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.     

Dynamic economic dispatch using harmony search algorithm with modified differential mutation operator

Dynamic economic dispatch (DED), which is a complex non-linear constrained optimization problem, has a pivotal role in power system operation. It is one of the prime functions of power generation and control, where the aim is to operate an electrical power system most economically while the system operation is within its security limits. This problem possess non-convex characteristic when generation unit valve-point effects are considered. This paper proposes to solve DED problem with valve-point effects, using a modified form of recently developed differential harmony search algorithm. A five- and ten-unit system with non-smooth fuel cost function is used to establish the effectiveness of the proposed method over various other methods. It is shown that the proposed method is capable of providing better quality solutions.     

Dynamic economic dispatch using artificial immune system for units with valve-point effect

Dynamic economic dispatch (DED) is an important dynamic problem in power system operation and control. The objective of the problem is to schedule power generation for the online units over a time horizon, satisfying the unit and ramp-rate constraints. In this paper, clonal selection based artificial immune system (AIS) algorithm is used to solve the dynamic economic dispatch problem for generating units with valve-point effect. The feasibility of the proposed method is validated with ten and five unit test systems for a period of 24 h. Results obtained with the proposed approach are compared with other techniques in the literature. The results obtained substantiate the robustness and proficiency of the proposed methodology over other existing techniques in terms of solution quality and computational efficiency.     

An Efficient Modified HPSO-TVAC-Based Dynamic Economic Dispatch of Generating Units

Abstract

This paper proposes a novel particle swarm optimization (PSO) algorithm with population reduction, which is called modified new self-organizing hierarchical PSO with jumping time-varying acceleration coefficients (MNHPSO-JTVAC). The proposed method is used for solving well-known benchmark functions, as well as non-convex and non-smooth dynamic economic dispatch (DED) problems for a 24?h time interval in two different test systems. Operational constraints including the prohibited operating zones (POZs), the transmission losses, the ramp-rate limits and the valve-point effects are considered in solving the DED problem. The obtained numerical results show that the MNHPSO-JTVAC algorithm is very suitable and competitive compared to other algorithms and have the capacity to obtain better optimal solutions in solving the non-convex and non-smooth DED problems compared to the other variants of PSO and the state of the art optimization algorithms proposed in recent literature. The source codes of the HPSO-TVAC algorithms and supplementary data for this paper are publicly available at https://github.com/ebrahimakbary/MNHPSO-JTVAC.     

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.     

Multiple tabu search algorithm for economic dispatch problem considering valve-point effects

This paper presents a multiple tabu search (MTS) algorithm to solve the economic dispatch (ED) problem by taking valve-point effects into consideration. The practical ED problem with valve-point effects is represented as a non-smooth optimization problem with equality and inequality constraints that make the problem of finding the global or near global optimum difficult. The proposed MTS algorithm is the sequential execution of individual tabu search (TS) algorithm simultaneously by only one personal microcomputer. The MTS algorithm introduces additional techniques for improvement of search process, such as initialization, adaptive searches, multiple searches, replacing and restarting process. To show its effectiveness, the MTS is applied to test two studied systems consisting of 13 and 40 power generating units with valve-point effects. The optimized results by MTS are compared with those of conventional approaches, such as simulated annealing (SA), genetic algorithm (GA), TS algorithm and particle swarm optimization (PSO). Studied results confirm that the proposed MTS approach is capable of obtaining higher quality solution efficiently and lowest computational time.     

Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels

This paper presents an improved genetic algorithm with multiplier updating (IGA/spl I.bar/MU) to solve power economic dispatch (PED) problems of units with valve-point effects and multiple fuels. The proposed IGA/spl I.bar/MU integrates the improved genetic algorithm (IGA) and the multiplier updating (MU). The IGA equipped with an improved evolutionary direction operator and a migration operation can efficiently search and actively explore solutions, and the MU is employed to handle the equality and inequality constraints of the PED problem. Few PED problem-related studies have seldom addressed both valve-point loadings and change fuels. To show the advantages of the proposed algorithm, which was applied to test PED problems with one example considering valve-point effects, one example considering multiple fuels, and one example addressing both valve-point effects and multiple fuels. Additionally, the proposed algorithm was compared with previous methods and the conventional genetic algorithm (CGA) with the MU (CGA/spl I.bar/MU), revealing that the proposed IGA/spl I.bar/MU is more effective than previous approaches, and applies the realistic PED problem more efficiently than does the CGA/spl I.bar/MU. Especially, the proposed algorithm is highly promising for the large-scale system of the actual PED operation.     

