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 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 Power Flow Using a Hybrid Optimization Algorithm of Particle Swarm Optimization and Gravitational Search Algorithm

Abstract—This article presents a hybrid algorithm based on the particle swarm optimization and gravitational search algorithms for solving optimal power flow in power systems. The proposed optimization technique takes advantages of both particle swarm optimization and gravitational search algorithms by combining the ability for social thinking in particle swarm optimization with the local search capability of the gravitational search algorithm. Performance of this approach for the optimal power flow problem is studied and evaluated on standard IEEE 30-bus and IEEE 118-bus test systems with different objectives that reflect fuel cost minimization, voltage profile improvement, voltage stability enhancement, power loss reduction, and fuel cost minimization with consideration of the valve point effect of generation units. Simulation results show that the hybrid particle swarm optimization–gravitational search algorithm provides an effective and robust high-quality solution of the optimal power flow problem.     

Impact of the penetration of distributed generation on optimal reactive power dispatch

Optimal reactive power dispatch (ORPD) is a complex and non-linear problem, and is one of the sub-problems of optimal power flow (OPF) in a power system. ORPD is formulated as a single-objective problem to minimize the active power loss in a transmission system. In this work, power from distributed generation (DG) is integrated into a conventional power system and the ORPD problem is solved to minimize transmission line power loss. It proves that the application of DG not only contributes to power loss minimization and improvement of system stability but also reduces energy consumption from the conventional sources. A recently proposed meta-heuristic algorithm known as the JAYA algorithm is applied to the standard IEEE 14, 30, 57 and 118 bus systems to solve the newly developed ORPD problem with the incorporation of DG. The simulation results prove the superiority of the JAYA algorithm over others. The respective optimal values of DG power that should be injected into the four IEEE test systems to obtain the minimum transmission line power losses are also provided.     

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.     

基于全有效解整数微分进化算法的含分布式发电配网重构

以降低网络损耗为目标函数,采用微分进化（DE）算法求解配网重构问题。根据配电网的特点,采用基于独立环路的整数编码方法以降低变量维数。此外,针对进化中存在的无效解问题,以图论代数连通度结论为基础,提出一个能完全去除无效解的判据,进一步缩小了解空间,该方法适用于复杂的实际配电网络计算。在重构网络中引入分布式电源（DG）,有效降低了网损,改善了电压质量。最后,对IEEE33节点配网测试系统进行了仿真计算,算例结果表明所提方法具有良好的收敛性和全局搜索能力。     

Distributed control algorithm for optimal reactive power control in power grids

Reactive power generation has been commonly used for power loss minimization and voltage profile improvement in power systems. However, the opportunity cost of reactive power generation should be considered since it affects the frequency control capability of the generator to some degree. This paper proposed a distributed nonlinear control based algorithm to achieve the optimal reactive power generation for multiple generators in a power grid. The reactive power control setting update for each generator only requires local measurement and information exchange with its neighboring buses. It is demonstrated that the proposed algorithm can reduce the non-convex objective function monotonically till convergence and achieve comparable solutions to the centralized technique: particle swarm optimization with faster convergence speed. The proposed algorithm has been tested on the IEEE 9-bus, 39-bus and 162-bus systems to validate its effectiveness and scalability.     

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.     

Network loss minimization with voltage security using differential evolution

This paper presents a differential evolution (DE) based optimal power flow (OPF) for reactive power dispatch in power system planning studies. DE is a simple population-based search algorithm for global optimization and has a minimum number of control parameters. The problem is formulated as a mixed integer non-linear optimization problem taking into account both continuous and discrete control variables. The proposed method determines control variable settings such as generator voltages (continuous), tap positions (discrete) and the number of shunt reactive compensation devices to be switched (discrete) for real power loss minimization in the transmission system using DE algorithm. Most of the evolutionary algorithm applications to optimization problems apply penalty function approach to handle the inequality constraints, involving penalty coefficients. The correct combination of these coefficients can be determined only by a trial and error basis. In the proposed approach, the inequality constraints are handled by penalty parameterless scheme. Voltage security margin was evaluated using continuation power flow (CPF), to ensure the feasibility of the optimal control variable setting. The suitability of the method was tested on IEEE 14 and IEEE RTS 24-bus systems and results compared with sequential quadratic programming (SQP) method. The DE provides near global solutions comparable to that obtained using SQP.     

Differential evolution algorithm for emission constrained economic power dispatch problem

In this paper, a differential evolution (DE) algorithm is developed to solve emission constrained economic power dispatch (ECEPD) problem. Traditionally electric power systems are operated in such a way that the total fuel cost is minimized regardless of emissions produced. With increased requirements for environmental protection, alternative strategies are required. The proposed algorithm attempts to reduce the production of atmospheric emissions such as sulfur oxides and nitrogen oxides, caused by the operation of fossil-fueled thermal generation. Such reduction is achieved by including emissions as a constraint in the objective of the overall dispatching problem. A simple constraint approach to handle the system constraints is proposed. The performance of the proposed algorithm is tested on standard IEEE 30-bus system and is compared with conventional methods. The results obtained demonstrate the effectiveness of the proposed algorithm for solving the emission constrained economic power dispatch problem.     

Reactive power dispatch considering voltage stability with seeker optimization algorithm

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.     

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.     

