Improved Reactive Power Sharing for Parallel-operated Inverters in Islanded Microgrids

Abstract

The unequal impedances of the interconnecting cables between paralleled inverters in the island mode of microgrids cause inaccurate reactive power sharing when the traditional droop control is used. Many studies in the literature adopt low speed communications between the inverters and the central control unit to overcome this problem. However, the losses of this communication link can be very detrimental to the performance of the controller. This paper proposes an improved reactive power-sharing control method. It employs infrequent measurements of the voltage at the point of common coupling (PCC) to estimate the output impedance between the inverters and the PCC and then readjust the voltage droop controller gains accordingly. The controller then reverts to being a traditional droop controller using the newly calculated gains. This increases the immunity of the controller against any losses in the communication links between the central control unit and the inverters. The capability of the proposed control method has been demonstrated by simulation and experimental results using a laboratory scale microgrid.

I. INTRODUCTION

AC microgrids are aggregated systems of many distributed generation (DG) units, energy storage systems and local loads. They can operate either in the island mode or in the grid-connected mode. This increases the redundancy and reliability of the overall power system. When integrating renewable energy sources (such as solar, wind and hydro), power electronics-based inverters are used to interface these sources to the AC microgrid as shown in Fig. 1. The microgrid central controller (MGCC) exchanges information with the sources and their power electronic inverters via a low speed communication channel. A significant concern for these parallel-operated inverters is the load sharing issue. Many techniques use communication-based methods [1]-[6] to accomplish accurate load sharing. However, these techniques need a high-bandwidth communications infrastructure between all of the inverters. This increases the cost and decreases both the reliability and plug and play ability. Therefore, droop control, which mimics the behavior of synchronous generators [7]-[12], has been introduced to enable inverters to operate in parallel without any communication mechanism. However, the traditional droop control is known for its poor performance in reactive power sharing. For a droop controller to share reactive power accurately, the parallel-operated inverters must have the same output impedance including the cable’s impedance, and they must generate the same output voltage. However, this cannot be guaranteed in practice due to parameter tolerance in the inverters’ LC output filters, different interconnecting cable lengths and inaccuracy in the output voltage control.

Fig. 1.General microgrid structure.

Many strategies have been proposed to enhance reactive power sharing. An algorithm has been proposed in [13], which is based on an additional control signal injection. This solution injects signals with different frequencies (90Hz, 130Hz) to send information about the shared power between the inverters through the same distribution lines. However, this can increase the control complexity and can cause current distortion. Chia et al. [14] proposed a method to compensate for the line impedance mismatches, where the reactive power is controlled in proportion to the voltage derivative. Although this method minimizes the reactive power sharing error, it does not achieve equal sharing. It also adds more complexity to the system. In [15] a centralized controller has been proposed to compensate for the voltage drop caused by the droop controller and line impedances. However, this entire process is executed in the MGCC and all of the parameters are sent by a communication link. As a result, any loss of this link will lead to the traditional droop limitations.

Li et al. [16] proposed an online estimator of the voltage drop caused by the transmission lines which is then used to refine the droop control gain to give an accurate Q sharing in the island mode. However, this algorithm needs the inverters to operate in the grid-connected mode initially to obtain a proper estimation of the voltage. In addition, the controller’s complexity increases with the presence of local loads, which affects the estimation process.

In [17], a novel controller that is robust against computational errors and component mismatches is proposed. The accuracy of the controller does not depend on the output impedance. It measures the load voltage continuously through a wired link and employs an integral controller to achieve accurate sharing of the reactive power. However, this system works accurately for local inverters that are near each other and the local load. If the load is far away or the distance between the inverters is large, a wireless link could be used. However, any loss in this communication link - even for a short period of time - might lead to instability due to the existence of the integral controller. Furthermore, the controller does not take into account the cables’ impedances, which contribute to sharing inaccuracy if a local output voltage is fed back.

