电力系统经济负荷分配的混合粒子群优化算法

为解决电力系统中的经济负荷分配问题,提出一种将约束优化与粒子群优化算法相结合的混合算法,同时引入直接搜索方法。使得混合后的粒子群优化算法不但具有高效的全局搜索能力,而且具有较强的局部搜索能力,避免陷入局部最优,提高求解精度。对两个实例进行测试,与其他智能算法的结果比较,证明提出的算法可以有效找到可行解,避免陷入局部最优,实现问题的快速求解。     

考虑通信时滞的分布式电力经济调度算法设计

本文考虑发电机的输出限制和邻居间交换信息时的通信时滞,提出了一种新的权重平衡图下的分布式经济调度算法,该算法对所有发电成本函数为强凸的发电机组成的电力系统都适用.分析了算法的平衡点与发电机最优输出功率之间的关系,并基于Lyapunov稳定性理论和凸分析理论,采用时滞分割的方法,得到了使得算法收敛的充分条件.然后应用该条件,得到了给定参数下的时滞上界,并且定性分析了参数对系统收敛速度的影响.最后,五机电力系统的仿真结果验证了算法的可行性和优越性.     

An application of model predictive control to the dynamic economic dispatch of power generation

Two formulations exist for the problem of the optimal power dispatch of generators with ramp rate constraints: the optimal control dynamic dispatch (OCDD) formulation based on control system models, and the dynamic economic dispatch (DED) formulation based on optimization. Both are useful for the dispatch problem over a fixed time horizon, and they were treated as equivalent formulations in literature. This paper first shows that the two formulations are in fact different and both formulations suffer from the same technical deficiency of ramp rate violation during the periodic implementation of the optimal solutions. Then a model predictive control (MPC) approach is proposed to overcome such a technical deficiency. Furthermore, it is shown that the MPC solutions, which are based on the OCDD framework, converge to the optimal solution of an extended version of the DED problem and they are robust under certain disturbances and uncertainties. Two standard examples are studied: the first one of a ten-unit system shows the difference between the OCDD and DED, and possible ramp rate violations, and the second one of a six-unit system shows the convergence and robustness of the MPC solutions, and the comparison with OCDD as well.     

Algorithm for calculating the analytic solution for economic dispatch with multiple fuel units

The problem of economic dispatch with multiple fuel units has been widely addressed via different techniques using approximate methods due to the exponential complexity of full enumeration in the underlying combinatory problem. A method has recently been outlined by Min et al. (2008)[12], that allows the problem to be solved in an exact way in polynomial time. In this paper, we present an alternative technique and take this idea further, studying and comparing two algorithms of polynomial complexity: basic recurrence and divide-and-conquer. Moreover, we provide the exact solution to the problem by Lin and Viviani (1984)[1], that constitutes the traditional test for all approximate methods and present a comprehensive survey of several heuristic approaches.     

Glowworm swarm optimization algorithm with topsis for solving multiple objective environmental economic dispatch problem

A new glowworm swarm optimization (GSO) algorithm is proposed to find the optimal solution for multiple objective environmental economic dispatch (MOEED) problem. In this proposed approach, technique for order preference similar to an ideal solution (TOPSIS) is employed as an overall fitness ranking tool to evaluate the multiple objectives simultaneously. In addition, a time varying step size is incorporated in the GSO algorithm to get better performance. Finally, to evaluate the feasibility and effectiveness of the proposed combination of GSO algorithm with TOPSIS (GSO–T) approach is examined in four different test cases. Simulation results have revealed the capabilities of the proposed GSO–T approach to find the optimal solution for MOEED problem. The comparison with own coded weighted sum method incorporated GSO (WGSO) and other methods reported in literatures exhibit the superiority of the proposed GSO–T approach and also the results confirm the potential of the proposed GSO–T approach to solve the MOEED problem.     

