A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> The paper presents an integrated framework to analyze the issues of reactive power planning along with reactive power pricing. The planning problem involves optimal placement and sizing of capacitors in a network such that operating and investment costs are minimum. A simple bus-wise cost-benefit analysis (CBA) scheme is proposed which involves solving a modified optimal power flow problem (OPF) iteratively. The proposed CBA incorporates detailed hourly loading conditions at a bus and achieves a fairly accurate estimate of the benefits from capacitor placement. The formulation is directly handled by the well known MINOS code and is solved efficiently. It obviates the need to introduce integer variables and is thus suitable for large system applications. A two-part reactive power spot-pricing scheme is formulated, by which the investment and operational costs can be recovered by the utility. The proposed reactive power price has two parts-a fixed part to account for the investment costs of new capacitor at a bus and a variable spot price to account for the operating costs incurred in supplying the additional reactive power from generating units. <s> BIB001 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> This paper addresses some of the modeling and economic issues pertaining to reactive power planning. We present a new VAR planning model, propose an efficient solution algorithm, and discuss the economic issues. A contingency constrained OPF-based model incorporating (static) voltage stability constraints is developed to analyze VAR support decisions. DICOPT++, a state-of-the-art non-linear mixed integer programming (MINLP) algorithm, is proposed to solve the model efficiently. The sensitivity information elicited from the optimization model may also provide useful aid to network planning that are discussed. The VAR support cost allocation issue is addressed next. The Shapley value criterion of cooperative gaming is proposed to allocate VAR support costs among the loads contributing to voltage instability. The VAR planning model is implemented for the AEP 14-bus test system. The implications of the sensitivity information are discussed using the test system results. The result of the optimization approach is compared with two existing methods viz., Eigen Value (Modal) and Singular Value Decomposition (SVD) methods. Further, we discuss how the outcome of the Modal analysis could be integrated in the optimization model to form a hybrid approach. A numerical example of calculation of Shapley value is provided and, we also compare it with the conventional method of proportional allocation to gain better insight about this criterion. <s> BIB002 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> The particle swarm optimization (PSO) has been shown to converge rapidly during the initial stages of a global search, but around global optimum, the search pro~ess becomes very slow. On the other hand, the genetic algorithm is very sensitive to the initial population. In fact, the random nature of the GA operators makes the algorithm sensitive to initial population. This dependence to the initial population is in such a manner that the algorithm may not converge if the initial population is not well selected. In this paper, we have proposed a new algorithm which combines PSO and GA in such a way that the new algorithm is more effective and efficient and can find the optimal solution more accurately and with less computational time. Optimal location of SVC using this hybrid PSO-GA algorithm is found. We have also found the optimal place of SVC using GA and PSO separately and have compared the results. It has been shown that the new algorithm is more effective and efficient. An IEEE 68 bus test system is used for simulation. <s> BIB003 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> Abstract It is generally accepted that reactive power (or Var) compensation will bring benefits for utilities and industrial customers by providing local voltage and power factor support. However, there is a lack of a systematic approach to quantitatively identify the economic benefit. In addition, with the deregulation and restructuring, it is important to indicate the amount of benefit that each market participant may potentially receive given the right price signals. If such information can be easily obtained and presented, it will be more convenient for decision-markers to determine the cost benefit sharing of installing a Var compensator. This vision of this paper is to lay out a possible method for quantitatively evaluating the benefits from local reactive power compensation. The approach is to quantify the benefits into several categories such as reduced losses, shifting reactive power flow to real power flow, and increased transfer. The calculation of these benefits are illustrated with a simple two-bus power system model and then presented with a more complicated model using Optimal Power Flow to calculate the benefits. Simulation on the more complex system is conducted with seven buses in two areas. The simulation results show that the possible economic benefits can be significant,more » if compared with capacity payments to central generators or payment of power factor penalties applied by utilities. The potential economic value of local Var compensation may give various parties in electricity supply, delivery and end-use consumption a better understanding of the Var benefits to assist their cost-benefit analysis for Var compensation installation. Sensitivity analysis is also provided to illustrate that the benefits may not be monotonically increasing. Also, this paper suggests that the future reactive power market should consider local Var providers or other way to encourage load Var capability, since local Var benefit is significant.