Hybrid optimization to enhance power system reliability using GA, GWO, and PSO

: An optimization approach is described in the research study that deals with the issue of recon ﬁ gura - tion networks built with certain conditions of power loss reduction and reliability. Furthermore, the recon ﬁ gured networking system seeks optimization based on criteria a ﬀ ecting the limitations. This study optimises speci ﬁ c net - work faults subjecting resources with no supply during recon ﬁ guration to avoid the e ﬀ ect and possess through active power losses. These goals were met using the mathematical method of the optimisation process. The mathematical for - mulation is generated ﬁ rst in the system development pro - cess. As a result, a comprehensive methodology using genetic algorithm, Grey Wolf optimization ( GWO ) , and par - ticle swarm optimization ( PSO ) was developed. Finally, intended methodologies were estimated. Based on the results, it is clear that the proposed hybrid GWO - PSO approach outperforms all other methods in terms of node voltage, reliability, line currents, and computational dura - tion. Furthermore, when optimally sized distributed genera - tions are placed in optimal locations, total loss is reduced by up to 63% and voltage pro ﬁ les improve.


Introduction
Distribution networks in electrical power scenarios are significant. They are subject to certain divisions of transformation through denser condition and complexity with supply of system necessity [1]. As distribution networks become more complex, manual tasks must be automated. To help operate these networks, new advanced automation functions have emerged. These functions help the distribution network operator solve network problems [2]. For ensuring better economical aspect, safety, and optimization of the supply, the distribution networks can be reconfigured electrically as per the operator requirements and constraints.
Network reconfiguration using a distribution generation that changes the state during a state transition within a sectioned switch configuration. This generates the enhancement of certain circumstances [3].
Practical researchers have observed tremendous growth with the optimal case of distribution network based on the reconfiguration scheme. Enhancing reliability has always been an important goal [4]. Also, minimization of active power loss, voltage stability, load balancing, and security margin have received much attention [5][6][7].
A load flow algorithm is essential for analysing, optimizing, and planning distribution network reconfiguration. Individual design for the execution of certain techniques associated with optimization utilizes the process. The proposed load flow algorithm is a new application subjected to genetic algorithm (GA) and particle swarm optimization (PSO) for the reconfiguration of distribution network [8][9][10][11].
Chen et al. [12] proposed numerous load flow algorithms for the distribution system scheme. Moreover, under the structure of a radial and sparsely meshed network formation, the generic approach of developing using the Gauss implicit matrix technique aims to improve the explicit utilisation of distribution systems. Mohanty and Tripathy generated a novel thought to process the topology of distribution system [13], but these concepts facilitate with the information associated with data manipulation occurred within the system.
Sarma et al. [14] presented a hybrid variant of PSO called hybrid particle swarm optimization algorithm with mutation (HPSOM). The main idea of the HPSOM was to integrate PSO with GA mutation technique.
Saraf et al. [15] proposed a new hybrid populationbased algorithm (PSOGSA) with the combination of PSO and gravitational search algorithm (GSA). The main idea is to integrate the capability of exploitation in PSO with the capability of exploration in GSA to synthesize both variants' strength.
Hussain et al. [16] presented a hybrid variant combining PSO with a back-propagation (BP) variant called PSO-BP algorithm. This variant can make use of not only strong global searching ability of the PSOA, but also strong local searching ability of the BP algorithm.
Prommee et al. [17] presented a hybrid PSO variant, which combines the advantages of PSO and Nelder-Mead Simplex Method (SM) variant; it is put forward to solve systems of nonlinear equations and can be used to overcome the difficulty in selecting good initial guess for SM and inaccuracy of PSO because of being easily trapped into local optimum.
For resolving the issue, it is recommended that PSO and GA be implemented to reduce power loss and improve reliability. In addition, the system only accepts data from utilities regarding bus branches. This study develops a formulation that directly solves distribution load flow using distribution system topology [18][19][20][21][22]. The traditional Newton Raphson and Gauss implicit matrix algorithms require laborious work ahead with the substitution for the development of Jacobian matrix or admittance matrix. Load flow solutions are obtained by multiplying two matrices, under certain implementation of bus-injection within the branch-current and equivalently with branch-current to bus-voltage. The capsule network studied and used in previous studies [23][24][25][26][27][28] could also be used for effective PSO.
Several optimization algorithms were proposed in the literature for distributed generation (DG) allocation and sizing in EDS with the purpose of minimizing system power losses and improving network voltage profile. The majority of the planned algorithms in the literature have emphasized on active power losses only in their formulations. But the reactive power losses which are key to the operation of power systems are given less concentration. Injection of reactive power into a practical distribution system plays a critical role in maintaining voltage stability; thus minimization of reactive power losses is chosen and incorporated in optimizing DG placement for network voltage profile improvement. This research work focuses on a hybrid optimization algorithm by combining concepts of PSO and Grey Wolf optimization (GWO) to optimize DG allocation with sizing while considering both real and reactive power losses [29][30][31][32][33][34][35].
When using the proposed strategy, the DG integration problem can be framed like a mixed integer nonlinear optimization problem that features highly nonlinear equality and inequality constraints. Using this approach, the optimal location and size of the DG units can be determined, with the aim of minimizing the multi-objective function. This involves the aspect of real power losses. The branch current's real and reactive losses can be decreased through injections of real and reactive power via capacitors, along with appropriately rated DG units positioned at suitable locations and having suitable voltage profiles. These DG units are restricted with specific constraints in the distribution network.

