A review of meta-heuristic algorithms for reactive power planning problem <s> The e-constraint 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> BIB001 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The e-constraint approach <s> Abstract This paper presents a new approach for scheduling of reactive power control variables for voltage stability enhancement using particle swarm optimization (PSO). Cost function selected is maximization of reactive reserves of the system. To get desired stability margin a Schur’s inequality based proximity indicator has been selected whose threshold value along with reactive power reserve maximization assures desired static voltage stability margin. PSO has been selected because not only it gives global optimal solution but also its mechanization is very simple and computationally efficient. Reactive generation participation factors have been used to decide weights for reactive power reserve for each of generating bus. Developed algorithm has been implemented on 6-bus, 7-line and 25-bus 35-line standard test systems. Results have been compared with those obtained using Devidon–Fletcher–Powell’s (DFP) method. <s> BIB002 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The e-constraint 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> BIB003 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The e-constraint approach <s> This paper presents the application of Covariance matrix adapted evolution strategy (CMAES) to reactive power planning (RPP) problem by minimizing the combined total cost of energy loss and the allocation cost of additional reactive power sources. Voltage stability index (L-index) is considered as an additional constraint in order to include the system stability into account. To improve the search efficiency of CMAES, penalty parameter-less scheme is employed for constraint handling. To determine the performance of the CMAES method on reactive power planning problem, IEEE-30 bus test system and Tamil Nadu Electricity Board (TNEB)-69 bus system (a practical system in India) are taken. For comparison purposes, the results of real-coded GA (RGA), particle swarm optimization (PSO), sequential quadratic programming (SQP), and Broyden–Fletcher–Goldfarb–Shanno (BFGS) methods are considered. The simulation results reveal that the CMAES algorithm performs better in terms of energy cost, investment cost, and consistency in getting optimal solution. Karush–Kuhn–Tucker (KKT) conditions are also applied on the best solution obtained using CMAES algorithm to substantiate a claim on optimality. Copyright © 2010 John Wiley & Sons, Ltd. <s> BIB004 </s> A review of meta-heuristic algorithms for reactive power planning problem <s> The e-constraint approach <s> Abstract This work proposes a two-phase iterative simulation optimization approach to solve the optimal volt-ampere reactive (VAR) sources planning problem. In the upper phase, an Ordinal Optimization (OO)-based method is employed as the optimization methodology, which performs ranking and selection to choose better solutions from a candidate solution set based on the structural information of system extracted from the simulation methodology performed in the lower phase. The simulation methodology, which is based on the Dual Projected Pseudo Quasi-Newton (DPPQN) method, is employed in the lower phase. The proposed OO-based approach consists of four levels. The size and solution quality of the resulting candidate solution set is reduced and improved level by level, and the best solution obtained in the final level is the good enough capacitor placement pattern that we seek. Via numerous tests, this work demonstrates the efficiency of the proposed approach with respect to the genetic algorithm (GA) and tabu search (TS) on the IEEE 118-bus system. Test results show that the proposed approach is an excellent alternative for the optimal VAR sources planning problems. <s> BIB005
The e-constraint approach has been used in tackling multiobjective problems of reactive power planning and control  BIB001 BIB005 BIB003  BIB004 . This method optimizes the main objective (F m ) as a single objective optimization problem while, it considers other objectives as constraints restricted by some chosen threshold levels. where e i is a threshold level specified by the user for each objective (F i ). Choosing e i is easier than choosing adequate values for weight factors (x), but the optimal solution still depends on its value. In BIB005 , the capacitors has been installed to minimize the real losses (main objective) while its investment cost has been handled with budget limit (econstraint). Also, the loading parameter (k) has been a constrained to guarantee a minimum voltage stability margin in  BIB001 . In BIB002 , Schur's inequality has been used to assure required static voltage stability margin. The eigenvalue analysis has been used as a stability margin proximity indicator where a threshold value of proximity indicator must be specified for secure operation. Also, the objective of enhancing the voltage stability has been achieved by restricting the static voltage stability index (L-index) by a maximum level  BIB004 .