Distribution network reconfiguration considering DGs using a hybrid CS-GWO algorithm for power loss minimization and voltage profile enhancement

This paper presents an implementation of the hybrid Cuckoo search and Grey wolf (CS-GWO) optimization algorithm for solving the problem of distribution network reconfiguration (DNR) and optimal location and sizing of distributed generations (DGs) simultaneously in radial distribution systems (RDSs). This algorithm is being used significantly to minimize the system power loss, voltage deviation at load buses and improve the voltage profile. When solving the high-dimensional datasets optimization problem using the GWO algorithm, it simply falls into an optimum local region. To enhance and strengthen the GWO algorithm searchability, CS algorithm is integrated to update the best three candidate solutions. This hybrid CS-GWO algorithm has a more substantial search capability to simultaneously find optimal candidate solutions for problems. The obtained test results for the 33-bus system show that minimization of active power loss was enhanced by 74.73%,73.35%, and 80.37% for light, nominal, and heavy load conditions, respectively, and similarly for 69- bus system is 81.50%, 84.74%, and 88.86%. The minimum voltage value for 33- bus system under nominal load condition was enhanced from 0.9130 p.u to 0.9865 p.u and similarly for the 69-bus system is 0.9094 p.u to 0.9842 p.u. Respectively. Furthermore, to validate the effectiveness and performances of the proposed hybrid CS-GWO algorithm with existing methods is presented. This method is tested and evaluated for standard IEEE 33-bus and 69-bus RDSs by considering different scenarios. Finally, the comparative analysis shows that the proposed algorithm was more efficient in minimizing power losses and enhancing the voltage profile of the system.


INTRODUCTION
The distribution system (DS) is the final stage in the construction and planning electrical power system, which delivers the power between the transmission and end-user consumer. Transmission networks operate in loops/radial structures and distribution networks always operate in radial structure to reduce the short circuit currents. Distribution network reconfiguration (DNR) is defined as the process of varying the topological arrangement of distribution feeders by changing the open/closed status of sectionalizing and tie switches concerning system constraint and satisfying the operator objectives. The most common practice methods used by researchers widely for power loss (PL) reduction and voltage profile improvement in DS is network reconfiguration (NR) and DGs integration in DS [1,2]. Generally, distribution networks/systems are reconfigured to minimize the system PL and relieve overload. However, dynamic loads in the system may increase total system loads; it may be higher than its generation capacity sometimes, making it difficult to relieve the load on the feeders. Due to this problem system voltage profile may not be enhanced to the required In this context, the significant contribution of this paper is highlighted as follows: • The application of a hybrid CS-GWO algorithm is introduced to solve the DNR problem considering DGs allocation simultaneously for the first time. • In this context, voltage deviation at load buses and percentage voltage improvement are also calculated. • The proposed method is applied, tested successfully on standard IEEE 33-bus and 69-bus systems for different scenarios. The remaining of the paper is arranged according to the following: Section 2, Describe the problem formulation. The implementation of the hybrid CS-GWO algorithm and pseudocode along with a flowchart to solve the DNR problem considering DGs simultaneously is presented in Section 3. Section 4 explains test results and a comparative analysis of the proposed technique with existed techniques were discussed on different IEEE test systems considered. The study is concluded in Section 5.

PROBLEM FORMULATION
The problem of DNR and optimal allocation of DGs simultaneously is to find the optimal radial structure of the network and the best location and sizing of DGs to minimize total active power loss, voltage deviation and improve the voltage profile of DS. In this work, five different scenarios were considered to solve the DNR problem considering DG installation simultaneously in order to estimate the effectiveness of the proposed hybrid CS-GWO algorithm.

Objective functions
The main objective of this work is to minimize the active PL, voltage deviation and improve voltage profile of the system considering DGs while satisfying all the system operating constraints. Mathematically, the DNR problem considering DGs installation simultaneously is formulated as follows: Where, X = ( Δ + Δ ) and Y = Δ (Δ =Voltage deviation at load buses) PL in the DS is real and reactive power. In a balanced RDS, which has m branches, the power loss connecting buses and + 1 were calculated using Equation 2 [65].

