Reactive power sharing among distributed generators in a microgrid by using virtual current

Eder A. Molina-Viloria, John E. Candelo-Becerra, Fredy E. Hoyos Velasco Tecnologico de Antioquia, Institución Universitaria, Facultad de Ingeniería, Medellín, Colombia Universidad Nacional de Colombia Sede Medellín Facultad de Minas Departamento de Energía Eléctrica y Automática, Medellín, Colombia Universidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de Física, Medellín, Colombia


INTRODUCTION
In recent years, there has been a trend toward the decentralization of electricity generation; hence, the penetration of distributed generation (DG) has significantly increased and microgrids (MGs) are becoming an important concept to integrate these generation units [1]. Thus, the MG concept has been introduced as a very effective technology to integrate renewable energy sources in the network [2] and, when compared with conventional distribution systems, new partial systems can operate either while connected to the main power grid or isolated mode operation [3], [4]. A droop control scheme is generally used by paralleling multiple inverters [5]- [7] in which the voltage and frequency of each inverter are adjusted in order to control the active and reactive power.
In an MG in island operation mode, power must be properly shared to loads by the multiple DG units that conform the network. Conventionally, the frequency and voltage magnitude droop control is adopted with the objective to share active and reactive power in an MG, and performed in a decentralized manner without using any communication between DG units [1], [3], [8], [9]. In this control category, the active and reactive power are calculated using low-pass filters [10]; consequently, the main focus of droop control is the exchange of average active and reactive power.
Active power sharing is accurate, whereas reactive power sharing depends on line impedances [11], [12]. To improve MG performance, some modified droop control methods have been presented in literature. In [13], an interesting method of dropping Q-V points is proposed, where the authors show a new cooperative harmonic filtering strategy for the interface converters of distributed generation sources. A droop control method based on the reactive volt-ampere consumption of harmonics of each interface converter is designed and implemented. However, the shared reactive power errors can hardly be completely eliminated using this method, especially in weak MGs.
Furthermore, the island operation can be considered as one of the most attractive features of an MG, as it guarantees service continuity in the case of network interruption [14]. When the MG is in island operation mode, the DG units must be able to cooperatively regulate the voltage and frequency, and maintain the balance between power generation and the power consumed by the load within the MG. Consequently, the concepts of droop control have been widely adopted in [9], [15], [16] to provide decentralized control of power sharing without relying on communications.
As the MG allows DG units to work in an island operation mode, the system can improve reliability and power quality for customers [14]. However, when operating in island mode, some challenging issues appears such as the difficulty of maintaining the power balance between generation and loads and reactive power sharing [15], [17]. When an MG operates in island mode, the droop control technique provides a decentralized control capability that does not depend on external communication links in the control strategy; although the frequency droop technique can manage active power sharing accurately, the voltage droop technique generally results in a poor reactive power sharing due to the mismatch in the impedances of the DG unit feeders and, also, due to the different values of DG units [18]. Consequently, the reactive power sharing problem in an MG working in island operation mode has received considerable attention in the literature and many control techniques have been developed to address this problem [19]- [23].
Commonly, in high voltage networks, reactive power sharing among generators is not usually a major concern due to capacitive compensation between loads and transmission lines. However, in lowvoltage MGs, the low capacity to supply reactive power from generation sources and compensators, and small distances between units, does not allow an exact distribution of reactive power to avoid overloads [24]. Line impedances and DG impedances significantly affect the reactive power sharing during the operating mode connected to the network and during the island mode due to voltage drops [21]. At present, the voltage controllers in the MGs are unable to share the demand for reactive power among even identical inverters operating in parallel [25]. Some researchers have previously worked on this issue as in [22], which proposes an alternative controller for reactive power sharing between parallel inverters with nominal voltages. Design of control strategies for Distributed generation systems is very important to achieve smoother transition between the grid connected and islanding modes of operation [26]- [28]. Also power management strategy of parallel inveters based system, to enhance the power generation capacity of the existing system with distributed energy sources [29].
The references consulted in this research show that previous works have focused more on performing an active power control while reactive power sharing still requires better applications to improve accuracy. Therefore, the objective of this work is to show that the reactive power can be shared between generators in an MG more accurately by using virtual current injected to the current controller of the inverter in order to optimize the output signal. The main contribution in this paper is related to the virtual currents calculated from each inverter based on the active output power of the inverter. This new current control achieves an accurate exchange of reactive power between generators of the MG when load variations are presented. Section 2 explains the new control strategy for sharing reactive power after each load variation and presents the mathematical formulation of the control method, small-signal model, current loop controller, three-phase half-bridge circuit, output LC filter, line impedance, and the inverter used in the control strategy.
In addition, Section 3 shows the results of the simulations performed in a distribution system test case using MATLAB/Simulink software. Finally, Section 4 presents the conclusions and future work.

