Re-Allocation of Distributed Generations Using Available Renewable Potential Based Multi-Criterion-Multi-Objective Hybrid Technique

Abstract

Integration of Distributed generations (DGs) and capacitor banks (CBs) in distribution systems (DS) have the potential to enhance the system’s overall capabilities. This work demonstrates the application of a hybrid optimization technique the applies an available renewable energy potential (AREP)-based, hybrid-enhanced grey wolf optimizer–particle swarm optimization (AREP-EGWO-PSO) algorithm for the optimum location and sizing of DGs and CBs. EGWO is a metaheuristic optimization technique stimulated by grey wolves, and PSO is a swarm-based metaheuristic optimization algorithm. Hybridization of both algorithms finds the optimal solution to a problem through the movement of the particles. Using this hybrid method, multi-criterion solutions are obtained, such as technical, economic, and environmental, and these are enriched using multi-objective functions (MOF), namely minimizing active power losses, voltage deviation, the total cost of electrical energy, total emissions from generation sources and enhancing the voltage stability index (VSI). Five different operational cases were adapted to validate the efficacy of the proposed scheme and were performed on two standard distribution systems, namely, IEEE 33- and 69-bus radial distribution systems (RDSs). Notably, the proposed AREP-EGWO-PSO algorithm compared the AREP at the candidate locations and re-allocated the DGs with optimal re-sizing when the EGWO-PSO algorithm failed to meet the AREP constraints. Further, the simulated results were compared with existing optimization algorithms considered in recent studies. The obtained results and analysis show that the proposed AREP-EGWO-PSO re-allocates the DGs effectively and optimally, and that these objective functions offer better results, almost similar to EGWO-PSO results, but more significant than other existing optimization techniques.

1. Introduction

Distributed generations (DGs) have become an attractive option for integrating power distribution systems due to their economic, technical, and environmental advantages [1,2]. Although DGs can offer several benefits to the system, their installation is subject to their primary energy source’s availability and geographical location [3]. On the other hand, DGs can cause undesired effects in the system, such as fluctuations in the voltage profile, increased fault current, and inversion in the power flow direction, etc. [4,5]. These effects become more evident when DGs use renewable energy resources (RER). RER play an energetic role in resolving environmental and security issues. They have a probabilistic nature, such as wind speed and solar irradiation [6]. Therefore, technical studies should be conducted to properly install DGs in passive systems, avoiding the degradation of reliability, system operation, and supply quality [3].

In a radial distribution system (RDS), the reactive power flow is considered the main reason for power quality issues [6]. The compensation of reactive power plays the leading part in power system planning. The capacitor banks (CBs) are treated as the familiar reactive power resources that offer loss reduction, voltage regulation, stability improvement, and a financial return for distribution companies when optimally installed in distribution systems [3,7,8].

To reduce the overall production costs and improve system reliability, both the DGs and CBs are commissioned as real and reactive power injection sources [7]. The installation of DG and the capacitor in the distribution network has various technical and economic benefits [9]. These multiple benefits cannot be achieved without the appropriate allocation of the DGs and CBs in power system networks. Further, the optimal allocation of both DG and CB can be carried out using optimization techniques using several methodologies [10]. The complete analysis of the existing works relating to the optimization is described in the following section.

The techniques proposed for the placement of DG and CB in distribution networks can be divided into four types: numerical, analytical, metaheuristic, and hybrid optimization [10,11]. The analytical methods have fast convergence, but their computational time and complexity become high when the type and number of DGs and CBs increases [12]. This is particularly true for multi-objective formulations with a large number of equality and inequality constraints. Analytical approaches require more robust algorithms to solve differential and nonlinear equations. In this respect, metaheuristic techniques are helpful in solving the distribution system problems which do not involve differential equations. However, the algorithms need to be appropriately tuned to reach the global solution for DG sizing and placement [12,13].

Among various metaheuristic optimization techniques, particle swarm optimization (PSO) is the most widely used for the siting and sizing DGs. PSO has significantly better computation efficiency, i.e., its functional evaluation. A vital issue with PSO is the trapping of particles into local optima that could consume a large amount of time to converge to an optimal solution. Additionally, there is no guarantee that the optimal solution will be global optima. As a result, several research works highlighted the hybridization of the standard PSO with analytical approaches or other optimization techniques for achieving better results [14]. By using a hybrid optimization technique, better optimization results can be produced by merging two optimization algorithms [9]. Instead of searching in the whole area, the search space is limited by loss sensitivity factor (LSF), increasing the possibility of finding a good solution. After selecting the candidate buses by LSF, an optimizer finds the optimum size of DGs and CBs on the buses. Consequently, a fast convergence is achieved without compromising the siting and sizing aspects [10,14].

2. Literature Surveys

A complete survey of numerous literary works associated with the optimal installation of DGs and CBs is elaborated in

Table 1. Survey of prevailing research works with respect to optimal installation of DGs and CBs.

