Decentralised inverter control for improved reactive power sharing and voltage proﬁle in a microgrid

This paper enhances a self-adjusting droop control strategy further to achieve an improved voltage proﬁle in a microgrid along with proportional reactive power sharing amongst its sources. The proposed enhancement consists of an additional term in the “self-adjusting” nominal voltage. The proposed strategy is entirely decentralised and does not require information about the feeder impedance or the network topology. The proposed technique is robust and found to improve the voltage proﬁle and the reactive power sharing for radial, meshed as well as reconﬁgured microgrid networks. Simulation studies have been performed on two test microgrids to assess and compare the performance of the proposed strategy. Experimental validation to conﬁrm further the viability of the proposed strategy for several topological structures of the microgrid is done on a laboratory-scale microgrid.


INTRODUCTION
Electric grid architecture is moving from being a centralised structure to a decentralised structure primarily due to penetration of distributed generation. The integration of distributed energy resources into the conventional power system has brought forward the concept of "microgrid" which can operate either in grid-connected mode or as an island. In the islanded mode of operation, the droop control technique is applied to the sources to achieve proportional power sharing [1]. It is well known that conventional droop helps in achieving proportional active power sharing among the sources [2,3]. However, proportional reactive power sharing among the sources using droop control is far from ideal. The primary reason for the unequal reactive power sharing (Q sh ) is unequal feeder impedances, presence of local loads and random placement and sizes of loads amongst others. Unequal Q sh among the sources may lead to overloading of the sources and circulating current amongst them. These issues can be minimised by improving/achieving the proportional Q sh amongst the sources.
Various control strategies to achieve power sharing among the sources are reviewed in [3]. These control strategies can be broadly classified into droop control based techniques [4][5][6][7][8][9][10][11][12][13][14][15] and virtual impedance-based techniques [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. For the conventional Q − V droop technique, improved Q sh can be been analysed in [11] by performing sensitivity analysis on a small-signal model of the microgrid. Further, a distributed optimal control strategy has been proposed in which Kalman filterbased estimator and regulator have been employed to reduce the error in the sharing of reactive power among the sources. A self-adjusting Q − V droop technique is proposed in [12], and an appreciative improvement in Q sh is achieved. However, the proposed method suffers from the voltage deviation issue, and the overall voltage of the network drops to a noticeable range. The drop in the magnitude of the voltage can be mitigated by implementing a correction using a secondary controller.
A two layer based control strategy has been proposed in [13] to improve the proportional reactive sharing among the sources in the islanded microgrid in which the bottom layer deals with the electrical network while the top layer concerns a communication-based network composed of agents. The agents exchange information with their neighbours to improve the reactive power sharing. In [14], separate energy server units and energy routers have been proposed to achieve proportional active and reactive power sharing among the sources separately. This scheme is costlier in comparison to other schemes due to an increased number of energy server units. A decentralised control scheme has been proposed in [15] to improve the reactive power sharing among the sources and to restore the system frequency to its nominal value. An integral controller based on the difference in the average active power output and instantaneous active power output has been added in the conventional Q − V droop to reduce the error in the reactive power sharing among the sources. However, the proposed modification is functional only under the transient condition.
Another well-known method for improving Q sh is to insert either fixed or adaptively varying virtual impedance (Z v ). Z v is designed so as to almost equalise the unequal feeder impedances and also to make the network inductive in nature. However, improper design of Z v affects voltage quality and may degrade the Q sh . Z v based control technique have been implemented in two ways: (i) without using communication [16][17][18][19][20][21][22][23][24] and (ii) by utilising communication [25][26][27][28][29][30][31]. A feeder impedance equalisation method using Z v has been proposed in [17] to improve the Q sh . However, in this method, information of feeder parameter is required. A correction in the voltage droop is proposed using adaptive virtual capacitance in [18]. However, the tuning of the virtual capacitance under varying network topology is difficult, and hence, the proposed technique may not work satisfactorily in the reconfigured/meshed network.
The design of Z v affects the power sharing, the transient response, voltage quality as well as the stability of the network. Hence, a trade-off needs to be achieved while designing Z v . The design of Z v is more challenging when the loads and the network condition keeps on changing. Moreover, improper design of Z v may result in poorer voltage quality, transient response, violation of power flow constraints, and sometimes it may also lead to instability. Considering these factors, authors in [21] have optimised a range for Z v for improved Q-sharing among the sources under varying load condition. An alternative approach to design Z v considering damping, node voltage constraint and P/Q decoupling information is presented in [22]. It is found that for the networks having significant differences in feeder impedances, obtaining the optimal value of Z v is difficult. Another approach to obtain an optimal value of Z v for the meshed network using genetic algorithm has been proposed in [23]. The found method is network-specific, and it requires offline calculations when the network topology changes. Communication-based approaches for Z v design can give better Q sh , but these techniques are found to be quite expensive and computationally intensive [27][28][29][30].
It is desired that the control scheme should work irrespective of the network structure (radial, meshed, reconfigured). A change in network topology causes a change in impedance as seen by the sources, which may also cause an increase in the coupling between the real and reactive power. This coupling may lead to poor performance in power sharing. Authors in [20] have implemented Z v based modification, which is found to be satisfactory for the reconfigured/meshed networks. However, the proposed technique requires a communication link to send the reference bus data to the local controllers. A method to improve the Q sh for reconfigured/meshed network without any communication channel is not found in the literature so far.
Control strategies to improve the Q sh based on either droop control or Z v based control cause voltage deviations from the nominal values. The deviation should be restored or minimised for the effective operation of the microgrid. It can either be minimised by modifying the existing droop techniques or by implementing the secondary controller. Frequency and voltage restoration technique using communication is proposed in [32][33][34][35]. A consensus-based distributed voltage control is proposed in [36], which keeps the output voltage in the permissible range of operation. However, the proposed technique requires distributed communication among the sources. The self-adjusting Q − V droop technique proposed by us in our previous work [12] also suffers from the voltage deviation issue. To the best of the authors' knowledge, voltage profile improvement in addition to improved Q sh without the use of communication network is not found in the literature so far. This paper presents a robust droop control strategy (RDCS) for improved voltage profile in addition to proportional Q sh without the use of communication. It is to be noted that the proposed control modification is based on the authors' previous work presented in [12]. In this work: • An RDCS is proposed by modifying the self-adjusting Q − V droop technique to improve the voltage profile in addition to improving Q sh in a droop based microgrid.
• The proposed RDCS is tested for different microgrid topologies, including network reconfiguration and mesh formation.
The significance of the work are as follows. The proposed technique is able to maintain the voltage of the network closer to 1.0 pu without sacrificing the improvement achieved in Q sh in [12]. Moreover, application of the proposed RDCS alleviates the task of voltage regulation which is usually taken care by a secondary controller. The paper is organised as follows: RDCS is presented in Section 2. Simulation studies are presented in Section 3.
Selection of control parameter, eigenvalue analysis and mathematical approach to obtain the effect of the control parameter on Q sh is presented in Section 4. Section 5 contains the experimental validation followed by conclusion in Section 6.

