Artificial immune system for dynamic economic dispatch

Dynamic economic dispatch determines the optimal scheduling of online generator outputs with predicted load demands over a certain period of time taking into consideration the ramp rate limits of the generators. This paper proposes artificial immune system based on the clonal selection principle for solving dynamic economic dispatch problem. This approach implements adaptive cloning, hyper-mutation, aging operator and tournament selection. Numerical results of a ten-unit system with nonsmooth fuel cost function have been presented to validate the performance of the proposed algorithm. The results obtained from the proposed algorithm are compared with those obtained from particle swarm optimization and evolutionary programming. From numerical results, it is found that the proposed artificial immune system based approach is able to provide better solution than particle swarm optimization and evolutionary programming in terms of minimum cost and computation time.     

Enhanced cross-entropy method for dynamic economic dispatch with valve-point effects

This paper proposes an enhanced cross-entropy (ECE) method to solve dynamic economic dispatch (DED) problem with valve-point effects. The cross-entropy (CE) method, originated from an adaptive variance minimization algorithm for estimating probabilities of rare events, is a generic approach to combinatorial and multi-extremal optimization. Exploration capability of CE algorithm is enhanced in this paper by using chaotic sequence and the resultant ECE is applied to DED with valve-point effects. The performance of the proposed ECE method is rigorously tested for optimality, convergence, robustness and computational efficiency on a 10-unit test system. Additional test cases with different load patterns and increased number of generators are also solved by ECE. Numerical results show that the proposed ECE approach finds high-quality solutions reliably with faster convergence. It outperforms CE and all the previous approaches.     

A new rooted tree optimization algorithm for economic dispatch with valve-point effect

This work proposes a new optimization method called root tree optimization algorithm (RTO). The robustness and efficiency of the proposed RTO algorithm is validated on a 23 standard benchmark nonlinear functions and compared with well-known methods by addressing the same problem. Simulation results show effectiveness of the proposed RTO algorithm in term of solution quality and convergence characteristics. In order to evaluate the effectiveness of the proposed method, 3-unit, 30 Bus IEEE, 13-unit and 15-units are used as case studies with incremental fuel cost functions. The constraints include ramp rate limits, prohibited operating zones and the valve point effect. These constraints make the economic dispatch (ED) problem a non-convex minimization problem with constraints. Simulation results obtained by the proposed algorithm are compared with the results obtained using other methods available in the literature. Based on the numerical results, the proposed RTO algorithm is able to provide better solutions than other reported techniques in terms of fuel cost and robustness.     

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.     

计及阀点效应负荷经济分配的杂交粒子群算法

提出了一种用于求解复杂的非凸、非线性具有阀点效应的火电有功负荷经济分配问题的杂交粒子群算法（HPSO）。HPSO通过粒子追随自己找到的最优解和整个群的最优解来完成优化,并在此基础上将遗传算法的杂交思想引入到PSO算法当中,使其避免局部最优。算例的仿真结果表明：本文的算法有效、可行,可望应用于更广泛的优化问题。     

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.     

Efficient hybrid optimization approach for emission constrained economic dispatch with nonsmooth cost curves

Power plants usually operate on the strategy of economic dispatch (ED) regardless of emissions produced. Environmental considerations have become one of the major management concerns. Under these circumstances, the alternative strategy of environmental/economic dispatch (EED) is becoming more and more desirable for not only resulting in great economical benefit, but also reducing the pollutants emission.Based on the literature survey, few attempts have been made at considering valve-point effects for the realistic environmental/economic dispatch (EED) problem. This paper proposes a new efficient hybrid differential evolution algorithm with harmony search (DE–HS) to solve the multiobjective environmental/economic dispatch (EED) problems that feature nonsmooth cost curves. The proposed approach combines in the most effective way the properties of differential evolution (DE) and harmony search (HS) algorithms. To enhance the local search capability of the original DE method, the fresh individual generation mechanism of the HS is utilized.Numerical results for three case studies have been presented to illustrate the performance and applicability of the proposed hybrid method. The comparative results with some of the most recently published methods confirm the effectiveness of the proposed strategy to find accurate and feasible optimal solutions for practical EED problems.     