Ref. No.	Year	Optimization Algorithm	Objectives	Constraints	Allocation		Inferences	Limitations
					DG	CB
[17]	2018	Improved grey wolf optimizer (IGWO)	Minimizing generation cost, power loss, and voltage deviation	Equality, generator, transformer, bus voltage, line loading, and installed reactive power resource constraints		√	Improved rate of convergence with quality solution	Voltage stability and power factor constraints are neglected
[10]	2018	Modified power loss index + Crow search (MPLI + CS)	Minimize active power loss and cost	Bus voltage, reactive power injected, complex power, capacitor size and power factor		√	Reduced search space, accurate and quick convergence	Voltage stability is not considered
[18]	2019	Voltage stability index + Genetic algorithm (VSI + GA)	Minimize feeder current, voltage deviation and power losses	Voltage and branch current carrying capacity	√	√	Hourly variation of load demand is modelled	Relaxed network constraints and single test system
[7]	2020	Enhance grey wolf algorithm (EGWA)	Minimize total investment costs, maximize voltage profile, loading capacity, and benefits from the reduction of losses and purchased power	Equality constraints, DG penetration level, power factor limit, CB size, node voltage, and branch current limits	√	√	Improved performance, highly stable and superior capabilities	Voltage stability and emission perspectives are ignored
[3]	2016	Tabu search + Chu–Beasley genetic algorithm (TS + CBGA)	Minimize investment and operation costs	Technical and operational constraints	√	√	Very efficient and used for planning the system	Single test system and stability constraint is ignored
[19]	2017	Grasshopper optimization algorithm + Cuckoo search algorithm (GOA + CSA)	Minimize voltage deviation, line losses, and cost	Equality, load bus voltage and DG capacity	√		Less complexity with reduced computational time	Limited type of DGs, voltage stability, and emission analysis are ignored
[11]	2017	Hybrid grey wolf optimizer (HGWO)	Minimizing total real power losses	Equality, Bus voltage, DG unit size, and power factor	√		Algorithm performance is enhanced without tuning	Demand uncertainties and reliability are not considered
[20]	2017	Harmony search algorithm + Particle artificial bee colony (HSA + PABC)	Minimize real power loss, line loading, and voltage deviation	Bus voltage, thermal limit of the lines, maximum power injection from DGs and CBs	√	√	Enhanced performance with fast convergence	Economic and voltage stability constraints are ignored
[21]	2018	HGWO-PSO	Minimizing power losses	Equality, bus voltage, line current, total generated power, and DG size	√		Optimal solution with less iteration.	Power factor and voltage stability constraints are ignored
[13]	2019	Multi-objective hybrid teaching learning-based optimization-grey wolf optimizer (MOHTLBOGWO)	Minimizing power losses and improving reliability	Equilibrium, bus voltage, DG size, and line capacity	√		Improved speed of convergence and no local trapping	Solar PV and wind resources are only considered
[12]	2019	Hybrid teaching-learning based optimization	Minimize power losses, voltage deviation and maximize voltage stability index	Equality, active and reactive power balance, voltage and thermal limits, and DG penetration	√		Avoidance of local minima/maxima trappings and improved convergence	Tuning of algorithm parameters are required; limited type of DGs
[22]	2019	Hybrid Whale optimization algorithm—Salp swarm algorithm (WOA-SSA)	Minimize power losses and voltage deviation	Bus voltage magnitude, DG number, and capacity	√		More effective and better execution time	Convergence is ignored, and limited types of DGs
[23]	2019	Hybrid weight improved particle swarm optimization + gravitational search algorithm (WIPSO + GSA)	Maximize total cost benefit	DG and capacitor power limits, voltage limits of bus	√	√	Feeder’s failure rate is evaluated through compensation coefficients, greater convergence speed	DGs with reactive power capabilities and stability are ignored
[1]	2020	Hybrid GA + PSO	Minimize active, reactive power losses and voltage deviation	Active and reactive power balance, voltage, line, and DG power limits	√		More realistic, accurate, improved performance, and easy to apply	Cost analysis, stability, and environmental factors are ignored
[14]	2020	Analytical hybrid PSO (AHPSO)	Minimize total cost	Real power of DG, angle deviation limit, and line current flow	√		Modified 2/3rd rule is used, faster convergence	No power factor and voltage stability assessment
[24]	2020	Hybrid Parameter improved PSO—Sequential quadratic programming (PIPSO-SQP)	Minimize real power loss	Net power flow, DG limit and node voltage	√		Highly stable, rapid convergence and less computation time	No power factor, cost analysis, and voltage stability assessment
[25]	2020	Hybrid Phasor PSO and GSA (PPSOGSA)	Minimize active power losses	Equality, bus voltage, THD of voltage, branch flow, DG and capacitor capacity, and positions	√	√	Different constraints are used, solutions are effective, robust with high-quality and less no. of iterations	Limited type of DGs, power factor constraint, stability, and economic issues are ignored
[26]	2020	Hybrid CBGA—Vortex search algorithm (CBGA- VSA)	Minimize power loss	Complex power and network voltage	√		Successive approximation power flow is used. More efficient and better solution with low computational times	Limited type of DGs, emission, and stability investigations are ignored
[27]	2021	Hybrid empirical discrete metaheuristic—Steepest descent method (EDM-SDM)	Minimize power losses	Active and reactive power balance, DG status and limits, and voltage	√		High-quality and straightforward solutions with low tuning parameters	Stability and economic evaluations are ignored

[15,16].

The existing works demonstrate the optimal allocation of DGs without considering the potential of the renewable resources. Further, optimal DG allocation combined with the potential assessment of renewable energy sources (RESs) could save time, effort, and planning for current and future DG unit installations [28] for real-time systems. This work examines the available renewable energy potentials (AREPs) at all the locations of IEEE 33- and 69-bus RDSs. The renewable energy technologies in this study include solar photovoltaic (PV), wind turbine (WT), and gas turbine (GT).

A summary of the limitations of existing works is as follows:

• DGs with unity power factor (UPF) alone has been considered in few approaches.
• In a few cases, CBs and/or DGs locations were fixed.
• Economic and environmental implications and a few network constraints have been ignored.
• The simulation time and the results have been non-optimal in few existing techniques.
• Re-allocation of DGs based on available renewable energy potential (AREP) has not been considered.

Based on these limitations, the distribution network performance needs to be improved further using DGs in accordance with AREP. Therefore, a new multi-objective AREP-based hybrid optimization technique is proposed by combining enhanced grey wolf optimizer with particle swarm optimization (AREP-EGWO-PSO). This hybridization can incorporate the benefits of both methods and overcome the drawbacks, simultaneously and optimally achieving the solution [21].

The proposed AREP-based hybrid EGWO-PSO targets to accomplish the optimal re-allocation of DGs based on AREP in RDSs with multi-objectives are as follows:

• To enhance the technical objectives, viz., power loss and voltage deviation reduction and voltage stability index improvement.
• To minimize costs of CBs and generated power.
• To resolve the environmental implications by reducing emissions from the generated units.

The above-described multi-objectives can be demonstrated through five operational cases of DGs/CBs to discover the technical, economic, and environmental impacts through the proposed AREP-EGWO-PSO method.

The rest of the article is organized as follows: the problem statement is described in Section 3. The proposed AREP-based hybrid EGWO-PSO optimization algorithm is demonstrated in Section 4. In Section 5, various test systems and cases are discussed to examine the proposed algorithm’s efficacy. Section 6 deliberates the numerical results and discussions in detail. A conclusion of the entire work based on the observed results is presented in Section 7.

3. Problem Statement

The problem statement involves finding the optimal placement and sizing of CBs and DGs with multi-objective functions (MOBJs) while ensuring the equality and inequality operational constraints as detailed below.

3.1. Objective Functions

The primary purpose of the proposed method is to achieve three conflicting objectives such as technical, economic, and environmental functions.

3.1.1. Technical Objectives

• The distribution network power losses (obj₁) can be minimized [29] by

$${\mathrm{obj}}_1=\min ({{\displaystyle \sum }}_{\mathrm{j}=1}^{\mathrm{nbr}}\left|{\mathrm{I}}_{\mathrm{j}}^2\right|{\ast \mathrm{R}}_{\mathrm{j}}),$$

(1)

where I_j is the current magnitude of jth branch, R_j is the jth branch resistance, and nbr is the aggregate number of distribution network branches.

• The voltage deviation index (obj₂) can be minimized [30] using Equation (2).

$${\mathrm{obj}}_2=\min (\mathrm{VDI})=\min ({{\displaystyle \sum }}_{\mathrm{i}=1}^{{\mathrm{N}}_{\mathrm{LD}}}{({\mathrm{V}}_{\mathrm{j}}-1)}^2),$$

(2)

where V_j defines the voltage magnitude at jth bus, N_LD is the aggregate number of PQ or load buses.

