A Literature Review on the Optimal Placement of Static Synchronous Compensator (STATCOM) in Distribution Networks

Abstract

The existing distribution networks were designed at a time when there was virtually no embedded generation. The design methods ensured the voltage at various parts of the network remained within the limits required by standards, and for the most part, this was very successfully achieved. As Distributed Energy Resources (DERs) started to grow, the rise in voltage due to injected currents and the local impedances started to push network voltages toward, and even above, the desired upper limits. Voltage limits are based on typical appliance requirements, and long-term over-voltages will ultimately result in unacceptably short appliance life spans. Distribution Static Compensators (dSTATCOMs) are shunt-connected devices that can improve low-voltage networks’ performance by injecting currents that do not transfer real power. The currents can be reactive, negative or zero sequence, or harmonic. System performance can be improved by reducing conduction loss, improving voltage profile and voltage balance, or reducing Total Harmonic Distortion (THD). To obtain these benefits, optimal sizes of dSTATCOMs need to be placed at optimal locations within the distribution network. This paper has considered seventy research articles published over the past years related to the optimal placement and sizing of dSTATCOMs. In this study, minimization of power losses, voltage profile improvement, loadablity factor, voltage sag mitigation, and reduction in annual operating costs are considered fitness functions that are subjected to multiple constraint sets. The optimization algorithms found in the literature are categorized into six methods: analytical methods, artificial neural network-based methods, sensitivity approaches, metaheuristic methods, a combination of metaheuristic and sensitivity analysis, and miscellaneous. This study also presents a comparison among distribution network types, load flow methods optimization tools, etc. Therefore, a comprehensive review of optimal allocation and sizing of dSTATCOMs in distribution networks is presented in this paper, and guidance for future research is also provided.

1. Introduction

Voltage drop becomes a significant issue in low voltage (LV) distribution networks. It will manifest at the feeders’ end, increasing the network’s power loss. Distribution networks incur 10–13% $I^{2}R$ losses of the whole generated power due to low voltage and high current [1,2]. Reactive compensation or phase balancing devices can reduce Ohmic losses. Optimal capacitors can be used as reactive compensating shunt devices at optimal locations for voltage profile improvement and the minimization of losses [3]. However, capacitors cannot vary reactive power under variable load conditions [4]. Again, capacitors bring in resonance effect that will lead to voltage and current amplification and that will aggregate thermal degradation and equipment failure [5]. Custom power devices (CPDs) can be used as alternative solutions to capacitors by improving the power quality of the distribution networks. Some of the recently used CPDs are dynamic voltage restorers (DVRs) [6], static synchronous compensators (STATCOMs) [7], static VAR compensators (SVCs) [8], and unified PQ conditioners (UPQCs) [9]. Among all the CPDs, dSTATCOM is getting much attention nowadays due to its several functions such as reactive power compensation, power factor (PF) correction, and harmonic suppression [7,10,11,12]. This is a shunt voltage source converter that can supply or absorb reactive power [13]. Furthermore, STATCOM is used to improve power quality (voltage profile, voltage stability, power loss) in distribution networks [14,15,16]. One of the most attractive features of dSTATCOM is that it can be used in conjunction with photovoltaic systems. This will lead to the sustainable growth of renewables in the distribution network [17,18].

A dSTATCOM is a voltage source converter connected to a particular bus parallel to the network. It compensates for the inductive or capacitive reactive power or sequence power, depending on the needs of the power system [19]. It can also supply or sink active power if it is connected to a battery energy storage system (BESS) [20]. Only one article has considered integrating BESS with dSTATCOM [21]. A dSTATCOM consists of a DC link capacitor, a three-phase three-wire DC/AC voltage source converter (VSC), and a coupling transformer shown in Figure 1 connected in parallel between bus $i$ and bus $k$ [22,23]. The voltages of sending end bus $i$ and receiving end bus $k$ are $V_i$ and $V_k$, and the angles of these buses are ${\delta }_i$ and ${\delta }_k$, respectively. Resistance and reactance of the line between these two buses are $R_{i,k}$ and $X_{i,k}$, respectively. $P_{i,k}$ and $Q_{i,k}$ are the active and reactive power flowing from bus $i$ to bus $k$, respectively. The current flowing through the line is $I_{i,k}$, and $I_d$ is the dSTATCOM current. The hysteresis controller based on pulse width modulation (PWM) is used to control the VSC [24]. In [25], dSTATCOM is considered as three current sources connected to three controllable switches. These switches can be turned on and off to supply or absorb the required amount of reactive power. The state averaging technique is used to model VSC in dSTATCOM [26]. However, the benefits of dSTATCOMS are realized when they are placed in optimal locations and sizes. They cannot be placed in all bus locations, which makes them unnecessary and economically unviable. Therefore, an extensive search on the optimal allocation of dSTATCOMs is important to reduce power losses and cost, improve stability and load balancing, and moreover, enhance the power quality of the distribution network [27,28]. As a result, a growing interest in research is seen in the optimal placement and sizing of dSTATCOM. Figure 2 shows the number of publications from 2011 to 2023. 2011 has the highest number of articles so far, and 2023 shows an increasing trend of publications. Though there are approximately seventy articles found in the literature regarding optimal placement, only one article presents a literature review. Hence, there is an urge for a comprehensive survey to be performed on the existing literature. The main contributions of this paper are:

Figure 1. dSTATCOM connected to the network.

Figure 2. The number of publications from 2011 to 2023.