Reserve Constrained Dynamic Dispatch of Units With Valve-Point Effects

This paper addresses a hybrid solution methodology integrating particle swarm optimization (PSO) algorithm with the sequential quadratic programming (SQP) method for the reserve constrained dynamic economic dispatch problem (RCDEDP) of generating units considering the valve-point effects. The cost function of the generating units exhibits the nonconvex characteristics, as the valve-point effects are modeled and imposed as rectified sinusoid components. The hybrid method incorporates the PSO algorithm as the main optimizer and SQP as the local optimizer to fine-tune the solution region whenever the PSO algorithm discovers a better solution region in the progress of its run. Thus, the SQP guides PSO for better performance in the complex solution space. To validate the feasibility of the proposed method, a ten-unit system is taken and studied under three different load patterns. The effectiveness and computation performance of the proposed method for the RCDEDP of units with valve-point effects is shown in general.     

基于交叉熵的蒙特卡洛法在发电系统充裕度评估中的应用

针对传统蒙特卡洛法对稀有事件的敏感性等问题,提出了一种基于交叉熵的蒙特卡洛法,将其应用于发电系统充裕度评估中。基本思想是使用重要抽样密度函数,通过求解最优问题获得该函数的最优参数,从而提高传统蒙特卡洛法的抽样效率。最后使用可靠性测试系统IEEE-RTS以及修改后的测试系统对提出的方法进行验证,将仿真结果与使用传统蒙特卡洛法得到的结果进行比较,表明该方法在保证评估精度的基础上大大提高了计算速度。     

Application of pattern search method to power system valve-point economic load dispatch

Direct search (DS) methods are evolutionary algorithms used to solve constrained optimization problems. DS methods do not require any information about the gradient of the objective function at hand, while searching for an optimum solution. One of such methods is pattern search (PS) algorithm. This study presents a new approach based on a constrained pattern search algorithm to solve well-known power system economic load dispatch problem (ELD) with valve-point effect. For illustrative purposes, the proposed PS technique has been applied to various test systems to validate its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method has been assessed and investigated through comparison with results reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving power system economic load dispatch problem.     

考虑发电机阀点效应的改进拉格朗日松弛有功调度策略

发电机阀点效应导致的非凸非光滑特性增加了有功经济调度模型的复杂度,从而增大了求解难度.文中提出一种考虑发电机阀点效应影响的改进拉格朗日松弛有功调度算法.首先,提出一种二次多项式分段拟合算法,从而将发电机阀点效应成本分解为多个分段二次多项式形式;其次,将拟合后的表达式代入拉格朗日松弛子问题中,从而将原问题转化为分段二次规划问题,并采用比较对称轴及优化变量上下限的方法快速求解,避免了引入整数变量造成的求解效率偏低问题.同时,为防止多个局部最优解导致的优化过程不收敛问题,提出一种基于近端梯度法的增广求解策略,通过在目标函数中引入辅助变量及惩罚项来加强子问题的凸性,加快收敛速度.最后,基于40机和48机测试系统对所提方法的有效性进行了测试.     

一种基于混沌序列的动态差分进化算法在电力系统动态经济调度中的应用

针对电力系统动态经济调度(DED)问题,引入差分进化算法,提出一种基于混沌序列的动态差分进化算法(ＡＤＤＥＣＳ)。该算法采用混沌序列动态调整差分进化算法的参数设置,保持种群的多样性。动态搜索策略被用于提高算法的整体搜索性能,它由全局搜索策略和局部搜索策略2部分组成。为了加速收敛和解决DED复杂的约束处理问题,采用基于多目标概念的约束处理机制,并提出一种根据机组调节能力来按比例分摊不可行解约束违反量的新方法。同时在搜索过程中,通过采用不同的变异策略结合改进的随机搜索策略来避免算法早熟,增强全局最优解的搜索能力。提出的方法的可行性和有效性由10机测试系统来证明,和其他方法相比,ADDECS方法计算速度快,计算精度高且鲁棒性强。     

A hybrid HNN-QP approach for dynamic economic dispatch problem

This paper introduces a solution of the dynamic economic dispatch (DED) problem using a hybrid approach of Hopfield neural network (HNN) and quadratic programming (QP). The hybrid algorithm is based on using enhanced HNN; to solve the static part of the problem; the QP algorithm for solving the dynamic part of the DED. This technique guarantees the global optimality of the solution due to its look-ahead capability. The new algorithm is applied and tested to an example from the literature and the solution is then compared with that obtained by some other techniques to prove the superiority and effectiveness of the proposed algorithm.     

Kinetic gas molecule optimization for nonconvex economic dispatch problem

This paper presents kinetic gas molecule optimization (KGMO) algorithm to solve economic dispatch problems with non-smooth/non-convex cost functions. KGMO is based on kinetic energy and the natural motion of gas molecules. The effectiveness of the proposed method has been verified on four different non-convex economic dispatch problems with valve-point effects, prohibited operating zones with transmission losses, multiple fuels with valve point effects and the large-scale Korean power system with valve-point effects and prohibited operating zones. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed KGMO based approach is able to provide better solution.     

