Virtual Impedance-based Decentralized Power Sharing Control of an Islanded AC Microgrid

The future of power systems depends on the microgrid (MG) which includes distribution generators utilizing Renewable Energy Resources (RERs) and storage facilities. Decentralized control techniques are more reliable and stable in comparison with centralized controlled techniques. In this paper, a decentralized control strategy is presented for an islanded AC MG system. The control strategy includes improved droop control and virtual impedance. Control strategy with PI controllers to control the voltage and current is implemented to two Voltage Source Inverter (VSI) distribution generation units connected in parallel through a Point of Common Coupling (PCC). Circulating current and power-sharing deviations caused by the mismatched line impedance were taken into account. The proposed control scheme was tested in MATLAB/Simulink. Power-sharing accuracy and circulating current suppression were obtained by implementing the proposed virtual impedancebased decentralized control strategy. Keywords-PI controller; decentralized control; droop control; virtual impedance


INTRODUCTION
Globally, power systems are often overburdened due to the excessive electricity usage. The inclusion of Renewable Energy Resources (RERs) in modern power systems is one of the most popular solutions to cope up with the electricity demand. More and more RERs are being added to the power systems which may cause many critical issues regarding control and management [1,2]. Microgrids (MGs) may face different challenges with different operating modes. In the islanded mode, power sharing according to the capacity of the inverterbased DG units connected in parallel, and combined with loads to form a complete system, is not accurate, whereas in the connected mode, the case is not same [3]. Voltage Source Inverters (VSIs) are solely responsible for voltage and frequency control in islanded MGs. Different kinds of issues may occur in isolated MG, for example voltage and frequency errors, line impedance mismatch and the consuquent production of circulating current [4,5]. When many DG units are operating in parallel in the same system, the overall impact of circulating currents could be very high and could damage the entire system. Unlike the traditional power systems, in which the circulating currents do not affect the system due to the large synchronous generators, in MGs even the presence of the smaller line impedance is considered to be a serious issue that needs to be handled carefully [6]. In the literature, virtual impedance is implemented, most of the times, in order to get  [11,12], the dependency of line impedance was eliminated by utilizing a method which can control droop gains. Unfortunately, the droop coefficient regulation technique has some serious concerns related to voltage and system stability. A frequency controller with nonlinear matrix inequality was presented to ensure the stability of the system in [9] and the improved droop-based control with autonomous operation for AC-DC MG control was proposed in [10]. Modification in droop with complex line impedance has been implemented in [13] for power sharing accuracy but the system stability and reliability was not considered. An adaptive virtual impedance multi-agent consensus control scheme was presented in [14]. The scheme significantly improves power sharing accuracy but with slow system response. However, control techniques related to power sharing control and circulating current suppression have different issues.
This paper presents an improved droop-based simple control technique for power sharing and circulating current suppression in AC islanded MGs. The proposed control technique is implemented to two VSI units and their virtual impedance is also considered. Proportional Integral (PI) controllers control the voltage and current for accurate power sharing between the two VSIs connected in parallel at the Point of Common Coupling (PCC). Moreover, the circulating currents between the VSIs are suppressed in the proposed control scheme.
II. SYSTEM DESCRIPTION This paper presents a virtual impedance-based, voltage source inverter, VSI-based islanded MG power sharing control scheme which is implemented on two DG inverters as shown in Figure 1. The system is composed of LCL output filters and distribution lines. It worth mentioning, that the system is designed considering ideal DC voltage sources where storage and losses are not considered. The system has resistive inductive load which is shared by two DG inverters. Figure 1 shows the islanded MG with two identical DG inverters connected to the LCL filter, virtual impedance, and distribution lines. Both the DG inverters are connected to the PCC and a load is connected directly to the PCC.

III. REACTIVE POWER ANALYSIS AND DROOP CONTROL
In inverter-based systems, more and more DG units are connected in parallel to increase the capacity of the MG. A single phase of parallel connection of the MG is given in Figure 2. Input voltage and currents for DG1 and DG2 with their respective power angle δ and impedance angle θ are: V o1 <δ 1 , V o2 <δ 2 , I 1 <θ 1 , and I 2 <θ 2 respectively. The active and reactive powers (P and Q) for the i th inverter are expressed in (1), (2).
When X V +X L is much greater than R and the angle δ is very small, the above equations can be simplified as: where X≃X V +X L . P and Q are providing the conventional droop basics which are expressed as: where ω*, V*, and n, m are the nominal frequency, and voltage and droop coefficients respectively. Droop control is good for active power sharing accuracy while reactive power sharing is not easily achieved because of the effect of line impedance mismatch.

A. Inner Voltage and Current Loop
For the sake of voltage regulation, a proportional resonant controller is employed. Figure 3 shows the voltage and current control loops with the filter. The transfer function for the PI controller is: Pathan et al.: Virtual Impedance-based Decentralized Power Sharing Control of an Islanded AC Microgrid where K pv and K pi are related to the controller (PI) gains. The closed loop transfer function with no virtual impedance is given as: where G(s) and Z o are voltage gain and output impedance respectively.