Materials and methods
In this section, the techniques and practices utilized for the accomplishment of outcomes within the research study are discussed.

Mathematical model developed for distribution network reconfiguration problem 2.1.1 Generalizations
The research defines certain issues raised with optimization difficulty or objective function [36]. This can be limited. Mathematically, a mono-objective optimization problem looks like the following: Under the constraints: and h(x) are equality and inequality constraints associated with the optimisation of a mono-objective function. x exemplifies with vector of n parameters, and x min and x max gives constraints domain case.

Objective function interpretation with issue of reconfiguration
Research objective is to analyse the reconfigured distribution network feasible to diminish active power loss and energy with no supply (ENS) index within the goals identified for optimization challenge.

Criteria of no supply energy
In the case of deregulated power sector, the reliability of distribution network has grown. Reconfiguration attained for the distribution network is an economical approach for enhancing the reliability of the system. Furthermore, ENS refers to customer-interrupted electricity in distribution system planning studies. Distribution system failures cause most customer interruptions. The ENS index predicts energy lost based on the periodical failure. Certainly, the ENS index prediction is capable of planning for the design to facilitate the consumers to attain power at a reliable approach that enhances the affordable circumstances.
where P j is the unpowered load point's active power (kW); n b signifies the radial branches, N c is the total consumers; and i j , l ij , and t ij are the line's failure rate, length, and repair and commissioning time, respectively.

Total loss
where F 1 denotes the single objective function for power loss minimization, N indicates the bus branch number, and S iTotal loss denotes the total loss of complex power. Distributed generation offers a viable and sustainable way to improve energy efficiency while also lowering the cost of energy. Because of this, DG is being increasingly integrated into distribution systems and must therefore be added to the analysis of power flow. Active and reactive power flows that include DG in bus k may be expressed as in [12].

Voltage deviations
For various reasons, distribution systems may experience voltage variations. For example, line impedances may lead to major voltage drops, or the available reactive generation may be unable to satisfy increasing customer demand for reactive power. Also, the use of long radial feeders in rural locations may prevent reactive power transmission. This will cause a drop in voltage at customer-connection load points. For these reasons, load bus voltage positioned at remote ends is typically lower compared to load bus voltage positioned closer to substations. Variations in voltage are referred to as voltage deviations. These may be defined as differences between actual and nominal voltage levels, such that the smaller the bus voltage deviation from nominal voltage, the more functional the system. The total voltage deviation (TVD) refers to the sum total of the squared value of absolute voltage differences between nominal and actual voltage in all buses within a given system. This may be expressed as follows: where V n indicates bus voltage value for bus n, V ref indicates reference voltage typically equal to 1 p.u., and N indicates the bus number. F 2 is the second objective function represented by TVD.

Voltage stability index (VSI)
In the present work, VSI represents a distribution system's security level and measures each bus system's vulnerability to voltage collapse using the following equation.
Higher VSI values indicate a more stable bus and a relatively low potential for voltage collapse.
where VSI k indicates the voltage stability index for at the bus k and F 3 indicates the third objective function represented by VSI.

Constraint interpretation
Security-based constraints require network nodal voltages and line currents.

Constraints based on voltages
Constraint based on voltages has been identified through the optimization technique integrating with subsequent approach: where V i signifies network nodal voltage at "i"; V i min stands for nominal voltage of 1 p.u., minimum voltage, −10%; and V i max stands for nominal voltage of 1 p.u., maximum voltage, +10%.

Current constraints
Distribution network operators must also consider the currents flowing through the branches. Currents cannot exceed limits under steady-state condition. Furthermore, constraint is mathematically formulated as follows: where I ij is the branch current, and the maximum value of branch current gives I max adm ij at (i, j) estimated within the current values estimated based on load-flow analysis.

Constraints based on topological analysis
Topological analysis-based constraints when conducting a topological survey, it is imperative that the topology be configured in a way that adheres to security criteria. When theoretical graphing is used to translate topological constraints, the spanning tree constructed to satisfy the requirements is an approximation of the tree.
• Have (N − 1) reached edges to the criterion systemized for the vertex count divided to N graphs based on average vertices that ensure the connectivity, which actually characterizes the loop absence.