• Control systems for reactive power compensation have been identified and discussed;
• dSTATCOM is used in the distribution network to reduce power losses, energy losses, and operating costs and improve voltage profile and reliability. The importance of dSTATCOMs has been reported by pointing out the quantitative figures from the existing literature;
• A generalized approach has been undertaken for the optimization of dSTATCOM placement and sizing by considering different fitness functions and constraints;
• The algorithms used for optimization have been classified into six categories, which are briefly discussed;
• This paper also gives an insight into power flow methods, test systems, and optimization tools being used in the existing literature;
• A future research direction has been suggested.

2. Importance of the Optimal Placement of STATCOMs

With the increase in the high penetration of renewable energy sources to the grid, the network tends to operate closer to its technical limits. The power system faces many technical problems, as stated in [29,30,31].

• Power losses;
• Energy losses;
• Voltage violation;
• The need for network updates over time;
• Reliability.

These technical problems can be overcome to some extent by installing dSTATCOMs within the network. The benefits of optimal dSTATCOM placement are shown in Figure 3. The optimal solutions of locations, sizes, and number of dSTATCOMs can have both technical and economic advantages such as reactive power compensation, power factor correction, harmonic suppression, annual operating cost savings, network upgrade cost savings, etc. A literature survey shows the degree of improvement in these sectors in the following section.

Figure 3. Advantages of dSTATCOM placement.

2.1. Power Losses

The optimal placement and sizing of dSTATCOMs can significantly reduce power losses. After placing dSTATCOMs, 18.45%, 24.54%, and 27.66% reductions in power losses have been achieved for industrial, residential, and commercial loads, respectively [32]. Similarly, the Whale Optimization Algorithm (WOA) has been proposed to reduce the losses by 21.60%, 30.71%, and 22.03% for residential, commercial, and industrial loads [33]. The optimal solution proposed in [34] decreases the expected losses by 49.6591%. A reduction in power losses of 29.25% has been achieved by placing STATCOM using the BAT algorithm [35]. In [36], dSTATCOM has been placed with Distributed Generators (DGs) to minimize the losses by 87.67% using a fuzzy-based RAO-3 algorithm. Again, to minimize the power losses, a method combining particle swarm pptimization and the general algebraic modeling system has been proposed, and a 32.54% loss reduction has been achieved [37]. A combined algorithm called the firefly algorithm–sine–cosine acceleration coefficients–particle swarm optimization (FA-SCAC-PSO) has been proposed to minimize losses by 44.83% by installing dSTATCOMs [38]. A STATCOM has been placed optimally through an analytical solution to minimize the losses by 31.01% [39]. A Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ) has been proposed to minimize the losses by 27.15% after placing STATCOM [40].

2.2. Energy Losses

The authors in [41] proposed an analytical method to reduce energy losses by 6.396% after placing dSTATCOM in the optimal location. This paper considered the voltage unbalances in the distribution network and developed a method to reduce the unbalance between phases while reducing energy losses.

2.3. Annual Installation and Operating Cost

Articles [42,43] proposed a mixed-integer second-order cone programming (MI-SOCP) model and a stochastic mixed-integer convex (SMIC) model to minimize the annual operating cost by 14.71% and 29.25%, respectively. The estimated investment cost per STATCOM is found to be USD 9900.26. The optimal solution for the investment cost of STATCOM is USD 17182.21 [34]. A master–slave optimization method has been developed to estimate the annual operating cost of STATCOMs, which was found to be USD 77870.16 for meshed grid topology [44]. The annual operating cost consists of energy loss cost and investment cost. Similar results have been found in [45,46,47,48]; annual operation costs of USD 77,834.42, USD 77,685.48, USD 98,497.89, and USD 109,455.96 were found by applying the generalized normal distribution optimizer (GNDO), the discrete sine–cosine algorithm (DSCA), the discrete continuous vortex search algorithm (DCVSA), and the Chu and Beasley genetic algorithm–second order cone programming (CBGA-SOCP), respectively. The authors in [49] have proposed a discrete–continuous Chu–Beasley genetic algorithm (DC-CBGA) to calculate the expected operation cost of USD 108,196.458. An approximate mixed-integer convex and conic programming algorithm has been proposed to calculate the investment cost of USD 96,767.67 [50]. Annual cost savings of USD 27,776.97 has been reported in [37] after dSTATCOMs installation.

2.4. Voltage Profile Improvement

The voltage deviation index (VDI) is improved by 80.6594%, 85.43%, 70.5%, and 42.25% by placing STATCOMs at optimal locations within the network [34,35,40,51]. The minimum per unit (p.u.) voltage is increased from 0.902 to 0.981 by installing dSTATCOMs, which is an 8.64% increase in voltage profile [36]. Voltage is improved from 0.9131 p.u. to 0.9367 p.u by installing two dSTATCOMs in [52]. After dSTATCOM placement, the distribution network voltage has gone from 0.937 p.u. to 0.96 p.u. [38]. The network voltage profile improvement index (NVPII) is considered in [53] to evaluate the enhancement of voltage profile and is found to be 1.661, which indicates a good enhancement of voltage. dSTATCOM placement has improved the voltages from 0.8948 to 0.9767 p.u. [54]. The minimum voltage is 0.9046 p.u. without dSTATCOM, and after the installation of dSTATCOM, the voltage improved to 0.9305 p.u [39]. A 22.45% voltage improvement has been reported in [55].

2.5. Voltage Stability Improvement

The voltage stability index (VSI) is considered to show the stable operation of the network. The authors in [56] reported a 12.8% improvement in voltage stability. In [55], the VSI improved from 0.6610 p.u. to 0.7228 p.u. The minimum VSI is 0.6610 p.u, and after installing dSTATCOM, it increased to 0.9113 p.u [57]. For 100% load level, the VSI is reported to increase from 57.3865 to 64.4264 [58]. The authors in [40] have reported an increase in the VSI from 0.6951 p.u. to 0.768 p.u. to show the system’s stability improvement.

