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Article

Optimal Planning of Solar Photovoltaic (PV) and Wind-Based DGs for Achieving Techno-Economic Objectives across Various Load Models

1
US-Pakistan Center for Advanced Studies in Energy (USPCAS-E), National University of Sciences and Technology (NUST), H-12, Islamabad 44000, Pakistan
2
Department of Electrical and Computer Engineering, Sungkyunkwan University, Seoul 16419, Republic of Korea
*
Authors to whom correspondence should be addressed.
Energies 2023, 16(5), 2444; https://doi.org/10.3390/en16052444
Submission received: 4 January 2023 / Revised: 20 February 2023 / Accepted: 24 February 2023 / Published: 3 March 2023

Abstract

:
Over the last few decades, distributed generation (DG) has become the most viable option in distribution systems (DSs) to mitigate the power losses caused by the substantial increase in electricity demand and to improve the voltage profile by enhancing power system reliability. In this study, two metaheuristic algorithms, artificial gorilla troops optimization (GTO) and Tasmanian devil optimization (TDO), are presented to examine the utilization of DGs, as well as the optimal placement and sizing in DSs, with a special emphasis on maximizing the voltage stability index and minimizing the total operating cost index and active power loss, along with the minimizing of voltage deviation. The robustness of the algorithms is examined on the IEEE 33-bus and IEEE 69-bus radial distribution networks (RDNs) for PV- and wind-based DGs. The obtained results are compared with the existing literature to validate the effectiveness of the algorithms. The reduction in active power loss is 93.15% and 96.87% of the initial value for the 33-bus and 69-bus RDNs, respectively, while the other parameters, i.e., operating cost index, voltage deviation, and voltage stability index, are also improved. This validates the efficiency of the algorithms. The proposed study is also carried out by considering different voltage-dependent load models, including industrial, residential, and commercial types.

1. Introduction

Due to a rapidly increasing population, the consumption of electricity has likewise increased. As a result, the performance of distribution systems (DSs) has been decreased because of greater power losses and voltage drops due to the higher R/X ratio in the existing DSs [1]. To meet the rising demand for electricity, electric utility companies are constantly planning to expand their existing electrical systems. The conventional planning approach is to build a new grid or enlarge an existing one [2]. However, this is not a feasible solution in economic and environmental terms, as most of the existing networks are radial in nature and are powered by fossil fuels [3], which affects the environment through the emission of harmful gases. Thus, an attractive substitution to meet this rising demand is the use of distributed generation (DG) in DSs. DGs such as PV and wind are small power sources installed near to the end users [4]. Due to the environmentally friendly, reliable, and cost-effective benefits of renewable DGs such as solar and wind power, etc., these power sources are now extensively used to generate energy on a larger scale [5,6]. DGs play a vital role in enhancing the DSs’ efficiency and reliability by decreasing power losses and voltage drops and enhancing voltage stability. However, the improper allocation of DGs has an adverse effect on the DSs’ performance by increasing the power losses and voltage drops and reducing the voltage stability of the network. Thus, to enhance the system’s technical, economic, and environmental benefits, the optimal allocation of DGs (OADG) in DSs needs to be established cautiously.
The optimal placement and sizing of DGs in DS present a challenging problem in the literature. Therefore, researchers have taken various studies and developed different optimization methods, including analytical and metaheuristic approaches, to address the problem of OADG with different operating requirements for optimizing a single-objective function (SOF) and multi-objective function (MOF). In Ref. [7], a simplified analytical technique has been suggested for determining OADG and the optimal power factor (OPF) to enhance the active power loss (APL) reduction for three different radial distribution systems (RDSs), i.e., IEEE 12-, 33-, and 69-bus RDSs. To enhance the APL reduction, voltage profile, and economic benefits, an analytical approach has been recommended in Ref. [8] for determining the optimal placement and sizing of various types of DGs. The effectiveness of the suggested approach was also validated by testing on standard IEEE 33- and 69-bus RDSs for different loading scenarios. A modified version of the analytical method has been developed by the authors of [9] for OAPVDG, with the aim of enhancing the economic benefits and technical benefits (APL reduction and voltage stability margin enhancement) offered by DS planning. For defining the optimal placement of DGs, the line loss sensitivity factor (LSF) was utilized, while particle swarm optimization (PSO) with a constriction factor was employed for ascertaining the optimal DG capacity. The described approach was examined on IEEE 33-bus RDS. The authors of [10] proposed an MINLP model, solved through GAMS, for determining the OADG, with the aim of improving PL reduction. To validate the robustness of the approach, two standard test systems, IEEE 33- and 69-bus RDSs, were used. The proposed approach was also employed on a real 27-node test DS to optimally locate a PV-DG, assuming a sunny day. In another study [11], a new VSI-based LQP index was utilized to find the optimal DG location, while optimal DG capacity was ascertained by reducing APL. The suggested approach was examined on an IEEE 33-bus RDS. In Ref. [12], the voltage stability margin index (VSMI) was utilized to find the optimal placement of DG; optimal DG capacity was ascertained using the curve-fitting technique (CFT). The suggested approach was examined on IEEE 33- and 69-bus RDSs. In Ref. [13], a decision-making algorithm has been developed for ascertaining the OADG of different types with the aim of minimizing total APL and QPL and improving the voltage profile of the DSs. The suggested method was tested on an IEEE 33-bus RDS. A heuristic approach has been suggested in one study [14] for determining OADG and capacitor banks (CBs) to minimize the APL and enhance the voltage profile of the DSs. The described technique was tested on IEEE 33-, 69- and 119- test bus RDSs at OPF.
Analytical approaches are used wherein the DGs are placed one by one; however, these are not suitable for a multi-objective problem as their accuracy is incompatible with the integration of multiple DGs. The solution obtained by MILP is least consistent for complex problems due to the linearization nature of the algorithm, while heuristic algorithms offer a feasible solution with greater accuracy compared to linearized approaches with a higher computational burden. Metaheuristic methods are used globally, due to their easy implementation, to solve multi-objective problems with robust searching capabilities. Although metaheuristic algorithms do not ensure optimality, they offer feasible and efficient solutions with improvements in accuracy to converge the solution, compared to MILP and the heuristic approach to solving complex problems.
Due to their robust searching abilities to calculate the optimal solution for larger DNs, metaheuristic techniques have been widely used to solve the problem of OADG in DSs with SOFs and MOFs. In SOFs, only a single objective is optimized, while optimizing multiple objectives simultaneously is considered more suited to MOFs. Most of the metaheuristic techniques, such as multileader particle swarm optimization (MLPSO) [1], the improved stochastic fractal search algorithm (CFSA) [15], fine-tuned PSO [16], the strawberry plant propagation algorithm (SPPA) [17], and Aquila optimization (AO) [18], used SOF to allocate multiple DGs for minimizing the APL while enhancing the voltage profile of the system. Moreover, to minimize the APL and enhance the voltage profile, a hybrid of binary PSO and shuffled frog leap (SLFA), BPSO-SLFA, has been proposed by the authors of [19] for solving the OADG problem, along with network configuration. The suggested algorithm was tested on standard IEEE 33- and 69-bus RDSs. An improved version of forensic-based investigation (FBI), quasi oppositional FBI (QOBI) has been recommended by the authors of [20] for solving the problem of optimal placement and sizing, along with the OPF of various types of DGs, with the aim of minimizing the APL and improving the voltage profile of the system. In Ref. [21], the authors proposed the Coulomb–Franklin algorithm (CFA) for OADG, along with capacitor banks (CBS) in DS, to minimize the APL. The above-mentioned techniques were only implemented for a constant power load model. The authors of [22] suggested using a genetic algorithm (GA) for solving the problem of OADG, to minimize the APL while enhancing the voltage profile of the system. The suggested algorithm was validated on a standard IEEE 33-bus RDS with different load states and load models by considering the daily and yearly load profiles.
Compared with SOFs, MOFs are used to optimize multiple objectives simultaneously by converting them into SOFs through various multi-objectivity methods. To optimize the MOF based on the reduction of APL, VD, and VSI maximization for solving the problem of optimal placement and the sizing of multiple and various types of DGs in DN, different multi-objectivity methods have been employed using various metaheuristic techniques. A quasi-oppositional chaotic symbiotic organism search (QOCSOS) [23], quasi-oppositional differential evolution Lévy flights algorithm (QODELFA) [24], manta ray foraging optimization (MRFO) [25], and improved grey wolf optimizer-PSO (I-GWOPSO) [26] have used the weighted sum method, while an improved decomposition-based evolutionary algorithm (I-DBEA) [27] used the e-constraints method; the chaotic sine cosine algorithm (CSCA) [28], and an improved Harris hawk optimization (IHHO) method [29] used grey relation analysis to find the best optimal solution from a Pareto optimal solution. An enhanced artificial ecosystem-based optimization (EAEO) algorithm [30] used a fuzzy decision-making approach to find the best optimal solution from the Pareto optimal solution, while adaptive PSO and gravitational search algorithm (GSA) approaches have used the Pareto optimal front, e-constraints, and aggregated sum methods. Moreover, to solve MOFs based on technical (APL, VD, and VSI), economic (cost of CB and the cost of power produced), and environmental (pollutant emissions) objective improvements for aiming the OADG and CB, the salp swarm algorithm (SSA) [31] was used with the weighted sum method. A multi-objective differential evolution (MODE) algorithm [32] has used a fuzzy approach to solve the MOF for improving technical, economic, and environmental objectives. The suggested approach was implemented on standard IEEE 33-, 69-bus, and 62-bus real RDSs. In another study [33], the authors introduced a multi-objective firefly algorithm (MOFA) to minimize the PL, VD, THD, the cost of DG, and GHG emissions and maximized the VSI as a MOOP for ascertaining the optimal allocation of DG (OADG) The optimal solution was determined using a fuzzy decision-making approach. The recommended system was tested on an IEEE 33-bus RDN and an actual 62-bus Indian distribution system.
In Ref. [34], the hybrid optimization technique (GSA + GAMS) was implemented for OADGs (solar, wind, and hydropower sources) with network reconfiguration in DN to optimize the MOF, based on the improvement of technical (APL) and economic (cost) benefits. In this study, the authors used GSA to find the optimal placement of DGs and the optimal capacity of DG GAMS. To check the validity and effectiveness of the algorithm, a standard IEEE 33-bus RDN and a real-time varying DN were utilized. A multi-objective opposition-based chaotic differential evolution (MOCDE) algorithm has been proposed by the authors of [35] to solve the OADG problem for optimizing the MOF to achieve technical objectives (minimization of PL and reduction of VD); and economic objective (minimization of yearly economic loss cost). The suggested algorithm was tested on standard IEEE 33- and 69-bus RDNs. In Ref. [36], the author introduced the artificial bee colony (ABC) optimization algorithm for the optimal situating and sizing of DGs to minimize the APL, voltage drops, and total energy costs concurrently, as a multi-objective problem (MOP). The suggested algorithm was tested on standard IEEE 33- and 69-test-bus RDNs.
An opposition-based chaotic differential evolution (OTCDE) system was proposed in Ref. [37] for OADG, to deal with MOPs consisting of technical (voltage deviation and line flow capacity) and economic objectives. The proposed system was tested on standard IEEE 33-, 69-, and 118-bus RDNs. The stud krill herd algorithm (SKHA) [38] was recommended to solve the problem of OADG in DN for optimizing MOFs, based on APL, VD, and OC. The MOF in question was solved using the weighted sum approach. In Ref. [39], the authors proposed an ant colony optimization (ACO) algorithm for the optimal allocation of renewable-based DGs with the aim of optimizing MOFs, based on the APL index, VD index, and OCI. The suggested approach was tested on an IEEE 33-bus and actual 85-bus Indian DS. The authors of [40] proposed an artificial hummingbird algorithm (AHA) to solve the problem of the optimal allocation of renewable DGs considering uncertainties for optimizing the MOF, based on APL, VD, VSM, and total annual energy savings, using the weighted sum method. The suggested technique was tested on a standard IEEE 33- and 69-bus RDS for different load states. A comprehensive review of the optimization methods used for OADG to achieve different objectives is presented in Table 1.
It can be seen from Table 1 that various optimization methods had been investigated for solving the problem of the optimal allocation of DGs for achieving technical and economic objectives while considering only the constant power (CP) load model by optimizing SOF and MOF. Very few studies have considered VP load models. However, in some [50,52], voltage-dependent load models have been utilized to solve the problem of OADG, to achieve only technical objectives. In this study, two metaheuristic algorithms, Tasmanian devil optimization (TDO) and artificial gorilla troops optimization (GTO), are proposed. The application of TDO and GTO algorithms is employed in the field of engineering to solve complex problems. The reason for using these metaheuristic algorithms is that their ability to solve complex and high-dimensional problems is more efficient than other metaheuristic algorithms, such as PSO and GA, due to their ability to explore and exploit phases efficiently. Every metaheuristic algorithm has its pros and cons. In terms of solving high-dimensional and complex problems, GTO and TDO perform well in finding a globally optimal solution by balancing between exploration and exploitation phases, while GA and PSO trap into local minima and demand high computational time. The tuning of the parameters in PSO is also the main issue that led to premature convergence. The main issue of the GTO algorithm is its longer running time. Although the run-time of the GTO algorithm is longer, it is, however, useful as it is capable of solving high-dimensional problems with higher performance. To check the performance of the TDO and GTO algorithms, they are compared with other well-known optimization algorithms that validate the effectiveness of the algorithms for solving the problem of the optimal allocation of DGs.
Thus, in this study, the CP load model, as well as VP load models, are considered to solve the problem of OADG in DN, to achieve techno-economic objectives by optimizing SOF and MOF. The following are the main contributions of this paper:
  • The proposed optimization algorithms are identified as GTO and TDO.
  • The proposed techniques are analyzed for renewable DGs such as Photovoltaic (PV) type and wind turbine (WT) type at unity and combined power factor (pf).
  • The GTO and TDO techniques address the OADG problem to minimize APL and QPL using SOF.
  • The GTO and TDO techniques address the OADG problem to improve APL reduction, VD, VSI, and OCI (the investment, operation, and maintenance costs of DG) concurrently with the MOF.
  • The robustness of the proposed algorithms is examined on two standard test bus systems, i.e., IEEE 33- and 69-bus RDNs, and are compared with each other.
  • The proposed techniques are further explored for voltage-dependent load models consisting of residential, commercial, and industrial load models, which make the problem more practical than with the CP load model.
  • The proposed techniques generate a better result than the existing optimization techniques, which validates the methodology.
  • The proposed GTO technique outperforms the other proposed TDO techniques in terms of convergence characteristics and optimizing the SOF.
The remainder of this paper is organized as follows: Section 2 represents the problem formulation, including the objective functions, with system constraints and load modeling. Section 3 introduces the summary of proposed algorithms, i.e., TDO and GTO. In Section 4, the simulation results and discussions are presented. Finally, the conclusions are presented in Section 5.