Jinwei et al. [18] proposed a synchronized algorithm for guiding all of the units to share reactive power accurately by incorporating the measured reactive power in the frequency droop equation. However, this intentionally disturbs the active power sharing accuracy. In addition, if the load changes after compensation, the accuracy of the sharing deteriorates and the algorithm needs to be executed again. The authors in [19,20] proposed an online estimation technique for line impedance using the harmonics of the line current and the PCC voltage to regulate the virtual impedance and to enhance the reactive power sharing accuracy. However, in addition to increasing complexity, this scheme is dependent on the existence of significant harmonics, which assumes the existence of non-linear loads during the estimation period.

In this paper, a novel controller for improving reactive power sharing is proposed. It reduces the risk of communication loss so it has a negligible effect on the stability and sharing accuracy. The proposed algorithm employs infrequent measurements of the PCC voltage to estimate the output impedance between the inverters and the PCC, and it readjust the voltage droop controller gains accordingly. The controller then reverts to being a traditional droop controller using the newly calculated gains. Therefore, it does not need to measure the PCC voltage continuously. This increases its immunity to losses of the communication links between the central control unit and the inverters. The controller can maintain good accuracy in the presence of changes in the load after the execution of the proposed algorithm. The capability of the proposed control method is demonstrated using simulation and experimental results obtained with a laboratory scale microgrid.

The paper is organized as follows: a small signal analysis of the reactive power sharing is discussed in section II; in sections III the proposed controller is presented; some simulation and experimental results are shown in sections IV and V, respectively; and finally some conclusions are given in section VI.

 

II. REACTIVE POWER FLOW IN ISLANDED MICROGRIDS

Fig. 2 shows a simple microgrid consisting of two inverters. Each inverter is modelled by a two-terminal Thevenin equivalent circuit where V and Xo represent the Thevenin voltage and impedance, respectively [21]. For a dominantly resistive output impedance, the P-V and Q-ω droop control is commonly used, while for an inductive output impedance, the P-ω and Q-V control is used [22]. In this paper, the output impedance is guaranteed to be inductive by using an inductive virtual impedance as described in [23]. As a result, the P-ω and Q-V droop control is employed. The two inverters are connected through different feeder impedances XL1 and XL2. The traditional droop control equations for the inverter i are given by:

where ωi and Vi are the output frequency and voltage, ω∗ and V∗ are the frequency and voltage set-points, mi and ni are the frequency and voltage droop gains, and Pi and Qi are the active and reactive power, respectively.

Fig. 2.Model of a simple islanded microgrid.

A small signal deviation (denoted by ‘~’) in the output voltage in (3) is given by:

This means that a small deviation in Vi with respect to a small deviation in Qi (around the equilibrium point) is a linear line with a slope of -ni and that the behavior of Vi is determined by:

By choosing the equilibrium point Veq to be V∗, the small signal expression is:

The current flow causes a voltage drop across Xo and XL. Hence, the voltage at the point of common coupling VPCC will be different from V1 and V2.

By defining the total impedance of the inverter i as Xi = Xoi + XLi , the reactive power generated by the inverter i can be shown to be given by:

where δi is the power angle between Vi and VPCC. For a small power angle, cos δi ≈ 1. Hence, the reactive power can be approximated as:

where:

A small change (denoted by ‘~’) in the reactive power due to a change in the voltage is given by:

where ΔVeq and Veq are the equilibrium voltage difference ΔVi and inverter output voltage Vi, respectively, around which the small signal perturbation is performed. The symbol denotes a small change in ΔVi. In other words . Because ΔVeq ≪ Veq, and by choosing the equilibrium point Veq = V∗, a small change in reactive power can be approximated by:

By deviating ΔVi in (8), substituting it into (10) and rearranging, the inverter output voltage behavior around the equilibrium point can be expressed as:

Both (5) and (11) define the relationship between Vi and around the equilibrium. For inverter 1, Fig. 3(a) represents (5) and (11) graphically as two linear lines. The delivered reactive power is determined when the two lines intersect. If one inverter has a higher total impedance Xi, the slope Xi⁄V∗ in (11) will be higher. In order to deliver the same reactive power as the other inverter, the voltage droop coefficient ni (slope in (5) ) needs to be reduced. This is illustrated in Fig. 3(b), where inverter 2 has a higher total impedance than inverter 1, X2 > X1. Therefore, for the two inverters to share the reactive power equally, the voltage droop coefficient of inverter 2 needs to be reduced accordingly.

