RETRACTED: A New Hybrid Algorithm for Multi-Objective Reactive Power Planning via FACTS Devices and Renewable Wind Resources

: The power system planning problem considering system loss function, voltage profile function, the cost function of FACTS (flexible alternating current transmission system) devices, and stability function are investigated in this paper. With the growth of electronic technologies, FACTS devices have improved stability and more reliable planning in reactive power (RP) planning. In addition, in modern power systems, renewable resources have an inevitable effect on power system planning. Therefore, wind resources make a complicated problem of planning due to conflicting functions and non-linear constraints. This confliction is the stochastic nature of the cost, loss, and voltage functions that cannot be summarized in function. A multi-objective hybrid algorithm is proposed to solve this problem by considering the linear and non-linear constraints that combine particle swarm optimization (PSO) and the virus colony search (VCS). VCS is a new optimization method based on viruses’ search function to destroy host cells and cause the penetration of the best virus into a cell for reproduction. In the proposed model, the PSO is used to enhance local and global search. In addition, the non-dominated sort of the Pareto criterion is used to sort the data. The optimization results on different scenarios reveal that the combined method of the proposed hybrid algorithm can improve the parameters such as convergence time, index of voltage stability, and absolute magnitude of voltage deviation, and this method can reduce the total transmission line losses. In addition, the presence of wind resources has a positive effect on the mentioned issue


Introduction
Nowadays, the importance of reactive power (RP) supply is more evident.Even though the RP load flow affects the line losses and the bus voltage and the active power load flow and its costs, unfortunately, the costs of producing and transmitting RP have received little attention [1][2][3][4][5][6][7][8][9][10][11][12].One reason for this lack of attention is the inherent difficulty in understanding this issue, particularly by economists [12][13][14][15][16][17][18][19][20].Another reason for the lack of serious attention to RP is the low production price compared to active power [21][22][23][24][25][26][27][28][29][30].However, according to economics and market calculations, RP is not less valuable than active power [31][32][33][34][35][36][37][38][39][40].The management and control of RP both in traditional and competitive systems have been one of the main concerns of exploiters [41][42][43][44][45][46][47][48][49][50].RP in systems was optimized via adjusting the voltage of generators, tap transformers capable of changing tap under load, and the size of parallel capacitors.Due to the expansion of power networks, the exploitation of RP resources for increasing voltage profile and reduction has attracted considerable attention.Although the production of RP does not incur any costs itself, it influences the total cost due to its impact on system losses.In general, RP planning involves the two issues of locating and operating [51][52][53][54][55][56][57][58][59][60].The issue of locating includes determining the type of RP resources, while the issue of operating emphasizes the optimal arrangement of available RP resources.Parameters that need to ordered RP flow problems are the voltage of controlled buses, tap transformers with the capability to change tap under load, and the size of parallel capacitors.While solving RP flow, it is assumed that economic load flow has been completed, and the amount of real power produced by each generator is determined [61][62][63][64][65][66][67][68].Therefore, RP planning can be expressed in ways that have functions and constraints [69][70][71][72].
For solving this problem, various objective functions can be considered.RP planning is considered minimizing capital expenditure (CAPEX) and operating expense (OPEX) because their constraints are fulfilled in most papers.CAPEX includes the costs of purchasing, setting up, and conserving novel RP resources in the network.OPEX is considered, and the aim is to minimize these costs [73].An objective function was considered the primary function and other functions as the constraints, and optimization was conducted to solve this problem.It is challenging to implement such a method to solve multi-objective nondifferentiable constraint optimization problems where the solution space is non-convex.In [74], the non-convex and discontinuous constraint in the simplex algorithm is eliminated by implementing the Big M method, which models this disjunctive constraint through a mixed-integer formulation.
On the other hand, due to greenhouse gases and ozone layer depletion, renewable energies such as wind power are currently developing rapidly in most countries.The notion of expansion is synonymous with protection concerning the natural environment and is also discussed in GDP and the use of natural and environmental resources [75][76][77].The imminent end of fossils has urged researchers to discover renewable energies for substituting the standard energy system [78].RP control has become more complicated under the influence of renewable resources.
The reasons mentioned above led power industry engineers to revise the existing power systems' design and present the design of flexible AC transmission systems (FACTS).This design, which involves the use of power electronics devices to increase the transmission capacity and controllability of power systems, has established a new approach to current dynamic problems and control of power systems and has introduced new solutions in this field along with the advancements in power electronics technology and the introduction of the concept of flexible AC transmission systems called FACTS [79].Planners have found it interesting that concerning RP, FACTS technology provides new chances to control and improve the operational capacity of systems and the new and upgraded lines.
The possibility of controlling the flow within a transmission line at a reasonable cost makes it possible to increase the capacity of the existing lines in the form of lines with more prominent conductors and to increase power flow through such lines under normal and unpredictable conditions by using one of the FACTS controllers [78].In RP planning, various methods have been proposed that can be divided into mathematics and optimization intelligence.
The first category is based on mathematical models such as non-linear, linear, and quadratic programming [80][81][82].Unfortunately, the methods described above lose their effectiveness despite the success achieved when the system has many variables in the non-linear structure.
The second category is based on optimization intelligence, which is generally faster and more reliable than the mathematical methods.The volume of computations in this