• The voltage stability index (obj₃) can be maximized using Equation (3) [16,28]:

obj₃ = max (VSI),

(3)

$$\mathrm{VSI} (\mathrm{k})=\{\left|{\mathrm{V}}_{\mathrm{m}}^4\right|-4{({\mathrm{P}}_{\mathrm{n}}{\mathrm{X}}_{\mathrm{mn}}-{\mathrm{Q}}_{\mathrm{n}}{\mathrm{R}}_{\mathrm{mn}})}^2-4({\mathrm{P}}_{\mathrm{n}}{\mathrm{R}}_{\mathrm{mn}}+{\mathrm{Q}}_{\mathrm{n}}{\mathrm{X}}_{\mathrm{mn}}){\left|{\mathrm{V}}_{\mathrm{m}}\right|}^2\}$$

(4)

where V_m terms the voltage magnitude at mth node, P_n and Q_n are the real and reactive power of the load at nth node, respectively, and R_mn and X_mn are the resistance and reactance of the branch between the nodes m and n, respectively. Moreover, the stability of a distribution system with ‘j’ number of nodes describes the function as VSI (k) ≥ 0, for k = 2, 3,…, j.

3.1.2. Economic Objective

To minimize the total costs of electric power generated, the following expressions can be applied [16]:

$${\mathrm{obj}}_4=\min ({{\displaystyle \sum }}_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{DG}}}({\mathrm{C}}_{\mathrm{DGj}})+{\mathrm{C}}_{\mathrm{SS}}+{\mathrm{C}}_{\mathrm{CB}}),$$

(5)

where N_DG is the aggregate number of DG units. Further, the cost of generation for an individual DG unit (C_DGj) can be determined as:

$${\mathrm{C}}_{\mathrm{DGj}}=\mathrm{f}+\mathrm{v}\ast {\mathrm{P}}_{\mathrm{DGj}}$$

(6)

where P_DGj is the active power at jth DG unit, and the fixed cost coefficient of generation ‘f’ and variable cost coefficient of generation ‘v’ can be evaluated as follows:

$$\mathrm{f}=\frac{\mathrm{Capital} \mathrm{cost} \mathrm{of} \mathrm{DG} \left(\$/\mathrm{kW}\right)\ast \mathrm{DG} \mathrm{capacity} \left(\mathrm{kW}\right)\ast {\mathrm{B}}_{\mathrm{r}}}{\mathrm{life} \mathrm{time} \left(\mathrm{year}\right)\ast 8760\ast \mathrm{LDF}},$$

(7)

v = (DG fuel cost ($/kWh) + DG operation and maintenance cost ($/kWh)),

(8)

where B_r is the rate of benefit per annum, and LDF denotes the DG load factor.

Moreover, the substation generated cost (C_SS) can be determined as follows:

C_SS = P_gSS ∗ P_rSS,

(9)

where, P_gSS is the active power generated in the substation and P_rSS is the cost of real power generated at the substation. Further, the CB cost of investment (C_CB) can be determined by Equation (10).

$${\mathrm{C}}_{\mathrm{CB}}=\frac{{{\displaystyle \sum }}_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{CB}}}\left({\mathrm{I}}_{\mathrm{j}}+{\mathrm{P}}_{\mathrm{j}}\left|{\mathrm{Q}}_{\mathrm{CBj}}\right|\right)}{\mathrm{life} \mathrm{time} \left(\mathrm{year}\right)\ast 8760}$$

(10)

N_CB is the total number of CB units, I_j and P_j are the installation and purchase costs, respectively, and Q_CBj is the reactive power rating of the jth CB unit.

3.1.3. Environmental Objective

The most critical pollutants, namely, carbonic acid gas (CO₂), sulphur dioxide (SO₂), and oxides of nitrogen (NO_x), are produced by the power-generating units. The mathematical equation for the minimization of the generation units’ emissions (obj₅) can be derived as follows [29]:

$${\mathrm{obj}}_5=\min ({{\displaystyle \sum }}_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{DG}}}{\mathrm{E}}_{{\mathrm{DG}}_{\mathrm{j}}}+{\mathrm{E}}_{\mathrm{SS}}),$$

(11)

E_DGj = (CO₂^DG + NO_x^DG + SO₂^DG) ∗ P_DGj,

(12)

E_SS = (CO₂^SS + NO_x^SS + SO₂^SS) ∗ P_gSS.

(13)

3.2. Constraints

3.2.1. Power Balance

In a power distribution network, the sum of incoming power is to be equivalent to the sum of outgoing power as follows [31,32]:

$${\mathrm{P}}_{\mathrm{sl}}+{{\displaystyle \sum }}_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{DG}}}{\mathrm{P}}_{\mathrm{DGj}}={{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{nb}}{\mathrm{P}}_{\mathrm{Lossk}}+{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{dk} },$$

(14)

$${\mathrm{Q}}_{\mathrm{sl}}+{{\displaystyle \sum }}_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{DG}}}{\mathrm{Q}}_{\mathrm{DGj}}+{{\displaystyle \sum }}_{\mathrm{k}=1}^{{\mathrm{N}}_{\mathrm{CB}}}{\mathrm{Q}}_{\mathrm{CBk}}={{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{nb}}{\mathrm{Q}}_{\mathrm{Lossk}}+{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{n}}{\mathrm{Q}}_{\mathrm{dk}} .$$

(15)

where P_sl and Q_sl are slack bus real and reactive powers, respectively, P_DGj and Q_DGj are the capacity of DG real and reactive powers at jth bus, respectively, P_Lossk and Q_Lossk are the line real and reactive power losses of kth bus, respectively, P_dk and Q_dk are the real and reactive power demands at kth bus, respectively, and ‘n’ is the aggregate number of buses in the distribution network.

3.2.2. Inequality Constraints

• Generator performance [16]:

P_DGj^min ≤ P_DGj ≤ P_AREP^max,

(16)

Q_DGj^min ≤ Q_DGj ≤ Q_DGj^max.

(17)

where P_DGj^min is the DG real power minimum capacity at jth bus, P_AREP^max is the maximum available active power of RES, and Q_DGj^mini and Q_DGj^maxi are the minimum and the maximum capacity of DG reactive power at jth bus, respectively.

• Sizing of DGs [33]:

$${{\displaystyle \sum }}_{\mathrm{j}=1}^{{\mathrm{N}}_{\mathrm{DG}}}{\mathrm{P}}_{\mathrm{DGj}}\le {\mathrm{P}}_{\mathrm{AD}}.$$

(18)

where P_AD is the aggregate real power demand.

• Reactive power from DG and CB resources:

The reactive power supplied by DGs and CBs are subjected to lowest and highest limits [17,28], as expressed in Equation (19):

Q_Rj^min ≤ Q_Rj ≤ Q_Rj^max_, = 1 … N_RR.

(19)

where Q_Rj is the reactive power from the DG and CB at jth node, Q_Rjmin and Q_Rjmax are minimum and maximum capacity limits of reactive power from CB and DG resources, respectively, N_RR is the number of commissioned resources of reactive power.

• Bus voltage:

The bus voltage constraints [34] are expressed as:

V_dj ^min ≤ V_dj ≤ V_dj^max, j = 1 … N_D.

