Effective transmission constrained economic dispatch for production costing

In this paper, an effective Schur complement method is presented to solve transmission‐constrained dispatch (TCD) for Monte Carlo production costing. Several techniques for improving TCD performance are also proposed by taking the advantages of TCD special problem structures. Numerical testing on a real‐life large‐scale power system is presented to illustrate the performance of these proposed methodologies. Copyright © 2015 John Wiley & Sons, Ltd.     

含多种分布式电源的微电网经济调度研究

微电网的优化调度是一个新的具有重要社会和经济效益的复杂问题。基于实际风光资源、负荷和微电网运行成本数据,将用户效益、环境保护以及社会效益量化为运行及维护成本、未满足负荷、污染气体排放量、容量短缺等指标,采用模糊评价函数将多目标转化为单目标,提出了针对该微网的短期经济优化调度模型。选取一年中的典型情况为算例进行经济运行分析,并采用小生境遗传算法进行求解,得出了在各典型情况下各微电源的最优出力和最佳电能交易计划,验证了所提调度策略的正确性与有效性。     

Equal embedded algorithm for economic load dispatch problem with transmission losses

This paper presents equal embedded algorithm (EEA) to solve the economic dispatch (ED) problem with quadratic and cubic fuel cost functions and transmission losses. The proposed algorithm involves selection of lambda values, then the expressions of output powers of generators are derived in terms of lambda by interpolation and finally optimal value of lambda is evaluated from the power balance equation by Muller method. The proposed method is implemented and tested by considering 3, 15 and 26 generators to solve the ED problem. Simulation results such as quality of solution, convergence characteristic and computation time of the proposed method are compared with some existing methods like genetic algorithm (GA), particle swarm optimization (PSO) and Lambda iterative method. It is observed from different case studies that the proposed EEA algorithm provides the qualitative solution with less computational time irrespective of the size of the system.     

贵州节能发电调度经济补偿研究

节能发电调度模式下，高能耗的中小型发电企业必然在利用小时数上低于低能耗的大型发电企业。讨论相关的经济补偿办法，确保高能耗中小型发电企业能维持基本的运转，保证电网具有合理的备用容量以及电网安全稳定运行。     

Robust economic dispatch considering automatic generation control with affine recourse process

A robust economic dispatch (ED) considering automatic generation control (AGC) with affine recourse process is proposed in this paper. The approach co-optimizes the base points and participation factors of the AGC units using preemptive goal programming and robust optimization while considering the uncertain nodal power injections and the network constraints. The proposed approach is realized by two steps. The aim of the first step is to maximize the system effective acceptable disturbance range (EADR) while minimize the generation costs and reserve costs with respect to the obtained EADR in the second step. The novelty of the approach is as follows: (a) The security of the power system is optimized by maximizing the system EADR. The approach can obtain a solution which can cover the disturbance as much as possible even when the system does not have enough adjustable capacity to cover it all. The obtained nodal EADR can quantitatively represent the anti-disturbance capability of a node. (b) The economics of the system is significantly improved by minimizing the generation costs and reserve costs while the constraint of EADR requirement is respected. (c) The conservative level of the solution can be tuned according to the user’s requirements. A simplified one-step linear model is also deduced. The effectiveness and validity of the proposed approach are demonstrated by a 6-bus system, the IEEE 118-bus system, and a real 445-bus system.     

Optimal dynamic economic dispatch of generation: A review

This paper presents a review of the research of the optimal power dynamic dispatch problem. The dynamic dispatch problem differs from the static economic dispatch problem by incorporating generator ramp rate constraints. There are two different formulations of this problem in the literature. The first formulation is the optimal control dynamic dispatch (OCDD) where the power system generation has been modeled as a control system and optimization is done in the optimal control setting with respect to the ramp rates as input variables. The second one is a later formulation known as the dynamic economic dispatch (DED) where optimization is done with respect to the dispatchable powers of the committed generation units. In this paper we first outline the two formulations, then present an overview on the mathematical optimization methods, Artificial Intelligence (AI) techniques and hybrid methods used to solve the problem incorporating extended and complex objective functions or constraints. The DED problem in deregulated electricity markets is also reported.     

A hierarchical system for economic dispatch with environmentalconstraints

This paper presents a new hierarchical power dispatch system which uses a combination of the offline and the online subsystems to both minimize the cost and reduce the SO₂ emission. A hierarchical structure is introduced in the offline subsystem which enables the subsystem to generate a coarse-to-fine guideline for balancing the cost and the emission. The online dispatch is computed according to the guideline provided by the offline system. The dispatch is fed back to update the offline computation layer by layer. In this way, the offline guideline can always be adapted to the current situation, and the overall dispatch tends to be optimal for a whole year period. The system is tested by using the data from the Cincinnati Gas and Electric Company     

Dynamic optimal economic dispatch under system availability constraints and transmission losses

In this paper we have developed a dynamic optimal economic dispatch policy on the basis of a stochastic availability model and a piece-wise constant incremental fuel cost model. Using these models the optimal economic dispatch under the system availability constraints and transmission losses is formulated as a dynamic nonlinear optimization problem. The problem is solved by an algorithm recently developed by the authors (Electr. Power Syst. Res., 9 (1985) 11–27). In order to illustrate the effectiveness of the proposed method, an example is presented with detailed numerical results.     

