The Improved Control Method of Parallel Microgrid Inverters

The parallel of inverters is inevitable in the operation of distributed generation with a Microgrid. However, due to the difference in line impedance between each parallel inverter and the public AC bus in the microgrid, the m available control method is insufficient to overcome the disadvantages such as unbalancing distribution of power, large circulating current, and poor dynamic characteristics, etc., especially when the line impedance difference is large. To conquer the above problems, the paper proposed an improved droop control strategy, in which a differential module is adapted to the droop control to improve the dynamic response. Further, a modified adaptive virtual resistance is proposed, so that the system can maintain high response speed, high stability, and robustness. These can effectively benefit power sharing and circulation suppression of parallel inverters while ensuring excellent dynamic characteristics of the system. Finally, the effectiveness of the improved control method is verified by the simulation results.


Introduction
Due to the great pressure of environmental protection and energy shortage, Microgrid composed of distributed power generation has becomes the focus of research and development all over the world.Generally, DGs are connected to the microgrid bus through inverter interfaces, and it is obvious that parallel operation of inverters is inevitable.Therefore, the related control technology of parallel inverters determines whether the system can operate stably [1][2] .
Due to the reasons such as that DG inverters may spread out in a wide area, the impedances of transmission lines that connect different DG inverters and the point of common coupling (PCC) may be different.It may result in inaccurate power sharing and large circulating current between parallel inverters.Also, if the load of the individual inverters varies greatly, it may cause an overload of an inverter and poor dynamic characteristics.So the appropriate control methods must be used to achieve satisfactory characteristics and balance power sharing.Now, several control methods are available for inverters' parallel operation [1][3] [4] .Among these methods, though centralized control, master-slave control, and decentralized logic methods are simple and accurate, they all need to use interconnected communication lines for information exchange, which increases the system's cost and reduces the system's reliability.The droop control [5] is the most widely recognized control procedure utilized in parallel DGs because it has good redundancy, high reliability, and good dynamic characteristics.The droop control technique is based on locally measured information is no information loss of communication means.The conventional droop control adjusts its output power through the frequency and voltage of the DG unit to share load according to its respective capacity [6] .However, the conventional droop control technique will rely on the line impedances and load characteristics, consequently, the power will be not evenly distributed and the dynamic performance will be poor.
To eliminate or alleviate the influences, modifications to the conventional droop control are necessary.The main methods are proposed through improved power and frequency control under power decoupling control [7] , droop coefficient improvement [8], and impedance modifications control [9]   .Impedance control is divided into passive [10] and active.Passive is simple and easy, but the economy is poor.Active virtual impedance has a good economy [11] .The droop coefficient control method can realize accurate power distribution and consider power quality.The improved droop control has achieved good results in power sharing and circulating currents.
However, the problem of poor dynamic response, especially when the difference in line impedance is large, has not been well overcome [12] .Since the switching of inverter and load occurs at any time because of the volatility of new energy, it is very important to maintain the good dynamic performance of DGs composed of distributed generation.Therefore, a modified droop control method is proposed in this paper.The differential link is designed in the droop control to modify the dynamic response.This modification can improve the response speed of the control system but may reduce the stability of the system to a certain extent [13] .Therefore, the improved adaptive virtual resistance of the differential term is designed.The improved adaptive virtual resistance strategy combined with the modified droop control can maintain high response characteristics, excellent power sharing, and good circulation suppression.

Parallel operation system of inverters
The investigated parallel operation inverters for distributed generation are shown in Fig. 1.Each inverter circuit is composed of a pulse width modulation (PWM) inverter and an LC filter.L1, L2, L3, C1, C2, and C3 are the filter inductance and filter capacitance of each DG unit respectively.Z1, Z2, and Z3 are the impedance of each line respectively, the distributed power supply is connected to the public bus and connected to the main power grid by the grid connection switch.ZL1 and ZL2 are different public loads.
Two parallel inverter branches as an example, principles can be derived from the equivalent circuit depicted in Fig. 2, in which the two inverters are for simplicity replaced by voltage sources (U1, U2) with phase angles 1 and 2.Load is represented by impedance ZL and voltage Upcc.R1, R2, X1, and X2 are equivalent resistance and reactance between the inverter and load.
Fig. 1 The parallel structure of inverters for microgrid Fig.

The conventional droop control
When inverter branch impedance is inductive, especially Xi≫Ri, i0,i=90.Thus, the active and reactive power supplied by the inverter to the common bus can be expressed as formulas (1) and (2) [3] .
( ) Equations ( 1) and (2) indicate that the value of active power Pi is predominately affected by the phase of the inverter output voltage i.And yet the value of reactive power Qi is related to the value of the magnitude of this voltage (Ui).The droop control theory is expressed by Equations ( 3) and (4) [3] .
where mi is the droop coefficient of frequency; ni is the droop coefficient of voltage.fi is the frequency of the ith inverter; fN is the nominal operating frequency; Ui is the voltage of the ith inverter; UN is the nominal operating voltage of the inverter.In this paper, mi is taken as 510 -5 , and ni is 610 -4 .

