A review of meta-heuristic algorithms for reactive power planning problem <s> The Pareto optimality approach <s> This paper proposes an application of the Differential Evolution optimization algorithm to reactive power planning. This problem could be formulated mathematically as a nonlinear, non smooth, mixed-integer, multiobjective optimization problem. One of the objectives deals with the minimization of the real power losses that result in a reduction of the operational costs and improving the voltage profile across the system. The other objective minimizes the allocation of additional reactive power sources throughout the system. The proposed approach has been tested in a modified version of the IEEE 30-bus test system with satisfactory results. These results were compared with those obtained by another evolutionary computation technique (Evolutionary Programming). <s> BIB001 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The Pareto optimality approach <s> Increased load forecasts can severely deteriorate the performance of a power system. Reactive compensation devices are a common method to allow a power system to return to an acceptable performance level for an expected load. Reactive power planning (RPP) is used to determine the optimal placement of reactive devices for a set of objectives. RPP is a large scale multiple objectives highly constrained and partially discrete optimization problem that is very difficult to solve. Evolutionary algorithms have been used to solve RPP problems. However, new multi-objective evolutionary computational techniques have shown the ability to consider an optimization problem's objectives independently for the determination of Pareto Optimal solutions. This paper aims at applying the Non-Dominated Sorting Genetic Algorithm II (NSGAII) to a multi-objective RPP. The results from the case study presented show that there is great potential in the use of evolutionary computation for solving the multi-objective RPP. <s> BIB002 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The Pareto optimality 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> BIB003 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The Pareto optimality approach <s> Abstract This paper addresses an application of modified NSGA-II (MNSGA-II) by incorporating controlled elitism and dynamic crowding distance (DCD) strategies in NSGA-II to multiobjective optimal reactive power dispatch (ORPD) problem by minimizing real power loss and maximizing the system voltage stability. To validate the Pareto-front obtained using MNSGA-II, reference Pareto-front is generated using multiple runs of single objective optimization with weighted sum of objectives. For simulation purposes, IEEE 30 and IEEE 118 bus test systems are considered. The performance of MNSGA-II, NSGA-II and multiobjective particle swarm optimization (MOPSO) approaches are compared with respect to multiobjective performance measures. TOPSIS technique is applied on obtained non-dominated solutions to determine best compromise solution (BCS). Karush–Kuhn–Tucker (KKT) conditions are also applied on the obtained non-dominated solutions to substantiate a claim on optimality. Simulation results are quite promising and the MNSGA-II performs better than NSGA-II in maintaining diversity and authenticates its potential to solve multiobjective ORPD effectively. <s> BIB004 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The Pareto optimality 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> BIB005 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The Pareto optimality 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> BIB006 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The Pareto optimality 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> BIB007
Multi-objective RPP problem has been achieved using the concept of Pareto-optimality BIB006 BIB003 16(Ch. 4) ,  BIB002 BIB007 BIB004 BIB005 BIB001  . The solution is said to be Pareto-optimal if there is no a better solution in terms of all objectives.