-voltage control link mainly realizes reactive power-voltage sag control, and the output voltage amplitude command E ref is obtained according to the current output reactive power and the given sag relationship.
where E n is the rated voltage, K q is reactive power sag coefficient, Q n is the rated reactive power of VSG, Q e is the reactive power of the VSG output.The voltage amplitude U m feedback from the filter capacitor is introduced, and the internal potential E is obtained after PI link control, so that the VSG output voltage can quickly track the voltage command.
Synchronous generator control and characteristics.Generator control includes prime mover governor (GOV) and automatic voltage regulator (AVR).For the convenience of analysis, the GOV and AVR of synchronous generators are simplified by single closed-loop PI control, and the prime mover and its speed regulation characteristics and exciter dynamic characteristics are equivalent by first-order inertia links respectively.The control block diagram is shown in Fig. 3, K ps and K qs are the active power-frequency and reactive power-voltage sag coefficients of synchronous generators respectively.T d is the time constant of the first order inertia link of the prime mover and its speed regulating mechanism.T e is the time constant of the first order inertia link of exciter.E f is the generator excitation voltage.P M is the input mechanical power of prime mover.

Transient power unevenness between VSG and SG.
The physical and control structures of the two kinds of power supply are different.When the load increase or decrease suddenly, VSG and SG can't realize transient power sharing equally.Build the simulation model as shown in Fig. 4, and the system equipment parameters are shown in Table 1 and Table 2.
Simulation conditions: initially, two VSG and two SG are put into operation at the same time with 600 + j450 kVA resistance inductance load; when t = 20 s, the resistive and inductive load of 600 + j450 kVA suddenly increases; when t = 30 s, the resistive and inductive load of 600 + j450 kVA is suddenly reduced.As shown in Fig. 5, the simulation results show that there is a large overshoot in the active and reactive power output of each VSG.This kind of current overshoot in transient process may lead to inverter overcurrent.If a part of inverter  www.nature.com/scientificreports/capacity is reserved to ensure that overcurrent hazard does not occur during transient loading, the inverter capacity will not be fully utilized.

Mechanism of uneven distribution of transient power
In order to suppress the output active power oscillation in grid-connected VSG without affecting the steadystate output power, an improved VSG control strategy based on transient electromagnetic power compensation is proposed in this section.
Equivalent circuit model.The output voltage frequency and amplitude of synchronous generator are determined by prime mover governor and excitation controller, respectively.The equivalent output impedance of synchronous generator is the sum of q-axis reactance X q and line impedance.During the transient process, q-axis is affected by the sub-transient process of damping winding, and the sub-transient reactance X′ q of q-axis transients rapidly to synchronous reactance X q .
In VSG control, voltage and current double closed-loop control has high bandwidth, and its output signal can track the given value quickly, so its influence is ignored in this paper.VSG is equivalent to a controlled voltage source with ideal AC power supply and impedance in series.Low-voltage transmission lines generally present resistivity, but inverter can make the output line present inductance by configuring isolation transformer and designing virtual impedance.www.nature.com/scientificreports/Establish the equivalent circuit of VSG and SG parallel power supply shown in Fig. 6.U VSG is the output phase voltage amplitude of reactive power-voltage control loop in VSG, θ VSG is the phase generated by virtual rotor motion equation in VSG control algorithm, X VSG is the sum of load side filter reactance, transmission line reactance and virtual reactance.U SG is the transient electric potential E ' q of the synchronous generator, θ SG is determined by the rotation angle of the synchronous generator, and X SG is the sum of the generator output reactance and the transmission line reactance.

Difference analysis of active power-frequency control link.
According to the equivalent circuit model shown in Fig. 6, the line impedance is purely inductive, ignoring the influence of voltage amplitude change, the output voltage of VSG and SG and the voltage amplitude of common point are considered to be constant.The expressions of VSG and SG output active power are derived and analyzed by small signal: where the subscript "k" represents VSG or SG, δ k is the phase difference between the output voltage of VSG or SG and the voltage of the common connection point, δ k = ∫(ω k -ω pcc )ω n dt, U pcc and ω pcc are the phase voltage amplitude and angular frequency of the common connection point respectively, K ck = 3U k U pcc cosδ k0 /2X k .
According to the control block diagram and (5), the transfer function relationship between VSG output power and angular frequency of common connection point is represented as (6), the transfer function relationship between SG output power and angular frequency of common connection point is described as (7).K P2p and K P2i in (7) are the proportional and integral parameters of PI2 module in Fig. 2 respectively; H SG and D SG are inertia time constant and damping coefficient of generator respectively.
The transfer functions between VSG and SG output power and load power in parallel operation can be obtained from ( 8) and ( 9), respectively.
Considering the relevant parameters of VSG 1 and SG 1 in Fig. 4, the influence of the difference of active power-frequency control links on transient active power distribution is mainly analyzed here.Considering the influence of output impedance on power distribution in the initial stage of transient process, X SG = Xʺ q + X l_SG1 .The step response of VSG and SG output power to load is shown in Fig. 7, VSG output power can respond to load changes quickly, resulting in VSG bearing most of the load during transient process.