Fig. 3.Reactive power sharing affected by the voltage drop.

By substituting (5) into (11) the following is obtained:

Hence, for the two inverters to share reactive power equally the following condition needs to be satisfied:

In order to have equal sharing of the reactive power, the droop gain ni needs to be adjusted in proportion to 1/Xi. Thus, inverters with a higher output impedance will have the voltage droop gains reduced. The new voltage droop gain is proposed to be calculated as:

where Xoi is the nominal output impedance of the inverter. The output impedance Xi includes the inverter output impedance Xoi and the interconnecting cable impedances so that Xi = Xoi + XLi (see Fig. 2). The impedance Xoi should be known for each inverter while the impedance Xi can be estimated as:

To calculate the required value of Xi that is needed to scale the droop gain to finally improve the reactive power sharing, the value of Xi has to be calculated when all of the inverters share the reactive power adequately. Consequently, once an accurate reactive power sharing is obtained by using VPCC [17] which is also used to calculate the voltage drop ΔVi = Vi - VPCC, the output reactive power is measured and then the output impedance is estimated. Therefore, after the estimation process and retrieving the traditional droop controller with the new gain, it gives adequate sharing without VPCC.

By readjusting the voltage droop gain according to (14), it can be guaranteed that the new droop gain is smaller than or equal to the original droop gain. This is quite important because if the droop gain is increased beyond the designed value, instability can occur [8]. Furthermore, the designer can add a limit on the droop gain range to ensure that the system stability has a higher priority than the reactive power sharing accuracy. It is worth mentioning that it is possible to measure the output impedance between the inverter and the PCC at the design stage, and to calculate the required droop gains. However, for an inverter within a microgrid, the impedances of the distribution cables and the other parallel inverters have a significant effect, which means that the output impedance will be variable, and a single gain value may not be sufficient.

 

III. PROPOSED REACTIVE POWER SHARING CONTROLLER

The proposed controller scheme is shown in Fig. 4. It consists of two stages: in the first stage, the controller uses the PCC voltage to obtain accurate sharing between the inverters, to estimate Xi, and to calculate the new droop gain ; in the second stage, the reactive power control uses the traditional voltage droop incorporating the new calculated droop gain . The two stages are explained below.

Fig. 4.Proposed controller scheme (a) Stage 1: Accurate power sharing. (b) Stage 2: Voltage compensation.

A. Stage 1

In this stage, the voltage drop V∗ - VPCC is calculated and compared to ni*Qi, and the error signal is fed back to the controller through an integrator as proposed in [17] and shown in Fig. 4(a). The gain Kqis used to accelerate the transient response as required. In the steady state condition, the input to the integrator is zero which means that the reactive power is given by:

If all of the inverters have the same n, the right hand side of (16) is the same in all of the inverters. Thus, equal sharing is achieved even if the output impedances are different. When the steady state condition is reached (determined by zero input to the integrator), the output impedance Xi is estimated using (15) and the new droop gain is calculated using (14). All of the new droop gains are set in proportion to 1/Xi. Thus, the traditional droop control can be used without using the PCC voltage.

B. Stage 2

In this stage, a smooth transition from the closed loop control, which involves a measurement of the PCC voltage, to the traditional droop control using the newly calculated droop gains is performed. At the end of stage 1 (once the steady state condition is reached), the inverter output voltage is given by:

In stage 2, after adopting the new droop gain n´ with the traditional droop loop, the inverter output voltage is given by:

where the offset α is added to make sure that the inverter voltage at the beginning of stage 2 is the same as that at the end of stage 1. Therefore, (17) and (18) should be equal. Hence, α is given as in (19) and it is calculated at the end of stage 1 as shown in Fig 4(a).

In stage 2 the offset α is added via a ramp function as shown in Fig. 4(b).

