A new algorithm for on-line security constrained economic dispatch

A new approach, the constant reduced Hessian matrix (CRHM) algorithm for the on-line security constrained economic dispatch (OSED) problem, is presented in this paper. The proposed method, in which repeating the AC load flow program has been avoided, satisfies both load flow equations and security limits exactly. The computational speed and the excellent convergence of this algorithm are demonstrated by applying it to a sample system.     

基于启发式线性规划的大规模安全约束调度快速求解方法

提升大规模安全约束经济调度优化模型的求解性能是开展大电网跨省区电力电量全局优化平衡的前提与基础。首先分析问题的物理特性,通过并行计算求解不考虑机组爬坡约束的分时段约束松弛模型。基于对松弛解的分析获得可用于指导安全约束经济调度模型改进的有用信息,以约束剔除和约束增加的方式提出了基于启发式线性规划的大规模安全约束经济调度快速求解方法。将所提算法运用于新英格兰10机扩展系统和中国实际电网,验证了所提算法的正确性和有效性。     

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.     

基于实用化安全约束经济调度扩展建模策略

安全约束经济调度是提高电网运行可靠率,实现节能减排,提高调度计划精细化管理水平的有效技术手段。现有安全约束经济调度研究多集中在常见目标与约束建模以及优化算法等方面,较少考虑实际生产因素,因此计划结果执行率偏低,安全约束经济调度在实际生产中实用化困难。针对上述问题,针对计划编制的优化目标,“三公”调度、计划出力曲线形状以及基础数据区间处理等实际需求,提出了基于实用化的安全约束经济调度扩展模型。将所提的建模策略应用于多个生产实例,证明了所提模型在增强“三公”调度准确率、改善计划出力曲线形状以及提高计划结果执行率上有着较好的工程实用性。     

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.     

Solving non-convex economic dispatch problem with valve point effects using modified group search optimizer method

This paper presents a novel solution based on the group search optimizer (GSO) methodology in order to determine the feasible optimal solution of the economic dispatch (ED) problem considering valve loading effects. The basic disadvantage of the original GSO algorithm is the fact that it gives a near-optimal solution rather than an optimal one in a limited runtime period. In this paper, a new modified group search optimizer (MGSO) is presented for improving the scrounger and ranger operators of GSO. The proposed MGSO is applied on different test systems and compared with most of the recent methodologies. The results show the effectiveness of the proposed method and prove that MGSO can be applicable for solving the power system economic load dispatch problem, especially in large scale power systems.     

Evolutionary algorithm solution and KKT based optimality verification to multi-area economic dispatch

This paper is aimed at exploring the performance of the various evolutionary algorithms on multi-area economic dispatch (MAED) problems. The evolutionary algorithms such as the Real-coded Genetic Algorithm (RGA), Particle Swarm Optimization (PSO), Differential Evolution (DE) and Covariance Matrix Adapted Evolution Strategy (CMAES) are considered. To determine the efficiency and effectiveness of various EAs, they are applied to three test systems; including 4, 10 and 120 unit power systems are considered. The optimal results obtained using various EAs are compared with Nelder–Mead simplex (NMS) method and other relevant methods reported in the literature. To compare the performances of various EAs, statistical measures like best, mean, worst, standard deviation and mean computation time over 20 independent runs are taken. The simulation experiments reveal that CMAES algorithm performs better in terms of solution quality and consistency. Karush–Kuhn–Tucker (KKT) conditions are applied to the solutions obtained using EAs to verify optimality. It is found that the obtained results are satisfying the KKT conditions and confirm the optimality. Also, the effectiveness of KKT error based stopping criterion is demonstrated.     

安全约束经济调度中有功潮流调整方法

计算电网的计划潮流是安全约束经济调度的重要内容。针对计划潮流中外网等值粗糙、结果偏差较大的问题,提出了一种改进的安全约束经济调度中有功潮流调整方法。首先获取计划数据和网络模型,进行无网络约束计划编制,然后结合准稳态灵敏度、联络线自适应等值和有功平衡等方法计算计划潮流,如果潮流越限则增加网络安全约束重新编制计划。该方法简单易行,能提高计划潮流精度,为计划编制提供可信的潮流信息。通过实际工程算例测试表明,该方法能满足实用要求,具有良好的可靠性和实用性。     

基于PSO-BBO混合优化算法的动态经济调度问题

动态经济调度(Dynamic Economic Dispatch,DED)问题是电力系统运行与控制领域比较经典的多变量、非线性、强约束优化问题。为解决该问题,提出了将粒子群优化算法(Particle Swarm Optimization,PSO)和基本生物地理学优化算法(Biogeography-Based Optimization,BBO)相结合的改进生物地理学优化算法,并将该改进方法应用于一天24时段10机39节点标准算例。在考虑网损与不考虑网损两种情况下分别进行仿真分析,并将仿真结果与PSO和基本BBO算法以及参考文献中提出的六种智能算法进行对比,验证了该改进算法的有效性及在寻优能力上的提高。     

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.     

Solution to scalarized environmental economic power dispatch problem by using genetic algorithm

Nowadays, the widespread use of fossil based fuels in power generation units requires the consideration of the environmental pollution. Therefore, in this study, the solution of scalarized environmental economic power dispatch problem in which the environmental pollution has been taken into consideration has been analyzed by using genetic algorithm (GA). In order to turn the environmental economic power dispatch problem into the single objective optimization problem, the conic scalarization method (CSM) has been used. Also, weighted sum method (WSM) has been utilized in the scalarization of the same problem for comparison with CSM. The solution algorithm is tested for the electric power system of thermal units which has been solved by different methods in the literature. The best solution values that give minimum total fuel cost and minimum total emission values have been obtained (Pareto optimal values) for different weight values under electric constraints via CSM and WSM. The obtained Pareto optimal values for different scalarization methods have been compared with each other.     