2.6. Total Harmonic Distortion (THD) Reduction

Total Harmonic Distortion (THD) is reduced by 1.15% after the optimal placement of multiple DGs and dSTATCOMs [59]. Authors have proposed a firefly algorithm (FA) to mitigate THD in all buses to meet the IEEE standard requirements [60,61].

3. Power Flow Analysis

The distribution network has a higher R/X ratio compared to the transmission line. Therefore, the optimum load flow solutions cannot be guaranteed by using the existing following algorithm [32]:

• Newton–Raphson method;
• Gauss–Seidal method;
• Fast decoupled method.

The existing literature has reported the backward/forward sweep (BFS) load flow analysis algorithm as the most efficient one to calculate voltages and power losses at each bus [22,33,39,40,51,62,63]. To solve load flow, a direct approach is adopted in [54,64] to find the voltages and power losses at each node of the network.

3.1. Problem Formulation

An optimization algorithm would need fitness function and associated constraints in a logical manner [65]. A fitness function could be single- or multi-objective, which will define the problems under consideration [66]. Single fitness functions will include the minimization of power losses, energy cost minimization, network voltage profile enhancement, voltage stability improvement, THD reduction, etc. Multi-objective fitness functions will have a combination of two or more single-objective functions. A general procedure and the most common objection functions found in the literature will be discussed as follows.

3.2. Fitness Function

The fitness function can be minimized or maximized depending on the criteria. When the associated constraints are applied, the fitness function is optimized by the algorithm [67,68].

The multi-objective fitness function containing all single-objective fitness functions is expressed in Equation (1).

$$z=y_1+y_2+\dots \dots \dots .+y_n={\sum }_{k=1}^n{y}_n$$

(1)

where $n$ is the number of objective functions that will make a fitness function.

Network Power Losses: The fitness function is formulated to minimize the power losses of the electrical distribution network by the following equation [32,34,37,69,70]:

$$y_1=\min \left(P_{loss}\right)$$

(2)

$$P_{loss}={\sum }_{i=1}^M{\left|I_i\right|}^2{R}_i$$

(3)

where

• $M$ is the total number of lines;
• $I_i$ is the current at $i\mathrm{t}\mathrm{h}$ line;
• $R_i$ is the resistance of $i\mathrm{t}\mathrm{h}$ line.

Total Harmonic Distortion (THD): The objective is to minimize the THD level of the whole system, and the fitness function is given as follows [59,60]:

$$y_2={\sum }_{i=1}^N{THD}_i$$

(4)

$${THD}_i=\frac{\sqrt{{H_1}^2+{H_2}^2+\dots .}}{H_1}$$

(5)

• $N$ = number of buses;
• $H_2,H_3$ = amplitude of all harmonics;
• $H_1$ = fundamental component.

Voltage profile: The fitness function is expressed below [71], and the objective is to maximize the fitness function:

$$y_3={\sum }_{i=1}^N{(V_r-V_i)}^2$$

(6)

where

• $V_r$ = reference voltage;
• $V_i$ = voltage at $i\mathrm{t}\mathrm{h}$ bus.

Loadability factor: The objective is to maximize the equation by increasing the loadability factor ($\lambda$) [51]:

$$y_4={\sum }_{i=1}^N\lambda S_i$$

(7)

where $S_i$ = apparent power at $i\mathrm{t}\mathrm{h}$ bus.

Voltage sag: The fitness function for calculating the total number of sags for all faults is given as follows [72]:

$$y_5=V_{N,sag}+V_{L,sag}+V_{T,sag}$$

(8)

$$N_{sag}={\mu }_N\ast N$$

(9)

where

• $N_{sag}$ = the number of voltage sags due to faults on buses;
• ${\mu }_N=$ the bus fault rate;
• $V_{L,sag}=$ number of sags on faulted distribution lines;
• $V_{T,sag}$ = number of sags on the faulted transformer.

Annual operating cost: The annual operating cost consists of two costs: annual energy loss cost and annual investment cost. The fitness function is expressed as follows [49]:

$$y_6=C_1+C_2$$

(10)

$$C_1=C_{kWh}T{\sum }_{h\in \mathbb{H}}{\sum }_{i\in \mathbb{N}}{\sum }_{j\in \mathbb{N}}{Y}_{ij}{V}_{ih}{V}_{jh}\mathrm{c}\mathrm{o}\mathrm{s}({\delta }_{ih}-{\delta }_{jh}-{\theta }_{ij}){∆}_h$$

(11)

$$C_2=T\left(\frac{b_1}{b_2}\right){\sum }_{i\in \mathbb{N}}(\alpha {\left(Q_i\right)}^2+\beta Q_i+\gamma )Q_i$$

(12)

where

• $C_{kWh}$ = the average cost per $\mathrm{k}\mathrm{W}\mathrm{h}$;
• $T$ = 365 days;
• $Y_{ij}$ = admittance matrix of $i$ and $j$ buses with angle ${\theta }_{ij}$;
• $V_{ih}$ = voltage at $i$bus with angle ${\delta }_{ih}$;
• $V_{ih}$ = voltage at $j$bus with angle ${\delta }_{jh}$;
• ${∆}_h$ = load flow evaluation time;
• $\mathbb{H}$ = a set of periods;
• $\mathbb{N}$ = a set of the number of buses;
• $b_1$= annualized investment costs;
• $b_2$ = dSTATCOM lifespan;
• $Q_i=$ reactive power at $i$th bus;
• $\alpha ,\beta ,\gamma$ = installation cost constant.

