# Optimal Power Flow Incorporating Thyristor-Controlled Series Capacitors Using the Gorilla Troops Algorithm

Authors: Ahmed Ginidi; Ehab Elattar; Abdullah Shaheen; Abdallah Elsayed; Ragab El-Sehiemy; Hassen Dorrah
Journal: International Transactions on Electrical Energy Systems
 (2022)

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## Abstract

The optimal power flow issue (OPFI) can be solved in this work using the recently developed algorithm, gorilla troops algorithm (GTA). The goal of OPFI is to reduce numerous functions such as minimizing fuel costs, emissions, and power losses and improving the voltage stability related to electric power networks (EPNs). The GTA is inspired by gorillas’ social habits, which include migration to a strange region, migration toward a specified spot, traveling to other gorillas, competing for adult females, and escorting the silverback. The developed GTA is tested with and without the inclusion of the Thyristor-Controlled Series Capacitor (TCSC) devices in the system. The proposed GTA is applied on a practical Egyptian West Delta-EPN (WD-EPN) and the standard IEEE 57-bus EPN and with and without the inclusion of the TCSC devices to appraise the GTA algorithm’s performance in the OPFI. In addition, the proposed GTA is applied on a large-scale IEEE 118 bus system with higher outperformance compared to particle swarm optimization. The results illustrate that the fuel costs, emissions, voltage stability, and power losses are reduced for the standard IEEE 57-bus EPN with and without TCSC devices by a percentage of (18.847% and 18.818%), (59% and 58.97%), (13.405% and 11.507%), and (64.337% and 65.178%), respectively, while fuel costs, emissions, voltage stability, and power losses are reduced for WD-EPN with and without TCSC devices by a percentage of (8.547%, 8.565%), (13.641%, 13.6%), and (61.949%, 61.954%), respectively. A comparison study is conducted to demonstrate the GTA’s effectiveness when compared with other recently developed algorithms such as improved Salp Swarm Algorithm, quasi-reflection jellyfish search, Salp Swarm Algorithm, improved heap-based algorithm, bat search algorithm, social network search algorithm, electromagnetic field optimization, and other well-known algorithms as well. According to the comparison with these algorithms, the GTA demonstrates the best results among the attained results.


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## Body

## 1. Introduction

The optimal power flow issue (OPFI) is considered a primary tool for managing electrical power networks, where it provides electrical power at the lowest possible cost while maintaining high quality [1, 2]. Its major goal is to optimize objective functions such as system losses, cost of fuel, and emissions with meeting a set of equality and inequality constraints such as generator bus voltage magnitude, valve-point constraints, generator real power, transformer taps, and reactive power of shunts while optimizing a given objective function [3].A numerous optimization approaches were developed to solve the OPFI over the last few decades. Classic optimization methods and evolutionary algorithms are the two categories of optimization approaches [4, 5]. A plethora of mathematical approaches was addressed to tackle the OPFI such as programming based on semidefinite [6], linear [7, 8], fuzzy linear [9], nonlinear [10], and quadratic [11, 12] frameworks, sequential unconstrained minimization technique [13], Newton-based method [14, 15], and interior point approach [16–18]. Although these approaches have produced encouraging outcomes, they do have certain drawbacks.Numerous researchers have turned for utilizing several nature-inspired algorithms to solve the shortcomings of traditional optimization methods [19, 20]. These algorithms do not require derivative information, and instead, they employ random probabilities for optimization rather than deterministic probabilities. It can be noticed that these nature-inspired algorithms are capable of solving large-scale nonlinear problems and jumping out of the local optimum. As a result, a variety of evolutionary algorithms have been used to solve OPFI in recent years [21, 22].Examples of the nature-inspired algorithms are electromagnetism-like mechanism [23], colliding bodies optimization algorithm [24], biogeography-based optimization (BBO) [25], particle swarm optimization (PSO) [26, 27], genetic algorithm (GA) [28], grey wolf optimization and differential evolution (DE) [29], simulated annealing optimization [30], and teaching-learning-based optimization [31]. Moreover, to get the optimal solution for the large-scale OPFI, recent algorithms were elaborated such as chaotic salp swarm optimizer (CSSO) [32], quantum computing with moth flame technique (QMFT) [33], water cycle emerged with moth flame technique (WCEMFT) [34], and coyote optimization algorithm [35]. Several optimization algorithms have been characterized to tackle the OPFI in recent years with numerous objective function formulations. Wind and solar power integration have become one of the most quickly developing forms of electricity generation [36, 37].Various algorithm strategies have been demonstrated in the literature to identify the optimal OPFI solution as illustrated in Table1.Table 1
Various algorithm strategies for OPFI.
Ref.YearApplied algorithmFeature[38]2021Adaptive constraint differential evolutionIt has been introduced to solve the 30-bus system with different objectives which are voltage stability, real active power losses, voltage deviation, fuel cost considering the valve-point effect, and emission. However, it has been used without the inclusion of the TCSC devices[39]2020Improved adaptive differential evolution (IADE)It has been applied to the OPFI with the self-adaptive penalty constraint technique. However, it has been used without voltage stability and the inclusion of the TCSC devices[40]2020Manta-ray foraging algorithmIt has been employed on EPNs with/without combination with voltage source converter stations to optimize the fuel costs, emissions, and losses[41]2018Quasi-oppositional-based learning with Jaya AlgorithmIt has been used to support exploration capability and convergence properties for the OPFI solution. However, it has been used without the inclusion of the TCSC devices[42]2019Improved social spider optimizerIt has been manifested to reduce fuel costs, power losses, and emissions. However, it has been used without voltage stability and the inclusion of the TCSC devices[43]2020Emended moth swarm algorithm (EMSA)It has been introduced to modify quasi-opposition-based learning and applied to the OPFI. However, it has been used without voltage stability and the inclusion of the TCSC devices[44]2016Adaptive group search technique (AGST)It has been applied on emission, fuel cost, and losses with diverse constraints. However, it has been used without voltage stability and the inclusion of the TCSC devices[45]2019An improved NSGA-IIIIt is developed by decreasing the selection attempts and was proposed to optimize the objectives of fuel costs, emission, and losses. However, it has been used without voltage stability and the inclusion of the TCSC devices[46]2019Modified JAYAIt has been demonstrated by proposing a modified equation that depends on the best and worst solutions and employed on voltage profile, fuel cost, emission, and losses. However, it was used without practical systems and the inclusion of the TCSC devices[47]2021Fuzzy adaptive-based selfadaptive differential evolution and particle swarm optimization (FAHSDE-PSO)It has been demonstrated to solve OPFI with various objectives on IEEE 30-bus, 57-bus, and 118-bus systems. However, it has been used without practical systems and the inclusion of the TCSC devices[48]2017An improved-strength Pareto evolutionary algorithm (ISPEA)It has been used for solving an OPFI with diverse test systems. However, it has been used without practical systems and the inclusion of the TCSC devices[49]2020Multiobjective evolutionary algorithm with superiority of feasible solutions based on decomposition (MOEA/SF-D)It has been proposed to solve the OPFI and employed on standard IEEE 30-bus and 57-bus test systems with an effective constraint-handling method[50]2018Multiobjective dimension-based firefly algorithm (MODFA)It has been proposed with nine operational cases with different objective functions and applied on IEEE 30-bus, 57-bus, and 118-bus systems. However, it has been used without practical systems and the inclusion of the TCSC devices


### 1.1. Research Gap and Contributions

Although these algorithms have been widely employed in the literature to deal with OPFI, there is a lack of comparative analysis of these algorithms in terms of solution quality exists. This research investigates the computing efficiency of GTA on the standard IEEE 57-bus EPN and WD-EPN with and without the inclusion of the TCSC devices.The active power losses throughout the system, fuel cost, and emissions are all factors in the objective function. There are two goals in this paper. The first is to use the gorilla troops algorithm (GTA) [51, 52], a recently developed metaheuristic optimization algorithm, to solve the OPFI in EPNs with and without TCSC devices. The second goal is to solve the OPFI with four different objectives which are fossil fuel cost, transmission losses, voltage stability, and emission. Simulations were run on normal and modified IEEE 57-bus EPN and WD-EPN, as well as comparative examinations of other approaches in the literature are conducted in this study. The simulation results demonstrated the GTA’s effectiveness in solving the OPFI using TCSC devices. The key contributions of this work are summarized as follows:(i)
The GTA is adopted to handle the OPF including TCSC devices.(ii)
The GTA is utilized to reduce numerous functions such as minimizing the fuel rates, pollutant emissions, voltage deviation, and power losses related to EPNs.(iii)
The proposed GTA is applied on the standard IEEE 57-bus EPN and a WD-EPN with and without the inclusion of the TCSC devices. In addition, the proposed GTA is applied on a large-scale IEEE 118 bus system with higher outperformance than the particle swarm optimization (PSO).(iv)
The OPFI, including TCSC devices, is solved with diverse objective functions which are minimizing thermal generation cost, voltage stability, transmission power loss, and emission.(v)
A comparative study is conducted between the proposed GTA and recently developed algorithms such as ISSA, QRJFS, SSA, IHBA, SNSA, EFO, and MICA.The remainder of the work is divided into the following sections: the OPFI construction is elaborated in Section2, while Section 3 characterizes the intended GTA for OPFI. In addition, Section 4 contains the simulated findings and comments, while Section 5 has the concluding notes.


## 1.1. Research Gap and Contributions

Although these algorithms have been widely employed in the literature to deal with OPFI, there is a lack of comparative analysis of these algorithms in terms of solution quality exists. This research investigates the computing efficiency of GTA on the standard IEEE 57-bus EPN and WD-EPN with and without the inclusion of the TCSC devices.The active power losses throughout the system, fuel cost, and emissions are all factors in the objective function. There are two goals in this paper. The first is to use the gorilla troops algorithm (GTA) [51, 52], a recently developed metaheuristic optimization algorithm, to solve the OPFI in EPNs with and without TCSC devices. The second goal is to solve the OPFI with four different objectives which are fossil fuel cost, transmission losses, voltage stability, and emission. Simulations were run on normal and modified IEEE 57-bus EPN and WD-EPN, as well as comparative examinations of other approaches in the literature are conducted in this study. The simulation results demonstrated the GTA’s effectiveness in solving the OPFI using TCSC devices. The key contributions of this work are summarized as follows:(i)
The GTA is adopted to handle the OPF including TCSC devices.(ii)
The GTA is utilized to reduce numerous functions such as minimizing the fuel rates, pollutant emissions, voltage deviation, and power losses related to EPNs.(iii)
The proposed GTA is applied on the standard IEEE 57-bus EPN and a WD-EPN with and without the inclusion of the TCSC devices. In addition, the proposed GTA is applied on a large-scale IEEE 118 bus system with higher outperformance than the particle swarm optimization (PSO).(iv)
The OPFI, including TCSC devices, is solved with diverse objective functions which are minimizing thermal generation cost, voltage stability, transmission power loss, and emission.(v)
A comparative study is conducted between the proposed GTA and recently developed algorithms such as ISSA, QRJFS, SSA, IHBA, SNSA, EFO, and MICA.The remainder of the work is divided into the following sections: the OPFI construction is elaborated in Section2, while Section 3 characterizes the intended GTA for OPFI. In addition, Section 4 contains the simulated findings and comments, while Section 5 has the concluding notes.


