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.     

Large-scale economic dispatch by genetic algorithm

This paper presents a new genetic approach for solving the economic dispatch problem in large-scale power systems. A new encoding technique is developed. The chromosome contains only an encoding of the normalized system incremental cost in this encoding technique. Therefore, the total number of bits of chromosome is entirely independent of the number of units. The salient feature makes the proposed genetic approach attractive in large and complex systems which other methodologies may fail to achieve. Moreover, the approach can take network losses, ramp rate limits, and prohibited zone avoidance into account because of genetic algorithm's flexibility. Numerical results on an actual utility system of up to 40 units show that the proposed approach is faster and more robust than the well-known lambda-iteration method in large-scale systems     

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.     

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。     

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.     

Combined heat and power economic dispatch using exchange market algorithm

Combined heat and power economic dispatch (CHPED) is one of the critical issues in power systems, playing key role in economic performance of the system. CHPED is a challenging optimization problem of non-linear and non-convex type. Thus, evolutionary and heuristic algorithms are employed as effective tools in solving this problem. This paper applies newly proposed exchange market algorithm (EMA) on CHPED problem. EMA is a powerful and robust algorithm. With two powerful absorbing operators pulling solutions toward optimality and two smart searching operators, EMA is able to extract optimum point in optimization problem. In order to examine the proposed algorithm’s capabilities and find optimum solution for CHPED problem, several test systems considering valve-point effect, system power loss and system constraints are optimized. The obtained results prove high capability of EMA in extracting optimum points. The results also show that this algorithm can be utilized as an efficient and reliable tool in solving CHPED problem.     

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。     

基于协同进化遗传算法的微网经济环保调度

为合理调度分布式电源使微网经济和可靠运行,提出一种基于协同进化遗传算法实现微电网分布式电源出力调度的方法。建立了冷热电联产型的微网经济环保调度模型,新增考虑热备用约束条件;建立分阶段目标函数,将蓄电池虚拟放电和充电价格计入群体寻优目标函数;给合协同进化遗传算法,使用群体寻优目标函数和精英寻优目标函数寻求分阶段经济调度最优解;给出了孤网和并网运行方式下的调度策略。通过算例分析了并网和孤网两种运行方式下冬季的经济调度方案,结果表明调度模型和算法是有效的。     

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.     

Optimal power dispatch in multinode electricity market using genetic algorithm

The application of the genetic algorithm to solve the optimal power dispatch problem for a multi-node auction market is proposed in this paper. The optimal power dispatch problem is a non-linear optimisation problem with several constraints. The objective of the proposed genetic algorithm is to maximise the total participants’ benefit at all nodes in the system. The proposed algorithm is simple to implement and can easily incorporate additional constraints. The algorithm was tested on a 17-node, 26-line system. The results have shown that the proposed algorithm yields good results that are consistent with typical market behaviour.     

A hybrid genetic algorithm and bacterial foraging approach for dynamic economic dispatch problem

Dynamic economic dispatch (DED) is one of the most significant non-linear complicated problems showing non-convex characteristic in power systems. This is due to the effect of valve-points in the generating units’ cost functions, the ramp-rate limits and transmission losses. Hence, proposing an effective solution method for this optimization problem is of great interest. The original bacterial foraging (BF) optimization algorithm suffers from poor convergence characteristics for larger constrained problems. To overcome this drawback, a hybrid genetic algorithm and bacterial foraging (HGABF) approach is presented in this paper to solve the dynamic economic dispatch problem considering valve-point effects, ramp-rate limits and transmission losses. The HGABF approach can be derived by integrating BF algorithm and genetic algorithm (GA), so that the BF’s drawback can be treated before employing it to solve the complex and high dimensioned search space of the DED problem. To illustrate the effectiveness of the HGABF approach, several test systems with different numbers of generating units are used. The results of HGABF approach are compared with those obtained by other published methods employing same test systems. These results show the effectiveness and the superiority of the introduced method over other published methods.     

Combined heat and power economic dispatch by harmony search algorithm

The optimal utilization of multiple combined heat and power (CHP) systems is a complicated problem that needs powerful methods to solve. This paper presents a harmony search (HS) algorithm to solve the combined heat and power economic dispatch (CHPED) problem. The HS algorithm is a recently developed meta-heuristic algorithm, and has been very successful in a wide variety of optimization problems. The method is illustrated using a test case taken from the literature as well as a new one proposed by authors. Numerical results reveal that the proposed algorithm can find better solutions when compared to conventional methods and is an efficient search algorithm for CHPED problem.     

