Solution of optimal reactive power dispatch of power systems using hybrid particle swarm optimization and imperialist competitive algorithms

Management of reactive power resources is essential for secure and stable operation of power systems in the standpoint of voltage stability. In power systems, the purpose of optimal reactive power dispatch (ORPD) problem is to identify optimal values of control variables to minimize the objective function considering the constraints. The most popular objective functions in ORPD problem are the total transmission line loss and total voltage deviation (TVD). This paper proposes a hybrid approach based on imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) to find the solution of optimal reactive power dispatch (ORPD) of power systems. The proposed hybrid method is implemented on standard IEEE 57-bus and IEEE 118-bus test systems. The obtained results show that the proposed hybrid approach is more effective and has higher capability in finding better solutions in comparison to ICA and PSO methods.     

Optimal reactive power dispatch using ant colony optimization algorithm

This paper proposed a procedure to solve the optimal reactive power dispatch (ORPD) problem using ant colony optimization (ACO) algorithm. The objective of the ORPD problem is to minimize the transmission power losses under control and dependent variable constraints. Proposed sensitivity parameters of reactive power at generation and switchable sources are derived based on a modified model of fast decoupled power flow. The proposed ACO-based algorithm is applied to the IEEE standard 14-bus, 30-bus systems, and a real power system at West Delta Network as a part of the Unified Egyptian Network. The obtained simulation results are compared with those of conventional linear programming, genetic algorithm, and particle swarm optimization technique. Simulation results show the capability of the proposed ACO-based algorithm for solving the ORPD problem, especially with increasing the system size.     

Optimal reactive power dispatch using quasi-oppositional teaching learning based optimization

This paper presents a newly developed teaching learning based optimization (TLBO) algorithm to solve multi-objective optimal reactive power dispatch (ORPD) problem by minimizing real power loss, voltage deviation and voltage stability index. To accelerate the convergence speed and to improve solution quality quasi-opposition based learning (QOBL) concept is incorporated in original TLBO algorithm. The proposed TLBO and quasi-oppositional TLBO (QOTLBO) approaches are implemented on standard IEEE 30-bus and IEEE 118-bus test systems. Results demonstrate superiority in terms of solution quality of the proposed QOTLBO approach over original TLBO and other optimization techniques and confirm its potential to solve the ORPD problem.     

Optimal VAR control for real power loss minimization using differential evolution algorithm

Differential evolution algorithm (DEA) is an efficient and powerful population-based stochastic search technique for solving optimization problems over continuous space, which has been proved to be a promising evolutionary algorithm for solving the ORPD problem and many engineering problems. However, the success of DEA in solving a specific problem crucially depends on appropriately choosing trial vector generation strategies (mutation strategies) and their associated control parameter values. This paper presents a differential evolution technique with various trial vector generation strategies based on optimal reactive power dispatch for real power loss minimization in power system. The proposed methodology determines control variable settings such as generator terminal voltages, tap positions and the number of shunts compensator to be switched, for real power loss minimization in the transmission systems. The DE method has been examined and tested on the IEEE 14-bus, 30-bus and the equivalent Algerian electric 114-bus power system. The obtained results are compared with two other methods, namely, interior point method (IPM), Particle Swarm Optimization (PSO) and other methods in the literature. The comparison study demonstrates the potential of the proposed approach and shows its effectiveness and robustness to solve the ORPD problem.     

Optimal Location of Thyristor-controlled Series Capacitor to Enhance Power Transfer Capability Using Firefly Algorithm

Abstract—The optimal power flow problem seeks to find an optimal profile of active and reactive power generations along with voltage magnitudes in such a manner as to minimize the total operating costs of a power system while satisfying network security constraints. This article presents a firefly algorithm to solve the optimal power flow problem incorporating a thyristor-controlled series capacitor. A thyristor-controlled series capacitor is considered to find the optimal location in transmission lines to enhance the power transfer capability of the transmission line. To assess the effectiveness of the proposed algorithm, it was tested on a 5-bus test system, an IEEE 14-bus system, and a modified IEEE 30-bus system, and it was compared with the genetic algorithm and differential evolution with and without a thyristor-controlled series capacitor. It has also been observed that the proposed algorithm can be applied to larger systems and does not suffer with computational difficulties. The results show that the firefly algorithm produces better results than others and has fast computing time for solving the optimal power flow problem with a thyristor-controlled series capacitor.     