Difference analysis of reactive power-voltage control link.
According to the third-order mathematical model of synchronous generator, the following relation can be obtained.
where T′ d0 is the d-axis transient open-circuit time constant, E fd is the stator excitation electric potential, E′ q is the q-axis transient electric potential, X d is the d-axis synchronous reactance of synchronous generator, X′ d is the d-axis transient reactance of synchronous generator.
Equation (10) shows that there is a first-order inertia link between SG transient electric potential E′ q and excitation voltage, which makes the output voltage unable to respond to the change of reactive load immediately, and armature reaction will also have an impact on excitation voltage regulation.In VSG control algorithm, the output variable E of reactive power-voltage control link is the output port voltage of inverter, which is equivalent to the amplitude of internal electric potential of VSG, and does not involve the simulation of electromagnetic transient process of excitation winding.In the parallel power supply system of VSG and SG, VSG can quickly respond to the change of reactive load and bear most reactive load in transient process.
Output impedance difference analysis.During the transient process, the equivalent output impedance of the synchronous generator transients quickly from the sub-transient reactance Xʺ q to the q-axis synchronous reactance X q .In the per unit system of synchronous generator, the value range of X q is 1.0 ~ 2.3, while the filter reactance of low-voltage inverter is generally 0.2 ~ 1, and the output impedance of VSG only needs to consider the filter reactance of load side.The output impedance of SG is much larger than that of VSG.The output impedance difference determines the power distribution in the initial power frequency periods of load mutation, and is approximately inversely proportional to the output impedance 22 , so VSG will bear more loads in the initial stage of load mutation.( 7) Step response of VSG and SG output power to active load.

Improved algorithm for transient power equalization
Improve control algorithm and process.To realize transient power equalization of VSG and SG parallel power supply system, virtual speed control, virtual excitation control and dynamic virtual impedance are introduced into the traditional VSG control algorithm during parallel operation.At the same time, in order to ensure the fast voltage regulation and frequency modulation ability of VSG when it runs independently, it switches to the traditional VSG algorithm when it runs independently.A mode switching control strategy based on state tracking is designed, which ensures that the input voltage reference values of frequency and voltage outer loop in the two modes are consistent at switching time, prevents the impact caused by sudden change of phase and voltage reference values during switching, and realizes smooth switching between independent and parallel operation modes.
The operation flow chart is shown in Fig. 8, and the improved control algorithm is shown in Fig. 9.When running independently, the switch S is set to "1".When receiving the networking instruction, if ω 2 = ω 1 and E′ q = E, all mode switching switches S are switched to "2", and the pre-synchronization control switch S 1 is closed at the same time, check whether the amplitude, phase and frequency of voltage on both sides of the grid meet the networking conditions, if the conditions are met, the closing operation is completed, and the pre-synchronization switch S 1 is disconnected.When receiving the separation instruction, if ω 2 = ω 1 and E′ q = E, all the switching switches S are switched to "1", and then the separation is performed.The following is a detailed introduction to each improved control link.
Improvement of active power-frequency control link.The improved active power-frequency control link is shown in Fig. 9a.When running independently, S is set to "1", and the active power-frequency control link keeps the traditional VSG control.When the network is running in parallel, S is set to "2", the dynamic response of the speed control link of prime mover and the equivalent inertia link of the speed control mechanism can be simulated.In steady-state operation, the output frequency and power of the two modes meet the droop relationship, and the output frequency values of positions "1"and "2" are the same, which can ensure that the phase before and after switching does not change abruptly.

Independent operation, S set "1"
Received networking instructions?

Networking conditions
The networking switch is on, and S1 is off www.nature.com/scientificreports/ The design principle of related parameters is as follows: In traditional VSG control, the virtual damping coefficient D affects the droop characteristics of the control, and 1/K p + D is the equivalent frequency-active droop coefficient.However, in the improved control method, the virtual damping coefficient D' no longer affects the droop control effect, and 1/K' p is the equivalent frequency-active droop coefficient, which determines the steadystate power sharing between VSG and SG, and should be matched with the active-frequency droop coefficient K ps in SG governor.T d is set with reference to the equivalent inertia time constant of synchronous generator speed regulating mechanism.The virtual inertia time constant H ' and virtual damping coefficient D ' are consistent with SG, so that the output power response characteristics of VSG are consistent with SG.