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Sensors 2021, 21, 5246 3 of 32 method is less than that of the classical methods.In this category, the following references can be referred to.Shaheen et al. [81] used a modified multi-agent evolutionary model of the RP planning problem.The weakest buses are selected for the installation of RP.Then they are solved using the evolutionary algorithm and target functions based on loss costs and losses.The proposed method in this reference is applied in various standard systems, and the results obtained are compared using genetic and harmonic search algorithms.Bin et al. [82] proposed a multi-objective group search method to accommodate capacitors with different target functions optimally.The voltage drop in lines and the cost of capacitor installation are selected as the target functions.In this paper, the capacitor is used ideally and continuously, and, therefore, the result obtained cannot be applied directly and without changes.
Bhattacharyy et al. [83] addressed the teacher-student learning method for solving RP planning problems by considering linear and non-linear constraints.The proposed method in this reference is applied in a variety of standard systems.Shaheen et al. [84] provide a comprehensive overview of all available methods in the first and the second categories.In this reference, the weaknesses and strengths of the available methods are described meticulously.In [85,86], the gravitational search method is employed to RP problems with FACTS devices presence.Xian et al. [87] modeled the effect of energy on economic distribution for power and pollution.In this model, probabilistic methods are employed for wind energy modeling.El-sobky et al.'s [88] method based on a reliable search area was used for solving the dynamic distribution problem of pollution.Arul et al. [89] used the self-adaptive harmony search algorithm for solving the problem.Control coefficients are focused in a self-regulated manner with program repetitions.The chaos theory based on logistics has also been utilized to improve local search.Despite the methods mentioned earlier, due to the non-linear, discrete, and continuous nature of the constraints in the RP programming problem, a hybrid model that can cover this issue more accurately is required.For overcoming this weakness, the virus colony search optimization algorithm is presented [90].Because voltage limits and variations are introduced as a constraint, the bus voltage can decrease to a maximum, which increases the probability of voltage instability in those buses.This issue is fundamental in power systems under stress that has been brought on in recent years due to economic issues.Therefore, in this paper, two other target functions, namely, increasing the system security and minimizing the voltage bias of the bus, are considered, and the problem is taken into account as multi-objective programming.The proposed method, coded as a multi-objective method, is one of the highlights that has never been presented in studies thus far.
The model efficiency was investigated on sample systems with FACTS resources formed on proper criteria, and the obtained data were compared to another model.According to the explanations mentioned earlier, the following points can be made about the innovation and highlights of this paper: (A).Improving local and general search via algorithm form on virus search, particle swarm optimization.This hybrid algorithm tries to employ its powerful searching operators in the optimization problem.In addition, it develops the standard particle swarm optimization with the best guiding during the search.Furthermore, it presents a fuzzy mechanism to select the best solution from several solutions.(B).Modeling the practical constraints in RP programming with continuous and discrete variables in an optimization problem and considering the wind units and FACTS devices to make an accurate model of power system (C).Consider several analyses and scenarios to evaluate the proposed model and optimization algorithm.In addition, present some comparisons with another optimization algorithm.(D).The second section deals with modeling RP distribution by considering renewable sources and FACTS devices.The third section is devoted to modeling the proposed multi-objective hybrid algorithm.The fourth section describes how to implement the algorithm on the RP programming, and the fifth section presents simulation data.The sixth section was dedicated to a conclusion.

Materials and Methods
Due to the increase in electric power consumption over the past decades, electric power supply systems have been expanded to such an extent that today the optimal distribution of RP for optimal programming and utilization of power systems between energy production units with the lowest cost has become widespread and complex in power system issues.The formulation of the problem of RP programming by considering linear and non-linear constraints is defined as follows.

RP with FACTS without Wind Unit
In this paper, to achieve more comprehensive RP programming, different target functions have been applied according to the following descriptions.

Loss Function
It is an essential function in RP programming and aims to reduce network losses, increasing network efficiency.To calculate network losses, the Newton-Raphson method has been employed [48]: V i and V j represent voltage for the beginning and last of lines i and j, and the θ i and θ j show the angles at the beginning and end of the line, respectively.

Voltage Equalization
Common issues in RP programming are network voltage stability.As the nature of the network voltage is different from that of the loss function, a new function called network voltage equalization, which indicates difference for desired per bus and obtained after each run of the load distribution program, is as follows: In the above relation, N is the candidate bus number for installation in RP sources, V act is the value obtained from the load distribution problem with RP sources, and V des is the expected value according to the constraints on the power system network.

The Cost of FACTS Devices
The cost of equipment performance consists of two parts: the cost of the active power and the cost including shunt equipment.The target is obtained via: C E is the cost of losses ($), and C Sh is the cost of shunt capacitors ($).C E generally increases by considering system losses.In this paper, installing shunt equipment cost, installing equipment cost, and the cost of energy losses have been considered to be equal to 3 $/kVar, 1000 $, and 0.06 $/KWh, respectively.Now, the target function for RP programming is expressed by considering the FACTS equipment as follows: As seen above, the final target function is presented separately for each section.The target should be considered as consisting of all of the above points.The final target function proposed in this paper is based on the value of losses, voltage fluctuations, and the assignment of FACTS devices and the related constraints as follows: where NG, N, N L , and N c represent generators, buses, load levels, and Var resource numbers.k shows load levels, and k, T (k) , α, β, and y i represent kth load level, cost of energy, coefficient of the maintenance cost, cost of allocating the equipment, and the binary variable, respectively.If y i = 1, the Var equipment in that busbar is installed; otherwise, y i = 0. PG i , QG i , PL i , and QL i represent the output of the active power of generators, the output of the RP, the active load, and load in request in ith, respectively.S ij k is the current flowing from the i-j line.When S ij k is not equal to zero, then Q ci will be a specific capacity of Var for the bus i, and Q ci k is the value of Var required at k. P tieline is power flowing with communication lines between them.TTC(Q c (k) ) is a one-way interpolation following Formula (4) for voltage stability.Q c is the total set of Q ci candidates.
The y and x were Var capacities, p(x,y), TTC, and Var function capacity.Equation ( 7) addresses the minimization of cost, voltage stability, and system losses.As stated previously, one of the goals of the present paper is to ensure the system voltage stability during optimal load distribution.The most crucial issue is voltage stability for both standard and critical (unwanted) conditions.For an extensive system with a probability of various errors, these two modes are a challenge.In order to address this problem, the following formulation are able to guarantee system stability under different working conditions: where Q 0 Li and P 0 Li are the initial demand for active RP in ith busbar, respectively.P ij0 , P ij (k) were the initial power and the current power flowing in the line between the i-j busbars.K = 1, . . ., N cntg shows the different working conditions, including normal conditions and those containing the error.