ROBUST DROOP CONTROL STRATEGY
In this section, the proposed RDCS has been presented. Conventional P − droop control ( = n − m p P) has been applied to the sources for active power sharing. The voltage control has been implemented in the dq reference frame wherein the d-axis reference voltage is completely aligned to the d-axis output voltage (V ) of the inverter and the q-axis reference voltage is set to zero. The conventional Q − V droop is given as follows: The voltage at a node based on the self-adjusting Q − V droop proposed by authors in the previous work [12] is given by : where is a tuning parameter, V pu and pu are per unit output voltage and system frequency respectively. It is found that the application of the above technique results in a noticeable drop in voltage in the network. In the proposed RDCS, the nominal voltage V n adjusts automatically in such a way that the voltage profile of the network and the Q sh among the sources improves simultaneously. To minimise the voltage deviation, following RDCS is proposed.
The control parameter add in (3) plays a significant role in the voltage improvement process. The selection of add is critical (as will be explained later in Section 4). Voltage deviation of the DG connected at the i th node, ΔV i (V n − V i ) has been determined for droop laws expressed in (1)- (3). Voltage deviation in the case of (1) is given by: Voltage deviation in case of (2) is given by: Since pu ≈ 1, the second term on the right hand side of (5) can be neglected, and ΔV i simplifies to n qi Q i (1 + 1 ). Hence, a positive value of causes the ΔV i to increase further as compared to (4). Furthermore, the introduction of add in the pro- As seen from the above equation, ΔV i decreases for a positive value of add . This explains the reduction in the voltage deviation by the application of the RDCS.

