Reverse droop control strategy with virtual resistance for low - voltage microgrid with multiple distributed generation sources

: In the island operation mode of the microgrid, the rated capacity and feeder impedance of each parallel distributed generation inverter are di ﬀ erent and the output power is di ﬃ cult to be reasonably distributed when the tra - ditional droop control strategy is adopted, which reduces the stability of the system. In order to solve this problem, the power transmission characteristics of low - voltage microgrid are analyzed and the leading factors a ﬀ ecting the reasonable power distribution are obtained. A control strategy of virtual resistor is proposed and the di ﬀ erence between the actual output power and the expected output power is used to control the power compensation coe ﬃ cient and proportional integration to adjust the reference voltage of each DG inverter. The control strategy can automatically adjust the change in the output power of the distributed power supply in real time, adjust the voltage change caused by the line impedance mismatch in time, improve the power quality, reduce the system circulation, and realize the rea - sonable distribution of power. Finally, the simulation model veri ﬁ es the e ﬀ ectiveness of the strategy.


Introduction
Microgrids are small power distribution systems which comprise various micro sources, energy storage systems, energy conversion devices, loads, and control and protection systems. The microgrid itself is a self-contained system capable of self-control, self-protection, and selfmanagement. It can also be connected to the utility grid as a whole through the point of common coupling, operating in islanding or grid-connected mode according to the need of grid system and user loads [1,2].
As the name implies, peer-to-peer control means that every DG in the microgrid system shares the same control position. Each DG can exert control based on local measurements instead of communications equipment [3]. Droop control method is usually adopted in each DG, which can share the random fluctuation of load and energy automatically. It can realize microgrids' plug and play at the same time. When the microgrid's operation mode is switched under droop control, there is no need to change the control method [4]. The conventional droop control method uses the P-f and Q-V characteristic curves to emulate the external characteristic of the synchronous motor in the utility grid [5]. So that DGs adjust the amplitude and frequency of output voltage according to their own droop control curves in order to achieve rational allocation of power.
The virtual impedance is introduced to the conditional droop control for better power decoupling control [6,7]. However, the effect of virtual impedance on the output voltage drop is not considered and the reactive power distribution issues with the unbalanced line impedance have not been solved in this work. As for the shortcomings of the conditional virtual impedance method, a virtual negative impedance method was proposed to make the total output impedance purely inductive, offsetting the resistive component of impedance and restraining the system current circulation, but without enhancements of voltage quality and power distribution accuracy [8]. In another approach [9], dynamic virtual impedance is adopted to makes it change with the load current and voltage drop, thus enhancing the power quality. But the unbalanced line impedance has been neglected. In order to reduce the reactive power sharing errors in conditional droop control, a virtual impedance optimization method based on the minimization of system global reactive power sharing error was proposed in ref. [10]. Nevertheless, the optimization calculation of the power sharing error function is complicated and the effect of virtual impedance on the output voltage is not considered in this work. In ref. [11], the output voltage is regulated by the cooperation of coarse and fine adjustment to accommodate changes in load power, resulting in good sharing of the load power and better power quality. However, the article does not consider the situation that the rated capacities of inverters are different.
The line impedance is predominantly resistive for low-voltage microgrid [12], where reverse droop control strategy is more suitable. Reverse droop control strategy, which is very similar to the conditional droop control, utilizing the droop characteristics of active power-voltage (P-V) and reactive power-frequency (Q-f), when the line impedance is resistive [13], is easy to implement with low loss and small frequency variation [14]. Similarly, this control method also has an active power sharing problem when the line impedance is unbalanced [15]. In ref. [16], virtual impedance is added on the basis of droop control so that the total output impedance is matched with the rated capacity of the inverter to improve the power distribution. However, the effect of the virtual impedance on the output voltage needs to be reduced by modifying the droop characteristic curve [17].
As for the low-voltage microgrid system with multiple micro sources which are in different rated capacities, an improved reverse droop control strategy based on the introduction of virtual impedance was proposed, which can achieve a reasonable sharing of power according to DGs' capacities and guarantee a certain output power quality in the condition of unbalanced line impedances [18,19]. On the basis of reverse droop control, the feedback compensation term of line impedance's voltage drop is introduced, which is essentially a kind of virtual impedance methods [20,21]. Finally, a specific microgrid system is constructed and simulated in Matlab/Simulink platform in order to verify the effectiveness of the proposed control strategy.