The proposed controller can be realized using a low-bandwidth communication link to connect each inverter with the MGCC as shown in Fig. 5. This link sends the PCC voltage to all of the units simultaneously for stage 1 to get accurate Q sharing. Once the steady state condition is reached (Stage 1A) and flagged by the zero input to the integrator, the new droop gain n´ and the offset α are calculated as shown in the process timeline in Fig. 6. At the end of stage 1, a synchronization flag is sent so that all of the inverters activate stage 2 at the same time. In this stage, the new calculated value of n´is used as the droop gain instead of the old value n.

Fig. 5.Communication scheme for the proposed controller.

Fig. 6.Proposed algorithm stages timeline.

 

IV. SIMULATION RESULTS

A model of a microgrid with two inverters was built using Matlab/Simulink. Each inverter is modeled as an ideal voltage source with a series inductive output impedance as shown in Fig. 2. The system parameters are shown in Table I. The two inverters have identical parameters. However, an extra impedance is inserted between inverter 2 and the PCC to model the impedance of a long feeder. This part of the simulation is carried out to verify the proposed controller under different load conditions and to compare its performance with that of the traditional droop controller.

TABLE ISIMULATION PARAMETER VALUES

Fig. 7 shows the reactive power of the two inverters with the traditional droop control under different load conditions; low, medium and high corresponding to 10%, 50%, and 100% of the maximum reactive power rating of the microgrid (20kVar), respectively. It can be noticed that the two inverters do not share the reactive power equally. Table II summarizes the steady state values of the simulation results.

Fig. 7.Inverter’s output power when low, medium and high loads are supplied using traditional droop control.

TABLE IITRADITIONAL AND PROPOSED CONTROLLER REACTIVE OUTPUT POWER

Fig. 8 shows the reactive power with the proposed controller under different load conditions. The traditional droop controller is used until time t = 5.5 sec when stage 1 is activated and the new droop gain n´ and the offset α are being calculated. At time t = 21 sec, stage 2 is activated and the controller reverts to the traditional droop control but with the new calculated droop gain n´. At t = 21 sec, there is a dip in the reactive power, which is due to the difference between the inverter voltage at the end of stage 1 and at the beginning of stage 2. This is fixed by adding the offset α which is done gradually via a ramp function. After the controller is settled and at time t = 32 sec, a sudden change in the reactive load is applied to test the ability of the proposed controller to maintain good reactive power sharing. In Fig. 8(a), the activation of the proposed controller occurs when the reactive load is low, followed by a sudden change in the reactive load from low to high. In Fig. 8(b), the activation of the proposed controller occurs when the reactive load is medium, followed by a sudden change in the reactive load from medium to high. In Fig. 8(c), the activation of the proposed controller occurs when the reactive load is high, followed by a sudden change in the reactive load from high to low. Finally, in Fig. 8(d), the activation of the proposed controller occurs when the reactive load is high, followed by a sudden change in the reactive load from high to medium. The simulation results for these simulation conditions are summarized in Table II which reveals an improvement of the reactive power sharing due to the proposed controller when compared with the performance of the traditional control under different load conditions. It is noted that the total reactive power is different before and after activating the proposed controller. This is due to the change of VPCC as it increases due to the action of the voltage drop compensation in stage 1 as seen in Fig. 9.

Fig. 8.Simulation results of the proposed controller after a new load step at 32sec from (a) low to high (b) medium to high (c) high to low (d) high to medium.

Fig. 9.PCC voltage before and after activating the proposed controller (in all cases).

Fig. 10 depicts the risk of a potential communication loss for controllers that rely on continuous measurements of the PCC voltage, such as the one reported in [17], if a wireless link is used between the PCC and the inverters. Initially, the two inverters are supplying load 1 and adopting the traditional droop control until the moment t=5.5sec when the algorithm reported in [17] is activated and accurate reactive power sharing is achieved. One of the two inverters lose the PCC voltage measurements at t=20sec for 100ms. As can be seen, the output voltages of both inverters exceed the limit which causes the inverter to trip.

Fig. 10.Output voltages when PCC voltage is lost at t=20 sec for 100ms.

The load might change during Stage 1. Therefore, the controller will not proceed to Stage 2 until the steady state input of the integrator reaches zero. This action is depicted in Fig. 11 where a new load is connected at t=15sec. The controller is transferred to Stage 2 only after the steady state is reached at t=20sec.