2. Problem Formulations

The main objective of this study is to optimally allocate the DGs to solve the SOF and MOF. The SOF includes the reduction of total power losses, i.e., APL and QPL, while the MOF includes the reduction of APL, minimization of VD, maximization of VSI, and minimization of total OC, including investment, operation, and the maintenance costs of DGs.

2.1. Objective Functions

The mathematical modeling for SOF and MOF is presented in the following subsections.

2.1.1. Reduction of Active Power Loss (APL)

In the RDN, the APL is computed using the following equation [26,56]:
A P L = j = 1 M b r I j 2 .   R j  
Here, j is a branch number, the total number of branches is represented by M b r , and I j represents the absolute current passing through the branch of resistance, R j . The first objective function ( O F 1 ) is represented as:
O F 1 = M i n A P L   .

2.1.2. Reduction of Reactive Power Loss (QPL)

In the RDN, the QPL is computed using the following equation:
Q P L = j = 1 M b r I j 2 .   X j   .
Here, j is a branch number, the total number of branches is represented by M b r , and the absolute current I j represents the absolute current passing through the branch of inductive reactance, X j . The second objective function, O F 2 , is represented as:
O F 2 = M i n   Q P L   .

2.1.3. Minimization of Voltage Deviation (VD)

The lifetime and performance of the equipment are affected by the deviation of the voltages. Therefore, we keep in mind that the reason for the minimization of voltage deviation is taken as OF. VD is calculated using the following equation [57]:
V D = j = 1 m   ( V r e f V j ) 2  
where V r e f denotes the reference voltage of value, 1.0 p.u. The “m” denotes the number of total buses in the radial distribution system, whereas “ V j ” denotes the voltage of the receiving bus. The third OF ( O F 3 ) is represented as:
O F 3 = M i n   V D   .

2.1.4. Minimization of Voltage Deviation (VD)

Along with VD, VSI is another crucial component to take into account when determining the security level of the DN. Due to a variety of factors, when a bus in a DN exceeds the permitted voltage limits, the entire system may experience voltage instability, or VSI. All the buses in a DN must maintain VSI at a stable limit for steady operation. Equation (7) is used to compute the VSI [41]:
V S I k + 1 = V k 4 4   P k + 1 x k Q k + 1 r k 2 4   V k 2 P k + 1 r k Q k + 1 x k   .
In Equation (7), P k + 1 and Q k + 1 represent the real and reactive load demands, respectively; the k represents the sending bus number, and V k denotes the voltage of the sending bus, whereas the line resistance is denoted by r k and the line reactance is represented by x k , which feed the receiving bus (k + 1). For the secure and stable operation of the RDN, the VSI value must be greater than zero. The fourth OF ( O F 4 ) is represented as:
O F 4 = M a x M i n   V S I k + 1   .

2.1.5. Minimization of Operating Cost Index (OCI)

The total price for obtaining electricity from the grid consists of the power loss price and the price of the power supplied to the customer. The total operating cost before DG integration is computed using the following equation [39]:
O C b a s e = t = 1 T p P W F t × P L + P T l o a d × T × C e  
where P L denotes the power loss in the base case and P T l o a d denotes the supplying power to the customer, while T refers to the time period (hr/year), T p refers to the planning years and the cost of energy, and price, C e , is 49 (USD/MWh). P W F is a present worth factor and is evaluated as:
P W F = 1 + I n f _ R 1 + i n t _ R  
Here, inf _ R is the inflation rate, with a value of 9%, and i n t _ R is the interest rate, with a value of 12.5%.
The annual operational cost can be broken down into the following four elements. The first element is the maintenance cost of DG, which is determined using the following equation:
D G m = t = 1 T p i = 1 N d g P W F t × P D G , i × T × K M ,   D G  
where K M ,   D G denotes the DG maintenance cost and its value is taken as 7 (USD/MWh), P D G , i represents the power of installed DG, and N d g represents the number of DG installed units.
The second element is the DG operational cost, which is computed through the following equation:
  D G O = t = 1 T p i = 1 N d g P W F t × P D G , i × T × K O ,   D G  
where K O ,   D G denotes the DG operation cost and its value is taken as 29 (USD/MWh).
The third component is the DG installation cost, which is computed through the following equation:
D G I C = K I C , D G   i = 1 N d g P D G ,   i  
where K I C , D G is the DG installation cost and its value is taken 400,000 (USD/MWh).
The last element is the cost of operation after DG integration, which is calculated using the following equation:
O C D G = t = 1 T p P W F t × P L + P T l o a d × T × C e  
where P L denotes the power loss after integrating DG and P T l o a d denotes the supplying power to the customer.
Thus, the annual operating cost can be constructed as:
  O C T D G = D G M + D G O + D G I C + O C D G .
The fifth OF ( O F 5 ) is represented as:
O F 5 = M i n   O C T D G O C b a s e   .

2.2. Formulation of a Multi-Objective Function (MOF)

Unlike SOFs, in MOFs, two or more conflicting objective functions are dealt with simultaneously. To establish the TEOF, each of the objective functions is divided by its base value and corresponding weight. For MOFs, the weighted sum method is used. The TEOF is formulated as:
T E O F = M i n   ( α 1 × R P L R P L b a s e + α 2 × T V D T V D b a s e + α 3 × V S I 1 V S I b a s e 1 + α 4 × O C T D G O C b a s e )   ,
and
i = 1 4 α i = 1 ;   α   0 , 1   ,
where R P L b a s e , T V D b a s e , V S I b a s e 1 , and O C b a s e are the base values of real power losses, total voltage deviation, the voltage stability index and operating cost, respectively. α 1 , α 2 , α 3 , and α 4 are the different weights given to the individual objective function. Their values are 0.5, 0.35, 0.15, and 0.1, respectively. The preference for weights shown is given to the technical objectives over the economic objective.

2.3. System Constraints

The MOF that is calculated in Equation (17) is subjected to the following constraints.

2.3.1. Equality Constraints

The flow of powers in the distribution system must be balanced. In other words, the power drawn from the substation and the power generated from the DG units should be sufficient to meet the following requirements for load demand and power losses [39]:
P s + i = 1 N d g P G   i = P D + A P L  
Q s + i = 1 N d g Q G   i = Q D + Q P L  
where P s and Q s are the active and reactive powers drawn from the substation, respectively. P G and Q G are the incoming powers that are generated from the installed DG units. P D , Q D ,   R P L , and Q P L are the active and reactive load demands and the real and reactive power losses, respectively.

2.3.2. Inequality Constraints

Voltage Limits

The voltage magnitude of the bus in the network should be within permissible limits; that is, they can be expressed as [26,58]:
0.95   p . u .     V i   1.05   p . u .

Branch Current Limits

The maximum limit of a branch’s current should not be exceeded [26], as stated by:
I j ,   i     I j ,   i m a x   .

DG Capacity Limits

The range of the output power of DG units is expressed as [39,43]:
P G m i n     P G     P G m a x  
Q G m i n     Q G     Q G m a x   .

DG power factor limit

The following range of power factors can be used to operate DG units [26,44]:
p . f D G m i n     p . f D G     p . f D G m a x   .

2.4. Load Modeling

Most of the studies in the literature have focused on the power flow issue using constant load models, or constant active and reactive powers. However, actual load characteristics show how much load power depends on the bus voltage. The distribution system’s load can often be divided into three categories: industrial, residential, and commercial loads. In this study, a real-life problem is considered by modeling voltage-dependent load industrial, residential, and commercial load models. The mathematical formulation of voltage-dependent load models is expressed as:
P = P o V n α  
Q = Q o V n β
where active and reactive powers are represented by P and Q , respectively; P o and Q o refer to the values of active and reactive powers at nominal voltage, respectively; V n denotes the magnitude of the voltage, whereas α and β are the values of the active and reactive power exponents. The values of the α and β used in this study for various types of loads are shown in Table 2, which has been taken from Refs. [50,58].

3. Methodology

The aim of this study is to use a metaheuristic algorithm to optimize the SOF and MOF, based on APL, VD, VSI, and OCI for the optimal allocation of DGs in DN. In this section, two newly metaheuristic optimization algorithms, named artificial gorilla troops optimization (GTO) and Tasmanian devil optimization (TDO), are presented.

3.1. Artificial Gorilla Troop Optimization (GTO)

In 2021, Abdollahzadeh and Miralilli [59] introduced a novel bio-inspired metaheuristic algorithm, named gorilla troop optimization (GTO), based on gorilla group behavior in the wild when finding food and living as a troop. Each troop has a silverback gorilla that serves as the troop’s leader; it is responsible for ensuring the safety of the troop by taking crucial decisions. The silverback gorilla is supported by young male gorillas (known as black-backs) to provide backup protection for the group.
As with other optimization techniques, for optimization operation, two phases are used by the GTO algorithm, known as the exploration and exploitation phases.

