Optimal reactive power dispatch solution by loss minimization using moth-flame optimization technique

In this paper, a newly surfaced nature-inspired optimization technique called moth-flame optimization (MFO) algorithm is utilized to address the optimal reactive power dispatch (ORPD) problem. MFO algorithm is inspired by the natural navigation technique of moths when they travel at night, where they use visible light sources as guidance. In this paper, MFO is realized in ORPD problem to investigate the best combination of control variables including generators voltage, transformers tap setting as well as reactive compensators sizing to achieve minimum total power loss and minimum voltage deviation. Furthermore, the effectiveness of MFO algorithm is compared with other identified optimization techniques on three case studies, namely IEEE 30-bus system, IEEE 57-bus system and IEEE 118-bus system. The statistical analysis of this research illustrated that MFO is able to produce competitive results by yielding lower power loss and lower voltage deviation than the selected techniques from literature.     

Optimal reactive power dispatch by particle swarm optimization with an aging leader and challengers

This study presents a particle swarm optimization (PSO) with an aging leader and challengers (ALC-PSO) for the solution of optimal reactive power dispatch (ORPD) problem. The ORPD problem is formulated as a nonlinear constrained single-objective optimization problem where the real power loss and the total voltage deviations are to be minimized separately. In order to evaluate the performance of the proposed algorithm, it has been implemented on IEEE 30-, 57- and 118-bus test power systems and the optimal results obtained are compared with those of the other evolutionary optimization techniques surfaced in the recent state-of-the-art literature. The results presented in this paper demonstrate the potential of the proposed approach and show its effectiveness and robustness for solving the ORPD problem of power system.     

Optimal reactive power dispatch with uncertainties in load demand and renewable energy sources adopting scenario-based approach

Optimizing reactive power flow in electrical network is an important aspect of system study as the reactive power supports network voltage which needs to be maintained within desirable limits for system reliability. A network consisting of only conventional thermal generators has been extensively studied for optimal active and reactive power dispatch. However, increasing penetration of renewable sources into the grid necessitates power flow studies incorporating these sources. This paper presents a formulation and solution procedure for stochastic optimal reactive power dispatch (ORPD) problem with uncertainties in load demand, wind and solar power. Appropriate probability density functions (PDFs) are considered to model the stochastic load demand and the power generated from the renewable energy sources. Numerous scenarios are created running Monte-Carlo simulation and scenario reduction technique is implemented to deal with reduced number of scenarios. Real power loss and steady state voltage deviation of load buses in the network are set as the objectives of optimization. Success history based adaptive differential evolution (SHADE) is adopted as the basic search algorithm. SHADE has been successfully integrated with a constraint handling technique, called epsilon constraint (EC) handling, to handle constraints in ORPD problem. The effectiveness of a proper constraint handling technique is substantiated with case studies for deterministic ORPD on base configurations of IEEE 30-bus and 57-bus systems using SHADE-EC algorithm. The single-objective and multi-objective stochastic ORPD cases are also solved using the SHADE-EC algorithm. The results are discussed, compared and critically analyzed in this study.     

Using the gray wolf optimizer for solving optimal reactive power dispatch problem

This paper presents the use of a new meta-heuristic technique namely gray wolf optimizer (GWO) which is inspired from gray wolves’ leadership and hunting behaviors to solve optimal reactive power dispatch (ORPD) problem. ORPD problem is a well-known nonlinear optimization problem in power system. GWO is utilized to find the best combination of control variables such as generator voltages, tap changing transformers’ ratios as well as the amount of reactive compensation devices so that the loss and voltage deviation minimizations can be achieved. In this paper, two case studies of IEEE 30-bus system and IEEE 118-bus system are used to show the effectiveness of GWO technique compared to other techniques available in literature. The results of this research show that GWO is able to achieve less power loss and voltage deviation than those determined by other techniques.     