Generation of circulating current
From the circuit in Fig. 2, the current flow between two parallel branches is given by Equations ( 5) and ( 6).
The expression of circulating current iC is 2 1 . So, a small difference in the line impedance and the voltage amplitude and its phase.

Modelling and stability analysis of the proposed control method
To improve the dynamic response characteristics of the parallel inverter, especially when the line impedance difference is large, the proposed improved control method in this paper is shown in Fig. 3.

Modification of droop control
In droop control, power calculation usually needs to go through a low-pass filter, and the bandwidth of the filter is much lower than the closed-loop bandwidth of the inverter.When conventional droop control is adopted, the transient response of the system is comprehensively affected by the power calculation method, low-pass filter parameters, droop coefficient, line impedance, and other factors.
To improve the dynamic response, an actual differential link is added to the control equation.The improved droop control is shown in Equation ( 7).
where Tpi1 is the active differential time constant, Tpi2 is the active lag time constant, Tqi1 is the reactive differential time constant, and Tqi2 is the reactive lag time constant.The control method uses Tpi1, Tpi2, Tqi1, and Tqi2 of differential links to maintain stability and good dynamic characteristics.

Small signal model of modified droop control
According to Equations ( 3) and ( 4), the small signal disturbance is carried out at the working balance point Ui.The control structure block diagram of frequency droop and voltage droop can be obtained, as shown in Fig. 4. Where: ∆fN and ∆UN are set to the constant value, so its variation is ignored.Because the loop contains a low-pass filter, the bandwidth of the outer voltage loop and the inner current loop is higher than that of the low-pass filter.Then the dynamics of the inner loop can be ignored.

Fig. 4 Modified droop control block diagram
According to Fig. 4, the closed-loop transfer functions of active power versus ΔP/Δf and reactive power versus ΔQ/ΔU can be obtained.
( ) ( ) In Equations ( 8) and ( 9), ( ) ) Thus, the characteristic equations can be expressed as Equations (10) and (11).5(a), when the active differential time constant Tp11 changes from 0 to , the root locus is on the left side of the imaginary axis.It means that a change in the Tp11 value will not cause system instability.In the range of 0Tp113.410 - , the three roots are always on the real axis; In the range of 3.410 -8 Tp112.210 - , with the increase of Tp11, a pair of real roots will quickly move away from the real axis and become a pair of conjugate complex roots, which indicates that the system oscillation increases.The other real root will always be on the real axis and gradually approach the virtual axis, thus the dynamic performance is enhanced.Compromise stability and dynamic performance.The value of Tp11 is 110 -6 .
According to Fig. 5(b), when the active lag time constant Tp12 changes from 0 to , the root locus is always on the left side of the imaginary axis, which indicates that the change of the Tp12 value will not cause system instability.In the range of Tp12 = 0, there are only two real roots.In the range of 0Tp123.010 - , with the increase of Tp12, the three roots are always on the real axis; In the range of 3.010 -3 Tp1210.9,with the increase of Tp12, a pair of real roots first quickly move away from the real axis, become a pair of conjugate complex roots, and then quickly approach the real axis.The trajectory forms an ellipse, the system oscillation increases and then decreases, and the other real root will start on the real axis and gradually approach the imaginary axis, which means the dynamic performance is enhanced; When 10.9Tp12<, three roots are always on the real axis.Compromising stability and dynamic performance, the value of Tp12 is set to 0.01.
Similarly, Tq11 is set as 610 -4 and Tq12 is set as 0.01.The parameters of the parallel inverter for solving the problem are shown in Table 1.

Improved adaptive virtual impedance control
For the unreasonable power distribution caused by the difference of equivalent line impedance [1][2], [9] , a modified adaptive virtual impedance method is proposed.In the extreme case that the line impedance varies greatly, the reactive power sharing of the parallel inverter becomes significantly worse and the circulating current increases significantly.To further improve the stability and accuracy of power-sharing in the parallel inverter, a differential term is added to the adaptive virtual impedance.The improved control equation is obtained as follows.
=   + ( where XVi is the initial value of traditional virtual impedance, Qi is the output reactive power value calculated by collecting its output current and voltage for i DG units, and Qset is the set value of reactive power distributed according to the proportion of DG unit capacity.T1 is the differential time constant, and T2 is the lag time constant.

Small signal model of improved adaptive virtual impedance control
The linearized model equation after a small signal disturbance is obtained is as follows.

Stability analysis and parameter setting of improved adaptive virtual impedance
The reasonable selection of differential time constant T1 and lag time constant T2 can improve the dynamic characteristics of an adaptive virtual impedance loop and maintain its stable operation.The root locus diagram of the characteristic root is drawn according to Equation (24), and the design of these two parameters can be discussed.The adaptive virtual impedance loop of the parallel system is a typical fifth-order system.According to Fig. 6(a), in the range of 4.5T14.510 - , with the increase of T1 in this range, the real part of the characteristic root is less than 0, which proves that the system can operate stably in this range.As T1 continues to increase, in the range of T14.510 -3 (As shown in Fig. 6(a), the direction of T1 increase), the real part of two characteristic roots in the system characteristic equation is greater than 0, and the system is unstable.Therefore, to keep the system from losing stability, the differential time constant T1 cannot be too large.In this paper, T1 is selected as 410 -4 .
Similarly, T2 is selected as 0.01 according to Fig. 6(b).The parameters of the parallel inverter for solving the eigenvalue distribution are shown in Table 2.