Corrective economic dispatch in a microgrid

In this paper, a corrective economic dispatch problem formulation for distributed generators in a microgrid is presented, which considers the transition from grid‐connected operation to islanded operation. Various constraints related to the operation of a microgrid are modeled, such as spinning reserve requirement for the variation of load demand and the output of intermittent sources, the flow limits between the control areas, and ramping limits of distributed generators. The resulting problem is then solved by an interior point method. Numerical tests based on a three‐area ten‐unit microgrid system show the effects of these constraints on the generation cost. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Economic dispatch with generation contingency constraints

This paper presents a new model of the generation contingency constrained economic dispatch problem and proposes a method for its solution. The operating policy of Northern Ireland Electricity was the basis for the formulation, and software was implemented to support it. Since the Northern Ireland Electricity power system operates in relative isolation, the operating security criteria are rather stringent. In particular, it is required that loss of generation of any generating unit in the system must be covered by fast, 3 or 30 second generation reserves on other units in the system. The fast response unit reserve capabilities are represented by concave curves. The solution method is based a nonlinear version of Dantzig-Wolfe decomposition principle. Numerical results are presented     

Reserve constrained economic dispatch with prohibited operatingzones

A method is described for solving the reserve constrained economic dispatch problem when some of the online generating units have prohibited operating zone(s). For a unit with prohibited zone(s), the zone(s) divide the operating region between the minimum generation limit (Pmin) and the maximum generation limit (Pmax) into disjoint convex subregions. These disjoint subregions form a nonconvex decisions space and the associated economic dispatch problem is thus a nonconvex optimization problem. As a result, the conventional Lagrangian relaxation (LR) approach (e.g. the λ-δ iterative approach) cannot be applied directly. The method proposed decomposes the nonconvex decision space into a small number of subsets such that each of the associated dispatch problems is either infeasible or one that can be directly solved via the conventional LR approach. Based on the decomposition, the optimal solution is the least costly one among all the feasible solutions of the associated dispatch problems. Examples are also given to illustrate the proposed method     

An improved tabu search for economic dispatch with multiple minima

This paper develops an improved tabu search algorithm (ITS) for economic dispatch (ED) with noncontinuous and nonsmooth cost functions. ITS employs a flexible memory system to avoid the entrapment in a local minimum and developed the ideal of "distance" to the fitness to accelerate optimization. The new approach extends simple tabu search algorithm (STS) to real valued optimization problem and applies parallelism to weaken the dependence of the convergence rate of modified tabu search algorithm (NITS) on the initial condition. Effectiveness of the method was compared with many conventional methods. Results show that the proposed algorithm can provide accurate solutions with reasonable performance and has a great potential for other applications in the power system     

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。     

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.     

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.     

提高单回链式电网及有源终端变供电可靠性的一种方法

单回链式电网技术有源终端变化供电系统由于其接线特点可靠性低,但是如今依然在许多经济不发达地区被广泛应用.提出一种通过改进线路保护装置中重合闸功能的方法来提高该类型电网的供电可靠性.该方法对提高无人值守变电站的事故处理效率也有极大的帮助.此方法已经在三明地区投入运行,效果良好.供调度运行及保护整定人员参考.     

Atavistic genetic algorithm for economic dispatch with valve point effect

This paper presents a new approach on using genetic algorithms for economic dispatch problem for valve point discontinuities. The proposed approach in this paper on genetic algorithms improves the performance to solve economic dispatch problem through combination of penalty function with death penalty, generation-apart elitism, atavism and heuristic crossover. Numerical results on a test system consisting of 13 thermal units show that the proposed approach has an ability to find the better solutions than the conventional genetic algorithm.     

Differential evolution for economic load dispatch problems

In this work, differential evolution (DE) algorithm was studied for solving economic load dispatch (ELD) problems in power systems. DE has proven to be effective in solving many real world constrained optimization problems in different domains. ELD problems are complex and nonlinear in nature with equality and inequality constraints and here special measures were taken to satisfy those. Five ELD problems of different characteristics were used to investigate the effectiveness of the proposal. Comparing with the other existing techniques, the current proposal was found better than, or at least comparable to, them considering the quality of the solution obtained.     

Hierarchical economic dispatch for multi-area power systems

In a multi-area power system, power exchange through tie lines such that the overall cost of the system operation is a minimum is a major economic dispatch problem. In this paper, techniques and methods are presented for solving the economic dispatch problem of radially interconnected power systems. The proposed method, based on a multi-area approach, uses an hierarchical control concept to improve the computation efficiency and accuracy; it has certain advantages over the conventional single-area approach. Theoretical formulations are derived and discussed from a simple power transfer concept. An efficient algorithm is organized. Numerical examples have been tested for a fictitious three-area system. The simulation results strongly support the proposed method with real-time application capability.