## 2. OPFI Formulation considering TCSC Devices Incorporation

In OPFI, the reactive power injections of switching capacitors and reactors and the generators’ real power output are denoted by (Qcr1, Qcr2, …, QcrNqr) and (Pgr1, Pgr2, …, PgrNgr), respectively. The voltages of the generators and the tap changer settings are designated by (Vgr1, Vgr2, …, VgrNgr) and (Tp1, Tp2, ……, TpNtr), respectively. Here, Nqr, Ntr, and Ngr represent the number of reactive power sources, on-load tap changers, and generators, respectively. The dependent variables are load bus voltage magnitudes, generator reactive power outputs, and transmission flow limits, as shown by (VL1, …, VLNPQ), (Qgr1, Qgr2, …, QgrNgr), and (SF1, …, SFNF), where NF and NPQ represent the number of transmission lines and load buses, respectively. This problem can be expressed numerically as follows:(1)Min OJF=OJF1l,x,OJF2l,x,…,OJFul,x.Subject to(2)Cl,x=0,Dl,x≤0,where OJF characterizes the modeled objective function of numerous u aims and the symbols (l and x) denote the control and state variables, whereas C (l, x) and D (l, x) illustrate the equality and inequality constraints of the OPFI, respectively.


### 2.1. Modelling of TCSC Devices

The TCSC is one of the most prominent series of FACTS devices, with several advantages such as high performance, quick reaction, and inexpensive cost. It offers several benefits over series capacitors. TCSC devices have two reactive operational modes which are inductive and capacitive. In both modes, the reactance of the corresponding transmission line can be, accordingly, lowered or raised.Figure1 depicts TCSC modeling in power systems that are connected in series with a line. Therefore, the reactance of the TCSC is represented as a function of the transmission-line reactance (XLine). The needed value of the TCSC device (XTCSC) to avoid transmission line overcompensation may be computed using the following equation [53, 54]:(3)−0.5XTCSC≤XLINE≤0.5XTCSC.Figure 1
TCSC modeling in power systems.


### 2.2. Objectives

#### 2.2.1. Aim 1: Fuel Cost

The goal of (Aim 1) is to keep costs down while meeting electricity demands. A quadratic relationship exists between fuel cost and generated power (OJF1) which can be expressed in dollars per hour and formulated as follows:(4)OJF1=∑p=1NgrAp+BpPgrp+CpPgrp2,where Ap, Bp, and Cp elaborate the cost coefficients of generator p.


#### 2.2.2. Aim 2: Emissions

The goal of (Aim 2) is to reduce emissions produced by the power plants. The emissions (OJF2) can be expressed in ton/h and formulated as follows:(5)OJF2=∑p=1NgrζpeλpPgrp+γpPgrp2+βpPgrp+αp100,where γp, βp, αp, ξp, and λp designate the emission coefficients of generator p.


#### 2.2.3. Aim 3: Losses

The goal of (Aim 3) is to reduce the overall transmission system power loss. The emissions (OJF3) can be formulated as follows [55]:(6)OJ3=∑p=1Npq∑p≠qNpqGpqVp2+Vq2−2VpVqcosθp−θq,where Gpq illustrates the transfer conductance between buses p and q, V is the voltage; Nbq is the number of buses, and θ refers to the phase angle.


#### 2.2.4. Aim 4: Voltage Stability

The goal of (Aim 4) is to improve voltage stability by minimizing the maximum voltage stability index (L-index) that is illustrated in Reference [56]. To illustrate, the L-index for each bus j (Lj) can be mathematically formulated as follows:(7)Lj=1−∑i=1NgFjiViVj∠θij+δi−δj,(8)Fji=−YLL−1YLG.The voltage stability of the system can be maximized using the maximum L-index, and this index can be mathematically formulated as follows:(9)OJ4=Lmax=MaxLj,j=1,2,………Nb.


### 2.3. System Constraints

The equality constraints are as follows:(10)Pgrj−PLj−Vgrj∑p=1NpqVgrpGjpcosθjp+Bjpsinθjp=0,j=1,…,Npq,Qgrj+Qcj−QLj−Vj∑k=1NpqVpGjpsinθjp−Bjpcosθjp=0,j=1,2,…,Npq,where QL and PL illustrate the consumed power consumption of its reactive and active components, respectively. Furthermore, Gjk and Bjk characterize the mutual conductance and susceptibility of a transmission line connected between buses j and k.The inequality constraints are as follows:(11)Pgrpmin≤Pgrp≤Pgrpmax,p=1,2,…,Ngr,(12)TpTrmin≤TpTr≤TpTrmax,Tr=1,2,…,Nt,(13)Qgrpmin≤Qgrp≤Qgrpmax,p=1,2,…,Ngr,(14)Vgrpmin≤Vgrp≤Vgrpmax,p=1,2,…,Ngr,(15)VLjmin≤VLj≤VLjmax,j=1,2,…,NPQ,(16)QcVARmin≤QcVAR≤QcVARmax,VAR=1,2,…,Nq,(17)Sfl≤Sflmax,fl=1,2,…,Nf,where Sfl illustrates the power flow via line fl and VLj signifies the load voltage at bus j.


## 2.1. Modelling of TCSC Devices

The TCSC is one of the most prominent series of FACTS devices, with several advantages such as high performance, quick reaction, and inexpensive cost. It offers several benefits over series capacitors. TCSC devices have two reactive operational modes which are inductive and capacitive. In both modes, the reactance of the corresponding transmission line can be, accordingly, lowered or raised.Figure1 depicts TCSC modeling in power systems that are connected in series with a line. Therefore, the reactance of the TCSC is represented as a function of the transmission-line reactance (XLine). The needed value of the TCSC device (XTCSC) to avoid transmission line overcompensation may be computed using the following equation [53, 54]:(3)−0.5XTCSC≤XLINE≤0.5XTCSC.Figure 1
TCSC modeling in power systems.


## 2.2. Objectives

### 2.2.1. Aim 1: Fuel Cost

The goal of (Aim 1) is to keep costs down while meeting electricity demands. A quadratic relationship exists between fuel cost and generated power (OJF1) which can be expressed in dollars per hour and formulated as follows:(4)OJF1=∑p=1NgrAp+BpPgrp+CpPgrp2,where Ap, Bp, and Cp elaborate the cost coefficients of generator p.


### 2.2.2. Aim 2: Emissions

The goal of (Aim 2) is to reduce emissions produced by the power plants. The emissions (OJF2) can be expressed in ton/h and formulated as follows:(5)OJF2=∑p=1NgrζpeλpPgrp+γpPgrp2+βpPgrp+αp100,where γp, βp, αp, ξp, and λp designate the emission coefficients of generator p.


### 2.2.3. Aim 3: Losses

The goal of (Aim 3) is to reduce the overall transmission system power loss. The emissions (OJF3) can be formulated as follows [55]:(6)OJ3=∑p=1Npq∑p≠qNpqGpqVp2+Vq2−2VpVqcosθp−θq,where Gpq illustrates the transfer conductance between buses p and q, V is the voltage; Nbq is the number of buses, and θ refers to the phase angle.


### 2.2.4. Aim 4: Voltage Stability

The goal of (Aim 4) is to improve voltage stability by minimizing the maximum voltage stability index (L-index) that is illustrated in Reference [56]. To illustrate, the L-index for each bus j (Lj) can be mathematically formulated as follows:(7)Lj=1−∑i=1NgFjiViVj∠θij+δi−δj,(8)Fji=−YLL−1YLG.The voltage stability of the system can be maximized using the maximum L-index, and this index can be mathematically formulated as follows:(9)OJ4=Lmax=MaxLj,j=1,2,………Nb.


## 2.2.1. Aim 1: Fuel Cost

The goal of (Aim 1) is to keep costs down while meeting electricity demands. A quadratic relationship exists between fuel cost and generated power (OJF1) which can be expressed in dollars per hour and formulated as follows:(4)OJF1=∑p=1NgrAp+BpPgrp+CpPgrp2,where Ap, Bp, and Cp elaborate the cost coefficients of generator p.


## 2.2.2. Aim 2: Emissions

The goal of (Aim 2) is to reduce emissions produced by the power plants. The emissions (OJF2) can be expressed in ton/h and formulated as follows:(5)OJF2=∑p=1NgrζpeλpPgrp+γpPgrp2+βpPgrp+αp100,where γp, βp, αp, ξp, and λp designate the emission coefficients of generator p.


## 2.2.3. Aim 3: Losses

The goal of (Aim 3) is to reduce the overall transmission system power loss. The emissions (OJF3) can be formulated as follows [55]:(6)OJ3=∑p=1Npq∑p≠qNpqGpqVp2+Vq2−2VpVqcosθp−θq,where Gpq illustrates the transfer conductance between buses p and q, V is the voltage; Nbq is the number of buses, and θ refers to the phase angle.


## 2.2.4. Aim 4: Voltage Stability

The goal of (Aim 4) is to improve voltage stability by minimizing the maximum voltage stability index (L-index) that is illustrated in Reference [56]. To illustrate, the L-index for each bus j (Lj) can be mathematically formulated as follows:(7)Lj=1−∑i=1NgFjiViVj∠θij+δi−δj,(8)Fji=−YLL−1YLG.The voltage stability of the system can be maximized using the maximum L-index, and this index can be mathematically formulated as follows:(9)OJ4=Lmax=MaxLj,j=1,2,………Nb.


## 2.3. System Constraints

The equality constraints are as follows:(10)Pgrj−PLj−Vgrj∑p=1NpqVgrpGjpcosθjp+Bjpsinθjp=0,j=1,…,Npq,Qgrj+Qcj−QLj−Vj∑k=1NpqVpGjpsinθjp−Bjpcosθjp=0,j=1,2,…,Npq,where QL and PL illustrate the consumed power consumption of its reactive and active components, respectively. Furthermore, Gjk and Bjk characterize the mutual conductance and susceptibility of a transmission line connected between buses j and k.The inequality constraints are as follows:(11)Pgrpmin≤Pgrp≤Pgrpmax,p=1,2,…,Ngr,(12)TpTrmin≤TpTr≤TpTrmax,Tr=1,2,…,Nt,(13)Qgrpmin≤Qgrp≤Qgrpmax,p=1,2,…,Ngr,(14)Vgrpmin≤Vgrp≤Vgrpmax,p=1,2,…,Ngr,(15)VLjmin≤VLj≤VLjmax,j=1,2,…,NPQ,(16)QcVARmin≤QcVAR≤QcVARmax,VAR=1,2,…,Nq,(17)Sfl≤Sflmax,fl=1,2,…,Nf,where Sfl illustrates the power flow via line fl and VLj signifies the load voltage at bus j.


## 3. Gorilla Troops Optimization Technique

The gorilla troops algorithm (GTA) relies on gorillas’ group dynamics throughout five strategic options. Such strategic options involve movement with other gorilla, migrating to an unknown place, migrating toward an established site, competing for female adults, and accompanying the silverback. These strategic options can be categorized into two stages which are the exploration and exploitation stages as explained in the next paragraphs.


