1. Introduction
In the past few decades, due to the proliferation of renewable energy sources (RESs) and government policies for a reduction in the use of fossil fuel resources, the microgrid has gained attention. The concept of microgrid was introduced in 2000 to improve the reliability, sustainability, and efficiency of modern electric power systems [
1]. An increasing number of distributed generators (DGs) have been incorporated into power distribution systems. DGs include different power generation units such as wind power, solar power, energy storage, and biomass energy. In a small-scale three-phase microgrid, low-capacity DGs are connected to the microgrid system in the form of single-phase devices.
Although DGs have some advantages when used in microgrids, due to the unbalance in loads and uncertainty of power generations in DGs, some issues such as network protection, unbalanced problem, load shedding, voltage regulation, provision of reactive power, and bidirectional power-flow balancing should be considered [
2,
3,
4,
5,
6,
7]. The power generation of DGs is not very stable due to weather conditions. For example, a wind power unit generates electricity on a windy day. A solar power unit cannot supply a sufficient amount of electricity on a cloudy day. Therefore, the microgrid suffers the impact of bidirectional power flow. Moreover, most of the loads mounted on distribution feeders are unbalanced. For example, residential loads are single-phase loads with a lagging power factor. Excessive inductive loads can cause a voltage drop in the power distribution system. Thus, a microgrid with many unbalanced loads and DGs causes problems of unbalanced voltage and current, additional power loss, voltage regulation, and bidirectional power-flow balancing. This increases the difficulty of operating and managing a microgrid, especially for a microgrid with islanding operation ability. Hence, it is crucial to maintain the electric power quality (EPQ) and bidirectional power-flow balancing in a microgrid.
The effects of DGs on distribution systems have been the subject of many research investigations. Authors in [
8] mention the behavior of a microgrid while DGs are in terms of the location of the connection point, and control strategies are considered for a better system performance. Much research has been proposed to improve the reliability of microgrids. In [
9], a two-stage energy management strategy for the contributions of local wind power and plug-in electric vehicles in demand response (DR) programs of commercial building microgrids is addressed, and the power balance can be achieved between the power supply and the load. To enhance the resilience of a photovoltaic-based microgrid equipped with battery storage for supplying a typical commercial building, an optimization is achieved by solving a linear optimization programming problem while the conditional value at risk (CVaR) is incorporated in the objective function [
10]. Authors in [
11] propose a heuristically guided optimization algorithm for the optimum use of existing electrical/thermal resources in home microgrids (H-MGs). In [
12], a smart transactive energy (TE) framework is proposed to maximize the profit and energy-balancing efficiency of H-MGs. In [
13,
14,
15], authors explore a reverse power problem and load-balancing technique in a microgrid. Authors in [
16,
17,
18,
19,
20] have discussed reactive power control and voltage regulation issues in microgrids. However, a compensation scheme integrating bidirectional power-flow balancing and EPQ improvement in a three-phase microgrid is seldom seen.
SVCs and STATCOMs have been frequently used in power distribution systems as load compensation and voltage regulation devices to enhance EPQ [
21,
22,
23,
24]. In this study, a shunt-type, delta-connected universal compensator was developed for improving the operation performance of a three-phase, distribution-level microgrid with unbalanced DGs and loads. The symmetrical components method was employed to derive a feedforward compensation principle for the compensator. For practical application, the universal compensator can be used as SVCs, STATCOMs, active filters, and a combination of delta-connected reactors and capacitors without using an energy storage element. The major contribution of this work is that the proposed compensator can easily achieve the bidirectional power-flow balancing and EPQ improvement caused by unbalanced DGs and loads in a three-phase, distribution-level microgrid.
Section 2 in this paper describes the structure of a microgrid with unbalanced DGs and loads that is used as the test system. In
Section 3, use of the symmetrical components method derived the feedward compensation principle for the compensator. A bidirectional power-flow balancing was achieved. The power quality of the microgrid was also improved using the compensator. Several definitions of power quality performance indexes used in the study are introduced in
Section 4.
Section 5 uses the MATLAB/SimuLink program (R2017a, The MathWorks, Inc., Natick, MA, USA) to implement the microgrid as the test system. The operation performance of the microgrid with the proposed shunt compensators was investigated.