Chaotic krill herd algorithm for optimal reactive power dispatch considering FACTS devices

Conventionally, optimal reactive power dispatch (ORPD) is described as the minimization of active power transmission losses and/or total voltage deviation by controlling a number of control variables while satisfying certain equality and inequality constraints. This article presents a newly developed meta-heuristic approach, chaotic krill herd algorithm (CKHA), for the solution of the ORPD problem of power system incorporating flexible AC transmission systems (FACTS) devices. The proposed CKHA is implemented and its performance is tested, successfully, on standard IEEE 30-bus test power system. The considered power system models are equipped with two types of FACTS controllers (namely, thyristor controlled series capacitor and thyristor controlled phase shifter). Simulation results indicate that the proposed approach yields superior solution over other popular methods surfaced in the recent state-of-the-art literature including chaos embedded few newly developed optimization techniques. The obtained results indicate the effectiveness for the solution of ORPD problem of power system considering FACTS devices. Finally, simulation is extended to some large-scale power system models like IEEE 57-bus and IEEE 118-bus test power systems for the same objectives to emphasis on the scalability of the proposed CKHA technique. The scalability, the robustness and the superiority of the proposed CKHA are established in this paper.     

Optimal reactive power dispatch for real power loss minimization and voltage stability enhancement using Artificial Bee Colony Algorithm

Reactive Power Dispatch (RPD) plays important role in power system reliability and security. This paper proposes the Optimal Reactive Power Dispatch (ORPD) for real power loss minimization, voltage deviation minimization and voltage stability enhancement using Artificial Bee Colony (ABC) Algorithm. ORPD is a mixed integer nonlinear optimization problem which includes both continuous and discrete control variables. The ABC algorithm is used to find the setting of control variables such as generator voltage magnitude, tap position of tap changing transformer and reactive power output of the compensation devices. The proposed algorithm is tested on IEEE 30 and 57 bus systems, Simulation results show that the proposed approach converges to better solutions and much faster than the earlier reported approaches in the literature. The optimization strategy is general and can be used to solve other power system optimization problems.     

A novel fuzzy adaptive configuration of particle swarm optimization to solve large-scale optimal reactive power dispatch

Management and scheduling of reactive power resources is one of the important and prominent problems in power system operation and control. It deals with stable and secure operation of power systems from voltage stability and voltage profile improvement point of views. To this end, a novel Fuzzy Adaptive Heterogeneous Comprehensive-Learning Particle Swarm Optimization (FAHCLPSO) algorithm with enhanced exploration and exploitation processes is proposed to solve the Optimal Reactive Power Dispatch (ORPD) problem. Two different objective functions including active power transmission losses and voltage deviation, which play important roles in power system operation and control, are considered in this paper. In order to authenticate the accuracy and performance of the proposed FAHCLPSO, it applied on three different standard test systems including IEEE 30-bus, IEEE 118-bus and IEEE 354-bus test systems with six, fifty-four and one-hundred-sixty-two generation units, respectively. Finally, outcomes of the proposed algorithm are compared with the results of the original PSO and those in other literatures. The comparison proves the supremacy of the proposed algorithm in solving the complex optimization problem.     

Weighted elitism based Ant Lion Optimizer to solve optimum VAr planning problem

In this paper, a newly proposed Ant-Lion Optimizer (ALO) is applied to solve Optimal Reactive Power Dispatch (ORPD) problem of power system. The ORPD is a VAr planning problem and is a highly non linear, non convex, challenging optimization problem; usually devised as constrained Optimal Power Flow (OPF). This paper also proposes the improvement in the search capability of ALO. A novel weighted elitism concept is introduced in the elitism phase of the original ALO to improve the exploration property of the algorithm. The proposed Modified ALO (MALO) intelligently balances both exploration and exploitation, which enhances the hunting capability of ALO. Both ALO and MALO is used to determine the optimal settings of generator voltages, tap positions of tap changer transformers and VAr output of shunt capacitors to optimize objectives: like, the active power loss, total voltage deviation and voltage stability index. The proposed algorithm is programmed and simulated on MATLB and tested on IEEE-30 and 57 bus systems. The results are compared with ALO and other methods. The effectiveness of MALO is further verified by solving few benchmark mathematical functions. The numerical results reveal that, MALO gives better optimum solutions for the benchmark functions compare to original ALO and outperforms several other methods used in the literature to solve ORPD problems. The t-Test and parametric analysis confirms the robustness and consistency of the MALO over ALO and other similar methods.     