SIMULATION STUDIES
Time

Microgrid test system 1
The performance of the RDCS is assessed and compared with the previous work in case of common load (CL) and for the case of common plus local load (LL). Microgrid test system 1 (MG1) shown in Figure 1 is adapted from [12]. The line and load data are given in Table 1. The value of is set to 0.2 for both MG1 and MG2 for all the cases. It is also assumed that all the DGs are of the same rating. The inverter parameters for MG1 are: L f = 3 mH, C f = 50 F, n = 314.16 rad/s, V dc = 450 V and V n = 155.6 V. The controller parameters for MG1 are:  = 0.2 and add = 0.004. An upper and a lower limit is set for both the d-axis output current (i od ) and the q-axis output current (i oq ) for all the DGs. It is very common to set these current limits to 1.5 times of their rated values. The rating and current limits are: i od = 48 A (corresponding to 5.0 kW, i od rated = 32 A), i oq = 29 A (corresponding to 3 kVAr, i oq rated = 19.3 A).

MG1: Case-1 (common load)
The common load is located at the ac bus. Active power (P), reactive power (Q) and v odr of the sources operating in conventional droop, self-adjusting Q − V droop and proposed RDCS is shown in Figure 2 and is also tabulated in Table 2. The error in reactive power sharing for the k th source, Q err−k can be defined as follows: where Q exp is the expected share of reactive power desired from the k th source. For example, for three equally rated sources, ; while for sources whose ratings are in the ratio of 1: holds. It can be seen that proportional active power sharing among the sources are achieved due to P − droop. The Q sh among the sources with conventional droop is not proportional to their ratings. The Q sh is improved in case of the self-adjusting Q − V droop technique [12]. However, the voltage deviations in this method are higher in comparison to the conventional Q − V droop. It can be seen from Table 2 that the Q sh among the sources in the case of self-adjusting Q − V droop technique and RDCS are similar. The minimum value of DG output voltage (v odr ) in the case of self-adjusting Q − V droop technique is 0.968 pu which is improved to 0.986 pu in case of the proposed RDCS. The additional term in the voltage deviation ( add V n ) in (6) in comparison to (5) improves the minimum DG output voltage in the network from 0.968 pu to 0.986 pu. It is to be noted that the loads considered for all the case studies are constant impedance loads. The power consumed by these loads is directly proportional to the square of the applied voltage. Therefore, as seen in Figure 2, the active power consumed by the loads drop significantly during the 'B' period as compared to the 'A' and the 'C' period because of a drop in the voltage magnitude.

MG1: Case-2 (common plus local load)
The local load is connected at the output of DG 1 while keeping the common load intact into the network. Active power (P), reactive power (Q) and v odr of the sources operating in conventional droop, self-adjusting Q − V droop and proposed RDCS is shown in Figure 3 and is also tabulated in Table 3. It can be seen that the Q sh among the sources for the conventional Q − V droop technique is not proportional, which Test system MG2 gets improved due to the self-adjusting Q − V droop. However, the voltage deviation is high in this method. It can be seen that the minimum value of DG output voltage (v odr ) in the case of self-adjusting Q − V droop technique is 0.958 pu which is improved to 0.976 pu in case of the proposed RDCS.

Microgrid test system 2
The network Microgrid test system 2 (MG2) as shown in Figure 4 is used to assess the performance under different network topologies (radial, reconfigured and meshed network). MG2 is adapted from [37] to test the performance of all the three methods in case of the reconfigured and meshed network. The line and load data of MG2 are as shown in Table 4. The switch position and topological structure of the microgrid is shown in Table 5. The inverter parameters for MG2 are: L f = 1.8 mH, C f = 65 F, n = 314.16 rad/s, V dc = 1000 V and V n = 380 V. The controller parameters for MG2 are: m p = 1e − 4 rad/(W s), n q = 1.3e − 3 V/VAr, c = 6.28 rad/s, = 0.2 and add = 0.001. An upper and a lower limit is set for both the d-axis output current (i od ) and the q-axis output current (i oq ) for all the DGs. It is very common to set these current