Voltage stability index: The voltage stability index (VSI) is used to indicate the stable operation of the distribution network, and it should be $j>0$. The fitness function is calculated at each bus as follows [3,54,73,74,75]:

$$y_7={\left|V_i\right|}^4-4{\left[P_{j,eff}\ast X_i-Q_{j,eff}\ast R_i\right]}^2-4[P_{j,eff}\ast R_i+Q_{j,eff}\ast X_i]{\left|V_i\right|}^2$$

(13)

where

• $P_{j,eff}$ = effective real power fed through bus $j$;
• $Q_{j,eff}$ is effective reactive power fed through bus $j$;
• $X_i$ line reactance between $i$ and $j$ bus;
• $R_i$ line resistance between $i$ and $j$ bus;
• $V_i$ voltage magnitude at $i$th bus.

Reliability index: The distribution authorities should supply reliable electric power to its consumers. If there are any outages or disruptions, the index number helps the authorities to take decisions for future power system planning. The optimal placement and sizing of dSTATCOM can enhance the reliability of the system. To check the reliability of the system, there are different reliability indices such as the system average interruption duration index (SAIDI), the system average interruption frequency index (SAIFI), the customer average interruption frequency index (CAIFI), the customer average interruption duration index (CAIDI), energy not supplied (ENS), average energy not supplied (AENS), etc. [76,77,78,79,80]. The minimization of ENS denotes the improvement of system reliability [33,81,82]. The fitness function is expressed as follows:

$$y_8={\sum }_{i=1}^M{\sum }_{j=1}^{N_L}O{R}_i\ast L_i\ast T_i\ast {LD}_j$$

(14)

3.3. Constraints

The fitness function should satisfy all the constraints within the optimization algorithm. If the algorithm does not satisfy all the given constraints, then the optimum solution would not be achieved, which will lead to malfunctioning performance. The constraints used in the literature are discussed below, and they are used as a combination set by the algorithm [33,34,83]:

Active and reactive power balance constraint: The consumed active and reactive power of the network should be equal to the generated power of the system [84].

$$P_{sub}={\sum }_{m=1}^M{P}_{loss,m}+{\sum }_{i=1}^N{P}_{load,i}$$

(15)

$$Q_{sub}+{\sum }_{b=1}^{N_d}{Q}_{d,b}={\sum }_{m=1}^M{Q}_{loss,m}+{\sum }_{i=1}^N{Q}_{load,i}$$

(16)

where substation active and reactive power are denoted by $P_{sub}$ and $Q_{sub}$. Active and reactive line losses are denoted by $P_{loss}$ and $Q_{loss}$ and active and reactive loads are $P_{load}$ and $Q_{load}$. Reactive power injected by the dSTATCOM is referred as $Q_{d,b}$, and $N_d$ denotes the dSTATCOM numbers.

Voltage constraint: The bus voltages should be within allowable limits, and the constraint is expressed as follows [34]:

$$V_{min}\le \left|V_i\right|\le V_{max},i\in N$$

(17)

where $V_{min}$ and $V_{max}$ are the minimum and maximum voltages at $i\mathrm{t}\mathrm{h}$ node.

Voltage angle constraint: The voltage angle ($\delta$) should vary between the minimum and maximum limit at any particular node [37].

$${\delta }_{min}\le {\delta }_i\le {\delta }_{max},i\in N$$

(18)

dSTATCOM reactive power constraint: dSTATCOM can inject a certain amount of reactive power depending on its capacity [37]:

$$Q_{d,min}\le Q_{d,i}\le Q_{d,max},i\in N$$

(19)

Line capacity: The apparent power passed through the line ($S_L$) should be less than the maximum allowable limit ($S_{L,max}$) [33]:

$$S_{L,i}\le S_{L,max,}i\in M$$

(20)

Thermal constraint: The current flowing through each line ($I_i$) must be less than the maximum allowable current ($I_{max}$) [85]:

$$I_i\le I_{max},i\in M$$

(21)

Size constraint: For each dSTATCOM, there is a limitation in available sizes ($\xi$) [34]:

$${\xi }_{min}\le \xi \le {\xi }_{max}$$

(22)

where ${\xi }_{min}$ and ${\xi }_{max}$ refer to the minimum and maximum dSTATCOM sizes.

Power factor (PF) constraint: The distribution network PF should be within allowable limits as follows [33]:

$${PF}_{min}\le PF\le {PF}_{max}$$

(23)

where the minimum and maximum power factors are denoted by ${PF}_{min}$ and ${PF}_{max}$, respectively.

THD constraint: The THD should be limited to the allowable standard of the distribution network (${THD}_{max}$) [59]:

$${THD}_i\le {THD}_{max}$$

(24)

4. A Generalized Algorithm for Optimal Sizing and Placement of dSTATCOM

A generalized approach is followed in all optimization algorithms to solve the fitness function for dSTATCOMs sizing and locations, which is illustrated as follows:

Step 1:

read the network data such as line data, bus data, and load data;

Step 2

execute the load flow algorithm;

Step 3:

calculate bus voltages and power losses;

Step 4:

determine the optimization algorithm;

Step 5:

determine fitness function (single-/multi-objective) and define inputs of the chosen algorithm;

Step 6:

create the initial population;

Step 7:

compute fitness function;

Step 8:

check whether constraints are satisfied or not;

Step 9:

if not satisfied, go to step 6;

Step 10:

if constraints are satisfied, then the optimum solution is achieved.

The optimization procedure consisting of input data, fitness function, constraint, and output solution is shown in Figure 4.

Figure 4. A generalized optimization procedure for optimal placement and sizing of dSTATCOM.

5. Methods for the Optimal Placement and Sizing of dSTATCOM in Distribution Networks

The literature shows six major categories of methods and techniques being used for optimal sizing and placement of dSTATCOMs, as follows:

• Analytical methods;
• Artificial neural network-based methods;
• Sensitivity approaches;
• Metaheuristic methods;
• A combination of metaheuristic and sensitivity analysis;
• Miscellaneous.