Section 6 presents the conclusion.
2. The Microgrid Circuit Model
Figure 1 presents a radial-type microgrid with unbalanced DGs and loads. The microgrid is a three-phase, three-wire, seven buses, radial-type microgrid with unbalanced (single-phase) DGs and loads. These single-phase DGs are connected between phase
b and phase
c at Bus 2, 4, 5, and single-phase loads are connected between phase
a and phase
b at Bus 2, 3, 4, and 6. The proposed shunt compensator can be installed on selected buses to improve the EPQ and achieve bidirectional power-flow balancing.
The symmetrical components method can simplify the unbalanced microgrid system for conducting a steady-state analysis. The required compensation principle of the proposed shunt compensator can also be derived.
Figure 2 presents the equivalent circuit model between two neighboring buses in
Figure 1. Equation (1) can be obtained by applying Kirchhoff’s Voltage Law. Equation (2) presents the impedance matrix of the three-phase distribution lines, where
,
, and
are self-impedance and
,
, and
are mutual impedance. In general, the mutual impedance can be neglected in a power distribution system [
25]. By combining Equations (1) and (2), Equation (3) is obtained. By using the symmetrical components method, the sequence networks are derived by using Equation (4). In Equation (4),
T is the symmetrical components transformation matrix and
T−1 is the inverse symmetrical components transformation matrix, as presented in Equation (5).
A sequence circuit equation is obtained by solving Equation (4). The sequence circuit equation is presented in Equation (6), which can also be used to represent sequence networks between two neighboring buses in
Figure 1.
As presented in
Figure 2, the three-phase load side current comprises currents of the single-phase DG and load that are connected between phase
b and phase
c, and phase
a and phase
b, respectively. Hence, the sequence currents are expressed as a combination of the two currents, as presented in Equation (7).
Figure 3 shows the sequence circuit models of
Figure 2, which were used to derive the compensation principle of the compensator in
Section 3.
3. Compensation Principle
Figure 4 presents the main circuit structure and the corresponding sequence circuit models of the proposed compensator in the paper.
Figure 4a is the three-phase, delta-connected main circuit model of the shunt compensator, which can be converted into sequence circuit models, as illustrated in
Figure 4b.
Figure 5 shows the system for deriving the real-time compensation scheme of the compensator. The load side current comprises the currents of the single-phase DG and load connected between different phases. The shunt compensator is used to compensate for the unbalanced load side current.
The three-phase line voltages of the compensator presented in
Figure 5 are expressed in Equation (8). Phase
a to neutral was selected as the phase angle reference.
is the effective value of the line-to-neutral voltage. The three-phase line currents of the load side are expressed in Equation (9), in which the relationship of
is used. By using the symmetrical components method, the positive- and negative-sequence components of the load side currents are obtained in Equations (10)–(12). The zero-sequence component is zero in a three-phase, three-wire power system.
The three arm currents and the synthesized line currents of the compensator are expressed in Equations (13) and (14), respectively. By using Equations (13) and (14), the sequence components of the synthesized compensator line currents are obtained using Equation (15). By substituting Equation (14) into Equation (15), the positive- and negative-sequence components of the compensator line currents can be rewritten as Equations (16) and (17), respectively. In Equation (15), the zero-sequence component of the line currents is zero in a delta-connected compensator.
For unbalanced-load current compensation, the compensator should eliminate the entire negative-sequence component and the imaginary part of the positive-sequence component of the load current, as shown in Equations (18) and (19) [
26,
27]. By combining Equations (18) and (19), the compensation command of the delta-connected compensator is obtained for each arm, as presented in Equation (20). The rating of the compensator can also be determined from Equation (20).
Figure 6 displays the positive- and negative-sequence circuits presented in
Figure 1, where the proposed compensator is installed at Bus 1. Equation (21) presents the positive- and negative-sequence load side currents at each bus including the DG’s contribution. The compensator connected at Bus
n can compensate for the imaginary part of the positive-sequence load side current and the entire negative-sequence load side current. For example, if the compensator is connected at Bus 1, then the compensator executes the compensation rule presented in Equations (18) and (19). Thus, the power source side only supplies a balanced three-phase current with a unity power factor, and the power quality is improved.
where,
n = 2, 3, 4, 5, 6.