Multi-Objective Optimal Location of Distributed Generators & Capacitor Banks into Radial Distribution Network by Novel Metaheuristic Optimisation

Abstract

The integration of renewable-based distributed units into distributed systems has been aided by recently developed technologies based on renewable energy, changes to utility infrastructure, and progressive government regulations. In this paper, an improved version of the golden jackal optimization (IGJO) is implemented to incorporate distributed generators (DGs) and capacitor banks (CBs) into the distribution system. The existing studies give only DG unit insertion, but in this work, simultaneous integration of different kinds of DG with a capacitor bank is used to analyze the impact. The main emphasis of this study is to minimize power loss along with the upgradation of the voltage profile. Improvement in voltage stability index and minimization of total voltage deviation (TVD) were also achieved by placing the DG and CB units in a suitable position. Load modeling is also considered here to validate the results. Seven types of loading, including constant power (half load and heavy load), constant current, constant impedance, residential, industrial, and commercial loads, are used to show the effect of integration of DG and capacitor bank into a 33-bus and 118-bus radial distribution system. Comparison of the proposed method with previous studies shows the better performance of the implemented method over other techniques.

1. Background

The distribution system plays an essential role in linking the transmission network to end users; thus, the distribution system is a vital topic of study. Demand for power rises due to fast industrialization, and continuous population growth leads to preference for decentralized power generation instead of centralized methods. From this perspective, distributed generation (DG) has been an effective option for producing power in close proximity to demand centers [1]. The unpredictable nature of consumers load pattern makes it difficult to balance the flow of power and appropriate supply voltage while meeting operational requirements in parallel, and the quality of power and stability is therefore affected. In addition, inductive loads also cause a lagging power factor and more system loss [2]. Therefore, it is necessary to reduce loss and maintain consistent voltage supply throughout the distribution network.

Reactive power compensation using a capacitor bank is the best option to nullify the aforementioned problems [3]. Day-to-day increase in demand for power encourages the incorporation of distributed generation near the consumer end, to avoid the demand for additional new infrastructure. Using CBs and DGs together in the distribution system offers many benefits, such as mitigation of losses, improved voltage supply, lowering cost, lowering branch current, and improvement in power factor along with power quality [4]. Additionally, utilizing DG improves environmental effects. However, if both CBs and DGs are not placed correctly, this causes problems such as over-voltage, bidirectional power flow issues, and increased losses. Because of these issues, it is mandatory to allocate proper sized DG units and CBs at the correct positions in the distribution network, to minimize loss and ensure effective operation within acceptable limits; only then can it boost the system performance and reliability as well [5].

Reactive power compensation is typically provided by capacitor banks (CBs). Numerous studies have addressed the critical issue of location and assessing the capacity of CBs prior to their installation in the electrical system. The cuckoo search algorithm (CSA) [6] optimally allocates the static capacitor into RDN with 69 and 118 nodes, with consideration of various loading conditions. The main emphasis of that work was to achieve an improved voltage waveform and make the system economically beneficial. A flower pollination algorithm for 10, 69, and 118 bus systems to reduce the overall cost of the infrastructure and to increase net savings is presented in [7]. The techno-economic analysis is presented in RDN with 33 and 69 nodes, positioning the shunt capacitor in an optimal location. Constriction factor particle swarm optimization (CFPSO) was employed to enhance system stability along with the voltage magnitude and to mitigate the cost and loss of the system [8].

The existing literature on DG placement into radial distribution systems with optimal location and size has offered substantial contributions through a variety of metaheuristic optimization methods. Nature-inspired metaheuristic algorithms have the potential to deal with the challenges in the existing power distribution system. A multi-objective optimization (MOO) using adaptive particle swarm optimization (APSO) and modified gravitational search algorithm (MGSA) was applied to an IEEE distribution system with 69 and 85 buses. Multiple DGs were used to improve the performance of a network by minimizing active power loss and by improving the voltage profile [9]. The whale optimization algorithm (WOA) described in [10], inspired by the hunting nature of humpback whales, was used for loss mitigation and enhancement in voltage profile on IEEE 15, 33, 85 and 69 bus distribution systems. An MOF (multi-objective function) was used for optimal placement of DG into a radial distribution system with 33, 69, and 54 buses considering load models [11]. For an IEEE 85 and 69 test system, multi-objective differential evolution (MODE) algorithm were utilized to reduce power loss by allocating suitable DGs [12].

In some research, hybrid techniques have been employed to insert the DG and capacitor simultaneously. The moth flame optimization and sine cosine algorithm (MFO-SCA) is a hybrid technique to allocate single and multiple units of DG and capacitors on 33-node and 69-node RDS; a single objective function is used to emphasize the reduction of active power loss [13]. Likewise, a hybrid technique, EGWO-PSO, combining enhanced grey wolf optimizer and particle swarm optimization to enhance economic, environmental and technical benefits was used [14] for standard IEEE 33 and 69 bus distribution networks to evaluate the results using a multi-objective function, i.e., to minimize emission, power loss, and cost of energy and to enhance the voltage deviation index (VDI). The incomprehensible but intelligible in time logic algorithm (ILA) to place different types of DG units with different power factors and various loading conditions for mitigation of power loss and for betterment of VDI is explained in [15].

Previous research articles have also described the simultaneous allocation of DGs and a shunt bank of capacitors. The enhanced genetic algorithm (EGA) was used in order to simultaneously allocate the DG/SCs on a 33, 69, and 119 IEEE test bus system [16]. The FFA and BSA method for integration of DG and SC together into 33 and 69 bus system to improve voltage and reduce power loss is described in [17]. The CTLBO algorithm to enhance the stability and to reduce loss for a 33, 69, and 118 bus system is explained in [18]. DG and capacitors were used simultaneously for mitigating the loss of power, energy, and voltage deviation in association with improving the VSI in 33bus, 69 bus, and real-time network of Egypt by applying the water cycle algorithm (WCA) [19]. The cuckoo search algorithm (CSA) is also utilized for the similar task and presented in [20]. The integration of DG and CBs simultaneously into the RDS for standard IEEE systems for minimization of power loss is mentioned in [21]. Constriction factor particle swarm optimization (CFPSO) was used for simultaneous integration of DG and shunt capacitor in the IEEE 33 bus and the practical Brazil 136 bus RDS, to achieve the objectives related to voltage deviation, voltage stability index, and power loss [22]. A combination of different types of DGs with shunt capacitors used fuzzy logic and a genetic algorithm (GA) to obtain the objective of loss reduction, active and reactive power supply management, voltage profile, and stability upgradation [23]. The power voltage sensitivity constant (PVSC) is used to allocate DGs and CBs on a standard 69 bus system and a 130 bus real system of jamawaramgarh Jaipur to mitigate the power loss and improve the voltage profile is explained in [24]. The intersect mutation differential evolution (IMDE) algorithm for positioning of DG and CBs, both in the correct position on 33 and 69 IEEE bus distribution systems with the aim of cost and loss, is depicted in [25]. A population based meta-heuristic optimization technique known as the arithmetic optimization algorithm (AOA) is proposed for active loss minimization and voltage variations in the IEEE 33-bus and 69- bus system is described in [26]. The method of injecting different types of DGs with capacitors in different combinations for the IEEE 33-bus system using JAYA optimization algorithm to evaluate the results is implemented in [27]. The teaching-learning based optimization (TLBO) for analysing constrained and unconstrained real time criterion optimization problems. TLBO shows better performance when compared with the other methods dealing with large-scale problems in given in [28]. A combination of competitive search optimization (CSO) with chaotic and fuzzy logic is analysed on a 69-bus radial distribution system to mitigate loss and improve the profile of the voltage wave is demonstrated in [29]. The arithmetic optimization algorithm (AOA) is demonstrated in [30] using voltage stability indicator for DG placement in IEEE 33 bus system. Evolutionary algorithm (EA) method for individual and simultaneous integration of DG in 33 and 118 bus IEEE systems is presented in [31]. A binary collective animal behavior optimization algorithm is used to mitigate voltage variation and loss in IEEE radial system by incorporation DG and CB together is presented in [32]. The improved binary BAT algorithm is given for multiple DG allocation to mitigate loss for IEEE 33 and 69 bus systems are given in [33]. A Enhanced jelly fish search optimizer (EJS) is used to assign different types of DG in IEEE 33, 69 and 94 bus systems to minimize loss and voltage deviation is presented in [34]. The improved analytical method is utilized for loss curtailment for IEEE 33, 69 bus systems by adding multiple DGs on network. The loss sensitivity factor (LSF) and exhaustive load flow (ELF) are also presented in [35]. A review of previous studies made in the allocation of DG, energy storage technologies and systems, and review on technique used for integration of DG and a capacitor simultaneously is given by [36] and [37]. The weight improved particle swarm optimization-gravitation search algorithm (WIPSO-GSA) is utilized for integrating DG and capacitor together in 33 and 85 bus system energy loss reduction is depicted in [38]. New heuristic method is used to integrated DG and CB together into 33, 69 and 119 bus test system for loss mitigation is given in [39].