(20)

where V_dj^min and V_dj^max are minima and maximum acceptable voltage values at jth node, respectively, V_dj is the RMS voltage of jth load bus, N_D is an aggregate number of buses with the load. In addition, the standard IEEE 1547 indicates the voltage is to be regulated between the limits ± 5%. Thus, V_dj^min and V_dj^max are allowed to vary between the values of 0.95 p.u. and 1.05 p.u., respectively [35].

• Power factor of DG [11,16]:

0.7 ≤ DG_PF ≤ 1.

(21)

where DG_PF is the power factor of DGs of Type-I and Type-III.

3.3. LSF Based Optimal Location of DGs and CBs

The location of candidate buses for DGs and CBs in the distribution network are identified by the LSF, and it can be calculated using Equation (22) at each bus of the network from the solution of base case load-flow. Then, the priority list is formulated by sorting the LSF values in descending order [36].

$${\mathrm{LSF}}_{\mathrm{ij}}=\frac{\partial {\mathrm{P}}_{\mathrm{ij} \mathrm{loss}}}{\partial {\mathrm{Q}}_{\mathrm{j}}}=\frac{2{\mathrm{Q}}_{\mathrm{j}}{\mathrm{R}}_{\mathrm{ij}}}{{\left|{\mathrm{V}}_{\mathrm{j}}\right|}^2}$$

(22)

Moreover, the normalized voltages are determined using Equation (23) for all the buses. The candidate’s buses are selected if the normalized voltage values are lower than 1.01 [32,37].

V_i,normalized = V_i/0.95.

(23)

Furthermore, DGs can be shown as negative loads of real and reactive powers [38,39], and the modified active as well as reactive powers at the jth node (P_newj and Q_newj) can be determined using the following Equations:

P_newj = P_L − P_DG,

(24)

Q_newj = Q_L − Q_DG.

(25)

where P_L and Q_L are the active and reactive power load, respectively, P_DG and Q_DG are the active and reactive power supplied from DGs, respectively.

4. AREP-Based Hybrid EGWO-PSO Optimization Algorithm

The combination of improved GWO and PSO metaheuristic techniques is utilized for the hybrid EGWO-PSO technique. The AREP is included with this hybrid method and has been described in detail. Similar to the conventional GWO algorithm, the social hierarchy modeling of grey wolves in the EGWO algorithm considers alpha (α) an appropriate solution, while the β and δ are considered to be the second and third finest solutions, respectively. Moreover, the remainder of the solutions is treated as ω in the population. In this method, the hunting process is executed by α, β, and δ wolves, whereas ω wolves trail these wolves to reach the global minimum [40,41]. The values of ‘a₁’ are linearly reduced from 2 to 0 in the conventional GWO algorithm, however it causes an exploratory result which reduces the rate of convergence. To improve a balance between the exploration and exploitation, the convergence rate of the traditional GWO technique and the amendment proposed in [17] are utilized as described below:

$${\mathrm{a}}_1=\mathsf{\varsigma } \exp (-\mathsf{\varphi }\ast \mathrm{t}),$$

(26)

where ς and ϕ regulates the GWO rate of convergence over ‘t’ iterations. In addition, to maintain the exploratory feature and accelerate the algorithm’s convergence rate, the vector ‘a₁’ is transformed into a random nonlinear vector.

The wolves’ position Y is updated by averaging the best three grey wolves α, β, and δ in the conventional GWO algorithm. It causes premature convergence and imperfect quality of nonconvex in the optimization problems [16]. To improve the efficiency of the traditional GWO algorithm, the weighted distance method proposed in [17] is utilized in this work. Consequently, the positions are updated in each iteration and weighted (wt) using the following expressions [16]:

$${\mathrm{wt}}_1={\mathrm{A}}_{\mathsf{\alpha }}·{\mathrm{C}}_{\mathsf{\alpha }},\hspace{1em}{\mathrm{wt}}_2={\mathrm{A}}_{\mathsf{\beta }}·{\mathrm{C}}_{\mathsf{\beta }},\hspace{1em}{\mathrm{wt}}_3={ \mathrm{A}}_{\mathsf{\delta }}·{\mathrm{C}}_{\mathsf{\delta }},$$

(27)

$$\mathrm{Y}\left(\mathrm{t}+1\right)=\frac{{\mathrm{wt}}_1.{\mathrm{Y}}_1+{\mathrm{wt}}_2.{\mathrm{Y}}_2+{\mathrm{wt}}_3.{\mathrm{Y}}_3}{{\mathrm{wt}}_1+{ \mathrm{wt}}_2+{ \mathrm{wt}}_3}.$$

(28)

where the terms A and C are GWO coefficients, Y is the grey wolf position, and t is the current iteration. The coefficients, namely A and C, are determined using the following Equations [42]:

A = a₁(2r₀ − 1),

(29)

C = 2r₁,

(30)

where r₀ and r₁ are random numbers that are selected uniformly in the range between 0 and 1.

The positions of grey wolves, α, β, and δ are randomly updated according to the position of the best search agent, and this entire hunting process can be mathematically modeled as follows [42]:

$${\mathrm{D}}_{\mathsf{\alpha }}=\left|{\mathrm{C}}_{\mathsf{\alpha }}·{\mathrm{Y}}_{\mathsf{\alpha }}-\mathrm{Y}\right|, {\mathrm{D}}_{\mathsf{\beta }}=\left|{\mathrm{C}}_{\mathsf{\beta }}·{\mathrm{Y}}_{\mathsf{\beta }}-\mathrm{Y}\right|, {\mathrm{D}}_{\mathsf{\delta }}=\left|{\mathrm{C}}_{\mathsf{\delta }}·{\mathrm{Y}}_{\mathsf{\delta }}-\mathrm{Y}\right|,$$

(31)

$${\mathrm{Y}}_1={ \mathrm{Y}}_{\mathsf{\alpha }}-{\mathrm{A}}_{\mathsf{\alpha }}·{\mathrm{D}}_{\mathsf{\alpha }}, {\mathrm{Y}}_2= \mathrm{Y}-{\mathrm{A}}_{\mathsf{\beta }}·{\mathrm{D}}_{\mathsf{\beta }}, {\mathrm{Y}}_3={\mathrm{Y}}_{\mathsf{\delta }}-{\mathrm{A}}_{\mathsf{\delta }}·{\mathrm{D}}_{\mathsf{\delta }}.$$

(32)

The search can be completed when the algorithm attains the desired number of iterations. The exploration capability of the EGWO algorithm is utilized in the PSO algorithm to improve the exploitation ability of PSO and further enhance the quality and stability of the final solution. In the PSO technique, each particle denotes a candidate solution characterized by its position and velocity. The preceding experience, current velocity, and the neighbor’s knowledge are used to alter the positions with respect to time. The enhanced GWO randomly creates and updates the initial population. The updated solutions are again updated with the individual position and velocity in the iteration (t + 1) as follows [43]:

$${\mathrm{v}}_{\mathrm{j}}^{\mathrm{t}+1}={\mathrm{W}}^{\mathrm{t}}{\mathrm{v}}_{\mathrm{j}}^{\mathrm{t}}+{ \mathrm{c}}_1{ \mathrm{r}}_1 \left({\mathrm{PBest}}_{\mathrm{i}}^{\mathrm{t}}-{\mathrm{x}}_{\mathrm{j}}^{\mathrm{t}}\right)+{ \mathrm{c}}_2{\mathrm{r}}_2 \left({\mathrm{GBest}}^{\mathrm{t}}-{\mathrm{x}}_{\mathrm{j}}^{\mathrm{t}}\right)$$