Reverse droop control design
The voltage source distributed generation inverter is an important way to connect the distributed power supply and the power grid in the microgrid. The regulation characteristics of the DG inverter are crucial for the power distribution between the distributed generation sources. The DG inverter with droop control can adjust its own frequency and power according to the measured active and reactive powers [22].
The following is an overview of the basics of droop control using Figure 1 to analyze the output power of two DG inverters operating in parallel. The sum of the line and output impedance of the DG inverter 1 and DG inverter 2 is given as follows [23,24]: The load equivalent impedance is given by The equivalent circuit impedance Z n 1, 2 n ( ) = is given by P n is the output active power of DG inverter n; Q n is the output reactive power of DG inverter n; and i n ⁎ is the output current conjugate. When the impedance of the DG inverter system is inductive θ 90 = ∘ , the active and reactive powers of the DG inverter output, respectively, are as follows: When the impedance of the DG inverter system is resistive θ 0 = ∘ , the active and reactive powers of the DG inverter output, respectively, are as follows: In the case of low-voltage resistive transmission lines, the system power transmission equations (6) and (7) that are introduced in the absence of line inductance indicate that at this time, the active power output by the distributed system is only related to the voltage amplitude difference; reactive power is only related to the phase angle difference. In this way, the basic principle of reverse droop control is obtained. The active power output from the inverter is adjusted to control the voltage amplitude and the reactive power output from the inverter is adjusted to control the frequency. In this way, the reverse droop control strategy can be derived [25,26] as follows: where f ref is the nominal frequency of the system and f is the actual frequency of the system; V ref is the rated voltage of the system and V is the actual output voltage of the system. Q ref is the system rated reactive power and Q is the actual output reactive power; m PV is the reverse droop (P-V) coefficient and n Qf is the reverse (Q-f) droop coefficient. Figure 2 shows the droop characteristics of reverse droop control [11].

Block diagram of reverse droop control
Microgrid as a whole is composed of a voltage source inverter using reverse droop control as shown in Figure 3. Then assuming that the DG inverter dc bus voltage V dc essentially unchanged, L f1 and L f2 are three phase filter inductor, r 1 and r 2 are filter inductor equivalent resistance, and C f1 and C f2 are three phase filter capacitor.
Comprehensive equivalent line impedance of the transmission line of two DG inverters is expressed as Z 1 = R 1 + jX 1 and Z 2 = R 2 + jX 2 . PCC represents a common connection point for DG inverters. It is necessary to provide voltage and frequency support for microgrid operation and distribute load reasonably [11].
Under the condition of no communication, the power distribution is achieved by reverse droop control to regulate the parallel system of multiple DG inverters. The principle is as follows: Each inverting DG source detects its own output power and compares it with the load power and then obtains the reference value of the output voltage amplitude and frequency according to the droop

Reference Generator
Voltage and current dual loop control characteristics, so that the voltage amplitude and frequency are continuously adjusted in a loop and finally each DG inverter is realized. The DG source output power is consistent with the load power [26,27] When the distributed inverter power supply with different capacity is running in parallel, it is necessary to realize the exact load sharing according to the rated capacity, and the condition that the droop coefficient of each inverter is inversely proportional to the rated capacity, namely, equations (10) and (11).
The reverse droop control strategy, the conditions for accurately distributing the active and reactive powers according to the rated capacity ratio are satisfied by the equations (12), (13), and (14), as follows: Equations (12), (13), and (14) show that the parallel operation of inverters with different capacities can accurately share the load according to the rated capacity ratio and the following conditions must be met at the same time [25]: 1. The reference voltage and the set value of the reference voltage under the rated power of each inverter in the droop controller are the same; 2. The droop coefficient of each inverter is inversely proportional to its rated capacity; 3. The transmission impedance of the inverter to the load is inversely proportional to the rated capacity of the inverter; 4. The amplitude and phase of the output voltage of each inverter in parallel operation should be consistent.
The line impedance of each DG inverter unit to the common bus is also uncertain. It is related to its geographical location and it is difficult to meet the condition that the line impedance is inversely proportional to the capacity.
Therefore, according to the reverse droop control method, it is very difficult to realize that the DG inverter can share the load accurately according to the rated proportion and the application in the distributed generation system has certain limitation. So, reverse droop control method has to be improved.