Fig. 11.Load change during Stage 1.

The proposed strategy is based on the assumption that the network is predominantly inductive as shown in Equ. (15). Therefore, the accuracy of the proposed controller is degraded if the network is predominantly resistive. In this case, the virtual impedance plays an important role in improving the accuracy of the controller. A larger resistive output impedance (X⁄R = 0.3) for both of the inverters is used with feeder resistance of R = 0.15Ω. The simulation results in Fig. 12 show the controller performance without [Fig 12(a)] and with [Fig 12(b)] the inductive virtual impedance. The controller is activated at t=5sec and new loads are connected at t=32sec. The results reveal that the accuracy of the proposed controller decreases with a more resistive network. Nevertheless, adopting an inductive virtual impedance provides more accurate steady state values.

Fig. 12.The proposed controller performance (a) without and (b) with the virtual impedance in resistive network.

 

V. EXPERIMENTAL RESULTS

A laboratory-scale microgrid was built to validate the proposed controller. It consists of two inverters connected in parallel. Each inverter consists of a Semikron single phase H-bridge and an output LCL filter. The experimental setup diagram is shown in Fig. 14. A dSPACE 1103 control unit is used to implement and realize the proposed control scheme in real time. The dSPACE interfacing board is equipped with eight analog to digital channels (ADC) to interface the measured signals. The software code is generated by the Real-Time-Workshop under the Matlab/Simulink environment. The experimental setup parameters are listed in Table III. A picture of the experimental setup is shown in Fig. 13. A detailed simulation model of the experimental setup was also built using Matlab SimPowerSystem. The two inverters have identical parameters. However, an extra impedance is inserted between inverter 2 and the PCC to model the impedance of a long feeder.

Fig. 13.View of the laboratory setup.

Fig. 14.Experimental setup diagram.

TABLE IIIEXPERIMENTAL PARAMETER VALUES

Fig. 15 shows that the reactive power flows from the two inverters during the entire process. The initial PCC load was Load 1 as defined in Table III. The microgrid was initially operating using the traditional droop method. The inverters do not share reactive power equally due to a mismatch in the feeder impedances. Stage 1 began at t=5.5sec and at t=20sec the Q sharing was achieved thanks to the integral controller using VPCC. By the end of stage 1, the new droop gain and the voltage offset were calculated to be used in the next stage. Stage 2 began at t=20.5sec and the controller switched to the traditional droop method using the new calculated droop gain and the integral controllers using VPCC were stopped. At the beginning of stage 2, the voltage offset is added gradually using a ramp function and the whole process finished at t=26sec. At t=32sec, a step load was applied by connecting Load 2 at the PCC and the two inverters shared it equally. The figure also shows the inverters’ output voltage responses during the whole process. The experimental results show good agreement with the simulation results and confirm the reliability of the proposed controller against load changing.

Fig. 15.Reactive output power and output voltages results of the proposed controller: (a) simulation (b) experimental.

 

VI. CONCLUSION

In this paper, a novel power-sharing algorithm was proposed to enhance the reactive power sharing between parallel inverters in the island mode of microgrids. The proposed strategy uses an intermittent measurement of the PCC voltage to accomplish accurate reactive power sharing. Under this condition it is possible to estimate the value of the output impedance of the inverters (which is assumed to be dominantly inductive), including that of the cables. The new estimated impedance values are then used to calculate a new value for the gain of the traditional droop controller. This takes over the control of the reactive power sharing when the PCC voltage measurement is not available. The new droop configuration improves the reactive power sharing without needing to measure the PCC voltage continuously – intermittent measurements can be repeated and transmitted to the inverters over a slow communication link to handle any changes in the network. This increases the reliability of the system against communication link loss. Since the proposed controller assumes a predominantly inductive output impedance, there might be a decrease in the sharing accuracy when it has significantly resistive value. In addition, discrete measurements of the PCC voltage are managed according to the changes in the structure of the microgrid (loads, cables length and number of inverters). Finally, simulation and experimental results are presented to validate the performance and effectiveness of the proposed controller.