Reduction of power loss using DNR
DNR is a technique used for finding the best possible network topology of the DS that will minimize the PL. Simultaneously, specified operating constraints such as the current capacity of the feeder, system voltage profile, and radiality structure of the DS must be satisfied. The total PL of a line section linking busses between and + 1 after the DNR is calculated using Equation (4). Represents the summation of losses in all branches after the accomplishment of DNR, written as in equation (5).
The net PL reduction Δ In DS are computed using Equation (6), i.e., the difference of power loss value before and after DNR.

Reduction of power loss using DG installation
Installing DGs in DS at the optimal location and proper size results in several advantages: reducing line losses, peak demand shaving, improving voltage profile, reducing environmental impacts, and reducing the burden on lines. Consider an RDS with branches, DG is located at node , and be set of branches linking the source and node . Let us assume that the DG generate active power ( ) to the system, and reactive power ( ) supplied or consumed from the system depending upon the source of the DG. Thus, real power and reactive current flows in the system will alter the apparent power components of the present branch set. Total apparent power at ℎ node is calculated using Equation (7). = = ∑( + ) = 1,2,3 … . (7) And the current at ℎ node was computed using Equation (8) To integrate the DG model in the network, the apparent power demand at ℎ node, where a DG unit is located is obtained using the Equations (9) The DG power at ℎ node was calculated using Equation (10).
Then the total new apparent power at ℎ node was calculated using Equation (11).
The new current at ℎ node is computed using Equation (12).
By using the new current Obtained from Equation (12) and the power losses reduction due to DG installation were calculated using Equation (13). Δ = ∑ 2 * (13) The total power loss reduction due to DNR considering DGs installation simultaneously in RDS is calculated as

Voltage deviation at load buses
The voltage deviation (Δ ) of the network structure is computed using the eq. (15) as [66]: : represents the prespecified voltage magnitude at load bus ( =1.0 p.u) and : represents minimum bus voltage

• Constraints
Considering the DNR problem, the equality and inequality constraints are; a. Voltage value should be within the specified limits for each bus: and represents the minimum and maximum bus voltages. b. Current value should be within specific limits at each line: where , +1 represents the current between busses and + 1. c. The DG units should be sized within specific limits: where , and , represents the minimum and maximum power provided by DG. d. The total power generation of the system is (20) e. Network must be radial structure and all loads must be supplied power after DNR.

Grey wolf optimizer (GWO)
Seyedali Mirjalili and Andrew Lewis implement the GWO algorithm to solve various optimization problems in different fields [67]. This algorithm performs the common behaviour of the grey wolves (GWs) in cooperatively hunting their prey. It is a large-scale search method centered on three optimal samples. This algorithm's main motivation is the social leadership hierarchy and the hunting mechanism of GWs in nature. Different forms of GWs used to simulate the hierarchy of leadership are alpha ( ), beta ( ), and delta ( ), and omega ( ). GW's hunting process is as follows; Stage 1: Includes activities like Tracking, chasing and approaching the prey. Stage 2: Consists of activities like Pursuing, encircling, and harassing the prey until it stops moving. And the final step is attacking the prey.