Fuzzy Classification
One of the essential points in RP was investigated optimal location for FACTS devices.In other words, the most crucial point in RP was determining the proper location of the Var equipment in order to reduce calculation time and ensure voltage stability.In this paper, interactive fuzzy classification is proposed to obtain FACTS location devices.Fuzzy classification combines standard fuzzy classification and regression [49].In the proposed fuzzy method, the distance (d ij ) between each data (x i ) and the center of the class (v) is expressed based on the standard fuzzy distance and regression: f uzzy−regression distance (10) where x j ∈ X and y j ∈ Y are input and output data, respectively.nd in the index j = 1, . . ., nd is the data number in a vector for training.c in the index i = 1, . . ., c is the number of centers of the classes.ŷj = β T i x is the polynomial estimation, where β is a polynomial coefficient.Based on the above definitions, the membership function u j (x i ) can be expressed as follows: where η > 0 is considered as a constant value.In order to optimize fuzzy members, the error of the regression is considered in the following objective function: error of fuzzy regression (12) where µ ik is the undefined function from the kth input vector in the ith fuzzy category.m is the degree of fuzzification that expresses the amount of overlap between the categories.As the abovementioned relationship shows, J MFC m consider two parts.The first part, which is similar to the standard fuzzy classification mechanism (FCM), controls the categorization accuracy.The second part is the sum of the error squares ( f category.This section checks the error rate due to the fuzzy classification based on the fuzzy function, the matrix (τ), and the "or" and "and" constraints.Based on the new fuzzy distance defined in the above relation, we can introduce the new fuzzy membership function as follows: In the new membership function, the centrality of each category can be expressed as follows: The above formula states that the membership function for x i depends on the distance between that variable and all v i categories.The categories created in this paper can be defined based on the loss factor, voltage stability, and the cost of installing FACTS equipment.

RP with FACTS and Wind Unit
Rapid progress in wind power generation has led to a significant increase in the installation of wind turbines in the world.Research centers worldwide are extensively studying and researching various aspects of the optimal utilization of this energy resource.Simulation of wind turbines by software is a research tool for investigating the behavior of wind turbines.In addition, increasing the simulation parameters and considering the system details increase the accuracy of the simulations and the simulation time.Therefore, various dynamic models of generators for power generation from wind have been studied, one of which is electricity generation from the double-fed induction generator (DFIG) [6].DFIG can be a good option for systems with variable speed (approximately 30% synchronous speed).Figure 1 shows the schema of a DFIG [91].
where ik μ is the undefined function from the k th input vector in the i th fuzzy category.m is the degree of fuzzification that expresses the amount of overlap between the categories.As the abovementioned relationship shows, FC M m J consider two parts.The first part, which is similar to the standard fuzzy classification mechanism (FCM), controls the categorization accuracy.The second part is the sum of the error squares ( ( ) i f τ ) derived from the i th category.This section checks the error rate due to the fuzzy classification based on the fuzzy function, the matrix (τ ), and the "or" and "and" constraints.Based on the new fuzzy distance defined in the above relation, we can introduce the new fuzzy membership function as follows: In the new membership function, the centrality of each category can be expressed as follows: The above formula states that the membership function for xi depends on the distance between that variable and all vi categories.The categories created in this paper can be defined based on the loss factor, voltage stability, and the cost of installing FACTS equipment.