Improvement of reactive power-voltage control link. The improved reactive power-voltage link is
shown in Fig. 9b, and the reactive power-voltage sagging link maintains the relationship of (4) when operating independently and in parallel.Switching control is introduced into the inverter output voltage tracking control link after droop link.When running independently, all switching switches S are set to "1", keeping the traditional VSG control algorithm, and the output internal electrical potential amplitude instruction E is directly obtained by PI3 control link, and E is taken as the reference value of control variable E′ q , and E′ q virtual tracking E is realized by PI2 control link.During network operation, S is set to "2", VSG introduces the electromagnetic transient process of synchronous generator excitation winding through (9), E′ q is the output internal electrical potential amplitude of VSG in parallel operation mode, where T′ d0 , X d and X′ d are set with reference to the standard value parameters of parallel SG, E′ q is taken as the reference value of control variable E, and E virtual tracking E′ q is realized through PI3 control link.The experimental results of parallel operation of traditional VSG and SG network are shown in Fig. 11, the output active power, reactive power and output current of VSG have large overshoot.When t = 30 s, the load surge makes the maximum active power overshoot per unit reach 0.15 and the maximum reactive power overshoot per unit reach 0.21.
After adopting the improved control algorithm, the experimental results are shown in Fig. 12. Compare with the experimental results of the traditional VSG control algorithm in Fig. 11, the shock current of the system is decreased significantly, VSG and SG can better share the load in transient process, and the output power overshoot of VSG and SG is very small.At t = 15 s and t = 60 s, smooth switching between parallel operation and independent operation of heterogeneous power supply network can be realized.www.nature.com/scientificreports/If switching control is not designed and the algorithm with additional control link in parallel mode is still maintained when operating independently, the dynamic drop and rise of VSG frequency and the recovery time of frequency will be seriously affected.Figure 13 compares the frequency characteristics of VSG control algorithm with or without mode switching control under the conditions of sudden increase and sudden decrease of load in independent operation.The existence of additional links makes the dynamic overshoot of frequency reach 0.6Hz, and the frequency recovery time is about 2s.When switching to traditional VSG control, the frequency change has no overshoot, and the frequency recovery time is about 1.25s.It can be seen that the mode switching control not only ensure the fast dynamic response when VSG operates independently, but also realize transient power equalization between heterogeneous power sources when VSG operates in parallel with SG network.

Conclusion
Differences between traditional VSG and SG in speed regulation, excitation and output impedance result in uneven transient power distribution between VSG and SG in isolated island microgrid.Based on the analysis of uneven transient power distribution and considering the fast dynamic response characteristics of VSG in independent operation, an improved transient power equalization control method based on mode switching is proposed.By introducing virtual speed regulation, virtual excitation and dynamic virtual impedance algorithm, the transient power of VSG and SG can be equally distributed in heterogeneous power supply parallel operation mode.Maintain traditional VSG control in independent operation mode to provide fast voltage regulation and frequency modulation capability.Smooth switching control based on state tracking is designed between the two modes.Hardware-in-loop experiment results show that the improved control method can significantly improve the transient power distribution between virtual synchronous generator and synchronous generator, and can smoothly switch between independent and networked parallel operation modes.

Figure 1 .
Figure 1.Traditional VSG topology and control system structure.

Figure 2 .
Figure 2. Bird diagram of impedance gain G z (s) and voltage gain G u (s) of VSG.

Figure 3 .
Figure 3. Speed control and exception control block diagram of synchronous generator.

Figure 5 .Figure 6 .
Figure 5. Simulation results of load mutation in parallel operation of traditional VSG and SG.

Figure 7 .
Figure 7.Step response of VSG and SG output power to active load.

Figure 8 .
Figure 8. Operation process of improved control algorithm.

Figure 10 .Figure 11 .
Figure 10.Hardware in loop experience system based on RT-LAB.

Figure 12 .
Figure 12.Experimental results of parallel operation of improved VSG and SG.

Figure 13 .
Figure13.VSG independent running frequency dynamic feature with or without mode switching control.

Table 1 .
Virtual synchronous generator electronic and control parameters.

Table 2 .
Synchronous generator electronic and control parameters.