The Binary random dynamic arithmetic optimization algorithm (BRDAOA) is applied to the standard IEEE system, having 33 buses for choosing the best location for Electrical vehicle charging station (EVCSs). The main emphasis of the work is to reduce losses, Total harmonic distortion (THD), and deviation in voltages. Arithmetic optimization algorithm (AOA) and Dynamic arithmetic optimization algorithm (DAOA) are also presented in [40]. The Local particle swarm optimization variant algorithm (LPSOV) algorithm used for placement of DG optimally to achieve better profile of voltage and lower value of loss in the IEEE 33 and 118 bus systems with different penetration levels is explained in [41] and degree of freedom concept is also presented in this work. The LPSOV algorithm is proposed for placing DGs optimally in the IEEE standard test system, having 33 nodes is presented in [42]. Main objective of this work is to mitigate the energy loss. For achieving the goal of loss minimization, DG is placed optimally in the typical 30 and 33 bus systems. The PSO with its three versions i.e., global particle swarm optimization variant algorithm (GPSO), Local particle swarm optimization variant algorithm (LPSO), and unified particle swarm optimization variant algorithm (UPSO) is utilized in [43]. The UPSO is utilized in [44] for solving the problem related to optimal siting and sizing of RESs. RES modified 33 and 118 Test systems are used in this work. PVs and WTs are inserted to minimize the system losses, considering the capacity factor (CF) ratio and weather conditions are also taken into consideration. The SA algorithm is implemented on the IEEE 33, 69, and 118 bus systems. Loss sensitivity factor is also considered in [45] for achieving less power loss using DGs on different power factors. The SSO algorithm for placing capacitors into the IEEE 34 bus and IEEE 118 bus test system is utilized in [46] with the objective of obtaining higher reduction in losses and better VSI and profile of voltages. For maintaining losses as low as possible within operational constraints, the analytical method withPower voltage sensitivity constant

(PVSC) for siting of DG and Capacitors is utilized in [47]. This work is carried out upon the IEEE 69 and 118 bus test system. The Adaptive quantum-inspired evolutionary algorithm (AQiEA) is explained in [48] for allocating the dispersed generation unit in the large DSs having 85 and 118 buses to attain a higher reduction in power loss and improvement in voltage profiles. Outcomes of the work are also validated with different voltage-dependent load models. The multi-objective optimization by using GA to attain the minimum loss, operating cost, and to enhance the voltage profile is proposed in [49]. Loss sensitivity factor (LSF) is also incorporated in the simulation under 34-bus and 118-bus test systems. The African vultures optimization algorithm (AVOA) is implemented in test systems having 85 and 118 node points to attain high net profit and to lower the loss and cost of the system is elaborated in [50]. The osprey optimization algorithm (OOA) is explained in [51] to integrate PV-based DG and capacitors together for reducing the loss, and Total voltage deviation (TVD) for the IEEE 69,118 bus system. The results are also validated on 37 bus Tala Egyptian RDS. The Crested porcupine optimization algorithm (CPOA) implementation on the IEEE 85 and 118 bus test system for maintaining loss to a lower value with consideration of operational constraints of the system is given in [52]. Previous researches are given in

Table 1. Previous research compilation.

Ref	Author’s Name	Year	Technique	Bus Systems	Objectives			Connected Unit	Goal
					Tech	Eco	Environ
[28]	R.V. Rao et al.	2012	TLBO	-	√	-	-	-	Constraint and unconstraint real time problem solving
[2]	S Gopika Naik et al.	2013	Analytical approach	12/33	√	-	-	Simultaneous CB and DG	Real power loss minimization
[35]	Hung, D. Q., et al.	2013	IA	16/33/69	√	-	-	DG only	Loss mitigation
[45]	S.K. Injeti et al.	2013	SA	33/69/118	√	-	-	DG only	Loss mitigation
[6]	El-Fergany A et al.	2014	CSA	69/118	√	√	-	Only Capacitor	Minimization of cost and loss, voltage improvement
[32]	N. Ali khan et al.	2015	BCABO	12/33/69	√	-	-	Simultaneous CB and DG	Loss and TVD minimization
[41]	Paschalis A. Gkaidatzis et al.	2015	L-PSO-V	33/118	√	-	-	Only DG	Loss reduction
[7]	Abdelaziz, Almoataz et al.	2016	FPA	10/69/118	√	√	-	Only Capacitor	Diminishing cost and increased savings
[11]	M. Dubey et al.	2016	GA/PSO	33/69/54 bus practical RDN	√	√	-	Only DG	Loss and cost mitigation
[24]	Nawaz sarfaraz et al.	2016	Analytical approach	69/130 practical network of Jaipur city	√	-	-	Simultaneous CB and DG	Loss reduction
[25]	Amin Khodabakhshin et al.	2016	IMDE	33/69	√	√	-	Simultaneous CB and DG	Loss and cost reduction
[46]	N. Gnanasekaran	2016	SSO	34/118	√	√	-	Only CB	Loss and cost Mitigation, VSI enhancement
[47]	Sarfaraz Nawaz	2016	Analytical approach (PVSC)	69/118	√	-	-	Simultaneous CB and DG	Loss Mitigation
[42]	Paschalis A. Gkaidatzis et al.	2017	LPSO	33	√	-	-	Only DG	Loss Mitigation
[10]	D. P. Readdy et al.	2017	WOA	15/33/69/85	√	-	-	Only DG	Diminishing system loss and upgrading the system’s voltage profile and reliability
[43]	Paschalis A. Gkaidatzis et al.	2017	UPSO, LPSO, GPSO	33/30	√	-	-	Only DG	Loss Mitigation
[17]	Satish Kumar Injeti et al.	2018	FFA & BSA	33/69	√	-	-	Simultaneous CB and DG	Voltage improvement and power loss reduction
[18]	Imran Ahmad Quadri et al.	2018	CTLBO	33/69/118	√	-	-	Only DG	Loss minimization and rise in stability
[19]	A.A.A. El-Ela et al.	2018	WCA	33/69/Real part of Egyptian nw	√	-	-	Simultaneous CB and DG	Diminishing the power and energy loss, voltage deviation, and improving the VSI.
[4]	Khalil Gholami et al.	2019	SSA	33/69	√	-	-	Simultaneous CB and DG	Power loss mitigation.
[12]	S.R. Bahera et al.	2019	MODE	69/85	√	-	-	Only DG	Diminishing the power line loss.
[23]	Gampa, S.R et al.	2019	Fuzzy GA	69/51	√	-	-	Simultaneous CB and DG	Improvement in voltage stability branch current and voltage and mitigation of loss
[39]	Bayat A. et al.	2019	Heuristic approach	33/69/119	√	-	-	Simultaneous CB and DG	Power loss mitigation
[44]	Paschalis A. Gkaidatzis et al.	2019	UPSO	33/118	√	-	-	Only DG	Mitigation in power loss
[9]	Eid A. et al.	2020	APSO-MGSA	69/85	√	-	-	Only DG	Power loss and TVD reduction and voltage stability enhancement
[16]	Emad Ali Almabsout et al.	2020	Hybrid local search GA	33/69/119	√	-	-	Simultaneous CB and DG	Minimize losses and TVD
[22]	Korra Balu et al.	2020	CFPSO	33/Practical Brazil 136 bus	√	-	-	Simultaneous CB and DG	Reduction in system loss and voltage deviation, improvement in VSI
[38]	Rajendran A. et al.	2020	WIPSO -GSA	33/85	√	-	-	Simultaneous CB and DG	Energy loss mitigation
[48]	G. Manikanta	2020	AQiEA	85/118	√	-	-	Only DG	Power loss reduction and voltage improvement
[49]	Sayed mir shah Danish et al.	2020	LSF	34/118	√	-	-	Only CB	Loss reduction and voltage stability enhancement
[13]	Hussein abdel-mawgoud et al.	2021	MFO-SCA	33/69	√	-	-	Simultaneous CB and DG	System loss mitigation and voltage improvement
[14]	Chandrasekaran venkatesan et al.	2021	EGWO-PSO	33/69	√	√	√	Simultaneous CB and DG	Loss minimisation along with economic and environmental effects
[3]	Luan D.L et al.	2022	probabilistic generation models	-	√	√	-	Simultaneous CB and DG	Reduction in annual loss of power
[21]	Mohamed A. Elseify et al.	2022	HBA	69	√	-	-	Simultaneous CB and DG	Loss minimization
[33]	Saxena, N. et al.	2022	Improved binary bat algorithm	33/69	√	-	-	Multi DG	Loss mitigation
[50]	S.R. Biswal et al.	2022	AVOA	85/118	√	√	-	Simultaneous CB and DG	Loss minimization, voltage profile upgradation and increase in profit
[30]	Mohd Tauseef Khan et al.	2023	AOA	33	√	-	-	Only DG	Minimization of loss and voltage deviation
[31]	Aamir Ali et al.	2023	MINLP	33/69/118	√	√	√	Simultaneous CB and DG	Technical, Economic, and Environmental Benefits
[34]	Ali Salim et al.	2023	EJS	33/69/94	√	-	-	Only DG	Minimization of loss and voltage deviation, improving VSI
[8]	S.A. Salimon et al.	2024	CFPSO	33/69	√	-	-	Capacitor only	Minimization of power loss
[15]	Nitin Saxena et al.	2024	ILA	16/33/69/118	√	√	-	Only DG	Mitigation of losses, cost, VD, and improvement in voltage level
[20]	Ram Prakash et al.	2024	CSA	33	√	√	-	Only DG	Achieve technical and economic benefits
[26]	Pamuk, N.; Uzun et al.	2024	AOA	33/69	√	-	-	Simultaneous CB and DG	Mitigate loss and voltage deviation
[29]	Shifeng Wang et al.	2024	CSO	69	√	-	-	Simultaneous CB and DG	Mitigate loss and uplift voltages
[40]	Georgios Fotis	2024	BRDAOA	33	√	-	-	EVCs and DG	Reduction in poll, THD, and TVD
[27]	Bhatti, M. I et al.	2025	JAYA	33	√	-	-	Simultaneous CB and DG	Loss reduction
[51]	P. Rajkumar et al.	2025	OOA	69/118/real time Tala Egyptian	√	-	-	Simultaneous CB and PV based DG	Reduction loss and TVD, improvement in VSI
[52]	S. Phatak et al.	2025	CPOA	85/118	√	√	-	Simultaneous CB and DG	Mitigate loss, TVD and cost, enhancement in VSI

below.

2. Significance of Research

Because of more power loss due to a higher resistance to reactance ratio in the distribution network, it is harder to deal with such kind of a system compared to the transmission system. Refinement of voltage waves results in upgradation of the overall performance of the system, which relates directly to lowering of system losses. Due to the aforementioned reason, mitigation of losses becomes the topmost priority nowadays in the scenario of the distribution system. This accelerates the need for integration of a distributed resource unit into the distribution system. Consequently, optimal penetration of dispersed generators in network has become a prominent research domain in recent years.

Based on real and reactive power supply, DG can be classified in four ways:

(i)

Type-I DG: It supplies real power at unity power factor, e.g., PV arrays, biogas plants, etc.

(ii)

Type-II DG: It operates on zero power factor and supplies reactive power, e.g., capacitor bank, inductor bank, synchronous condenser, etc.