3.1.1. Exploration Phase

In GTO, three different strategies are used for the exploration phase. In the first strategy, the gorilla moves toward an unknown place, while in the second strategy, the gorilla moves in the direction of another gorilla; in the third strategy, it moves to a known place. The X and GX represent the position of the gorilla and the silverback, respectively. The following are expressions for the mathematical formulas used in this phase:
G X t + 1 = u b l b R 1 + l b ,   r a n d < P  
G X t + 1 = R 2 C X r t + L H ,   r a n d 0.5  
G X t + 1 = X i L ( L ( X ( t ) G X r ( t ) ) + R 3 ( X ( t ) G X r ( t ) ) ) ,   r a n d < 0.5 .
In Equation (28), ub and lb represent the upper and lower bound, respectively. R1, R2, and R3 are random numbers in the range of [0, 1], whereas t represents the current iteration. p is a predetermined value in the interval of [0, 1], which is used to select the movement of the gorilla to an unknown site, as in the above strategies. rand denotes the random value in the interval of 0-1. GXr and Xr are the randomly selected solutions from the population, whereas other parameters are calculated using Equations (29), (31) and (32):
C = F 1 i t m a x i t  
F = cos 2 R 4 + 1  
L = C l  
H = Z X t  
Z = C , C  
where it and maxit denote the current and max number of iterations, respectively. R4 is a random parameter in the range of 0–1. The value of l is in the range of [−1, 1].

3.1.2. Exploitation Phase

In the exploitation phase, two different mechanisms are used; either the gorilla’s troop follows the silverback gorilla’s decision or it competes for the adult females. The probability of selecting the mechanism is based on the value of C. If C >= W, the gorilla’s troop follows the silverback’s instructions. This behavior is shown as follows:
G X t + 1 = L M X t X s i l v e r b a c k + X t  
M = 1 N i = 1 N G X i t g 1 g  
g = 2 L  
where the silverback’s position is represented by X s i l v e r b a c k . If C < W, competition for the adult females is selected and this behavior is expressed as follows:
G X i = X s i l v e r b a c k X s i l v e r b a c k Q X t Q   A  
Q = 2 R 5 1  
A = β E  
E = N 1 ,   r a n d   0.5 N 2 ,   r a n d < 0.5  
where Q represents impact force, R5 is a random number in the interval [0, 1], and β is a predefined variable. The value of rand is between 0 and 1. “E” will be equal to random values in the problem matrix and the Gaussian distribution, when rand >= 0.5; conversely, “E” will be from just the Gaussian distribution, when rand < 0.5. A flow chart showing the process of the GTO technique to address OADG in DN is depicted in Figure 1 and an explanation of the flow chart is described in Algorithm A1 in the Appendix A section.

3.2. Tasmanian Devil Optimization (TDO)

In 2022, Dehghani introduced a novel bio-inspired metaheuristic algorithm [60], named the Tasmanian devil optimizer (TDO), based on the Tasmanian devil’s behavior in the wild during feeding. Two different approaches/strategies are used by the Tasmanian devil during the feeding process. The first one is eating carrion, while the second is eating prey. The mechanism of these approaches is discussed below.

3.2.1. Feeding by Eating Carrion (Exploration Phase)

In the TDO algorithm, the Tasmanian devil’s approach to feeding by eating carrion is mathematically designed using Equations (41) and (42). The process of choosing carrion is mimicked in Equation (41):
C i = X k ,   i = 1 ,   2 ,   3 ,   .   .   .   . ,   N ,   k   ϵ   1 ,   2 ,   .   .   . ,   N | k i  
where C i denotes the carrion selected by the ith Tasmanian devil and X represents the Tasmanian devil population. A new position for the Tasmanian devil within the search space is determined, based on the chosen carrion. The updated location of the Tasmanian devil can be formulated using Equation (42).
x i   ,   j n e w   ,   S 1 = x i   , j + r c i   , j l x i   , j ,   F C i < F i x i   , j + r x i   , j c i   , j ,   o t h e r w i s e  
In Equation (42), x i   , j represents the candidate value from the candidate solution for the jth variables, r denotes a random number in the range of [0, 1], l is a predefined parameter of value 1 or 2, while F C i is a value of objective fitness function for the selected carrion.
X i =   X i n e w   ,   S 1   ,           F i n e w   , S 1 < F i X i   ,     o t h e r w i s e  
In Equation (43), X i n e w   ,   S 1 denotes the new position of the ith Tasmanian devil and x i   ,   j n e w   ,   S 1 represents its value for the jth variable, while   F i n e w   , S 1 represents its objective function value.

3.2.2. Feeding by Eating Prey (Exploitation Phase)

In this approach, there are two steps that the Tasmanian devil follows during attacking behavior. In the first step, it chooses the prey and launches an attack on it after scanning the surroundings. After reaching the prey, it chases it in the second step, to stop it from escaping and begin feeding. Therefore, the first step is designed in the same manner as that designed for the first approach of Tasmanian devil feeding. The process of choosing prey is mimicked in (44):
P i = X k ,   i = 1 ,   2 ,   3 ,   .   .   .   . ,   N ,   k   ϵ   1 ,   2 ,   .   .   . ,   N | k i  
where P i denotes the prey selected by the ith Tasmanian devil. A new position for the Tasmanian devil in the search space is determined, based on the chosen prey. The updated location of the Tasmanian devil can be formulated using Equation (45).
x i   ,   j n e w   ,   S 2 = x i   , j + r p i   , j l x i   , j ,   F p i < F i x i   , j + r x i   , j p i   , j ,   o t h e r w i s e  
In Equation (45), x i   , j represents the candidate value from the candidate solution for the jth variables, r denotes a random number in the range of [0, 1], l is a predefined parameter of value 1 or 2, while F p i is a value of objective fitness function for the selected prey.
X i =   X i n e w   ,   S 2   ,       F i n e w   , S 2 < F i X i   ,     o t h e r w i s e  
In Equation (46), X i n e w   ,   S 1 denotes the new position of the ith Tasmanian devil, x i   ,   j n e w   ,   S 1 represents its value for the jth variable, and   F i n e w   , S 1 represents its objective function value.
The second step during the attacking behavior demonstrated by the Tasmanian devil is the chasing process, which is designed using Equations (47)–(49). At this point, the Tasmanian devil’s location is regarded as the hub of the area where the process of pursuing the prey is occurring. The Tasmanian devil follows its victim over a range that corresponds to this neighborhood’s radius, which is computed using (47).
R = 0.01   1 t T  
Here, R represents the attack location’s immediate surroundings, t denotes the current iteration, and T represents the maximum number of iterations. A new position for the Tasmanian devil is determined, based on the chasing task. The updated location of the Tasmanian devil can be formulated using Equation (48).
x i   , j n e w = x i   , j + 2 r 1 R x i   , j  
X i =   X i n e w   ,               F i n e w   < F i X i   ,     o t h e r w i s e  
In Equation (49), X i n e w denotes the new position of the ith Tasmanian devil in the district of X i , x i   ,   j n e w represents its value for the jth variable, and   F i n e w represents its objective function value. The flow chart of the TDO technique to address OADG in a DN is depicted in Figure 2; its explanation using pseudo code is presented in Algorithm A2 in the Appendix A section.

4. Simulation Results and Discussion

To evaluate the validity and effectiveness of the proposed algorithms, they have been implemented on two IEEE benchmark RDSs, including IEEE 33-bus and IEEE 69-bus systems, to optimize the SOF and MOF, while considering the CP load model as well as the VP load models, which consist of residential, commercial, and industrial load models. The reduction of APL and QPL by the optimal placement and sizing of DG units is accomplished by optimizing the SOF, while the minimization of APL, VD, and OCI and the maximization of VSI is simultaneously achieved by optimizing the MOF. The control parameter settings for the suggested methods are demonstrated in Table 3.
In this study, PV-DGs and WT-DGs are considered, PV-DGs having a unity pf while WT-DG has a combined pf (0.85). The period considered for this study is over 20 years. The proposed algorithms are simulated using MATLAB 2021b software and Windows 2010Pro, with Intel(R) Core (TM) i5-4210U CPU (2.4 GHz) and 8 GB of RAM. To verify the robustness of the algorithms, the following scenario and cases are considered for the studied systems:
Scenario 1: Optimizing SOF by integrating 3 DGs:
  • Case 1: Minimizing APL for both CP and VP load models
  • Case 2: Minimizing QPL for both CP and VP load models.
Scenario 2: Optimizing MOF by integrating 3 DGs:
  • Case 1: Minimizing APL, VD, and OCI, and maximizing VSI for both CP and VP load models.

4.1. IEEE 33-Bus Test System

The proposed algorithms are first tested on a standard IEEE 33-bus RDS. A single-line diagram of the 33-bus RDS is shown in Figure 3. It consists of 33 buses and 32 branches, and the information about the line and load data of the system has been obtained from Ref. [61]. The total load demand of the system is (3.715 + j2.300) MVA, with a base voltage and base MVA of 12.66 KV and 100 MVA, respectively.

4.1.1. Scenario 1: Evaluation of a Single-Objective Function (SOF)

In this scenario, the TDO and GTO algorithms are used to solve the problem of the optimal placement and sizing of DGs, to reduce the total active and reactive power losses as SOFs for the CP load model and VP load model, i.e., industrial, residential, and commercial load models for three PV (unity pf) and three WT (0.85 pf).

CP Load Model

The total power loss of the system without the integration of DGs (the base case) is calculated by using the forward-backward power flow method, which is expressed as (210.07 KW + j142.44 KVAR). In the base case, active power loss and reactive power loss remain the same, while the losses are reduced as the number of DG units is increased in the system. In the base case, the minimum voltage is 0.904 p.u. at bus 18, the voltage deviation is 0.1328 p.u., and the VSI is 0.6672 p.u. Table 4 represents the results of the OADG in the CP load model when used to optimize the SOF at unity pf (PV type). It can be seen from Table 4 that by using both the TDO and GTO algorithms, the total APL is reduced to 70.64 KW, which is a 66.37% reduction with respect to the base value. The results are compared with other existing optimization techniques. The result of the APL reduction is better than for the other BAT [50], SOS-NNA [57], IHHO [29], GAMS [10], CFA [21], and QOFBI [20] techniques mentioned in Table 4.
Likewise, the results of the OADG for APL minimization at 0.85 pf (WT type) are presented in Table 5. By employing the TDO and GTO algorithms, the APL is reduced to 14.39 KW, which is a 93.15% reduction, as can be seen in Table 4. The obtained results are compared with another optimization approach, I-DBEA [27]. The proposed algorithms yield better results in terms of APL reduction.
Moreover, the SOF is optimized to solve the problem of OADG with the integration of three PV (unity pf) and three WT (0.85 pf) for QPL minimization. The results and their discussion are presented in Table A1 and Table A2 in Appendix A.
Table 4. Results comparison of the OADG for a 33-bus RDN for SOF (APL minimization) at unity pf (PV type) in a CP load model.
Table 4. Results comparison of the OADG for a 33-bus RDN for SOF (APL minimization) at unity pf (PV type) in a CP load model.
MethodsLocationDG Size (KW)APL (KW)
APLR (%)
VD (p.u.)VSI (p.u.)
Base case--210.070.13280.6672
BAT [50]13, 25, 30380, 490, 99072.78 (65.5)-0.8652
SOS-NNA [57]13, 24, 30801.8, 1091.3, 1053.672.7853 (65.5)0.0151131.1358
IHHO [29]14, 24, 30775.54, 1080.83, 1066.6972.79 (65.50)--
GAMS [10]14, 24, 30770.9, 1096.9, 1065.872.79 (65.50)--
CFA [21]30, 24, 131059.32, 1090.16, 801.8872.79 (65.50)--
QOFBI [20]24, 30, 131091.33, 1053.64, 801.7172.78 (65.5)--
TDO [P]30, 14, 241213, 866, 118670.64 (66.37)0.0115410.8940
GTO [P]24, 30, 141186, 1213, 86670.64 (66.37)0.0115410.8940
Table 5. Results comparison of OADG for a 33-bus RDN for the SOF (with APL minimization) at 0.85 pf (WT type) in the CP load model.
Table 5. Results comparison of OADG for a 33-bus RDN for the SOF (with APL minimization) at 0.85 pf (WT type) in the CP load model.
MethodsLocationDG SizeAPL (KW)
APLR (%)
VD (p.u.)VSI (p.u.)
KWKVAR
Base case---210.070.13280.6672
I-DBEA [27]13, 24, 30749.1, 1042, 1239.5-14.57 (92.81)0.00020.9733
TDO [P]30, 24, 131333, 1147, 836826, 640, 48614.39 (93.15)0.0006040.9669
GTO [P]24, 30, 131147, 1333, 836640, 826, 48614.39 (93.15)0.0006040.9669