« less <s> BIB004 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> Abstract People have paid more attention to enhancing voltage stability margin since voltage collapses happened in some power systems recently. This paper proposes an optimal reactive power flow (ORPF) incorporating static voltage stability based on a multi-objective adaptive immune algorithm (MOAIA). The main idea of the proposed algorithm is to add two parts to an existing immune algorithm. The first part defines both partial affinity and global affinity to evaluate the antibody affinity to the multi-objective functions. The second part uses adaptive crossover, mutation and clone rates for antibodies to maintain the antibodies diversity. Hence, the proposed algorithm can achieve a dynamic balance between individual diversity and population convergence. The paper describes ORPF’s multi-objective functional mathematical model and the constraint conditions. The problems associated with the antibody are also discussed in detail. The proposed method has been tested in the IEEE-30 system and compared with IGA (immune genetic algorithm). The results show that the proposed algorithm has improved performance over the IGA. <s> BIB005 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> Optimal reactive power dispatch (ORPD) has a growing impact on secure and economical operation of power systems. This issue is well known as a non-linear, multi-modal and multi-objective optimization problem where global optimization techniques are required in order to avoid local minima. In the last decades, computation intelligence-based techniques such as genetic algorithms (GAs), differential evolution (DE) algorithms and particle swarm optimization (PSO) algorithms, etc., have often been used for this aim. In this work, a seeker optimization algorithm (SOA) based method is proposed for ORPD considering static voltage stability and voltage deviation. The SOA is based on the concept of simulating the act of human searching where search direction is based on the empirical gradient by evaluating the response to the position changes and step length is based on uncertainty reasoning by using a simple Fuzzy rule. The algorithm's performance is studied with comparisons of two versions of GAs, three versions of DE algorithms and four versions of PSO algorithms on the IEEE 57 and 118-bus power systems. The simulation results show that the proposed approach performed better than the other listed algorithms and can be efficiently used for the ORPD problem. <s> BIB006 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> This paper proposes an optimization based method of planning reactive power control for electric transmission systems to endow them with the capability of being reconfigured to a secure configuration under a list of contingencies. The overall objective function is to minimize the installation cost of new controls such as mechanically switched capacitors, while satisfying the requirements of voltage stability margin and voltage magnitude under a contingency list. The backward/forward search algorithm with linear complexity is used to select candidate locations for switched capacitors. Optimal locations and amounts of new switch controls are obtained by solving a sequence of mixed integer programming problems. The modified New England 39-bus system and a North American power system with 6358 buses are adopted to illustrate the effectiveness of the proposed method. <s> BIB007 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> Optimal reactive power dispatch problem in power systems has thrown a growing influence on secure and economical operation of power systems. However, this issue is well known as a nonlinear, multimodal and mixed-variable problem. In the last decades, computation intelligence-based techniques, such as genetic algorithms (GAs), differential evolution (DE) algorithms and particle swarm optimization (PSO) algorithms, etc., have often been used for this aim. In this work, a seeker optimization algorithm (SOA)-based reactive power dispatch method is proposed. The SOA is based on the concept of simulating the act of human searching, where the search direction is based on the empirical gradient by evaluating the response to the position changes and the step length is based on uncertainty reasoning by using a simple Fuzzy rule. In this study, the algorithm's performance is evaluated on benchmark function optimization. Then, the SOA is applied to optimal reactive power dispatch on standard IEEE 57- and 118-bus power systems, and compared with conventional nonlinear programming method, two versions of GAs, three versions of DE algorithms and four versions of PSO algorithms. The simulation results show that the proposed approach is superior to the other listed algorithms and can be efficiently used for optimal reactive power dispatch. <s> BIB008 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> This