Optimal reactive power control via loss minimization and voltage control

This paper presents a mathematical formulation of optimal reactive power control problem via loss minimization and voltage control. The model minimizes real power losses, deviation from the optimal active power despatch policy, and the difference between percentage sharing of reactive power by controlling the generator terminal voltage magnitudes, transfer tap setting, and reactive power sources. The constraints set include power flow equations and limits on the variables. A method is developed to solve this problem using reduced gradient and Fletcher's update. Several test problems were solved using the developed technique. Correction to the groups of decision variables are applied simultaneously as well as hierarchically, and the results are compared for 6-bus, 30-bus, and 103-bus sample systems.     

A new hybrid approach for the solution of nonconvex economic dispatch problem with valve-point effects

Economic dispatch (ED) generally formulated as convex problem using optimization techniques by approximating generator input/output characteristic curves of monotonically increasing nature results in an inaccurate dispatch. The genetic algorithm has previously been used for the solution of problem for economic dispatch but takes longer time to converge to near optimal results. The hybrid approach is one of the methodologies used to fine tune the near optimal results produced by GA. This paper proposes new hybrid approach to solve the ED problem by using the valve-point effect. The approach we propose combines the genetic algorithm (GA) with active power optimization (APO) based on the Newton's second order approach (NSO). The genetic algorithm acts as a global optimizer giving near optimal generation schedule, which becomes the input for generation buses in APO algorithm. This algorithm acting as local search technique dispatching the generated active power of units for minimization of cost and gives optimum generation schedule. Three machines 6-bus, IEEE 5-machines 14-bus, and IEEE 6-mchines 30-bus systems have been tested for validation of our approach. Results of the proposed scheme compared with results obtained from GA alone give significant improvements in the generation cost showing the promise of the proposed approach.     

全局安时无功优化调度的MAS方法

电力系统无功优化调度问题在数学上属于一种具有多目标、多不确定因素、多约束、多极值、非线性的组合最优化问题。通常的寻优方法遇到了许多困难，因此目前无功优化调度技术的应用还停留在计算规模较小的地区局部电网中。为实现电网全局实时的无功优化调度，提出一种基于分布式人工智能中多Agent系统(MAS)的无功优化调度模型。将全网无功调度按区域分解为若干个相互关联的调度子系统进行分布式求解，全局调度系统采用网络控制结构，各调度子系统则采用分层控制结构。在各子网局部实现无功优化的基础上，采用多Agent智能协调技术实现全网的全局无功优化。     

Quasi-oppositional differential evolution for optimal reactive power dispatch

This paper presents quasi-oppositional differential evolution to solve reactive power dispatch problem of a power system. Differential evolution (DE) is a population-based stochastic parallel search evolutionary algorithm. Quasi-oppositional differential evolution has been used here to improve the effectiveness and quality of the solution. The proposed quasi-oppositional differential evolution (QODE) employs quasi-oppositional based learning (QOBL) for population initialization and also for generation jumping. Reactive power dispatch is an optimization problem that reduces grid congestion with more than one objective. The proposed method is used to find the settings of control variables such as generator terminal voltages, transformer tap settings and reactive power output of shunt VAR compensators in order to achieve minimum active power loss, improved voltage profile and enhanced voltage stability. In this study, QODE has been tested on IEEE 30-bus, 57-bus and 118-bus test systems. Test results of the proposed QODE approach have been compared with those obtained by other evolutionary methods reported in the literature. It is found that the proposed QODE based approach is able to provide better solution.     

基于自适应差分算法的电力系统稳定器参数设计

自适应差分算法强大高效,是一种基于群体的随机搜索技术,一般用于连续空间优化问题求解,被广泛应用于科学和工程领域.自适应差分算法是在差分进化算法基础上经过改进得到的算法,其实验向量生成策略及其相关的控制参数值拥有自适应能力,这种能力是通过从前期生成可能解的过程中学习得来的.在利用Simulink建立起单机无穷大系统仿真模型的基础上,根据时间乘绝对误差积分准则(ITAE准则)设计寻优问题的目标函数,将电力系统稳定器的参数设计问题转化为最小化问题,并用自适应差分算法求解.最后在单机无穷大系统上进行仿真实验,结果表明经过优化设计的电力系统稳定器拥有良好性能.     

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.     

Integration of Distributed Generation in Power Networks Considering Constraints on Discrete Size of Distributed Generation Units

Abstract—An optimization algorithm based on a novel discrete particle swarm optimization technique is proposed in this article for optimal sizing and location of distributed generation in a power distribution network. The proposed algorithm considers distributed generation size and location as discrete variables substantially reducing the search space and, consequently, computational requirements of the optimization problem. The proposed algorithm treats the generator sizes as real discrete variables with uneven step sizes that reflect the sizes of commercially available generators, meaning that it can handle a mixed search space of integer (generator location), discrete (generator sizes), and continuous (reactive power output) variables while substantially reducing the search space and, consequently, computational burden of the optimization problem. The validity of the proposed discrete particle swarm optimization algorithm is tested on a standard 69-bus benchmark distribution network with four different test cases. Two optimization scenarios are considered for each test case: a single objective optimization study where network real power loss is minimized and a multi-objective study in which network voltages are also considered. The proposed algorithm is shown to be effective in finding the optimal or near-optimal solution to the problem at a fraction of the computational cost associated with other algorithms.