A new hybrid approach for the solution of nonconvex economic dispatch problem with valve-point effects

Economic dispatch (ED) generally formulated as convex problem using optimization techniques by approximating generator input/output characteristic curves of monotonically increasing nature results in an inaccurate dispatch. The genetic algorithm has previously been used for the solution of problem for economic dispatch but takes longer time to converge to near optimal results. The hybrid approach is one of the methodologies used to fine tune the near optimal results produced by GA. This paper proposes new hybrid approach to solve the ED problem by using the valve-point effect. The approach we propose combines the genetic algorithm (GA) with active power optimization (APO) based on the Newton's second order approach (NSO). The genetic algorithm acts as a global optimizer giving near optimal generation schedule, which becomes the input for generation buses in APO algorithm. This algorithm acting as local search technique dispatching the generated active power of units for minimization of cost and gives optimum generation schedule. Three machines 6-bus, IEEE 5-machines 14-bus, and IEEE 6-mchines 30-bus systems have been tested for validation of our approach. Results of the proposed scheme compared with results obtained from GA alone give significant improvements in the generation cost showing the promise of the proposed approach.     

Quantum genetic algorithm for dynamic economic dispatch with valve-point effects and including wind power system

An optimization algorithm is proposed in this paper to solve the problem of the economic dispatch that includes wind power generation using quantum genetic algorithm (QGA). In additional to the detail introduction for models of general economic dispatch as well as their associated constraints, the effect of wind power generation is also included in this paper. On the other hand, the use of quantum genetic algorithms to solve the process of economic dispatch is also discussed and real scenarios are used for simulation tests later on. After comparing the algorithm used in this paper with several other algorithms commonly used to solve optimization problems, the results show that the algorithm used in this paper is able to find the optimal solution most quickly and accurately (i.e. to obtain the minimum cost for power generation in the shortest time). At the end, the impact to the total cost saving for the power generation after adding (or not adding) wind power generation is also discussed. The actual operating results prove that the algorithm proposed in this paper is economical and practical as well as superior. They are quite valuable for further research.     

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.     

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.     

AGC机组调配经济性的改进免疫算法研究

对于电力市场的买卖双方,成交电量及价格直接关系到厂网的经济效益。采用考虑机组调节容量和调节速度约束条件的机组数学模型,提出了一种解决电力系统AGC（自动发电控制）机组调配问题的改进免疫算法。采用启发式方法产生初始解,对参调机组与参调容量进行双层优化,使优化调度问题的收敛速度和效率有了显著的提高。通过实际系统的算例分析以及与常用算法的效果比较,验证了本算法在优化机组调配经济性方面应用的优越性及有效性。     

Combined heat and power economic dispatch using opposition-based group search optimization

This paper presents opposition-based group search optimization to solve non-smooth non-convex combined heat and power economic dispatch problem. Valve-point loading and prohibited operating zones of conventional thermal generators are taken into account. Group search optimization inspired by the animal searching behavior is a biologically realistic algorithm. Opposition-based group search optimization has been used here to improve the effectiveness and quality of the solution. The proposed opposition-based group search optimization employs opposition-based learning for population initialization and also for iteration wise update operation. The effectiveness of the proposed method has been verified on four test systems. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed opposition-based group search optimization based approach is able to provide better solution.     

A novel modified hybrid PSOGSA based on fuzzy logic for non-convex economic dispatch problem with valve-point effect

Gravitational Search Algorithm (GSA) is a novel stochastic optimization method inspired by the law of gravity and interaction between masses. This paper proposes a novel modified hybrid Particle Swarm Optimization (PSO) and GSA based on fuzzy logic (FL) to control ability to search for the global optimum and increase the performance of the hybrid PSOGSA. In order to test the performance of the modified hybrid PSOGSA based on FL (FPSOGSA), it has been applied to solve the well-known 23 benchmark test functions. In order to evaluate the efficiency and performance of the proposed approach, standard power systems including IEEE 5-machines 14-bus, IEEE 6-machines 30-bus, 13 and 40 unit test systems are used. These are non-convex economic dispatch problems including the valve-point effect and are computed with and without the losses. The results obtained from the proposed FPSOGSA approach are compared with those of the other heuristic techniques in the literature. The results of the comparison demonstrate that the proposed approach can converge to the near optimal solution and improve the performance of the standard hybrid PSOGSA approach.     