VP Load Model

This section extends the OADG issue for practical non-linear loads to show how strongly power demands rely on the voltage of the network. In the base case, the APL for industrial load models is 163.22 KW, for residential load models, it is 158.76 KW, and for commercial load models, it is 152.32 KW. Table 6 shows the results of the SOF based on APL minimization for the optimum placement and sizing of DGs at unity pf (PV-type). It can be seen from the table that by employing the TDO and GTO algorithms, APL is reduced to 34.55 KW (78.83%) for industrial, 42.05 KW (73.51%) for residential, and 44.80 KW (70.59%) for commercial load models. The results are compared with another optimization method, BAT [50], as mentioned in Table 6. The results obtained by employing the proposed algorithms are better in terms of APL reduction.
Likewise, Table 7 represents the results of the OADG at 0.85 pf (WT type) for APL minimization with different load models. The APL is reduced to 10.53 KW (93.55%), 10.38 KW (93.46%), and 10.33 KW (93.22%) for the industrial, residential, and commercial load models, respectively, for both the TDO and GTO algorithms. It can be concluded that the APL minimization is at maximum for the industrial load models for PV (unity pf).
Furthermore, the study has been expanded to solve the problem of the optimal allocation of DGs for reactive power loss minimization (QPL) for VP load models, with the integration of three PV (unity pf) and three WT (0.85 pf). The results of the QPL minimization and a discussion of the findings are presented in Table A3 and Table A4 in Appendix A.

Voltage Profiles for 33 Bus RDS

Figure 4 illustrates the impact of the installation of various types of DGs on the voltage profile for a 33-bus RDS under various types of loads, i.e., constant, residential, commercial, and industrial load models. In Figure 4, “Const” stands for constant, “Res” denotes residential, “Comm” denotes commercial, and ”Ind” denotes industrial load models. The outer values of the graphs represent the “bus number” and the inner values represent “bus voltage”, corresponding to the particular bus number.

Active Power Losses for a 33-Bus RDS

Figure 5 depicts the APL information for each bus of a 33-bus RDS after the integration of three PV (unity pf) and three WT (0.85 pf) under various types of loads, i.e., constant, residential, commercial, and industrial loads, under scenario 1.

Convergence Characteristics for a 33-Bus RDS

Figure 6a,b displays the convergence characteristics of the GTO and TDO algorithms at various power factors (unity and 0.85) for the CP load model. It is apparent from the figure below that the GTO algorithm has a higher efficiency than the TDO algorithm.

4.1.2. Evaluation of Multi-Objective Function (MOF)

In this scenario, the TDO and GTO algorithms are employed to optimize the MOF, based on APL, VD, VSI, and OCI, to solve the problem of OADG in RDS, considering the CP load model and VP load models for three PV (unity pf) and three WT (0.85 pf).

CP Load Model

The total power loss of the system in the base case is (210.07KW + j142.44KVAR), the VD is 0.1328 p.u., VSI is 0.6672, and the operating cost is 16.837972 million USD (M$). Table 8 presents the results of the MOF in terms of APL reduction, VD minimization, VSI maximization, and the minimization of an operating costs index for the optimum placement and sizing of DGs for three PV (unity pf) and three WT (0.85 pf) for the CP load model.
It can be seen from the table that at unity pf (PV type), the APL is reduced to 71.74 KW (65.85%) for the TDO algorithm and 72.02 KW (65.72%) for the GTO algorithm. The VD obtained by employing the TDO and GTO algorithms is 0.007390 p.u. and 0.006894 p.u., respectively, while the value of VSI computed for the TDO and GTO algorithms is 0.9160 p.u. and 0.9189 p.u., respectively; the operating cost index for both the TDO and GTO algorithms is 8084 and 8075, respectively. Furthermore, the cost savings after 20 years at unity pf (PV-type) are 19.16% and 19.25% for the GTO and TDO algorithms, respectively.
Similarly, at 0.85 pf (WT type), the APL is reduced to 14.65 KW (93.03%) for the TDO algorithm and 14.66 KW (93%) for the GTO algorithm. The VD obtained by employing the GTO and TDO algorithms is 0.000287 p.u. and 0.000291 p.u., respectively, while the value of VSI computed for both the TDO and GTO algorithms is 0.9753 p.u., and the operating cost index for the TDO and GTO algorithms is 7987 and 7977, respectively. Moreover, the cost savings after 20 years at 0.85 pf (WT type) for the TDO and GTO algorithms are 20.13% and 20.23%, respectively.
It can be concluded that the results obtained at 0.85 pf (WT type) in terms of APL reduction, the minimization of VD, the minimization of OCI, and the maximization of VSI are improved compared to the results obtained at unity pf (PV type). Furthermore, the cost saving is at a maximum, at 0.85 pf (PV type).

VP Load Model

The results of MOF in terms of APL reduction, VD minimization, VSI maximization, and the minimization of the operating cost index for the optimum placement and sizing of DGs for VP load models for three PV (unity pf) and three WT (0.85 pf) are shown in Table 9 and Table 10.
It can be seen from Table 9 that at unity pf (PV type), by employing the TDO algorithm, the APL is reduced to 35.09 KW (78.50%) for the industrial load model, 42.69 KW (73.11%) for the residential load model, and 45.50 KW (70.11%) for the commercial load model, while by employing the GTO algorithm, the reduction in APL for industrial load is 35.09 KW (78.50%), for residential load, it is 42.70 KW (73.10%), and for commercial load, it is 45.50 KW (70.13%). The obtained VD from the TDO algorithm for the industrial load model is 0.00374 p.u., for the residential load model, it is 0.00472 p.u., and for the commercial load model, it is 0.00498 p.u., while the VD obtained from the GTO algorithm is 0.00373 p.u., for the industrial load model, 0.00472 p.u. for the residential load model, and 0.00485 p.u. for the commercial load model. The VSI that has been computed for the industrial load model is 0.9385 p.u., for the residential load model it is 0.9331 p.u., and for the commercial load model, it is 0.9319 p.u., established by employing the TDO algorithm, while by employing the GTO algorithm, the VD for the industrial load model is 0.9386 p.u., for the residential load model, it is 0.9333 p.u., and for the commercial load model, it is 0.9302 p.u. The operating cost index obtained from the TDO and GTO algorithms for an industrial load is 0.8141, for a residential load it is 0.8158 and 0.8155, and for a commercial load, it is 0.8173 and 0.8164, respectively. Besides this, the cost saving after 20 years for the industrial load will be 18.59% for both the TDO and GTO algorithms, for a residential load, it will be 18.42% and 18.45% for the TDO and GTO algorithms, and for a commercial load, it will be 18.27% and 18.36% for the TDO and GTO algorithms.
Moreover, the results of the OADG for MOF at 0.85 pf (WT type) are shown in Table 10. By employing TDO, the APL is reduced to 10.69 KW (93.45%) for the industrial load model, to 10.50 KW (93.39%) for the residential load, and 10.44 KW (93.15%) for the commercial load, while by employing the GTO algorithm, the APL is reduced to 10.69 KW (93.45%), 10.51 KW (93.38%), and 10.45 KW (93.14%) for industrial, residential, and commercial load models, respectively. The obtained VD from the TDO algorithm for industrial, residential, and commercial models is 0.000291 p.u., 0.000294 p.u., and 0.000294 p.u., respectively, while the VD obtained from the GTO algorithm is 0.000288 p.u. for industrial load, 0.000294 p.u. for residential load, and for commercial load, it is 0.000293 p.u. The VSI that was computed by employing the TDO algorithm for the industrial load model is 0.9755 p.u., for the residential model, it is 0.9755 p.u., and for the commercial model, it is 0.9755 p.u., while by employing the GTO algorithm, the VSI computed for the industrial load model is 0.9756 p.u., for the residential model it is 0.9755 p.u., and for the commercial load model, it is 0.9756 p.u. The operating cost index obtained from the TDO and GTO algorithms for industrial load is 0.8122 and 0.8120, for residential load, it is 0.8117 and 0.8113, and for commercial load, it is 0.8123 and 0.8119, respectively.
Besides this, the cost saving after 20 years for an industrial load will be 18.78% and 18.80% for the TDO and GTO algorithms, for a residential load, 18.83% and 18.87% for the TDO and GTO algorithms, and for a commercial load, it will be 18.77% and 18.81% for the TDO and GTO algorithms.
It can be concluded that compared to unity pf (PV type), the results of the MOF in terms of APL reduction, the minimization of VD and OCI, and the maximization of VSI are improved at 0.85 pf (WT type). Furthermore, the maximum cost saving is achieved at 0.85 pf (WT type) for industrial, residential, and commercial load models.

4.2. IEEE 69-Bus Test System

In this section, the conclusions of standard IEEE 69-bus RDSs are achieved by the suggested techniques. Figure 7 displays a 69-bus DS single-line diagram. It has 69 buses and 68 branches, and the information about the line and load data of the system has been obtained from Ref. [62]. The base voltage and base MVA of the system are 12.66 KV and 100 MVA, respectively, while the total load demand is (3.8 + j2.69) MVA.

4.2.1. Scenario 1: Evaluation of a Single-Objective Function (SOF)

In this scenario, the TDO and GTO algorithms are used to solve the problem of the optimal allocation of DGs in a distribution network to reduce the total active and reactive power losses as the SOF for a CP load model and VP load models, i.e., industrial, residential, and commercial load models for three PV (unity pf) and three WT (0.85 pf).

CP Load Model

The forward-backward load flow method is used to determine a power flow solution. The total power loss of the system in the base case is (225.60KW + j101.99KVAR) and the minimum voltage is 0.9102 p.u. at bus 65. The VD and VSI in the base case are 0.09803 p.u. and 0.6855 p.u., respectively. The results of the proposed algorithms for OADG at unity pf (PV type) in the CP load model are presented in Table 11. It can be seen from the table that the total APL is reduced to 68.68 KW for both the TDO and GTO algorithms, that is, a 69.42% reduction with respect to the base value. The obtained results are compared with other optimization approaches, BAT [50], SOS-NNA [57], IHHO [29], I-DBEA [27], and QOFBI [20], and are presented in the table. The proposed algorithms performed well in terms of APL reduction.
Likewise, the results of OADG for APL minimization at 0.85 pf (WT type) are presented in Table 12. By employing the TDO and GTO algorithms, the APL is reduced to 7.03 KW, which is a 96.87% reduction; this is better than the other optimization approach, I-DBEA [27], as mentioned in Table 12.
Moreover, the SOF is optimized to solve the problem of OADG with the integration of three PV (unity pf) and three WT (0.85pf) for QPL minimization. The results and a discussion of the findings are presented in Table A5 and Table A6 in Appendix A.

