An Enhanced Distributed Voltage Regulation Scheme for Radial Feeder in Islanded Microgrid

: Even the simplest version of the distribution networks face challenges such as maintaining load voltage and system frequency stability and at the same time minimizing the circulating reactive power in grid-forming nodes. As the consumers at the far end of the radial distribution network face serious voltage ﬂuctuations and deviations once the load varies. Therefore, this paper presents an enhanced distributed control strategy to restore the load voltage magnitude and to realize power-sharing proportionally in islanded microgrids. This proposed study considers the voltage regulation at the load node as opposed to the inverter terminal. At the same time, a supervisory control layer is put on to observe and correct the load voltage and system frequency deviations. This presented method is aimed at replacing paralleled inverter control methods hitherto used. Stability analysis using system-wide methodical small-signal models, the MATLAB/Simulink, and experimental results obtained with conventional and proposed control schemes verify the effectiveness of the proposed methodology.


Introduction
A reliable and stable distribution network represents a crucial aspect to successful power distribution to load demands. Suppling electrical power to loads can be enhanced using a well-organized distribution system [1,2]. Radial distribution networks (RDNs) are considered the most frequently employed distributed network [2,3]. RDNs are chains of conducting lines, which are divided into smaller branches for power delivery to customer's premises. RDNs are more convenient than other configuration, as it is only fed at one end with low initial network cost. Moreover, it has easy circuit protection schemes to coordinate and design owing to its simplicity in establishing system component rating requirements [4]. As per the power network configuration, RDNs can be divided into three categories, i.e., "AC and DC networks", "single-phase and three-phase networks", and "balanced and unbalanced networks" [5]. Most of the developing countries use the AC distribution network as opposed to the DC network. Using DC distribution is a new technology, which requires fewer conductors for power dispersal, which reduces the line losses and cost of the conductors [6]. On the other side, the AC system could be either a single-phase or three-phase system [7]. A three-phase AC network can be further be classified as a balanced or unbalanced system: a balanced network contains the positive load varies. In this study, the two DG units are connected to MG through interfacing power inverters. Droop control scheme of parallel-connected inverters is employed at consumers end as opposed to inverter terminal. In islanded mode, the inverter droop control should regulate the user voltage, system frequency, and share-power proportionally. Further, the major contributions of this work are listed below,

•
An enhanced distributed control scheme is presented, which can be used for a limited number of grid-forming nodes; • A distributed secondary control layer is employed to restore the load voltage and frequency deviations. Modeling and analysis of an autonomous operation of inverterbased MG being verified through stability analysis using system-wide mathematical small-signal models; • MATLAB/Simulink and experimental results are discussed with a comparison of conventional control schemes under load disturbances.
The remainder of this paper is organized as follows. Section 2 presents the operation principle of the system used in this proposed study. Section 3 outlines the derivations of the small-signal model for this MGs system with the employed controls. Section 4 elaborates the stability analysis of the system under the discussed controls. Further, it also presents the simulation and experimental results in detail with a comparison of the conventional and proposed control scheme, and Section 5 concludes the paper.

Proposed Control Strategy
This section presents the MG setup used in this proposed study. To adequately describe the proposed control scheme, we systematically go about describing the mathematical model and power flow control along with the necessary mathematical representations.

Microgrid Power Network Model
A radial distribution network with a three-phase, three-wire configuration is used in this study, as shown in Figure 1. Power converters and RL load are connected through feeder 1 and feeder 2. This network can work autonomously in an "islanded" mode. Tables 1 and 2 express the rated system parameters for stability analysis, simulation, and experimental prototype. In this study, load voltage magnitude restoration is considered unlikely the voltage regulation at the inverter terminal. By using the reference frame transformation, the load voltage is transformed into d-q axis components. Based on such sensed measurements at ith node of each inverter, the apparent power S is calculated and dispatched to droop controllers of every ith inverter via low-pass filters. Depending on the received information, the droop controllers further send the reference voltage command to inner voltage and current layers. Distributed secondary layer periodically corrects the load voltage and system frequency deviations.