Mathematical model and algorithm
The mathematical models of the GWO algorithm are stated as follows; (1). Social hierarchy of GWO-In this hierarchy, an appropriate solution is considered to be alpha ( ), beta ( ), and delta ( ) are regarded as the three best solutions, respectively. Assume omega ( ) is the remaining candidate solution. In this algorithm, hunting (optimization) is handled by alpha ( ), beta ( ), and delta ( ). Omega ( ) wolves move accordingly to alpha ( ), beta ( ), and delta ( ). (2). Encircling Prey-GWs encircle prey during hunting. Equation (21) to Equation (27) is used for mathematically modeling the encircling behaviour of the GWs where denotes the current iteration, & ⃗⃗⃗⃗ represent the position vector of the GW and the prey, and , represents coefficient vectors. ▪ The , vectors were determined by Equations (23) and (24).
where the components which is linearly reduces from 2 to 0 throughout the repetition process and 1 ⃗⃗⃗ and 2 ⃗⃗⃗ denotes the arbitrary vectors [0,1]. Using Equations (21) and (22), the GW will update its position in any random location in the space around the prey. c). Hunting-GWs can recognize and encircle the location of prey, and alpha regularly guides the hunting process. Beta ( ) and delta ( ) may occasionally participate in hunting. This process is mathematically simulated by considering that alpha ( ), beta ( ), and delta ( ) have provided better info about the potential location of the prey. Alpha ( ), beta ( ), and delta ( ) are optimal solutions obtained so far during the process. The objective function in the problem is prey. Omega ( ) wolf's solution will update their location, according to the , , and locations. The hunting process is formulated using Equations (25) and (26).
where ⃗⃗⃗⃗⃗ , ⃗⃗⃗⃗ and ⃗⃗⃗⃗ are the position vectors of the GWs in the population w.r.t , , and wolves. The 1 ⃗⃗⃗⃗⃗ , 2 ⃗⃗⃗⃗⃗ and 3 ⃗⃗⃗⃗⃗ were the generated arbitrary numbers in the range [0,2], is the search agents, i.e., population, ⃗⃗⃗⃗ , ⃗⃗⃗⃗ and ⃗⃗⃗⃗ were the best search agents related to the optimal solutions. 1 ⃗⃗⃗⃗ , 2 ⃗⃗⃗⃗ and 3 ⃗⃗⃗⃗ were arbitrary numbers that depend on the . The encircling behaviour is implied to obtain the new positions of GWs using Equation (27).
Finally, alpha ( ), beta ( ), and delta ( ) predict the prey's location, and the remaining wolves randomly change their position around the prey. When the prey stops moving hunting, the process is ended. Alpha ( ), beta ( ), and delta ( ) wolves predict the feasible location of the prey throughout iterations. The is gradually reduced from 2 to 0 to make emphatic exploration and characteristics of the algorithm. Every candidate solution updates its distance from the prey. If | | > 1, Candidate solutions move towards diverging from the prey. If | | < 1 converge near the prey. Finally, the algorithm comes to an end with satisfaction.

Integration GWO with Cuckoo search algorithm (CS)
Yang and Deb have proposed implementing a meta-heuristic algorithm known as the cuckoo search algorithm to obtain an optimal solution using a minimum no. of parameters for various optimization problems [68]. This algorithm is mainly inspired by the obligate brood parasitism of some cuckoo species. This species lay their eggs in the nests of other host birds of different species. This algorithm is combined with the unique nesting way of cuckoo birds and levy flight behaviour of birds. The levy flight style is a common feature of flight behaviours for several animals and insects. This flight style performs a smaller movement range, but it may have a minimum probability of broad range jump and vary from the activities' mean value. Due to this CS algorithm jumps out of the optimum local region.
Levy flights perform random walks in different directions, and step lengths are obtained using the levy distribution function. These Levy flights are represented by a series of straight flights, proceeded by quick turns. Levy flights are more competent in finding large-scale search areas due to the deviation of species direction much faster when compared to traditional random walks. Using the levy flight search in the cuckoo search algorithm may reduce the number of iterations in algorithm execution. And computation time to obtain an optimal solution may be reduced compared to a standard random walk. "The CS algorithm implementation is done based on the rules explained as follow: • Cuckoo birds select nests randomly and they only place one egg at once. • Next, the best nests will persist in being the next generations.
• Further, the number of bird nests and the probability of egg discover are fixed. Suppose the host bird finds an outsider bird's egg. Then the host bird will leave the nest and create a new one." The nests are updated according to the following equations during the iteration process by satisfying the above rules.
Where the product ⊕ denotes entry-wise multiplication. ( + 1) represents new solutions for cuckoo, . ( ) represents the current solutions. Since > 0 controls the step size and is set to 1. The following probability distribution equation provides the Levy-flight: Hence, this algorithm may search solutions widely in space effectively because its step length varies with short distance finding and random long-distance walking.