RP with FACTS and Wind Unit
Rapid progress in wind power generation has led to a significant increase in the installation of wind turbines in the world.Research centers worldwide are extensively studying and researching various aspects of the optimal utilization of this energy resource.Simulation of wind turbines by software is a research tool for investigating the behavior of wind turbines.In addition, increasing the simulation parameters and considering the system details increase the accuracy of the simulations and the simulation time.Therefore, various dynamic models of generators for power generation from wind have been studied, one of which is electricity generation from the double-fed induction generator (DFIG) [6].DFIG can be a good option for systems with variable speed (approximately 30% synchronous speed).Figure 1 shows the schema of a DFIG [91].In a DFIG, the injection of RP for the network depends on the control system and the size of the converter.Figure 2 shows the P-Q characteristic for wind turbines (WTs) used in this paper.Specifications of this turbine (Gamesa WT G80-2.0MW) can be obtained from the reference [92].This turbine provides a 0.98 power factor in the pre-phase mode In a DFIG, the injection of RP for the network depends on the control system and the size of the converter.Figure 2 shows the P-Q characteristic for wind turbines (WTs) used in this paper.Specifications of this turbine (Gamesa WT G80-2.0MW) can be obtained from the reference [92].This turbine provides a 0.98 power factor in the pre-phase mode and 0.96 in the post-phase mode.Therefore, its reactivity depends on the generation of active power, as shown in Figure 3.The green line in Figure 3 shows the P-Q of the wind turbine (WT) at the power factor 1. For power less than 10 megawatts, the cables have a more significant effect than the transformer, while the transformer is more influential in the high-power WT.In addition, if the wind farm (WF) receives the RP of a capacitor lower than the range of the active power generation, then WTs are set to the selfie mode.Based on the above explanations, since WFs can inject or receive RP, we need to adjust them optimally.In order to optimize RP, STATCOM or capacitor is used.The ultimate target function, by taking into account the loss function, is as follows:  and 0.96 in the post-phase mode.Therefore, its reactivity depends on the generation of active power, as shown in Figure 3.The green line in Figure 3 shows the P-Q of the wind turbine (WT) at the power factor 1. For power less than 10 megawatts, the cables have a more significant effect than the transformer, while the transformer is more influential in the high-power WT.In addition, if the wind farm (WF) receives the RP of a capacitor lower than the range of the active power generation, then WTs are set to the selfie mode.Based on the above explanations, since WFs can inject or receive RP, we need to adjust them optimally.In order to optimize RP, STATCOM or capacitor is used.The ultimate target function, by taking into account the loss function, is as follows:  The green line in Figure 3 shows the P-Q of the wind turbine (WT) at the power factor 1. For power less than 10 megawatts, the cables have a more significant effect than the transformer, while the transformer is more influential in the high-power WT.In addition, if the wind farm (WF) receives the RP of a capacitor lower than the range of the active power generation, then WTs are set to the selfie mode.Based on the above explanations, since WFs can inject or receive RP, we need to adjust them optimally.In order to optimize RP, STATCOM or capacitor is used.The ultimate target function, by taking into account the loss function, is as follows:

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Minimize J(Var x , Var y ) = Min P losses ( 15) where Var y shows the location of the tapped transformer.The optimal configuration of STATCOM and capacitor is performed independently, which includes the following constraints: There is also a non-linear constraint.RP demand for PCC to adjust voltage is modeled as follows: In this paper, the condition of obtaining the possible response is given in Equation ( 20) to guarantee that the set of solutions covers the limits imposed on the system: Since Constraint ( 19) is an equality constraint, to apply it non-linearly, we can use the following equation based on error (ε): Based on the explanations mentioned earlier, Figure 4 shows the strategy used in this paper.where Vary shows the location of the tapped transformer.The optimal configuration of STATCOM and capacitor is performed independently, which includes the following constraints: min max , 1,2,..., There is also a non-linear constraint.RP demand for PCC to adjust voltage is modeled as follows: In this paper, the condition of obtaining the possible response is given in Equation (20) to guarantee that the set of solutions covers the limits imposed on the system: Since Constraint ( 19) is an equality constraint, to apply it non-linearly, we can use the following equation based on error (ε): Based on the explanations mentioned earlier, Figure 4 shows the strategy used in this paper.

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Definitions and Basic Concepts VCS algorithm form on viruses population, and it was founded for two virus behaviors.Viruses require host cells to ensure their survival, production, and plurality.In what follows, the strategy of viruses has been described, including host cell contamination [22].
The function of the immune system is also considered as the opposite relationship between these two stages.These stages are explained in more detail as follows: (1) Virus replication: Viruses randomly scan the cells to find the raw materials needed for survival.In this process, a random walk method can be the best mathematical model for expressing the function of viruses to detect host cells.(2) The infection or influence of host cells: When a virus selects a cell, it tries to replicate itself in the best manner.In other words, the virus replicates itself based on the essential materials in the host cell until the host cell dies and acts like a virus.To model this behavior, the CMA-ES mathematical model is a covariance matrix-based method.(3) Function of the immune system: The immune system has the essential task of protecting the cell against the replication and spread of the virus.In addition, more powerful viruses save themselves from reproducing in the proper position.

• Matching mathematical models
Virus algorithm has three models: (1) Gaussian model to virus propagation that utilized for recognition improving; (2) CMA-ES model to cell damage modeling that utilized for social behavior improving; and (3) evolution strategy to resist a virus that utilized for improving two other strategies [93].Therefore, the virus colony algorithms have five steps: 1.
Vpop virus and Hpop cells were utilized in the VCS model.

2.
Virus for transferring has unique behavior.

3.
Viruses can desire to infect the cell.4.
Virus reproduction was formed on cell destruction to find survival.

5.
Best viruses can remain for replication.

• Virus transmission
Gaussian model is formulated via this equation: The Ì standard deviation was calculated via log(g)/g.(Vpop i − G g best ) the log(g)/g is used to increase virus search.The G g best , τ is produced the best answer for virus searching via vector (r 1 .G The cell was infected, and it can be modeled via CMA-ES in these steps: Step 1: Update the Hpop via: where σ g > 0. X g mean was obtained via this equation: Step 2: Select vector γ and obtain parents vector via this equation: In the above relation, γ = [N/2], w i is the coefficient of the combination, and two mentioned paths are obtained via: The parameters were set via C σ = (γ ω + 2)/(N + γ ω + 3), s.

Immune system
The evolutionary movement is obtained via these steps: Step 1: P r to V pop population: Step 2: Each individual grows individually to V pop via this equation: The response is tried to save the best stage value, and other unusual response can be obtained via this equation:

Modified Particle Swarm Optimization
Eberhart has introduced a swarm optimization model by the group search for food by birds or fish [94].In the past decade, a variety of topologies has been proposed for the PSO algorithm.Topologies used to exchange information between particles in the PSO algorithm include star, ring, and square topologies [95].Figure 5 shows the relationship between particles in different topologies.