Application of pattern search method to power system security constrained economic dispatch with non-smooth cost function

Direct search methods are evolutionary algorithms used to solve 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 paper presents a new approach based on a constrained pattern search algorithm to solve a security constrained power system economic dispatch problem (SCED) with non-smooth cost function. Operation of power systems demands a high degree of security to keep the system satisfactorily operating when subjected to disturbances, while and at the same time it is required to pay attention to the economic aspects. Pattern recognition technique is used first to assess dynamic security. Linear classifiers that determine the stability of electric power system are presented and added to other system stability and operational constraints. The problem is formulated as a constrained optimization problem in a way that insures a secure-economic system operation. Pattern search method is then applied to solve the constrained optimization formulation. In particular, the method is tested using three different test systems. Simulation results of the proposed approach are compared with those reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving security constrained power system economic dispatch problem (SCED). In addition, valve-point effect loading and total system losses are considered to further investigate the potential of the PS technique. Based on the results, it can be concluded that the PS has demonstrated ability in handling highly nonlinear discontinuous non-smooth cost function of the SCED.     

Feasible solution for dynamic economic load dispatch using feasible operation region

High penetration of renewable energy in the future power system will pose a big problem to the load dispatch operation. The large disturbance and high forecast error must be considered when scheduling a limited number of controllable generators to follow rapid change in load. This paper proposes a dynamic economic load dispatch (DELD) problem approach based on the concept of a feasible operation region (FOR). FOR is defined as the region that committed generators may operate in to match the load profile without violating the ramp‐rate constraints. The DELD problem is solved in two stages. In the first stage, FOR of each generator is computed using recent real‐time forecasted load as well as renewable energy generation. In the second stage, a generation schedule is determined by solving the DELD problem interval by interval while considering ramp‐rate constraints and FOR constraints. The method can gives feasible solution for feasible load and specify the amount of compensation required for feasible solution for infeasible load. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

基于电网分区和辅助问题原理的电力系统多区域有功负荷经济调度

随着电网规模的扩大,电网计算优化问题中计算时间长、收敛速度慢等问题变得严重。针对此问题,该文利用基于电网分区和辅助问题原理APP(Auxiliary Prob lem Princ ip le)的分布式并行优化模型来解决多区域有功负荷的经济调度,并且把各个区域内的虚拟发电机看成真实发电机,推导出其耗量特性曲线。仿真结果表明,本方法具有较强的收敛性和快速性。     

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。     

改进的混合蛙跳算法性能分析及其在电力系统经济调度中的应用

针对基本混合蛙跳算法收敛速度慢,优化精度低的问题,提出了改进的混合蛙跳算法:通过引入自适应因子,保持了算法开发与探索的平衡,维持了种群的多样性,提高了个体向局部最优或全局最优个体学习的能力,加快了算法的收敛速度。通过对4个测试函数和电力系统中经济调度问题进行优化实验,并与基本混合蛙跳算法和相关文献中的改进算法进行比较,实验结果表明所提出的改进算法取得了更加理想的运算结果,具有更好的优化性能。     

电力系统经济负荷分配的量子粒子群算法

本文首次将量子粒子群算法用于电力系统经济负荷分配中。该算法是以粒子群中粒子的收敛特性为基础,依据量子物理理论提出的,改变了传统粒子群算法的搜索策略,可使粒子在整个可行解空间中搜索寻求全局最优解。同时该算法的进化方程中不需要速度向量,而且进化方程的形式更简单,参数较少且容易控制。对两个算例进行仿真测试,证实该算法可有效解决经济负荷分配问题;性能对比显示,该算法求得的解优于已有的改进粒子群算法及其它优化算法所求得的解。本文为量子粒子群算法用于经济负荷分配的实用化研究奠定了必要的理论基础。