(iii)

Type-III DG: It supplies both actual and reactive power for the system at a 0.8 to 0.99 leading power factor e.g., tidal wave, wind, and geothermal sources.

(iv)

Type-IV DG: It operates at a power factor of 0.8 to 0.99 lagging. It supplies reactive power to the network while absorbing real power from the system, e.g., DFIG, wind mill.

After placing the right-sized DG in the correct position in the network, notable performance results regarding loss curtailment. Practical repercussions of DGs encompass technical, environmental and economic aspects, listed below:

(i)

Incorporation of the DG unit near load centers curtails the losses in a significant manner.

(ii)

In case of natural disaster or outage, or grid failure, DG provides backup power, which makes the system more reliable and stable.

(iii)

To maintain the faraway and weak bus voltages.

(iv)

DG avoids the need of quick and expensive upgradation of systems (transmission lines, distribution lines, transformers, feeders) as it can provide power locally.

(v)

DG can be considered as a green energy source, so that it can mitigate environmental issues.

(vi)

By supplying on-site power, DG eliminates the need for costly, centralized infrastructure.

(vii)

DG has the benefit of flexibility to install. Due to its modular design, it can be quickly and easily deployed.

3. Problem Formulation

Power flow analysis is one of the basic tasks in transmission and distribution networks, as it computes the bus voltage magnitudes and angles. This information is then utilized in the subsequent process of calculating power flows and quantifying system power loss.

3.1. Objective

The crucial objective of the proposed work is to mitigate system loss. Along with this, cost reduction and improvements in the voltage deviation index (VDI) and voltage stability index (VSI) are also in the scope of work represented by Equation (1).

$$\mathrm{F}=w1\mathrm{f}1+w2\mathrm{f}2+w3\mathrm{f}3+w4\mathrm{f}4$$

(1)

where $\mathrm{f}1={\displaystyle \frac{RPL}{{RPL}_{Base}}}$, $\mathrm{f}2={\displaystyle \frac{TVD}{{TVD}_{Base}}}$, $\mathrm{f}3={\displaystyle \frac{{VSI}^{-1}}{{VSI}_{Base}^{-1} }}$ & $\mathrm{f}4=a{P}_{DG}^2+b{P}_{DG }+c$.

The values of a = 0, b = 20, c = 0.25, and $\mathrm{w}1$, $\mathrm{w}2$, $\mathrm{w}3$, $\mathrm{w}4$ are the weighting factors. Summation of all four weighting factors is equal to 1, and every weight has a different magnitude.

RPL is a reduction in power loss, TVD is the total voltage deviation, VSI is the voltage stability index, and $P_{DG }$ is the real power of DG.

3.2. Constraints/Boundaries

There are some limitations that are linked to the objectives. These boundaries are classified into two categories, as described below.

3.2.1. Equality Constraints

The power balance equation lies under this category, expressed in Equations (2) and (3).

$$P_{S/S}+{\displaystyle {\sum }_{d=1}^D}{P}_{DG}\left(d\right)={\displaystyle {\sum }_{t=1}^T}{P}_{loss}\left(t\right)+{\displaystyle {\sum }_{n=1}^N}{P}_D\left(n\right)$$

(2)

$$Q_{S/S}+{\displaystyle {\sum }_{d=1}^D}{Q}_{DG}\left(d\right)+{\displaystyle {\sum }_{m=1}^M}{Q}_{cap}\left(m\right)={\displaystyle {\sum }_{t=1}^T}{Q}_{loss}\left(t\right)+{\displaystyle {\sum }_{n=1}^N}{Q}_D\left(n\right)$$

(3)

where

$P_{S/S} \&$ $Q_{S/S}$ are the total real and reactive power from slack bus;

$P_{DG}\left(d\right) \& Q_{DG}\left(d\right)$ are the real and reactive power generation from DG;

$P_D\left(n\right) \& Q_D\left(n\right)$ are the real and reactive power demand;

$P_{loss}\left(t\right) \& Q_{loss}\left(t\right)$ are the real and reactive power loss;

$Q_{cap}\left(m\right)$ is the power generation by capacitor.

3.2.2. Inequality Constraints

The inequality constraints are given as follows:

(a) Voltages limit can be shown as $V_{min}\le V_i\le V_{max} and I_i\le I_{\max i}$;

(b) Real and reactive power limits can be given as ${P_{DG}^{min}\le P_{DG}\le P_{DG}^{max},Q}_{DG}^{min}\le Q_{DG}\le Q_{DG}^{max}$;

(c) The reactive power injection limit is defined in the equation $Q_{cap}^{min}\le Q_{cap}\le Q_{cap}^{max}$.

3.3. Load Model

In classical power flow analysis, loads are typically assumed to be constant. However, this assumption is unrealistic for dynamic and complex power system operations. Inaccurate load modelling can lead to significant errors in estimating losses, operational costs, and system performance indices. In practice, both static and dynamic analysis account for loads that vary with voltage and/or frequency. Voltage-dependent loads are generally categorized as residential, industrial, or commercial. Ashish Kumar Bohre et al. [11] proposed mathematical expressions for various practical load models, presented in Equations (4) and (5), respectively.

$$P_{Li}=P_{0i}\left[w_O\ast {\left({\displaystyle \frac{V_i}{V_o}}\right)}^{{\alpha }_0^{\prime }}+w_R\ast {\left({\displaystyle \frac{V_i}{V_o}}\right)}^{{\alpha }_R^{\prime }}+w_I\ast {\left({\displaystyle \frac{V_i}{V_o}}\right)}^{{\alpha }_I^{\prime }}+w_C\ast {\left({\displaystyle \frac{V_i}{V_o}}\right)}^{{\alpha }_C^{\prime }}\right]$$

(4)

$$Q_{Li}=Q_{0i}\left[w_O\ast {\left({\displaystyle \frac{V_i}{V_o}}\right)}^{{\beta }_0^{\prime }}+w_R\ast {\left({\displaystyle \frac{V_i}{V_o}}\right)}^{{\beta }_R^{\prime }}+w_I\ast {\left({\displaystyle \frac{V_i}{V_o}}\right)}^{{\beta }_I^{\prime }}+w_C\ast {\left({\displaystyle \frac{V_i}{V_o}}\right)}^{{\beta }_C^{\prime }}\right]$$

(5)

where

$P_{Li} \&{ Q}_{Li}$—The active and reactive power loads at the ith bus;

$P_{0i} \& Q_{0i}$—The active and reactive operation point loads at the ith bus, respectively;

$V_i{ and V}_o$—Voltage of ith bus and voltage of the operating point, respectively;

For the CP (constant power) load model: $w_O$ = 1, $w_R{=w}_I=w_C=0$ and ${\alpha }_0^{\prime }= {\beta }_0^{\prime }=0$;

For a light load, the CP load model is halved, whereas for a heavy load constant power load model is multiplied by 1.6;

For a constant current load: $w_O$ = 1, $w_R{=w}_I= w_C=0$ and ${\alpha }_0^{\prime }= {\beta }_0^{\prime }=1$;

For a constant impedance load: $w_O$ = 1, $w_R{=w}_I= w_C=0$ and ${\alpha }_0^{\prime }= {\beta }_0^{\prime }=2$;

$\mathrm{F}\mathrm{o}\mathrm{r} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l} \mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d} \mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}:w_R$ = 1, $w_O{=w}_I= w_C=0$ and ${\alpha }_R^{\prime }= 0.92, {\beta }_R^{\prime }=4.02$;

For the industrial load model: $w_I$ = 1, $w_R{=w}_O= w_C=0$ and ${\alpha }_R^{\prime }=0.18 ,{\beta }_R^{\prime }=6$;

For the commercial load model:$w_C$ = 1, $w_R{=w}_I= w_O=1$ and ${\alpha }_R^{\prime }=1.51,{\beta }_R^{\prime }=3.4$.

4. Golden Jackal Optimization (GJO)

The golden jackal optimization technique is based on an artificial intelligence system, initially presented by Nitish Chopra et al. in 2022 [53]. Golden jackals utilize a variety of scavenging tactics; these tactics for finding food serve as one of the primary sources of this algorithm. The GJO procedure replicates the cooperative behavior of foraging by altering the viewpoint of the prey. The starting position of the prey is chosen at random using the global search space. After an update, the male golden jackal is in the best place, but the female golden jackal is in an unacceptable region, and the location of the victim population is altered based on the specific coordinates of the golden jackal pair. Golden jackals are solitary animals but work in pairs. They have the ability of multi-tasking as they can move, forage, and hunt all at the same time. This quality gives them the potential to acquire more desirable prey in a specific region. Synchronized investigation is more fruitful compared to that carried out individually. In tandem, jackals often employ fewer tactics to win more sieges. Without delay, they capture their prey by swiftly employing the relay technique. When their prey is encircled, they continue to relentlessly assault the target. When the prey begins to lose its strength and gets tired, the jackals launch a group attack to finish the fight. This algorithm can be divided into three phases i.e., seeking, encompassing, and firing. The golden jackal pair searches for a quarry when there is high prey vitality; on the other hand, when vitality is low, they take turns assaulting the victim.