MG2: Case-1 (radial network)
For the radial structure of the MG2 shown in Figure 4, the switch S 1 is closed and switch S 2 is kept open. Active power (P), reactive power (Q) and v odr of the sources operating in conventional droop, self-adjusting Q − V droop and proposed RDCS is shown in Figure 5 and is also tabulated in Table 6. It can be seen that the Q sh among the sources for the con-

MG2: Case-2 (reconfigured network)
For the reconfigured structure of the MG2 shown in Figure 4, the switch S 1 is kept open and switch S 2 is closed. Active power (P), reactive power (Q) and v odr of the sources operating in conventional droop, self-adjusting Q − V droop and proposed RDCS is shown in Figure 6 and is also tabulated in Table 7. It can be seen that the Q sh among the sources for the conventional droop is not proportional, which is further improved by implementing the self-adjusting Q − V droop technique. However, the voltage deviation is high in the case of self-adjusting

MG2: Case-3 (meshed network)
For the meshed structure of the MG2, both the switches S 1 and S 2 are kept closed. Active power (P), reactive power (Q) and v odr of the sources operating in conventional droop, self-adjusting Q − V droop and proposed RDCS is shown in Figure 7 and is also tabulated in Table 8. It can be seen that the Q sh among the sources for the conventional droop is disproportional, which is further improved by implementing the self-adjusting Q − V droop technique. However, the voltage deviation is high in the case of self-adjusting Q − V droop as compared to the conventional droop. It can be seen that the minimum value of DG output voltage (v odr ) in the case of self-adjusting Q − V droop technique is 0.985 pu which gets improved to 0.990 pu by the use of RDCS.

Comparison of RDCS to virtual impedance technique
The performance of the RDCS is compared with the virtual impedance technique for common plus local load case. The local load is connected near the DG 1 as shown in Figure 1. Four case studies have been performed by implementing the virtual impedance technique. The P, Q and v odr values have been obtained for the following cases: • Case-1: Value of R v kept constant (0 Ω) and the value of X v varies from 0.1 to 1.0 Ω in the steps of 0.1 Ω (results are presented in Table 9).  Table 10). • Case-III: Value of X v kept constant (0.5 Ω) and the value of R v varies from 0.1 to 0.5 Ω in the steps of 0.1 Ω (results are presented in Table 11).  Table 12).
It can be seen from Tables 9 and 10 that for the fixed value of R v (case-I: R v = 0 and case-II: R v = 0.1) the error in Q sh decreases if the value of X v is increased. However, P output and the average value of the Q output of the sources decreases, which is a drawback of the virtual impedance control. The nominal value of P decreases from 3.40 to 3.05 kW and the average value of Q also decreases from 1.68 to 1.51 kVAr for the value of R v = 0 and X v = 1 (refer to Table 9). For the R v = 0.1 and X v = 1, the nominal value of P decreases from 3.40 to 3.01 kW and the average value of Q also decreases from 1.68 to 1.49 kVAr (refer to Table 10).
Whereas P and average Q for RDCS is 3.35 kW and 1.65 kVAR, respectively which is better in comparison to the virtual impedance technique. The error in reactive power sharing is less in the case of RDCS in comparison to the lower value of X v in virtual impedance technique. However, for the higher values of X v , the error in reactive power sharing in virtual impedance technique is less in comparison to the proposed RDCS.
Refer to Table 11, increasing value of R v by keeping X v constant does not bring significant change in the Q err . However, increasing value of R v by keeping X v constant results in noticeable decrement in P and average value of Q output of the sources which is not desirable. Table 12 presents the effect of negative value of R v on Q sh among the sources. The value of X v is kept constant (0.5 Ω) and the value of R v is decreased in the steps of 0.1 Ω from −0.1 to −0.5 Ω. Decreasing the value of R v increases the P and average value of Q output of the sources. It has minimal effect on Q err . However, for the lower values of R v , oscillation in power output is observed.
The results obtained using the virtual impedance technique have been compared with the results obtained using the RDCS. It has been observed that for the higher values of X v , Q err is lesser in comparison to the RDCS. However, the total sum of active power output and reactive power output of the sources decreases in comparison to RDCS, which is not at all desirable. Apart from the drawback of P/Q reduction, implementation of virtual impedance technique also needs feeder current information which is not usually accessible. The RDCS does not require any feeder current information or communication among the sources.