An improved bacterial foraging algorithm for combined static/dynamic environmental economic dispatch

Economic dispatch is carried out at the energy control center to find out the optimal output of thermal generating units such that power balance criterion is met, unit operating limits are satisfied and the fuel cost is minimized. With growing environmental awareness and strict government regulations throughout the world, it has become essential to optimize not only the total fuel cost but also the harmful emissions, both, under static as well as dynamic conditions. The static environment economic dispatch finds the optimal output of generating units for a fixed load demand at a given time, while the dynamic environmental economic dispatch schedules the output of online generators with changing power demands over a certain time period (normally one day) so as to minimize these two conflicting objectives, simultaneously. In this paper, the price penalty factor approach is employed for simultaneous minimization of cost and emission. The generator ramp rate constraints, non-convex and discontinuous nature of cost function and the large number of generators in practical power plants, make this problem very difficult to solve. Here, a fuzzy ranking approach is employed to identify the solution which offers the best compromise between cost and emission objectives.     

双局部粒子群算法解决环境经济调度问题

提出一种基于双局部最优的多目标粒子群优化算法,与可行解为优的约束处理方法相结合,来求解决非线性带约束的多目标电力系统环境经济调度问题。该算法针对传统多目标粒子群算法多样性低的局限性,通过对搜索空间的分割归类来增加帕累托最优解的多样性;并采用一种新的双局部最优来引导粒子的搜索,从而增强了算法的全局搜索能力。算法加入了可行解为优的约束处理方法对IEEE30节点六发电机电力系统环境经济负荷分配模型分别在几个不同复杂性问题的情况进行仿真测试,并与文献中的其他算法进行了比较。结果表明,改进的算法能够在保持帕累托最优解多样性的同时具有良好的收敛性能,更有效地解决电力系统环境经济调度问题。     

Symbiotic organisms search algorithm for dynamic economic dispatch with valve-point effects

Abstract

In this study, symbiotic organisms search (SOS) algorithm is proposed to solve the dynamic economic dispatch with valve-point effects problem, which is one of the most important problems of the modern power system. Some practical constraints like valve-point effects, ramp rate limits and prohibited operating zones have been considered as solutions. Proposed algorithm was tested on five different test cases in 5 units, 10 units and 13 units systems. The obtained results have been compared with other well-known metaheuristic methods reported before. Results show that proposed algorithm has a good convergence and produces better results than other methods.     

基于快速自适应差分进化算法的电力系统经济负荷分配

提出一种求解复杂电力系统经济负荷分配问题的快速自适应差分进化算法(FSADE).从矢量运算角度对变异算子进行分析,提出了一种改进的变异算子,大大提高了算法的收敛速率.根据个体的进化过程,引入自学习机制,对个体的变异和交叉概率常数进行自适应地调整,提高了算法的鲁棒性.3个不同规模的算例仿真结果表明,与其他4种典型智能优化算法相比, FSADE具有更好的计算精度和计算速度,是一种求解电力系统经济负荷分配问题的有效方法.     

自适应差分进化算法及对动态环境经济调度问题应用

为了应对动态环境经济调度(DEED)问题的高维性和大规模约束性,提出了一种自适应多目标差分进化算法(ADEA)。设计自适应差分交叉模块,提出改进的current to best/1交叉策略提高种群的多样性,有效地提高传统进化算法的探索与开采能力,提出一种修补策略处理功率平衡约束和爬坡率约束。为了验证该方法的有效性,数值仿真将ADEA应用于10机系统进行测试,并与同类算法展开比较,仿真结果表明ADEA具有较好的收敛能力,获得的Pareto前沿具有较好的均匀性和延展性,通过模糊决策获得的最好折中解能为电力系统调度人员提供较为合理的调度方案。     

基于修补策略的约束多目标动态环境经济调度优化算法

针对传统的优化算法求解多目标动态环境经济调度(MODEED)模型时极难获得高质量的可行解,且收敛速度慢等问题,根据MODEED模型约束特征,设计了一种约束修补策略;然后将该策略嵌入非支配排序算法(NSGAⅡ),进而提出一种修补策略的约束多目标优化算法(CMEA/R);接着借助模糊决策理论给出了多目标问题的最优决策向量;最后,以经典的10机系统为例,验证了CMEA/R的求解能力,并比较了不同群体规模下CMEA/R与NSGAⅡ的性能。仿真结果表明,在不同群体规模下,与NSGAⅡ相比,CMEA/R的污染排放平均减少了480 lb(217.7 kg),燃料成本平均减少了7 800美元,执行时间平均减少了0.021 s;覆盖率(HR)性能优于NSGAⅡ,且收敛速度较NSGAⅡ快。     

