Bee colony optimization for combined heat and power economic dispatch

This paper presents a novel optimization approach to the combined heat and power economic dispatch problem by using bee colony optimization algorithm. The algorithm is a swarm-based algorithm inspired by the food foraging behavior of honey bees. The performance of the proposed algorithm is validated by illustration with a test system. The results of the proposed approach are compared with those of particle swarm optimization, real-coded genetic algorithm and evolutionary programing techniques. From numerical results, it is seen that bee colony optimization based approach is able to provide a better solution at a lesser computational effort.     

Differential evolution approach for optimal reactive power dispatch

Differential evolution based optimal reactive power dispatch for real power loss minimization in power system is presented in this paper. The proposed methodology determines control variable settings such as generator terminal voltages, tap positions and the number of shunts to be switched, for real power loss minimization in the transmission system. The problem is formulated as a mixed integer nonlinear optimization problem. A generic penalty function method, which does not require any penalty coefficient, is employed for constraint handling. The formulation also checks for the feasibility of the optimal control variable setting from a voltage security point of view by using a voltage collapse proximity indicator. The algorithm is tested on standard IEEE 14, IEEE 30, and IEEE 118-Bus test systems. To show the effectiveness of proposed method the results are compared with Particle Swarm Optimization and a conventional optimization technique – Sequential Quadratic Programming.     

An effective cuckoo search algorithm for large-scale combined heat and power economic dispatch problem

Neural Computing and Applications - This paper develops an effective cuckoo search algorithm (ECSA) for searching optimal solutions for the problem of combined heat and power economic dispatch. The...     

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.     

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.

     

Combined heat and power economic dispatch by mesh adaptive direct search algorithm

The optimal utilization of multiple combined heat and power (CHP) systems is a complex problem. Therefore, efficient methods are required to solve it. In this paper, a recent optimization technique, namely mesh adaptive direct search (MADS) is implemented to solve the combined heat and power economic dispatch (CHPED) problem with bounded feasible operating region. Three test cases taken from the literature are used to evaluate the exploring ability of MADS. Latin hypercube sampling (LHS), particle swarm optimization (PSO) and design and analysis of computer experiments (DACE) surrogate algorithms are used as powerful SEARCH strategies in the MADS algorithm to improve its effectiveness. The numerical results demonstrate that the utilized MADS–LHS, MADS–PSO, MADS–DACE algorithms have acceptable performance when applied to the CHPED problems. The results obtained using the MADS–DACE algorithm are considerably better than or as well as the best known solutions reported previously in the literature. In addition to the superior performance, MADS–DACE provides significant savings of computational effort.     

Environmental economic dispatch in multi-area power system employing improved differential evolution with fuzzy selection

In a deregulated multi-area electrical power system the objective is to determine the most economical generation dispatch strategy that could satisfy the area load demands, the tie-line limits and other operating constraints. Usually, economic dispatch (ED) deals only with the cost minimization, but minimization of emission content has also become an equally important concern due to the mandatory requirement of pollution reduction for environmental protection. Environmental economic dispatch (EED) is a complex multi-objective optimization (MOO) problem with conflicting goals. Normally a fuzzy ranking is employed to rank the large number of Pareto solutions obtained after solving a MOO problem. But in this paper the preference of the decision maker (DM) is used to guide the search and to select the population for the next generation. An improved differential evolution (DE) method is proposed where the selection operation is modified to reduce the complexity of multi-attribute decision making with the help of a fuzzy framework. Solutions are assigned a fuzzy rank on the basis of their level of satisfaction for different objectives before the population selection and then the fuzzy rank is used to select and pass on better solutions to the next generation. A well distributed Pareto-front is obtained which presents a large number of alternate trade-off solutions for the power system operator. A momentum operation is also included to prevent stagnation and to create Pareto diversity. Studies are carried out on three test cases and results obtained are found to be better than some previous literature.     

Recurrent neural network for combined economic and emission dispatch

Recently, the combined economic and emission dispatch (CEED) problem, which aims to simultaneously decrease fuel cost and reduce environmental emissions of power systems, has been a widespread concern. To improve the utilization efficiency of primary energy, combined heat and power (CHP) units are likely to play an important role in the future. The goal of this study is to propose an approach to solve the CEED problems in a CHP system which consists of eight power generators (PGs), two CHP units and one heat only unit. Owing to the existence of power loss in power transmission line and the non-convex feasible region of CHP units, the proposed problem is a nonlinear, multi-constraints, non-convex multi-objectives (MO) optimization problem. To deal with it, a recurrent neural network (RNN) combined with a novel technique is developed. It means that the feasible region is separated into two convex regions by using two binary variables to search for different regions. In the frame of the neurodynamic optimization, existence and convergence of the dynamic model are analyzed. It shows that the convergence solution obtained by RNN is the optimal solution of CEED problem. Numerical simulation results show that the proposed algorithm can generate solutions efficiently.     