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Sensors 2021, 21, 5246 12 of 32

Modified Particle Swarm Optimization
Eberhart has introduced a swarm optimization model by the group search for food by birds or fish [94].In the past decade, a variety of topologies has been proposed for the PSO algorithm.Topologies used to exchange information between particles in the PSO algorithm include star, ring, and square topologies [95].Figure 5 shows the relationship between particles in different topologies.In the star topology for D-dimensional space, the best personal status for particle i is indicated by → p i = (p i1 , p i2 , . . . ,p iD ) and the group's best position → g = (g 1 , g 2 , . . . ,g D ).The relations between the velocity and movement of particle i in the next moment or repetition are obtained by the following relations [29].
c 1 and c 2 are called the cognitive and the social parameters, respectively, which are usually set to 2. To randomize the nature of velocity, the coefficients c 1 and c 2 are multiplied by the random numbers rand 1 and rand 2 .Usually, in the implementation of the PSO, the value of ω decreases linearly from one to zero.Generally, the inertia coefficient ω is governed by the following equation.
The value of v max is usually chosen in such a manner that v max = kx max and 0.1 < k < 1. x max specifies the length of the search.As is clear from Formula (34), the coefficients c 1 and c 2 are usually considered constant, which is the dark point in the local and final search for the particle swarm model.These coefficients can be suggested to improve the efficiency of virus search: The correlation coefficient c 1i is updated in each replication.If c 1i has a small value, then c 1i r 1 is small and local search is strengthened.Conversely, it has an immense value if it has a significant value, thus improving the overall search.To select the best value for c 1i , two thresholds of T 1 < 0 and T 2 > 0 and two variables of R 1 in the range (0, T 1 ) and R 2 in the range (0, T 2 ) are used and defined as c 1i = 2 R 1 and c 2i = 2 R 2 .As a result, the two vector populations with coefficients of c 1i and c 2i are generated.When T 1 < 0, then R 1 is negative, and c 1i has a small value, thus improving local search.

The Proposed Hybrid Algorithm
This section introduces the structure of the hybrid modified particle swarm optimization and HMPSO-VCS model.Figure 6 shows a schema of the HMPSO-VCS.It also shows that the hybrid VCS and particle swarm optimization algorithm is started for an initial population.When N-dimensional problem is obtained, then the hybrid algorithm has 4N members generated entirely randomly.Next, 4N members are sorted according to their eligibility, and the upper 2N members enter the VCS as a virus.VCS formulations create the new 2N member population.The mechanism of optimizing the particle swarm is applied to the 2N lower members as particles.In applying the mechanism of particle swarm optimization, the population is obtained via VCS.The P gbest is the corresponding member is used in Equation (37).The population generated by applying the mechanism of the particle swarm optimization to the population obtained via virus colony search

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Sensors 2021, 21, 5246 13 of 32 algorithm was merged, and the 4N new member population is sorted according to the eligibility, and the previous process is repeated until convergence is achieved.

The Proposed Multi-Objective Algorithm
The proposed algorithm has been used based on the entropy accumulation to label each objective function.Entropy optimization is based on the Pareto criterion.In this method, for optimization in each step, a set is labeled as a better response and enters the next step.The criterion for the multi-objective problem can be obtained via: The X1 was no worse than X2, and X1 were better than X2, and mathematical terms are stated via: In addition, the The steps for the HMPSO-VCS algorithm are as follows: (1) Random generation of the initial population with 4N members as initial responses (2) Evaluating and sorting the population according to its eligibility (3) Applying the VCS algorithm to the 2N upper members of the population based on the mutation and crossover of the generations

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Selection: For the target population, the best 2N members are selected based on their eligibility.

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Crossover: For a well-chosen population, we use the crossover of two parents to produce a new generation.

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Mutations: 20% of the new population is mutated.
(4) The particle swarm optimization algorithm is applied to another 2N population based on the production relations of the new population, and the new population is produced.Next, 2N population is combined with the 2N population generated by the virus colony search algorithm.(5) Repeat the previous steps from Step (2) until the convergence or termination requirements are met.

The Proposed Multi-Objective Algorithm
The proposed algorithm has been used based on the entropy accumulation to label each objective function.Entropy optimization is based on the Pareto criterion.In this method, for optimization in each step, a set is labeled as a better response and enters the next step.The criterion for the multi-objective problem can be obtained via: The X 1 was no worse than X 2, and X 1 were better than X 2, and mathematical terms are stated via: Sensors 2021, 21, 5246 14 of 32 In addition, the X ∈ X f is stated non-dominated of relation to Therefore, we can assume that the vector X is optimal [96].The non-dominated decision vectors sets is obtained via: Set A was equal to X f , then P(A) is produced Pareto optimal front.An ideal point and anti-ideal point, objective functions are minimal and maximal, respectively.

Combining Fuzzy Logic with the Proposed Algorithm
Figure 7 indicates membership µ c [97] for fuzzy that states cost concept.
Sensors 2021, 21, x FOR PEER REVIEW 14 of 30 Therefore, we can assume that the vector X is optimal [96].The non-dominated decision vectors sets is obtained via: Set A was equal to Xf, then P(A) is produced Pareto optimal front.An ideal point and anti-ideal point, objective functions are minimal and maximal, respectively.