Mathematical Model
To understand the varying power relationship corresponding to change in amplitude and frequency, the complex power delivered to the ith ac bus is expressed in term of network voltages and admittances. The complex power delivered to the ith bus can be expressed as: Applying the algebraic multiplication to Equation (A6) shown by Appendix A and then collecting the real part P i and imaginary part Q i results: Power angle ϕ in medium-voltage lines are small, assuming sinϕ = ϕ and cosϕ = 1, the Equations (2) and (3) re-expressed: where the mathematical expression of term ϕ ij and (V i − V j ) is given in Appendix B. Equations (4) and (5) illustrates a direct relationship among the real power P i and power angle ϕ as well as between the reactive power Q i and voltage difference V i − V j .

Power Flow Control
DC power source is connected with the ith inverter bridge, and its output voltage and frequency are adjusted by the power controller and inner voltage and current controllers. All the operating DG units within the system are individually formulated in their d-q frame, which is based on their angular frequency ω i and angle ϕ i . Power electronics inverters interfaced among each DG unit and grid are converted to the d-q frame by using transformation equation as follows: The angle of ith DG unit's d-q fame can be written: Droop control-based power controller block is shown in Figure 2a. Its purpose is to dispatch the voltage reference v * odi and v * oqi to inner control layers. Average output powers (P i , Q i ) are obtained from instantaneous power passing low-pass filters, where the instantaneous real P and reactive Q power in the d-q rotating frame can be written as p i = v odi .i odi+ v oqi .i oqi and q i = v odi .i oqi+ v oqi .i odi . On individual frame d-q, v odi , v oqi , i odi and i oqi are the load voltage and line current of an ith inverter. Droop strategy demonstrates the relationship among the active power and system frequency p-ω, and between the reactive power and feeder load node voltage magnitude Q-V, can be illustrated as, Pi and n Qi are nominal frequency, voltage and droop coefficients, respectively, of each ith DG unit. Further, the reference voltage to the inner voltage layer is denoted by v* odi . Q-V droop control strategy by considering the load node voltage magnitude can be written by (8), illustrated in Figure 2a.
where V ref is the nominal voltage of all inverters, while v* odi is responsible for restoring the feeder load node load voltage, which regulates the voltage deviation caused by the droop controllers.

Distributed Secondary Control Layer: Voltage and Frequency Regulation
Distributed secondary control layers are used to restores the voltage and frequency deviations as the strategy expressed by Equations (9) and (10).
where the ω ref is the reference frequency, ω DGi is the measured system frequency that is being sensed at all the nodes of ith inverters. The frequency correction term ςω i is sent to the frequency reference of each ith inverter shown in Figure 1. K pf and K if are the proportional and integral gains for controllers.
Load voltage regulations schemes can be expressed as: where V ref and V DGi are the nominal reference voltage and measured system voltage, respectively, in d-axis, which is sensed at each inverter's nodes. K pf and K if are the proportional and integral gains for controllers. The updated voltage correction ςω term is applied to the voltage reference of each ith inverter.

Small-Signal Analysis of the Microgrid System
Intermittent latencies and delay of component communication links may result in power imbalances between generation sources, deviations in node voltages, and system frequency. Therefore, the stability of the system is analyzed by variations in P-f droop gain m P and communication delay T d . The small-signal modeling strategy is based on three important sub-modules, which are the inverter, network, and loads. State equations of the network and the connected loads with any ith DG inverter are presented in the reference frame by using the transformation strategy.

Primary Controller
From measured output current and voltage, the instantaneous power can be written as p = v odi .i odi + v oqi .i oqi and q = v odi .i oqi − v oqi .i odi . The small signal modeled for active power can be obtained as given in (11) by linearization.
Algebraic modeling for the voltage controller and the current controller can be expressed as follows, The small-signal state-space modeling for voltage and current loop is given in Appendix D.

Grid Side Filter Model
The small-signal model of LC output filter and coupling inductance by assuming that voltage provided by the inverter is the same as demand voltage is expressed as in (17)- (19).
The LC filter and coupling inductance, their linearization small-signal equations are represented by Appendix E.

Complete Model of an ith Inverter
The output variables need to the converter in a common reference frame to connect at ith inverter with the rest of the system. In our case, the output currents are the output variables of ith inverters, which can be expressed in vector form ∆i odqi . ∆io DQi , which is a small-signal output current, can be expressed by Appendix E.1. The bus voltage on the common reference frame is the input signal to the ith inverter model. Therefore, by using reverse transformation, the bus voltage can be converted into an ith individual inverter reference frame.
By combining the aforementioned state-space models for three controllers of an ith inverter, which are power controller, voltage controller and current controller, and output grid side LCL filter, the complete small-signal model can be obtained. where The matrices A invi , B invi , B iwcom , C invwi , and C invci are the system matrices described by Appendix C.