Implementation of Hybrid CS-GWO for DNR and DG allocation simultaneously
It is observed that the GWO algorithm updates the positions of wolves using equation (27) by randomly search and the highest fitness value is computed. Thus, the random search's fitness value may lead to weak global search ability and fall easily into the optimum local region, mainly when performed on largedimensional data sets. The CS algorithm updates the nest's positions using a levy flight search to avoid this problem. This search method can quickly find the random best positions of birds very rapidly by changing birds' directions with sudden turns. Furthermore, the solution obtained can soon jump from the current area to other areas to get an optimal solution less competitively due to this CS algorithm feature.
Based on this advantage, the CS algorithm is integrated into the GWO algorithm to obtain a better optimal solution for optimization problems. The GWO algorithm combined with cuckoo search was implemented by Xu, H., Liu, X., & Su, J. in 2017 as the CS-GWO algorithm to solve the optimization problems [69]. In 2020, Abhishek Gupta proposed implementing a hybrid GWO-CS algorithm to test different benchmark optimization functions and found that the performance is better in finding the optimal solution than the GWO algorithm alone [70].
The flow chart of the CS-GWO algorithm is shown in Fig. 1 and the pseudo-code explanation of the hybrid CS-GWO algorithm is as follows: The pseudo-code of the CS-GWO algorithm is presented as follows [69]

. Implementation of CS-GWO for DNR considering DGs installation:
Step 1: Initialization of problem and parameters of the algorithm The optimization problem is specified as follows: Minimize ( ) (30) Subjected to ∈ = 1,2, … Where ( ) is an objective function; is the set of each decision variable ; is the set of the possible range of values for each decision variable (lower and upper bound values). The decision variable in this algorithm is considered as opened switches, DGs size and Buses number. The grey wolf and cuckoo search parameters are specified in this step. The dimension of search agent=12, Number of search agents =200 wolfs, Max. iteration=100, = 0.25 (probability of alien eggs discovery). The grey wolf-cuckoo search memory (GWCM) is a location where all the solution vectors are stored (opened switches, DGs location and size, power loss value). Here the grey wolf coefficient vectors , will be updated based on the components )]) which is linearly reduced from 2 to 0 throughout the repetition process and 1 ⃗⃗⃗ and 2 ⃗⃗⃗ denotes the arbitrary vectors [0,1].
Step2: Initialize GWCM In this step, the GWCM is filled with as many randomly generated solution vectors as the grey wolf population size (wolfs =200). Step 3: Compute the fitness by using eq (1) of each search agent in the pack (each configuration randomly generated) using load flow analysis. For = 1: . ℎ Calculate fitness value End for Set obtained ⃗⃗⃗⃗ , ⃗⃗⃗⃗ and ⃗⃗⃗⃗ According to fitness.
Step 4: Initialize =0; Then = 0 (for current iteration) %%% main Loop%%% ℎ ( ≤ . ) For each search agent (each network configuration, DGs location and size) Update the position of the current search agent by eq. (27) (based on power loss value obtained) End for %%%% Update , and using eq. (23 and 24) Run load flow analysis with constraints Compute the fitness value Update ⃗⃗⃗⃗ , ⃗⃗⃗⃗ and ⃗⃗⃗⃗ according to the fitness (where ⃗⃗⃗⃗ , ⃗⃗⃗⃗ and ⃗⃗⃗⃗ are best three search agents related to the optimal solution obtained during the iteration process) The matrix size of the ⃗⃗⃗⃗ [1 × 11] include best network reconfiguration topology (switches to open), DGs location at bus number and size depending on minimum power loss.
Step 5: Incorporating a cuckoo search algorithm using the levy flight method to find the best configuration and DGs location and size. For ⃗⃗⃗⃗ , ⃗⃗⃗⃗ and ⃗⃗⃗⃗ obtained in step 4 are given as the input to the cuckoo search algorithm [14] Levy flight method generates a new solution using eq. (28) If rand> %%% controlling is sending back to GWO algorithm%%%%% Update , in GWO algorithm according to the random best position obtained by cuckoo search algorithm (i.e., updating wolf position according to the obtained random values 1 ( ) ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ and 2 ( ) ⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗⃗ from levy flight method) Compute the fitness function and update it according to fitness Compute the new position of a grey wolf using eq. (27) Iteration= +1 End ℎ Output alpha_score (displays the Open switches, DGs location at which bus number and DGs size) The application of the hybrid CS-GWO algorithm for PL reduction problem and voltage profile improvement with DNR and DGs installation simultaneously is validated with the standard IEEE 33-bus test system. This test system comprises five tie switches, normally opened and represented as 33 (32) is used to determine the optimal solution by choosing the best-reconfigured switches open in the loop. Equation (33) is used to solve scenarios III and IV, determining the optimum location and sizing of three DG units. Equation (34) is used to solve scenario V to perform simultaneous DNR with DGs installation to reduce PL and improve minimum system voltage magnitude.
In the proposed CS-GWO method, only three control parameters need to be adjusted, including the number of wolves, the maximum number of iterations and = 0.25 (probability of alien eggs discovery). The remaining parameters, such as switches to be opened in the loop, DG location at bus number, and DG size, are randomly selected. These parameters can easily be predetermined depending on the tested systems. The proposed method is executed independently for each scenario to obtain the optimal solution. The implemented algorithm has been coded in MATLAB R2017a software and simulated on a computer desktop with Intel Core (TM) i3 PC with 2.0 GHz of speed and 8 GB of RAM.