paper presents a particle swarm optimization (PSO) approach for solving the contingency constrained optimal reactive power planning (CCORPP) problem. Generator bus voltage magnitudes, transformer tap settings and reactive power generation of capacitor bank are taken as the control variables. While solving the RPP problem using particle swarm optimization, the voltage magnitudes, the transformer tap setting and the reactive power generations of capacitor are taken as continuous variables. The proposed algorithm has been applied to find the optimal reactive power control variables in IEEE 30-bus system and is found to be more effective than the conventional methods and the Evolutionary Programming. <s> BIB009 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> Voltage stability assessment and control form the core function in a modern energy control centre. This paper presents an improved Genetic algorithm (GA) approach for voltage stability enhancement. The proposed technique is based on the minimization of the maximum of L-indices of load buses. Generator voltages, switchable VAR sources and transformer tap changers are used as optimization variables of this problem. The proposed approach permits the optimization variables to be represented in their natural form in the genetic population. For effective genetic processing, the crossover and mutation operators which can directly deal with the floating point numbers and integers are used. The proposed algorithm has been tested on IEEE 30-bus and IEEE 57-bus test systems and successful results have been obtained. <s> BIB010 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> This paper addresses an optimal Reactive Power Planning (RPP) of power system. The Static Var Compensator (SVC) is introduced into power system in order to reactive power support and voltage control. The locations and the outputs of SVCs are determined using our proposed optimal reactive power planning model. The proposed method optimizes several objective functions at the same time within one general objective. The optimized objectives are minimization of total investment in reactive power support, average voltage deviation and minimization of total system loss. These objective functions are one of the most important objectives for every transmission and distribution systems. Harmony Search Algorithm (HS) is used to solve the optimization problem. The validity of the proposed method is tested on a typical power system. <s> BIB011 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> Static Var compensator (SVC) is normally used in power system to improve voltage profile and reduce system power losses. In this paper, a relatively new optimization technique named as the improved harmony search algorithm (IHS) is applied to determine optimal location and size of SVC devices in a transmission network. A multi-criterion objective function comprising of both operational objectives and investment costs is considered. The results on the 57-bus test system showed that the IHS algorithm give lower power loss and better voltage improvement compared to the particle swarm optimization technique in solving the SVC placement and sizing problem. <s> BIB012 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> The optimal Reactive Power Dispatch (RPD) problem is a nonlinear constrained optimization problem. This paper presents true multi-objective solution set for multi-objective RPD problem. The objective functions are real power loss minimization and control variable adjustment costs. In this paper, a Modified Non-Dominated Sorting Genetic Algorithm version II (MNSGA-II) is proposed for solving RPD problem. For maintaining good diversity in the performance of NSGA-II, the concept of Dynamic Crowding Distance (DCD) is implemented in NSGA-II algorithm and given name as MNSGA-II. The standard IEEE 30-bus and IEEE 118 bus test systems are used. The results obtained using MNSGA-II are compared with NSGA-II and validated with reference Pareto front generated by conventional weighted sum method using Covariance Matrix Adapted Evolution Strategy (CMA-ES). The performance of NSGA-II and MNSGA-II are compared with respect to best, mean, worst and standard deviation of multi-objective performance measures.The results show the effectiveness of MNSGA-II and confirm its potential to solve the multi-objective RPD problem. <s> BIB013 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> In deregulated electric power systems, one of the most important topics is to augment the total system social welfare. Many different methods have been carried out for this problem. One of the most viable methods to increasing system social welfare is to supply the reactive demands as locally. In this way, the reactive demands are supplied via locally reactive sources and the capacity of transmission lines is not used to transfer reactive power of demands. Thus, the congestion of lines is not reached and the system social welfare which is related to the congestion of lines is increased. In this scope, this study addresses an optimal Reactive Power Planning (RPP) in a deregulated power system. The proposed method optimizes two objective functions at the same time within one general objective. The optimized objectives are minimization of total investment in reactive power support and maximizing of total system social welfare. Genetic Algorithm (GA) is used to solve the optimization problem. The validity of the proposed method is verified on a typical power system. <s> BIB014 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> This paper presents a multi-objective optimization methodology to solve the Optimal Reactive Power Flow (ORPF) problem. The e-constraint approach is implemented for the Multi-objective Mathematical Programming (MMP) formulation. The solution procedure uses Mixed Integer Non-Linear Programming (MINLP) model due to discrete variables, such as the tap settings of transformers and the reactive power output of capacitor banks. The optimum tap settings of transformers are directly determined in terms of the admittance matrix of the network since the admittance matrix is constructed in the optimization framework as additional equality constraints. The optimization problem is modeled in General Algebraic Modeling System (GAMS) software and solved using DICOPT solver. Simulation results are implemented on the IEEE 14-, 30-, and 118-bus test systems to simultaneously optimize the total fuel cost, power losses and the system loadability as objective functions. The simulation results show that the proposed algorithm is suitable and effective for the reactive power planning. <s> BIB015 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> This paper discusses the application of Modified Non-Dominated Sorting Genetic Algorithm-II (MNSGA-II) to multi-objective Reactive Power Planning (RPP) problem. The three objectives considered are minimization of combined operating and VAR allocation cost, bus voltage profile improvement and voltage stability enhancement. For maintaining good diversity in nondominated solutions, Dynamic Crowding Distance (DCD) procedure is implemented in NSGA-II and it is called as MNSGA-II. The standard IEEE 30-bus test system, practical 69-bus Indian system and IEEE 118-bus system are considered to analyze the performance of MNSGA-II. The results obtained using MNSGA-II are compared with NSGA-II and validated with reference pareto-front generated by conventional weighted sum method using Covariance Matrix Adapted Evolution Strategy (CMA-ES). The performance of NSGA-II and MNSGA-II are compared with respect to best, mean, worst and standard deviation of multi-objective performance measures namely gamma, spread, minimum spacing and Inverted Generational Distance (IGD) in 15 independent runs. The results show the effectiveness of MNSGA-II and confirm its potential to solve the multi-objective RPP problem. A decision-making procedure based on Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is used for finding best compromise solution from the set of pareto-solutions obtained through MNSGA-II. <s> BIB016 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> Abstract Reactive power dispatch (RPD) is one of the major issues of modern energy management system. This article presents an efficient genetic algorithm (GA) approach for modelling and solving RPD problem of power system in the framework of fuzzy goal programming (FGP) in uncertain environment. In the proposed approach, the objectives of the problem concerned with RPD problem are fuzzily described. In the solution process, the proposed GA method is used in the framework of FGP model in an iterative manner to reach a satisfactory decision. The proposed approach is tested on the standard IEEE 6-Generator 30-Bus System and compared with the solutions obtained in previous study. <s> BIB017 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> This paper proposes an efficient differential evolution (DE) algorithm for the solution of the optimal reactive power dispatch (ORPD) problem. The main objective of ORPD is to minimize the total active power loss with optimal setting of control variables. The continuous control variables are generator bus voltage magnitudes. The discrete control variables are transformer tap settings and reactive power of shunt compensators. In DE algorithm the other form of differential mutation operator is used. It consists to add the global best individual in the differential mutation operator to improve the solution. The DE algorithm solution has been tested on the standard IEEE 30-Bus test system to minimize the total active power loss without and with voltage profile improvement. The results have been compared to the other heuristic methods such as standard genetic algorithm and particle swarm optimization method. Finally, simulation results show that this method converges to better solutions. <s> BIB018 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> This paper presents a model for long-term reactive power planning where a deterministic nonlinear model is expanded into a multi-stage stochastic model under load uncertainty and an N-k contingency analysis. Reactive load shedding is introduced in the objective function to measure the reactive power deficit after the planning process. The objective is to minimize the sum of investment costs (IC), expected operation costs (EOC) and reactive load shedding costs optimizing the sizes and locations of new reactive compensation equipment to ensure power system security in each stage along the planning horizon. An efficient scenario generation and reduction methodology is used for modeling uncertainty. Expected benefits are calculated to establish the performance of the expected value with perfect