Combined Model of N Inverters
In MG, the N number of DG inverters may be operating as a source at variable distances among each other. In this section, our approach is to discuss the possible submodel form of all individual ith to k th DG inverters and combine them with the existing corresponding network. The combined small-signal model of the "N" number of DG inverters is expressed by: where the system matrices are given by Appendix F.

Network and Load Model
If an ith feeder line is connected between node j and k, mathematical modeling can be presented as follows.
where A LOAD , B 1LOAD , B 2LOAD , A LOADi , and B 1LOADi are the system matrices described in Appendix G.

Complete Microgrid Model
It can have observed that the node voltages are used as inputs to every subsystem. In the assurance of well-defined node voltage, a virtual resistor r N is supposed among all m nodes and grounds, which symbolic form can be defined as The diagonal elements of matrix R N is equal to r N, which has a size of 2 m * 2 m matrix. The mapping matrix M INV and M load are the size of 2 m * 2 m and 2 m * 2 p, respectively. M NET matrix maps the connecting transmission lines onto the network nodes having a size of 2 m * 2 n. Finally, the complete MG small-signal model is given by Equation (30).
where A MG is the state matrix and given as

Results and Discussion
In this section, the stability analysis, simulation, and experimental results for power sharing, voltage, and frequency regulation, are discussed. The simulations on MAT-LAB/Simulink are conducted on circuit configuration given in Figure 1 for three-phase 50 Hz islanded MG wherein the two paralleled connected DG1 and DG2 are connected to the RL load via feeder impedance X1-R1 and X2-R2. Moreover, the photo of the lab-scaled experiment hardware is illustrated in Figure 3. System and controller parameters that have been used in conventional and proposed control schemes are shown in Tables 1 and 2.

Modeling Results
The complete model of the test system under the proposed control scheme is achieved and used to analyze the stability of the system under varying communication latencies and control gains. MATLAB/Simulink and linear analysis tools have been used to obtain modeling results by analyzing this complex system through perturbing dynamical equations. Figure 4a,b shows the stability plot for the proposed control framework by varying real power droop gain m P to trace the network trajectory. The control values of the droop gain m P where system poles appear to be in the vicinity of the unit origin are maximum allowable limits. Therefore, using the poles zero evolutions, the control gain sensitivity and system stability are predicted. The maximum and minimum m P gain values used for the proposed control scheme are 1 × 9.5 −9 and 1 × 9.5 −5 , respectively. Figure 4c demonstrates the pole and zero traces resulting from the behavior of the MG system by varying the time delays with the proposed control scheme. Movement of system poles is captured by starting with time delay t d = 0 and increasing it step by step to a maximum time delay of t d = 3 s. Poles are observed in the stable region for the time delay values 0 > td < 1 s and outside the unit circle for the td > 1 s, which makes the MG system divergent and unstable.

Simulation Results
In this section, the MATLAB/Simulink-based results obtained with conventional and proposed control strategies are discussed. The simulation verifications are composed of two cases. Case 1 outlines the results obtained with a conventional control scheme, while case 2 validates the effectiveness of the proposed control strategy. The initial conditions and control parameters as shown by Tables 1 and 2 are the same for both cases. Figure 5 shows the results obtained with a conventional control scheme. The objective of this scheme is to hold the load voltage at its original state, i.e., V ref = 300 V, in the presence of load disturbance. To examine the methodology, the disturbance load (L d1 = 10 mH, R d1 = 20 Ω) is exerted at time t 1 , and later the conventional control scheme is activated at the time t 2 . Figure 5a illustrates the load voltage deviation of 2 V even the load disturbance is not yet exerted. This load voltage further deviates and is set at 393.5 V once the disturbance load is added at time t 1, as shown by Figure 5b. The load voltage drop of 4.5 V is removed once the conventional control strategy is activated at t 2 . Although the conventional scheme is activated, still 2.3 V load voltage deviation is observed, as shown by Figure 5c. Real and reactive power sharing is illustrated by Figure 5d, while Figure 5e,f show the magnified results of real and reactive power, respectively.  Figure 6 shows the results obtained with the proposed control scheme. As opposed to the conventional scheme, the initial load voltage is observed at the desired value, i.e., V ref = 300 V, as shown by Figure 6a. Once the disturbance load jX d1 /R d1 is exerted at t 1 , an obvious 3 V load voltage drop is depicted, as illustrated by Figure 6b. The proposed control scheme is activated at t 2, as shown in Figure 6c, where load voltage has resorted to nearly its original state. Figure 6d,g show the real and reactive power-sharing results, respectively, while Figure 7 demonstrates the frequency restoration result using the proposed methodology.