(i)

Initial stage

In this phase, initialization of the golden jackal takes place; it can be formulated by Equation (6) as follows:

$$X_0=X_{MIN}+RAND\ast (X_{MAX}-X_{MIN})$$

(6)

(ii)

Exploration phase

GJs are able to recognize and follow their prey with great skill, yet it is not always easy to capture them, depending on the circumstances. As a consequence of this, the golden jackal waits for its turn and searches for more prey. Most of the hunting is done by male jackals. Both the male and female jackals follow the lead of their partner. This phase of exploration can be explained mathematically by Equations (7)–(14).

$${\mathrm{Y}}_{\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{e}\ast \left|{\mathrm{Y}}_{\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-{\mathrm{R}}_1\ast \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(7)

$${\mathrm{Y}}_2\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{f}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{e}\ast \left|{\mathrm{Y}}_{\mathrm{f}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-{\mathrm{R}}_1 \ast \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(8)

$$\mathrm{e}=e_1\ast e_0$$

(9)

$$e_0=2\ast R-1$$

(10)

$$e_1=C_1\ast [1-({\displaystyle \frac{t}{T}})]$$

(11)

$${\mathrm{R}}_1=0.05\ast \mathrm{L}\mathrm{e}\mathrm{v}\mathrm{y} \mathrm{F}\left(\mathrm{y}\right)$$

(12)

After evolving the cycle value of $e_1$ declined from 1.5 to zero value,

$$\mathrm{L}\mathrm{e}\mathrm{v}\mathrm{y} \mathrm{F}\left(\mathrm{y}\right)=0.01\ast {\displaystyle \frac{(\mathsf{\mu }\ast \mathsf{\alpha })}{{\left|\mathsf{\nu }\right|}^{\frac{1}{\mathsf{\beta }}}}}$$

(13)

The position of the Jackal is updated using the following formula:

$${\mathrm{Y}}_{\mathrm{t}+1}^{\mathrm{E}\mathrm{x}\mathrm{p}.\mathrm{P}\mathrm{h}.}={\displaystyle \frac{{\mathrm{Y}}_1\left(\mathrm{t}\right)+{\mathrm{Y}}_2\left(\mathrm{t}\right)}{2}}$$

(14)

At the (t+1)th iteration, Y(t+1) is the position of Jackal.

(iii)

Development phase

Initially, the prey that has been infected by the jackal has less energy to disperse than any other prey. The following formula indicates that both male and female Jackals are present together during the hunting process. Using Equations (15)–(17), it is possible to ascertain the current location of the jackal.

$${\mathrm{Y}}_1\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{e}\ast \left|{\mathrm{R}}_1\ast {\mathrm{Y}}_{\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(15)

$${\mathrm{Y}}_2\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{f}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{e}\ast \left|{\mathrm{R}}_1\ast {\mathrm{Y}}_{\mathrm{f}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(16)

$${\mathrm{Y}}_{\mathrm{t}+1}^{\mathrm{D}\mathrm{e}\mathrm{v}.\mathrm{P}\mathrm{h}.}={\displaystyle \frac{{\mathrm{Y}}_1\left(\mathrm{t}\right)+{\mathrm{Y}}_2\left(\mathrm{t}\right)}{2}}$$

(17)

• Need for an improved golden jackal optimization algorithm (IGJO)

Due to less convergence speed and a tendency to get stuck in the local minima, there is a need to improve the algorithm and develop an improved version, i.e., an improved golden jackal optimization algorithm (IGJO) [54], which does not become stuck in local minima because it starts off randomly and learns from failure and changes with time.

• Enhanced methods for updating positions during development:

At the point when escape energy is below 1, the prey trapped by the jackal infestation ends up in a local optimal state. In this condition, GJ is unable to evade the global search for a better one. Additionally, the prey still has an opportunity to flee, regardless of the diminished escape energy.

In the initial phase of the cycle, the prey shows a strong desire to escape, which causes it to speed up quickly. As a result, the ideal fitness values of golden jackal individuals were used to generate the elite matrix Y_e (t). After that, top individuals start the exploration process globally. The position of prey is updated via the Brownian random walk method, shown in Equations (18) and (19).

$${\mathrm{Y}}_1\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{M}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{e}\ast {\mathrm{D}}_1$$

(18)

$${\mathrm{Y}}_2\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{F}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{e}\ast {\mathrm{D}}_1$$

(19)

$${\mathrm{D}}_1=\mathrm{R}\mathrm{B}\ast \left|{\mathrm{Y}}_{\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{R}\mathrm{B}\ast \mathrm{p}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(20)

RB consists of random numbers evolved by the Brownian random walk method. The speed and strength of prey decrease when it is confined for a long time. During the intermediate phase of iteration, when both the prey and golden jackal attain the same speed, the golden jackal splits up its action. 50% of GJs follow Levy’s flying strategy while the other 50% pursue Brownian walk-based exploration.

Development criteria are based on Levy’s flying strategy, denoted by Equations (21)–(23).

$${\mathrm{Y}}_1\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{M}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{e}\ast {\mathrm{D}}_2$$

(21)

$${\mathrm{Y}}_2\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{F}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{e}\ast {\mathrm{D}}_2$$

(22)

$${\mathrm{D}}_2=\mathrm{R}\mathrm{L}\ast \left|{\mathrm{Y}}_{\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{R}\mathrm{L}\ast \mathrm{P}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(23)

The Brownian walk criteria for exploration can be expressed by Equations (24) and (25).

$${\mathrm{Y}}_1\left(\mathrm{t}\right)={\mathrm{Y}}_2\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{e}\ast {\mathrm{D}}_3$$

(24)

$${\mathrm{D}}_3=\mathrm{R}\mathrm{B}\ast \left|\mathrm{R}\mathrm{B}\ast {\mathrm{Y}}_{\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(25)

After the completion of the iteration, the golden jackal loses its energy and its velocity decelerates. At this instant, Levy’s nomadic method is utilized by the golden jackal to develop further. Due to reduced escape energy to flee, GJs encircle the prey and attack. This can be represented mathematically by Equations (26) and (27), as follows:

$${\mathrm{Y}}_1\left(\mathrm{t}\right)={\mathrm{Y}}_2\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{e}\ast {\mathrm{D}}_4$$

(26)

$${\mathrm{D}}_4=\mathrm{R}\mathrm{L}\ast \left|\mathrm{R}\mathrm{L}\ast {\mathrm{Y}}_{\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(27)

Methods for steering clear of natural threats: While pursuing dominance, the GJs pair may encounter natural food rivals due to global or local circumstances. Therefore, to protect themselves natural predators, they must incorporate avoidance tactics. Due to this, the escape factor (EF) is incorporated. EF values higher than 2.5 imply that the GJ pair avoided a natural predator by getting closer to the elites. But if its value is below 2.5, it indicates a safe situation. This can be written mathematically via Equations from (28) to (33), as follows:

If EF < 0.25

$${\mathrm{Y}}_1\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-{\mathrm{B}}_1\ast {\mathrm{B}}_2\ast \left|{\mathrm{Y}}_{\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(28)

$${\mathrm{Y}}_2\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{f}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-{\mathrm{B}}_1\ast {\mathrm{B}}_2\ast \left|{\mathrm{Y}}_{\mathrm{f}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(29)

If EF ≥ 0.25

$${\mathrm{Y}}_1\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{e}}\left(\mathrm{t}\right)-{\mathrm{B}}_1\ast {\mathrm{B}}_2\ast \left|{\mathrm{Y}}_{\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(30)

$${\mathrm{Y}}_2\left(\mathrm{t}\right)={\mathrm{Y}}_{\mathrm{e}}\left(\mathrm{t}\right)-{\mathrm{B}}_1\ast {\mathrm{B}}_2\ast \left|{\mathrm{Y}}_{\mathrm{f}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{e}}\left(\mathrm{t}\right)-\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{y}\left(\mathrm{t}\right)\right|$$

(31)

$${\mathrm{B}}_1=\mathrm{t}\mathrm{a}\mathrm{n}(2\times \mathrm{\Pi }\times \mathrm{r})$$

(32)

$$B_2=1-{\displaystyle \frac{1}{1+e^{(\frac{t}{t^2}-\frac{1}{2T})\times 10}}}$$

(33)

• Cross-mutation

In order to achieve the local optimum, this strategy is incorporated similarly to differential evolution. This technique is applied to GJ’s current and new place. From the population, four persons are chosen randomly, excluding the current one, and then the crossover operation is executed. Then, an eager selection is carried out. The crossover operation is mathematically represented by Equation (34), as follows:

$${\mathrm{Y}}_{\mathrm{i},\mathrm{j}}^{\mathrm{n}\mathrm{e}\mathrm{w}}=\left\{\begin{array}{c}{\mathrm{Y}}_{\mathrm{i},\mathrm{j}}^{\mathrm{m}\mathrm{u}} , \mathrm{i}\mathrm{f} \mathrm{R} \le \mathrm{f} \\ {\mathrm{Y}}_{\mathrm{i},\mathrm{j}}^{\mathrm{o}\mathrm{l}\mathrm{d}} , \mathrm{i}\mathrm{f} \mathrm{R}>\mathrm{f}\end{array},\mathrm{j}=\mathrm{1,2},\dots \dots .,\mathrm{d}\mathrm{i}\mathrm{m}\right.$$

(34)

• Intersection strategy

The algorithm executes two types of crossovers, namely, vertical and horizontal, at each iteration’s generation, to supply a golden jackal population that fits inside the local optimal escape route. Horizontal crossover occurs when two distinct individuals intersect in the same direction, expressed by Equations (35) and (36), while vertical crossing occurs between two different dimensions of particles inside a population, expressed by Equation (37). After each crossing, progeny generations are created. The competition operator seamlessly blends the two crossing techniques. At each intersection, the competition operator competes with the parent generation and selects the best one for the subsequent iteration.

$${\mathrm{M}}_{\mathrm{i},\mathrm{D}}^{\mathrm{H}\mathrm{c}}={\mathrm{R}}_2\ast \mathrm{X}\left(\mathrm{i},\mathrm{D}\right)+\left(1-{\mathrm{R}}_2\right)\ast \mathrm{X}\left(\mathrm{i},\mathrm{D}\right)+{\mathrm{c}}_1\ast (\mathrm{X}\left(\mathrm{i},\mathrm{D}\right)-\mathrm{X}\left(\mathrm{i},\mathrm{D}\right))$$

(35)

$${\mathrm{M}}_{\mathrm{i},\mathrm{D}}^{\mathrm{H}\mathrm{c}}={\mathrm{R}}_3\ast \mathrm{X}\left(\mathrm{i},\mathrm{D}\right)+\left(1-{\mathrm{R}}_3\right)\ast \mathrm{X}\left(\mathrm{i},\mathrm{D}\right)+{\mathrm{c}}_2\ast (\mathrm{X}\left(\mathrm{i},\mathrm{D}\right)-\mathrm{X}\left(\mathrm{i},\mathrm{D}\right)$$

(36)

$${\mathrm{M}}_{\mathrm{i},\mathrm{D}1}^{\mathrm{V}\mathrm{c}}={\mathrm{R}}_4\ast \mathrm{X}\left(\mathrm{i},\mathrm{D}1\right)+\left(1-{\mathrm{R}}_4\right)\ast \mathrm{X}\left(\mathrm{i},\mathrm{D}2\right)$$

(37)

Pseudo code of improved golden jackal optimization is given below (Algorithm 1).