Chaotic differential evolution methods for dynamic economic dispatch with valve-point effects

The dynamic economic dispatch (DED), with the consideration of valve-point effects, is a complicated non-linear constrained optimization problem with non-smooth and non-convex characteristics. In this paper, three chaotic differential evolution (CDE) methods are proposed based on the Tent equation to solve DED problem with valve-point effects. In the proposed methods, chaotic sequences are applied to obtain the dynamic parameter settings in DE. Meanwhile, a chaotic local search (CLS) operation for solving DED problem is designed to help DE avoiding premature convergence effectively. Finally, in order to handle the complicated constraints with efficiency, new heuristic constraints handling methods and feasibility based selection strategy are embedded into the proposed CDE methods. The feasibility and effectiveness of the proposed CDE methods are demonstrated for two test systems. The simulation results reveal that, compared with DE and those other methods reported in literatures recently, the proposed CDE methods are capable of obtaining better quality solutions with higher efficiency.     

考虑阀点效应的电力系统经济分配算法

经济分配（ED）对于电力系统的节能至关重要,适当的分配方法可以为电厂节约巨额生产成本,然而阀点效应使得实际ED问题呈现出不光滑和非凸的特性,导致一些经典的优化算法和启发式算法无法在合理时间内发现最优解。提出一种新的改进教与学优化算法来求解计及阀点效应的经济分配问题,并采用一种新的修正策略取代罚函数法来处理约束条件。为了验证新算法的有效性和鲁棒性,选取典型的benchmark函数和ED实例进行仿真计算,结果表明与其他代表性算法相比,该方法求解精度高、收敛速度快,为计及阀点效应的经济分配问题求解提供了一条新途径。     

Combined heat and power economic dispatch problem solution by implementation of whale optimization method

Neural Computing and Applications - Combined heat and power economic dispatch (CHPED) is introduced as a difficult optimization problem, which provides optimal generation scheduling of heat and...     

融合均匀变异与高斯变异的蝙蝠优化算法

为提高蝙蝠算法的寻优精度和收敛速度,提出一种融合均匀变异和高斯变异的蝙蝠优化算法.算法引入变异开关函数,该函数使所有蝙蝠个体在任何时期都有概率发生变异,使种群保持较高的多样性和活跃性.同时在算法整个寻优过程中融入均匀变异和高斯变异,两种变异机制共同协作使算法首先快速定位到全局最优解区域,随后完成局部精确搜索.仿真结果表明,改进后的算法寻优性能显著提高,具有较快的收敛速度和较高的收敛精度.     

Synergic predator-prey optimization for economic thermal power dispatch problem

This paper introduces a synergic predator-prey optimization (SPPO) algorithm to solve economic load dispatch (ELD) problem for thermal units with practical aspects. The basic PPO model comprises prey and predator as essential components. SPPO uses collaborative decision for movement and direction of prey and maintains diversity in the swarm due to fear factor of predator, which acts as the baffled state of preys’ mind. In the SPPO, the decision making of prey is bifurcated into corroborative and impeded parts. It comprises four behaviors namely inertial, cognitive, collective swarm intelligence, and prey's individual and neighborhood concern of predator. The prey particle memorizes its best and not-best positions as experiences. In this research work, to improve the quality of prey swarm, which influence convergence rate, opposition based initialization is used. To verify robustness of proposed algorithm general benchmark problems and small, medium, and large power generation test power system are simulated. These test systems have non-linear behavior due to multi-fuel options and practical constraints. The constraints of prohibited operating zone and ramp rate limits of power generators’ are handled using heuristics. Newton–Raphson procedure is exploited to attain the transmission losses using load flow analysis. The outcomes of SPPO are compared with the results described in literature and are found satisfactory.     

Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems

Economic Load Dispatch (ELD) is an important and difficult optimization problem in power system planning. This article aims at addressing two practically important issues related to ELD optimization: (1) analyzing the ELD problem from the perspective of evolutionary optimization; (2) developing effective algorithms for ELD problems of large scale. The first issue is addressed by investigating the fitness landscape of ELD problems with the purpose of estimating the expected performance of different approaches. To address the second issue, a new algorithm named “Estimation of Distribution and Differential Evolution Cooperation” (ED-DE) is proposed, which is a serial hybrid of two effective evolutionary computation (EC) techniques: estimation of distribution and differential evolution. The advantages of ED-DE over the previous ELD optimization algorithms are experimentally testified on ELD problems with the number of generators scaling from 10 to 160. The best solution records of classical 13 and 40-generator ELD problems with valve points, and the best solution records of 10, 20, 40, 80 and 160-generator ELD problems with both valve points and multiple fuels are updated in this work. To further evaluate the efficiency and effectiveness of ED-DE, we also compare it with other state-of-the-art evolutionary algorithms (EAs) on typical function optimization tasks.     

Distributed fixed step-size algorithm for dynamic economic dispatch with power flow limits

In this study,a discrete-time distributed algorithm is proposed for solving the dynamic economic dispatch problem with active power flow limits and transmission...     

Simulated annealing algorithm for combined economic and emission power dispatch using max/max price penalty factor

A new recurrent neural model for crack growth process of aluminium alloy is developed in this work. It is shown that a recurrent neural network with the feedback loops at the output layer is constructed to model the dynamic relationship between the crack growth and cyclic stress excitations of aluminium alloy. The output feedback loops in the neural model play the role of capturing the fine changes of crack growth dynamics. The Extreme Learning Machine is then used to uniformly randomly assign the input weights in a proper range and globally optimize both the output weights and feedback parameters, to ensure that the dynamics of crack growth under variable-amplitude loading can be accurately modeled. The simulation results with the averaged experimental data of the 2024-T351 aluminium alloy show that the excellent modeling and prediction performance of the recurrent neural model can be achieved for fatigue crack growth of aluminium alloys.     

Modified neo-fuzzy neuron-based approach for economic and environmental optimal power dispatch

At the central energy management center in a power system, the real time controls continuously track the load changes and endeavor to match the total power demand with total generation in such a manner that the operating cost is minimized while all the operating constraints are satisfied. However, due to the strict government regulations on environmental protection, operation at minimum cost is no longer the only criterion for dispatching electrical power. The idea behind the environmentally constrained economic dispatch formulation is to estimate the optimal generation schedule of generating units in such a manner that fuel cost and harmful emission levels are both simultaneously minimized for a given load demand. Conventional optimization techniques become very time consuming and computationally extensive for such complex optimization tasks. These methods are hence not suitable for on-line use. Neural networks and fuzzy systems can be trained to generate accurate relations among variables in complex non-linear dynamical environment, as both are model-free estimators. The existing synergy between these two fields has been exploited in this paper for solving the economic and environmental dispatch problem on-line. A multi-output modified neo-fuzzy neuron (NFN), capable of real time training is proposed for economic and environmental power generation allocation.This model is found to achieve accurate results and the training is observed to be faster than other popular neural networks. The proposed method has been tested on medium-sized sample power systems with three and six generating units and found to be suitable for on-line combined environmental economic dispatch (CEED).     

电力系统经济负荷分配的族群优化方法

经济负荷分配（Economic Load Dispatch,ELD）是电力系统中一种重要的优化问题,它可归为一类高维、离散、非线性的多约束函数优化问题。针对这类问题,提出了一种基于线性截取策略的改进族群进化算法——EGEA/LT,并使用EGEA/LT对IEEE的3机、6机和15机3个仿真系统进行了优化实验,将实验结果与其他典型算法优化结果进行比较,说明了EGEA/LT是一种求解ELD问题的有效方法。     

Solving dynamic economic emission dispatch problem considering wind power by multi-objective differential evolution with ensemble of selection method

Natural Computing - Clean energy resources such as wind power are playing an important role in power generation recently. In this paper, a modified version of multi-objective differential evolution...     

An economic dispatch algorithm of combined cycle units

This paper presents a method to solve the economic dispatch (ED) problem for thermal unit systems involving combined cycle (CC) units. The ED problem finds the optimal generation of each unit in order to minimize the total generation cost while satisfying the total demand and generating-capacity constraints. A CC unit presents multiple configurations or states, each state having its own unique cost curve. Therefore, in performing ED, we need to be able to shift between these cost curves. Moreover, the cost curve is not convex for some of these states. Hence, ED becomes a non-convex optimization problem, which is difficult to solve by conventional methods. In this paper we present a new technique, developed to find the global solution, that is based on the calculation of the infimal convolution. The paper includes the results for a case test and we compare our solution with other techniques.