Optimal reactive power dispatch based on harmony search algorithm

This paper presents a harmony search algorithm for optimal reactive power dispatch (ORPD) problem. Optimal reactive power dispatch is a mixed integer, nonlinear optimization problem which includes both continuous and discrete control variables. The proposed algorithm is used to find the settings of control variables such as generator voltages, tap positions of tap changing transformers and the amount of reactive compensation devices to optimize a certain object. The objects are power transmission loss, voltage stability and voltage profile which are optimized separately. In the presented method, the inequality constraints are handled by penalty coefficients. The study is implemented on IEEE 30 and 57-bus systems and the results are compared with other evolutionary programs such as simple genetic algorithm (SGA) and particle swarm optimization (PSO) which have been used in the last decade and also other algorithms that have been developed in the recent years.     

Optimal reactive power dispatch using hybrid Nelder–Mead simplex based firefly algorithm

This paper presents a novel hybrid algorithm combining Firefly Algorithm (FA) and Nelder Mead (NM) simplex method for solving power system Optimal Reactive Power Dispatch (ORPD) problems. The ORPD is a very important aspect of power system operation and is a highly nonlinear, non-convex optimization problem, consisting of both continuous and discrete control variables. Like many other general purpose optimization methods, the original FA often traps into local optima and in order to overcome the shortcoming, in this paper, an efficient local search method called NM simplex subroutine is introduced in the internal architecture of the original FA algorithm. The proposed Hybrid Firefly Algorithm (HFA) avoids premature convergence of original FA by exploration with FA and exploitation with NM simplex. The proposed method is applied to determine optimal settings of generator voltages, tap positions of tap changing transformers and VAR output of shunt capacitors to optimize two different objective functions; such as minimization of real power loss and voltage deviations. The program is developed in Matlab and the proposed hybrid algorithm is examined on two standard IEEE test systems for solving the ORPD problems. For validation purpose, the results obtained with the proposed approach are compared with those obtained by other methods. It is observed that the proposed method has better convergence characteristics and robustness compared to the original version of FA and other existing methods. It is revealed that the proposed hybrid method is able to provide better solutions.     

Optimal Reactive Power Dispatch Considering Costs of Adjusting the Control Devices

The traditional model of optimal reactive power dispatch (ORPD) for power systems is based on the principle of income maximization, which aims at minimizing active power loss of the whole networks. However, such a model may bring on excessive operations of device-control devices in real-time application. To realize reactive power dispatch, power utilities should increase equipment investment and added manpower for operation and maintenance. On the other hand, the operations would augment the fault probability of power systems. Therefore, the costs of adjusting the control devices (CACDs) are investigated, and a novel mathematical model of ORPD is presented in this paper, whose objective function is to minimize the energy loss at the current time interval and the CACD. A simulation test is presented to demonstrate that the proposed model reflects the principle of profit maximization and describes the ORPD problem with time-varying loads appropriately since it can decrease active power loss and avoid excessive controls simultaneously.     

A smart distribution system reconfiguration algorithm with optimal active power scheduling considering various types of distributed generators

This paper presents an efficient way of solving the distribution system reconfiguration (DSR) problem in electrical power systems with consideration of different types of distributed generators (DGs). The objective of a DSR is to minimize the system power loss while satisfying the system constraints and keeping the topology of the system radial. In this paper, a new DSR algorithm based on a modified particle swarm optimization (PSO) is proposed to incorporate DGs with the constant voltage control mode. The proposed method is very efficient because it avoids an extra iteration loop for computing the reactive power at PV buses in order to keep the voltage at a specified magnitude. Furthermore, if the reactive power requirement is not met in between the extreme limits, the proposed algorithm strictly searches for the best possible tie switch combination to simultaneously reduce the power loss and ensure that the DGs operate in PV mode within acceptable reactive power limit. The proposed algorithm also integrates hourly DSR with optimal DG active power scheduling considering the DG type, generation limit constraints, and the allowable DG penetration level. The validity and the effectiveness of the proposed method has been tested using standard IEEE 33‐bus and 69‐bus distribution networks with various case studies. Test results show that the proposed method is robust and delivers a minimal average power loss compared with different methods, and it efficiently models DGs in DSR, demonstrating that the presence of DGs can further reduce the system loss. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