5.1. Analytical Methods

The authors in [86] followed an exhaustive search technique to find the optimal location and size of dSTATCOM. The fitness function includes the minimization of voltages and enhancement of voltage. The proposed method computes the fitness function at each bus to find the minimum value. The proposed method is tested on the IEEE 33 bus network. The limitation of this article is that it is applicable to only one dSTATCOM placement in the distribution network.

In [23], an analytical method is proposed to find the optimal sizing and siting of DG and dSTATCOMs. The stability index and loss sensitivity factor (LSF) are considered in this article to minimize power losses and improve the voltage profile. The proposed method is tested on the IEEE 33 bus network. One of the limitations of analytical approaches is that they do not consider the complexity and nonlinearity of the optimization problem.

The optimal location of dSTATCOM is found by carrying out multiple analytical approaches in [87]. These techniques include the power loss index (PLI), the voltage profile index (VPI), the loss sensitivity factor (LSF), and the performance indicator (PI) to reduce the power losses and improve the voltage profile.

An exhaustive search is carried out for power loss minimization and voltage profile improvement by placing dSTATCOM in the optimal position. The proposed mathematical model calculates the injected reactive power by dSTATCOM and the corresponding power loss at every node of the IEEE 30 network [39]. Again, a similar approach is carried out in [52].

A methodology is developed in [41] to use voltage unbalance detection for optimal placement of a single dSTATCOM. The unbalance of voltages is detected from load flow analysis, and a dSTATCOM is placed on most higher unbalance terminals. However, the method requires a large amount of data to model the distribution network accurately.

5.2. Artificial Neural Network (ANN) Based Methods

In [53], the optimal incorporation of PV, the battery energy storage system (BESS), and dSTATCOM is determined by a fuzzified extended nondominant sorting genetic algorithm (E_NSGA II). Improvement in the voltage profile, environmental benefit, reliability of the network, and a reduction in costs are considered in the fitness function. The test is performed by the IEEE 69 network, and a comparison is made with the multi-objective genetic algorithm (MOGA) [88], strength-Pareto evolutionary algorithm (SPEA) [89], and multi-objective particle swarm optimization (MOPSO) [90]. The proposed methodology takes less computational time and preserves diversity among solutions than the others.

NSGA II is also used as an optimization method along with fuzzy decision-making (FDM) for dSTATCOM placement in [40]. The fitness function includes the VDI, VSI, and power loss. The proposed method is carried out on the IEEE 33 bus system and the Portuguese 94 bus real distribution network considering load uncertainty. The proposed method shows better performance than the immune algorithm (IA) [22] and bat algorithm (BA) [35] by improving the VDI, VSI, and annual cost savings.

A fuzzy-based RAO-3 algorithm is proposed to determine the optimal positioning and sizing of dSTATCOM [36]. The article seeks to mitigate the power loss, improve the power factor, and improve the voltage profile. Rao has proposed the RAO-3 population-based algorithm, which is named after him [91]. An IEEE 69 bus system is considered for implementing this algorithm and shows better performance than the two-stage fuzzy multi-objective method proposed in [92].

5.3. Metaheuristic Methods

An immune algorithm (IA) is proposed in [22] to search for the best location and size of dSTATCOM. The paper seeks to minimize loss and installation costs and enhance voltage and current profiles. The immune algorithm is inspired by the immune system of the human body and is applied to solve optimization problems [93]. The algorithm is tested on the IEEE 33 and 69 bus systems and shows a comparison between the genetic algorithm (GA) and the IA. The IA shows less convergence time, power loss, and installation cost, and has a smaller dSTATCOM size than the GA.

In [85], the differential evolution (DE) algorithm has been applied to optimally place dSTATCOM in the distribution network. The main contribution of the paper is to improve the voltage profile, minimize the power loss, minimize the energy loss and investment cost, and maximize the net saving. Differential evolution is a population-based metaheuristic method that has four stages: initialization of vectors known as chromosomes, mutation with different chromosomes, crossover, and selection [94]. Compensation through dSTATCOMs has been performed on IEEE 30 bus, IEEE 33, and IEEE 69 bus at light, medium, and peak load levels. The paper shows better cost reduction and less convergence time than the immune algorithm and gravitational search algorithm proposed in [22,95], respectively.

Optimal placement problems and reconfiguration are considered in [51] to reduce power loss and improve voltage profile and loadability. Multi-objective particle swarm optimization (MOPSO) is used to create a set of solutions and techniques for order performance by similarity to the ideal solution (TOPSIS), which is used to rank these solutions according to the weighting factors. The proposed methodology is tested on the IEEE 33 and 69 bus systems.

The bacterial foraging algorithm (BFA) requires a high convergence time with higher complexity in selecting parameters and is possibly stuck at local minima [96]. In order to avoid these drawbacks, an improved bacterial foraging algorithm (IBFA) is developed to improve voltage profile and stability and reduce power loss [56]. The difference between the BFA and IBFA is to consider two parameters, such as run time and cell-to-cell signaling mechanisms. The IBFA is tested on a 78-bus Quha feeder of Lachi and shows improvement in voltage profile and stability and a reduction in power losses than the conventional BFA.

A discrete continuous vortex search algorithm (DCVSA) is proposed to reduce the total power losses and annual investment cost of dSTATCOMs by placing them in optimal positions [47]. The VSA, a metaheuristic algorithm, is built upon the vortical demeanors of stirred fluids [97] An improvement of the VSA method is proposed to include the hybrid environment of the problem, named the DCVSA. Optimal sizes and locations are determined by the continuous and discrete codification, respectively. To validate the effectiveness of the algorithm, the IEEE 33 and 69 bus systems are used.

