Environmental/economic power dispatch using a fuzzified multi-objective particle swarm optimization algorithm

The environmental issues that arise from the pollutant emissions produced by fossil-fueled electric power plants have become a matter of concern more recently. The conventional economic power dispatch cannot meet the environmental protection requirements, since it only considers minimizing the total fuel cost. The multi-objective generation dispatch in electric power systems treats economic and emission impact as competing objectives, which requires some reasonable tradeoff among objectives to reach an optimal solution. In this paper, a fuzzified multi-objective particle swarm optimization (FMOPSO) algorithm is proposed and implemented to dispatch the electric power considering both economic and environmental issues. The effectiveness of the proposed approach is demonstrated by comparing its performance with other approaches including weighted aggregation (WA) and evolutionary multi-objective optimization algorithms. All the simulations are conducted based on a typical test power system.     

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.     

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.     

Multi-objective optimal reactive power dispatch using multi-objective differential evolution

This paper presents multi-objective differential evolution (MODE) to solve multi-objective optimal reactive power dispatch (MORPD) problem by minimizing active power transmission loss and voltage deviation and maximizing voltage stability while varying control variables such as generator terminal voltages, transformer taps and reactive power output of shunt VAR compensators. MODE has been tested on IEEE 30-bus, 57-bus and 118-bus systems. Numerical results for these three test systems have been compared with those acquired from strength pareto evolutionary algorithm 2 (SPEA 2).     

基于Queen-bee进化的遗传算法在电力系统经济调度中应用

为提高遗传算法的寻优能力,引入模拟自然界蜂王繁殖的改进型遗传算法(QEBGA)。概述了QEBGA的实现过程,指出基本遗传算法(SGA)采用轮盘赌选择机制选择种群个体,以普通变异算子对种群作变异操作;而QEBGA采用启发式选择机制选择种群个体,按比例分别以普通变异算子和强变异算子对种群作变异操作。详述了电力系统经济调度问题表述为极小化下的总费用函数及约束优化问题。最后,用6台发电机系统和13台发电机系统的模拟实验比较了QEBGA和SGA两种算法在优化性能上的差异,实验结果说明了相同种群规模下,QEBGA的寻优时间小于SGA;系统规模越大,QEBGA在计算精度上的优势就越突出。     

Low-carbon emission/economic power dispatch using the multi-objective bacterial colony chemotaxis optimization algorithm considering carbon capture power plant

To study the constrained emission/economic dispatch problem involving competing objectives in electric power systems with carbon capture system (CCS) technology, this paper proposes a multi-objective optimization approach based on bacterial colony chemotaxis (MOBCC) algorithm. In this algorithm, a Lamarckian constraint handling method based approach is improved to update the bacterial colony and the external archive. Finally, the optimization tests of the proposed algorithm are carried out in the IEEE 30-bus test system. Results demonstrate this approach has the advantage of dealing with highly non-linear and multi-objective functions of carbon capture thermal generator’s emission/economic dispatch problem.     

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。     

Reserve constrained multi-area economic dispatch employing differential evolution with time-varying mutation

For a power pool that involves several generation areas interconnected by tie-lines, the objective of economic dispatch (ED) is to determine the most economical generation dispatch strategy that could supply the area load demands without violating the tie-line capacity constraints. The objective of multi-area economic dispatch (MAED) is to determine the generation levels and the interchange power between areas which would minimize total fuel cost while satisfying power balance constraint, upper/lower generation limits, ramp rate limits, transmission constraints and other practical constraints. In reserve constrained MAED (RCMAED) problem inter-area reserve sharing can help in reducing the operational cost while ensuring that spinning reserve requirements in each area are satisfied. The tie-line limits too play a pivotal role in optimizing the cost of operation. The cost curves of modern generating units are discontinuous and non-convex which necessitates the use of powerful heuristic search based methods that are capable of locating global solutions effectively, with ease. This paper explores and compares the performance of various differential evolution (DE) strategies enhanced with time-varying mutation to solve the reserve constrained MAED (RCMAED) problem.The performance is tested on (i) two-area, four generating unit system, (ii) four area, 16-unit system and (iii) two-area, 40-unit system. The results are found to be superior compared to some recently published results.     

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.     

采用多目标纵横交叉算法的电力系统动态环境经济调度

针对带非线性约束的电力系统动态环境经济调度问题,提出一种多目标纵横交叉算法。对动态调度中燃料费用和污染排放两个相互约束、冲突的目标同时进行优化。求解过程中,结合非约束支配策略,提出一种双交叉机制,增强粒子穿越非可行区域的能力,使得生成的帕累托最优解落在可行区域内。通过边缘探索,增强算法的全局搜索能力。同时,采用外部存档集合储存非劣解,并通过拥挤度对比,保持非劣解的多样性。最后,采用模糊决策理论获得最优折中解。对10机电力系统的仿真结果验证了所提方法的有效性与优越性。     

基于改进多目标引力搜索算法的电力系统环境经济调度

建立了综合考虑系统运行成本和污染物排放成本的电力系统环境经济调度模型,并提出了一种改进多目标引力搜索算法(IGSA)对该模型进行求解。该算法将NSGA-II中的非劣解排序和拥挤距离的思想引入基本引力搜索算法用于处理个体偏序关系。其次针对基本引力搜索算法收敛速度慢的问题,在更新个体位置过程中受粒子群优化算法的启发对引力搜索算法的位置更新公式进行了改进;同时为了引导群体向Pareto最优解集区域靠近并保证算法解集均匀分布,采用精英保留策略;最后采用模糊集理论产生最佳折中解,为决策人员提供调度方案。算例分析验证了所提算法的可行性和有效性,为实现电力系统经济性与环保性的均衡优化提供了一条新的方法。     