Solution of economic dispatch problems by seeker optimization algorithm

Seeker optimization algorithm (SOA), a novel heuristic population-based search algorithm, is utilized in this paper to solve different economic dispatch (ED) problems of thermal power units. In the SOA, the act of human searching capability and understanding are exploited for the purpose of optimization. In this algorithm, the search direction is based on empirical gradient by evaluating the response to the position changes and the step length is based on uncertainty reasoning by using a simple fuzzy rule. The effectiveness of the algorithm has been tested on four different small, as well as, large scale test power systems to solve the ED problems. The outcome of the present work is to establish the SOA as a promising alternative approach to solve the ED problems in practical power systems. Both the near-optimality of the solution and the convergence speed of the algorithm are promising. The results obtained are compared with those published in the recent literatures.     

Chaotic electromagnetism-like mechanism algorithm for economic load dispatch of power system

Chaotic electromagnetism-like mechanism algorithm (CEMA) is first proposed in this paper, which is the integration of electromagnetism-like mechanism algorithm (EMA) and chaos theory. EMA simulates the attraction and repulsion mechanism for particles in the electromagnetic field. Every solution is a charged particle, and it moves to optimum solution according to certain criteria which need several steps. To enrich the searching behaviour and to avoid being trapped into local optimum, chaotic dynamics is incorporated into EMA. CEMA possesses excellent global optimal performance, simple programming realisation and good convergence, and it is used in economic load dispatch of power systems. Through performance comparison, it is obvious that the solution is superior to other optimisation algorithms. It can be applied to other research problems in power systems.     

基于环境经济调度问题的空间自适应划分多目标优化

提出一种基于空间自适应划分的多目标优化算法. 为了增强种群的收敛性和多样性, 多维搜索空间被划分成多个网格, 网格内的粒子通过共享“引导”粒子的经验信息调整自身的速度和位置, 并引入年龄观测器实时记录引导粒子对Pareto 解集所做的贡献, 及时更新引导粒子, 以增强算法的全局搜索能力. 对多目标测试函数以及环境经济调度问题进行了仿真实验, 实验结果表明, 所提出算法能对解空间进行更加全面、充分的探索, 快速找到一组分布具有较好的逼近性、宽广性和均匀性的最优解集合.

     

Orthogonal PSO algorithm for economic dispatch of thermal generating units under various power constraints in smart power grid

Particle swarm optimization (PSO) algorithm has been successfully applied to solve various optimization problems in science and engineering. One such popular one is called global PSO (GPSO) algorithm. One of major drawback of GPSO algorithm is the phenomenon of “zigzagging”, that leads to premature convergence by falling into local minima. In addition, the performance of GPSO algorithm deteriorates for high-dimensional problems, especially in presence of nonlinear constraints. In this paper we propose a novel algorithm called, orthogonal PSO (OPSO) that alleviates the shortcomings of the GPSO algorithm. In OPSO algorithm, the m particles of the swarm are divided into two groups: active group and passive group. The d particles of the active group undergo an orthogonal diagonalization process and are updated in such way that their position vectors become orthogonally diagonalized. In the OPSO algorithm, the particles are updated using only one guide, thus avoiding the conflict between the two guides that occurs in the GPSO algorithm. We applied the OPSO algorithm for solving economic dispatch (ED) problem by taking three power systems under several power constraints imposed by thermal generating units (TGUs) and smart power grid (SPG), for example, ramp rate limits, and prohibited operating zones. In addition, the OPSO algorithm is also applied for ten selected shifted and rotated CEC 2015 benchmark functions. With extensive simulation studies, we have shown superior performance of OPSO algorithm over GPSO algorithm and several existing evolutional computation techniques in terms of several performance measures, e.g., minimum cost, convergence rate, consistency, and stability. In addition, using unpaired t-Test, we have shown the statistical significance of the OPSO algorithm against several contending algorithms including top-ranked CEC 2015 algorithms.     