### 3.1. Exploration Stage

In the exploratory stage, three distinct tendencies are characterized: the first tendency is to advance GTA exploration which is called (movement to an unknown destination), while the second tendency is to augment the consistency between exploratory and exploitation which is called (movement of other gorillas). Moreover, the third tendency is to promote GTA capabilities to determine myriads of computation spaces which are called (gorilla’s movement in the path of a familiar destination). These three tendencies can be mathematically represented as depicted in equation (17). In this equation, the movement to an unknown destination tendency is chosen once a factor (Pr) is greater than a random value. Furthermore, the tendency of (movement in the path of an identifiable place) is chosen once a random value is more than or equal to 50%, whilst the tendency of (a movement in the path of a recognized site) is selected once a random value is less than 50%.(18)GoXItr+1=LB+rv1×UB−LB,Pr>rv,Z×XItr×Q+XrIrt×rv2−D×1−ItrMxItr,0.5≤rv,XItr+XItr−GoXrt×rv3−XItr−GoXrItr×Q2,0.5≤rv,(19)D=cos2×rv4+1,(20)Q=D×1−ItrMxItr×s,(21)Z=−D×1−ItrMxItr,D×1−ItrMxItr,where X (Itr) and GoX (Itr+1) describe the entire and prospective vectors of gorilla location in the next iterations, respectively, whereas rv, rv1, rv2, and rv3 signify random values between [0, 1]. The factor (Pr) represents the likelihood of selecting a migrating method to an undetermined location and can be given in the range [0 : 1]. The variables Xr and GoXr depict a gorilla among the current group and a candidate position that can be arbitrarily assigned, accordingly. The variables’ minimum and maximum bounds are denoted by LB and UB, correspondingly. Equations (2)-(5), consecutively, could be used to describe the variables D and Q mathematically. The terms (Itr) and (MxItr) signify the present and maximum iteration number of the optimizing process, respectively, and rd4 denotes a random value inside the bound [0 : 1]. Moreover, the abbreviations (s) and Z indicate random values between [−1:1] and −D×1−Itr/MxItr,D×1−Itr/MxItr, respectively.


### 3.2. Exploitation Stage

According to the factorD×1−Itr/MxItr and by comparing it to the variable (Y), two tendencies could be determined. To manifest, if the value of D×1−Itr/MxItr is greater than or equal to the value of Y, the approach of the silverback that can direct the others to sources of food could be chosen. This can be illustrated in equation (22) that can be used to exemplify this tendency as follows:(22)GoXItr+1=Q×RItr×XItr−Xsiverback+XItr,(23)RItr=1Nog∑i=1NogGoXiItr2Q1/2Q.X (Itr) is the vector of gorilla location, and Xsilverback indicates the best solution which is the silverback. Furthermore, GoXi(Itr) represents the location of each potential gorilla vector in iteration Itr, while Nog represents the population of gorillas.If the termD×1−Itr/MxItr is less than Y, the approach of competing for female adults could be chosen [57]. This can be illustrated in equation (22) which can be used to exemplify this tendency as follows:(24)GXItr=Xsiverback−Xsiverback×L−XItr×L×A,(25)L=2×rv5−1,(26)A=β×E,E=Nog1,rv≥0.5,Nog2,rv≥0.5.L represents the force of impact, which could be expressed as in equation (23), whereas rv5 represents random value within bound [0 : 1]. The factor (A) indicates a vector that provides the level of violence in a fight and may be calculated by equation (26). From that equation, β refers to a preoptimization value, and E is utilized to mimic the violence efficacy.If the cost ofGoX (Itr), at the end of the exploitation stage, is less than X(Itr), the GoX(Itr) solution will replace X (Itr). Figure 2 illustrates the key procedures of the GTA [52].Figure 2
Flowchart of the main stages of the proposed GTA.


### 3.3. Proposed Solution-Based GTA for OPFI in EPNs

The Newton–Raphson Approach (NRA) could be utilized to meet the equality principles that describe power flow balancing models. It meets the balance restrictions and illustrates the operation of electric grids in a steady state. As a result, MATPOWER uses the NRA as a crucial framework for demonstrating three-phase systems [58]. Also, the dependent/independent variable constraints must be maintained. The following are the operational limits of the independent variables:(27)GoXm=GoXmminifGoXm≤GoXmmin,GoXmmaxifGoXm≥GoXmmax,m=1,2,…,Dim.As can be seen, the variables dramatically continue to reach their limits, and if one of them exceeds the ratings, it is regenerated at random within the necessary bounds. Furthermore, the target cost objective widens and penalizes the restrictions of the second category. Consequently, in the next round, if the gorilla’s location surpasses any of the proper limitations, it will be discarded.


## 3.1. Exploration Stage

In the exploratory stage, three distinct tendencies are characterized: the first tendency is to advance GTA exploration which is called (movement to an unknown destination), while the second tendency is to augment the consistency between exploratory and exploitation which is called (movement of other gorillas). Moreover, the third tendency is to promote GTA capabilities to determine myriads of computation spaces which are called (gorilla’s movement in the path of a familiar destination). These three tendencies can be mathematically represented as depicted in equation (17). In this equation, the movement to an unknown destination tendency is chosen once a factor (Pr) is greater than a random value. Furthermore, the tendency of (movement in the path of an identifiable place) is chosen once a random value is more than or equal to 50%, whilst the tendency of (a movement in the path of a recognized site) is selected once a random value is less than 50%.(18)GoXItr+1=LB+rv1×UB−LB,Pr>rv,Z×XItr×Q+XrIrt×rv2−D×1−ItrMxItr,0.5≤rv,XItr+XItr−GoXrt×rv3−XItr−GoXrItr×Q2,0.5≤rv,(19)D=cos2×rv4+1,(20)Q=D×1−ItrMxItr×s,(21)Z=−D×1−ItrMxItr,D×1−ItrMxItr,where X (Itr) and GoX (Itr+1) describe the entire and prospective vectors of gorilla location in the next iterations, respectively, whereas rv, rv1, rv2, and rv3 signify random values between [0, 1]. The factor (Pr) represents the likelihood of selecting a migrating method to an undetermined location and can be given in the range [0 : 1]. The variables Xr and GoXr depict a gorilla among the current group and a candidate position that can be arbitrarily assigned, accordingly. The variables’ minimum and maximum bounds are denoted by LB and UB, correspondingly. Equations (2)-(5), consecutively, could be used to describe the variables D and Q mathematically. The terms (Itr) and (MxItr) signify the present and maximum iteration number of the optimizing process, respectively, and rd4 denotes a random value inside the bound [0 : 1]. Moreover, the abbreviations (s) and Z indicate random values between [−1:1] and −D×1−Itr/MxItr,D×1−Itr/MxItr, respectively.


## 3.2. Exploitation Stage

According to the factorD×1−Itr/MxItr and by comparing it to the variable (Y), two tendencies could be determined. To manifest, if the value of D×1−Itr/MxItr is greater than or equal to the value of Y, the approach of the silverback that can direct the others to sources of food could be chosen. This can be illustrated in equation (22) that can be used to exemplify this tendency as follows:(22)GoXItr+1=Q×RItr×XItr−Xsiverback+XItr,(23)RItr=1Nog∑i=1NogGoXiItr2Q1/2Q.X (Itr) is the vector of gorilla location, and Xsilverback indicates the best solution which is the silverback. Furthermore, GoXi(Itr) represents the location of each potential gorilla vector in iteration Itr, while Nog represents the population of gorillas.If the termD×1−Itr/MxItr is less than Y, the approach of competing for female adults could be chosen [57]. This can be illustrated in equation (22) which can be used to exemplify this tendency as follows:(24)GXItr=Xsiverback−Xsiverback×L−XItr×L×A,(25)L=2×rv5−1,(26)A=β×E,E=Nog1,rv≥0.5,Nog2,rv≥0.5.L represents the force of impact, which could be expressed as in equation (23), whereas rv5 represents random value within bound [0 : 1]. The factor (A) indicates a vector that provides the level of violence in a fight and may be calculated by equation (26). From that equation, β refers to a preoptimization value, and E is utilized to mimic the violence efficacy.If the cost ofGoX (Itr), at the end of the exploitation stage, is less than X(Itr), the GoX(Itr) solution will replace X (Itr). Figure 2 illustrates the key procedures of the GTA [52].Figure 2
Flowchart of the main stages of the proposed GTA.


## 3.3. Proposed Solution-Based GTA for OPFI in EPNs

The Newton–Raphson Approach (NRA) could be utilized to meet the equality principles that describe power flow balancing models. It meets the balance restrictions and illustrates the operation of electric grids in a steady state. As a result, MATPOWER uses the NRA as a crucial framework for demonstrating three-phase systems [58]. Also, the dependent/independent variable constraints must be maintained. The following are the operational limits of the independent variables:(27)GoXm=GoXmminifGoXm≤GoXmmin,GoXmmaxifGoXm≥GoXmmax,m=1,2,…,Dim.As can be seen, the variables dramatically continue to reach their limits, and if one of them exceeds the ratings, it is regenerated at random within the necessary bounds. Furthermore, the target cost objective widens and penalizes the restrictions of the second category. Consequently, in the next round, if the gorilla’s location surpasses any of the proper limitations, it will be discarded.


## 4. Simulation Results

First of all, the performance analysis of GTA for standard well-known mathematical functions is performed and compared with well-known established optimization algorithms such as the particle swarm optimization (PSO) [59] and grey wolf optimization (GWO) [60] as illustrated in Table 2 in the Appendix. It is manifested from this table that the proposed GTA has a higher performance and efficiency than PSO and GWO in the tested mathematical functions which verify the robustness of GTA in obtaining the optimal solution of these mathematical functions. In the next subsections, the proposed GTA is applied to three test EPNs with different scenarios.Table 2
Performance analysis of GTA for standard mathematical functions in comparison with metaheuristic technique.
FunctionMathematical representationDimensionRangeFminGTAGWOPSOF1fx=∑i=1dxi230[−100, 100]d0Best0.0000 E+001.3068E−012.4635 E+03Mean0.0000 E+002.4126E−013.5154 E+03Worst0.0000 E+004.2039E−014.8032 E+03STD0.0000 E+006.9701E−026.1530 E+02F2fx=maxixi,1≤i≤d30[−100, 100]d0Best1.0392E−2047.2506 E+011.3764 E+01Mean1.2771E−1907.8413 E+011.5660 E+01Worst2.5843E−1898.5165 E+011.7638 E+01STD0.0000 E+003.3976 E+008.6534E−01F3fx=∑i=1d=1100xi+1−xi22+xi−1230[−30, 30]d0Best2.5289E−041.0197 E+032.4927 E+05Mean1.0147 E+021.0555 E+033.3299 E+05Worst9.8841 E+021.1400 E+034.4661 E+05STD3.0070 E+023.1904E+015.0670 E+04F4fx=−20exp−0.21/d∑i=1dxi2−exp1/d∑i=1dcos2πxi+20+e30[−32, 32]d0Best8.8818E−161.2469E−027.8819 E+00Mean8.8818E−161.8284E−028.6221 E+00Worst8.8818E−162.−4657E−029.5002 E+00STD0.0000 E+002.6578E−033.0715E−01F5fx=14000∑i=1dxi2−Πi=1dcosxi/i+130[−600, 600]d0Best0.0000 E+006.5815E−051.6806 E+03Mean0.0000 E+001.2159E−021.7776 E+03Worst0.0000 E+001.1380E−011.8915 E+03STD0.0000 E+003.1647E−024.6628 E+01F6fx=1/500+∑i=1251/i+∑j=12xj−aj,i6−12[−65, 65]d1Best9.9800E−019.9800E−019.9800E−01Mean9.9800E−014.2305 E+001.6270 E+00Worst9.9800E−011.2671 E+015.9288 E+00STD0.0000 E+004.0855 E+001.1164 E+00F7fx=∑i=1dai−x1bi2+bix2/bi2+bix3+x424[−5, 5]d−1.0316Best3.0749E−043.0810E−043.0749E−04Mean3.9905E−043.7814E−031.1453E−03Worst1.2232E−032.0363E−022.0363E−02STD2.7940E−047.5471E−033.6434E−03F8fx=1+x1+x2+1219−14x1+3x12−14x2+6x1x2+3x22×30+2x1−3x22×18−32x1+12x12+48x2−36x1x2+27x222[−2, 2]d3Best3.0000 E+003.0000 E+003.0000 E+00Mean3.0000 E+005.7000 E+003.0000 E+00Worst3.0000 E+008.4000 E+013.0000 E+00STD7.1892E−161.4789 E+011.7337E−15F9fx=∑i=14aiexp−∑j=13bijxj−pij23[1, 3]d−3.86Best−3.8628 E+00−3.8628 E+00−3.8628 E+00Mean−3.8628 E+00−3.8626 E+00−3.8620 E+00Worst−3.8628 E+00−3.8609 E+00−3.8549 E+00STD2.7101E−154.3099E−042.4049E−03F10fx=∑i=15X−aiX−aiT+ci−14[0, 10]d−10.1532Best−1.0153 E+01−1.0153 E+01−1.0153 E+01Mean−1.0153 E+01−9.3828 E+00−5.3115 E+00Worst−1.0153 E+01−2.3316 E+00−2.6305 E+00STD6.5642E−152.0417 E+003.3425 E+00Firstly, the standard IEEE 57-bus EPN is considered as described in Figure3, whereas a practical Egyptian WD-EPN is manifested in Figure 4. In addition to that, the proposed GTA is applied to the large-scale IEEE 118-bus EPN. Thirty simulation runs are conducted using the proposed GTA with gorillas’ group of 50 members and peak iterations of 500. The first EPN involves 17 on-load tap changing transformers; 57 buses; three capacitive sources on buses 18, 25, and 53; and seven generators on buses 1, 2, 3, 6, 8, 9, and 12, 80 lines. The data of this test system are extracted from [63]. For this EPN, two TCSC devices are considered to be installed on lines 8 and 15 [54]. Secondly, the WD-EPN involves 52 buses with voltages in the ranges between 1.06 and 0.94 p.u. For this EPN, two TCSC devices are considered to be installed on lines 4 and 9 [53]. Lastly, the standard IEEE 118-bus EPN is considered which has 118 buses, 9 on-load tap transformers, 186 routes, 14 capacitor devices, and 54 generators [64]. Therefore, the proposed GTA is applied for 130 decision variables where each gorilla position comprises a vector of 130 elements.Figure 3
IEEE 57-bus power system [61].Figure 4
Real WD-EPN [9, 62].The simulation runs were conducted using MATLABR2017b with 8 GB of RAM and CPU of Core (TM) i7-7200U - (2.5 GHz) Intel(R).