TEST RESULTS
The standard IEEE test systems 33-bus and 69-bus systems are considered for this work to show the proposed hybrid CS-GWO algorithm's effectiveness and robustness to solve the considered problem. Different type of scenarios was considered as follows: • Scenario I: Base case (without DNR and DGs installation).
• Scenario II: DNR is done, depending on existing switches.
• Scenario III: DGs are installed in the DS before DNR (Only DG units).
• Scenario IV: DGs are installed after the DNR.

Test system-I: IEEE 33-bus system
The topology of test system-I consists of 5 tie switches from 33-37, normally opened and 32 SS from 1-32 generally closed [71]. The system load data under the base case were 3715 kW and 2300 kVAR, respectively. The range of apparent power injected by the DGs is 0 to 2 MW & 2 MVAR, respectively. The base parameters are 100 MVA, 12.66 kV. Table 1 shows the simulation results of test system 1 for different loading conditions and voltage deviation at load buses. Table 2 shows the CS-GWO algorithm's effectiveness compared with existing algorithms in obtaining optimal configuration, sizing, and location of DGs for all the scenarios considered and simulation results are presented. Fig. 2  From the obtained results, the DNR with DG installation minimizes voltage deviation closer to zero, improving voltage stability and network performance. The optimal network structure after simultaneous DNR, considering the DGs installation for scenario V, is 8,12,15,29,31 with DGs size (MW) 0.8075,0.7311,1.4805 located at buses 27,18,25 having PL of 51.01 kW respectively. The voltage profile curve for scenario I-V under nominal load is shown in Fig. 3. From this Figure, it is observed that the voltage profile for scenario V is better compared to other scenarios. The minimum voltage magnitude (in p.u) of DS is 0.9130, which is enhanced to 0.9424,0.9804,0.9855 and 0.9865 using scenarios I-V. Table 2 represents the comparison of results obtained by hybrid CS-GWO with different algorithms such as RGA [5], HSA [6], ACSA [14], GA [15], FWA [43], MPGSA [44], UVDA [48] and SFA [58].
• For scenario II, hybrid CS-GWO optimized NR with opened switches: 7-9-14-32-37, estimated PL and minimum voltage magnitude as 139.55 kW and 0.9424 p.u, the obtained results do not vary when compared to other methods.   Convergence characteristics are also estimated for two scenarios II and V by considering the IEEE 33-bus system and depicted in Fig. 4a and 4b, respectively. In Fig. 4a, it is observed that, from the 1 st iteration onwards, PL decreased from 140.77 kW to 139.55 kW for scenario II. From Fig. 4b at 30 th iteration onwards, PL decreased from 60.00 kW to 54.01 kW for scenario V. From Fig. 4a, it is pertinent to note that the proposed hybrid CS-GWO technique has converged to an optimal solution after 2 nd iteration for scenario II, showing that by integrating cuckoo search in GWO algorithm may find a better solution within less computation time of convergence process. Similarly, from Fig. 4b, it is found that the algorithm converges at the 28 th iteration providing an optimal solution with minimum power loss in scenario V compared to other algorithms found in the exhaustive literature survey.  The reduction in active PL obtained in the base case and to those obtained from different scenarios for light, nominal and heavy load conditions is represented as a bar graph in Fig. 5, From which the active PL (in kW) in the base case for nominal load is 202.68, and it is reduced drastically to 139. 55, 71.40, 58.55, 51.98 for scenarios II, III, IV, V respectively. From Table 2, it is concluded that the PL reduction obtained by the proposed hybrid technique is higher than the results obtained with GA, UVDA, MPGSA, SFS, and FWA methods. From these results, the percentage PL reduction by the proposed hybrid CS-GWO method for scenarios II, III, IV, and V were 31.14%, 64 70.95%, and 72.50%} respectively. Hence the performance in terms of active PL minimization and voltage profile improvement, the proposed hybrid CS-GWO algorithm proved better performance for obtaining optimal solution when compared to the other optimization techniques.