CONTROL PARAMETERS AND add SELECTION, EIGENVALUE ANALYSIS AND EFFECT OF add on Q sh
In this section, the process followed in selecting and add is presented. It is important to study the effect of add on small signal stability margin, and on the Q sh . Eigenvalue analysis is performed to study the same.

Selection of control parameters ( and add )
The selection of the control parameters and add is critical to the performance of the system. To obtain a suitable value of for system-1, has been varied starting from 100 and is decreased until 0.05 as shown in Table 13. The values related to the Q sharing, voltage magnitudes, and the dominant poles determined using eigenvalue analysis have been listed in Table 13.
It can be observed that as the value of reduces, the magnitude of Q err (1−3) decreases, indicating an improved Q sharing. However, for the value of below 0.1 causes an oscillatory behaviour in power output. For of 0.05, the system eigenvalues move towards the unstable region. Hence, a balance has to be achieved between the achievable Q sharing and the sys-tem stability. Hence, a value of 0.2 has been chosen for for system-1.
The same study has been carried out for system-2 considering all the three topological structures (radial, reconfigured and meshed). Results for the radial system is shown in Table 14 and the most appropriate value of is found to be 0.20.
Once the value of gets fixed, the value of add needs to be determined. To obtain a suitable value of add , same steps have been carried out as performed for choosing . Several case studies have been performed for system-1 with common load case and with common plus local load case. The results for variation of add for common plus local load case have been included in Table 15. As seen from the dominant eigenvalues listed in Table 15, add has minimal effect on the stability of the system as well as on the Q sharing performance. add should be selected such that the value of v odr reaches nearer to 1 pu. Besides, maintaining voltage across the network nearer to 1 pu also facilitates synchronisation with other microgrids or with the grid without resorting to the secondary controller-based voltage restoration. It can be observed that for add of 0.004, the voltages are most nearer to 1 pu. Hence, a value of 0.004 is set for add for system-1.
Similar case studies have been performed for setting the value of add for system-2 considering several topological structure (radial, reconfigured and meshed). The results for the system-2 for radial network are as shown in Table 16. A value of 0.001 is found to be appropriate for system-2.

Eigenvalue analysis
Eigenvalue plots and eigenvalue traces of the microgrid utilising the RDCS is obtained by varying add for all the case studies. The eigenvalue plot of the MG1 (case-2) is as shown in  Figure 8. The eigenvalues can be classified into three groups: low-frequency, medium-frequency and high-frequency modes. Low-frequency modes correspond to the power controller loop of the voltage source inverter [38]. The droop controller is associated with the power controller loop, and hence, the lowfrequency modes are sensitive to the parameters related to the droop controller. Eigenvalue trace is obtained by varying the add as shown in Figure 9. add is varied from 0.0 to 0.1 in the step of 0.0001. Little variation (towards imaginary axis) in the sensitive eigenvalues corresponding to the modes associated to DG-1 and DG-2 ( 12 ) and DG-2 and DG-3 ( 23 ) is observed. From the eigenvalue trace, it is found that the parameter add has minimal effect on the stability of the network.

Effect of add on Q sh : Mathematical approach
In this section, the effect of add on the improvement in Q sh is discussed. The Q sh obtained using the proposed RDCS is compared with the Q sh obtained using the self-adjusting Q − V droop technique. The expression of i oq1 − i oq2 as shown below roughly corresponds to the circulating current among the two sources. The following is assumed in this study: • The islanded microgrid consists of two equally rated sources (n q1 = n q2 = n q and m p1 = m p2 = m p ).
• The difference in the q-axis component of the output currents (i oq1 − i oq2 ) is analogous to the difference in Q-sharing between the DG 1 and DG 2 . The difference in the q-axis component of currents [12] is: where A similar exercise to obtain i oq1 − i oq2 for the RDCS has been carried out. The difference in the q-axis component of currents obtained for the proposed RDCS equation is given as follows: It can be seen from (8) and (9) that the denominator of the fractional term in the denominator is changed from V n to ( + add )V n . However, rest all terms remain the same. It is observed that the value of add is very small in comparison to the value of . Hence, the value of ( + add ) ≈ and the effect