Combining Fuzzy Logic with the Proposed Algorithm
Figure 7 indicates membership μc [97] for fuzzy that states cost concept.The fi(Pgi) is stated via μi(Pgi) in this equation: The lower limits of i th objective function: The FDM k function is obtained via: The decision maker is selected the best solution by considering the function in actual conditions.The f i (P gi ) is stated via µ i (P gi ) in this equation: The lower limits of ith objective function: The FDM k function is obtained via: The decision maker is selected the best solution by considering the function in actual conditions.

Implementation of Problem of RP Planning
To solve RP with FACTS presence, the following steps are performed: Step 1: The set initial parameters of the suggested algorithm are studied.The initial population with N units is produced as follows: In this regard, the number of FACTS devices, tap transformers, and shunt capacitors is encoded as mentioned above.Subnets n, m, and o represent the number of variables used.Variables are also generated based on the upper and lower bounds: The initial responses should be placed within the constraints to create a better search for the algorithm at this stage.
Step 2: Apply the limitations on the problem, arrange them on the cost function.
Step 3: Use the proposed fuzzy cluster algorithm to select the best load bus bars for installing the FACTS devices.
Step 4: Choose the best response, and these sets of responses are replaced in initial responses that are considered null.
Step 5: Use the target function introduced for the loss function, voltage, and cost of FACTs installation, calculate the fitness of responses and select the best response.
Step 6: Compare good response and stored response.
Step 7: Sort data based on the Pareto criterion and choose the best response sets as the best current response.
Step 8: Replace the worst responses by random data and use a modified particle swarm to find the best response.
Step 9: Is termination completed?In this case, leave the program; if not, go to Step 3.
Figure 8 shows the flowchart of the proposed algorithm.

Determination of Optimal Location by the Proposed Fuzzy Method
First, we propose a fuzzy method for obtaining FACTS installation.The purpose of this action is to determine the most talented buses for installing these resources.To determine these locations, criteria such as L-index, U/U 0 , and voltage stability have been used.
(A).U/U 0 criterion: This criterion is considered based on the voltage range for all buses as follows: The U and U 0 are the voltage range vector of the normal state for all buses and the voltage range vector of all bass when all loads are zero.
(B).L-Index criterion: Generally, increasing load and the optimal performance of the power system are considered more than before.A voltage failure can be created suddenly in the system, resulting from weaker buses.For the jth bus, the rate of voltage drop or failure is expressed as follows: Y 1 and Y 2 matrices were below the invertible submatrices for Y BUS matrix, which are obtained by sorting them according to the following matrix: (C).Voltage stability criterion is expressed in Formula (2).

IEEE 30-Bus Standard
The 30-bus system is the most popular in power engineering.This system consists of 6 power plants and 46 transmission lines.Table 1 presents the results of applying the fuzzy method and determines the most talented bus for SVC.As the numerical results show, according to the L-Index, the most talented buses are {3, 7, 9, 14, 15, 17, 23, and 24}.According to the U/U 0 criterion, these talented buses are {4, 7, 15, 17, 20, 21, and 25}.Finally, based on the voltage criterion, the best buses for installation are {4, 7, 15, 16, 17, 21, and 24}.Based on the criteria described, the candidate buses are not the same in all three modes.By fuzzy classification, the best buses are classified as follows: {7, 15, 17, 21}, {4, 24}, and {9, 16}.Similarly, fuzzy classification is performed for TCSC, and the best candidates are lines 5, 25, 28, and 41.Now, we should consider the RP planning with the presence FACTS devices in the system under study.Tables 2-4 shows these results with the presence of FACTS devices.As mentioned previously, two types of SVC equipment have been used as shunt and TCSC series in line with the present study.Table 3 indicates a comparison of the costs and losses of the 30-bus standard system in RP planning.According to this table, it is clear that when FACTS equipment operates in sync with RP devices such as tap transformers and RP generators, the system operation costs and losses considerably improve compared with when FACTS devices are not present.In addition, the results reveal that the mentioned model has better performance than another models.0.9 (11) 0.9133 (12) 0.9 (15) 0.9010 (36) 0.0174 (7) 0.0468 (15) 0.0025 (17) 0.0209 (21) EPSO [98] 0.1462 (2) 0.2642 (5) 0.2977 (8) 0.1061 (11) 0.2213 (13) 0.9026 (11) 0.9 (12) 0.9 (15) 0.9 (36) 0.0 (7) 0.0 (15) 0.0295 (17) 0.0 ( 21) As can be seen from the results of Tables 2-4, the proposed method has been able to obtain far fewer answers compared to other methods in terms of cost criteria, loss rate, and operating cost.On average, it can be seen that the proposed method worked about 5% better.