Test system-II: IEEE 69-bus system
The topology of the test system consists of 68 SS (1-68) and 5 tie switches from (69)(70)(71)(72)(73) and system data were considered from [72]. The total load data under the base case were 3.80 MW and 2.694 kVAR, respectively. Table 3 shows the simulation results of test system 2 with installed DGs for different loading conditions and also computed voltage deviation Δ (p.u.) at load buses. Table 4 shows the effectiveness of the hybrid CS-GWO algorithm compared with existing algorithms in obtaining optimal configuration, sizing and location of DGs for all the scenarios considered and simulation results are presented. Fig. 6 depicts the SLD of test system 2 with different loops and DGs placement. Depending on the number of tie switches, five loops have been formed as 1 to 5 , these switches are operated during fault cases, load balancing conditions and to reduce the system losses. L1= [ 3,4,5,6,7,8,9,36,37,38,39,40,41,42,35]; L2= [ 11,12,13,14,44,43,45]; L3 = [ 15,16,17,18,19,20]; L4= [ 21,22,23,24,25,26,59,60,61,62,63,64]; L5 = [ 47,48,49,53,54,55,56,57,52,46,58]  To evaluate the effectiveness of proposed method, test system 2 is also simulated at different load levels such as light (0.5), nominal (1.0), and heavy (1.6), and obtained results are conferred in Table 3. From Table 3, we can infer that base case PL in the DS (in kW) at light load is 51.60, which is reduced to 23.43, 18.14, 11.54 and 9.545 using scenarios II, III, IV, and V, respectively. Similarly, at nominal load, base case PL in the system (in kW) is 224.70, which is reduced to 98. 12 This represents that for all load levels, PL reduction using scenario-V by the proposed hybrid CS-GWO algorithm is highest, proving the proposed method's effectiveness over the GWO method. As load level rises from light to heavy, enhancement in percentage PL reduction in all scenarios is nearly the same. It is pertinent from table 3 that reduction in PL and voltage profile improvement for scenario V is higher in comparison with scenario IV. As well as, this  From the obtained results, the DNR with DG installation minimizes voltage deviation closer to zero, which will improve voltage stability and network performance. After simultaneous DNR, considering the DGs installation for scenario V, the network's optimal structure is 13,56,69,24,18 with DGs size (MW) as 0.3738,0.3888,1.6764 located at buses 24,32,61 having power losses of 34.28 kW and minimum voltage magnitude of 0.9842 p.u respectively. The voltage profile curve for scenario I-V under nominal load is depicted in Fig. 7. From this Figure, it is observed that the voltage profile for scenario V is better compared to other scenarios. For example, the minimum voltage magnitude (in p.u) of the DS is 0.9094, which is later enhanced to 0.9495,0.9784,0.9834 and 0.9842 using scenarios I-V.  Table 4 represents the comparison of results obtained by hybrid CS-GWO with different algorithms such as RGA [5], HSA [6], ACSA [14], GA [15], FWA [43], and UVDA [48].
•  Convergence characteristics are also estimated for two scenarios II and V by considering the IEEE 69-bus system and depicted in Fig. 8a and 8b. From Fig. 8a at the 1 st iteration onwards, PL decreased from 110.00 kW to 98.12 kW for scenario II, and from Fig. 8b at 30 th iteration onwards, PL decreased from 60.10 kW to 34.28 kW for scenario V. From Fig. 8a, it is found that the proposed hybrid CS-GWO technique has converged to an optimal solution after 3 rd iteration for scenario II, showing that by integrating cuckoo search in GWO algorithm may find a better solution within a short time of convergence process. Similarly, from Fig.  8b, it is found that the algorithm converges at the 30 th iteration providing an optimal solution with minimum PL in scenario V in comparison with other algorithms in the literature. The reduction in active PL obtained in the base case to those obtained from different scenarios for light, nominal and heavy load conditions is represented as a bar graph in Fig. 9. It can be noticed from Fig. 9