### 4.1. Outcomes of the GTA Applications for the First EPN

For this EPN, four scenarios are examined with and without considering the TCSC devices:(i)
Scenario 1: OJ1 minimization described in equation (4)(ii)
Scenario 2: OJ2 minimization described in equation (5)(iii)
Scenario 3: OJ3 minimization described in equation (6)(iv)
Scenario 4: OJ4 minimization described in equation (7)


#### 4.1.1. Minimization of the Fuel Costs (Scenario 1)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices, and the results are shown in Table3. Furthermore, Figure 5 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the fuel costs from 51345 $/h in the initial scenario to 41668.02 $/h with a reduction percentage of 18.847%. In the second case by considering the TCSC devices, the suggested GTA reduces the fuel costs from 51345 $/h in the initial scenario to 41682.64 $/h with a reduction percentage of 18.818%. For these reasons, the suggested GTA is operating the TCSC devices on lines 8 and 15 at compensation levels of −32.768% and 49.9686%, respectively.Table 3
Outcomes of the proposed GTA for Scenario 1 with and without considering TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.010001.060001.05998221.010001.0584121.05775831.010001.0525551.05059161.010001.0597221.058981.010001.061.0691.010001.0398671.043105121.010001.0457331.052959Tap4-180.970000.9874841.0230224-180.978001.0246321.09998221-201.043000.9891941.08133224-251.000001.0099961.02268424-251.000001.0176431.02892124-261.043001.0128151.0173267-290.967000.9523250.96455234-320.975000.9575750.98380411-410.955000.9000260.94487215-450.955000.9485760.93997514-460.900000.9422010.93168110-510.930000.9484340.94096613-490.895000.9230790.91419711-430.958000.9287280.93601140-560.958000.992081.0206239-570.980000.9396611.0449919-550.940000.9714230.960974Qc1810.0000028.5718724255.900014.5939515.5536.300013.1196427.5Pg1478.63500143.3567142.767320.0000092.2724290.00291340.0000044.7978244.9833760.0000069.6463272.305138450.00000458.7721459.007190.0000096.9184295.2429212310.00000359.8742361.6572TCSC8 compensation %——-32.768TCSC15 compensation %——49.9686Fuel costs5134541668.0241682.64Losses27.8350014.83815.16592Figure 5
Convergent characteristics of the proposed GTA for Scenario 1 with and without considering the TCSC devices.In addition, Figure6 shows the comparisons of the outcomes of Scenario 1 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to social spider optimization (SSO) [42], real-coded biogeography-based optimization (RCBBO) [25], improved Salp Swarm Algorithm (ISSA) [65], jellyfish search (JFS) [66], quasi-reflection jellyfish search (QRJFS) [66], Salp Swarm Algorithm (SSA) [67], differential search algorithm (DSA) [68], heap-based algorithm (HBA) [69], improved heap-based algorithm (IHBA) [69], bat search algorithm (BSA) [70], genetic algorithm (GA) [45], improved genetic algorithm (IGA) [45], social network search algorithm (SNSA) [71], electromagnetic field optimization (EFO) [72], and modified imperialist competitive algorithm (MICA) [73]. As shown, the proposed GTA provides the superior performance in minimizing the fuel costs with the least value of 41668.02 $/h. On the other side, the minimum costs related to RCBBO [25], SSO [42], ISSA [65], JFS [66], QRJFS [66], SSA [67], DSA [68], HBA [69], IHBA [69], BSA [70], GA [45], IGA [45], SNSA [71], EFO [72], and MICA [73] are, respectively, 41686.0000, 41734.3370, 41675.0200, 41689.4652, 41667.1077, 41672.3000, 41686.8200, 41701.6640, 41674.4206, 41686.8200, 41796.8400, 41719.8900, 41685.5000, 41706.1170, and 41738.4400 $/h.Figure 6
Comparisons for Scenario 1 without considering the TCSC devices.


#### 4.1.2. Minimization of the Emissions (Scenario 2)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to minimize the produced emissions, and the results are shown in Table4. Furthermore, Figure 7 illustrates the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the produced emissions from 2.528 ton/h in the initial scenario to 1.036393 ton/h with a reduction percentage of 59%. In the second case by considering the TCSC devices, the suggested GTA reduces the produced emissions from 2.528 ton/h in the initial scenario to 1.037115 ton/h with a reduction percentage of 58.97%. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of −24.486% and 19.6084%, respectively.Table 4
Outcomes of the proposed GTA for Scenario 2 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC devicesVg11.010001.0599999891.0621.010001.060001.05999997931.010001.0599999861.0661.010001.0551604731.05352530181.010001.0563501141.05797915491.010001.0325465251.034495012121.010001.0298705661.033485992Tap4-180.970000.900001.14-180.978001.0000866190.9769117521-201.043001.0037750691.02188400224-251.000001.051911951.02565107624-251.000001.0999999411.0024085224-261.043000.9950068031.0999998667-290.967000.9529870591.04283969734-320.975000.9882681970.95215295811-410.955000.9000003930.9502531915-450.955000.9377778130.93695745914-460.900000.9283371050.93803599210-510.930000.9522718740.95376568513-490.895000.9116157910.91289629211-430.958000.9202815621.01341578840-560.958000.987924251.08732531639-570.980000.9653907431.023639669-550.940000.9391206141.054417598Qc1810.000007.1641581129.5255.9000017.2549809315.5536.3000012.9034780410.5Pg1478.63500331.6895448331.685220.0000099.99999999100340.00000140139.99999160.0000099.999999971008450.00000262.9513257263.229630790.0000010010012310.00000238.0579115238.0983622TCSC8 compensation %——-24.486TCSC15 compensation %——19.6084Fuel costs5134548553.7548563.69Emissions2.5281.0363931.037115Losses27.83521.8987822.21318Figure 7
Convergent characteristics of the proposed GTA for Scenario 1 with and without considering the TCSC devices.In addition, Figure8 shows the comparisons of the outcomes of Scenario 1 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to SNSA [71], IGA [45], GA [45], SSO [42], enhanced SSO [42], MICA [73], teaching-learning based optimization (TLBO) [63], JFS [66], and QRJFS [66].Figure 8
Comparisons for Scenario 2 without considering the TCSC devices.As shown, the proposed GTA provides the superior performance in minimizing the produced emissions with the least value of 1.036393 ton/h. On the other side, the minimum costs related to SNSA [71], IGA [45], GA [45], SSO [42], enhanced SSO [42], MICA [73], TLBO [63], JFS [66], and QRJFS [66] are, respectively, 1.0375, 1.0830, 1.1210, 1.0393, 1.7024, 1.2246, 1.0772, 1.0473, 1.0410, and 1.0377 ton/h.


#### 4.1.3. Minimization of the Power Losses (Scenario 3)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to minimize the power losses, and the results are shown in Table5. Furthermore, Figure 9 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the power losses from 27.835 MW in the initial scenario to 9.92662 MW with a reduction percentage of 64.337%. In the second case by considering the TCSC devices, the suggested GTA reduces the power losses from 27.835 MW in the initial scenario to 9.692474 MW with a reduction percentage of 65.178%. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of 49.9995% and 34.7962%, respectively.Table 5
Outcomes of the proposed GTA for Scenario 3 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.010001.061.05998921.010001.0546381.05460931.010001.061.05998761.010001.0594191.05745381.010001.0598671.0691.010001.0423161.042094121.010001.049391.048461Tap4-180.970000.924580.9271464-180.978001.10.9684821-201.043001.0149060.98547324-251.000001.10.98507524-251.000001.0012761.03679424-261.043001.0953811.0002357-290.967001.0377250.95537234-320.975000.9774320.94908511-410.955000.9348730.90131215-450.955000.9472820.94416514-460.900000.9296350.94499210-510.930000.9368950.94633413-490.895000.9048580.93182411-430.958000.9261421.02109840-560.958001.0030191.00275539-570.980001.0246490.9840549-550.940001.0270270.950339Qc1810.00000305.5255.9000018.1423915536.3000019.5733515Pg1478.63500204.4293202.420720.000005.74E-081.189606340.0000014014060.000001001008450.00000307.6783306.882390.0000010010012310.00000410409.9999TCSC8 compensation %——49.9995TCSC15 compensation %——34.7962Fuel costs5134545058.3545027.8Emissions2.5281.5526491.554878Losses27.8359.926629.692474Figure 9
Convergent characteristics of the proposed GTA for Scenario 3 with and without considering the TCSC devices.In addition, Figure10 shows the comparisons of the outcomes of Scenario 3 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to SNSA [71], differential evolution (DE) [74], SSO [42], SSA [67], MICA [73], GA [45], IGA [45], and Stud Krill Herd Algorithm (SKHA) [75]. As shown, the proposed GTA provides the superior performance in minimizing the power losses with the least value of 9.92662 MW. On the other side, the minimum costs related to SNSA [71], IGA [45], GA [45], SSO [42], enhanced SSO [42], MICA [73], TLBO [63], JFS [66], and QRJFS [66] are, respectively, 10.1952, 10.558, 10.614, 11.320, 11.883, 11.814, 10.516, and 10.688 MW.Figure 10
Comparisons for Scenario 3 without considering the TCSC devices.