MATERIALS AND METHOD 2.1. Control method
A strategy using virtual current is proposed as a method to control the reactive power and voltage in the MG when the load changes in certain periods of time. Figure 1 shows a detailed configuration of a DG unit using the proposed control strategy. The P-ω controller is adopted to regulate the frequency and achieve an accurate exchange of active power between the different distributed generators that conform the MG. The design of the controller starts by measuring the current in the capacitor and the output voltage . Besides, the active power and reactive power are calculated by using the output voltage and the current measured in the output of the system , both transformed into coordinates. Then, the reference voltage is calculated using the droop control and used to calculate the voltage error. Finally, in the inner loop the voltage error is amplified by the proportional resonant (PR) and used to subtract both the virtual current obtained as the square root of the activate power divided by a virtual impedance, and the current measured in the capacitor and transformed into coordinates. The final signal obtained in the inner loop is multiply by a gain P, which increases the signal that is sent to the PWM to make the switch in the inverter obtain the desired current and voltage values.

Small-signal model
To analyze the stability of the controller, a small-signal model of the inverters with the proposed control strategy is included. Each inverter is modeled with individual reference and includes the dynamics of the voltage and current controller, LC filter, and line impedance to reach equilibrium. The internal voltage controller is based on a PR structure in the steady-state reference, where generalized integrators are used to achieve a zero steady-state error. Based on the abc/dq-coordinated transformation principle, a three-phase system can be modeled in two independent single-phase systems. Thus, the block diagram of Figure 2 shows the voltage controller in a synchronous reference frame that includes all feedback terms and the four states and . The corresponding state equations can be expressed as in (1) and (2): Thus, the algebraic equations are expressed as in (3) and (4): The linearized small-signal state space models of the voltage controller are presented in (5): Where the terms is the system matrix. 1 and 2 are the input matrices as shown in (6), (7), and (8): The linearized small-signal state space models of the voltage controller are presented in (9): Where the term is the output matrix and the terms 1 , 2 , and 3 are the feed-forward matrices as shown in (10)-(13):

Current loop controller
The internal current controller is based on a stationary frame structure as shown in Figure 3. The input currents on the and axes for the controller are and , which are the result of the algebraic sum of the output current of the voltage controller * and * , minus the virtual current as expressed in (14) and (15): Next, the previous equations related to the and axes are obtained by replacing the value of the virtual current * * and * * With its equivalent: The algebraic equations for the reference current can be expressed as (16) and (17): The linearized small-signal state space models of the above equations can be represented in a simple way as shown in (18): where the terms and are matrices that can be represented as (19) and (20): The linearized small-signal state space models of the current controller loop are presented in (23)- (25): where the terms 1 and 2 are matrices that contain the control parameters as shown in (24) and (25): Based on (11)-(14), the output of the current controller ∆ * can be derivated as in (26):

Three-phase half-bridge circuit and output LC filter
The corresponding state equations are expressed as shown in (27) The output variables of the LC filter are the state variables . Thus, the (31) represents the linearized small-signal state space: where the terms , 1 , and 2 are matrices that consider the parameters of the system as presented in In (19), the output of the controller in the current loop ∆ * can be replaced by (26); then, (31) can be expressed as in (35):

Line impedance
Line impedances are considered in the MG to connect each inverter and the load; thus, real line impedance must be considered in the model to identify the power losses of the circuit. The corresponding state equations can be expressed as in (36) and (37): The output variables of the line impedance are the state variables . Linearized models of smallsignal state space are as in (38): where the terms , 1 , and 2 are matrices that consider the parameters of the system as presented in (39)-(41):

Complete model of the inverter
A complete small-signal state space model of the inverter, as expressed in (42) and (43), can be obtained by combining the status space models of the voltage controller, current controller, LC output filter, and line impedance given by (5), (18), (35), and (38), respectively: Next, the complete small-signal state space model of the inverter is obtained with the proposed of applying the control strategy that modifies the current controller by combining the different state space models. Herein, the terms , 1 , and 2 correspond to the matrices shown in (44)

RESULTS
This section shows the results related to the response of the power inverter applied to each generator when the control strategy presented in Section 2 is considered. This control strategy is related to the virtual current considered as an input for the current control of the inverter. This strategy allows sharing the reactive power with precision and regulating the voltage in the nodes. The simulations were carried out by considering a distribution network test case where the loads are connected and disconnected at different periods of time.