考虑环境因素的分布式发电多目标优化配置

分布式发电优化布置与定容问题是智能电网发展中所面对的一个重要课题。该文在节点有功、无功网损微增率基础上,通过负荷功率法将两者结合,提出等效网损微增率的概念。通过计算该微增率并对其进行排序,可确定分布式发电(distributed generation,DG)的最优安装位置,并且最小化输电线路网损。对于DG定容问题,该文同时考虑了有功网损、电压改善程度和环境改善程度这3个重要指标,将DG优化容量确定问题转化为一个多目标非线性规划问题。采用目标逼近和二次序列规划方法对提出的算法进行求解。算例结果表明,采用该方法确定DG在系统中的布置位置和容量可有效提高系统运行电压,降低有功网损,减少电厂排放的污染气体。该方法对DG在规划阶段的选址和定容问题有着一定的实用价值。     

Solving multiobjective optimal reactive power dispatch using modified NSGA-II

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.     

Optimal reactive power dispatch using self-adaptive real coded genetic algorithm

In this paper, self-adaptive real coded genetic algorithm (SARGA) is used as one of the techniques to solve optimal reactive power dispatch (ORPD) problem. The self-adaptation in real coded genetic algorithm (RGA) is introduced by applying the simulated binary crossover (SBX) operator. The binary tournament selection and polynomial mutation are also introduced in real coded genetic algorithm. The problem formulation involves continuous (generator voltages), discrete (transformer tap ratios) and binary (var sources) decision variables. The stochastic based SARGA approach can handle all types of decision variables and produce near optimal solutions. The IEEE 14- and 30-bus systems were used as test systems to demonstrate the applicability and efficiency of the proposed method. The performance of the proposed method is compared with evolutionary programming (EP) and previous approaches reported in the literature. The results show that SARGA solves the ORPD problem efficiently.     

Optimal Allocation and Operating Point of DG Units in Radial Distribution Network Considering Load Pattern

Distributed generation (DG) is a new approach for solving some problems of older power networks. Due to the increasing power demand in recent power systems, the importance of power loss reduction and maintaining system voltages within an acceptable range has given rise to the wide use of DG units in power systems. On the other hand, unplanned and non-optimal application such as installation and operation of DG units might cause other technical problems. In addition, it is important to consider the load pattern in the network, and the best decision for DG unit's operation must be chosen accordingly. In this paper, a method is introduced in order to make the optimal placement and find an optimal operating point for the DG units, which means the power output of DG units, considering the load pattern of the network. This load pattern has an average load of 24 hr a day, four seasons a year. In the proposed method, optimization has two goals: first, is optimizing the DG unit's placement based on improvement of the voltage profile, and the second is operating DG units with optimum power factor, minimizing power loss, and improving voltage profile, with regard to the load pattern. In order to solve this problem, the gravitational search algorithm and genetic algorithm are used. The proposed method is applied on the IEEE 33-bus test system, and the result shows the effectiveness of the proposed method. In order to solve the optimization problem, MATLAB software is used.     

Optimal power flow for distribution networks using gravitational search algorithm

This paper presents a gravitational search algorithm (GSA)-based approach to solve the optimal power flow (OPF) problem in a distribution network with distributed generation (DG) units. The OPF problem is formulated as a nonlinear optimization problem with equality and inequality constraints, where optimal control settings in case of fuel cost minimization of DG units, power loss minimization in the distribution network, and finally simultaneous minimization of the fuel cost and power loss are obtained. The proposed approach is tested on an 11-node test system and on a modified IEEE 34-node test system. Simulation results obtained from the proposed GSA approach are compared with that obtained using a genetic algorithm approach. The results show the effectiveness and robustness of the proposed GSA approach.     

Power loss minimization in distribution systems using multiple distributed generations

In this work, an efficient analytical method is proposed for optimally allocating distributed generations (DGs) in electrical distribution systems to minimize power losses. The proposed analytical method can be employed for obtaining the optimal combination of different DG types in a distribution system for loss minimization. The validity of the proposed method is demonstrated using two test systems with different configurations by comparing with the exact optimal solution obtained from the exhaustive optimal power flow (OPF) algorithm. The calculated results and the comprehensive comparisons with existing methods prove the superiority of the proposed method in terms of accuracy and calculation speed. The proposed loss minimization method can be a useful tool for any general DG allocation problem since it provides effective and fast loss evaluation taking into account other benefits. © 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Optimal corrective actions for power systems using multi-objective genetic algorithms