#### 4.1.4. Minimization of theLmax (Scenario 4)

(1) LmaxMinimizing (Scenario 4). Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to improve the voltage stability by minimizing the index (Lmax), and the results are shown in Table 6. Furthermore, Figure 11 illustrates the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the stability index from 0.3000 in the initial scenario to 0.259785 with a reduction percentage of 13.405%. In the second case by considering TCSC devices, the suggested GTA reduces the stability index from 0.3000 in the initial scenario to 0.265479 with a reduction percentage of 11.507%. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of 24.1205% and -50%, respectively.Table 6
Outcomes of the proposed GTA for Scenario 4 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC devicesVg11.010001.0599831.03562621.010001.0433591.02241731.010001.0340031.02903761.010001.0326521.03203981.010001.0576311.04540691.010001.0294841.031654121.010001.023791.06Tap4-180.970000.9611060.9750224-180.978000.9859391.09298621-201.043001.0090050.99496624-251.000001.0107561.03791324-251.000001.0999641.04631924-261.043000.9793061.0371117-290.967000.9567640.92822434-320.975000.90.911-410.955000.9939531.09831515-450.955000.9265150.91282314-460.900000.9039851.02929810-510.930000.9493560.96627713-490.895000.90.9074411-430.958000.9000970.92399240-560.958001.0994461.09990339-570.980001.0139670.9395619-550.940000.9557481.097816Qc1810.000001.15563730255.9000018.107517.5536.3000029.9417630Pg1478.63500371.9249314.068720.000000.0004994.95E-08340.0000012.988330.06313960.000000.7413330.1685148450.00000371.9531549.792390.000001002.71E-0912310.00000409.7994409.7321TCSC8 compensation %——24.1205TCSC15 compensation %——-50Fuel costs5134546728.345264.89Lmax0.30000.2597850.265479Losses27.83516.6075823.02473Figure 11
Convergent characteristics of the proposed GTA for Scenario 4.


### 4.2. Outcomes of the GTA Applications for the Second EPN

For this EPN, three scenarios are examined with and without considering the TCSC devices:Scenario 5: OJ1 minimization described in equation (4)Scenario 6: OJ3 minimization described in equation (6)Scenario 7: OJ4 minimization described in equation (7)


#### 4.2.1. Minimization of the Fuel Costs (Scenario 5)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices, and the results are shown in Table7. Furthermore, Figure 12 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the fuel costs from 25098.70 $/h in the initial scenario to 22953.42 $/h with a reduction percentage of 8.547%. In the second case by considering the TCSC devices, the suggested GTA reduces the fuel costs from 25098.70 $/h in the initial scenario to 22948.95 $/h with a reduction percentage of 8.565%. For these reasons, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of −45.836% and −35.71%, respectively. In addition, Figure 13 shows the comparisons of the outcomes of Scenario 5 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to the grey wolf algorithm (GWA) [76], SSA [77], novel bat algorithm (NBA) [78], improved spotted-hyena algorithm (ISHA) [79], crow search algorithm (CSA) [80], and modified CSA [80]. As shown, the proposed GTA provides the superior performance in minimizing the fuel costs with the least value of 22953.42 $/h. On the other side, the minimum costs related to SSA [77], GWA [76], NBA [78], ISHA [79], CSA [80], and modified CSA [80] are, respectively, 22965.590, 22957.720, 22960.810, 22958.780, 22959.360, and 22955.550$/h.Table 7
Outcomes of the proposed GTA for Scenario 4 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.001.0601.06021.001.0601.06031.001.0601.06041.001.0601.06051.001.0601.06061.001.0601.06071.001.0455581.04545981.00189.57081.05167Pg185.69001.051726190.79622157.40010103139.3100214.6983214.31164113.6900180.419180.0245166.48001010631.7100234.0315233.908792.056.2989856.173198122.49032.1859232.03292TCSC4 compensation %——-45.836TCSC9 compensation %——-35.71Fuel costs25098.7022953.4222948.95Losses19.015037.4545437.49588Figure 12
Convergent characteristics of proposed GTA for scenario 5.Figure 13
Comparisons for scenario 5 without considering the TCSC devices.


#### 4.2.2. Minimization of the Power Losses (Scenario 6)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to minimize the power losses, and the results are shown in Table8. Furthermore, Figure 14 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the power losses from 19.015 MW in the initial scenario to 7.235351 MW with a reduction percentage of 61.949%. In the second case by considering TCSC devices, the suggested GTA reduces the power losses from 19.015 MW in the initial scenario to 7.234384 MW. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of −18.215% and 34.398%, respectively.Table 8
Outcomes of the proposed GTA for scenario 6 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.001.0595891.05905821.001.0601.06031.001.0601.06041.001.0601.06051.001.0601.06061.001.0601.06071.001.0601.06081.001.0601.060Pg185.690060.4619660.639652157.40058.8187958.648093139.3100180.6457180.65144113.6900130.7557130.75995166.4800117.9838117.9631631.7100105.4723105.474792.000156.5708156.57068122.49086.2763186.27771TCSC4 compensation %——-18.215TCSC9 compensation %——34.398Fuel costs25098.7024773.0824771.64Losses19.01507.2353517.234384Figure 14
Convergent characteristics of the proposed GTA for scenario 6 with and without considering the TCSC devices.


#### 4.2.3. Minimization of theLmax (Scenario 7)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to improve the voltage stability by minimizing the index (Lmax), and the results are shown in Table 9. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the stability index from 0.173 in the initial scenario to 0.149417 with a reduction percentage of 13.641%. In the second case by considering the TCSC devices, the suggested GTA reduces the stability index from 0.173 in the initial scenario to 0.149417. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of 6.0923% and -28.321%, respectively.Table 9
Outcomes of the proposed GTA for Scenario 4 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.001.0601.05044621.001.0600.95848531.001.0601.06041.001.0601.06051.001.0600.95700161.001.0600.95036571.001.0600.97418381.001.0601.037331Pg185.690235.3035164.52252157.4015.249832503139.310029.63804104113.6900250105166.480037510631.710031.2169810792.00014.976952508122.49015.20074250TCSC4 compensation %——6.0923TCSC9 compensation %——−28.321Fuel costs25098.7027031.1128299.95Lmax0.1730.1494170.149417


### 4.3. Outcomes of the GTA Applications for the Third EPN

For the IEEE 118-bus large-scale network, the proposed GTA is applied in comparison to the PSO technique, which is one of the well-established algorithms to deal with such OPF problems, for minimizing the fuel costs. Based on those circumstances, the obtained results using the proposed GTA and PSO techniques are tabulated in Table10, while the regarding convergence properties are described in Figure 15. As illustrated, the proposed GTA achieves lower fuel cost value of 129752.2 $/hr than the implemented PSO that achieves fuel costs of 129990.8$/hr. Also, Table 11 describes a comparison with reported results of well-established techniques of the differential algorithm [74] and PSO [81]. As shown, the proposed GTA provides better performance than the differential algorithm [74] and PSO [81], which obtain fuel costs of 130518.5 and 130288.21 $/h, respectively.Table 10
Optimal results of the proposed GTA and PSO for the third EPN.
VariablePSOProposed GTAVariablesPSOProposed GTAVariablePSOProposed GTAVG10.9785011.014395VG1001.0203451.042152PG26278.3602281.6778VG41.0126481.044675VG1031.022871.036934PG2712.9439514.59936VG61.0097431.032677VG1041.0192591.024966PG316.8752795.944698VG81.061.06VG1051.0157931.022219PG3211.9103313.59129VG101.061.06VG1071.018941.021821PG348.4748887.400459VG121.0017821.028617VG1101.0069491.021915PG3610.443211.255318VG150.9985211.022519VG1111.0143021.026412PG4044.5161752.60187VG181.0089141.030823VG1121.0007181.014982PG4239.0215738.54453VG191.0001081.024811VG1131.0071931.037776PG4620.9262121.22069VG240.9962451.043987VG1161.061.037198PG49191.5003193.514VG251.0219841.058359TP8-51.0296121.005706PG5444.3837247.85186VG261.0045941.06TP26-251.0344381.060425PG5535.9945925.86789VG271.0022321.041299TP30-171.001461.018817PG5628.7231932.81963VG310.9940911.031925TP38-371.0123021.021673PG59144.8207150.8728VG320.9926771.038484TP63-591.041271.026101PG61136.0841147.0345VG340.9990191.035797TP64-610.9917750.99852PG622.1606565.044222VG360.9917771.033989TP65-660.9816331.021505PG65355.0331342.99VG400.9829771.029688TP68-691.0207880.956823PG66345.8028341.7799VG420.981631.036631TP81-801.0306690.984893PG69448.6191451.2607VG461.0007251.038833QC51.9001942.032134PG707.0968636.386357VG491.0245891.051785QC341.072053.101457PG722.0824894.940006VG541.0041021.032799QC371.1190562.663295PG735.3715815.033392VG551.0002341.031209QC441.7397391.982284PG7416.806423.05925VG561.0022181.031322QC453.7248532.341122PG7623.2178722.03655VG591.0284981.043654QC463.5695822.160515PG776.6110355.41385VG611.061.042242QC481.4215013.422638PG80421.4037425.8186VG621.0513881.036809QC743.7107992.733545PG852.030233.645089VG651.061.06QC793.8616012.265789PG873.7884293.849221VG661.0529571.054528QC821.8292462.46713PG89486.7405492.4201VG691.0203151.06QC832.0498162.819053PG907.1340416.021877VG700.9852611.036728QC1052.8624613.904263PG911.9745610VG720.9836341.034832QC1071.3264824.015503PG926.5700161.1E-09VG730.9821361.029527QC1102.9058782.806326PG992.5239115.239772VG740.9702821.019137PG127.32622.81094PG100233.3448229.2691VG760.9606481.011218PG46.5159645.352099PG10337.5073838.60442VG770.9895061.034381PG63.5128794.709697PG1045.4792264.005683VG801.0030651.045973PG803.802367PG1055.8707365.861348VG851.0020841.040072PG10388.7673398.088PG10725.7470231.70121VG871.0376671.052759PG1283.8244584.19864PG11010.025137.202108VG891.020581.06PG1525.6000517.7294PG11135.8273934.93683VG901.0142891.033737PG1818.4807112.3412PG11242.3142733.53649VG911.0127341.025402PG1921.0221919.84697PG1131.7249014.683022VG921.0043391.041442PG241.5314880.007257PG1160.7538470VG991.0228441.027761PG25187.9791183.6368Fuel Costs129990.8129752.2Figure 15
Convergent characteristics of the proposed GTA and PSO for the third EPN.Table 11
Comparisons for the third EPN.
MethodProposed GTAImplemented PSODifferential algorithm [74]PSO [81]Cost129752.2129990.8130518.5130288.210


## 4.1. Outcomes of the GTA Applications for the First EPN

For this EPN, four scenarios are examined with and without considering the TCSC devices:(i)
Scenario 1: OJ1 minimization described in equation (4)(ii)
Scenario 2: OJ2 minimization described in equation (5)(iii)
Scenario 3: OJ3 minimization described in equation (6)(iv)
Scenario 4: OJ4 minimization described in equation (7)