The optimal allocation problem of DG and dSTATCOM is solved by the grey wolf optimizer (GWO) under different load levels [98]. The purpose of this is to reduce power losses and improve voltage stability. The GWO is inspired by the hunting behavior and leadership hierarchy of grey wolves and consists of three main phases: tracking, encircling, and attacking the prey [99]. The proposed method is tested on the IEEE 85 bus system and shows an improvement in power loss reduction and voltage profile.

In [38], the firefly algorithm with the sine–cosine acceleration coefficient–particle swarm optimization (FA-SCAC-PSO) is proposed for the optimal placement of DG and dSTATCOM. The objectives considered in this paper are short circuit level (SCL), voltage deviation level (VDL), net saving level (NSL), environmental pollution reduction level (EPRL), and active power loss level (APLL). The proposed method is compared with other methods proposed in the literature, such as adaptive acceleration coefficient PSO (AAC-PSO) [100], autonomous particles groups for PSO (APG-PSO) [101], time-varying acceleration for PSO (TVA-PSO) [102], nonlinear dynamic acceleration coefficient PSO (NDAC-PSO) [103], and sine–cosine acceleration coefficient (SCAC-PSO) [104], and shows better performance in terms of loss and pollution reduction and improvement in voltage profile and cost saving.

The Whale Optimization Algorithm (WOA) is proposed in [33] to minimize the power loss and energy not supplied (ENS) and enhance voltage profile. The WOA mimics the metaphor of the hunting behavior of humpback whales, which includes fewer operators than evolutionary algorithms. This algorithm consists of three stages: recognizing and encircling the prey, the bubble net attacking method, and searching for prey [105]. The proposed algorithm is implemented on the IEEE 33 and 69 bus networks at residential, commercial, and industrial load levels. The article compares the results with the methods in [35,55,83,106,107] to show better performance in terms of loss reduction and enhancement of voltage profile.

In [48], the Chu and Beasley genetic algorithm (CBGA), along with second-order cone programming, is used to determine the optimal location and size of dSTATCOM, respectively. The algorithm seeks to minimize the annual energy loss costs and investment costs. The CBGA is an evolutionary-based metaheuristic algorithm consisting of three stages: selection, recombination, and mutation [108]. The proposed method is implemented on the IEEE 33 bus system.

The discrete–continuous version of the Chu–Beasley genetic algorithm (CBGA) is proposed, where the locations and sizings are determined by the discrete and continuous codification, respectively [49]. The fitness function consists of a reduction in the annual operating costs of dSTATCOM. The method is tested on the IEEE 33 bus network, both on radial and meshed configurations, which shows better performance than the genetic–convex model [48].

The authors in [44] have proposed a salp swarm algorithm (SSA) with backward/forward power flow as a master–slave approach to find the optimal sizing and siting of dSTATCOMs. The fitness function is associated with a reduction in annual energy loss costs and investment costs. The SSA mimics the behavior of forming a salp chain by gelatinous salps to have better locomotion in the deep ocean [109]. The IEEE 33 bus system is selected as a test feeder to check the effectiveness of the proposed method. One of the limitations of the paper is the application of the proposed method only on distribution feeders without voltage-controlled nodes. If there are multiple voltage-controlled sources, this method will not be applicable.

A generalized normal distribution optimizer (GNDO) along with a successive approximation power flow is proposed in [46] to reduce the annual operating costs of the networks after installing dSTATCOMs. The GNDO is inspired by Gaussian distribution theory to describe the physical and natural phenomena and follows two main steps: local and global exploration [110]. The two-stage optimization method is validated on the IEEE 33 bus network for both radial and meshed topology. A comparison is made with the SSA, and the GNDO demonstrates less operational cost than the SSA.

A population-based metaheuristic algorithm named the discrete sine–cosine algorithm (DSCA) is proposed in combination with the BONMIN solver in GAMS software [45]. This paper offers two stage processes: the master stage uses the DSCA to find the locations and the slave stage uses GAMS software to find the optimal sizes by using the locations found in the master stage. The DSCA uses trigonometric sine and cosine functions to explore and exploit the space vector by varying the amplitude over a number of iterations [111]. GAMS software is a versatile optimization tool to solve linear, nonlinear, and mixed-integer problems by taking lesser convergence time and offering an interface with MATLAB [112]. For these reasons, this software is used in [45] as an interface with MATLAB to find the optimal locations and sizes of dSTATCOMs. The proposed method is tested on the IEEE 33 bus system and shows better performance than the genetic convex algorithm [48] and the discrete Chu and Beasley genetic algorithm (DCBGA) [49].

5.4. Sensitivity Analysis

A sensitivity analysis is proposed for the optimal sizing of dSTATCOM [113]. The aim of the paper is to provide fast recovery of voltages at generator buses at abnormal conditions by injecting reactive power compensation through dSTATCOM. The proposed methodology is tested on 16 and 43 bus systems and considers different DGs, such as wind and solar. This method has reduced the number of dSTATCOM units required for the distribution network, which in turn reduces the costs.

In [59], the voltage stability index is used for solving the optimization problem of dSTATCOM allocation. This solves a multi-objective function consisting of power loss reduction, along with THD and voltage profile enhancement. In this article, a harmonic load flow analysis is used where nonlinear loads are considered as current injectors. The proposed method is carried out on the IEEE 34 bus system.

A two-stage sensitivity analysis is proposed in [114] for optimal sizing and siting of dSTATCOM. The total system loss sensitivity index is used for finding the optimal location, and load flow analysis performed by the Newton–Raphson method, which is used for the optimal sizing of dSTATCOM. The problem considers loss reduction as a fitness function. The proposed method is implemented in the IEEE 14 bus network.