information (EVPI) and the value of the stochastic solution (VSS) methodologies. The efficacy of the proposed model is tested and justified by the simulation results using the Ward-Hale 6-bus and the IEEE 14-bus systems. <s> BIB019 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> Abstract In this paper a mathematical model for solving simultaneous transmission network expansion and reactive power planning problem (TEPRPP) via an AC model has been presented. A Real Genetic Algorithm (RGA) combined an Interior Point Method (IPM) aimed to obtaining a significant quality solution for such a problem has been employed. The proposed algorithm is tested on three systems; IEEE 24-bus system, 46-bus south Brazilian and the Southeast Network of Iran (SNI). The obtained results show the capability and the viability of the proposed methodology incorporating the AC model of the TEPRPP problem even in real world. <s> BIB020 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> Reactive Power Dispatch is one of the important tasks in the operation and control of power systems. It is a section of optimization problems in power system that minimizes the objective functions by satisfying a set of constraints and using a set of controllable variables. As the Reactive Power Dispatch is a nonlinear problem, it has multiple minima. So the conventional techniques and mathematical programming methods are not suitable to solving these problems. In this paper, the Seeker Optimization Algorithm (SOA) is considered to find a global optimum reactive power dispatch by minimizing the different objective functions. In this work, the objective functions are reducing active power losses, improving voltage deviation and increasing voltage stability. To show efficiency and powerful performance of SOA, it is applied to optimal reactive power dispatch on standard IEEE-30 bus power system. Finally, the obtained results of SOA are compared with Particle Swarm Optimization (PSO) algorithm, Multi Agent Particle Swarm Optimization (MAPSO) and Genetic Algorithm (GA) methods. <s> BIB021 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The weighted sum approach <s> This study proposes an optimisation-based method of planning static and dynamic VAR sources for the enhancement of electric power transmission systems under a set of contingencies. The overall objective function is to minimise the total installation cost of static and dynamic VAR sources, while satisfying the requirements of long-term voltage stability margin and transient voltage dip under a contingency list. The backward/forward search algorithm with linear complexity is used to select candidate locations for reactive power compensation. Optimal locations and amounts of static and dynamic VAR sources are obtained by solving a sequence of mixed integer programming problems. The New England 39 bus system is adopted to illustrate the effectiveness of the proposed method. The systematic applicability of the proposed method to a large scale practical system is also illustrated using a 16173-bus U.S. Eastern Interconnection system. <s> BIB022
Multi-objective RPP problem has been treated also using weighted objective functions BIB014 BIB017 BIB018 BIB011 BIB012 BIB006 BIB003 . Weighted sum of different objectives can be generally modeled as follows: where x i and F i are the weighting factor and the objective function for each goal i, respectively and N F is the total Figure 2 Family and subcategories of the solution algorithms for the RPP problem. BIB019 The load uncertainty and different contingencies have been considered in multi-scenarios extracted using a scenario tree reduction methodology. KNI-TRO implements the interior method where, the nonlinear programming problem is replaced by a series of barrier sub-problems Fast computational performance. Very suitable to handle with both continuous and discrete variables No need for calculating 1st or 2nd derivatives of the nonlinear objectives or constraints Iterative approach for computing steps It could be trapped in a local optimum and there is no guarantee to find the global optimum even if you run the algorithms for infinite long because the diversity of the solutions is limited The multi-objective functions have been treated mathematically sum for each scenario in BIB019 Neglecting the effect of transformer tap changing on the RPP problem in BIB020 Interior Point (IP) method BIB020 RPP problem has been formulated as a stage of TEP problem The candidate buses to install VAR sources have been selected based on L-index as a voltage stability index DIscrete and Continuous OPTimizer (DICOPT) solver * BIB015 BIB002 DICOPT solves a series of NLP and Mixed Integer Programming (MIP) sub-problems. It is based on outer approximation of the objective function, equality relaxation, and augmented penalty of the inequality constraints and the objective function. BIB007 BIB022 This method employed a sequence of MIP method where, sensitivities of voltage stability margin and voltage magnitude have been used in this RPP formulation In B&B, the search continues by creating two new sub-problems, each one is then solved by the same procedure, resulting in a search-tree of subproblems No need for restarting the tree search and only a single tree is required It is fast It provides good solutions for largescale power systems The formulation has been approximated to be linear