Civilized swarm optimization for multiobjective short-term hydrothermal scheduling

This paper presents a solution technique for multiobjective short-term hydrothermal scheduling (MSTHTS) through civilized swarm optimization (CSO) which is the hybrid of society–civilization algorithm (SCA) and particle swarm optimization (PSO). The intra and inter society communication mechanisms of SCA have been embedded into the food-searching strategy of PSO to form CSO. The MSTHTS problem is formulated by considering economic and emission objectives. A new ideal guide method has been proposed to find out the Pareto-optimal front. Multi-reservoir cascaded hydro power plants having nonlinear generation characteristics and thermal power plants with non-smooth cost and emission curves are considered for analysis. Other aspects such as, water transport delay, water availability, storage conformity, power loss and operating limits are fully accounted in the problem formulation. The performance of the proposed CSO is demonstrated through two MSTHTS problems and the results are compared with those presented in the literature. CSO along with the new ideal guide method outperforms all the previous approaches by providing quality Pareto-optimal fronts.     

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.     

A fuzzified multi objective Interactive Honey Bee Mating Optimization for Environmental/Economic Power Dispatch with valve point effect

In this paper, an improved multi objective Interactive Honey Bee Mating Optimization (IHBMO) is proposed to find the feasible optimal solution of the Environmental/Economic Power Dispatch (EED) problem with considering operational constraints of the generators. The EED problem is an important issue in power industry with considered the production of environmental pollution caused by fossil fuel consumption such as dangerous gases and carbon monoxide. The EED problem is formulated as a nonlinear constrained multi objective optimization problem which is solved by multi objective IHBMO techniques that has a strong ability to find the most optimal results. The three conflicting and non-commensurable: fuel cost, pollutant emissions and system loss, should be minimized simultaneously while satisfying certain system constraints. For achieve a good design with different solutions in a multi objective optimization problem, Pareto dominance concept is used to generate and sort the dominated and non-dominated solutions. Also, fuzzy set theory is employed to extract the best compromise solution. The propose method has been individually examined and applied to the standard IEEE 30-bus 6-generator, IEEE 180-bus fourteen generator and 40 generating unit (with valve point effect) test systems. The effectiveness of the proposed approach is demonstrated by comparing its performance with other evolutionary multi-objective optimization algorithms such as NSGA, NPGA, SPEA, MOPSO, MODE and MOHBMO. The computational results reveal that the multi objective IHBMO algorithm has excellent convergence characteristics and is superior to other multi objective optimization algorithms. Also, the results confirm its great potential in handling the multi-objective problems in power systems.     

An -dominance-based multiobjective genetic algorithm for economic emission load dispatch optimization problem

In this paper, a novel multiobjective genetic algorithm approach for economic emission load dispatch (EELD) optimization problem is presented. The EELD problem is formulated as a non-linear constrained multiobjective optimization problem with both equality and inequality constraints. A new optimization algorithm which is based on concept of co-evolution and repair algorithm for handling non-linear constraints is presented. The algorithm maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of -dominance. The use of -dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto-set approximation by choosing an appropriate value.The proposed approach is carried out on the standard IEEE 30-bus 6-genrator test system. The results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto-optimal non-dominated solutions of the multiobjective EELD problem in one single run. Simulation results with the proposed approach have been compared to those reported in the literature. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.     

Environmental/economic power dispatch problem using multi-objective differential evolution algorithm

This paper presents a multi-objective differential evolution (MODE) algorithm for environmental/economic power dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multi-objective problem with competing and non-commensurable objectives of fuel cost, emission and system loss. The proposed MODE approach adopts an external elitist archive to retain non-dominated solutions found during the evolutionary process. In order to preserve the diversity of Pareto optimality, a crowding entropy diversity measure tactic is proposed. The crowding entropy strategy is able to measure the crowding degree of the solutions more accurately. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed approach have been carried out on the IEEE 30- and 118-bus test system. The results demonstrate the capability of the proposed MODE approach to generate well-distributed Pareto optimal non-dominated solutions of multi-objective EED problem. The comparison with reported results of other MOEAs reveals the superiority of the proposed MODE approach and confirms its potential for solving other power systems multi-objective optimization problems.     