5.5. Combination of Metaheuristic and Sensitivity Analysis

The authors in [54] have proposed a bacterial foraging algorithm (BFA), a population-based search algorithm, to determine the optimal placement and sizing of dSTATCOM, along with Distribution Generation (DG). The BFA is used in conjunction with the loss sensitivity factor (LSF). The fitness function includes power loss and operational cost reduction and voltage profile improvement. E. coli bacteria, which are located in human intestines, show foraging behavior, and the BFA is inspired by this mechanism [115]. The proposed method is tested on the IEEE 33 and 119 bus networks for different load models, showing a 19.45% greater reduction in power losses compared to the immune algorithm [22].

The artificial fish swarm optimization algorithm (AFSOA) along with the VSI is used to find the optimal sizing and location of dSTATCOM. The objective of the proposed algorithm is to reduce the system power losses. The AFSOA is based on the habitual behavior of fish such as preying, swarming, and following the local fish for food [116]. The simulations are carried out on the IEEE 33 and 69 bus systems.

The bat algorithm (BA) along with the VSI is proposed in [35] under multi-load levels. The curve fitting technique (CFT) is to determine the optimal size of dSTATCOM when the load changes. The fitness function considers the minimization of power loss. The BA is based on the finding of prey by bats by using a special sound called echolocation [117]. To check the validity of the proposed method, it is tested on the IEEE 33 and 69 bus networks. The results are compared with the BFA [54] and show better performance in terms of power loss reduction, annual cost saving, and voltage profile improvement. The same approach is adopted in [118]. The only difference is that it does not consider different load levels.

The BA is also used in [69] to determine the optimal sizing while the location of DG and dSTATCOM, which are determined by the LSF and VSI. A reduction in power loss is included as a single objective in the fitness function. The IEEE 34 and 85 bus systems are used for simulations.

The authors in [32] have proposed a combination of the Cuckoo Search Algorithm (CSA), a metaheuristic method and the loss sensitivity factor (LSF) for the optimal placement of dSTATCOM. The LSF is used to find the optimal locations and the CSA is used to find the optimal sizing. The paper seeks to minimize the power losses and enhance the voltage profile considering four load models: constant, residential, commercial, and industrial. The CSA is based on the metaphor of cuckoo birds laying eggs on the other bird’s nest and has two solution populations created through Levy flights and random walk [119,120]. The proposed method is validated on the IEEE 33 bus and IEEE 69 bus systems and shows better performance in terms of minimizing power loss and voltage profile improvement than the methods proposed in [22,54,121,122].

The VSI and LSF are used to determine the optimal locations of dSTATCOM and DG in [107], whereas the CSA is used to find the optimal size of DG and dSTATCOM. The parameters that are to be considered for fitness function are minimizing power loss and improvement of voltage profile. The proposed method is tested on the IEEE 33 and IEEE 136 bus systems for different load levels. The CSA performs better than other methods, such as the backtracking search algorithm (BSA) [123], quasi-oppositional teaching learning-based optimization (QOTLBO) [124], and BFA [54] in terms of computational time and power loss reduction and voltage and power factor improvement.

In [24], the optimal sizing and siting of dSTATCOM and DG are detected by the LSF and dwarf mongoose optimization (DMO) methods. The LSF is used to find the primary location and DMO is used to find the final optimum location. DMO is based on the restrictive behavior of hunting prey of dwarf mongoose [125]. DMO with the LSF seeks to minimize the power loss and operation cost and improve the voltage profile. The performance of the proposed method is compared with the dragonfly algorithm (DA) [126], shell game optimization (SGO), and salp swarm algorithm (SSA) [109].

5.6. Miscellaneous

A Monte Carlo simulation (MCS) is an iterative process, and the convergence time gets smaller with the increase in iteration number. There are two types of MCS: probabilistic and deterministic [127]. Probabilistic evolutionary methods, such as Latin hypercube sampling (LHS) and the k-means-based data clustering method (DCM), have been used to evaluate the objective function in the particle swarm optimization (PSO) algorithm [34]. The proposed method plays a significant role in mitigating power loss, improving the VDI, and decreasing dSTATCOM installation costs considering the uncertain nature of renewable energy sources (RESs). In this article, wind turbine (WT) and solar photovoltaic (PV) cells are considered, which are the algorithms applied to the IEEE 69 bust system. However, there is no proof of comparison of the results found from this method and other existing literature.

A mixed-integer second-order cone programming (MI-SOCP) is a deterministic convex optimization model proposed in [43]. This model aims to minimize the annual installation and operating costs of dSTATCOMs by finding the global optimum. The proposed method has reduced the cost by 13.71% compared to the vortex search algorithm (VSA) discussed in [47]. However, one of the limitations of the proposed strategy is the application to only radial distribution feeders.

In [128], a mixed-integer convex method has been proposed to reduce the annual operating cost of the network by optimally placing dSTATCOMs. The fitness function includes the annual energy loss cost of dSTATCOM placement, which is a convex function due to the resistances of distribution lines, and other investment costs can be approximated to the convex component due to the smaller sizes of dSTATCOM. Therefore, the proposed method can solve the fitness function in a convex environment. To check the validity, it is tested on the IEEE 33 bus system in both radial and meshed configurations. However, similar results have been found in [44] in terms of annual cost savings.

A decoupled optimization technique is proposed in [50] that involves mixed-integer convex optimization reformulation. This includes a mixed-integer quadratic programming (MIQP) model to detect the optimal locations and a second-order cone programming (SOCP) model to select optimal sizes. The objective is to reduce the annual energy loss cost and annual investment cost of dSTATCOM. Simulations are carried out on the IEEE 33 and the 69 bus systems, and a numerical comparison is presented. The decoupled method shows better results than the DCVSA [47].