Virtual resistance
Decoupling the output power requires knowing exactly the information of the output impedance and requires real-time on-line impedance measurement. This technology is still under research and is not mature enough. Therefore, the output impedance of the DG inverter is altered using virtual resistance method as shown in Figure 4 [25,27].
The reverse droop control strategy based on virtual resistance includes three nested loops.
The inner loop is a dual loop consisting of current and voltage loop. The intermediate link introduces a virtual resistance, forcing the equivalent output impedance of the DG inverter to achieve better power sharing. The outer loop is a power loop, where active and reactive powers are calculated. When the load is suddenly changed, the voltage amplitude and frequency are adjusted to obtain a good power sharing effect. This method can achieve accurate power sharing, has better dynamic modification performance, and is suitable for resistive line impedance conditions [15,28].
Virtual resistor is expressed as follows: If the line impedance is resistive, virtual resistor is added the control loop of reverse (P-V/Q-f) droop control to improve the power decoupling effect. Impedance angle at 50 Hz is 1.9 ∘ as shown in the Figure 5. The parallel inverter output impedance tend to be more resistive, which has a major role in improving the power sharing.

Simulation results
In order to verify the feasibility of the direct and reverse droop control, simulation model of DG inverter is built in Matlab/Simulink and parameters are shown in appendix.
Initially direct droop control is applied to the parallel DG inverters and output power of parallel inverters does not reach a given proportional load sharing, because of the poor decoupling of power as shown in Figures 6 and 7. When the line impedance is resistive, direct droop control cannot realize the equalization of active and reactive powers.
The parallel inverter voltage amplitude drop is significantly more compared to the given rated voltage amplitude of 311 V and frequency variation in parallel inverters is more than ± 0.6 Hz compared with rate value of frequency 50 Hz. So, when the line impedance is resistive with direct droop control, frequency accuracy is            reduced, the voltage amplitude drop rate exceeds the specified range as shown in Figures 8 and 9. Now with the same parameters, reverse droop control is applied to each DG inverter and the inverters are able to share the load of active power P 1 = 588 W and P 2 = 586 W as shown in Figure 10 and reactive power of Q 1 = 50 VAR and Q 2 = 48 VAR as shown in Figure 11. Frequency and voltage amplitude variations in DG inverters have a small deviation, frequency fluctuation is not greater than 1% as shown in Figure 12 and the voltage amplitude has a slight decline, V 1 = 308.2 V and V 2 = 307.6 V, which is not greater than 5% as shown in Figure 13.
Reverse droop control is applied to each DG inverter and they are able to share the load of active power P 1 = 588 W and P 2 = 586 W as shown in Figure 14 and reactive power of Q 1 = 50 VAR and Q 2 = 48 VAR as shown in Figure 15 and at load change at 0.5 s, P 1 = 974 W, P 2 = 970 W, Q 1 = 80 VAR, and Q 2 = 76 VAR.
Frequency and voltage amplitude variations in DG inverters have a small deviation, frequency fluctuation is not greater than 1% as shown in Figure 16 and voltage amplitude has a slight decline V 1 = 308.2 V and V 2 = 307.6 V which is not greater than 5% as shown in Figure 17.

Conclusion
In low-voltage microgrids, the transmission line impedance is resistive, making the traditional reverse droop control unable to be used normally and the power coupling between active and reactive powers cannot achieve proportional load distribution. Based on the transmission characteristics, the difference between the microgrid and traditional grid droop control is analyzed, and the reverse droop control suitable for low-voltage microgrid is used as the basis for this study. Aiming at the coupling problem of active and reactive powers in low-voltage microgrid, the virtual resistance method is proposed to realize the decoupling control of active and reactive powers. A virtual resistor strategy is used to eliminate the effect of line impedance differences on power distribution. The influence of different line impedances on the power distribution of DG inverters is simulated and the effectiveness of the scheme is verified.
Conflict of interest: Authors state no conflict of interest.