基于免疫进化细菌觅食算法的多目标无功优化

为了更好地解决电力系统多目标无功优化问题,分析了当前多目标无功优化算法存在的缺陷,提出了一种基于免疫进化的改进多目标细菌觅食优化算法。该算法求得的Pareto最优解分布均匀,收敛性和鲁棒性好。IEEE14,IEEE30节点测试系统的算例结果表明所提的算法在多目标无功优化中具有良好的效果,为各目标之间的权衡分析提供了有效工具,是一种求解多目标无功优化问题的有效方法。     

Optimal multi objective placement and sizing of multiple DGs and shunt capacitor banks simultaneously considering load uncertainty via MOPSO approach

This study proposes a new application of multi objective particle swarm optimization (MOPSO) with the aim of determining optimal location and size of distributed generations (DGs) and shunt capacitor banks (SCBs) simultaneously with considering load uncertainty in distribution systems. The multi objective optimization includes three objective functions: decreasing active power losses, improving voltage stability for buses and balancing current in system sections. The uncertainty of loads is modeled by using fuzzy data theory. This method uses Pareto optimal solutions to solve the problem with objective functions and constraints. In addition, a fuzzy-based mechanism is employed to extract the best compromised solution among three different objective functions. The proposed method is implemented on IEEE 33 bus radial distribution system (RDS) and an actual realistic 94 bus Portuguese RDS and the results are compared with methods of Strength Pareto Evolutionary Algorithm (SPEA), Non-dominated Sorting Genetic Algorithm (NSGA), Multi-Objective Differential Evolution (MODE) and combination of Imperialist Competitive Algorithm and Genetic Algorithm (ICA/GA). Test results demonstrate that the proposed method is more effective and has higher capability in finding optimum solutions in cases where DG and SCB are located and sized simultaneously in a multi objective optimization.     

基于LS-SVM和SPEA2的电站锅炉燃烧多目标优化研究

利用最小二乘支持向量机(LS-SVM)对锅炉燃烧特性建模,构造了以锅炉效率与NOx排放为组合的锅炉燃烧多目标优化模型,并与BP神经网络建模比较,分析表明模型在泛化能力、收敛速度和最优性均优于神经网络模型;针对锅炉高效低污染燃烧多目标问题,提出利用多目标进化算法SPEA2(强度Pareto进化算法)实现运行工况寻优,然后根据模糊集理论在Pareto解集中求得满意解,获得锅炉燃烧优化调整方式.通过某600 MW机组的仿真计算,并与加权遗传算法比较,结果表明本文算法在Pareto前沿具有更好的多样化,克服了将多目标函数加权求和转化为单目标优化问题只能找到凸Pareto最优域及需要多次运行得到Pareto解集的缺陷,计算结果可指导运行人员进行参数优化调整,提高燃烧经济性.     

基于多目标粒子群算法的电力系统环境经济调度研究

提出了一种新的多目标粒子群优化(Multi-Objective Particle Swarm Optimization, MOPSO )算法,用于求解电力系统的环境/经济调度问题。通过设计特定的约束修正因子,将不可行解修正成可行解,并在此基础上用惩罚函数法构建了新的适用于多目标粒子群的适应度函数模型。根据帕累托占优条件形成历史帕累托最优解集和全局帕累托最优解集,引入稀疏度排序法选择全局最优解,基于帕累托最优前沿的斜率特性,提出用斜率法筛选非劣解,采用基于模糊数学的满意度评价模型选择POF的折衷最优解。最后,用IEEE-30节点标准测试系统对所提算法进行了仿真测试,并与其他算法进行了对比。仿真结果表明所提算法可行、有效。     

Multi-objective economic emission dispatch considering wind power using evolutionary algorithm based on decomposition

Due to the increasing deterioration of environmental problem, multi-objective Economic Emission Dispatch (EED) problem has become one of the active research areas in recent years. Meanwhile, the renewable energy such as wind energy is an important approach to reduce pollution emissions, as well as the dependence on fossil fuels. In this paper, a newly developed optimization technique, called Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D), has been applied to optimize the cost and emission of wind–thermal power system. MOEA/D provides a simple but efficient framework which decomposes a Multi-objective Optimization Problem (MOP) into a number of scalar optimization subproblems and optimizes them simultaneously. The stochastic nature of wind power is modeled by Weibull probability distribution function and the uncertainty of wind power is considered as system constraints with stochastic variables. To validate the effectiveness of the MOEA/D method, it is first applied to solve the traditional EED problem of standard IEEE 30-bus 6-generator system as the benchmark. Then, the effect of wind power penetration on cost and emission is analyzed by MOEA/D in a 6-generator system and a 40-generator system with wind farms based on the proposed EED model. A comparative analysis with other similar optimization methods reveals that the MOEA/D method is able to generate better performance in terms of both solution quality and computational efficiency.