IEEE 57-Bus Standard System
Here, to illustrate the proposed model, a more extensive 57-bus system is selected with the information mentioned in other papers.Similar to the previous section, in this section, the fuzzy classification method is used first.Based on this method, buses 25, 38, and 49 are the best option for SVC installation, and lines 13, 37, 57, and 61 are the best candidates for TCSC installation.Table 5 shows the comparison between system costs and losses of the 57-bus standard system in RP planning.The results indicate mentioned model is more successful than other models.This represents the better local and overall search of this algorithm to find the final result.This algorithm has shown better performance despite the increasing number of input variables.RP planning performance in the Mongolia system is studied.There are approximately 200 wind turbines installed in this system.Capacity is over 300 megawatts.With the help of T 2 transmissions, the output of these turbines is increased to 35 kV and is transmitted through the transmission lines to the distribution site.This wind farm contains 403 nodes, and more information is available in reference [99].Figure 9 shows a section of this network.To compensate for RP, the SVC compensator is installed in the nodes.The reference power in this system is 100 megawatts, and the most significant revenue generated from RP is approximately $500 million.Table 6 provides the comparison between the performance of the mentioned model and other models for RP planning.RP planning performance in the Mongolia system is studied.There are approximately 200 wind turbines installed in this system.Capacity is over 300 megawatts.With the help of T2 transmissions, the output of these turbines is increased to 35 kV and is transmitted through the transmission lines to the distribution site.This wind farm contains 403 nodes, and more information is available in reference [99].Figure 9 shows a section of this network.To compensate for RP, the SVC compensator is installed in the nodes.The reference power in this system is 100 megawatts, and the most significant revenue generated from RP is approximately $500 million.Table 6 provides the comparison between the performance of the mentioned model and other models for RP planning.As the results presented in the following tables demonstrate, the proposed method has produced significant improvements in responses to the problem.It is also clear from Table 6 that when the wind speed changes from 4 to 12 m/s, the loss rate increases significantly, but compared to other optimization methods, the proposed method has fewer losses.

RP Planning Based on the Possibility of Controlling Wind Turbines (WTs)
As the last analysis of the system under study, this section investigates RP planning by fully covering Section 2.2.RP planning is applied to the wind farm (WF) for this model, according to Figure 10.The short circuit current for the external network is 400 megawatts.In the wind farm, 12 connected wind turbines are considered.

RP planning based on the possibility of controlling wind turbines (WTs)
As the last analysis of the system under study, this section investigates RP planning 608 by fully covering subsection 2.2.For this mode, RP planning is applied to the wind farm 609 (WF) according to Fig. 10.The short circuit current for the external network is 400 mega-610 watts.Table 8 presents the information on this system.In the wind farm, 12 connected 611 wind turbines are considered.In addition, in this system, the STATCOM compensator is used at PCC.The objective in the scenario is to reduce the losses and keep the system error in the safe range based on setting the PCC setting point.Usually, such a function is considered for the demand for a large amount of RP.In addition, the tapped transformer and RP compensator are used as other control items.In order to control RP, six different control models are applied to control RP in the wind farm.Figure 11 shows the structure of these control systems.The maximum RP error based on the PCC adjustment system is approximately 5%.The strategies adopted are as follows: maximum, amount of RP was 4 MVAr.Figure 11b shows the structure of this strategy.
Strategy 3: In this case, RP planning was formed on the RP amount of wind turbine QWTi injected into the capacitor system and bank.Power production maximum, amount of RP was 4 MVAr and Q * PCC = 4 MVAr.Figure 11c shows the structure of this strategy.
Strategy 4: In this case, RP planning is based on adjusting the tapped transformer and the generation of RP from the wind turbine.Therefore, two control in this system are QWTi and tap transformer.RP value is equal to Q * PCC = 4 MVAr.Figure 11d shows the structure of this strategy.
Strategy 5: STATCOM compensator was installed for PCC.Therefore, in addition to the two previous variables, the STATCOM compensator is considered a new control parameter.Figure 11e shows the structure of this strategy.The STATCOM system with 30% of the total power and wind turbine capacity is selected.Therefore, the capacity of RP with the STATCOM compensator is approximately 1.22 MVAr.
Strategy 6 is similar to Strategy 5, but the difference is that the constraint Q * PCC is not considered.Virus search is employed, and Figure 11 shows the structure of this strategy.Strategy 1: The variables are RP for wind turbine Q WTi , location of the tapped transformer for PCC, and capacitor banks.The capacitor capacity was 0.96 MVAr. Figure 11a shows the structure of this strategy.
Strategy 2: RP of wind turbine Q WTi is the only control parameter.Power production maximum, amount of RP was 4 MVAr.Figure 11b shows the structure of this strategy.
Strategy 3: In this case, RP planning was formed on the RP amount of wind turbine Q WTi injected into the capacitor system and bank.Power production maximum, amount of RP was 4 MVAr and Q * PCC = 4 MVAr.Figure 11c shows the structure of this strategy.Strategy 4: In this case, RP planning is based on adjusting the tapped transformer and the generation of RP from the wind turbine.Therefore, two control parameters in this system are Q WTi and tap transformer.RP value is equal to Q * PCC = 4 MVAr.Figure 11d shows the structure of this strategy.
Strategy 5: STATCOM compensator was installed for PCC.Therefore, in addition to the two previous variables, the STATCOM compensator is considered a new control parameter.Figure 11e shows the structure of this strategy.The STATCOM system with 30% of the total power and wind turbine capacity is selected.Therefore, the capacity of RP with the STATCOM compensator is approximately 1.22 MVAr.
Strategy 6 is similar to Strategy 5, but the difference is that the constraint Q * PCC is not considered.Virus search is employed, and Figure 11 shows the structure of this strategy.
Tables 7 and 8 show RP data by the proposed algorithm based on the possible response under different working conditions and the corresponding It is found that different individual adjustment points are considered for WT because the distance and feature of PCC vary from one wind turbine to another.Table 9 represents the simulation results for strategies 2 to 6 (Figure 11).It is clear that lower power is obtained via STATCOM, and error is lower with Strategy 5 using the STATCOM and the proposed HMPSO-VCS.In Strategies 5 and 6, the results depict that RP error is more significant than PSO than the proposed HMPSO-VCS method.In the following, the proposed algorithms with other optimization methods are compared.For this purpose, Table 10 reports the list of different test functions which used in this simulation and Table 11 shows the results of the simulation.The proposed method is compared with many other methods and results shown that the proposed algorithm has worked much better than other methods [101][102][103][104][105][106][107].