Optimal reactive power dispatch by improved GSA-based algorithm with the novel strategies to handle constraints

Optimal reactive power dispatch (ORPD) is well known as a complex mixed integer nonlinear optimization problem where many constraints are required to handle. In the last decades, many artificial intelligence-based optimization methods have been used to solve ORPD problem. But, these optimization methods lack an effective means to handle constraints on state variables. Thus, in this paper, the novel and feasible conditional selection strategies (CSS) are devised to handle constraints efficiently in the proposed improved gravitational search algorithm (GSA-CSS). In addition, considering the weakness of GSA itself, the improved GSA-CSS (IGSA-CSS) is presented which employs the memory property of particle swarm optimization (PSO) to enhance global searching ability and utilizes the concept of opposition-based learning (OBL) for optimizing initial population. The presented GSA-CSS and IGSA-CSS methods are applied to ORPD problem on IEEE14-bus, IEEE30-bus and IEEE57-bus test systems for minimization of power transmission losses (P_loss) and voltage deviation (V_d), respectively. The comparisons of simulation results reveal that IGSA-CSS provides better results and the improvements of algorithm in this work are feasible and effective.     

Optimal power flow using an Improved Colliding Bodies Optimization algorithm

This paper proposes Improved Colliding Bodies Optimization (ICBO) algorithm to solve efficiently the optimal power flow (OPF) problem. Several objectives, constraints and formulations at normal and preventive operating conditions are used to model the OPF problem. Applications are carried out on three IEEE standard test systems through 16 case studies to assess the efficiency and the robustness of the developed ICBO algorithm. A proposed performance evaluation procedure is proposed to measure the strength and robustness of the proposed ICBO against numerous optimization algorithms. Moreover, a new comparison approach is developed to compare the ICBO with the standard CBO and other well-known algorithms. The obtained results demonstrate the potential of the developed algorithm to solve efficiently different OPF problems compared to the reported optimization algorithms in the literature.     

改进粒子群算法在无功优化中的应用

针对电力系统无功优化的特点,本文提出以有功网损最小为目标函数,以负荷节点电压质量和PV发电机节点无功出力为罚函数．以有功功率和无功功率为约束条件的数学模型,并应用改进的粒子群算法对无功优化问题进行求斛。该算法在权重系数和不活动粒子两方面进行改进,有效地解决了进化过程中陷入局部最优和搜索精度差的缺点。最后,将改进后的粒子群算法应用于IEEE14节电力系统进行无功优化算例分析,仿真结果验证了该算法解决电力系统无功优化问题的有效性和可行性。     

Multi-objective optimal power flow using quasi-oppositional teaching learning based optimization

This paper describes teaching learning based optimization (TLBO) algorithm to solve multi-objective optimal power flow (MOOPF) problems while satisfying various operational constraints. To improve the convergence speed and quality of solution, quasi-oppositional based learning (QOBL) is incorporated in original TLBO algorithm. The proposed quasi-oppositional teaching learning based optimization (QOTLBO) approach is implemented on IEEE 30-bus system, Indian utility 62-bus system and IEEE 118-bus system to solve four different single objectives, namely fuel cost minimization, system power loss minimization and voltage stability index minimization and emission minimization; three bi-objectives optimization namely minimization of fuel cost and transmission loss; minimization of fuel cost and L-index and minimization of fuel cost and emission and one tri-objective optimization namely fuel cost, minimization of transmission losses and improvement of voltage stability simultaneously. In this article, the results obtained using the QOTLBO algorithm, is comparable with those of TLBO and other algorithms reported in the literature. The numerical results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal non-dominated solutions of the multi-objective OPF problem. The simulation results also show that the proposed approach produces better quality of the individual as well as compromising solutions than other algorithms.     