### 4.1.1. Minimization of the Fuel Costs (Scenario 1)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices, and the results are shown in Table3. Furthermore, Figure 5 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the fuel costs from 51345 $/h in the initial scenario to 41668.02 $/h with a reduction percentage of 18.847%. In the second case by considering the TCSC devices, the suggested GTA reduces the fuel costs from 51345 $/h in the initial scenario to 41682.64 $/h with a reduction percentage of 18.818%. For these reasons, the suggested GTA is operating the TCSC devices on lines 8 and 15 at compensation levels of −32.768% and 49.9686%, respectively.Table 3
Outcomes of the proposed GTA for Scenario 1 with and without considering TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.010001.060001.05998221.010001.0584121.05775831.010001.0525551.05059161.010001.0597221.058981.010001.061.0691.010001.0398671.043105121.010001.0457331.052959Tap4-180.970000.9874841.0230224-180.978001.0246321.09998221-201.043000.9891941.08133224-251.000001.0099961.02268424-251.000001.0176431.02892124-261.043001.0128151.0173267-290.967000.9523250.96455234-320.975000.9575750.98380411-410.955000.9000260.94487215-450.955000.9485760.93997514-460.900000.9422010.93168110-510.930000.9484340.94096613-490.895000.9230790.91419711-430.958000.9287280.93601140-560.958000.992081.0206239-570.980000.9396611.0449919-550.940000.9714230.960974Qc1810.0000028.5718724255.900014.5939515.5536.300013.1196427.5Pg1478.63500143.3567142.767320.0000092.2724290.00291340.0000044.7978244.9833760.0000069.6463272.305138450.00000458.7721459.007190.0000096.9184295.2429212310.00000359.8742361.6572TCSC8 compensation %——-32.768TCSC15 compensation %——49.9686Fuel costs5134541668.0241682.64Losses27.8350014.83815.16592Figure 5
Convergent characteristics of the proposed GTA for Scenario 1 with and without considering the TCSC devices.In addition, Figure6 shows the comparisons of the outcomes of Scenario 1 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to social spider optimization (SSO) [42], real-coded biogeography-based optimization (RCBBO) [25], improved Salp Swarm Algorithm (ISSA) [65], jellyfish search (JFS) [66], quasi-reflection jellyfish search (QRJFS) [66], Salp Swarm Algorithm (SSA) [67], differential search algorithm (DSA) [68], heap-based algorithm (HBA) [69], improved heap-based algorithm (IHBA) [69], bat search algorithm (BSA) [70], genetic algorithm (GA) [45], improved genetic algorithm (IGA) [45], social network search algorithm (SNSA) [71], electromagnetic field optimization (EFO) [72], and modified imperialist competitive algorithm (MICA) [73]. As shown, the proposed GTA provides the superior performance in minimizing the fuel costs with the least value of 41668.02 $/h. On the other side, the minimum costs related to RCBBO [25], SSO [42], ISSA [65], JFS [66], QRJFS [66], SSA [67], DSA [68], HBA [69], IHBA [69], BSA [70], GA [45], IGA [45], SNSA [71], EFO [72], and MICA [73] are, respectively, 41686.0000, 41734.3370, 41675.0200, 41689.4652, 41667.1077, 41672.3000, 41686.8200, 41701.6640, 41674.4206, 41686.8200, 41796.8400, 41719.8900, 41685.5000, 41706.1170, and 41738.4400 $/h.Figure 6
Comparisons for Scenario 1 without considering the TCSC devices.


### 4.1.2. Minimization of the Emissions (Scenario 2)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to minimize the produced emissions, and the results are shown in Table4. Furthermore, Figure 7 illustrates the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the produced emissions from 2.528 ton/h in the initial scenario to 1.036393 ton/h with a reduction percentage of 59%. In the second case by considering the TCSC devices, the suggested GTA reduces the produced emissions from 2.528 ton/h in the initial scenario to 1.037115 ton/h with a reduction percentage of 58.97%. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of −24.486% and 19.6084%, respectively.Table 4
Outcomes of the proposed GTA for Scenario 2 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC devicesVg11.010001.0599999891.0621.010001.060001.05999997931.010001.0599999861.0661.010001.0551604731.05352530181.010001.0563501141.05797915491.010001.0325465251.034495012121.010001.0298705661.033485992Tap4-180.970000.900001.14-180.978001.0000866190.9769117521-201.043001.0037750691.02188400224-251.000001.051911951.02565107624-251.000001.0999999411.0024085224-261.043000.9950068031.0999998667-290.967000.9529870591.04283969734-320.975000.9882681970.95215295811-410.955000.9000003930.9502531915-450.955000.9377778130.93695745914-460.900000.9283371050.93803599210-510.930000.9522718740.95376568513-490.895000.9116157910.91289629211-430.958000.9202815621.01341578840-560.958000.987924251.08732531639-570.980000.9653907431.023639669-550.940000.9391206141.054417598Qc1810.000007.1641581129.5255.9000017.2549809315.5536.3000012.9034780410.5Pg1478.63500331.6895448331.685220.0000099.99999999100340.00000140139.99999160.0000099.999999971008450.00000262.9513257263.229630790.0000010010012310.00000238.0579115238.0983622TCSC8 compensation %——-24.486TCSC15 compensation %——19.6084Fuel costs5134548553.7548563.69Emissions2.5281.0363931.037115Losses27.83521.8987822.21318Figure 7
Convergent characteristics of the proposed GTA for Scenario 1 with and without considering the TCSC devices.In addition, Figure8 shows the comparisons of the outcomes of Scenario 1 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to SNSA [71], IGA [45], GA [45], SSO [42], enhanced SSO [42], MICA [73], teaching-learning based optimization (TLBO) [63], JFS [66], and QRJFS [66].Figure 8
Comparisons for Scenario 2 without considering the TCSC devices.As shown, the proposed GTA provides the superior performance in minimizing the produced emissions with the least value of 1.036393 ton/h. On the other side, the minimum costs related to SNSA [71], IGA [45], GA [45], SSO [42], enhanced SSO [42], MICA [73], TLBO [63], JFS [66], and QRJFS [66] are, respectively, 1.0375, 1.0830, 1.1210, 1.0393, 1.7024, 1.2246, 1.0772, 1.0473, 1.0410, and 1.0377 ton/h.


### 4.1.3. Minimization of the Power Losses (Scenario 3)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to minimize the power losses, and the results are shown in Table5. Furthermore, Figure 9 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the power losses from 27.835 MW in the initial scenario to 9.92662 MW with a reduction percentage of 64.337%. In the second case by considering the TCSC devices, the suggested GTA reduces the power losses from 27.835 MW in the initial scenario to 9.692474 MW with a reduction percentage of 65.178%. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of 49.9995% and 34.7962%, respectively.Table 5
Outcomes of the proposed GTA for Scenario 3 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.010001.061.05998921.010001.0546381.05460931.010001.061.05998761.010001.0594191.05745381.010001.0598671.0691.010001.0423161.042094121.010001.049391.048461Tap4-180.970000.924580.9271464-180.978001.10.9684821-201.043001.0149060.98547324-251.000001.10.98507524-251.000001.0012761.03679424-261.043001.0953811.0002357-290.967001.0377250.95537234-320.975000.9774320.94908511-410.955000.9348730.90131215-450.955000.9472820.94416514-460.900000.9296350.94499210-510.930000.9368950.94633413-490.895000.9048580.93182411-430.958000.9261421.02109840-560.958001.0030191.00275539-570.980001.0246490.9840549-550.940001.0270270.950339Qc1810.00000305.5255.9000018.1423915536.3000019.5733515Pg1478.63500204.4293202.420720.000005.74E-081.189606340.0000014014060.000001001008450.00000307.6783306.882390.0000010010012310.00000410409.9999TCSC8 compensation %——49.9995TCSC15 compensation %——34.7962Fuel costs5134545058.3545027.8Emissions2.5281.5526491.554878Losses27.8359.926629.692474Figure 9
Convergent characteristics of the proposed GTA for Scenario 3 with and without considering the TCSC devices.In addition, Figure10 shows the comparisons of the outcomes of Scenario 3 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to SNSA [71], differential evolution (DE) [74], SSO [42], SSA [67], MICA [73], GA [45], IGA [45], and Stud Krill Herd Algorithm (SKHA) [75]. As shown, the proposed GTA provides the superior performance in minimizing the power losses with the least value of 9.92662 MW. On the other side, the minimum costs related to SNSA [71], IGA [45], GA [45], SSO [42], enhanced SSO [42], MICA [73], TLBO [63], JFS [66], and QRJFS [66] are, respectively, 10.1952, 10.558, 10.614, 11.320, 11.883, 11.814, 10.516, and 10.688 MW.Figure 10
Comparisons for Scenario 3 without considering the TCSC devices.


### 4.1.4. Minimization of theLmax (Scenario 4)

(1) LmaxMinimizing (Scenario 4). Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to improve the voltage stability by minimizing the index (Lmax), and the results are shown in Table 6. Furthermore, Figure 11 illustrates the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the stability index from 0.3000 in the initial scenario to 0.259785 with a reduction percentage of 13.405%. In the second case by considering TCSC devices, the suggested GTA reduces the stability index from 0.3000 in the initial scenario to 0.265479 with a reduction percentage of 11.507%. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of 24.1205% and -50%, respectively.Table 6
Outcomes of the proposed GTA for Scenario 4 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC devicesVg11.010001.0599831.03562621.010001.0433591.02241731.010001.0340031.02903761.010001.0326521.03203981.010001.0576311.04540691.010001.0294841.031654121.010001.023791.06Tap4-180.970000.9611060.9750224-180.978000.9859391.09298621-201.043001.0090050.99496624-251.000001.0107561.03791324-251.000001.0999641.04631924-261.043000.9793061.0371117-290.967000.9567640.92822434-320.975000.90.911-410.955000.9939531.09831515-450.955000.9265150.91282314-460.900000.9039851.02929810-510.930000.9493560.96627713-490.895000.90.9074411-430.958000.9000970.92399240-560.958001.0994461.09990339-570.980001.0139670.9395619-550.940000.9557481.097816Qc1810.000001.15563730255.9000018.107517.5536.3000029.9417630Pg1478.63500371.9249314.068720.000000.0004994.95E-08340.0000012.988330.06313960.000000.7413330.1685148450.00000371.9531549.792390.000001002.71E-0912310.00000409.7994409.7321TCSC8 compensation %——24.1205TCSC15 compensation %——-50Fuel costs5134546728.345264.89Lmax0.30000.2597850.265479Losses27.83516.6075823.02473Figure 11
Convergent characteristics of the proposed GTA for Scenario 4.


## 4.1.1. Minimization of the Fuel Costs (Scenario 1)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices, and the results are shown in Table3. Furthermore, Figure 5 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the fuel costs from 51345 $/h in the initial scenario to 41668.02 $/h with a reduction percentage of 18.847%. In the second case by considering the TCSC devices, the suggested GTA reduces the fuel costs from 51345 $/h in the initial scenario to 41682.64 $/h with a reduction percentage of 18.818%. For these reasons, the suggested GTA is operating the TCSC devices on lines 8 and 15 at compensation levels of −32.768% and 49.9686%, respectively.Table 3
Outcomes of the proposed GTA for Scenario 1 with and without considering TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.010001.060001.05998221.010001.0584121.05775831.010001.0525551.05059161.010001.0597221.058981.010001.061.0691.010001.0398671.043105121.010001.0457331.052959Tap4-180.970000.9874841.0230224-180.978001.0246321.09998221-201.043000.9891941.08133224-251.000001.0099961.02268424-251.000001.0176431.02892124-261.043001.0128151.0173267-290.967000.9523250.96455234-320.975000.9575750.98380411-410.955000.9000260.94487215-450.955000.9485760.93997514-460.900000.9422010.93168110-510.930000.9484340.94096613-490.895000.9230790.91419711-430.958000.9287280.93601140-560.958000.992081.0206239-570.980000.9396611.0449919-550.940000.9714230.960974Qc1810.0000028.5718724255.900014.5939515.5536.300013.1196427.5Pg1478.63500143.3567142.767320.0000092.2724290.00291340.0000044.7978244.9833760.0000069.6463272.305138450.00000458.7721459.007190.0000096.9184295.2429212310.00000359.8742361.6572TCSC8 compensation %——-32.768TCSC15 compensation %——49.9686Fuel costs5134541668.0241682.64Losses27.8350014.83815.16592Figure 5
Convergent characteristics of the proposed GTA for Scenario 1 with and without considering the TCSC devices.In addition, Figure6 shows the comparisons of the outcomes of Scenario 1 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to social spider optimization (SSO) [42], real-coded biogeography-based optimization (RCBBO) [25], improved Salp Swarm Algorithm (ISSA) [65], jellyfish search (JFS) [66], quasi-reflection jellyfish search (QRJFS) [66], Salp Swarm Algorithm (SSA) [67], differential search algorithm (DSA) [68], heap-based algorithm (HBA) [69], improved heap-based algorithm (IHBA) [69], bat search algorithm (BSA) [70], genetic algorithm (GA) [45], improved genetic algorithm (IGA) [45], social network search algorithm (SNSA) [71], electromagnetic field optimization (EFO) [72], and modified imperialist competitive algorithm (MICA) [73]. As shown, the proposed GTA provides the superior performance in minimizing the fuel costs with the least value of 41668.02 $/h. On the other side, the minimum costs related to RCBBO [25], SSO [42], ISSA [65], JFS [66], QRJFS [66], SSA [67], DSA [68], HBA [69], IHBA [69], BSA [70], GA [45], IGA [45], SNSA [71], EFO [72], and MICA [73] are, respectively, 41686.0000, 41734.3370, 41675.0200, 41689.4652, 41667.1077, 41672.3000, 41686.8200, 41701.6640, 41674.4206, 41686.8200, 41796.8400, 41719.8900, 41685.5000, 41706.1170, and 41738.4400 $/h.Figure 6
Comparisons for Scenario 1 without considering the TCSC devices.