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.     

Generating Capacity Reliability Evaluation Based on Monte Carlo Simulation and Cross-Entropy Methods

This paper presents a new Monte Carlo simulation (MCS) approach based on cross-entropy (CE) method to evaluate generating capacity reliability (GCR) indices. The basic idea is to use an auxiliary importance sampling density function, whose parameters are obtained from an optimization process that minimizes the computational effort of the MCS estimation approach. In order to improve the performance of the CE-based method as applied to the GCR assessment, various aspects are considered: system size, rarity of the failure event, number of different units, unit capacity sizes, and load shape. The IEEE Reliability Test System is used to test the proposed methodology, and also various modifications of this system are created to fully verify the ability of the proposed approach against both, a crude MCS and an extremely efficient analytical technique based on discrete convolution. A configuration of the Brazilian South-Southeastern generating system is also used to demonstrate the capability of the proposed CE-based MCS method in real applications.      

Modified particle swarm optimization for nonconvex economic dispatch problems

This paper presents modified particle swarm optimization to solve economic dispatch problems with non-smooth/non-convex cost functions. Particle swarm optimization performs well for small dimensional and less complicated problems but fails to locate global minima for complex multi-minima functions. This paper proposes Gaussian random variables in velocity term which improves search efficiency and guarantees a high probability of obtaining the global optimum without considerably worsening the speed of convergence and the simplicity of the structure of particle swarm optimization. The efficacy of the proposed method has been demonstrated on four test problems and four different non-convex economic dispatch problems with valve-point effects, prohibited operating zones with transmission losses, multiple fuels with valve point effects and the large-scale Korean power system with valve-point effects and prohibited operating zones. The results of the proposed approach are compared with those obtained by other evolutionary methods reported in the literature. It is found that the proposed modified particle swarm optimization based approach is able to provide better solution.     

An Improved Particle Swarm Optimization for Nonconvex Economic Dispatch Problems

This paper presents an efficient approach for solving economic dispatch (ED) problems with nonconvex cost functions using an improved particle swarm optimization (IPSO). Although the particle swarm optimization (PSO) approaches have several advantages suitable to heavily constrained nonconvex optimization problems, they still can have the drawbacks such as local optimal trapping due to premature convergence (i.e., exploration problem), insufficient capability to find nearby extreme points (i.e., exploitation problem), and lack of efficient mechanism to treat the constraints (i.e., constraint handling problem). This paper proposes an improved PSO framework employing chaotic sequences combined with the conventional linearly decreasing inertia weights and adopting a crossover operation scheme to increase both exploration and exploitation capability of the PSO. In addition, an effective constraint handling framework is employed for considering equality and inequality constraints. The proposed IPSO is applied to three different nonconvex ED problems with valve-point effects, prohibited operating zones with ramp rate limits as well as transmission network losses, and multi-fuels with valve-point effects. Additionally, it is applied to the large-scale power system of Korea. Also, the results are compared with those of the state-of-the-art methods.      

Chaotic self-adaptive differential harmony search algorithm based dynamic economic dispatch

Dynamic economic dispatch (DED) is one of the main optimization problems in electrical power system operation and control. DED problem is a non-smooth and non-convex problem when valve point effect, ramp-rate limits and prohibited operating zones of generation units are taken into account. This paper proposes an efficient chaotic self-adaptive differential harmony search (CSADHS) algorithm to solve the complicated DED problem in the presence of valve point effect, ramp-rate limits and prohibited operating zones constraints. In the proposed algorithm, chaotic self-adaptive differential mutation operator is used instead of pitch adjustment operator in the harmony search (HS) algorithm, to enhance the searching performance to find the quality solution. The effectiveness of the proposed algorithm is demonstrated on 10, 15 and 30 unit systems for a period of 24 h. The simulation results obtained by the proposed algorithm are compared with the results obtained, using differential harmony search (DHS) algorithm, chaotic differential harmony search (CDHS) algorithm, and also with the results of other methods available in the literature. In terms of solution quality, the proposed algorithm is found to be better than other algorithms and in terms of speed of convergence, standard deviation of generation cost, and computational time, the proposed algorithm is better than DHS and CDHS algorithm.     

Artificial bee colony optimization for multi-area economic dispatch

This paper presents artificial bee colony optimization for solving multi-area economic dispatch (MAED) problem with tie line constraints considering transmission losses, multiple fuels, valve-point loading and prohibited operating zones. Artificial bee colony optimization is a swarm-based algorithm inspired by the food foraging behavior of honey bees. The effectiveness of the proposed algorithm has been verified on three different test systems, both small and large, involving varying degree of complexity. Compared with differential evolution, evolutionary programming and real coded genetic algorithm, considering the quality of the solution obtained, the proposed algorithm seems to be a promising alternative approach for solving the MAED problems in practical power system.