Algorithm 1. Pseudo code of IGJO

Initialization of population x = {x1, x2, x3….xn}, t, n Global solution found optimally, xp = {x1p x2p, ………xnp} Initialization of population, location of prey, and iteration count.      Evaluation of the fitness of all N individuals.      The location of both the male and female jackal is considered the optimal output and the suboptimal outcome, respectively.      Evaluate the energy of prey escape and the Levy’s flight motion’s random number. While t < T For each xm, m = 1, 2, 3……N if $\left|e\right|<1$      if t < T/3      Modify the location according to Equations (18) and (19)         else if t < 2T/3        Modify the location according to Equations (21) and (22)         else        Modify the location according to Equation (24)      end        else      Modify the location according to Equation (26)        end if if $\left|e\right|\ge 1$ Modify the location according to Equations (7) and (8) end if if mod EF < 0.25        Modify the location according to Equations (28) and (29)              else        Modify the location according to Equations (30) and (31) end if      Choose a random location to create a mutation vector for achieving cross-mutation      do crossbar strategy according to Equations (35)–(37)      end for        t = t + 1 end while

5. Simulation Results and Discussion

5.1. Test System I

The test system considered for study is a 33-node radial distribution network shown in Figure 1, with a base voltage of 12.66 KV and base MVA of 100 MVA. The real power load of the system is 3715 kW, and the reactive power load is 2300 kVAr. The line and bus data are cited from Baran and Wu et al. [55]. The real and reactive power losses of this network are 202.6771 kW and 135.14 kVAr, respectively, for the base case, and the value of V_min is 0.913 p.u., obtained at bus number 18. The simulation was conducted over MATLAB R 2021b (9.11.0.1769998) 64-bit Windows platform on a 12th Generation Intel (R) Core TM i3-1215U 1.20 GHz desktop.

In this section, the effect of applying the improved golden jackal algorithm (IGJO) for placing properly sized DGs and capacitors in suitable spots to IEEE 33 bus radial distribution systems is analysed. This system is used to test the effects of penetration of DG and capacitor installation. The distributed generators considered here are of type-I and type-III, and the capacitors are considered to be connected in shunt.

The different scenarios were designed for this study, and the effect of penetration of individual DGs, individual capacitors, and simultaneously placing the DG with the capacitors is analysed based on various parameters. Different load models with the integrated type-I DG are also considered to verify the efficacy of the system. The various scenarios are given in

Table 2. Different cases for integration of DGs and CBs into RDS.

Case Number	Case Name	Type-I	CB	Type-III
1	Case TA	1 unit	-	-
2	Case TB	2 unit	-	-
3	Case TC	3 unit	-	-
4	Case CP	-	1 unit	-
5	Case CQ	-	2 unit	-
6	Case CR	-	3 unit	-
7	Case TX	-	-	1 unit
8	Case TY	-	-	2 unit
9	Case TZ	-	-	3 unit
10	Case TACP	1 unit	1 unit	-
11	Case TACQ	1 unit	2 unit	-
12	Case TACR	1 unit	3 unit	-
13	Case TBCP	2 unit	1 unit	-
14	Case TBCQ	2 unit	2 unit	-
15	Case TBCR	2 unit	3 unit	-
16	Case TCCP	3 unit	1 unit	-
17	Case TCCQ	3 unit	2 unit	-
18	Case TCCR	3 unit	3 unit	-
19	Case TXCP	-	1 unit	1 unit
20	Case TXCQ	-	2 unit	1 unit
21	Case TXCR	-	3 unit	1 unit
22	Case TYCP	-	1 unit	2 unit
23	Case TYCQ	-	2 unit	2 unit
24	Case TYCR	-	3 unit	2 unit
25	Case TZCP	-	1 unit	3 unit
26	Case TZCQ	-	2 unit	3 unit
27	Case TZCR	-	3 unit	3 unit

as follows.

Table 3. Results obtained by inserting one, two, and three units of type-I DG.

Cases	DG Size and Location	P (MW)	Q	Power Loss (KW)	Loss Reduction%	${\mathbf{V}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$(p.u.)	Cost (USD/MW)	VSI	TVD
Case TA	1.81 (6)	1.81	-	105.78	47.8061	0.95 (13)	36.59	0.8145	1.0219
Case TB	1.09 (30) 0.86 (13)	1.95	-	86.02	57.5534	0.9659 (33)	39.40	0.8706	0.6738
Case TC	1.23 (24) 0.99 (30) 0.08 (14)	2.31	-	71.91	64.5186	0.9669 (33)	61.22	0.8742	0.5748

indicates the results attained after penetration of type-I DG into the 33 bus radial network. It is clear that real power is lost at a minimum when the maximum amount of DGs is included. The percentage reduction of the loss is reduced considerably by 16.7% when the integration level is increased from one unit to three DGs. Also, the voltage profile is improved by 0.0166 p.u. It is evident that the cost increases due to the greater number of units integrated into the system

Figure 2 shows the variation of power loss at different buses of the system for cases of integration of three units of type-I, type-III DGs, capacitor banks, and simultaneously putting type-I DGs with capacitors and type-III DGs with capacitors, in comparison with the losses occurring in the system when no unit for improvement is connected.

Table 4. Results of inserting one, two, and three units of capacitors into the IEEE 33 bus system.

Cases	Capacitor Size and Location	P	Q	Power Loss (KW)	Loss Reduction%	${\mathbf{V}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$ (p.u.)	Cost (USD/MW)	VSI	TVD
CP	1.14 (70)	-	1.14	127.4576	37.11	0.95 (9)	-	0.8145	1.1755
CQ	0.67 (24)	-	1.69	124.2518	38.69	0.95 (9)	-	0.8145	1.1583
	1.01 (27)
CR	0.52 (24)	-	1.77	121.699	39.95	0.95 (9)	-	0.8145	1.1461
	0.65 (30)
	0.60 (6)

shows the results when capacitors are connected to the system in an incremental fashion. Here, the loss reduction is not improved much, but the comparative analysis shows a considerable improvement with the proposed optimization method, in terms of losses, compared to the previous methods used.

The effect on improving the loss reduction is very noticeable when type-III DGs are integrated with the system under test (

Table 5. IEEE 33 bus system outcomes with one, two, and three units of type-III DGs.

Cases	DG Size and Location	P	Q	Power Loss (KW)	Loss Reduction%	${\mathbf{V}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$ (p.u.)	Cost (USD/MW)	VSI	TVD
TX	1.77/1.02 (29)	1.77	1.02	66.90	66.98	0.95 (18)	35.84	0.8145	0.6348
TY	0.79/0.46 (13)	2.08	1.20	32.05	84.18	0.9801 (25)	41.90	0.9230	0.2135
	1.28/0.74 (30)
TZ	1.03/0.59 (24)	2.92	1.68	15.54	92.32	0.9886 (18)	58.75	0.9552	0.1863
	0.67/0.38 (13)
	1.21/0.70 (30)

). A margin of 25.34% is clearly visible when units are improved, and the voltage rating is increased by 0.0386 p.u. Though the cost is increased by this effort, the rise in the cost is still below that seen in Table 3. The variation of the TVD is 0.45, instead of 0.5 in Table 3.

Figure 3 shows the convergence characteristic of the objective function for all the cases with three integrated units, while Figure 4 highlights the improvement in the voltage magnitude curve for each bus with respect to the no-DG case.

Table 6. IEEE 33 bus system with type-I and CB in combinations of one, two, and three units.

Cases	DG and Capacitor Size and Location	P	Q	Power Loss (KW)	Loss Reduction%	${\mathbf{V}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$ (p.u.)	Cost (USD/MW)	VSI	TVD
TACP	1.843 (7)	1.84	0.96	59.7316	70.52	0.9524 (18)	37.114	0.8228	0.7518
	0.96 (30)
TACQ	1.81 (8)	1.81	1.68	52.7644	73.96	0.9691 (18)	36.572	0.8820	0.4854
	1.12 (30)
	0.55 (7)
TACR	1.86 (8)	1.86	1.92	51.6576	74.51	0.9673 (33)	37.482	0.5470	0.8758
	0.73 (30)
	0.26 (10)
	0.92 (4)
TBCP	0.91 (29)	1.74	0.89	41.6012	79.47	0.9782 (25)	35.094	0.4965	0.9159
	0.83 (14)
	890 (30)
TBCQ	0.68 (14)	2.36	1.63	33.9419	83.25	0.9776 (33)	47.638	0.9137	0.2269
	1.68 (6)
	0.75 (30)
	0.88 (8)
TBCR	0.81 (11)	1.90	1.28	31.4858	84.46	0.9796 (25)	38.394	0.9211	0.3442
	1.09 (29)
	0.24 (16)
	0.37 (31)
	0.67 (30)
TCCP	0.94 (6)	2.44	1.08	32.4351	83.99	0.9808 (18)	49.104	0.9255	0.3071
	1.03 (29)
	0.46 (16)
	1.08 (29)
TCCQ	0.80 (14)	2.94	1.39	30.0944	85.15	0.9909 (25)	59.202	0.9641	0.0697
	0.50 (25)
	1.63 (28)
	0.255 (12)
	1.13 (28)
TCCR	1.38 (24)	3.28	1.73	14.7358	92.72	0.9941 (22)	65.934	0.9767	0.0069
	1.10 (29)
	0.80 (16)
	0.57 (30)
	0.35 (10)
	0.81 (28)

shows all the cases where a type-I DG is simultaneously placed with a capacitor bank in combination. When one type-I DG is placed with one capacitor, the power loss is reported as 59.73 kW, while adding one more capacitor will bring down the loss by 52.76 kW. When another capacitor is added, losses come to 51.65 kW.

A combination of two type-I DGs with one, two, and three units of capacitors reflects losses of 41.60, 33.94 and 31.48 kW. Hence, the loss is significantly reduced, and it is also observed that the voltage profile is improved from 0.95 p.u. to 0.9909 p.u.