Experimental Results
An accompanying experiment is carried out to investigate the proposed control scheme. The experiment is conducted for a three-phase, 50-Hz scaled islanded MG prototype, as depicted in Figure 3. The system consists of two identical paralleled DG units with a maximum rating of 3 A, 30 V, connected with RL load via feeder 1 and feeder 2. Ethernet module USR TCP 232 is used for serial communication transmission of data among the data terminal equipment (DTE) and data communication equipment (DCE). The whole platform of islanded MGs is controlled by the desktop control system, wherein LabVIEW has been used to control the DG units. Figure 8a shows the behavior of load voltage in the presence of disturbance load under a conventional control scheme. Load disturbance of value L d1 = 1 mH, R d1 = 5 Ω is added at t 1 as shown in Figure 8b (magnified). From the same figure, 1v load voltage deviation is observed once the disturbance load is added. This deviation is removed when the conventional control strategy is activated at t 2 . However, under the conventional control scheme, still, 2.5 V load voltage deviation is observed, as compared to its original state (V ref = 30 V) as shown in Figure 8c. Figure 8d shows the DGs and load voltage response in the presence of the disturbance load jX d1 /R d1 under the proposed control scheme. About 0.5 V load voltage deviation is noticed once the disturbance load is exerted at t 1 , as shown in Figure 8e (magnified result). This load voltage deviation is removed, and load voltage is restored to its original state (V ref = 30 V), as shown in Figure 8f (magnified result). System frequency error measured at inverter terminal is regulated within an acceptable range once the proposed control scheme is activated at t 2 , as in Figure 8g.

Conclusions
In this paper, an enhanced droop control scheme is presented for microgrids working in islanded mode. The control scheme is able to restore the load voltage deviations and fluctuations due to the droop effect and load effect. The proposed study consists of two decoupled methods, the Q-V control layer shares the reactive power proportionally and restores the load voltage magnitudes, while the P-f control layer addresses the active power sharing and frequency stability. Both sets of control layers have been implemented in a distributed manner. At the same time, the distributed secondary layer is used to regulate the system frequency. Mathematical small-signal models were employed to analyze the performance of the presented scheme using pole-zero evolutions with regard to system stability toward variations in control parameters. Various simulations and experimental results, in comparison to the conventional scheme, showed that the proposed methodology is very effective.

Appendix A
The current injection into ith bus written as where Y ij terms are admittance matrix elements. By substituting Equation (1) into (2), yields: where V i is a phasor term, have the magnitude and angle that can be expressed as V i = |V i |∠ϕ i . Y ij is the complex-valued admittance matrix element that can be defined G ij and B ij as the real and imaginary parts, i.e., Y i = G ij + jB ij ; therefore the Equation (A2) can be expressed as By converting the phasor expression into complex function of sinusoids, i.e., V=|V|∠ϕ = |V|(cosϕ + jsinϕ),

Appendix C. System Matrices
where A MG is the state matrix and given as

Appendix D. Inner Zero Control: Voltage and Current Controller Matrices
Small-signal state-space equations for voltage loop and current loop are Here, both ∆γ di and ∆γ qi are perturbations for PI controllers in the auxiliary state. K PCi and K ICi are the proportional and integral gains for the voltage controller loop, respectively, while i lqi and i ldi are system measurements.

Appendix E. Grid Side Filter Model
LC filter and coupling inductance, their linearization small-signal equations are represented in following equations, where w o , at a given operating point, is the steady-state frequency.
Appendix F.1. Network and Load Model The state equations for RL load connected via an ith node can be written as follows