Proposed approach for load flow methodology
With the research work, the load flow technique proposed utilizes the network tree to distribute for estimation of path projected to branch current in calculating the branch currents with the profile of nodal voltage and current. Certainly, the load flow method makes use of the deduced case of a two-network topology, which can then be inputted with the case of matrices into bus injection branch current and branch current bus voltage. Based on the load flow chart, the analysis estimated is depicted in Figure 1. Analysing each node separately has led to improvements in both the quality and quantity of the supply.

Optimization challenge approaches
Research work enables an exhaustive strategy that reconfigures with certain networks of GA and PSO approaches under the condition of distribution case.

Meticulous practice
The procedure considers all possible system configurations, ranks them, and then identifies the best possible related approach [37]. The research questions are listed under a comparison of the problem-solving strategies employed by various organisations. Take into account the two possible configurations of each movable line when the settings in an ideal manner. Therefore, in addition to the M solutions, there are 2 M solutions that represent M movable branches. For M solutions based on exploratory searching, a combined estimation based on operable featuring to closed branches and lines.

GA approach
This section's GA-based algorithm optimizes distribution network reconfiguration. GA is a single-chromosome state.

PSO methodology
With PSO analysis, individual coordinates of particles integrate within the vectors positioned at (xi) with velocity (vi).
That are dimensioned with xi and vi as per particles. In addition, particles within the swarm are categorised according to their locations within the surface, their exploration history, and their velocities within the vector that was created before the system was activated (Figure 2).

Simulation findings
Minimising the initial approach of ENS was of primary concern, as was the active power loss, which could be mitigated by optimisation after the network was reconfigured ( Figure 3).

Testing system with IEEE 33-bus
With 33 nodes and 37 branches, the IEEE 33-bus distribution network is presented in Figure 4.

ENS criterion minimization
With optimal topology, the IEEE 33-bus testing network scheme is found utilizing the meticulous analysis based on algorithms of GA and PSO. Maximizing reliability led to a good initial voltage profile ( Figure 5). Voltages are close to 1 p.u. All network nodes' voltage profiles improved. Security restrictions are also examined ( Table 1). Figure 6 shows the optimal ENS network configuration. 7-9-14-16-27 are OBs. Certainly, the structure of radial analysis under ENS is signified to be 4.82685 kW h/year with initial topology developed under minimal count of 66.57% (attained at 7.0980 kW h/year) with structure analysis. Figure 7 shows the IEEE 33-bus testing methods based on GA along with PSO convergence characteristics. This figure shows that the PSO algorithm is faster at finding the optimal solution than the others. The optimal solution took 25 fewer iterations ( Figure 8).   Hybrid optimization to enhance power system reliability  7

Minimization of the active losses criterion
Using the procedure of load flow, each branch's active power losses were calculated. Applying the proposed approaches reduced power losses. Table 2 depicts the decremental active power losses with 63.2579 kW within the formed count of 202.5862 kW at a rate of 31.15% less than the initial topology of Figure 5. Figure 9 shows OBs 7-9-14-32-37. Under the optimal network configuration for the IEEE 33-bus test system, power loss was observed to be minimal in all simulations. PSO accomplishes optimal configuration in fewer iterations than alternative techniques. The success rate of PSO attained 85%, whereas the GA with a meticulous strategy achieved between 61.0% and 8.1%. Figure 10 illustrates a comparison of the success rates of IEEE 33-bus test methodologies.
Implementing the study research's reconfiguration of PSO-based topology improves active power losses and reliability of the network. Furthermore, PSO is capable of permitting population integration to evolutionary procedures with advantages superior to optimisation practises. For instance, unlike many standard procedures, it  Figure 11: Convergence characterization ion for GA and PSO to minimize the active power losses measure. has no derivatives. It does not need further primary development analysis when iterating from its initial position (Tables 3 and 4).

Conclusions
A network reconfiguration study reduces active power loss and dependability. An effective strategy improves metaheuristic network reconfiguration methods. This approach solves distribution load flow directly using topological distribution system characteristics. ENS index and active power losses are considered for network reconfiguration objectives, topology and security restrictions, and monoobjective optimization support. Distribution reconfiguration methods include exhaustive, GA, and PSO. GWO-PSO outperforms comprehensive methodology and GA in network structure convergence and success rate. Since reconfiguration, simulation results show nodal voltage and branch current amplitudes. PSO converges faster than exhaustive and GA (Figures 10 and 11). Thus, GWO-PSO approach validation avoids real-time power system modification.
Acknowledgements: The authors are thankful to all who volunteered for the study.
Funding information: The authors state that no funding is involved in conducting this research.
Author contributions: R. Sireesha designed the simulation model of the concept presented in this article, performed system analysis and interpretation, and communicated with the journal committee. All the authors contributed to the writing and revision of this article.

Conflict of interest:
The authors state no conflict of interest.
Informed consent: Informed consent was obtained from all individuals included in this study.
Ethical approval: The conducted research is not related to either human or animals use.
Data availability statement: The datasets generated during the current study are available from the corresponding author on reasonable request.