## 4.1.2. Minimization of the Emissions (Scenario 2)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to minimize the produced emissions, and the results are shown in Table4. Furthermore, Figure 7 illustrates the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the produced emissions from 2.528 ton/h in the initial scenario to 1.036393 ton/h with a reduction percentage of 59%. In the second case by considering the TCSC devices, the suggested GTA reduces the produced emissions from 2.528 ton/h in the initial scenario to 1.037115 ton/h with a reduction percentage of 58.97%. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of −24.486% and 19.6084%, respectively.Table 4
Outcomes of the proposed GTA for Scenario 2 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC devicesVg11.010001.0599999891.0621.010001.060001.05999997931.010001.0599999861.0661.010001.0551604731.05352530181.010001.0563501141.05797915491.010001.0325465251.034495012121.010001.0298705661.033485992Tap4-180.970000.900001.14-180.978001.0000866190.9769117521-201.043001.0037750691.02188400224-251.000001.051911951.02565107624-251.000001.0999999411.0024085224-261.043000.9950068031.0999998667-290.967000.9529870591.04283969734-320.975000.9882681970.95215295811-410.955000.9000003930.9502531915-450.955000.9377778130.93695745914-460.900000.9283371050.93803599210-510.930000.9522718740.95376568513-490.895000.9116157910.91289629211-430.958000.9202815621.01341578840-560.958000.987924251.08732531639-570.980000.9653907431.023639669-550.940000.9391206141.054417598Qc1810.000007.1641581129.5255.9000017.2549809315.5536.3000012.9034780410.5Pg1478.63500331.6895448331.685220.0000099.99999999100340.00000140139.99999160.0000099.999999971008450.00000262.9513257263.229630790.0000010010012310.00000238.0579115238.0983622TCSC8 compensation %——-24.486TCSC15 compensation %——19.6084Fuel costs5134548553.7548563.69Emissions2.5281.0363931.037115Losses27.83521.8987822.21318Figure 7
Convergent characteristics of the proposed GTA for Scenario 1 with and without considering the TCSC devices.In addition, Figure8 shows the comparisons of the outcomes of Scenario 1 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to SNSA [71], IGA [45], GA [45], SSO [42], enhanced SSO [42], MICA [73], teaching-learning based optimization (TLBO) [63], JFS [66], and QRJFS [66].Figure 8
Comparisons for Scenario 2 without considering the TCSC devices.As shown, the proposed GTA provides the superior performance in minimizing the produced emissions with the least value of 1.036393 ton/h. On the other side, the minimum costs related to SNSA [71], IGA [45], GA [45], SSO [42], enhanced SSO [42], MICA [73], TLBO [63], JFS [66], and QRJFS [66] are, respectively, 1.0375, 1.0830, 1.1210, 1.0393, 1.7024, 1.2246, 1.0772, 1.0473, 1.0410, and 1.0377 ton/h.


## 4.1.3. Minimization of the Power Losses (Scenario 3)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to minimize the power losses, and the results are shown in Table5. Furthermore, Figure 9 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the power losses from 27.835 MW in the initial scenario to 9.92662 MW with a reduction percentage of 64.337%. In the second case by considering the TCSC devices, the suggested GTA reduces the power losses from 27.835 MW in the initial scenario to 9.692474 MW with a reduction percentage of 65.178%. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of 49.9995% and 34.7962%, respectively.Table 5
Outcomes of the proposed GTA for Scenario 3 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.010001.061.05998921.010001.0546381.05460931.010001.061.05998761.010001.0594191.05745381.010001.0598671.0691.010001.0423161.042094121.010001.049391.048461Tap4-180.970000.924580.9271464-180.978001.10.9684821-201.043001.0149060.98547324-251.000001.10.98507524-251.000001.0012761.03679424-261.043001.0953811.0002357-290.967001.0377250.95537234-320.975000.9774320.94908511-410.955000.9348730.90131215-450.955000.9472820.94416514-460.900000.9296350.94499210-510.930000.9368950.94633413-490.895000.9048580.93182411-430.958000.9261421.02109840-560.958001.0030191.00275539-570.980001.0246490.9840549-550.940001.0270270.950339Qc1810.00000305.5255.9000018.1423915536.3000019.5733515Pg1478.63500204.4293202.420720.000005.74E-081.189606340.0000014014060.000001001008450.00000307.6783306.882390.0000010010012310.00000410409.9999TCSC8 compensation %——49.9995TCSC15 compensation %——34.7962Fuel costs5134545058.3545027.8Emissions2.5281.5526491.554878Losses27.8359.926629.692474Figure 9
Convergent characteristics of the proposed GTA for Scenario 3 with and without considering the TCSC devices.In addition, Figure10 shows the comparisons of the outcomes of Scenario 3 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to SNSA [71], differential evolution (DE) [74], SSO [42], SSA [67], MICA [73], GA [45], IGA [45], and Stud Krill Herd Algorithm (SKHA) [75]. As shown, the proposed GTA provides the superior performance in minimizing the power losses with the least value of 9.92662 MW. On the other side, the minimum costs related to SNSA [71], IGA [45], GA [45], SSO [42], enhanced SSO [42], MICA [73], TLBO [63], JFS [66], and QRJFS [66] are, respectively, 10.1952, 10.558, 10.614, 11.320, 11.883, 11.814, 10.516, and 10.688 MW.Figure 10
Comparisons for Scenario 3 without considering the TCSC devices.


## 4.1.4. Minimization of theLmax (Scenario 4)

(1) LmaxMinimizing (Scenario 4). Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to improve the voltage stability by minimizing the index (Lmax), and the results are shown in Table 6. Furthermore, Figure 11 illustrates the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the stability index from 0.3000 in the initial scenario to 0.259785 with a reduction percentage of 13.405%. In the second case by considering TCSC devices, the suggested GTA reduces the stability index from 0.3000 in the initial scenario to 0.265479 with a reduction percentage of 11.507%. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of 24.1205% and -50%, respectively.Table 6
Outcomes of the proposed GTA for Scenario 4 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC devicesVg11.010001.0599831.03562621.010001.0433591.02241731.010001.0340031.02903761.010001.0326521.03203981.010001.0576311.04540691.010001.0294841.031654121.010001.023791.06Tap4-180.970000.9611060.9750224-180.978000.9859391.09298621-201.043001.0090050.99496624-251.000001.0107561.03791324-251.000001.0999641.04631924-261.043000.9793061.0371117-290.967000.9567640.92822434-320.975000.90.911-410.955000.9939531.09831515-450.955000.9265150.91282314-460.900000.9039851.02929810-510.930000.9493560.96627713-490.895000.90.9074411-430.958000.9000970.92399240-560.958001.0994461.09990339-570.980001.0139670.9395619-550.940000.9557481.097816Qc1810.000001.15563730255.9000018.107517.5536.3000029.9417630Pg1478.63500371.9249314.068720.000000.0004994.95E-08340.0000012.988330.06313960.000000.7413330.1685148450.00000371.9531549.792390.000001002.71E-0912310.00000409.7994409.7321TCSC8 compensation %——24.1205TCSC15 compensation %——-50Fuel costs5134546728.345264.89Lmax0.30000.2597850.265479Losses27.83516.6075823.02473Figure 11
Convergent characteristics of the proposed GTA for Scenario 4.


## 4.2. Outcomes of the GTA Applications for the Second EPN

For this EPN, three scenarios are examined with and without considering the TCSC devices:Scenario 5: OJ1 minimization described in equation (4)Scenario 6: OJ3 minimization described in equation (6)Scenario 7: OJ4 minimization described in equation (7)


### 4.2.1. Minimization of the Fuel Costs (Scenario 5)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices, and the results are shown in Table7. Furthermore, Figure 12 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the fuel costs from 25098.70 $/h in the initial scenario to 22953.42 $/h with a reduction percentage of 8.547%. In the second case by considering the TCSC devices, the suggested GTA reduces the fuel costs from 25098.70 $/h in the initial scenario to 22948.95 $/h with a reduction percentage of 8.565%. For these reasons, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of −45.836% and −35.71%, respectively. In addition, Figure 13 shows the comparisons of the outcomes of Scenario 5 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to the grey wolf algorithm (GWA) [76], SSA [77], novel bat algorithm (NBA) [78], improved spotted-hyena algorithm (ISHA) [79], crow search algorithm (CSA) [80], and modified CSA [80]. As shown, the proposed GTA provides the superior performance in minimizing the fuel costs with the least value of 22953.42 $/h. On the other side, the minimum costs related to SSA [77], GWA [76], NBA [78], ISHA [79], CSA [80], and modified CSA [80] are, respectively, 22965.590, 22957.720, 22960.810, 22958.780, 22959.360, and 22955.550$/h.Table 7
Outcomes of the proposed GTA for Scenario 4 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.001.0601.06021.001.0601.06031.001.0601.06041.001.0601.06051.001.0601.06061.001.0601.06071.001.0455581.04545981.00189.57081.05167Pg185.69001.051726190.79622157.40010103139.3100214.6983214.31164113.6900180.419180.0245166.48001010631.7100234.0315233.908792.056.2989856.173198122.49032.1859232.03292TCSC4 compensation %——-45.836TCSC9 compensation %——-35.71Fuel costs25098.7022953.4222948.95Losses19.015037.4545437.49588Figure 12
Convergent characteristics of proposed GTA for scenario 5.Figure 13
Comparisons for scenario 5 without considering the TCSC devices.


### 4.2.2. Minimization of the Power Losses (Scenario 6)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to minimize the power losses, and the results are shown in Table8. Furthermore, Figure 14 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the power losses from 19.015 MW in the initial scenario to 7.235351 MW with a reduction percentage of 61.949%. In the second case by considering TCSC devices, the suggested GTA reduces the power losses from 19.015 MW in the initial scenario to 7.234384 MW. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of −18.215% and 34.398%, respectively.Table 8
Outcomes of the proposed GTA for scenario 6 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.001.0595891.05905821.001.0601.06031.001.0601.06041.001.0601.06051.001.0601.06061.001.0601.06071.001.0601.06081.001.0601.060Pg185.690060.4619660.639652157.40058.8187958.648093139.3100180.6457180.65144113.6900130.7557130.75995166.4800117.9838117.9631631.7100105.4723105.474792.000156.5708156.57068122.49086.2763186.27771TCSC4 compensation %——-18.215TCSC9 compensation %——34.398Fuel costs25098.7024773.0824771.64Losses19.01507.2353517.234384Figure 14
Convergent characteristics of the proposed GTA for scenario 6 with and without considering the TCSC devices.