Simulation
To verify the feasibility of the proposed control scheme, the simulation is carried out under Matlab/Simulink.To verify the feasibility of the proposed improved control strategy scheme for parallel inverters, two inverters with the same capacity are investigated which operate in parallel with the linear load.Simulations of three cases are carried out: 1) Comparison of the conventional control method with the virtual impedance droop control method.2) Comparison of the improved control method in this paper with the method of virtual impedance droop control on power sharing and dynamic performance; 3) Verification of the feasibility of the improved method on the dynamic performance with large impedance difference.A simulation of the other parameters is in Table 3.
Table 3  Fig.7 and 8 show that the circulating current is large at startup under the adaptive virtual impedance, which is caused by the unequal line impedance of two inverters.But it is effectively suppressed within 0.02 s, which is only about 1/6 of that in the conventional control.So the adaptive virtual impedance control has the advantage of fast and effective suppression of circulating current.(a) Active power-sharing (b) Reactive power-sharing Fig. 9 Power sharing of two inverters (∆line=0.01Ω) with the adaptive virtual impedance Fig. 9 shows that when the line impedance difference is small (∆line=0.01Ω), the adaptive virtual impedance droop control is adopted.In the process of multiple load input and removal (including startup), the output power of the two inverters can be switched into the steady state within 0.05 s, showing a good response speed.The switching process is smooth and the waveform is good, which indicates the good dynamic characteristics of the system when the line impedance difference is small.
The output power of the two inverters maintains good power-sharing characteristics.In particular, the active power, even in the process of load switching and starting, still maintains the accurate powersharing characteristic, and the sharing error is about 0.2%.The reactive power-sharing effect is also good, and the steady-state sharing error is about 1.5%.
( From Figs. 10 and 11, when the line impedance difference is large (∆line=0.1 Ω), the adaptive virtual impedance droop control, and the dynamic performance of the system is very poor in the process of multiple load input and removal (including startup).12 and 13 indicate that the improved droop control improves the dynamic characteristic, active and reactive power sharing, and circulating current suppression, it is because the difference of line impedance is compensated, and the differential term is added to suppress the overshoot in the process of virtual impedance adjustment.Therefore, the dynamic performance of the system and its robustness are both improved with the proposed control strategy.

Conclusions
Aiming at the problems of power sharing and circulating current in parallel operation inverters, especially the poor dynamic characteristics when the line impedance difference is large, an improved the control method is proposed: (1) The droop control is modified to increase the dynamic characteristic and improve the response speed of the system.
(2) The modified adaptive virtual impedance is designed to compensate for the difference in line impedance.The differential term is added to suppress the overshoot in the process of virtual impedance regulation, which significantly modifies the dynamic performance and the robustness of the control method.
(3) the feasibility of the improved method is verified by the results of the simulation.

3 . 1 . 2 Fig. 5
Fig.5Root locus variation diagram of P-f droop control From Fig.5(a), when the active differential time constant Tp11 changes from 0 to , the root locus is on the left side of the imaginary axis.It means that a change in the Tp11 value will not cause system instability.In the range of 0Tp113.410 - , the three roots are always on the real axis; In the range of 3.410 -8 Tp112.210 - , with the increase of Tp11, a pair of real roots will quickly move away from the real axis and become a pair of conjugate complex roots, which indicates that the system oscillation increases.The other real root will always be on the real axis and gradually approach the virtual axis,

Fig. 6
Fig. 6 Root locus variation diagram of improved adaptive virtual impedance control

( 2 )
Parallel operation of starting inverter and load input and removal (∆line=0.01Ω)

Fig. 10 4 (
Fig.9Power sharing of two inverters (∆line=0.01Ω) with the adaptive virtual impedance Fig.9shows that when the line impedance difference is small (∆line=0.01Ω), the adaptive virtual impedance droop control is adopted.In the process of multiple load input and removal (including startup), the output power of the two inverters can be switched into the steady state within 0.05 s, showing a good response speed.The switching process is smooth and the waveform is good, which indicates the good dynamic characteristics of the system when the line impedance difference is small.The output power of the two inverters maintains good power-sharing characteristics.In particular, the active power, even in the process of load switching and starting, still maintains the accurate powersharing characteristic, and the sharing error is about 0.2%.The reactive power-sharing effect is also good, and the steady-state sharing error is about 1.5%.(3)Increase the impedance difference of lines (∆line=0.1 Ω)

4. 2 Fig. 12
Fig. 12 Circulating current under adaptive improved control at the start

Table 1 .
Parameters of inverter with LC

Table 2 .
Parameters of inverter with LC . Parameters of simulation