Combined heat and power economic emission dispatch using nondominated sorting genetic algorithm-II

This paper presents nondominated sorting genetic algorithm-II for solving combined heat and power economic emission dispatch problem. The problem is formulated as a nonlinear constrained multi-objective optimization problem. Nondominated sorting genetic algorithm-II is proposed to handle economic emission dispatch as a true multi-objective optimization problem with competing and noncommensurable objectives. The proposed algorithm is illustrated for two test systems and the test results are compared with those obtained from strength pareto evolutionary algorithm 2.     

Backtracking search optimization based economic environmental power dispatch problems

This paper presents the solution for a nonlinear constrained multi objective of the economic and emission load dispatch (EELD) problem of thermal generators of power systems by means of the backtracking search optimization technique. Emission substance like NO_X, power demand equality constraint and operating limit constraint are considered here. The aim of backtracking search optimization (BSA) is to find a global solution under the influence of two new crossover and mutation operations. BSA has capability to deal with multimodal problems due to its powerful exploration and exploitation capability. BSA is out of excessive sensitivity to control parameters as it has single control parameter. The performance of BSA is compared with existing newly developed optimization techniques in terms quality of solution obtained, computational efficiency and robustness for multi objective problems.     

Solving dynamic economic dispatch problem with security constraints using bacterial foraging PSO-DE algorithm

This paper presents a heuristic optimization methodology, namely, Bacterial foraging PSO-DE (BPSO-DE) algorithm by integrating Bacterial Foraging Optimization Algorithm (BFOA), Particle Swarm Optimization (PSO) and Differential Evolution (DE) for solving non-smooth non-convex Dynamic Economic Dispatch (DED) problem. The DED problem exhibits non-smooth, non-convex nature due to valve-point loading effects, ramp rate limits, spinning reserve capacity, prohibited operating zones and security constraints. The proposed hybrid method eliminates the problem of stagnation of solution with the incorporated PSO and DE operators in original bacterial foraging algorithm. It achieves global cost by selecting the bacterium with good foraging strategies. The bacteria with good foraging strategies are obtained in the updating process of every chemo-tactic step by the PSO operator. The DE operator fine tunes the solution obtained through bacterial foraging and PSO operator. A 3- and 7-unit systems for static economic dispatch, a 26-bus, 6-generator test system and an IEEE 39-bus, 10-unit New England test systems are considered to show the effectiveness of the proposed method over other methods reported in the literature.     

Hybrid genetic algorithm for economic dispatch with valve-point effect

This paper presents an efficient method for solving the economic dispatch problem (EDP) through combination of genetic algorithm (GA), the sequential quadratic programming (SQP) technique, uniform design technique, the maximum entropy principle, simplex crossover and non-uniform mutation. The proposed hybrid technique uses GA as the main optimizer, the SQP to fine tune in the solution of the GA run. Based on the maximum entropy principle, the cost function of EDP is approximated by using a smooth and differentiable function to improve the performance of the SQP. An initial population obtained by using uniform design exerts optimal performance of the proposed hybrid algorithm. The effectiveness of the proposed method is validated by carrying out extensive tests on two different EDP with incremental fuel-cost function taking into account the valve-point loadings effects. The result shows that the proposed hybrid genetic algorithm improves the solution accuracy and reliability compared to other techniques for EDP considering valve-point effects.     

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.     

An algorithm for combined heat and power economic dispatch

This paper presents a new algorithm for combined heat and power (CHP) economic dispatch. The CHP economic dispatch problem is decomposed into two sub-problems: the heat dispatch; and the power dispatch. The sub-problems are connected through the heat-power feasible region constraints of cogeneration units. The connection can be interpreted by the unit heat-power feasible region constraint multipliers in the Lagrangian function, and the interpretation naturally leads to the development of a two-layer algorithm. The outer layer uses the Lagrangian relaxation technique to solve the power dispatch iteratively. In each iteration, the inner layer solves the heat dispatch with the unit heat capacities passed by the outer layer. The binding constraints of the heat dispatch are fed back to the outer layer to move the CHP economic dispatch towards a global optimal solution     

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.