VP Load Model

This section extends the OADG issue for practical non-linear load models to show how strongly power demands rely on the voltage of the network. In the base case, the APL for an industrial load model is 171.72KW, for a residential load model, it is 165.31KW, and for a commercial load model, it is 157.39 KW. Table 13 shows the results of the SOF based on APL minimization for the optimum placement and sizing of DGs at unity pf (PV-type). It can be seen from the table that the APL is reduced to 28.71 KW (83.28%), 37.61 KW (77.25%), and 41.07 KW (73.91%) for industrial, residential, and commercial load models, respectively, for both the TDO and GTO algorithms. The obtained results are compared with another optimization method, BAT [50], as mentioned in Table 13. The proposed algorithms show better results in terms of APL reduction.
Likewise, Table 14 represents the results of the OADG at 0.85 pf (WT type) for APL minimization for the different load models. The APL is reduced to 3.89 KW (97.73) for the industrial load model, to 3.87 KW (97.66%) for the residential load model, and for a commercial load model, it is reduced to 3.83 KW (97.57%) for both the TDO and GTO algorithms.
Moreover, the study has been expanded to solve the problem of the optimal allocation of DGs for reactive power loss minimization (QPL) for VP load models, with the integration of three PV (unity pf) and three WT (0.85 pf). The results of the QPL minimization and a discussion of the findings are presented in Table A7 and Table A8 in Appendix A.

Voltage Profiles for a 69-Bus RDS

Figure 8 illustrates the impact of the installation of various types of DGs on the voltage profile for a 33-bus RDS under various types of loads, i.e., constant, residential, commercial, and industrial load models. In Figure 8, “Const” stands for constant, “Res” denotes the residential load, “Comm” denotes the commercial load, and ”Ind” stands for the industrial load. The outer values of the graphs represent the “bus number” and the inner values represent the “bus voltage” corresponding to the particular bus number.

Active Power Losses for a 69-Bus RDS

Figure 9 depicts the active power loss information for each bus of a 33-bus RDS after the integration of three PV (unity pf) and three WT (0.85 pf), under various types of loads, i.e., constant, residential, commercial, and industrial loads, under scenario 1.

Convergence Characteristics for 69 Bus RDS

Figure 10a,b displays the convergence characteristics of the GTO and TDO algorithms at various power factors (unity and 0.85) for the CP load model. It is apparent from the figure that the GTO algorithm has higher efficiency than the TDO algorithm.

4.2.2. Evaluation of Multi-Objective Function (MOF)

In this scenario, the TDO and GTO algorithms are employed to optimize the MOF, using APL, VD, VSI, and OCI to solve the problem of OADG in RDS, considering the CP load model and VP load models for three PV (unity pf) and three WT (0.85 pf).

CP Load Model

Table 15 presents the results of the MOF in terms of APL reduction, VD minimization, VSI maximization, and the minimization of the total operating costs for the optimum placement and sizing of DGs for three PV (unity pf) and three WT (0.85 pf). The total power loss of the system in the base case is (224.60KW + j101.99KVAR); the voltage deviation is 0.09803 p.u., the VSI is 0.6855, and the operating cost is 17.274315 million USD (M$).
It can be seen from Table 15 that at unity pf (PV type), the APL is reduced to 69.19 KW (69.19%) for the TDO algorithm and 68.20 KW (69.18%) for the GTO algorithm. The VD obtained by employing the TDO and GTO algorithms is 0.002093 p.u. and 0.002074 p.u., respectively, while the value of VSI computed for the TDO and GTO algorithms is 0.9477 p.u. and 0.9478 p.u., respectively, and the operating cost index for the TDO and GTO algorithms is 8280 and 8278, respectively. Furthermore, the cost savings for the GTO and TDO algorithms at unity pf (PV-type) after 20 years are 17.20% and 17.22%, respectively.
Similarly, at 0.85 pf (WT type), the APL is reduced to 7.21 KW (96.76%) for both the TDO and GTO algorithms. The VD obtained by employing the GTO and TDO algorithms is 0.000339 p.u. and 0.000332 p.u., respectively, while the value of VSI computed for both the TDO and GTO algorithms is 0.9773 p.u., and the operating cost index for the TDO and GTO algorithms is 8332 and 8330, respectively. Moreover, the cost savings for the TDO and GTO algorithms at 0.85 pf (WT type) after 20 years are 16.68% and 16.78%, respectively. It can be concluded that compared to 0.85 pf (WT type), the results of the cost-saving process for unity pf (PV type) are high.

VP Load Model

The results of MOF in terms of APL reduction, VD minimization, VSI maximization, and the minimization of total operating cost for the optimum placement and sizing of DGs for VP load models for three PV (unity pf) and three WT (0.85 pf) are shown in Table 16 and Table 17.
It can be seen from Table 16 that at unity pf (PV type), by employing the TDO algorithm, the APL was reduced to 29.44 KW (82.86%) for the industrial load model, for the residential load model, APL is reduced to 38.23 KW (76.87%), and for the commercial load model, APL is reduced to 41.70 KW (73.50%) while by employing the GTO algorithm, the APL is reduced to 29.44 KW (82.86%) for the industrial load model, 38.21 KW (76.88%) for the residential load model; for the commercial load model, APL is reduced to 41.73 KW (73.49%). The obtained VD from the TDO algorithm for an industrial load model is 0.000882 p.u., for a residential load model, it is 0.00117 p.u., and for a commercial load model, it is 0.00129 p.u., while the VD obtained from the GTO algorithms is 0.000876 p.u. for the industrial load model, 0.00117 p.u. for the residential load model, and for the commercial load model, it is 0.00127 p.u. The VSI computed by employing the TDO algorithm for the industrial load model is 0.9714 p.u., for residential is 0.9665 p.u. and for commercial load models is 0.9643 p.u. while for the GTO algorithm, it is 0.9714 p.u., 0.9660 p.u., and 0.9647 p.u. for industrial, residential, and commercial load models, respectively. The operating cost index obtained from the TDO and GTO algorithms for industrial load is 0.8311, for residential 0.8353 and 0.8352, and for commercial 0.8387 and 0.8383, respectively.
Besides this, the cost saving after 20 years for the industrial load model will be 16.89% for both the TDO and GTO algorithms; for a residential load it will be 16.47% and 16.48% for the TDO and GTO algorithms, and for a commercial load, it will be 16.13% and 16.17% for the TDO and GTO algorithms, respectively.
Moreover, the results of the OADG for MOF at 0.85 pf (WT type) are shown in Table 17. By employing TDO, the APL is reduced to 3.95 KW (97.70%) for the industrial load model, 3.93 KW (97.62%) for the residential load model, and 3.88 KW (97.54%) for the commercial load model, while by employing the GTO algorithm, the APL is reduced to 3.96 KW (97.69%), 3.93 KW (97.62%), and 3.88 KW (96.54%) for the industrial, residential, and commercial load models, respectively. The obtained VD from the TDO and GTO algorithms for the industrial load model is 0.0000890 p.u., and for the residential load model, it is 0000888 p.u., while the VD obtained from the TDO and GTO algorithms for a commercial load model is 0.0000887 p.u. and 0.0000882 p.u., respectively. The VSI computed for the industrial, residential, and commercial load models by employing both the TDO and GTO algorithms is 0.9778 p.u., 0.9777 p.u., and 0.9777 p.u., respectively. The operating cost index obtained from the TDO and GTO algorithms after 20 years for industrial load is 0.8317 and 0.8315, for residential load, it is 0.8336, and for commercial load, it is 0.8358, respectively. Besides this, the cost-saving after 20 years for the industrial load will be 16.83% and 16.85% for the TDO and GTO algorithms, for residential load, it will be 16.65% for both the TDO and GTO algorithms, and for commercial load, it will be 16.42% for both the TDO and GTO algorithms, respectively.
It can be concluded that compared to 0.85 pf (WT type), the results of the MOF in terms of APL reduction, the minimization of VD and OCI, and the maximization of VSI are improved at 0.85 pf (WT type). Furthermore, the maximum cost saving is achieved at 0.85 pf (WT- type) for the residential and commercial load models, while for the industrial load model, the maximum cost saving occurs when the DG operates at unity pf (PV type).

5. Conclusions

In this study, two metaheuristic optimization algorithms, the TDO and GTO algorithms, are employed to establish the optimal placement and sizing of renewable-based DGS (PV and WT) at unity and 0.85 pf. The proposed algorithms are utilized to optimize single- and multi-objective functions. A reduction in active and reactive power loss is achieved through optimizing a single-objective function, while a multi-objective function is optimized to reduce the active power loss, minimize the voltage deviation, maximize the voltage stability index, and minimize the total operating cost index. These objectives are achieved by using a multi-objectivity approach, i.e., a weighted sum method. The effectiveness and the validation of the proposed algorithms are examined on IEEE 33-bus and IEEE 69-bus RDNs. As the SOF, the active power loss for both the TDO and GTO algorithms at 0.85 pf is more reduced than other existing optimization algorithms, that is, 93.15% and 96.87% of the initial value for a 33-bus and for a 69-bus RDN, respectively. The proposed algorithms are also examined for PV-DG and WT-DG on IEEE 33- and IEEE 69-bus RDNs, considering voltage-dependent load models such as industrial, residential, and commercial load models; they also show better results compared to the existing optimization techniques, in terms of power loss reduction. For the SOF, the proposed GTO algorithm outperformed the other proposed TDO algorithm in terms of efficiency in converging for a solution, while for MOF, the results of APL minimization for the GTO algorithm are comparable to the other proposed TDO algorithm, but, in terms of other objectives, such as VD minimization, OCI minimization, and VSI maximization, the GTO algorithm offers better results than the TDO algorithm. Therefore, both the GTO and TDO algorithms can be used for the optimal placement and sizing of DGs in DN. In the future, subsequent studies can be extended to the higher bus systems while considering the intermittent nature of renewable sources and the uncertainties related to the load demand, working with daily load patterns and seasonal variations.

Author Contributions

Conceptualization, H.U.R. and A.H.; methodology, H.U.R., W.H., S.A.A.K. and S.A.A.; software, H.U.R., A.H. and S.A.A.; validation, H.U.R., W.H., M.H. and S.A.A.K.; formal analysis, M.H., A.H. and W.H.; investigation, H.U.R. and S.A.A.K.; resources, A.H., M.H. and W.H.; data curation, M.H., A.H., W.H. and S.A.A.; writing—original draft preparation, H.U.R., W.H., M.H. and S.A.A.K.; writing—review and editing, H.U.R., W.H., M.H. and S.A.A.K.; visualization, M.H., A.H. and W.H.; supervision, S.A.A.K. and W.H.; project administration, S.A.A.K. and W.H.; funding acquisition, A.H. and W.H. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Abbreviations

RDNRadial Distribution NetworkOCIOperating Cost Index
VDVoltage DeviationPDGActive Power of DG
APLActive Power LossPWFPresent Worth Factor
QPLReactive Power LossDGMDG maintenance cost
VSIVoltage Stability IndexDGODG operational cost
DGDistributed GenerationsDGINVDG investment cost
OADGOptimal Allocation of DGOCTDGTotal operating cost of DG
GTOArtificial Gorilla Troops OptimizationInf_RInflation Rate
TDOTasmanian Devil OptimizationInt_RInterest Rate