EXPERIMENTAL VALIDATION
The performance of the proposed RDCS is validated and compared with the conventional and the self-adjusting droop technique on a low-voltage laboratory prototype shown in Figure 10.
The circuit diagram of the prototype is as shown in Figure 11. The inverters (DG 1 , DG 2 and DG 3 ) are controlled using the Texas Instrument TMS320F28335 digital signal controller. The inverter and controller parameters are shown in Table 17. Line and load data are as shown in Table 18. Experiments are performed for the cases including base case, reconfigured case and mesh formation in the network. For the base case, switches S 1 , S 3 and S 4 are closed and S 2 is open. For the network reconfiguration, switches S 1 , S 2 and S 3 are closed while S 4 is open. For the meshed network case, all four switches are closed. The value of and add are chosen to be 0.4 and 0.02, respectively. The value of add is chosen in such a way that the maximum voltage in the network becomes ≈ 1.0 pu. It is to be noted that the value of m p and n q are kept the same for all the cases.

Base case
Initially, all the DGs are operating with conventional Q − V droop. At t = 6 s, self-adjusting Q − V droop technique is applied to all the DGs, and at t = 17 s the proposed RDCS is applied to all the DGs, respectively. The results for all the three droop techniques are shown in Table 19. Q err (in percentage) in the case of conventional droop is found to be −106, 31 and 75 for DG-1, DG-2 and DG-3, respectively. The   pu as seen in Figure 12. The maximum value of DG output voltage in the case of self-adjusting droop is 0.959 pu which gets improved to 0.998 pu (≈ 1.0 pu) in the case of proposed RDCS.

Reconfigured case
Initially, all the DGs operate with conventional droop technique. At t = 4.5 s, self-adjusting Q − V droop is applied to all DGs and at t = 19.5 s the proposed RDCS is applied to all the DGs respectively. The results are as shown in Table 20. Q err in the case of conventional droop is found to be −109, 23 and 85 for DG-1, DG-2 and DG-3, respectively. The self-adjusting Q − V droop reduces the percentage Q err (to −40, 9 and 31 for DG-1, DG-2 and DG-3, respectively) but the overall voltage profile of the network deteriorates and the minimum value of DG output voltage in the network reaches to 0.907 pu. In the case of proposed RDCS, the percentage Q err (−39, 8 and 31 for DG-1, DG-2 and DG-3, respectively) is similar to that of the self-adjusting droop but the overall voltage

Meshed network
Initially, all the DGs operating with conventional droop control. At t = 8 s, self-adjusting Q − V droop technique is applied to all DGs and at t = 22 s the proposed RDCS is applied to all the DGs respectively. The results are shown in Table 21.
The Q err in the case of conventional Q − V droop is found to be −110, 20 and 90 for DG-1, DG-2 and DG-,3 respectively. The self-adjusting Q − V droop reduces the percentage Q err (to −38, 6 and 32 for DG-1, DG-2 and DG-3, respectively). However, the overall voltage profile of the network deteriorates and the minimum value of DG output voltage in the network reduces from 0.957 pu to 0.907 pu. In the case of proposed RDCS, the percentage Q err (−39, 7 and 32 for DG-1, DG-2 and DG-3, respectively) is similar to that of the self-adjusting droop but the overall voltage profile of the network improves and the minimum value of DG output voltage in the network becomes 0.945 pu which can be seen in Figure 14. The maximum value of

CONCLUSION
A robust droop control strategy (RDCS) based on automatically adjusting the nominal voltage (V n ) has been proposed and validated to improve the voltage profile of the network in a decentralised manner in addition to improved reactive power sharing (Q sh ) among the sources in a droop-based microgrid. The proposed technique does not require data communication and information about feeder impedance and network topology. Various case studies by changing the topological structure of the microgrid, including network reconfiguration and mesh formation, have been performed in MATLAB/Simulink to validate the claim. The performance of RDCS has been found satisfactory for improved voltage profile and Q sh for all the cases. The viability of the proposed controller (RDCS) for different topo-logical structure has been confirmed from experimental validation on a laboratory-based microgrid prototype.

NOMENCLATURE
CL