(33)

$${\mathrm{x}}_{\mathrm{j}}^{\mathrm{t}+1}={\mathrm{x}}_{\mathrm{j}}^{\mathrm{t}}+{ \mathrm{v}}_{\mathrm{j}}^{\mathrm{t}+1}.$$

(34)

where v_j^t and v_j^t+1 are jth particle velocity in ‘t and t + 1′ iteration, respectively, x_j^t and x_j^t+1 are jth particle position vectors in ‘t and t + 1′ iteration, respectively, r₁ and r₂ denote random numbers, c₁ and c₂ denote acceleration constants. To increase the convergence speed, the inertia weight is updated using the following equation:

$${\mathrm{W}}^{\mathrm{t}}={\mathrm{W}}^{\mathrm{t}}\ast (1-\mathsf{\mu }).$$

(35)

where W^t denotes the inertia weight and μ represents update coefficient.

The algorithm continues to run until an optimum result is attained or the total number of iterations reaches a maximum predefined number.

The running time of the AREP-EGWO-PSO algorithm is increased because of the merged operation of PSO and enhanced GWO algorithms. This extended running time can be accepted based on the optimization problem type. The steps involved in implementing the proposed AREP-EGWO-PSO technique are demonstrated using the flowchart shown in Figure 1.

As bus number 1 is taken as the slack bus, the potential of PV, WT, and GT DG’s are assessed for the remaining buses in the system. The simulation can be terminated when it satisfies the stopping criterion and displays the re-allocated DG units of the distribution network while fulfilling all the constraints. The details of AREP for IEEE 33 and 69 bus systems are shown in Appendix A and Appendix B, respectively.

5. Case Study

The standard IEEE 33- and 69-bus radial distribution networks are considered to study the proposed AREP-based EGWO-PSO algorithm’s effectiveness, as illustrated in Figure 2 [16]. A simulation study was carried out using MATLAB, and MATPOWER was used to carry out the power flow simulations [44].

To validate the performance of the AREP-EGWO-PSO algorithm, five operational cases are presented for the optimal allocation of DGs. In this study, the EGWO-PSO technique allocates DGs/CBs initially, and the proposed algorithm re-allocates the DG’s based on AREP at various nodes of the distribution system except slack bus. Further, the optimal siting and sizing of CBs obtained by EGWO-PSO are retained for cases 2, 4, and 5.

• Case 1: Optimal allocation of DGs at UPF
• Case 2: Optimal allocation of DGs at UPF with fixed CBs
• Case 3: Optimal allocation of DGs at Lagging/leading power factor (LPF)
• Case 4: Optimal allocation of DGs at LPF with fixed CBs

Three technical objectives (obj₁, obj₂, obj₃) are evaluated for the above cases (1 to 4). The multi-objective function can be constructed using Equation (36):

MOBJ₁ = min (obj₁, obj₂, obj₃).

(36)

• Case 5: Optimal allocation of multi-DGs with fixed CBs

In this case, three different combinations of eq] (obj₁, obj₄, and obj₅) are taken into account, and their MOBJ can be stated using Equation (37):

MOBJ₂ = min (obj₁, obj₄, obj₅).

(37)

Different types of DGs have distinct properties of economic and environmental factors. Three DGs of a kind such as PV, WT, and GT are considered, as shown in

Table 2. Characteristics of DGs.

DG Type	Life Time (Year)	Rated Capacity (MW)	Capital Cost ($/kW)	Fuel Cost ($/kWh)	O&M Costs ($/kWh)	Emission Factors (lb/MWh)
						NOx	SO2	CO2
Grid	25	25	-	0.044	-	5.06	11.6	2031
PV	20	1	3985	-	0.01207	-	-	-
WT	20	5	1822	-	0.00952	-	-	-
GT	12	3	1224	0.0667	0.06481	0.279	0.93	1239.2

. Moreover, substation-generated power cost is assumed as 0.044 $/kWh, and Pi and Ii are deemed to be 30 and 1000 $/kVAR, respectively [29].

6. Results and Discussions

To show the effectiveness of the proposed AREP-based algorithm in an optimal allocation of DGs, the IEEE 33-bus and IEEE 69-bus test systems were utilized. Type I and Type III DG units were considered for the analysis. The algorithm was executed with the number of wolves or size of the population, which was 30, and it stopped when the maximum iteration number reached 50. The PSO algorithm considers inertia weight as 1, and social and cognitive component weights are the same, i.e., 2 [45]. Moreover, per unit (p.u.) system was used in all the calculations. The AREP-EGWO-PSO approach and the power-flow solution were executed using the software package MATPOWER 7.0 [44] embedded in MATLAB 2018a software with a configuration of i5 CPU, 1.60 GHz, 8.00 GB RAM, 4-bit operating system. The following sections analyze the results of the various test cases considered.

6.1. IEEE 33-Bus System

The standard IEEE 33-bus distribution network comprises of 33 buses and 32 radial distribution lines. The net complex power loads are 3.72 MW + j 2.3 MVAR [29]. The base values of 100 MVA and 12.66 kV are considered in this study. The voltage level of load buses declines towards the end node. The DGs and CBs are used to enhance the voltage profiles of various buses, thereby reducing the current flows and line losses. Moreover, the uncompensated real power loss for this distribution network is observed as 202.68 kW.

6.1.1. Case 1

Simulation results of the suggested AREP-EGWO-PSO method in comparison with existing optimization techniques are shown in

Table 3. Case 1 of 33-bus system with DGs operating at UPF.