Appendix A

The flow chart in Figure 1 for the optimal allocation of the DG with the GTO algorithm is explained through pseudo code for greater clarity in Algorithm A1.
Algorithm A1: Pseudo Code of GTO algorithm
1. Set size of population (gorilla’s) N, maximum iteration T, upper bound ub, lower bound lb
 GTO parameters p and β
2. Initialize the random gorilla locations Xi (i = 1, 2, 3, ……, N)
3. Calculate the objective fitness function for each gorilla
4.while (Termination criteria not met) do
5.     Update the value of C using Equation (29)
6.     Update the value of L using Equation (31)
7.% Exploration phase
8.     for i = 1: N do
9.        if rand < p then
10.            Gorilla location is updated using Equation (28a)
11.         else
12.            if rand ≥ 0.5 then
13.                Gorilla location is updated using Equation (28b)
14.            else
15.                Gorilla location is updated using Equation (28c)
16.            end if
17.         end if
18.     end for
19. Calculate the objective fitness function for updated gorilla location
20. If the fitness value of newly gorilla is better than the previous gorilla, replace with previous.
 Set the gorilla location best location so far
21.% Exploitation phase
22.    for i = 1: N do
23.        if C ≥ W then
24.            Gorilla location is updated using Equation (34)
25.         else
26.            Gorilla location is updated using Equation (37)
27.         end if
28.     end for
29. Calculate the objective fitness function for updated gorilla location
30. If the fitness value of newly gorilla is better than the previous gorilla, replace with previous.
 Set the gorilla location best location so far
31.end while
32. Display the best solution
Similarly, the flow chart in Figure 2 for the optimal allocation of the DG via the GTO algorithm is explained through pseudo code for greater clarity in Algorithm A2.
Algorithm A2: Pseudo Code of TDO algorithm
1. Set the size of population (Tasmanian devils) N, maximum iteration T, upper bound ub, lower bound lb
2. Initialize the random Tasmanian devil locations
3. Calculate the objective fitness function for each Tasmanian devil
4.while (Termination criteria not met) do
8.      for i = 1: N do
          pr = rand
9.          if pr < 0.5 then
 % Exploration phase (Selection of carrion and feeding by eating them)
11.                Choose the carrion by using Equation (41)
19.                Calculate the objective fitness function for the selected carrion then
20.                New location of the Tasmanian devil is calculated by using Equation (42) then
                Location of the Tasmanian devil is updated using Equation (43) based on the
 objective function fitness value
          else
21. % Exploitation phase (Selection of prey and attacking)
22.                 Choose the prey by using Equation (44)
23.                 Calculate the objective fitness function for the selected prey then
24.                 New location of the Tasmanian devil is calculated by using Equation (45) then
25.                 Location of the Tasmanian devil is updated using Equation (46) based on the
 objective function fitness value
                 Chasing of prey
                 The value of neighborhood radius (r) for chasing process is calculated by using Equation (47)
                 New location of the Tasmanian devil is for chasing process is calculated by using Equation (48)
                 Location of the Tasmanian devil is updated using Equation (49) based on the
 objective function fitness value
28.       end if
29. Calculate the objective fitness function for updated Tasmanian devil location
30. If the fitness value of new Tasmanian devil is better than the previous, replace with previous.
 Keep the best solution so far.
31.       end for
end while
32. Display the best solution
The results of Table A1 at unity pf show that with the integration of the three DGs, reactive power loss (QPL) is reduced to 49.22 KVAR for both the TDO and GTO algorithms, which is a 65.44% reduction with respect to the base value. Similarly, from Table A2, it can be seen that at 0.85 pf, the QPL is reduced to 11.68 KVAR for both the GTO and TDO algorithms after the integration of three DGs, which is a 91.80% reduction with respect to the base value. It can be concluded that the maximum reduction of the QPL is at 0.85 pf (WT type).
Table A1. Results of OADG for a 33-bus RDN for SOF (QPL minimization) at unity pf (PV type) in a CP load model.
Table A1. Results of OADG for a 33-bus RDN for SOF (QPL minimization) at unity pf (PV type) in a CP load model.
MethodsLocationDG Size (KVAR)QPL (KVAR)
QPLR (%)
VD (p.u.)VSI (p.u.)
Base case--142.440.13280.6672
TDO [P]13, 24, 30926, 1135, 116049.22 (65.44)0.0117660.8901
GTO [P]24, 30, 131135, 1160, 92649.22 (65.44)0.0117660.8901
Table A2. Results of OADG for a 33-bus RDN for SOF (QPL minimization) at 0.85 pf (WT type) in a CP load model.
Table A2. Results of OADG for a 33-bus RDN for SOF (QPL minimization) at 0.85 pf (WT type) in a CP load model.
MethodsLocationDG SizeQPL (KVAR)
QPLR (%)
VD (p.u.)VSI (p.u.)
(KW)(KVAR)
Base case---142.440.13280.6672
TDO [P]24, 13, 301104, 867, 1298599, 494, 80411.68 (91.80%)0.0006310.9671
GTO [P]24, 13, 301102, 869, 1299599, 492, 80511.68 (91.80%)0.0006310.9671
The QPL in the base case for an industrial load model is 110.42 KVAR, for a residential load model, it is 107.19 KVAR, and for a commercial load model, it is 102.70 KVAR. The results of the SOF, based on QPL minimization for the optimum placement and sizing of multiple DGs at unity pf (PV-type), are presented in Table A3. It can be seen that after the integration of three DGs, the QPL is reduced to 24.54 KVAR (77.77%) for the industrial load model, for residential APL, it is reduced to 29.48 KVAR (72.49%), and for a commercial load model, it is reduced to 31.24 KVAR (65.68%) for both the TDO and GTO algorithms.
Table A3. Results of OADG for a 33-bus RDN for SOP (QPL minimization) at unity pf (PV type) in a VP load model.
Table A3. Results of OADG for a 33-bus RDN for SOP (QPL minimization) at unity pf (PV type) in a VP load model.
ParametersUnity pf (PV Type)
IndustrialResidentialCommercial
Base caseQPL (KVAR)110.42107.19102.70
VD (p.u.)0.0986370.0978210.094018
VSI (p.u.)0.707410.709530.71526
TDO [P]QPL (KVAR)24.5429.4831.24
QPLR (%)77.7772.4965.68
Location13, 30, 2430, 24, 1313, 24, 30
DG Size (KW)901, 1112, 11301059, 1105, 849808, 1085, 1016
DG Size (KVAR)---
DG Size (KVA)314330132909
VD (p.u.)0.0059640.0073050.007765
VSI (p.u.)0.92080.91270.9103
GTO [P]QPL (KVAR)24.5429.4831.24
QPLR (%)77.7772.4965.68
Location13, 30, 2424, 30, 1313, 30, 24
DG Size (KW)901, 1112, 11301105, 1059, 849808, 1016, 1085
DG Size (KVAR)---
DG Size (KVA)314330132909
VD (p.u.)0.0059640.0073050.007765
VSI (p.u.)0.92080.91270.9103
Similarly, the results of OADG for QPL reduction at 0.85 pf (WT type) for the different load models are described in Table A4. The QPL for the industrial load model is reduced to 8.66 KVAR (92.15%), for the residential load model, QPL is reduced to 8.50 KVAR (92.07%), and for the commercial load model, QPL is reduced to 8.41 KVAR (91.81%) for both the TDO and GTO algorithms. From the results of Table A3 and Table A4, it can be concluded that with the integration of three DGs, the QPL minimization at 0.85pf (WT type) is at maximum compared to unity pf.
Table A4. Results of OADG for a 33-bus RDN for SOF (QPL minimization) at 0.85 pf (WT type) in a VP load model.
Table A4. Results of OADG for a 33-bus RDN for SOF (QPL minimization) at 0.85 pf (WT type) in a VP load model.
Parameters0.85 pf (WT Type)
IndustrialResidentialCommercial
Base caseQPL (KVAR)110.42107.19102.70
VD (p.u.)0.0986370.0978210.094018
VSI (p.u.)0.707410.709530.71526
TDO [P]QPL (KVAR)8.668.508.41
QPLR (%)92.1592.0791.81
Location24, 13, 3024, 30, 1313, 24, 30
DG Size (KW)1128, 895, 10971092, 1105, 825777, 1065, 1092
DG Size (KVAR)457, 259, 680505, 685, 329356, 523, 677
DG Size (KVA)341833823221
VD (p.u.)0.0005420.0005330.000518
VSI (p.u.)0.96940.96990.9705
GTO [P]QPL (KVAR)8.668.508.41
QPLR (%)92.1592.0791.81
Location30, 13, 2424, 13, 3030, 24, 13
DG Size (KW)1097, 895, 11281091, 1106, 8251092, 1065, 777
DG Size (KVAR)680, 259, 457504, 685, 329677, 522, 356
DG Size (KVA)341833823321
VD (p.u.)0.0005410.0005350.000517
VSI (p.u.)0.96950.96990.9705
The results of OADG at unity pf (PV type) for QPL minimization in a CP load model are presented in Table A5. It can be seen from the table that with the integration of the DGs, QPL is reduced to 31.63 KVAR for both the TDO and GTO algorithms, which is a 68.99% reduction with respect to the base value.
Similarly, the QPL is reduced to 3.96 KVAR for both the GTO and TDO algorithms after the integration of DGs, which is a 96.12% reduction with respect to the base value, as can be seen from Table A6. From the results, it can be concluded that the QPL minimization is at maximum at 0.85 pf (WT type), compared to the unity pf (PV type).
Table A5. Results of OADG for a 69-bus RDN for QPL minimization at unity pf (PV Type) in a CP load model.
Table A5. Results of OADG for a 69-bus RDN for QPL minimization at unity pf (PV Type) in a CP load model.
MethodsLocationDG Size (KVAR)QPL (KVAR)
QPLR (%)
VD (p.u.)VSI (p.u.)
Base case--101.990.098030.68548
TDO [P]50, 17, 61800, 617, 200031.63 (68.99%)0.0038040.9371
GTO [P]17, 61, 50617, 2000, 80031.63 (68.99%)0.0038040.9371
Table A6. Results of OADG for a 69-bus RDN for QPL minimization at 0.85 pf (WT type) with a CP load model.
Table A6. Results of OADG for a 69-bus RDN for QPL minimization at 0.85 pf (WT type) with a CP load model.
MethodsLocationDG Size QPL (KVAR)VD (p.u.)VSI (p.u.)
(KW)(KVAR)QPLR (%)
Base case---101.990.098030.68548
TDO [P]50, 12, 61830, 1076 1700503, 667 10543.96 (96.12%)0.001760.9577
GTO [P]50, 12, 61830, 1076 1700503, 667 10543.96 (96.12%)0.001760.9577
Furthermore, the QPL in the base case for the industrial load model is 79.23 KVAR, for the residential load model is 76.52 KVAR, and for the commercial load model, it is 73.13 KVAR. The results of the SOF based on QPL minimization for the optimum placement and sizing of multiple DGs at unity pf (PV-type) are presented in Table A7. After the integration of DGs, the QPL is reduced to 14.45 KVAR (81.76%) for the industrial load model, 18.23 KVAR (76.17%) for the residential load model, and QPL is reduced to 19.73 KVAR (73.02%) for the commercial load model for both the TDO and GTO algorithms.
Table A7. Results of OADG for a 69-bus RDN for QPL minimization at unity pf (PV type) in a VP load model.
Table A7. Results of OADG for a 69-bus RDN for QPL minimization at unity pf (PV type) in a VP load model.
ParametersUnity pf (PV Type)
IndustrialResidentialCommercial
Base caseQPL (KVAR)79.2376.5273.13
VD (p.u.)0.0798550.0764620.072316
VSI (p.u.)0.715050.72180.72986
TDO [P]QPL (KVAR)14.4518.2319.73
QPLR (%)81.7676.1773.02
Location61, 50, 1750, 17, 6117, 50, 61
DG Size (KW)1943, 798, 611796, 594, 1833581, 793,1748
DG Size (KVAR)---
DG Size (KVA)335232233122
VD (p.u.)0.0020710.0024770.002617
VSI (p.u.)0.95590.95120.9498
GTO [P]QPL (KVAR)14.4518.2319.73
QPLR (%)81.7676.1773.02
Location61, 50, 1717, 50, 6150, 61, 17
DG Size (KW)1942, 799, 612594, 796, 1833793, 1748, 581
DG Size (KVAR)---
DG Size (KVA)355332233122
VD (p.u.)0.0020680.0024770.002618
VSI (p.u.)0.95580.95120.9498
Similarly, the results of OADG for QPL reduction at 0.85 pf (WT type) for different load models are described in Table A8. The QPL for the industrial load model is reduced to 2.24 KVAR (97.17%), for the residential model, it is reduced to 2.17 KVAR (97.16%), and for the commercial load model, QPL is reduced to 2.12 KVAR (97.11%) for both the TDO and GTO algorithms.
Table A8. Results of OADG for a 69-bus RDN for SOF (QPL minimization) at 0.85 pf (WT type) in a VP load model.
Table A8. Results of OADG for a 69-bus RDN for SOF (QPL minimization) at 0.85 pf (WT type) in a VP load model.
ParametersUnity pf (PV Type)
IndustrialResidentialCommercial
Base caseQPL (KVAR)79.2376.5273.13
VD (p.u.)0.0798550.0764620.072316
VSI (p.u.)0.715050.72180.72986
TDO [P]QPL (KVAR)2.242.172.12
QPLR (%)97.1797.1697.11
Location18, 50, 6117, 50, 6150, 61, 17
DG Size (KW)627, 836, 1837602, 824, 1755828, 1709, 582
DG Size (KVAR)347, 517, 790362, 511, 959513, 1034, 360
DG Size (KVA)369136703656
VD (p.u.)0.0003530.0002830.000230
VSI (p.u.)0.98080.98110.9818
GTO [P]QPL (KVAR)2.242.172.12
QPLR (%)97.1797.1697.11
Location18, 50, 6117, 50, 6150, 61, 17
DG Size (KW)627, 836, 1837602, 824, 1755828, 1709, 582
DG Size (KVAR)347, 517, 790362, 511, 959513, 1034, 360
DG Size (KVA)369136703656
VD (p.u.)0.0003530.0002830.000230
VSI (p.u.)0.98080.98110.9818