With three units of type-I DG and an incremental number of capacitors, the loss is reported as 32.41, 30.09 and 14.73 kW, and for these cases, the voltage is improved from 0.9808 p.u. to 0.9941 p.u.

Similarly, the results obtained by placing type-III DG with capacitor bank in combination are given in

Table 7. Type-III DG and capacitors in one, two, and three unit combinations in IEEE 33 bus RDN.

Cases	DG and Capacitor Size and Location	P	Q	Power Loss (KW)	Loss Reduction%	${\mathbf{V}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$ (p.u.)	Cost (USD/MW)	VSI	TVD
TXCP	1.88/1.08 (26)	1.88	1.79	53.2478	73.72	0.9581 (18)	37.938	0.8426	0.5929
	0.70 (30)
TXCQ	1.73/1.00	1.73	2.32	52.8367	73.93	0.9637 (18)	34.912	0.8626	0.5395
	0.86 (30)
	0.45 (23)
TXCR	1.89/1.09 (27)	1.89	2.04	51.3756	74.65	0.9637 (18)	38.178	0.8626	0.4951
	0.62 (30)
	0.18 (13)
	0.14 (25)
TYCP	1.09/0.63 (30)	2.08	1.83	30.3971	85.00	0.9813 (18)	42.016	0.9275	0.0912
	0.99/0.57 (12)
	0.62 (28)
TYCQ	0.99/0.57 (29)	2.04	1.98	28.9594	85.71	0.9823 (25)	41.214	0.9313	0.1723
	1.04/0.60 (10)
	0.435 (23)
	0.370 (32)
TYCR	1.18/0.68 (30)	1.93	2.32	29.6107	85.39	0.9793 (25)	38.852	0.9199	0.2794
	0.74/0.43 (10)
	0.59 (25)
	0.35 (19)
	0.27 (8)
TZCP	1.11/0.64 (29)	3.00	2.11	15.4942	92.35	0.9918 (9)	60.296	0.9679	0.1405
	1.256/0.72 (24)
	0.63/0.36 (14)
	0.38 (29)
TZCQ	0.74/0.43 (15)	2.64	2.19	15.7385	92.23	0.9933 (8)	53.198	0.9735	0.0438
	0.97/0.56 (24)
	0.92/0.53 (31)
	0.10 (12)
	0.57 (30)
TZCR	1.32/0.76 (30)	3.01	2.33	12.0379	94.06	0.9941 (22)	60.642	0.9768	0.0236
	0.68/0.39 (13)
	1.01/0.58 (24)
	0.43 (4)
	0.50 (29)
	0.11 (15)

. Here, the loss is mitigated from 53.24 kW to 51.37 kW when different configurations of DGs are applied with various numbers of capacitors. The loss is significantly minimized to 12.03 kW when three DGs are integrated simultaneously with three capacitors.

Table 8. Comparative analysis of achieved outcomes against existing studies for 33-bus RDS.

Case	Method Used	Size MW (Site)			PL (KW)	%RL	Vmin	TVD	VSI
TC	Proposed method IGJO	1.23 (24)	0.99 (30)	0.81 (14)	71.91	64.51	0.9669 (33)	0.5748	0.8742
	[18] CTLBO 2018	0.80 (13)	1.09 (24)	1.05 (30)	72.79	65.50	-	0.0151	0.8805
	[38] WIPSO GSA 2018	0.84 (13)	0.86 (24)	0.86 (30)	74.78	64.56	-	-	-
	[13] MFO-SCO 2021	1.05 (30)	1.09 (24)	0.80 (13)	72.78	65.5	0.9687 (33)	-	-
	[39] HA 2019	0.79 (13)	1.07 (24)	1.02 (30)	72.84	65.47	-	-	-
TZ	Proposed method IGJO	1.03/0.59 (24)	0.67/0.38 (13)	1.21/0.70 (30)	15.54	92.32	0.9886 (18)	0.1863	0.9552
	[35] IA 2013	1.05 (6) opf-0.85 lag	1.05 (30) opf-0.85 lag	0.74 (14) opf-0.85 lag	23.05	89.09	0.9824 (25) opf-0.98 lag
		1.09 (6) opf-0.82 lag	1.09 (30) opf-0.82 lag	0.76 (14) opf-0.82 lag	22.29	89.45	0.9821 (25) opf-0.99 lag	-	-
	[38] WIPSO GSA 2018	1.02 (12) opf-0.85 lead	1.03 (24) opf-0.84lead	1.08 (30) opf-0.8 lead	16.48	92.19	-	-	-
CR	Proposed method IGJO	0.52 (24)	0.65 (30)	0.60 (6)	121.69	39.95	0.95 (9)	1.1461	0.8145
	[14] EGWO- PSO 2021	0.42 (13)	0.56 (24)	1.14 (30)	132.17	34.79	0.9377 (18)	-	0.775
	[38] WIPSO GSA 2018	0.47 (12)	0.53 (29)	0.53 (30)	141.84	32.78	-	-	-
	[13] MFO-SCA 2021	1.00 (30)	0.33 (24)	0.38 (13)	138.91	34.16	0.9307 (18)	1.2711	-
	[39] HA 2019	0.38 (13)	0.38 (25)	1.00 (30)	138.65	34.28	-	-	-
	[19] WCA 2018	0.40 (14)	0.45 (24)	1.0 (30)	130.91	35.40	0.95 (18)	-	-
TCCR	Proposed method IGJO	1.38 (24)/0.57 (30)	1.10 (29)/0.35 (10)	0.80 (16)/0.81 (28)	14.73	92.73	0.9941 (22)	0.0069	0.9767
	[14] EGWO-PSO 2021	0.75 (14)/0.53 (11)	1.08 (24)/0.71 (23)	1.05 (30)/1.00 (29)	15.15	92.52	0.9941 (22)	-	0.9786
	[38] WIPSO-GSA 2018	0.85 (13)/0.48 (12)	0.86 (25)/0.49 (29)	0.87 (30)/0.51 (30)	16.89	91.99	-	-	-
	[19] WCA 2018	0.56 (11)/0.53 (14)	0.97 (25)/0.46 (23)	1.04 (29)/0.56 (30)	24.69	87.82	0.980 (33)	-	-
TZCR	Proposed method IGJO	1.32/0.76 (30), 0.43 (4)	0.68/0.39 (13), 0.05 (29)	1.01/0.58 (24), 0.11 (15)	12.03	94.06	0.9941 (22)	0.0236	0.9768
	[14] EGWO-PSO 2021	0.78 (13)/0.52 (11) opf-1,	1.07 (24)/0.69 (23) opf-0.99,	1.03 (30)/1.00(29), Opf-0.99,	14.99	92.60	0.9940 (22)	-	0.9788
	[38] WIPSO-GSA 2018	0.97 (12)/0.20 (6), opf-0.9lead	0.98 (24)/0.12(30), opf-0.88lead	1.04 (30)/0.19(31), opf-0.83lead	12.90	93.89	0.9937	-	-
	[19] WCA 2018	0.99 (11)/0.32 (19) opf-0.905,	0.98 (31)/0.31 (23) opf-0.985,	1.65 (24)/0.54 (30) opf-0.959,	19.84	90.2	0.989 (18)	-	0.985

shows the effectiveness of the proposed IGJO technique over other methods. The losses with type-I DG placement are much better in comparison with other methods, but TVD and VSI are also included in the objective function. The reduction in losses with type-III DG and the capacitor is also remarkable compared to previous studies. The simultaneous placement of these devices together also provides better and improved results in terms of losses, voltage, TVD, and VSI. The important buses are 18, 22, 25, and 33.

Table 9. Performance analysis of the IEEE 33 bus system with various load models.

Parameter	CP 0.5 Load		CP 1.6 Load		CC Load		CI Load		Residential Load		Commercial Load		Industrial Load
	No DG	With DG	No DG	With DG	No DG	With DG	No DG	With DG	No DG	With DG	No DG	With DG	No DG	With DG
DG Size		0.48 (11)		1.75 (24)		1.24 (24)		0.74 (31)		0.97 (30)		0.99 (25)		0.71 (14)
		0.76 (23)		0.86 (11)		1.06 (30)		0.76 (11)		1.04 (24)		0.97 (30)		1.03 (24)
		0.48 (31)		1.89 (26)		0.73 (12)		0.86 (24)		0.65 (13)		0.53 (13)		1.08 (30)
PL (KW)	47.07	18.80	575.36	165.11	174.76	63.40	151.10	55.30	154.44	43.331	148.79	47.95	157.85	35.56
% (RPL)		60.04		71.30		63.71		63.39		71.944		67.77		77.46
QL (KVA)	31.35	13.08	384.26	109.07	116.25	44.04	100.27	37.76	102.54	30.25	98.72	33.49	104.89	25.12
% (RQL)		58.27		71.61		62.10		62.34		70.49		66.07		76.04
Vmin (p.u.)	0.9582 (18)	0.9845 (45)	0.8527 (18)	0.95 (10)	0.9198(18)	0.9685 (18)	0.9260 (18)	0.9676 (18)	0.9245 (18)	0.9743 (18)	0.9262 (18)	0.9703 (18)	0.9236 (18)	0.9797 (33)
cost		34.856		90.578		61.034		47.85		53.692		50.4		56.93
TVD	0.8188	0.2641	2.8713	1.1155	1.5763	0.5354	1.4621	0.5906	1.4802	0.5065	1.4528	0.5518	1.489	0.4145
VSI	0.8432	0.9395	0.5287	0.81448	0.7158	0.8798	0.7353	0.8767	0.7306	0.9013	0.7359	0.8867	0.7278	0.9215

is showing performance of integration of type-I DG over various load models. These load models are voltage dependent and establishes the effect of DGs.

Figure 5 is representing the power loss magnitude under various scenarios and it is found that the lowest loss value is obtained either by placing type-III DG (15.54 kW) or simultaneously putting type-I DG with capacitor (14.73 kW) or by integrating type-III DG with capacitor (12.03 kW).