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。     

Parallel micro genetic algorithm based on merit order loading solutions for constrained dynamic economic dispatch

This paper proposes a parallel micro genetic algorithm based on merit order loading solutions (PMGA-MOL) to solve constrained dynamic economic dispatch (DED) problems for combined cycle (CC) units with linear decreasing and decreasing staircase incremental cost (IC) functions. To minimize the synchronization overheads, the PMGA-MOL employs the load balancing and migration strategies among processors. This PMGA-MOL algorithm is implemented on the eight-processor scalable multicomputer implementation using low-cost equipment (SMILE) Beowulf cluster with a fast ethernet switch network on the generating unit system size in the range of 5–80 units over the entire dispatch periods. With different migration strategies, the proposed PMGA-MOL compromises the solution quality and speedup upper bounds for the best performance. PMGA-MOL is shown to be viable to the on-line implementation of constrained DED due to substantial generator fuel cost savings and high speedup upper bounds.     

Emission,reserve and economic load dispatch problem with non-smooth and non-convex cost functions using epsilon-multi-objective genetic algorithm variable

This paper addresses a novel method for the multi-objective economic load dispatch (ELD) problem. Power generation, spinning reserve costs and emission are considered in the objective function of the frequency ELD problem. The frequency deviation, minimum frequency limits and other practical constraints are also taken into account in this problem. It is a highly constrained multi-objective optimization problem that involves conflicting objectives with both equality and inequality constraints. In this paper, an elitist evolutionary multi-objective optimization algorithm based on the concept of ε-dominance, called ε-multi-objective genetic algorithm variable (εv-MOGA), is proposed to solve the frequency ELD problem. In this study, the performance of the proposed εv-MOGA algorithm is compared with the performance of other classic and intelligent algorithms. The proposed method is tested on 6, 10, 13 and 40 generating units, and the simulation results of four power systems demonstrate the advantages of the proposed method for reducing the cost function.     

A homogeneous linear programming algorithm for the securityconstrained economic dispatch problem

This paper presents a study of the simplified homogeneous and self-dual (SHSD) linear programming (LP) interior point algorithm applied to the security constrained economic dispatch (SCED) problem. Unlike other interior point SCED applications that consider only the N security problem, this paper considers both (N-1) and (N-2) network security conditions. An important feature of the optimizing interior point LP algorithm is that it can detect infeasibility of the SCED problem reliably. This feature is particularly important in SCED applications since line overloading following a contingency often results in an infeasible schedule. The proposed method is demonstrated on the IEEE 24 bus test system and a practical 175 bus network. A comparison is carried out with the predictor-corrector interior point algorithm for the SCED problem presented previously (see ibid., vol. 12, no.2, p.803-10, 1997)     

A clonal algorithm to solve economic load dispatch

This paper presents a novel optimization approach to constrained economic load dispatch (ELD) problem using artificial immune system (AIS). The approach utilizes the clonal selection principle and evolutionary approach wherein cloning of antibodies is performed followed by hypermutation. The proposed methodology easily takes care of transmission losses, dynamic operation constraints (ramp rate limits) and prohibited zones and also accounts for non-smoothness of cost function arising due to the use of multiple fuels. Simulations were performed over various systems with different number of generating units and comparisons are performed with other prevalent approaches. The findings affirmed the robustness, fast convergence and proficiency of proposed methodology over other existing techniques.     

A novel stochastic search method for the solution of economic dispatch problems with non-convex fuel cost functions

This paper develops a Novel Stochastic Search (NSS) method for the solution of economic dispatch problems with non-convex fuel cost functions. The NSS solution procedure consists of three steps, namely Direct Search (DS), Goal Neighborhood Approximation (GNA) and Marginal Cost Dispatch (MCD). The DS step identifies a set of feasible solutions in accordance with prescribed equality and inequality constraints. The GNA step processes those feasible solutions to identify an appropriate direction for searching the global optimal solution. Finally, in the MCD step, the marginal cost of each generating unit is regulated in order to establish the global optimal solution. The proposed NSS scheme is applied to solve three examples systems of increasing complexity. The results are compared to those obtained using the conventional Simulated Annealing (SA), Genetic Algorithm (GA), and Evolutionary Programming (EP) methods. The results demonstrate that the NSS method provides a fast, robust and highly effective scheme for the solution of economic dispatch.     

基于改进遗传算法的技术型虚拟发电厂最优化经济调度策略

提出了将技术型虚拟发电厂(technical virtual powerplant,TVPP)的技术性和商业型虚拟发电厂(commercial virtualpower plant,CVPP)的经济性结合起来的设想,即TVPP在满足向电网提供的电压控制条件下追求自身经济性最大化。建立基于IEEE-33节点配电网的TVPP经济调度优化模型:以TVPP的最大经济利润和网络节点电压偏差值最小为目标函数,以分布式电源自身限制条件、功率平衡约束和网络节点电压约束等为约束条件;通过改进遗传算法对上述优化模型进行仿真求解,得到了技术型虚拟发电厂在向配电网提供网络节点电压控制服务下的最优化经济调度策略,仿真结果验证了该最优化调度策略的可行性。     

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.     

基于机会约束高斯混合模型的含光热电站热电联供型微网鲁棒经济调度

为了提升不确定性环境中含光热电站热电联供型微网(CSP-CHPMG)优化调度的鲁棒性,基于机会约束高斯混合模型构造风电功率预测误差和负荷预测误差的不确定性集合,以实现对调度方案鲁棒性的准确描述;将鲁棒性作为协同优化目标,并计及电能需求响应构建CSP-CHPMG鲁棒经济多目标优化调度模型,以保障调度方案的鲁棒性和经济性,...