The authors in [42] proposed a stochastic mixed-integer convex (SMIC) optimization technique by transforming a nonlinear problem into a convex one. The fitness function is a multi-objective function that includes a reduction in annual operating costs. The proposed methodology is tested on the IEEE 33, 69, and 89 bus systems.

6. Comprehensive Literature Review

A comprehensive literature survey of different research works based on dSTATCOM allocation has been summarized in Appendix A Table A1.

6.1. Distribution Network

Most of the research papers have used the IEEE 33 bus network as a test case scenario, which includes 48% of the total publications shown in Figure 5. The IEEE 69 has also been used in many articles, consisting of 15% of the total publications. Only 19% of them have used real distribution network data.

Figure 5. Distribution network test system.

6.2. Load Flow Method

The backward/forward sweep method is one of the popular load flow methods used in the literature. Around 49% of the total publications have used the BFS as a load flow method, which is shown in Figure 6. A direct approach has been adopted in 16% of these publications. Another 13% have used successive approximation methods for load flow analysis.

Figure 6. Load flow methods used in research articles.

6.3. Optimization Methods

Figure 7 gives a complete set of algorithms being used in the publications, which fall under the six categories discussed earlier.

Figure 7. Different algorithms used in the literature.

6.4. Optimization Tool

Most of the research articles have used MATLAB, which is a very powerful tool. MATLAB has been used for both load flow and optimization execution. However, there are other tools that have been used by the researchers for load flow and optimization procedures such as GAMS, DigSILENT, etc. In many publications, BONMIN and COUENNE solvers in GAMS have been to model mixed-integer nonlinear problems. The CVX tool in MATLAB has been used in some of the articles. The percentage of tools being used in the analysis has been shown in Figure 8.

Figure 8. The usage of software tools to solve placement problems.

7. Review Findings

This article considers the continual growth of interest in the optimal placement and sizing of dSTATCOM in distribution networks. After a comprehensive review, the following findings are reported here:

• The published research considers single- and multi-objective fitness functions. The optimization problem becomes complex if there are more objectives within the fitness function. Some of the latest literature has considered the convexification of the cost function. However, there is still scope for more research in handing these multi-objective cost functions and associated constraints;
• Though the implementation of analytical approaches for finding optimal allocation is simpler, easier, and has high precision in solutions that can be achieved, they are not suitable for solving multi-objective and multi-constrained nonlinear problems [66,129]. Metaheuristic methods can handle multi-objective problems and require fewer iterations. However, this comes with the problems of premature convergence, trapping at local optima, and giving unstable results, and shows less diversity among solutions. Hybrid metaheuristic methods can have a faster convergence rate than the single metaheuristic method and can solve mixed environment problems, such as discrete and continuous. Again, they require more setting parameters and skilled persons for coding;
• When an algorithm is used to solve an optimization problem, it is very difficult to understand the validity of the results. A comparison with other existing methods will give an idea of the efficiency, efficacy, and convergence rate of the proposed algorithm;
• From 2021 to 2023, interest has grown in using two-stage (master–slave) optimization techniques for the optimal placement and sizing of dSTATCOM. This technique has just considered annual operating cost minimization as a fitness function. However, loss reduction and voltage profile improvement should also be included within these two-stage approaches;
• Very few articles have reported on the control system or modulator used for the dSTATCOM VSC. As dSTATCOM is the main component of the placement problem, the controller should be described. Moreover, the new controllers suggested in recent literature might increase the performance of the optimization procedure;
• Most of the literature has considered dSTATCOMs without attached energy storage. It is recommended to use dSTATCOM with energy storage to increase the power quality and system reliability;
• There is very little work being performed on unbalanced networks. dSTATCOM can be a useful device to mitigate voltage unbalance in the distribution network. Therefore, voltage unbalance should be considered while performing placement problems;
• The distribution network can have a radial or meshed configuration. Some of the articles have considered both. However, it is useful to test the optimization methods on both networks to check the validity of the results, though the results will be slightly different for both configurations;
• Load variation or uncertainties is another factor that needs to be considered while performing placement and sizing problems; their position and sizing might change depending on load change;
• Voltage sag mitigation can be considered as an objective for fitness function;
• Another important factor of power systems is THD reduction, which has been neglected in the existing literature. THD reduction can be included as an objective of the fitness function to solve for optimal allocation of dSTATCOM;
• The power system should sustain the sustainable growth of renewable energy sources (RES). Another emerging load is electric vehicles (EVs). A combination of RES, BESS, EV, and dSTATCOM should be considered while performing the optimal placement and sizing problem.

8. Conclusions

This article presents a comprehensive literature review of the optimal placement and sizing of dSTATCOM in distribution networks. If dSTATCOMs are placed at optimal locations and with optimal sizes, then the power system obtains the benefits of loss reduction, voltage profile improvement, voltage stability improvement, THD reduction, annual energy loss cost reduction, and annual investment cost reduction. Moreover, it helps to avoid the cost of network upgrades. This paper discusses load flow methods used for the power flow solution. This review also gives an idea of the number of publications over the past years. A comparison is carried out among the existing literature in terms of power loss reduction, annual cost reduction, THD reduction, voltage profile improvement, and voltage stability improvement. Again, it also articulates different algorithms that fall under six categories discussed in the earlier portion of this paper. Analytical methods seem to be easier, but they do not consider the complexity and nonlinearities of multi-objective problems. Therefore, artificial neural networks, metaheuristics, or hybrid approaches are more appropriate for this multi-objective application due to their faster response. This paper presents a complete picture of the existing literature based on the optimal placement and sizing of dSTATCOMs.