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.     

Multi-objective quasi-oppositional teaching learning based optimization for economic emission load dispatch problem

This paper proposes an efficient optimization approach, namely quasi-oppositional teaching learning based optimization (QOTLBO) for solving non-linear multi-objective economic emission dispatch (EED) problem of electric power generation with valve point loading. In this article, a non-dominated sorting QOTLBO is employed to approximate the set of Pareto solution through the evolutionary optimization process. The proposed approach is carried out to obtain EED solution for 6-unit, 10-unit and 40-unit systems. For showing the superiority of this optimization technique, numerical results of the four test systems are compared with several other EED based recent optimization methods. The simulation results show that the proposed algorithm gives comparatively better operational fuel cost and emission in less computational time compared to other optimization techniques.     

Multi-objective harmony search algorithm for optimal power flow problem

This paper proposes a multi-objective harmony search (MOHS) algorithm for optimal power flow (OPF) problem. OPF problem is formulated as a non-linear constrained multi-objective optimization problem where different objectives and various constraints have been considered into the formulation. Fast elitist non-dominated sorting and crowding distance have been used to find and manage the Pareto optimal front. Finally, a fuzzy based mechanism has been used to select a compromise solution from the Pareto set. The proposed MOHS algorithm has been tested on IEEE 30 bus system with different objectives. Simulation results are also compared with fast non-dominated sorting genetic algorithm (NSGA-II) method. It is clear from the comparison that the proposed method is able to generate true and well distributed Pareto optimal solutions for OPF problem.     

Multi-objective Economic Dispatch Considering Wind Power Penetration Using Stochastic Weight Trade-off Chaotic NSPSO

In this paper, a stochastic weight trade-off chaotic non-dominated sorting particle swarm optimization (SWTC_NSPSO) is proposed for solving multi-objective economic dispatch considering wind power penetration. Multi-objective functions including generator fuel cost and system risk are considered. The SWTC_NSPSO algorithm improves the solution search capability by balancing between global best exploration and local best utilization through the stochastic weight trade-off technique combining dynamistic coefficients trade-off methods. The proposed algorithm cooperates with the freak, lethargy factors, and chaotic mutation to enhance diversity and search capability. Non-dominated sorting and crowding distance techniques efficiently provide the optimal Pareto front. The fuzzy function is used to select the local compromise best solution. Using a two stage approach, the global best compromise solution is selected from a large number of local best compromise trial solutions. Simulation results on the modified IEEE 30-bus test system indicate that SWTC_NSPSO can provide a lower and wider Pareto front than non-dominated sorting genetic algorithm II (NSGAII), non-dominated sorting particle swarm optimization (NSPSO), non-dominated sorting chaotic particle swarm optimization (NS_CPSO), and a stochastic weight trade-off non-dominated sorting particle swarm optimization (SWT_NSPSO) in a less computation effort, leading to a lower generator fuel cost and a higher system reliability trade-off solution.     

Optimal location and setting of SVC and TCSC devices using non-dominated sorting particle swarm optimization

In this paper, a new method for optimal locating multi-type FACTS devices in order to optimize multi-objective voltage stability problem is presented. The proposed methodology is based on a new variant of particle swarm optimization (PSO) specialized in multi-objective optimization problem known as non-dominated sorting particle swarm optimization (NSPSO). The crowding distance technique is used to maintain the Pareto front size at the chosen limit, without destroying its characteristics. To aid the decision maker choosing the best compromise solution from the Pareto front, the fuzzy-based mechanism is employed for this task. NSPSO is used to find the optimal location and setting of two types of FACTS namely: Thyristor controlled series compensator (TCSC) and static var compensator (SVC) that maximize static voltage stability margin (SVSM), reduce real power losses (RPL), and load voltage deviation (LVD). The optimization is carried out on two and three objective functions for various FACTS combinations considering. For ensure the robustness of the proposed method and gives a practical sense of our study, N − 1 contingency analysis and the stress of power system is considered in the optimization process. The thermal limits of lines and voltage limits of load buses are considered as the security constraints. The proposed method is validated on IEEE 30-bus and realistic Algerian 114-bus power system. The simulation results are compared with those obtained by particle swarm optimization (PSO) and non-dominated sorting genetic algorithms (NSGA-II). The comparisons show the effectiveness of the proposed NSPSO to solve the multi-objective optimization problem and capture Pareto optimal solutions with satisfactory diversity characteristics.     