基于混合DE-PSO多目标算法的动态环境经济调度

电力系统中的动态环境经济调度(DEED)是一个多变量、强约束、非凸的多目标优化问题,传统方法很难进行求解。基于微分进化(DE)算法的快速收敛性和粒子群优化(PSO)算法的搜索多样性,提出一种融合2种算法优点的混合DE-PSO多目标优化算法来求解DEED问题,该算法基于外部存档集和Pareto占优原则,采用自适应参数的DE和PSO双种群更新策略以及一种改进的Pareto解集裁剪方法。引入3种指标评价算法的性能,并采用模糊决策技术从Pareto前沿中提取折中解以供决策者进行选择。经典算例的仿真结果表明所提方法能同时优化成本和排放这2个冲突的目标,且获得了比其他算法更为宽广和均匀的Pareto前沿,体现了所提方法的可行性和优越性。     

Multiobjective particle swarm optimization for environmental/economic dispatch problem

A new multiobjective particle swarm optimization (MOPSO) technique for environmental/economic dispatch (EED) problem is proposed in this paper. The proposed MOPSO technique evolves a multiobjective version of PSO by proposing redefinition of global best and local best individuals in multiobjective optimization domain. The proposed MOPSO technique has been implemented to solve the EED problem with competing and non-commensurable cost and emission objectives. Several optimization runs of the proposed approach have been carried out on a standard test system. The results demonstrate the capabilities of the proposed MOPSO technique to generate a set of well-distributed Pareto-optimal solutions in one single run. The comparison with the different reported techniques demonstrates the superiority of the proposed MOPSO in terms of the diversity of the Pareto-optimal solutions obtained. In addition, a quality measure to Pareto-optimal solutions has been implemented where the results confirm the potential of the proposed MOPSO technique to solve the multiobjective EED problem and produce high quality nondominated solutions.     

An improved partheno genetic algorithm for multi-objective economic dispatch in cascaded hydropower systems

The multi-objective economic dispatch (MOED) problem in cascaded hydropower systems is a complicated nonlinear optimization problem with a group of complex constraints. In this paper, an improved partheno genetic algorithm (IPGA) for resolving the MOED problem in hydropower energy systems based on the non-uniform mutation operator is proposed. In the new algorithm, the crossover operator is removed and only mutation operation is made, which makes it simpler than GA in the genetic operations and not generate invalid offspring during evolution. With the help of incorporating greedy selection idea into the non-uniform mutation operator, IPGA searches the solution space uniformly at the early stage and very locally at the later stage, which makes it avoid the random blind jumping and stay at the promising solution areas. Finally, the proposed algorithm is applied to a realistic hydropower energy system with two giant scale cascaded hydropower plants in China. Compared with other algorithms, the results obtained using IPGA verify its superiority in both efficiency and precision.     

Optimal power flow using differential evolution algorithm

This paper presents an efficient and reliable evolutionary-based approach to solve the optimal power flow (OPF) problem. The proposed approach employs differential evolution algorithm for optimal settings of OPF problem control variables. The proposed approach is examined and tested on the standard IEEE 30-bus test system with different objectives that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. The proposed approach results are compared with the results reported in the literature. The results show the effectiveness and robustness of the proposed approach.     

Optimal power flow using differential evolution algorithm

This paper presents an evolutionary-based approach to solve the optimal power flow (OPF) problem. The proposed approach employs differential evolution (DE) algorithm for optimal settings of OPF control variables. The proposed approach is examined and tested on the standard IEEE 30-bus test system with different objective functions that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. In addition, non-smooth piecewise quadratic cost function has been considered. The simulation results of the proposed approach are compared to those reported in the literature. The results demonstrate the potential of the proposed approach and show its effectiveness and robustness to solve the OPF problem for the systems considered.     

Optimal reactive power dispatch using an adaptive genetic algorithm

This paper presents an adaptive genetic algorithm (AGA) for optimal reactive power dispatch and voltage control of power systems. In the adaptive genetic algorithm, the probabilities of crossover and mutation, p_c and p_m, are varied depending on the fitness values of the solutions and the normalized fitness distances between the solutions in the evolution process to prevent premature convergence and refine the convergence performance of genetic algorithms. The AGA applied for optimal power system reactive power dispatch is evaluated on an IEEE 30-bus power system in which the control of bus voltages, tap position of transformers and reactive power sources are involved to minimize the transmission loss of the power system.     

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.     

Efficient hybrid optimization approach for emission constrained economic dispatch with nonsmooth cost curves

Power plants usually operate on the strategy of economic dispatch (ED) regardless of emissions produced. Environmental considerations have become one of the major management concerns. Under these circumstances, the alternative strategy of environmental/economic dispatch (EED) is becoming more and more desirable for not only resulting in great economical benefit, but also reducing the pollutants emission.Based on the literature survey, few attempts have been made at considering valve-point effects for the realistic environmental/economic dispatch (EED) problem. This paper proposes a new efficient hybrid differential evolution algorithm with harmony search (DE–HS) to solve the multiobjective environmental/economic dispatch (EED) problems that feature nonsmooth cost curves. The proposed approach combines in the most effective way the properties of differential evolution (DE) and harmony search (HS) algorithms. To enhance the local search capability of the original DE method, the fresh individual generation mechanism of the HS is utilized.Numerical results for three case studies have been presented to illustrate the performance and applicability of the proposed hybrid method. The comparative results with some of the most recently published methods confirm the effectiveness of the proposed strategy to find accurate and feasible optimal solutions for practical EED problems.