Methods	Power Loss (KW)	DGs Size (MW)/Position	Min. Voltage (p.u.)/Bus	VDI (p.u.)	VSI (p.u.)
Base case	202.68	--	0.913/18	0.1171	0.6968
Water cycle algorithm (WCA) [29]	71.05	0.855/14, 1.102/24, 1.181/29	0.973/33	--	--
Improved decomposition-based evolutionary algorithm (I-DBEA) [30]	94.85	1.098/13, 1.097/24, 1.715/30	--	0.0007	0.9650
Comprehensive teaching learning-based optimization (CTLBO) [34]	85.96	1.036/13, 1.163/24, 1.522/30	--	0.0026	0.9481
CTLBO ε-method [34]	96.17	1.193/13, 0.871/25, 1.629/30	--	0.0009	0.9638
Teaching learning-based optimization (TLBO) [46]	124.69	1.183/12, 1.191/28, 1.186/30	--	0.0011	0.9503
Quasi-oppositional TLBO (QOTLBO) [46]	103.40	1.083/13, 1.188/26, 1.199/30	--	0.0011	0.9530
GA [47]	106.30	1.500/11, 0.423/29, 1.071/30	0.981/25	0.0407	0.9497
PSO [47]	105.30	1.177/8, 0.982/13, 0.829/32	0.980/30	0.0335	0.9256
GA/PSO [47]	103.40	0.925/11, 0.863/16, 1.200/32	0.980/25	0.0124	0.9508
Fireworks algorithm (FWA) [48]	88.68	0.589/14, 0.189/18, 1.015/32	0.968	--	--
HSA [49]	96.76	0.572/17, 0.107/18, 1.046/33	0.967/29	--	--
Ant colony optimization and artificial bee colony (ACO-ABC) [49]	71.40	0.755/14, 1.099/24, 1.071/30	--	--	--
EGWO-PSO [16]	71.46	0.754/14, 1.099/24, 1.071/30	0.969/33	0.0135	0.8813
AREP-EGWO-PSO	72.53	0.823/13, 1.121/24, 0.934/31	0.970/30	0.0140	0.8871

. It was perceived that the EGWO-PSO algorithm allocates three DGs, initially with sizing 0.754, 1.099, and 1.071 MW at buses 14, 24, and 30, respectively. Since the AREP at bus numbers 14 and 30 are inadequate (Appendix A), the proposed method eliminates these two buses and re-allocates the DGs at new buses 13, 24, and 31 with penetration of 0.823, 1.121, and 0.934 MW, respectively. Under these operating conditions, active power loss becomes 72.53 kW, and minimum voltage occurs at node 30, though with an improved value of 0.970 p.u. The VDI is reduced from its original value to 0.0140 p.u. and VSI is improved from the base value to 0.8871 p.u.

6.1.2. Case 2

Table 4. Case 2 of 33-bus system with DGs operating at UPF and CBs.

Methods	Power Loss (KW)	DGs Size (MW)/Position	CBs Size (MVAR)/Position	Min. Voltage (p.u.)/Bus	VDI (p.u.)	VSI (p.u.)
Base case	202.68	--	--	0.913/18	0.1171	0.6968
WCA [29]	24.69	0.563/11, 0.973/25, 1.04/29	0.535/14, 0.465/23, 0.565/30	0.980/33	--	--
EGWO-PSO [16]	15.16	0.746/14, 1.078/24, 1.048/30	0.528/11, 0.712/23, 1.000/29	0.994/22	0.0003	0.9786
AREP-EGWO-PSO	16.00	0.811/13, 1.098/24, 0.921/31	0.528/11, 0.712/23, 1.000/29	0.994/22	0.0004	0.9767

demonstrates the output result of the EGWO-PSO technique that installs the DGs at buses 14, 24, and 30 and CBs at buses 11, 23, and 29, respectively. The proposed algorithm reserves the allocation of CBs and checks the AREP only for DG buses. On account of deficient AREP at nodes 14 and 30, these nodes are eliminated, and the proposed algorithm re-allocates the DGs at new nodes, namely 13, 24, and 31, with capacities of 0.811, 1.098, and 0.921 MW, respectively. When compared with other algorithms, power loss reduction of 16.001 kW is accomplished by the proposed algorithm. The bus voltage is minimum at bus 22 with 0.994 p.u. Additionally, VDI decreases from its base value to 0.0004 p.u. VSI is further improved to 0.9767 p.u.

6.1.3. Case 3

In the cases mentioned above, the DGs are disallowed to feed reactive power in the distribution system.

Table 5. Case 3 of 33-bus network with DGs operating at LPF.

Methods	Power Loss (KW)	DGs Size (MW)/Position/Power Factor	Min. Voltage (p.u.)/Bus	VDI (p.u.)	VSI (p.u.)
Base case	202.68	--	0.913/18	0.1171	0.6968
I-DBEA [30]	14.57	0.749/13/0.85, 1.042/24/0.85, 1.239/30/0.85	--	0.0002	0.9733
Loss sensitivity factor simulated annealing (LSFSA) [50]	26.70	1.383/6/0.85, 0.552/18/0.85, 1.063/30/0.85	--	0.0013	0.9323
EGWO-PSO [16]	11.68	0.779/13/0.91, 1.072/24/0.89, 1.036/30/0.72	0.993/8	0.0006	0.9707
AREP-EGWO-PSO	15.50	0.780/14/0.89, 1.103/24/0.89, 0.937/31/0.73	0.991/8	0.0009	0.9626

presents summary of the proposed method simulation results, accompanied by the existing approaches in the literature. From the AREP availability, it is found that there are inadequate capacities at nodes 13 and 30 allotted by the EGWO-PSO method. Then, the proposed technique eradicated these nodes and re-locates the DGs at buses 14, 24, and 31. The total DG size is reduced to 2.820 MW, but active power losses are increased to 15.50 kW. Further, VDI diminishes from 0.1171 p.u. to 0.0009 p.u. and VSI augments from 0.6968 p.u. to 0.9626 p.u. The minimum voltage of 0.991 p.u. is held at the same bus.

6.1.4. Case 4

Similar to case 2, the proposed AREP-EGWO-PSO algorithm retains the optimal allocation of CBs and examines the AREP for DG buses only. Since AREP at nodes 13 and 30 are insufficient, the proposed algorithm eliminates these nodes and re-allocates the DGs at nodes 14, 24, and 32 with penetration of 0.782, 1.109, and 0.909 MW, respectively. The multi-objectives (MOBJ1) are compared with other existing methods, as presented in

Table 6. Case 4 of 33-bus network with DGs operating at LPF and CB.

Methods	Power Loss (KW)	DGs Size (MW)/Position/Power Factor	CBs Size (MVAR)/Position	Min. Voltage (p.u.)/Bus	VDI (p.u.)	VSI (p.u.)
Base case	202.68	-		0.913/18	0.1171	0.6968
WCA [29]	19.85	0.992/11/0.91 0.982/31/0.98 1.650/24/0.96	0.325/19, 0.312/23, 0.543/30	0.989/18	0.0410	0.9850
EGWO-PSO [16]	14.99	0.778/13/1 1.072/24/0.99 1.035/30/0.99	0.524/11, 0.693/23, 1.000/29	0.994/22	0.0003	0.9788
AREP-EGWO-PSO	16.35	0.782/14/1 1.109/24/0.99 0.909/32/0.99	0.524/11, 0.693/23, 1.000/29	0.994/8	0.0004	0.9762

. The real power losses increased from 14.99 kW to 16.35 kW, and were obtained through the EGWO-PSO method. The bus voltage is minimum at bus 8 with 0.994 p.u. Furthermore, VDI decreased to 0.0004 p.u. and VSI increased to 0.9762 p.u from their actual values.

6.1.5. Case 5

Table 7. Case 5 of 33-bus system with multi-objective placement and sizing.