An improved multiobjective estimation of distribution algorithm for environmental economic dispatch of hydrothermal power systems

Environmental economic dispatch of fixed head of hydrothermal power systems is viewed as a mulitobjective optimization problem in this paper. The practical hydrothermal system possesses various constraints which make the problem of finding global optimum difficult. This paper develops an improved multiobjective estimation of distribution algorithm to solving the above problem. A local learning operation is added into the original regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) in the improved approach so as to improve the local search ability and enhance the convergence efficiency. Furthermore, a repair mechanism is employed to repair the searched infeasible solutions in order to be able to search in the feasible region. In the experiment, the results obtained by the proposed approach have been compared with those from other three MOEAs: NSGA-II, NNIA, and RM-MEDA. Results from some pervious reported methods have also been employed to compare with our method. In addition, the results demonstrate the superiority of this proposed method as a promising MOEA to solve this power system multiobjective optimization problem.     

Distributed fixed-time economic dispatch over directed graphs: An event-triggered approach

This paper introduces a novel distributed fixed-time algorithm that employs an event-triggered strategy to solve the economic dispatch problem within the framework of smart grids. Distinguishing from existing fixed-time and finite-time algorithms of distributed economic dispatch applied to undirected graphs, the proposed distributed optimization algorithm in this paper has been proven effective for directed graphs. The proposed algorithm ensures the continual satisfaction of the supply and demand balance constraints. Additionally, the incorporation of the event-triggered strategy not only conserves actuator updates but also avoids Zeno behavior. Finally, simulation cases verify the effectiveness of the proposed algorithm.     

Tournament-based harmony search algorithm for non-convex economic load dispatch problem

This paper proposes a tournament-based harmony search (THS) algorithm for economic load dispatch (ELD) problem. The THS is an efficient modified version of the harmony search (HS) algorithm where the random selection process in the memory consideration operator is replaced by the tournament selection process to activate the natural selection of the survival-of-the-fittest principle and thus improve the convergence properties of HS. The performance THS is evaluated with ELD problem using five different test systems: 3-units generator system; two versions of 13-units generator system; 40-units generator system; and large-scaled 80-units generator system. The effect of tournament size (t) on the performance of THS is studied. A comparative evaluation between THS and other existing methods reported in the literature are carried out. The simulation results show that the THS algorithm is capable of achieving better quality solutions than many of the well-popular optimization methods.     

Cultural quantum-behaved particle swarm optimization for environmental/economic dispatch

In this paper, a novel CMOQPSO algorithm is proposed, in which cultural evolution mechanism is introduced into quantum-behaved particle swarm optimization (QPSO) to solve multiobjective environmental/economic dispatch (EED) problems. There are growing concerns about the ability of QPSO to handle multiobjective optimization problems. Two important issues in extending QPSO to multiobjective context are the construction of exemplar positions for each particle and the maintenance of population diversity. In the proposed CMOQPSO, one particle is measured for multiple times at each iteration in order to enhance its global searching ability. Belief space, which is based on cultural evolution mechanism and contains different types of knowledge extracted from the particle swarm, is adopted to generate global best positions for the multiple measurements of each particle. Moreover, to maintain population diversity and avoid premature, a novel local search operator, which is based on the knowledge in belief space, is proposed in this paper. CMOQPSO is compared with several state-of-art algorithms and tested on EED systems with 6 and 40 generators respectively. The comparative results demonstrate the effectiveness of the proposed algorithm.     

A hybrid non-linear time-varying double-weighted particle swarm optimization for solving non-convex combined environmental economic dispatch problem

Fossil-fuel based power sources cause environmental pollution such as the degradation of air quality and climate change, which negatively impacts the life on the earth. Consequently, this demands that the power generation should consider the optimal management of thermal sources that are aimed at minimizing the emission of gasses in the generation mix. The production volume of multi-pollutant gasses (SO₂, NO_x, and CO₂) can be reduced through a combined environmental economic dispatch (CEED) approach. This study has proposed a hybrid algorithm based on a novel combination of a modified genetic algorithm and an improved version of particle swarm optimization abbreviated as MGAIPSO to solve CEED problem. The study utilizes three robust operators to enhance the performance of the proposed hybrid algorithm. In GA, a uniformly weighted arithmetic crossover and a normally distributed mutation operator have been implemented to produce elite off-springs in each iteration and diversify the solutions in the search space. In the case of PSO, a non-linear time-varying double-weighted (NLTVDW) technique is developed to obtain a substantial balance between exploration and exploitation. To further enhance the exploitation ability of the MGAIPSO, this study has implemented two movements correctional methods to continuously monitor and amend the position and velocity of the particles. Several numerical case studies ranging from small to large-scale are carried out to validate the practicality of the proposed algorithm.