Differential evolution approach for optimal reactive power dispatch

Differential evolution based optimal reactive power dispatch for real power loss minimization in power system is presented in this paper. The proposed methodology determines control variable settings such as generator terminal voltages, tap positions and the number of shunts to be switched, for real power loss minimization in the transmission system. The problem is formulated as a mixed integer nonlinear optimization problem. A generic penalty function method, which does not require any penalty coefficient, is employed for constraint handling. The formulation also checks for the feasibility of the optimal control variable setting from a voltage security point of view by using a voltage collapse proximity indicator. The algorithm is tested on standard IEEE 14, IEEE 30, and IEEE 118-Bus test systems. To show the effectiveness of proposed method the results are compared with Particle Swarm Optimization and a conventional optimization technique – Sequential Quadratic Programming.     

Application of firefly algorithm for multi-stage transmission expansion planning with adequacy-security considerations in deregulated environments

Electric energy is the most popular form of energy because it can be transported easily at high efficiency and reasonable cost. Nowadays the real-world electric power systems are large-scale and highly complex interconnected transmission systems. The transmission expansion planning (TEP) problem is a large-scale optimization, complicated and nonlinear problem that the number of candidate solutions increases exponentially with system size. Investment cost, reliability (both adequacy and security), and congestion cost are considered in this optimization. To overcome the difficulties in solving the non-convex and mixed integer nature of this optimization problem, this paper offers a firefly algorithm (FA) to solve this problem. In this paper it is shown that FA, like other heuristic optimization algorithms, can solve the problem in a better manner compare with other methods such genetic algorithm (GA), particle swarm optimization (PSO), Simulated Annealing (SA) and Differential Evolution (DE). To show the feasibility of proposed method, applied model has been considered in IEEE 24-Bus, IEEE 118-Bus and Iran 400-KV transmission grid case studies for TEP problem in both adequacy and security modes. The obtained results show the capability of the proposed method. A comprehensive analysis of the GA, PSO, SA and DE with proposed method is also presented.     

基于交替方向乘子法的电力系统完全分布式动态经济调度方法

本文基于交替方向乘子法(alternating direction multiplier method,ADMM)提出了一种完全分布式的跨区域电力系统动态经济调度方法.其中的经济调度模型以整个系统的运行成本最小为目标,并满足各种系统运行约束.为了实现模型的分布式求解,本文利用交替方向乘子法将各区域之间的联系解耦,将整个系统的大型优化问题分解为各个区域内部的子优化问题,通过迭代求解每个区域的子问题即可得到整个系统的最优解.进一步地,本文算法取消了负责乘子更新的数据中心,实现了完全分布式的调度策略.同时,为了兼顾电力系统中时间断面之间的紧密联系,本文的经济调度模型采用了多时段优化方法.最后,本文对基于IEEE标准测试系统的3区域互联系统算例进行了分析,验证了本文的调度策略的有效性.     

Multiobjective optimal power flow using interior search algorithm: A case study on a real-time electrical network

Optimal power flow (OPF) is a vital concern in an electrical network. In consequence of the intricacy of the power systems, the conventional formulations are not adequate for current situation. Hence, in this study, the multiobjective OPF (MOOPF) problem has been modeled to diminish the production cost, environmental emission, and losses and to enhance the voltage stability and voltage profile simultaneously. This study proposes the application of interior search algorithm (ISA) for resolving MOOPF problem. The simulations have been carried out on three various test systems such as IEEE 30-bus system, IEEE 57-bus system, and Tamil Nadu Generation and Distribution Corporation Limited, as a real part of 62 bus Indian utility system (IUS) to infer the efficacy of ISA in solving the OPF problems. The simulation results have been compared with other techniques. The comparison shows that ISA is used in resolving MOOPF problems.     