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。     

机组负荷分配的多目标优化和多属性决策

同时计及机组运行的经济性和污染排放,将基于进化算法的多目标优化技术与多属性决策方法联合运用,针对火电厂负荷优化分配问题进行了研究。对于多目标优化问题,采用改进的非支配解排序的多目标遗传算法(NSGAⅡ),求出Pareto最优解,由这些Pareto最优解构成决策矩阵,使用客观赋权的信息熵方法对最优解的属性进行权值计算,然后用逼近理想解的排序方法(TOPSIS)进行多属性决策(MADM)研究,对Pa-reto最优解给出排序。给出了3台机组负荷分配的优化算例,计算表明所提方法适应性好,结果合理可行。     

A Lexicographic Optimization and Augmented ϵ-constraint Technique for Short-term Environmental/Economic Combined Heat and Power Scheduling

Abstract—In recent years, combined heat and power units have become significant elements in conventional power stations due their numerous merits, including operational cost savings and reduced emissions. In this regard, this article proposes a short-term multi-objective framework for the combined heat and power economic/emission dispatch problem. In addition, to more precisely model the problem, the non-linear forms of fuel cost functions and valve-point loading along with power transmission loss are considered. The objectives of the problem are total cost minimization as well as minimization of pollutant emissions; lexicographic optimization and the augmented epsilon-constraint technique are employed to solve the multi-objective problem. Also, a fuzzy decision making technique has been used to select the most preferred solution among the Pareto solutions. Afterward, a comprehensive comparison is performed between the results obtained from the proposed method and those derived from the non-dominated sorting genetic algorithm II, strength Pareto evolutionary algorithm 2, and multi-objective line-up competition algorithm, verifying the superiority of the presented approach for lower execution time, total cost, and emission. Furthermore, the proposed model is implemented on a large-scale test system while the execution time is rational.     

基于改进遗传算法的风电场多目标无功优化

针对风电场并网运行的多目标无功优化和电压稳定问题,建立了基于异步发电机内部等值电路的含风电场的电力系统无功优化模型,提出了风电场无功优化的目标函数和约束条件。结合非支配排序思想、精英保留策略、改进的小生境技术,得到了一种将向量模适应度函数作为淘汰准则的改进Pareto遗传多目标优化算法。以某风电场接入IEEE 14节点标准测试系统为例,将改进算法用于含风电场的电力系统无功优化。仿真结果表明,应用改进的遗传多目标优化算法可以同时得到多组Pareto最优解,为决策者提供了更多的选择余地,使风电场并网点母线电压在允许范围内。     

基于改进多目标海樽群算法的电力系统优化调度

文中提出了一种新的多目标海樽群优化算法,将其与等式约束修正技术和可行解占优约束处理技术相结合,用于求解高度约束的电力系统环境经济优化调度问题。该算法采用高斯采样策略和变异操作增强其寻优性能;通过一种改进的基于动态拥挤距离的非支配排序方法获得分布均匀的帕累托最优前沿;应用模糊集理论为决策者提供最佳折中解。在IEEE 30节点6机组标准测试系统上进行算例仿真,并与其它优化算法进行了对比。结果表明,所提算法在求解电力系统环境经济调度问题时具有更好的优化效果。     

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.     

Multi-objective PID controller tuning for a FACTS-based damping stabilizer using Non-dominated Sorting Genetic Algorithm-II

Design of an optimal controller requires optimization of multiple performance measures that are often noncommensurable and competing with each other. Design of such a controller is indeed a multi-objective optimization problem. Non-Dominated Sorting in Genetic Algorithms-II (NSGA-II) is a popular non-domination based genetic algorithm for solving multi-objective optimization problems. This paper investigates the application of NSGA-II technique for the tuning of a Proportional Integral Derivate (PID) controller for a Flexible AC Transmission System (FACTS)-based stabilizer. The design objective is to improve the damping of power system when subjected to a disturbance with minimum control effort. The proposed technique is applied to generate Pareto set of global optimal solutions to the given multi-objective optimization problem. Further, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto solution set. Simulation results are presented and compared with a conventionally designed PID controller under various loading conditions and disturbances to show the effectiveness and robustness of the proposed approach. Finally, the proposed design approach is extended to a multi-machine power system to damp the modal oscillations with minimum control efforts.     

火电厂厂级负荷分配的多目标优化和决策研究

火电厂的负荷优化分配系统通常是以机组煤耗特性为基础的,其经济分配对应于满足稳态工况下全厂发电成本最低的要求。对于自动发电控制方式下的厂级负荷运行分配还要满足调整时间的要求,以尽可能快的速度满足目标负荷的调整。考虑机组运行的经济性和快速性,将基于进化算法的多目标优化技术与多属性决策方法联合运用,针对火电厂厂级负荷优化分配的问题进行研究。对于多目标优化问题,采用改进的非支配解排序的多目标遗传算法,求出Pareto最优解,由Pareto最优解构成决策矩阵,使用客观赋权的信息熵方法对最优解的属性进行权值计算,然后用逼近理想解的排序方法进行多属性决策研究,对Pareto最优解给出排序。文中给出了10台机组负荷分配的优化设计算例。     

考虑地理因素的改进量子粒子群算法在多目标电网规划中的应用

针对电网规划的多目标权衡优化问题,建立以可靠性和经济性为目标的电网规划模型,提出改进的量子粒子群算法,采用Pareto支配关系来更新粒子的个体和局部最优值,定义粒子紊流极大极小间距,并采用紊流间距方法裁剪非支配解,引入收敛因子K加快粒子跳出局部最优后的收敛速度。同时考虑电网规划存在的地理环境不确定因素的影响,在规划目标函数中引入地理障碍罚因子。通过18节点电网规划算例仿真结果表明,提出的改进算法与基于非支配遗传算法和基于多目标进化算法相比,所得的Pareto解数目,解的优劣情况以及分布效果都有明显提升。     