A. Virtual Impedance Loop
For frequency and voltage magnitude regulation, conventional droop control is commonly recommended, which may be in the form of P-ω or Q-V in MG control for medium voltage networks. In medium voltage MGs, the behavior of the lines is predominately inductive. Considering the low voltage MGs, the predominant inductive behavior does not exist, so the conventional droop control is not very effective while the mismatch in line impedance makes the control system more complicated. Complex virtual impedance is proposed to mitigate line impedance mismatch and power sharing accuracy can be attained. Voltage reference is adjusted by utilizing the virtual impedance.
From (12), * Z o can be written as: The overall block control diagram with the virtual impedance is shown in Figure 4. The droop control and the virtual impedance are utilized to overcome mismatch in line impedance and mitigate the circulating current. The impact of the virtual impedance as per the parameters given in Table I can be seen in the diagrams given in Figures 5-6. The output voltage of each unit connected in parallel successfully tracks its respective reference with negligible phase delay. With the proper voltage tracking and voltage controller design considering the complex virtual impedance given in the above equations, proper power sharing can be achieved. V. SIMULATION RESULTS The proposed control scheme was tested under in MATLAB/Simulink. The control strategy and the sub model are shown in Figure 5(a)-(b). The MATLAB/Simulink model is designed for three phase ideal voltage sources with power and control section. LC Filter 1 and LC Filter 2 are connected to the VSI 1 and VSI 2 respectively with common loads at the PCC. The utilization of virtual impedance ultimately enhances the power sharing accuracy in the two DG inverter model and suppresses the circulating current. In the proposed control, the predominating inductive output impedance is considered. The simulation results are taken at different time intervals to illustrate the effectiveness of the proposed control technique. Three different time intervals were taken into consideration: • From 0 to 1s, the system results are taken without using any virtual impedance loop, only the droop control is considered.
• From 1 to 2s, the virtual impedance Z V1 is applied. The addition of the virtual impedance compensates the output line impedance.
• From 2 to 3s, the virtual impedances Z v2 , Z v3 , and Z v4 are applied to the system. At the same time interval, an additional load equal to three times the previously connected load is applied to the system to prove the validity of the proposed control system for two parallel connected inverters.
The virtual impedances are added in the DG inverters in such a way that Z V1 and Z V4 are added in DG inverter 1 in order to compensate the output impedance mismatch and Z v2 and Z v3 are added to DG inverter 2. It can be seen in Figure 6 that the proposed control scheme is working properly and tracks the reference currents while enabling the two DG inverter systems to share power accurately. Thus, the system voltage quality is maintained. Voltage and current waveforms are given in Figure  6(a)-(b). The voltage remains the same and accurate even when the virtual impedance loops are added after 1s. Moreover, the voltage stays the same when the load is increased (Table I). Nevertheless, the current waveform is accurate at all the different conditions applied to the MG system. The current waveform is stable even after the addition of the load. In Figure 6(c), the MG total active power accuracy is shown. During 0-1s, the sharing is not accurate because there is no virtual impedance. There are some fluctuations and the same is observed just after the 1-2s interval. Droop control having P-f, can easily attain active power sharing accuracy. After 2s, the power is increased along with the additional load, but is still accurate as per the load. In Figure 6(d) the MG power sharing accuracy starts after 1s because during 0-1s there is no virtual loop. After 1s, the virtual loop is added and sharing is accurate. After 2s, when the triple load is added, MG reactive power and sharing of reactive power are shown in Figures 6(e)-(f). Before the addition of the virtual impedances the power sharing during 0-1s was not accurate. When virtual impedance was added (after t=2s), the power sharing of both the DG inverters is accurate despite their different output impedances. During the 2-3s time interval, the reactive power sharing remains accurate even after the addition of the triple load. Figures 6(g)-(h) show the accuracy of the voltage and frequency stability when there is convention setting. After the virtual impedances were added, the voltage drop was lower than the voltage drop after 2s because of the additional load. The circulating current is shown in Figure 6(i). It can be seen clearly that during 0-1s there are significant fluctuations and the circulating current is higher. During the 1-2s time interval and after the addition of the virtual impedances, the circulating current is approximately 0. From t=2s, when the additional load was added, it can be seen that the circulating current is suppressed effectively. VI. CONCLUSION In this paper, the virtual impedance loop was used to solve the power sharing issues of an MG without compromising the voltage quality of the system. Active and reactive power sharing accuracy can be attained very easily. Voltage drops due to the mismatch of output impedances were also minimized in this control scheme. The proposed control scheme is applied to the MG with two parallel connected inverters having different output impedances. The mismatch was covered by introducing the virtual impedance control loop. The system was tested with different load conditions and showed satisfactory results. One of the critical issues of islanded MGs with mismatch in line impedance is the production of circulating currents, something that is also addressed in this paper. The virtual impedance loop is helpful to mitigate the circulating current issues, even after the addition of extra load, the circulating current was effectively suppressed to almost zero.