CONCLUSION
In this paper, the proposed hybrid CS-GWO algorithm has been implemented to simultaneously solve the DNR, DGs installation problem in the RDSs to reduce active power loss and voltage profile improvement. Moreover, different scenarios aimed at system loss reduction, voltage profile improvement and minimum voltage deviation were considered here.
• • Analysis of the results obtained from the hybrid CS-GWO algorithm shows that simultaneous DNR, DG installation process in RDSs is a more effective method in minimizing system power loss and improving the system's voltage profile than results obtained by other optimization methods reported earlier in the literature. The results obtained by the proposed hybrid CS-GWO algorithm are compared with other optimization techniques such as HSA, GA, RGA, FWA, ACSA, UVDA, SFS and MPGSA. The comparison validates the effectiveness of the proposed technique shows that it is a better and promising method than the other optimization approaches in solving DNR, DGs installation problems simultaneously. Therefore, the proposed hybrid CS-GWO algorithm may be treated as a constructive method for optimizing DNR problem for complex and large-scale RDS and optimal location and sizing of the installed DGs. To minimize the power loss and improve the voltage profile.
• the proposed method has been found to be more efficient in reducing voltage deviation (VD) and power losses in the system. • the proposed algorithm was efficient in terms of reducing both the real and reactive power losses in the system. To optimally size and locate the DG on the feeder resulting in lowest total voltage deviation, total active and reactive power loss.
• The results showed that the total voltage deviation, active and reactive power losses are reduced to To mitigate power losses and improve the voltage profile by the optimal sizing and placing of DGs in the distribution network.
• The performance comparison of GrMHSA and MOPSO showed that GrMHSA performs better in terms of reducing voltage deviation and power losses in the system. • The results showed that the total voltage deviation, active and reactive power losses were reduced by 85.20%, 84.94%, and 85.73%, respectively. A. Selim, et.al., 2021, [77] Modified Whale Optimization (MOWOA) algorithm and fuzzy decision-making method Power loss and voltage deviation (VD) minimization and voltage stability index (VSI) optimize.
• IEEE 33,69-bus test system. • Competitive optimization algorithm having minimum convergences rate. • An effective method for finding optimal DGs placement and size in the system based on the fuzzy decision-making process. To minimize APL, total voltage deviation and voltage stability index of the RDSs consider different load models.
• The analytic hierarchy process is used to optimize the weighting factor. • An effective method to solve the optimal multiple DG allocation problem with minimum real power loss, less computational time, and a prominent convergence rate. I. Khonturaev, et.al., 2021, [82] Atom Search Optimization Algorithm To minimize power losses • IEEE 33-bus test system.
• Power loss sensitivity index method is used to find optimal buses for DGs installation. • An effective approach for finding optimal DGs placement and size in system.

DECLARATION OF COMPETING INTEREST
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

FUNDING INFORMATION
This research did not receive any specific grant from funding agencies in the public, commercial, or not-forprofit sectors.