R E T R A
C T E D

Conclusions
RP distribution in power systems is optimized by adjusting the voltage of generators, tap transformers with the ability to change under load, and the size of parallel capacitors.With the expansion of power networks and the development of renewable resources, considerable attention is devoted to RP resources in the network.With this end in view, objective functions based on losses, voltage, and cost of RP sources were applied in this paper.This paper presents a new model for optimal reactive power distribution.To bring the issue to a more realistic level, renewable resources and facsimiles have also been considered.On the other hand, by increasing the numbers of these types of equipment, if it is not possible to make an optimal and appropriate choice from them, the system's stability is not adequately established, but it also leads to more errors.For this reason, solving this problem has become an optimization, and a new hybrid algorithm based on virus search and particle clustering has been used to solve it.Using this hybrid model has been able to improve local and global search dramatically.The fuzzy theory was employed to install RP resources of shunt and the SVC and TCSC series.In this model, various criteria were used to determine the best position.In the method used in this scheme, the discrete variables are considered continuous and treated like any other continuous variables in the algorithm's space.At each stage, after reaching the new position, the discrete variables that have become continuous are now rounded off to the appropriate number before applying to the load program.For example, tapping tap changers is a discrete quantity.In the process of running the algorithm, when a value between the two tap changers is obtained for this quantity, this value is rounded off to the nearest step and then applied to the load program.Finally, the problem of RP planning was solved using a novel algorithm from on virus search.Appropriate search, choosing the best response at each stage, improving the set of responses, and the crossover of generations to give the best responses are among prominent features for the proposed method.The results obtained in different sections show that the proposed method has an average performance of 5% better.

Figure 1 .
Figure 1.Variable speed wind turbine with a DFIG.

Figure 1 .
Figure 1.Variable speed wind turbine with a DFIG.
96 in the post-phase mode.Therefore, its reactivity depends on the generation of active power, as shown in Figure3.
x y lo s s e s Minimize J(Var ,Var )=Min P(15)
x y lo s s e s Minimize J(Var ,Var )=Min P(15)

Figure 4 . 3 .
Figure 4. Solution search process.R E T R A C T E D

Figure 5 .
Figure 5. Topologies used in the PSO algorithm.Figure 5. Topologies used in the PSO algorithm.

Figure 5 .
Figure 5. Topologies used in the PSO algorithm.Figure 5. Topologies used in the PSO algorithm.

021, 21 , 30 Figure 6 .( 4 )
Figure 6.Combining the VCS ( ) and swarm optimization ( ).The steps for the HMPSO-VCS algorithm are as follows: (1) Random generation of the initial population with 4N members as initial responses (2) Evaluating and sorting the population according to its eligibility (3) Applying the VCS algorithm to the 2N upper members of the population based on the mutation and crossover of the generations • Selection: For the target population, the best 2N members are selected based on their eligibility.• Crossover: For a well-chosen population, we use the crossover of two parents to produce a new generation.• Mutations: 20% of the new population is mutated.(4) The particle swarm optimization algorithm is applied to another 2N population based on the production relations of the new population, and the new population is produced.Next, 2N population is combined with the 2N population generated by the virus colony search algorithm.(5) Repeat the previous steps from Step (2) until the convergence or termination requirements are met.

Figure 7 .
Figure 7.The membership function for the cost and loss function and the voltage synchronization.

Figure 7 .
Figure 7.The membership function for the cost and loss function and the voltage synchronization.

Figure 8 .
Figure 8. Applying the proposed algorithm and FACTS presence.Figure 8. Applying the proposed algorithm and FACTS presence.

Figure 8 .
Figure 8. Applying the proposed algorithm and FACTS presence.Figure 8. Applying the proposed algorithm and FACTS presence.

Figure 9 .Table 6 .Figure 9 .
Figure 9.The structure of the system under study with the presence of wind turbines.Table 6.Numerical comparison of the losses of the system under study with the presence of wind resources.Project Investment of RP Compensation (Million Yuan) The System Loss (kW) V = 4 m/s V = 8 m/s V = 12 m/s TGA [100] 338 1872 2480 3129 IGA [100] 336 1731 2292 2892

Figure 9 .
Figure 9.The structure of the system under study with the presence of wind turbines.

Figure 11 .
Figure 11.RP strategies, the proposed HMPSO-VCS, and basic VCS.Tables7 and 8show RP data by the proposed algorithm based on the possible response under different working conditions and the corresponding compensation.It is found that different individual adjustment points are considered for WT because the distance and feature of PCC vary from one wind turbine to another.

Table 1 .
The results of determining the most talented bus in SVC installation.

Table 2 .
The optimum range for RP resources for the 30-bus standard system without the presence of FACTS devices.

Table 3 .
The optimal range for RP sources for the 30-bus system with the presence of FACTS devices.

Table 4 .
Active power losses and operation costs for the 30-bus system with different optimization methods.

Table 5 .
Active power losses and operation costs for the 57-bus system with various optimization methods.

Table 6 .
Numerical comparison of the losses of the system under study with the presence of wind resources.

Table 7 .
Numerical comparison of the losses of the system under study with the presence of wind resources.

Table 7 .
Data of option I.

Table 8 .
Data of strategy I.

Table 9 .
Data for an option I.