Methods	Power Loss (KW)	Grid Real Power (MW)/Reactive Power (MVAR)/Position	CBs Reactive Power (MVAR)/Position	WT Real Power (MW)/Reactive Power (MVAR)/Position	PV Real Power (MW)/Reactive Power (MVAR)/Position	GT Real Power (MW)/Reactive Power (MVAR)/ Position	Cost ($/h)	Emission (lb/h)
Base case	202.68	--	--	--	--	--	304.896	8.027 × 106
WCA [29]	28.96	1.541/0.657/1	0.30/15 0.45/19 0/26	0.648/0.147/25	0.715/0.439/32 0.639/0.278/27	0.201/0.052/18	249.343	3.405 × 106
EGWO-PSO [16]	19.22	1.014/ 0.243/1	0.30/15 0.45/19 0/26	0.775/0.422/25	0.173/0.836/32 1.301/0.074/27	0.472/ 0.021/13	227.372	2.290 × 106
AREP-EGWO-PSO	21.49	0.842/ 0.026/1	0.30/15 0.45/19 0/26	1.064/ 0.429/24	0.723/ 0.186/28 0.598/ 0.882/30	0.501/ 0.0429/18	274.134	2.467 × 106

furnishes the multi-objective technical, economic, and environmental benefits (MOBJ2) of DGs allocations in a 33-bus network with pre-allocated CBs. It indicates that the proposed technique eliminates inadequate AREP nodes 13 and 27 and re-allocates the DGs at new nodes 18, 24, 28, and 30. The sizing of renewable DGs is PV at nodes 28 and 30 with 0.7231 MW and 0.59387 MW, respectively, WT at node 24 with 1.0642 MW, and GT at node 18 with 0.50067 MW. As the total sizing of DGs is increased to 2.8863 MW, the power losses, cost of power generated, and total emission all are escalated from the values obtained by the EGWO-PSO algorithm.

6.2. IEEE 69-Bus System

This standard distribution network comprises 69 buses with 68 distribution lines with net complex power loads (3.802 MW + j 2.694 MVAR) [29]. The base values of 10 MVA and 12.7 kV are considered. Among 69 buses, the buses 4, 8, 9, 11, and 12 have two branches, and bus 3 has three branches, whereas the remaining buses contain only a single branch associated with their subsequent bus. The uncompensated active power loss for this radial distribution network is observed as 225 kW.

6.2.1. Case 1

The simulation results of the proposed AREP-EGWO-PSO technique for three DGs operating at UPF are shown in

Table 8. Case 1 of 69-bus system with DGs operating at UPF.

Methods	Power Loss (KW)	DGs Size (MW)/Position	Min. Voltage (p.u.)/Bus	VDI (p.u.)	VSI (p.u.)
Base case	225	--	0.909/65	0.0993	0.6850
WCA [29]	71.50	0.775/61, 1.105/62, 0.438/23	0.987/65	--	--
I-DBEA [30]	78.35	2.149/61, 0.472/19, 0.713/11	--	0.0002	0.9772
CTLBO [34]	76.37	0.560/11, 0.427/18, 2.153/61	--	0.0008	0.9770
CTLBO ε-method [34]	79.66	0.966/12, 0.231/25, 2.134/61	--	0.0003	0.9770
TLBO [46]	82.17	1.013/13, 0.990/61, 1.160/62	--	0.0008	0.9745
QOTLBO [46]	80.59	0.811/15, 1.147/61, 1.002/63	--	0.0007	0.9769
GA [47]	89.00	0.929/21, 1.075/62, 0.984/64	--	0.0012	0.9706
PSO [47]	83.20	1.199/61, 0.796/63, 0.993/17	--	0.0049	0.9676
GA/PSO [47]	81.10	0.885/63, 1.193/61, 0.911/21	--	0.0031	0.9768
FWA [48]	77.85	0.226/27, 1.199/61, 0.409/65	0.974/62	--	--
HSA [49]	86.77	0.102/65, 0.369/64, 1.302/63	0.968	--	--
ACO-ABC [49]	69.43	0.559/11, 0.346/21, 1.715/61	--	--	--
EGWO-PSO [16]	69.43	0.527/11, 0.380/18, 1.719/61	0.979/65	0.0052	0.9205
AREP-EGWO-PSO	76.50	0.528/18, 1.361/60, 0.454/65	0.978/61	0.0063	0.9164

compared to existing methods. The EGWO-PSO method installs three DGs at buses 11, 18, and 61. Since the AREP is inadequate at nodes 11 and 61, the proposed algorithm removes it and re-allocates three DGs at new buses 18, 60, and 65, with penetration of 0.528, 1.361, and 0.454 MW, respectively. The active power loss is increased to 76.50 kW compared to the EGWO-PSO method. The minimum voltage is observed at node 61, about 0.978 p.u. The VDI decreased from its actual value to 0.0063 p.u. and VSI is augmented to 0.9164 p.u from its base value.

6.2.2. Case 2

In this case, three DGs at UPF are installed at buses 11, 17, and 61, and three CBs at buses 61, 64, and 69 (

Table 9. Case 2 of 69-bus system with DGs operating at UPF and CBs.

Methods	Power Loss (KW)	DGs Size (MW)/Position	CBs Size (MVAR)/Position	Min. Voltage (p.u.)/Bus	VDI (p.u.)	VSI (p.u.)
Base case	225	--	--	0.909/65	0.0993	0.6850
WCA [29]	33.34	0.541/17, 2.000/61, 1.159/69	1.188/2, 1.237/62, 0.269/69	0.994/50	--	--
EGWO-PSO [16]	7.86	0.496/11, 0.380/17, 1.655/61	1.000/61, 0.413/64, 0.476/69	0.994/50	0.0002	0.9794
AREP-EGWO-PSO	14.12	0.521/17, 1.295/60, 0.449/65	1.000/61, 0.413/64, 0.476/69	0.994/50	0.0003	0.9794

). The proposed technique maintains the CBs allocation and compares the AREP for DG buses only. Owing to the lack of AREP at nodes 11 and 61, these nodes are eliminated, and DGs are reinstalled at new nodes, 17, 60, and 65, with a sizing of 0.521, 1.295, and 0.449 MW, respectively, by the proposed algorithm. It is observed that there is an increase in a power loss of 14.12 kW when compared with EGWO-PSO; nevertheless, it is less compared to WCA. The value of VDI is further minimized to 0.0003 p.u. with an augmented VSI scale to 0.9794 p.u.

6.2.3. Case 3

Table 10. Case 3 of 33-bus system with DGs operating at LPF.