System test case
The MG used for this investigation is shown in Figure 4. This network is formed by two distributed generators designed to supply one load. The load considers five household consumptions that are connected and disconnected over time. The power of the distributed generators must be delivered considering the impedances of the lines in order to supply the power of the changing load. In addition, voltage regulation is achieved by using the inverter with the virtual current that changes based on the connected and disconnected loads.  During the first 12 seconds, a load of 10+j0.05 Ω is connected to the load node and both control strategies respond very well to the connection of the load with approximately 1000 W. In the 12-second period, a load of 15+j0.05 Ω is connected for a few seconds and the active power consumption of the load in the node increases by more than 100% based on the consumption of the previous period. The same load is disconnected from the MG at 24 seconds and, at the same period, a load of 20+j0.60 Ω is connected, where the power consumption is reduced. At 36 seconds, a load 25+j0.10 Ω is connected, which generates an active power consumption increase of almost 50% of the initial load. Finally, at 48 seconds, the load 10+j0.05 Ω is disconnected and a load 50+j0.20 Ω is connected, which causes the active power supplied by the two generators to decrease and allowing the system to deliver less active power. Figures 5(a) and 5(b) show that the new proposed controller responds faster and better than the droop controller when a load is connected and disconnected. Besides, both controllers share the active power accurately for the changes. However, the proposed control strategy manages to stabilize the active power much faster than the droop control strategy. The results show that the proposed virtual current control strategy manages better the reactive power sharing with different load changes than the droop control. During the first 12 seconds, a load of 10+j0.05 Ω is connected to identify the response of the control strategy and around 1500 VAR of power consumption is observed. Later, after the 12-second period, a load of 15+j0.05 Ω is connected for a few seconds and the reactive power increases and, based on the consumption of the previous period, this load is disconnected from the MG at 24 seconds. Then, at the same period, a load of 20+j0.60 Ω is connected to the node of the MG and the reactive power is reduced as the load 15+j0.05 Ω has been disconnected and the new connected load is not as large as the previous one. Over a period of 36 seconds, a load of 25+j0.10 Ω is connected to the network, which generates a reactive power consumption increase, and the control strategy responds quickly to stabilize the power and to share the reactive power with the same amount between the two generators. At 48 seconds, a load of 10+j0.05 Ω is disconnected and a load of 50+j0.20 Ω is connected, which causes a reactive power decrease in the two generators of approximately 50% of the previous load.

Active power supplied by DG
The results show that the droop control strategy does not allow reactive power to be shared accurately between the generation units as does the new proposed control strategy. The proposed control strategy manages to share with precision the reactive power between two DGs in the MG. Besides, the proposed new controller responds faster and better than the droop controller when a load is connected and disconnected at different times and power. Figure 7 shows the frequency of the system using both the droop and the virtual current controllers when considering different load variations. The figure shows in red the system frequency with the proposed control strategy and, in blue, the system frequency with the droop control strategy. This figure is obtained by considering multiple variations in power loads as described above for the active and reactive power.  Figure 7 shows how both control strategies act when the load changes during different periods of time and the results show that the new proposed controller responds faster and better than the droop controller. Furthermore, the results show that the proposed control strategy ensures that the frequency of the two generators stabilizes at a single value, a few seconds after the load changes. In addition, the more different the change in load on the MG connection, the more abrupt is the change in the frequency value. However, no matter how large the load changes (connection and disconnection of different electrical loads), the controller maintains the frequency close to 50 Hz, which is the desired value. Figure 8 shows the behavior of the RMS voltage at the node where the five electrical loads of the MG are connected. The figure shows in red the voltage in the load with the proposed control strategy and in blue the voltage in the load with the droop control strategy. These results show that at the beginning of the first load connection, the node voltage tends to drop sharply, but immediately the control strategy recovers the voltage close to the original value. Therefore, the proposed control strategy with a virtual current maintains a stable voltage value during the period in which the electrical loads are connected and disconnected. However, when the droop control strategy is used, the voltage drops beyond the proposed method as the proposed new control strategy responds faster and better than the droop controller. Figure 9 shows the current consumed in the node where the loads are connected. The figure shows in red the current in the load with the proposed control strategy and in blue the current in the load with the droop control strategy. The current is lower with the proposed current control strategy compared to the droop control strategy, which brings much benefit because there is less loss in the conductors and winding of the inductive load due to Joule effect.

CONCLUSION
The paper presented a new control strategy that uses a virtual current to share reactive power accurately between two DGs in an MG when electrical loads are connected and disconnected at different time periods. Results were obtained for a system with two distributed generators and a load with five different power consumptions, in which the reactive power shared was correctly distributed between the two generators of the MG, according to the time period that corresponds to the variation of the load. Therefore, within a few moments, the reactive power supplied by the distributed generators increases and, in another time period, it decreases to regulate the voltage in the MG. Therefore, the control strategy based on an adaptive virtual current related to the output power of the inverters works successfully. The proposed control strategy effectively regulates the frequency close to 50 Hz and also maintains the active and reactive power balance. The strategy can be easily adapted to the MG to share accurately the active and reactive power.