基于改进非劣分层遗传算法及基点和熵多属性决策的互联电网交易方法

利用改进非劣分层遗传算法（non—dominated sorting genetic algorithmⅡ,NSGA．Ⅱ）对互联电网多目标交易优化模型进行求解,得到多样化的帕雷托前沿,为决策提供丰富的信息,进一步与基于基点和熵的多属性决策方法结合,筛选出最优解。算例分析结果表明,该方法得出的解比用基于沙普利值的合作博弈...     

Application of Multi-Objective Evolutionary Optimization Algorithms to Reactive Power Planning Problem

This paper presents a new approach to treat reactive power (VAr) planning problem using multi-objective evolutionary algorithms (EAs). Specifically, strength Pareto EA (SPEA) and multi-objective particle swarm optimization (MOPSO) approaches have been developed and successfully applied. The overall problem is formulated as a nonlinear constrained multi-objective optimization problem. Minimizing the total incurred cost of the VAr planning problem and maximizing the amount of available transfer capability (ATC) are defined as the main objective functions. The aim is to find the optimal allocation of VAr devices in such a way that investment and operating costs are minimized and at the same time the amount of ATC is maximized. The proposed approaches have been successfully tested on IEEE 14 buses system. As a result a wide set of optimal solutions known as Pareto set is obtained and encouraging results show the superiority of the proposed approaches and confirm their potential to solve such a large-scale multi-objective optimization problem. Copyright © 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

多目标无功优化的向量评价自适应粒子群算法

为了克服粒子群算法在高维复杂问题寻优时有相当可能陷入局部极优的现象,提出了一种自适应粒子群算法。该算法利用种群多样性信息对惯性权重进行非线性的调整,并在算法的后期引入速度变异算子和位置交叉算子,使算法摆脱后期易于陷入局部最优点的束缚。对基于向量评价的粒子群算法进行了扩展,提出了基于向量评价的自适应粒子群算法(vector evaluated particle adaptive swarm optimization,VEAPSO)来解决多目标无功优化问题,求解出问题的Pareto最优解集。为帮助决策者从Pareto最优解集中选取合适的最优解,该文提出一种基于决策者偏好及投影寻踪模型的多属性决策法,使决策结果更加真实可靠。将该算法应用于多目标无功优化问题中,IEEE 30和IEEE 118节点系统算例仿真表明该方法用于解决多目标无功优化问题是有效可行的。     

多目标电能质量监测器的优化配置

针对电能质量监测器的优化配置问题,建立了以监测程度和监测器个数为指标的多目标优化配置模型。采用带精英策略的快速非支配排序遗传算法(non-domtnated soring genetic algorithm,NSGA-Ⅱ),获得此多目标优化问题的Pareto最优解集。该方法能保证种群的多样性,避免传统加权求解时权值的选择和解的偏好性。最后,对Pareto最优解集的各个目标函数进行归一化处理,将最大值对应的方案作为合适的最优解。通过对2个算例进行仿真,得到了合理的电能质量监测器的配置方案,验证了该方法的可行性和有效性。     

多目标环境经济发电调度的标准化法向约束方法

将标准化法向约束(normalized normal constraint,NNC)方法用于求解电力系统环境经济发电调度问题,同时考虑发电调度的发电成本和污染气体排放量最小两个优化目标。通过NNC方法将发电调度的多目标优化问题转化为一系列的单目标优化问题,求解这些单目标问题得到完整、均匀分布的Pareto解集,然后采用伪权向量法从中选择出满意的折中解。结合NNC方法粗粒度空间上可并行的计算优势,将其采用多核并行计算技术加以实现,以提高其计算效率。对IEEE-30和IEEE-118系统测试,验证该方法的有效性和可行性,采用多核并行计算实现后,可以快速、完整地得到环境经济发电调度多目标优化问题均匀分布的Pareto解集,具有广阔的应用前景。     

基于HSA-FNSA混合算法的配电网群故障恢复多目标优化决策

为快速获得系统故障后配电网群故障恢复优化方案,提出了一种基于启发式搜索-快速非支配排序混合算法（HSA-FNSA）的配电网群故障恢复多目标优化决策方法。首先,建立了配电网群故障前后的拓扑模型及故障类型的图论描述,并采用HSA算法获得故障恢复方案集;随后利用分层前推回代法求解配电网潮流以获得运行参数;进一步建立考虑配电网韧性、网损、电压不平衡量和开关操作次数的故障恢复多目标优化决策模型;引入FNSA算法获得帕累托非劣解集并确定终选方案。通过IEEE三馈线算例验证了所提方法在求解配电网群多类型故障恢复的可行性和优越性。