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Figure 1. Flow chart of the GTO algorithm to solve the problem of OADG.
Figure 1. Flow chart of the GTO algorithm to solve the problem of OADG.
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Figure 2. Flow chart of the TDO algorithm to solve the problem of OADG.
Figure 2. Flow chart of the TDO algorithm to solve the problem of OADG.
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Figure 3. Single-line diagram of a 33-bus RDS.
Figure 3. Single-line diagram of a 33-bus RDS.
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Figure 4. Voltage profiles for an IEEE 33-bus system for different loads in different cases for scenario 1.
Figure 4. Voltage profiles for an IEEE 33-bus system for different loads in different cases for scenario 1.
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Figure 5. Active power loss for a 33-bus RDS for various types of loads, under scenario 1.
Figure 5. Active power loss for a 33-bus RDS for various types of loads, under scenario 1.
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Figure 6. Convergence characteristics of the TDO and GTO algorithms for an IEEE 33-bus system under scenario 1 at different pf; (a) unity pf (b) 0.85 pf.
Figure 6. Convergence characteristics of the TDO and GTO algorithms for an IEEE 33-bus system under scenario 1 at different pf; (a) unity pf (b) 0.85 pf.
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Figure 7. Single-line diagram of a 69-bus RDS.
Figure 7. Single-line diagram of a 69-bus RDS.
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Figure 8. Voltage profiles for an IEEE 69-bus system for different loads at different cases in scenario 1.
Figure 8. Voltage profiles for an IEEE 69-bus system for different loads at different cases in scenario 1.
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Figure 9. Active power loss for 69 buses under various types of loads for scenario 1.
Figure 9. Active power loss for 69 buses under various types of loads for scenario 1.
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Figure 10. Convergence characteristics of the TDO and GTO algorithms for an IEEE 69-bus system for scenario 1 at different pf: (a) Unity pf (PV type), (b) 0.85 pf (WT type).
Figure 10. Convergence characteristics of the TDO and GTO algorithms for an IEEE 69-bus system for scenario 1 at different pf: (a) Unity pf (PV type), (b) 0.85 pf (WT type).
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Table 1. Summary of optimization techniques used for OADG in RDNs.
Table 1. Summary of optimization techniques used for OADG in RDNs.
Ref.YearOptimization MethodsObjective FunctionsLoad Model
APLQPLVDVSICostVP
[7]2019Analytical
[41]2019ASFL
[42]2019BBO
[43]2019MOHTLGOGWO
[15]2019CSFS
[44]2019LSF + GWO
[22]2019GA
[12]2019VSMI + CFT
[14]2019Heuristic
[24]2019QODELFA
[1]2020MLPSO
[23]2020QOCSOS
[45]2020IRRO
[28]2020CSCA
[37]2020OTCDE
[30]2020EAEO
[46]2020APSO and MGSA
[10]2020MINLP(GAMS)
[29]2020IHHO
[47]2020PSO and MOPSO
[19]2020BPSO-SLFA
[48]2020MSMO
[25]2020MRFO
[49]2020PPA
[27]2021I-DBEA
[36]2021ABC
[50]2021BAT
[16]2021Fine tunned PSO
[17]2021SPPA
[38]2021SKHA
[8]2022Analytical
[51]2022Improve MOPSO
[33]2022POFA
[26]2022I-GWOPSO
[39]2022ACO
[21]2022CFA
[20]2022QOFBI
[18]2022AO
[52]2022Modified FPA
[53]2023Mixed integer GA
[54]2023MOWOA
[55]2023NSGA-II
[P]2023TDO, GTO
Note: P—Proposed; VP—voltage-dependent (variable) power.
Table 2. Load types and exponent values.
Table 2. Load types and exponent values.
Load Typesαβ
Constant00
Residential0.924.04
Commercial1.513.40
Industrial0.186.0
Table 3. Control parameter settings.
Table 3. Control parameter settings.
AlgorithmsParameters
GTOpopulation = 50, max-iter = 200, DG-size (MVA) = 0–2000, β = 3, p = 0.03, W = 0.8
TDOpopulation = 50, max-iter = 200, DG-size (MVA) = 0–2000
Table 6. Results comparison of OADG for 33 bus RDN for the SOF (APL minimization) at unity pf (PV type) in the VP load model.
Table 6. Results comparison of OADG for 33 bus RDN for the SOF (APL minimization) at unity pf (PV type) in the VP load model.
MethodsParametersIndustrialResidentialCommercial
Base caseAPL (KW)163.22158.76152.32
VD (p.u.)0.0986370.0978210.094018
VSI (p.u.)0.707410.709530.71526
BAT [50]Location13, 25, 3013, 25, 3013, 25, 30
DG size (KW)790, 850, 1020720, 830, 980710, 820, 940
APL (KW)36.0143.7046.42
APLR (%)77.9972.5369.57
VD (p.u.)---
VSI (p.u.)0.90690.89740.8959
TDO [P]Location14, 24, 3024, 30, 1424, 30, 14
DG size (KW)843, 1187, 11631158, 1108, 7931132, 1065, 756
APL (KW)34.5542.0544.80
APLR (%)78.8373.5170.59
VD (p.u.)0.0058410.0071530.007595
VSI (p.u.)0.92450.91640.9139
GTO [P]Location14, 24, 3024, 14, 3030, 24, 14
DG size (KW)843, 1187, 11631158, 793, 11081064, 1136, 755
APL (KW)34.5542.0544.80
APLR (%)78.8373.5170.59
VD (p.u.)0.0058410.0071520.007599
VSI (p.u.)0.92450.91640.9139
Table 7. Results of the OADG for a 33-bus RDN for SOP (APL minimization) at 0.85 pf (WT type) in the VP load model.
Table 7. Results of the OADG for a 33-bus RDN for SOP (APL minimization) at 0.85 pf (WT type) in the VP load model.
Parameters0.85 pf (WT Type)
IndustrialResidentialCommercial
Base caseAPL (KW)163.22158.76152.32
VD (p.u.)0.0986370.0978210.094018
VSI (p.u.)0.707410.709530.71526
TDO [P]APL (KW)10.5310.3810.33
APLR (%)93.5593.4693.22
Location24, 13, 3030, 13, 2430, 24, 13
DG Size (KW)1181, 869, 11291137, 798, 11391123, 1111, 750
DG Size (KVAR)477, 250, 700704, 321, 531696, 553, 349
DG Size (KVA)348434453385
VD (p.u.)0.0005170.0005070.000486
VSI (p.u.)0.96940.96980.9705
GTO [P]APL (KW)10.5310.3810.33
APLR (%)93.5593.4693.22
Location24, 13, 3024, 13, 3030, 24, 13
DG Size (KW)1182, 868, 11291140, 798, 11371123, 1111, 750
DG Size (KVAR)477, 249, 700532, 321, 705696, 553, 350
DG Size (KVA)348434473385
VD (p.u.)0.0005160.0005050.000486
VSI (p.u.)0.96940.96980.9705
Table 8. Results of OADG for a 33-bus RDN for MOF in the CP load model.
Table 8. Results of OADG for a 33-bus RDN for MOF in the CP load model.
ParametersBase CaseUnity pf (PV Type)0.85 pf (WT Type)
TDO [P]GTO [P]TDO [P]GTO [P]
APL (KW)210.0771.74 72.0214.65 14.66
APLR (%)-65.85%65.72%93.03%93.02%
Location-30, 24, 1414, 30, 24 13, 30, 24 13, 30, 24
DG Size (KW)-1371, 1282, 913 922, 1393, 1273 884, 1368, 1205 874, 1367, 1239
DG Size (KVAR)-- 504, 848, 660 509, 847, 643
DG Size (KVA)-3566358840004013
VD (p.u.)0.13280.007390 0.0068940.0002870.000291
VSI (p.u.)0.66720.9160 0.91890.97530.9753
OCDG (M$)16.8379720.9469490.8537641.1696091.071008
DGM (M$)-2.1853732.1988562.1185742.132669
DGO (M$)-9.0536899.1095458.7769508.835345
DGIC (M$)-1.42641.4352 1.3828 1.3920
OCTDG (M$)16.83797213.61241213.59736513.44793313.431022
OCI1.00.80840.80750.79870.7977
Note: (M$)—Million USD.
Table 9. Results of the OADG for a 33-bus RDN for MOF at unity pf (PV Type) in a VP load model.
Table 9. Results of the OADG for a 33-bus RDN for MOF at unity pf (PV Type) in a VP load model.
ParametersUnity pf (PV Type)
IndustrialResidentialCommercial
Base caseAPL (KW)163.22158.76152.32
VD (p.u.)0.0986370.0978210.094018
VSI (p.u.)0.707410.709530.71526
OC (M$)16.48464815.85945415.371032
ParametersTDO [P]GTO [P]TDO [P]GTO [P]TDO [P]GTO [P]
With 3 DGsAPL (KW)35.09 35.0942.69 42.7045.50 45.50
APLR (%)78.50%78.50%73.11%73.10%70.13%70.13%
Location14, 30, 2424, 30, 1414, 24, 3014, 24, 3030, 14, 2424, 13, 30
DG Size (KW)893, 1255, 12611257, 1256, 894 829, 1224, 1230827, 1231, 12321199, 1197, 788 1199, 843, 1161
DG Size (KVAR)- - -
DG Size (KVA)34093407 3283 3290 31843203
VD (p.u.)0.003740.003730.004720.004720.004980.00485
VSI (p.u.)0.9385 0.9386 0.93310.93330.93190.9302
OCDG (M$)1.310889 1.3194781.2779431.247981.2539541.172408
DGM (M$)2.0891582.0879322.0119412.0162311.9512701.962914
DGO (M$)8.655083 8.6500058.335183 8.3529558.083833 8.132071
DGIC (M$)1.3636 1.36281.31321.3161.27361.2812
OCTDG (M$)13.41873013.420216 12.938267 12.933171 12.56265612.548593
OCI0.8141 0.81410.81580.81550.8173 0.8164
Table 10. Results of OADG for a 33-bus RDN for MOF at 0.85 pf (WT type) with a VP load model.
Table 10. Results of OADG for a 33-bus RDN for MOF at 0.85 pf (WT type) with a VP load model.
Parameters0.85 pf (WT Type)
IndustrialResidentialCommercial
Base caseAPL (KW)163.22158.76152.32
VD (p.u.)0.0986370.0978210.094018
VSI (p.u.)0.707410.709530.71526
OC (M$)16.48464815.85945415.371032
ParametersTDO [P]GTO [P]TDO [P]GTO [P]TDO [P]GTO [P]
With 3 DGsAPL (KW)10.69 10.69 10.50 10.51 10.44 10.45
APLR (%)93.45% 93.45%93.39 %93.38% 93.15% 93.14%
Location30, 24, 13 30, 24, 13 30, 24, 13 13, 24, 30 13, 30, 24 30, 24, 13