Statistical analysis based reactive power optimization using improved differential evolutionary algorithm

This study presents a novel improved differential evolutionary (IDE) algorithm for optimizing reactive power management (RPM) problems. The effectiveness of IDE algorithm is tested on different unimodal and multimodal benchmark functions. The objective function of the RPM is considered as the minimization of active power losses. Initially, the power flow analysis approach is employed to detect the optimal position of flexible AC transmission system (FACTS) devices. The proposed method is used to determine the optimal value of control variables such as generator's reactive power generation, transformer tap settings, and reactive power sources. Furthermore, the efficacy of the IDE approach is compared with other promising optimization methods such as variants of differential evolution algorithm, moth flame optimization (MFO), brainstorm-based optimization algorithm (BSOA), and particle swarm optimization (PSO) on various IEEE standard test bus (i.e., IEEE-30, -57, -118, and -300) systems with active and reactive loading incorporating FACTS devices. A Static VAR compensator (SVC) for shunt compensation and a thyristor-controlled series compensator (TCSC) for series compensation were used as FACTS devices. The proposed IDE method significantly reduces the active power loss, that is, 55.65% in IEEE 30, 39.68% in IEEE 57, 16.32% in IEEE 118, and 8.56% in IEEE 300 bus system at nominal loading. Finally, the statistical analysis such as Wilcoxon signed-rank test (WSRT) and ANOVA test were thoroughly analysed to demonstrate the firmness and accuracy of the proposed technique.     

差分进化粒子群算法求解发电资源调度问题

为了有效地解决水火电力系统资源短期优化调度问题,提出了一种基于差分进化粒子群的调度算法。设计了水火电力系统资源调度问题的数学模型,给出了差分进化粒子群优化算法的框架,通过PSO种群和DE种群之间的信息交流机制以寻求全局最优位置,从而使算法具有动态自适应性,能够较容易地跳出局部最优。实验结果表明,该算法能有效解决水火发电资源调度问题,具有较好的应用价值。     

Particle swarm optimization with an aging leader and challengers algorithm for the solution of optimal power flow problem

Solution of optimal power flow (OPF) problem aims to optimize a selected objective function such as fuel cost, active power loss, total voltage deviation (TVD) etc. via optimal adjustment of the power system control variables while at the same time satisfying various equality and inequality constraints. In the present work, a particle swarm optimization with an aging leader and challengers (ALC-PSO) is applied for the solution of the OPF problem of power systems. The proposed approach is examined and tested on modified IEEE 30-bus and IEEE 118-bus test power system with different objectives that reflect minimization of fuel cost or active power loss or TVD. The simulation results demonstrate the effectiveness of the proposed approach compared with other evolutionary optimization techniques surfaced in recent state-of-the-art literature. Statistical analysis, presented in this paper, indicates the robustness of the proposed ALC-PSO algorithm.     

考虑节点边际价格的热电联产机组主从博弈竞价策略

本文构建了以热电联产机组(combined heat and power unit,CHP)、电力市场和热力市场为参与者的主从博弈模型,并基于电力市场中节点边际电价(locational marginal electricity price,LMEP)的概念,提出了节点边际热价(locational marginal heat price,LMHP)的概念.在节点边际电价的求解中,采用了支路潮流(branch power flow,BPF)模型,考虑了配电网中的网络损耗从而可以得到更精确的计算结果.在节点边际热价的求解中,考虑了管道热损耗,并基于管道损耗方程分析了节点边际热价的分布规律.在此基础上,采用变步长迭代寻优算法求解热电联产机组、电力市场、热力市场各自最优出力和最优报价策略.最后,通过一个6节点电网–4节点热网的算例对所构建的主从博弈模型及热电联产机组的竞价策略进行了验证.