The lowest value of bus voltage attained for various scenarios was 0.95, but the most improved value obtained was 0.9941 p.u. at bus number 22, shown in Figure 6.

A comparative graphical representation is given in Figure 7 for all the types of voltage dependent loads, when no DG is connected and when type-I DG is integrated with the system.

5.2. Test System II

The single-line connection diagram of test system II, i.e., a standard 118 bus system, is shown in Figure 8. Individual and simultaneous integration of DG and CB units were examined using the constant power case and various load models. Base values of MVA and voltage were 100 MVA and 11 kV for this test system. Active and reactive power loss values were 1298.09 kW and 978.73 kVAr, respectively [5].

Table 10. Results obtained by inserting three, five, and seven units of type-I DG in 118 bus RDS.

Cases	DG Size and Location	P (MW)	Q	Power Loss (KW)	Loss Reduction%	${\mathbf{V}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$ (p.u.)	Cost (USD/MW)	VSI	TVD
3 T-I	2.12 (71) 1.76(47) 3.50 (108)	7.38	-	670.48	48.3509	0.95 (47)	147.98	0.8145	3.423
5 T-I	1.73(33) 3.38(110) 8.58(41) 3.36(69) 2.50 (86)	19.55	-	641.12	50.6123	0.95 (35)	237.23	0.8145	2.911
7 T-I	0.36(4) 3.28(47) 2.96 (111) 3.68(13) 1.83(90) 0.61(43) 1.92 (69)	14.64	-	616.51	52.5082	0.95 (54)	293.86	0.8145	2.653

shows the results obtained after integration of type-I DG into the 118 bus radial network. It is apparent that real power loss is reduced to a minimum when the maximum numbers of DGs are included. The percentage reduction in the loss increases considerably, by 4.15%, when the integration level is improved from three unit to seven units of DGs. The minimum value of the voltage obtained is 0.95 p.u. at node 47 in the case of three DGs and shifts to bus 54 when seven DGs are inserted. It is evident that the cost increases to almost double due to more units being integrated into the system. The VSI remains constant throughout the change in the level of integration, but the TVD is reduced from 3.423 to 2.653. When seven units of type-I DG are connected with 50% penetration of the full load, the reported power loss is 616.51 kW.

Figure 9 shows the power loss occurring at different buses of the system under various cases of integration of 7 units of type-I, type-III DGs, capacitor banks, and simultaneously placing type-I DGs with capacitors and integrating type-III DGs with capacitors, in comparison with the losses occurring in the system when no unit for improvement is connected.

Table 11. Results obtained by inserting three, five, and seven Shunt Capacitor units.

Cases	DG Size and Location	P (MW)	Q	Power Loss (KW)	Loss Reduction%	${\mathbf{V}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$ (p.u.)	Cost (USD/MW)	VSI	TVD
3 CB	1.19 (81) 1.12 (110) 1.11 (35)	-	3.42	770.40	40.6544	0.95 (35)	-	0.8145	3.801
5 CB	1.05 (110) 0.59 (111) 1.02 (79) 1.15 (34) 1.16 (69)	-	4.97	735.47	43.3441	0.95 (35)	-	0.8145	3.750
7 CB	1.13 (47) 1.14 (112) 0.86 (82) 0.74 (68) 0.28 (60) 0.91 (97) 0.79 (107)	-	5.85	715.46	44.8859	0.95 (35)	-	0.8145	3.647

shows the results when three, five, and seven capacitors are connected to the test system in an incremental fashion. Here, the loss reduction is improved by 4.23%, but the comparative analysis shows a considerable improvement with the proposed optimization method compared to the earlier methods used, when capacitor banks are integrated into the system. With the addition of four more banks, the loss is reduced from 770.40 to 715.46 kW, which is 114.69 kW less than the nearest reported loss in the previous literature. This shows the efficacy of the proposed approach compared with conventional device placement.

When type-III DGs are integrated with the system under test, the effect on improvement in loss mitigation is remarkable (

Table 12. Results obtained by inserting three, five, and seven units of type-III DG.

Cases	DG Size and Location	P (MW)	Q	Power Loss (KW)	Loss Reduction%	${\mathbf{V}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$ (p.u.)	Cost (USD/MW)	VSI	TVD
3 T-III	2.18/1.25 (89) 3.55/2.05 (109) 2.61/1.51 (73)	8.34	4.81	459.68	64.5896	0.95 (33)	167.17	0.8145	2.306
5 T-III	1.36/0.788 (2) 2.17/1.25 (80) 3.52/2.03 (112) 3.21/1.86 (47) 4.03/2.33 (77)	14.29	8.26	389.81	69.9715	0.961 (46)	286.52	0.8527	1.156
7 T-III	8.14/4.70 (28) 3.92/2.27 (65) 2.35/1.36 (10) 2.20/1.27 (72) 2.85/1.65 (51) 7.95/4.59 (100) 1.75/1.01 (110)	29.16	16.86	330.83	74.5145	0.964 (111)	584.32	0.8655	1.571

). An improvement from 459.68 kW to 330.83 kW is clearly visible when units are improved, and the voltage rating is increased from 0.95 p.u. to 0.964 p.u. Though the cost increases, the VSI is also increased to a value of 0.8655 instead of 0.8145, compared to type-I integration and capacitor placement. TVD is reduced by 0.736 p.u by increasing the number of DG units.

Figure 10 shows the convergence characteristic of the objective function for all the cases with seven integrated units, while Figure 11 highlights the improvement in the voltage magnitude curve for each bus with respect to the no-DG case.

Table 13. IEEE 118 bus system with type-I and CB with a combination of one, two, and three units.

Cases	DG Size and Location	P (MW)	Capacitor Location	Q (kVAR)	Power Loss (KW)	Loss Reduction%	${\mathbf{V}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$(p.u.)	Cost (USD/MW)	VSI	TVD
3 T-I with 3 CB	1.51(110) 3.49(71) 2.29 (48)	7.29	0.98 (73) 0.21 (54) 1.16 (106)	2.35	559.32	56.9133	0.95 (50)	146.05	0.8145	2.99
5 T-I with 5 CB	0.21(54) 3.55 (73) 4.77(29) 0.61 (99) 1.29 (111)	10.43	1.07 (78) 0.52 (105) 0.74 (24) 0.99 (70) 0.85 (74)	4.17	553.34	57.3742	0.95 (34)	209.38	0.8145	2.41
7 T-I with 7 CB	2.10(37) 0.22(26) 1.59(112) 1.92(47) 2.44(20) 4.88(79) 1.73 (72)	14.9	0.79 (61) 0.53 (81) 0.37 (78) 0.32 (106) 0.83 (91) 0.57 (19) 1.18 (110)	4.59	483.33	62.7677	0.95 (49)	158.65	0.8145	2.46

includes all the cases when type-I DG is simultaneously placed with capacitor banks in combination. When three type-I DG is placed with 3 capacitors, the power loss is reported as 559.32 kW, while increasing two more units of capacitor and DGs brings down the loss by 553.34 kW. When another two capacitor and DGs are added, losses are reduced to 483.33 kW. Hence, the loss is significantly reduced in this case with slight increment in the cost from three units to seven units. The minimum value of voltage found was 0.95 p.u. The vulnerable buses found were 50, 34, and 49. TVD in this case was not much improved with the increase in the number of devices.

When three units of type-I DG with three capacitor banks are integrated, the loss is reported as 559.32 kW, and with five units of both devices, the loss comes as 553.34 kW, but when seven units are integrated with the network, the real power loss reduces to 483.33 kW. For these cases, the total voltage deviation is improved from 2.99 to 2.46, with a constant minimum bus voltage of 0.95 p.u., and the cost for placing the DG increases to 158.65 from 146.05 USD/MW.

Similarly, the results obtained by placing type-III DG with capacitor bank in combination are given in

Table 14. IEEE 33 bus system with type-III and CB with a combination of one, two, and three units.

Cases	DG Size and Location	P (MW)	Capacitor Location	Q (kVAR)	Power Loss (KW)	Loss Reduction %	${\mathbf{V}}_{\mathbf{m}\mathbf{i}\mathbf{n}}$(p.u.)	Cost (USD/MW)	VSI	TVD
3 T-III with 3 CB	3.42/1.99 (108) 2.06/1.19 (74) 2.39/1.38 (78)	7.87/ 4.56	1.08 (82) 0.28 (52) 0.48 (97)	1.84	444.10	65.7895	0.95 (34)	158.65	0.8145	2.456
5 T-III with 5 CB	0.70/0.41 (91) 4.15/2.39 (71) 1.15/0.66 (110) 1.78/1.03 (112) 3.05/1.76 (34)	10.83/6.25	1.15 (35) 0.25 (25) 1.11 (79) 0.99 (93) 0.07 (44)	3.57	365.64	71.8332	0.9622 (46)	217.09	0.857	1.2755
7 T-III with 7 CB	2.35/1.36 (72) 2.88/1.66 (51) 10.70/6.18 (6) 2.65/1.53 (113) 2.18/1.26 (80) 0.7/0.40 (105) 2.90/1.67 (4)	24.3/14.06	0.78 (49) 0.33 (34) 1.13 (80) 0.48 (112) 0.63 (107) 0.60 (93) 0.29 (30)	4.24	325.98	74.8889	0.969 (99)	488.098	0.8816	0.8658

. Here, the loss is mitigated from 444.10 kW to 325.98 kW when a different configuration of DG is applied according to the various numbers of capacitors. The loss is significantly mitigated up to 74.88% in this scenario, compared to 74.51% loss reduction in the case of type-III integration when three DGs are integrated simultaneously with three capacitors. The major advantage of using capacitor bank in conjunction with type-III DG is that the cost is remarkably reduced.

Table 15. Comparative analysis of achieved outcomes against existing studies for 118-bus RDS.