DG Size (KW)1151, 1255, 901 1160, 1258, 894 1160, 1200, 824831, 1204, 1157 769, 1149, 1166 1151, 1170, 771
DG Size (KVAR)706, 484, 265708, 489, 267719, 531, 337331, 532, 717365, 712, 539713, 544, 360
DG Size (KVA)3613 3621 3558 3562 34823489
VD (p.u.)0.0002910.0002880.0002940.000294 0.000294 0.000293
VSI (p.u.)0.9755 0.9756 0.97550.97550.9755 0.9756
OCDG (M$)1.643765 1.6223481.564572 1.530298 1.532499 1.498209
DGM (M$)2.026649 2.029713 1.951270 1.9561731.8899861.894889
DGO (M$)8.396116 8.4088118.0838338.1041447.829943 7.850254
DGIC (M$)1.3228 1.3248 1.2736 1.2768 1.23361.2368
OCTDG (M$)13.389330 13.38567112.873275 12.86741412.48602912.480152
OCI0.8122 0.81200.8117 0.81130.8123 0.8119
Table 11. Results comparison of OADG for a 69-bus RDN for SOF (APL minimization) at unity pf (PV type) in the CP load model.
Table 11. Results comparison of OADG for a 69-bus RDN for SOF (APL minimization) at unity pf (PV type) in the CP load model.
MethodsLocationDG Size (KW)APL (KW)
APLR (KW)
VD (p.u.)VSI (p.u.)
Base case--224.600.098030.68548
BAT [50]12, 19, 61535, 340, 169368.97 (69.34)-0.9113
SOS-NNA [57]11, 18, 61526.8, 380.3, 171969.4284 (69.14)0.0052011.0887
IHHO [29]11, 17, 61527.2, 382.5, 1719.469.41 (69.15)--
QOFBI [20]11, 61, 18526.8, 1718.97, 380.0669.3972 (69.15)--
I-DBEA [27]61, 19, 112148.7, 471.7, 712.678.347 (65.17)0.00020.9772
TDO [P]18, 61, 11431, 1931, 52568.68 (69.42)0.0036130.9356
GTO [P]11, 18, 61525, 431, 193168.68 (69.42)0.0036130.9356
Table 12. Results comparison of OADG for a 69-bus RDN for the SOF (APL minimization) at 0.85 pf (WT type) with a CP load model.
Table 12. Results comparison of OADG for a 69-bus RDN for the SOF (APL minimization) at 0.85 pf (WT type) with a CP load model.
MethodsLocationDG SizeAPL (KW)
APLR (%)
VD (p.u.)VSI (p.u.)
KWKVAR
Base case---224.600.098030.68548
I-DBEA [27]61, 59, 161500, 370, 575-7.966 (96.45)0.0002660.9774
TDO [P]18, 61, 11428, 1700, 687265, 1054, 4267.03 (96.87%)0.0007180.9587
GTO [P]61, 18, 111700, 429, 6891054, 266, 4277.03 (96.87%)0.0007110.9588
Table 13. Comparative results of OADG for a 69-bus RDN for the SOF (APL minimization) at unity pf (PV Type) in a VP load model.
Table 13. Comparative results of OADG for a 69-bus RDN for the SOF (APL minimization) at unity pf (PV Type) in a VP load model.
MethodsParametersIndustrialResidentialCommercial
Base caseAPL (KW)171.7224165.3079157.3927
VD (p.u.)0.0798550.0764620.072316
VSI (p.u.)0.715050.72180.72986
BAT [50]Location12, 19, 6112, 19, 6112, 19, 61
DG size (KW)460, 320, 1670450, 310, 1570440, 300, 1480
APL (KW)28.8137.7341.33
APLR (%)83.1977.1173.66
VD (p.u.)---
VSI (p.u.)0.94310.93570.9314
TDO [P]Location61, 11, 18 18, 61, 1111, 61, 18
DG size (KW)1854, 543, 422 421, 1761, 424 517, 1656, 410
APL (KW)28.7137.5441.07
APLR (%)83.2877.2973.91
VD (p.u.)0.002009 0.0024280.002575
VSI (p.u.)0.9523 0.9477 0.9463
GTO [P]Location18, 11, 61 18, 11, 61 18, 11, 61
DG size (KW)424, 538, 1855 412, 523, 1748 402, 512, 1663
APL (KW)28.7137.5441.07
APLR (%)83.2877.2973.91
VD (p.u.)0.00201 0.002429 0.002575
VSI (p.u.)0.9523 0.9477 0.9463
Table 14. Results of the OADG for a 69-bus RDN for the SOF (APL minimization) at 0.85 pf (WT Type) in a VP load model.
Table 14. Results of the OADG for a 69-bus RDN for the SOF (APL minimization) at 0.85 pf (WT Type) in a VP load model.
Parameters0.85 pf (WT Type)
IndustrialResidentialCommercial
Base caseAPL (KW)171.7224165.3079157.3927
VD (p.u.)0.0798550.0764620.072316
VSI (p.u.)0.715050.72180.72986
TDO [P]APL (KW)3.893.873.83
APLR (%)97.7397.6697.57
Location11, 17, 6111, 61, 1861, 18, 11
DG Size (KW)546, 418, 1830544, 1711, 4021628, 400, 517
DG Size (KVAR)329, 217, 777337, 927, 239988, 248, 318
DG Size (KVA)309130522982
VD (p.u.)0.0001180.0001180.000118
VSI (p.u.)0.97780.97770.9777
GTO [P]APL (KW)3.893.873.82
APLR (%)97.7397.6697.57
Location11, 61, 1818, 61, 1161, 11, 18
DG Size (KW)546, 1830, 418403, 1712, 5421622, 539, 394
DG Size (KVAR)329, 777, 217239, 927, 336983, 334, 244
DG Size (KVA)309130522994
VD (p.u.)0.0001180.0001180.000116
VSI (p.u.)0.97780.97770.9777
Table 15. Results of OADG for a 69-bus RDN for MOF at unity pf (PV Type) and 0.85 pf (WT type) in a CP load model.
Table 15. Results of OADG for a 69-bus RDN for MOF at unity pf (PV Type) and 0.85 pf (WT type) in a CP load model.
ParametersBase CaseUnity pf (PV Type)0.85 pf (WT Type)
TDO [P]GTO [P]TDO [P]GTO [P]
APL (KW)224.6069.19 69.207.217.21
APLR (%)-69.19% 69.18%96.79% 96.79%
Location-61, 11, 1811, 61, 1717, 64, 6117, 61, 64
DG Size (KW)-2000, 682, 441 683, 2000, 444613, 350, 1678617, 1691, 338
DG Size (KVAR)---379, 217, 1040382, 1048, 209
DG Size (KVA)-31233127 3107 3112
VD (p.u.)0.098030.0020930.0020740.0003390.000332
VSI (p.u.)0.685480.94770.94780.97730.9773
OC (M$)17.2743153.2104583.193349 5.012274 4.990830
OCDG (M$)-1.913887 1.9163381.6185001.621564
DGM (M$)-7.9289607.939116 6.705214 6.717909
DGO (M$)-1.24921.25081.05641.0584
DGIC (M$)17.27431514.302505 14.29960314.39238814.388703
OCI1.00.82800.82780.83320.8330
Table 16. Results of OADG for 69 bus RDN for MOF at unity pf (PV Type) in VP load model.
Table 16. Results of OADG for 69 bus RDN for MOF at unity pf (PV Type) in VP load model.
ParametersUnity pf (PV Type)
IndustrialResidentialCommercial
Base caseAPL (KW)171.72165.31157.39
VD (p.u.)0.0798550.0764620.072316
VSI (p.u.)0.71510.72180.7299
OC (M$)16.90264416.30069215.831996
ParametersTDO [P]GTO [P]TDO [P]GTO [P]TDO [P]GTO [P]
With 3 DGsAPL (KW)29.44 29.44 38.23 38.21 41.7041.73
APLR (%)82.86% 83.86% 76.87% 76.88%73.50%73.49%
Location61, 18, 11 18, 61, 11 18, 61, 11 18, 11, 6118, 61, 1118, 61, 11
DG Size (KW)1996, 429, 616 431, 1996, 614419, 1887, 593 418, 601, 1882 411, 581, 1796 409, 1798, 590
DG Size (KVAR)- - -
DG Size (KVA)3041 30412899 2901 27882797
VD (p.u.)0.000882 0.000876 0.001170.00117 0.00129 0.00127
VSI (p.u.)0.9714 0.9714 0.9665 0.96600.9643 0.9647
OCDG (M$)3.2468203.2468143.3192583.310582 3.3755993.337137
DGM (M$)1.8636341.8636341.7766121.777837 1.708587 1.714102
DGO (M$)7.720771 7.7207717.3602487.365326 7.0784317.101281
DGIC (M$)1.2164 1.21641.15961.16041.11521.1188
OCTDG (M$)14.047625 14.04761913.615718 13.614146 13.27781713.271321
OCI0.83110.8311 0.83530.83520.83870.8383
Table 17. Results of the OADG for a 69-bus RDN for MOF at 0.85 pf (WT type) in the VP load model.
Table 17. Results of the OADG for a 69-bus RDN for MOF at 0.85 pf (WT type) in the VP load model.
Parameters0.85 pf (WT Type)
IndustrialResidentialCommercial
Base caseAPL (KW)171.72165.31157.39
VD (p.u.)0.0798550.0764620.072316
VSI (p.u.)0.71510.72180.7299
OC (M$)16.90264416.30069215.831996
ParametersTDO [P]GTO [P]TDO [P]GTO [P]TDO [P]GTO [P]
With 3 DGsAPL (KW)3.953.96 3.93 3.93 3.88 3.88
APLR (%)97.70%97.69%97.62%97.62%97.54%96.54%
Location18, 11, 61 11, 61, 18 18, 61, 11 61, 18, 11 61, 11, 18 61, 18, 11
DG Size (KW)422, 612, 1844 622, 1843, 418 406, 1732, 600 1727, 409, 602 1640, 595, 395 1641, 399, 590
DG Size (KVAR)220, 327, 775 323, 778, 220 241, 927, 335 928, 236, 352980, 354, 241 979, 242, 365
DG Size (KVA)3167 3171 3123 31303066 3071
VD (p.u.)0.0000890 0.00008900.0000888 0.0000888 0.0000887 0.0000882
VSI (p.u.)0.9778 0.9778 0.9777 0.9777 0.9777 0.9777
OCDG (M$)3.8367397 3.8153204 3.862792 3.862786 3.891135 3.891138
DGM (M$)1.763742 1.7668061.677945 1.677945 1.611759 1.611759
DGO (M$)7.306932 7.319626 6.951487 6.951487 6.677286 6.677286
DGIC (M$)1.1512 1.1532 1.0952 1.0952 1.052 1.052
OCTDG (M$)14.058613 14.054953 13.587424 13.587417 13.23218013.232183
OCI0.8317 0.83150.8336 0.8336 0.8358 0.8358
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Rehman, H.U.; Hussain, A.; Haider, W.; Ali, S.A.; Kazmi, S.A.A.; Huzaifa, M. Optimal Planning of Solar Photovoltaic (PV) and Wind-Based DGs for Achieving Techno-Economic Objectives across Various Load Models. Energies 2023, 16, 2444. https://doi.org/10.3390/en16052444

AMA Style

Rehman HU, Hussain A, Haider W, Ali SA, Kazmi SAA, Huzaifa M. Optimal Planning of Solar Photovoltaic (PV) and Wind-Based DGs for Achieving Techno-Economic Objectives across Various Load Models. Energies. 2023; 16(5):2444. https://doi.org/10.3390/en16052444

Chicago/Turabian Style

Rehman, Habib Ur, Arif Hussain, Waseem Haider, Sayyed Ahmad Ali, Syed Ali Abbas Kazmi, and Muhammad Huzaifa. 2023. "Optimal Planning of Solar Photovoltaic (PV) and Wind-Based DGs for Achieving Techno-Economic Objectives across Various Load Models" Energies 16, no. 5: 2444. https://doi.org/10.3390/en16052444

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