using voltage stability margin sensitivities and voltage magnitude sensitivities It finds locally optimal solutions * MINOS solver BIB001  BIB004 , and DICOPT solver BIB015 BIB002 have been formulated in GAMS software  . Since BLX-a is based on the interval process for real variables, the new off-springs depend on the location of both parents and so they will be close to the parents if both parents are close to each other, and vice versa BIB010 [30] A self-adaptive model of real coded genetic algorithm (SARGA) has been presented to solve the optimal reactive power dispatch (ORPD) problem The simulated binary crossover (SBX) operator has been used to create offsprings relative to the difference in parent solutions In this type of crossover, close-parent solutions are monotonically more likely chosen as offspring than solutions distant from parents It is highly dependent on crossover and mutation rates and effect on stability and convergence It finds sub-optimal solutions BIB010 Representation of both binary and real variables has been deemed This improved GA carried out the uniform mutation operator to the mixed variables with some modifications, the blend crossover operator (BLX-a), and simple crossover for real and integer parts, respectively Design for binary and real search spaces A Modified NSGA-II (MNSGA-II) has been applied to the RPP problem In BIB016 BIB013 , Paretofront has been created by converting the multiobjectives into single one using conventional weighted sum method and varying the weighting Dynamic modification of Pareto set using Dynamic Crowding Distance (DCD) High uniformity and maintains good diversity since the lowest DCD individual has been removed every time and DCD has been recalculated for the remaining individuals High computational complexity In BIB013 , the best compromise solution hasn't been included and the obtained Pareto front has been considered to give more choices to the decision The mutation factor has been changed dynamically instead of being constant as in the classic DE model  A new adaptive DE algorithm called (JADE-vPS) has been applied to minimize the total fuel cost with satisfying a minimum voltage stability margin for the optimal power flow. In this paper, an adaptive penalty function has been introduced where the penalty coefficients has been altered automatically from data gathered from the search process Not only mutation factor and crossover rate have been already self-adapted, but also population size has been automatically adapted in a very similar manner to the other two parameters. High computational burden and complexity Immune Algorithm (IA) BIB005 IA has been implemented in adaptive model to solve the reactive power flow in order to minimize power losses, voltage deviation, and enhance static voltage stability. Crossover rates, mutation rates and clone rates have been used all adaptive to change automatically at each generation related to the global affinity function Adaptive parameters avoid premature convergence and falling into a local optimal solution trap Good efficiency and convergence More computational burden and complexity Seeker Optimization Algorithm (SOA) BIB008 BIB021 In BIB008 , SOA has been executed to the ORPD problem to minimize the real losses as a single objective function. In BIB021 , SOA has been implemented to minimize the power losses, voltage deviation and increasing voltage stability using L-index. This ORPD has been handled as minimizing different single objective functions Easy to understand Suitable performance in balancing global search ability and convergence speed Although SOA handled only continuous variables, Refs. BIB008 BIB006 tackled this problem by searching in a continuous space, and then curtailing the corresponding dimensions of the seekers' real-values into the integers SOA may be stuck at a local optimum for multimodal functions SOA is heavily dependent on its structures and parameters BIB006 A multi-objective reactive power control has been addressed using SOA. In this paper, the multiobjective functions were to minimize the transmission loss and voltage deviations while the voltage stability margin would be maximized by minimizing the eigenvalue of the non-singular power flow Jacobian matrix PSO method has been applied to the RPP problem as a second stage to minimize of the VAR investment costs. This model considered load uncertainties and the uncertainties of wind turbine output obtained by a probability distribution function (PDF) using MCS while the reliability has been taken into consideration BIB009 PSO algorithm has been used for solving the RPP problem to minimize the operation cost and investment cost of reactive power sources Handling the integer variables has been done by rounding it to the nearest discrete after relating it as floating variable The state variables have been added to the objective as penalties, such complexity is existed to determine the penalty factors  The RPP problem has been solved using PSO technique incorporated with Pareto dominance to minimize real power losses and installation costs A well-distributed Pareto front by adding an external archive to decide whether a solution can be stored or not, based on Pareto dominance More computational burden and complexity to update the best positions based on the global best stored in the archive using crowding and roulette wheel selection [16 (Ch.