Case	Method Used	Size MW (Site)							PL (KW)	%RL	Vmin	TVD	VSI
7 T-I	Proposed method IGJO	0.36 (4)	3.28 (47)	2.96 (111)	3.68 (13)	1.83 (90)	0.61 (43)	1.92 (69)	616.51	52.50	0.95 (54)	2.6534	0.8145
	[45] LSFSA 2013	2.82 (75)	0.46 (116)	3.67 (56)	7.46 (36)	5.08 (103)	2.29 (88)	0.71 (48)	900.19	30.56	0.9324 (111)
	[47] Analytical2016	1.68 (51)	1.82 (74)	1.76 (111)	-	-	-	-	711	42.90	0.93	-	-
	[48] AQiEA 2020	1.5 (39)	1.49 (109)	1.5 (68)	1.49 (110)	1.5 (74)	-	-	686.23	47.13	0.933 (42)	-	-
7 T-III	Proposed method IGJO	8.14/4.70 (28)	3.92/2.27 (65)	2.35/1.36 (10)	2.2/1.27 (72)	2.85/1.65 (51)	7.95/4.59 (100)	1.75/1.01 (110)	330.83	74.51	0.9645 (111)	1.5708	0.8654
	[45] LSFSA 2013	2.75/1.59 (75)	0.50/0.29 (116)	4.31/2.49 (56)	6.11/3.52 (36)	5.33/3.08 (103)	0.62/0.36 (88)	2.17/1.25 (48)	638.96	50.71	0.9468 (111)	-	-
7 CB	Proposed method IGJO	1.13 (47)	1.14 (112)	0.86 (82)	0.74 (68)	0.28 (60)	0.91 (97)	0.79 (107)	715.46	44.88	0.95 (35)	3.6474	0.8145
	[46] SSO 2016	1.35 (6), 1.55 (82)	1.35 (21), 0.80 (90)	1.10 (32), 1.10 (109)	1.30 (39), 1.20 (110)	0.90 (40)	0.95 (47)	1.30 (73)	830.15	36.04	0.9145	-	0.6995
	[47] Analytical 2016	2.50 (74)							881.03	29.2	0.9053	-	-
	[49] LSF 2020	0.6 (20), 0.80 (97)	1.65 (36), 0.70 (104)	0.65 (42), 1.80 (111)	0.55 (58)	0.85 (70)	0.85 (74)	1.20 (80)	859.9	34	0.9292	-	0.6 (20), 0.80 (97)
7 TI With 7CB	Proposed method IGJO	2.10 (37)/ 0.79 (61)	0.22 (26)/0.53 (81)	1.59 (112)/0.37 (78)	1.92 (47)/0.32 (106)	2.44 (20)/0.83 (91)	4.88 (79)/0.57 (19)	1.73 (72)/ 1.18 (110)	483.33	62.76	0.95 (49)	2.46	0.8145
	[47] Analytical2016	DG—1.68 (51), 1.82 (74), 1.76 (111) CB -2.50 (74)							510.67	59	0.95	-	-
	[52] CPO 2025	1.17 (115)/0.25 (102)	8.72 (28)/0.26 (89)	1.08 (75)/0.82 (48)	1.65 (92)/0.76 (69)	2.93 (15)/0.86 (67)	1.47 (72)/0.13 (87)	1.80 (106)/1.07 (70)	540.61	58.35	0.95 (47)	2.1979	0.8145
	[53] EA 2023	DG-17.032 MW (89, 114, 37, 45, 78, 76, 99), C-12.743 MVAr (62, 73, 104, 112, 60, 35, 42)							558.2	56.998	-	-	-
7 T-III With 7CB	Proposed method IGJO	2.35/1.36 (72), 0.78 (49)	2.88/1.66 (51), 0.33 (34)	10.70/6.18 (6), 1.13 (80)	2.65/1.53 (113), 0.48 (112)	2.18/1.26 (80), 0.63 (107)	0.7/0.40 (105), 0.60 (93)	2.90/1.67 (4), 0.29 (30)	325.97	74.88	0.9689 (99)	0.8658	0.8816
	[50] AVOA 2022	DG-1.18 (32) PF-0.85, 1.86 (39) PF-0.85, 1.46 (43) PF-0.85, 0.26 (72) PF-085, 2.0 (74) PF-0.85, 1.82 (85) PF-0.86, 1.98 (91) PF-0.88, 1.7 (107) PF-0.92, 1.69 (111) PF-0.90, 0.78 (118) PF-0.85, C-1.50 (32)							207.93	83.97	0.963	-	-

shows the comparative analysis of the proposed method outcomes with the previous literature.

Table 16. Performance analysis of the IEEE 118-bus system with various load models.

Parameter	CP 0.5 Load		CP 1.6 Load		CC Load		CI Load		Residential Load		Commercial Load		Industrial Load
	Without DG	With DG	Without DG	With DG	Without DG	With DG	Without DG	With DG	Without DG	With DG	Without DG	With DG	Without DG	With DG
DG Size		0.49 (10)		5.00 (65)		0.08 (60)		1.83 (97)		0.25 (90)		3.25 (63)		1.83 (97)
		1.22 (113)		0.79 (49)		4.14 (105)		1.14 (17)		1.14 (36)		1.55 (83)		1.14 (109)
		1.69 (5)		3.88 (38)		1.21 (76)		2.42 (72)		1.05 (48)		1.63 (28)		2.42 (72)
		1.07 (92)		1.76 (82)		3.26 (8)		1.45 (0)		1.06 (52)		1.97 (109)		1.45 (60)
		0.48 (75)		3.89 (104)		2.33 (79)		7.22 (29)		1.02 (73)		2.16 (52)		7.22 (29)
		2.53 (8)		0.11 (98)		1.42 (94)		1.87 (112)		1.01 (109)		1.12 (29)		1.87 (112)
		0.16 (55)		3.28 (31)		1.39 (47)		0.80 (13)		1.04 (75)		1.55 (56)		0.80 (113)
PL (kW)	297.16	191.83	3800.17	1248.41	1085.33	560.63	914.74	490.89	936.61	490.93	896.15	461.92	966.70	389.0896
% (RPL)		35.44		67.14		48.34		46.33		47.58		48.45		59.7508
QL (kVA)	225.21	156.04	2839.25	1017.67	827.10	425.76	704.10	410.29	717.23	371.89	689.22	352.60	735.61	346.4178
% (RQL)		30.71		64.15		48.52		41.72		48.14		48.84		52.908
Vmin (p.u.)	0.9385 (77)	0.9597 (57)	0.7672 (77)	0.95 (24)	0.8851 (77)	0.95 (48)	0.8990 (77)	0.95 (47)	0.8947 (77)	0.95 (47)	0.8990 (77)	0.95 (68)	0.8910 (77)	0.95 (48)
cost		153.93		375.14		277.48		335.46		132.29		265.54		335.464
TVD	2.5194	1.6989	8.9225	4.3773	4.8357	2.7947	4.4693	2.002	4.5009	3.0356	4.4226	2.7788	4.5177	2.0237
VSI	0.7758	0.8486	0.3466	0.8144	0.6138	0.8144	0.6533	0.8145	0.641	0.7823	0.6532	0.8144	0.6304	0.8145

shows the performance of type-I DGs integrated over various load models. These static load models are voltage dependent and are used to establish the effect of type-I DGs when integrated into the system.

Figure 12 represents the percentage of power loss reduction under various scenarios; it can be found that the highest reduction percentage of loss is obtained either by placing seven type-III DGs (15.54 kW) or by integrating seven units of type-III DGs and capacitors (74.88%). The lowest change is brought by the integration of only capacitor (44.88%); hence, the inference can be drawn that the simultaneous integration gives a more viable option for the fulfilment of the objectives.

A comparative graphical representation is given in Figure 13, showing all the types of voltage dependent loads, when no DG is connected and when type-I DG is integrated with the system. It can be seen that the major change in the loss is visible in CPx(1.6) load, and the next major change is in industrial loading; however, industrial load is under many variable constraints, which are not considered in this study.

Figure 14 showcases the efficacy of the proposed technique in contrast with the previous literature, considered in Table 15, and it is clear that the improved golden jackal optimization technique shows superiority over other methods in many cases.

6. Superiority of the Proposed Algorithm over Existing Research Outcomes

This section demonstrates the efficiency of the proposed strategy to allocate different DG types with CBs simultaneously, compared with the existing DG types described in the literature. Table 8 and Table 15, above, summarize the comparative analysis of examined instances of concurrent allocation of DGs and CBs with currently available studies. Analysis shows that the suggested algorithm, i.e., IGJO, is preferable for simultaneous allocation of DGs and CBs compared with those already published for 33 bus and 118 bus radial networks, respectively. It can be observed that in the considered cases, the power loss attained by optimal placement by the proposed method is lower than in the previous comparable literature. The voltage improvement is noticeable, and the TVD and VSIs are also satisfactorily improved. The overall impression is that the optimization features associated with this technique are remarkable and superior to the earlier methods. Lastly, the analysis shows that proposed DGs and CBs are located in the correct position with the right capacity to significantly boost the performance of the radial distribution network in the context of loss reduction, voltage profile enhancement, and other criteria.

7. Conclusions

This study makes significant advances in the optimal allocation of various types of DG and various combinations of DGs with CBs into 33 bus and 118 bus RDNs, using the improved golden jackal optimization algorithm with the goal of minimizing the loss, cost, and voltage deviation and improving the voltage stability index. In addition to this, load models such as light load, heavy load, constant current load, constant impedance load, industrial, residential, and commercial load were also considered to evaluate the outcomes. However, the restrictions of this work are also acknowledged, indicating opportunities for upcoming research paths. Environmental consequences such as reduction in greenhouse gas emissions and sustainable development goal attainments are not considered in this work; these can be incorporated in further research to limit COx and NOx emissions. In order to make sure that mixed DG types are manageable and compatible, future research can include dynamic simulation of power quality, control methodologies, and communication frameworks. Analysis of return on investment and payback duration calculation has not been carried out. Moreover, fault situations and their effect on dependability and protection mechanisms were not taken into account within the scope of this research. In the present context, an electric vehicle can be used as a distributed generator, which can provide peak load support, supplying power during high-demand periods, voltage regulation, and frequency regulation by fast response power injection/absorption, backup power, and load levelling. Such situations can be considered for future research areas. In this study, the outcomes of implementing IGJO into 33 and 118 bus systems under comprehensive scenarios indicate that IGJO yielded superior performance for mitigation of power loss, cost, and improvement in voltage magnitude and VSI compared to other existing methods.