In this paper, optimal corrective control actions are presented to restore the secure operation of power system for different operating conditions. Genetic algorithm (GA) is one of the modern optimization techniques, which has been successfully applied in various areas in power systems. Most of the corrective control actions involve simultaneous optimization of several objective functions, which are competing and conflicting each other. The multi-objective genetic algorithm (MOGA) is used to optimize the corrective control actions. Three different procedures based on GA and MOGA are proposed to alleviate the violations of the overloaded lines and minimize the transmission line losses for different operation conditions. The first procedure is based on corrective switching of the transmission lines and generation re-dispatch. The second procedure is carried out to determine the optimal siting and sizing of distributed generation (DG). While, the third procedure is concerned into solving the generation-load imbalance problem using load shedding. Numerical simulations are carried out on two test systems in order to examine the validity of the proposed procedures.     

基于改进粒子群优化算法的DG准入容量与优化布置

为进一步优化配电网中分布式电源（distributed generation,DG）的准入容量和优化布置问题,以节点电压和线路载流量为约束条件建立了单电源和多电源准入容量的数学模型,以有功网损最小为目标函数建立了DG优化布置模型。为有效求解该模型,采用了基于粒子群优化（particle swarm optimization,PSO）算法和二次插值相结合的改进PSO算法,将该改进方法应用于IEEE 33节点标准算例,分别进行了DG的最优接入位置与最优容量的仿真,并与粒子群算法优化结果进行了对比,同时还分析了优化布置下的潮流分布。算例仿真结果表明该方法可有效减少DG接入后配电网的网损,提高配电网的供电质量。     

An analytical approach for sizing and siting of DGs in balanced radial distribution networks for loss minimization

This paper presents a novel analytical approach to determine the optimal siting and sizing of distributed generation (DG) units in balanced radial distribution network to minimize the power loss of the system. The proposed analytical expressions are based on a minimizing the loss associated with the active and reactive component of branch currents by placing the DG at various locations. This method first identifies a sequence of nodes where DG units are to be placed. The optimal sizes of DG units at the identified nodes are then evaluated by optimizing the loss saving equations and need only the results of base case load flow. To find out the best location for DG placement, a computational method is also developed. The proposed method has been tested and validated on two IEEE test distribution systems (DSs) consisting of 15 and 33-buses and it has been found that a significant loss saving can be obtained by placing DG units in the system using proposed analytical method.     

Secure multiobjective real and reactive power allocation of thermal power units

This paper presents best weight pattern evaluation approach to solve multiobjective load dispatch (MOLD) problem which determines the allocation of power demand among the committed generating units, to minimize a number of objectives. Operating cost, minimal impacts on environment, active power loss, are the objectives undertaken to be minimized subject to physical and technological constraints. MOLD problem is decomposed in two stages and is solved sequentially. In first stage, a optimization problem having multiple objectives which are function of only active power generation like operating cost, gaseous pollutant emissions, is solved to get optimal dispatch of active power generation, subject to meet the active power demand, generators’ capacity constraint and transmission active power line flow limits. In second stage, the system real power loss which is a function of reactive power generation is minimized, to get optimal reactive power generation, subject to meet reactive power demand, reactive power generators’ capacity constraint and transmission reactive power line flow limits, when active power generation is known in prior from first stage. The validity of the proposed method is demonstrated on 11-bus, 17-lines and 30-bus, 41-lines IEEE power systems.     

A two-point estimate method for uncertainty modeling in multi-objective optimal reactive power dispatch problem

Due to nonlinear and discrete variables and constraints, optimal reactive power dispatch (ORPD) is a complex optimization problem in power systems. In this paper, the purpose is to solve multi objective ORPD (MO-ORPD) problem considering bus voltage limits, the limits of branches power flow, generators voltages, transformers tap changers and the amount of compensation on weak buses. The objectives of this paper are real power losses and voltage deviations from their corresponding nominal values, which are conflicting objectives. Because of the stochastic behavior of loads, the MO-ORPD problem requires a probabilistic approach. Hence, in this paper, a two-point estimate method (TPEM) is proposed to model the load uncertainty in MO-ORPD problem. Moreover, the proposed method is compared with some other methods such as deterministic approaches and Monte Carlo simulations (MCS). The obtained results approve the efficiency of the proposed methodology. The proposed models are implemented and solved using GAMS optimization package and verified using IEEE 14-bus and IEEE 30-bus standard test systems.