Methods	Power Loss (KW)	DGs Size (MW)/Position/Power Factor	Min. Voltage (p.u.)/Bus	VDI (p.u.)	VSI (p.u.)
Base case	225	--	0.909/65	0.0993	0.6850
I-DBEA [30]	7.97	1.500/61/0.85, 0.370/59/0.85, 0.575/16/0.85	--	0.0003	0.9774
LSFSA [50]	16.26	0.549/18/0.85, 1.195/60/0.85, 0.312/65/0.85	--	0.0023	0.9678
EGWO-PSO [16]	4.27	0.495/11/0.81, 0.379/18/0.83, 1.674/61/0.81	0.994/50	0.0001	0.9794
AREP-EGWO-PSO	13.98	0.516/18/0.83, 1.312/60/0.81, 0.455/65/0.82	0.994/50	0.0005	0.9778

shows the results of the allocation of DGs operating at LPF. Primarily, the EGWO-PSO technique sites the buses at 11, 18, and 61, however buses 11 and 61 are eliminated by the proposed AREP-EGWO-PSO method because of inadequate AREP at these buses. Further, the algorithm re-allocates the DGs at buses 18, 60, and 65 with sizing of 0.516, 1.312, and 0.455 MW, respectively. The suggested method offered a real power loss of 13.98 kW, higher than that of the EGWO-PSO method. The minimum voltage is maintained, similar to case 2. The value of VDI is reduced to 0.0005 p.u. and VSI is increased to 0.9778 p.u. from their actual values.

6.2.4. Case 4

In this case, the optimal allocation of type III DGs with CBs offered better results than in

Table 11. Case 4 of 69-bus system with DGs operating at LPF and CB.

Methods	Power Loss (KW)	DGs Size (MW)/Position/Power Factor	CBs Size (MVAR)/Position	Min. Voltage (p.u.)/Bus	VDI (p.u.)	VSI (p.u.)
Base case	225	--	--	0.909/65	0.0993	0.6850
WCA [29]	18.70	1.825/61/0.88, 1.041/36/0.92, 0.106/19/0.90	0.019/15, 0.458/33, 0.559/22	0.994/50	0.0092	0.9687
EGWO-PSO [16]	7.21	0.494/11/1, 0.379/18/0.95, 1.653/61/1	1.000/61, 0.413/64, 0.476/69	0.994/50	0.0001	0.9794
AREP-EGWO-PSO	13.64	0.492/20/0.97 1.304/60/1 0.444/65/1	1.000/61, 0.413/64, 0.476/69	0.994/50	0.0002	0.9794

. The proposed technique reserves the CBs’ allocation and considers the AREP for DG buses only. The buses 11 and 61 are eliminated and new locations are identified as 20, 60, and 65, with DG sizing of 0.492, 1.304, and 0.444 MW, respectively, by the proposed method. The re-allocation of DGs increased the active power losses from 7.21 kW to 13.64 kW. The VDI is further decreased to 0.0002 p.u with an increased VSI value of about 0.9794 p.u. from their actual values.

6.2.5. Case 5

The multi-objective technical, economic, and environmental benefits (MOBJ2) of the allocation of multiple DGs with CBs are shown in

Table 12. Case 5 of 69-bus system with multi-objective placement and sizing.

Methods	Power Loss (KW)	Grid Real Power (MW)/Reactive Power (MVAR)/Position	CBs Reactive Power (MVAR)/Position	WT Real Power (MW)/Reactive Power (MVAR)/Position	PV Real Power (MW)/Reactive Power (MVAR)/Position	GT Real Power (MW)/Reactive Power (MVAR)/Position	Cost ($/h)	Emission (lb/h)
Base case	225	--	--	--	--	--	309.713	8.251
WCA [29]	22.36	1.747/0.295/1	0.60/23 0.60/62 0.30/42	0.703/0.274/63	0.102/0.035/58 0.731/0.291/66	0.5405/0.3130/64	297.470	4.247
EGWO-PSO [16]	8.84	1.289/0.507/1	0.30/23 0.45/42 0.60/62	1.334/0.028/63	0.547/0.355/11 0.356/0.005/20	0.2851/0.4603/64	250.537	2.992
AREP-EGWO-PSO	12.78	1.603/0.765/1	0.30/23 0.45/42 0.60/62	1.046/0.809/61	0.451/0/23 0.217/0.080/60	0.49798/0.29762/64	286.786	3.899

. The proposed method eliminates the insufficient AREP DG buses 11 and 63 and re-locates the DGs at 23, 60, 61, and 64 with total penetration of 2.212 MW. Notably, the active power losses, production costs, and pollutant emissions are lower than WCA but are higher than EGWO-PSO algorithms due to the re-allocation.

6.3. Comparative Analysis

A comparative study of active power loss, minimum bus voltage magnitude, VDI, and VSI for cases 1 to 4 of IEEE standard 33 and 69 radial distribution systems are shown in Figure 3. The simulation results indicate that the DGs operating at LPF with CBs (Case 4) minimizes the real power losses and voltage deviation and maximizes VSI compared with other cases. The minimum bus voltage level is improved in all the cases after the optimal re-allocation of DGs with/without CBs.

Further analysis is carried out for best case from four cases, i.e., case 4 (optimal allocation of DGs at LPF with fixed CBs). The voltage profiles before and after re-allocation of DGs are shown in Figure 4 for 33 and 69-bus RDSs. It is noticed that the voltage level is maintained at almost the same level for before and after re-allocation.

The technical objectives, i.e., real power losses, VDI minimization, and VSI maximization, are shown in Figure 5 for the best case.

Further, the economic and environmental objectives for case 4 are shown in Figure 6 and Figure 7, respectively. It is observed that the proposed re-allocation procedure shows superior performance compared with other existing methodologies and exhibits almost similar concert with the EGWO-PSO after re-allocation.

The proposed AREP-EGWO-PSO technique delivers a better solution to the different technical objectives, i.e., real power losses, VDI minimization, and VSI maximization, economic and environmental objectives in the various cases considered. It maintains the same consistency as that of the EGWO-PSO method in achieving all these objectives. The proposed method can be implemented to allocate the DGs in any practical system with the most optimal solutions using available renewable resources.

7. Conclusions

An AREP-based hybrid EGWO-PSO technique was proposed as a multi-criterion-multi-objective framework for the optimal re-allocation and re-sizing of DGs in distribution systems. It was observed that the AREP-EGWO-PSO technique could effectively re-allocate the DGs and re-size the capacity optimally. Notably, real power loss of the system was condensed significantly by up to 92.35% and 93.94% for 33 and 69 test systems, respectively, using AREP constraints. Further, the VSI of the system was greatly enhanced from its base value. Moreover, an excellent emission reduction had taken place by up to 69%, with a significant cost reduction of up to 10%. All these observed outcomes show superior performance compared with other existing optimization techniques. Notably, the AREP-based re-allocation and re-sizing of DGs offer closer performance with EGWO-PSO in all criteria (technical, economic, and environmental). Therefore, the AREP-based re-allocation and re-sizing of DGs using the EGWO-PSO algorithm can be employed to solve complex multi-objective problems for real-time systems.

The future developments accredited to dynamic load variations can be analyzed from the perspective of optimal power system operation. This research work can be extended to include reliability metrices with a reconfiguration of the distribution system. Moreover, a real-time potential assessment of an existing power system can be performed along with the reallocation of DGs based on AREP to validate the effectiveness of the proposed EGWO-PSO algorithm.