### 4.2.3. Minimization of theLmax (Scenario 7)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to improve the voltage stability by minimizing the index (Lmax), and the results are shown in Table 9. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the stability index from 0.173 in the initial scenario to 0.149417 with a reduction percentage of 13.641%. In the second case by considering the TCSC devices, the suggested GTA reduces the stability index from 0.173 in the initial scenario to 0.149417. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of 6.0923% and -28.321%, respectively.Table 9
Outcomes of the proposed GTA for Scenario 4 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.001.0601.05044621.001.0600.95848531.001.0601.06041.001.0601.06051.001.0600.95700161.001.0600.95036571.001.0600.97418381.001.0601.037331Pg185.690235.3035164.52252157.4015.249832503139.310029.63804104113.6900250105166.480037510631.710031.2169810792.00014.976952508122.49015.20074250TCSC4 compensation %——6.0923TCSC9 compensation %——−28.321Fuel costs25098.7027031.1128299.95Lmax0.1730.1494170.149417


## 4.2.1. Minimization of the Fuel Costs (Scenario 5)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices, and the results are shown in Table7. Furthermore, Figure 12 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the fuel costs from 25098.70 $/h in the initial scenario to 22953.42 $/h with a reduction percentage of 8.547%. In the second case by considering the TCSC devices, the suggested GTA reduces the fuel costs from 25098.70 $/h in the initial scenario to 22948.95 $/h with a reduction percentage of 8.565%. For these reasons, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of −45.836% and −35.71%, respectively. In addition, Figure 13 shows the comparisons of the outcomes of Scenario 5 with numerous alternative techniques without considering the TCSC devices. The described results are reported to be related to the grey wolf algorithm (GWA) [76], SSA [77], novel bat algorithm (NBA) [78], improved spotted-hyena algorithm (ISHA) [79], crow search algorithm (CSA) [80], and modified CSA [80]. As shown, the proposed GTA provides the superior performance in minimizing the fuel costs with the least value of 22953.42 $/h. On the other side, the minimum costs related to SSA [77], GWA [76], NBA [78], ISHA [79], CSA [80], and modified CSA [80] are, respectively, 22965.590, 22957.720, 22960.810, 22958.780, 22959.360, and 22955.550$/h.Table 7
Outcomes of the proposed GTA for Scenario 4 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.001.0601.06021.001.0601.06031.001.0601.06041.001.0601.06051.001.0601.06061.001.0601.06071.001.0455581.04545981.00189.57081.05167Pg185.69001.051726190.79622157.40010103139.3100214.6983214.31164113.6900180.419180.0245166.48001010631.7100234.0315233.908792.056.2989856.173198122.49032.1859232.03292TCSC4 compensation %——-45.836TCSC9 compensation %——-35.71Fuel costs25098.7022953.4222948.95Losses19.015037.4545437.49588Figure 12
Convergent characteristics of proposed GTA for scenario 5.Figure 13
Comparisons for scenario 5 without considering the TCSC devices.


## 4.2.2. Minimization of the Power Losses (Scenario 6)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to minimize the power losses, and the results are shown in Table8. Furthermore, Figure 14 depicts the convergent properties of the suggested GTA for this scenario considering both cases. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the power losses from 19.015 MW in the initial scenario to 7.235351 MW with a reduction percentage of 61.949%. In the second case by considering TCSC devices, the suggested GTA reduces the power losses from 19.015 MW in the initial scenario to 7.234384 MW. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of −18.215% and 34.398%, respectively.Table 8
Outcomes of the proposed GTA for scenario 6 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.001.0595891.05905821.001.0601.06031.001.0601.06041.001.0601.06051.001.0601.06061.001.0601.06071.001.0601.06081.001.0601.060Pg185.690060.4619660.639652157.40058.8187958.648093139.3100180.6457180.65144113.6900130.7557130.75995166.4800117.9838117.9631631.7100105.4723105.474792.000156.5708156.57068122.49086.2763186.27771TCSC4 compensation %——-18.215TCSC9 compensation %——34.398Fuel costs25098.7024773.0824771.64Losses19.01507.2353517.234384Figure 14
Convergent characteristics of the proposed GTA for scenario 6 with and without considering the TCSC devices.


## 4.2.3. Minimization of theLmax (Scenario 7)

Using such a situation, the suggested GTA is used both with and without the inclusion of the TCSC devices in order to improve the voltage stability by minimizing the index (Lmax), and the results are shown in Table 9. As illustrated, the suggested GTA reduces, in the first case without considering the TCSC devices, the stability index from 0.173 in the initial scenario to 0.149417 with a reduction percentage of 13.641%. In the second case by considering the TCSC devices, the suggested GTA reduces the stability index from 0.173 in the initial scenario to 0.149417. For this case, the suggested GTA is operating the TCSC devices at lines 8 and 15 at compensation levels of 6.0923% and -28.321%, respectively.Table 9
Outcomes of the proposed GTA for Scenario 4 with and without considering the TCSC devices.
VariableInitial scenarioWithout TCSC deviceWith TCSC deviceVg11.001.0601.05044621.001.0600.95848531.001.0601.06041.001.0601.06051.001.0600.95700161.001.0600.95036571.001.0600.97418381.001.0601.037331Pg185.690235.3035164.52252157.4015.249832503139.310029.63804104113.6900250105166.480037510631.710031.2169810792.00014.976952508122.49015.20074250TCSC4 compensation %——6.0923TCSC9 compensation %——−28.321Fuel costs25098.7027031.1128299.95Lmax0.1730.1494170.149417


## 4.3. Outcomes of the GTA Applications for the Third EPN

For the IEEE 118-bus large-scale network, the proposed GTA is applied in comparison to the PSO technique, which is one of the well-established algorithms to deal with such OPF problems, for minimizing the fuel costs. Based on those circumstances, the obtained results using the proposed GTA and PSO techniques are tabulated in Table10, while the regarding convergence properties are described in Figure 15. As illustrated, the proposed GTA achieves lower fuel cost value of 129752.2 $/hr than the implemented PSO that achieves fuel costs of 129990.8$/hr. Also, Table 11 describes a comparison with reported results of well-established techniques of the differential algorithm [74] and PSO [81]. As shown, the proposed GTA provides better performance than the differential algorithm [74] and PSO [81], which obtain fuel costs of 130518.5 and 130288.21 $/h, respectively.Table 10
Optimal results of the proposed GTA and PSO for the third EPN.
VariablePSOProposed GTAVariablesPSOProposed GTAVariablePSOProposed GTAVG10.9785011.014395VG1001.0203451.042152PG26278.3602281.6778VG41.0126481.044675VG1031.022871.036934PG2712.9439514.59936VG61.0097431.032677VG1041.0192591.024966PG316.8752795.944698VG81.061.06VG1051.0157931.022219PG3211.9103313.59129VG101.061.06VG1071.018941.021821PG348.4748887.400459VG121.0017821.028617VG1101.0069491.021915PG3610.443211.255318VG150.9985211.022519VG1111.0143021.026412PG4044.5161752.60187VG181.0089141.030823VG1121.0007181.014982PG4239.0215738.54453VG191.0001081.024811VG1131.0071931.037776PG4620.9262121.22069VG240.9962451.043987VG1161.061.037198PG49191.5003193.514VG251.0219841.058359TP8-51.0296121.005706PG5444.3837247.85186VG261.0045941.06TP26-251.0344381.060425PG5535.9945925.86789VG271.0022321.041299TP30-171.001461.018817PG5628.7231932.81963VG310.9940911.031925TP38-371.0123021.021673PG59144.8207150.8728VG320.9926771.038484TP63-591.041271.026101PG61136.0841147.0345VG340.9990191.035797TP64-610.9917750.99852PG622.1606565.044222VG360.9917771.033989TP65-660.9816331.021505PG65355.0331342.99VG400.9829771.029688TP68-691.0207880.956823PG66345.8028341.7799VG420.981631.036631TP81-801.0306690.984893PG69448.6191451.2607VG461.0007251.038833QC51.9001942.032134PG707.0968636.386357VG491.0245891.051785QC341.072053.101457PG722.0824894.940006VG541.0041021.032799QC371.1190562.663295PG735.3715815.033392VG551.0002341.031209QC441.7397391.982284PG7416.806423.05925VG561.0022181.031322QC453.7248532.341122PG7623.2178722.03655VG591.0284981.043654QC463.5695822.160515PG776.6110355.41385VG611.061.042242QC481.4215013.422638PG80421.4037425.8186VG621.0513881.036809QC743.7107992.733545PG852.030233.645089VG651.061.06QC793.8616012.265789PG873.7884293.849221VG661.0529571.054528QC821.8292462.46713PG89486.7405492.4201VG691.0203151.06QC832.0498162.819053PG907.1340416.021877VG700.9852611.036728QC1052.8624613.904263PG911.9745610VG720.9836341.034832QC1071.3264824.015503PG926.5700161.1E-09VG730.9821361.029527QC1102.9058782.806326PG992.5239115.239772VG740.9702821.019137PG127.32622.81094PG100233.3448229.2691VG760.9606481.011218PG46.5159645.352099PG10337.5073838.60442VG770.9895061.034381PG63.5128794.709697PG1045.4792264.005683VG801.0030651.045973PG803.802367PG1055.8707365.861348VG851.0020841.040072PG10388.7673398.088PG10725.7470231.70121VG871.0376671.052759PG1283.8244584.19864PG11010.025137.202108VG891.020581.06PG1525.6000517.7294PG11135.8273934.93683VG901.0142891.033737PG1818.4807112.3412PG11242.3142733.53649VG911.0127341.025402PG1921.0221919.84697PG1131.7249014.683022VG921.0043391.041442PG241.5314880.007257PG1160.7538470VG991.0228441.027761PG25187.9791183.6368Fuel Costs129990.8129752.2Figure 15
Convergent characteristics of the proposed GTA and PSO for the third EPN.Table 11
Comparisons for the third EPN.
MethodProposed GTAImplemented PSODifferential algorithm [74]PSO [81]Cost129752.2129990.8130518.5130288.210


## 5. Conclusion

This research investigates a new nature-inspired algorithm called the gorilla troops algorithm (GTA) to solve the OPFI with and without the inclusion of the Thyristor-Controlled Series Capacitor (TCSC) devices in the system. Numerous objective functions are minimized throughout regulating the generator bus voltage magnitude, generator real power, reactive power of shunts, and transformer taps. Seven scenarios with and without the inclusion of the TCSC devices in the system are evaluated, and each scenario involves the goal function of transmission losses, fuel costs, voltage stability, and emissions. The efficiency of the GTA has been verified using the standard IEEE 57-bus EPN and a practical Egyptian West Delta-EPN (WD-EPN) with and without the inclusion of the TCSC devices to appraise the GTA algorithm’s performance in the OPFI. In addition to that, the proposed GTA is applied on the large-scale IEEE 118-bus EPN. The simulation findings demonstrate that integrating TCSC devices in an OPFI framework can significantly improve voltage stability and reduce the operation cost, active power losses, and emissions. In addition to this, the findings obtained by the GTA have outperformed the recently developed powerful and well-known algorithms in the literature. With the incredible efficacy of the provided GTA in this paper, it is suggested that the proposed GTA can be tested on the OPFI for compensated power systems by considering static var converters (SVCs) or a combination of TCSC and SVC. Moreover, it is recommended that the proposed GTA can be investigated in the future for resolving the OPFI in power grids with high renewable energy penetration. The future extension can be added for the GTA improvement and the possible network limitations under competitive systems.



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*Source: 9448199-2022-08-24.xml*