大型水火电力系统短期最优机组启停调度

给出了描述大型水火电力系统短期机组启停调度的数学模型,应用大系统分散控制理论将这一复杂问题分解为3个简单的子问题,分别用一维动态规划和网络规划法术解,最后,通过拉格朗日乘子协调控制得出最优可行解。该算法也可同时考虑火电的最优启停机计划和水电的优化调度。     

Dual programming methods for large-scale thermal generationscheduling

The problem of thermal generation scheduling is considered in the framework of the short-term hydro-thermal coordination problem. Dual programming methods are applied to the large-scale problem deriving from a fine subdivision of the daily optimization horizon for networks with hundreds of thermal units. The starting point for the dual approach is obtained from the solution of a thermal scheduling problem with discarded generation ramp-rate constraints. The relaxed daily scheduling decouples into as many smaller dispatch problems as the number of subintervals. Two dual programming methods are implemented: the former is the dual active set algorithm by Goldfarb and Idnani while the latter is based on the application of continuation method techniques. These approaches are extensively tested with reference to both a small sample system and to the daily thermal generation scheduling of the Italian (ENEL) system (over 100 thermal units and 96 quarter hour subintervals). Incorporating the dual programming approach within the ENEL hydro-thermal coordination procedure is also considered     

考虑检修计划的中长期水火电联合优化调度方法

在中长期水火发电调度中考虑检修计划的影响是目前中长期水火发电调度面临的难题。利用现代整数代数建模技术,建立发电计划和检修计划协调优化的多场景调度模型。在该模型中,鉴于设备检修计划的连续性,在预测场景树的基础上,将场景节点划分成不同的场景,通过节点和场景关联矩阵,实现多场景下设备检修模型的构建。同时,鉴于中长期调度计划中发电计划和检修计划对时段间隔要求的不同,分别设置电量相关节点和电力相关节点,实现中长期发电计划和检修计划的协调。上述模型是一个大规模混合整数线性规划(mixed integer linear programming,MILP)问题,采用商用MILP求解器进行求解。大规模实际水火电系统的实例分析结果表明,所提模型和方法是可行、有效的。     

Coordination of Midterm Outage Scheduling With Short-Term Security-Constrained Unit Commitment

The proposed model solves the coordinated generation and transmission maintenance scheduling with security-constrained unit commitment (SCUC) over the scheduling horizon of weeks to months. The model applies the Lagrangian relaxation technique to decompose the optimization problem into subproblems for generation maintenance scheduling, transmission maintenance scheduling, and short-term SCUC. The decomposition and cooperation strategy is applied to the first two subproblems for the scheduling of generation and transmission maintenance. The SCUC solution is based on the mixed integer programming (MIP) technique. The optimal hourly results for maintenance scheduling, generation unit commitment, and transmission flows are obtained using a chronological load curve. Effective strategies are applied for accelerating the convergence of the hourly solution. The numerical examples demonstrate the effectiveness of the proposed model.     

考虑梯级耦合的水火电检修计划与机组组合协同优化

为避免传统的非协同优化模式下水火电系统检修计划和机组组合方案之间可能存在的冲突,本文以最小化系统总成本和检修计划调整成本为目标,考虑梯级水电耦合特性,建立水火电检修计划与机组组合协同的优化模型,并将其转换为混合整数线性规划模型。提出采用目标标度集合方法加速求解,分两个阶段对该模型进行求解。第一阶段：标度目标函数中整数变量的系数,探测可能为0的整数变量;第二阶段,确定取0值的整数变量并将其固定,求解简化的混合整数线性规划模型。最后,以6机水火电系统和某实际省级86机水火电系统为测试系统,验证了本文所提模型与非协同优化相比能够得到更经济合理的检修计划和机组组合方案,所采用的目标标度集合方法能够有效提高求解速度。     

基于进化捕食策略法的风-水-火电短期负荷分配优化

考虑负荷与风电的不确定性,建立了基于机会约束规划的风-水-火电短期负荷分配优化模型。为了更好地权衡局部搜索与全局搜索性能,应用进化捕食策略法求解水-火电短期优化调度与风-水-火电短期负荷分配问题。算例结果表明,与其他算法相比,进化捕食策略法在水-火电短期优化调度中能够搜索到更优的解,同时基于机会约束规划的优化方法为系统旋转备用容量的合理设置提供了依据。     

Short-term resource scheduling with ramp constraints [powergeneration scheduling]

This paper describes a Lagrangian relaxation-based method to solve the short-term resource scheduling (STRS) problem with ramp constraints. Instead of discretizing the generation levels, the ramp rate constraints are relaxed with the system demand constraints using Lagrange multipliers. Three kinds of ramp constraints, startup, operating and shutdown ramp constraints are considered. The proposed method has been applied to solve the hydro-thermal generation scheduling problem at PG&E. An example alone with numerical results is also presented     

基于可信性理论的水火电机组检修计划

水电机组同时存在着水电电量模糊性和机组强迫停运的随机性这两类不同的不确定性,因此水火电机组检修计划本质上是一个具有随机模糊双重不确定性的混合整数优化问题。但是,因概率论与模糊论在基础数学领域内是相互独立的理论体系,传统的机组检修计划只能对随机性或模糊性这两类不确定性中的一类进行建模,然后采用随机规划或模规划来求解。可信性理论是2004年基础数学领域完成的数学分支,它给出了基于测度论的模糊论公理化体系,并提糊供了随机性与模糊性综合评估的严格数学基础。文中基于可信性理论,建立了水、火电机组检修计划的混合整数随机模糊双重不确定性优化模型(原始模型),并在这一个模型中同时考虑随机性与模糊性2种不确定性。利用Benders分解法,将原始模型分解为多目标整数规划(主问题)和随机模糊规划(运行子问题)2大问题进行分散协调,利用改进Balas算法求解主问题,综合利用可信性理论与半不变量法求解运行子问题。对吉林电力系统中的95台机组安排了全年的检修计划,结果表明:该算法和软件在实际系统中应用是可行、有效的。     

A probabilistic approach to generation maintenance scheduler with network constraints

Most generating unit maintenance scheduling packages consider the preventive maintenance schedule of generating units over a one or two year operational planning period in order to minimize the total operating cost while satisfying system energy requirements and maintenance constraints. In a global maintenance scheduling problem, we propose to consider network constraints and generating unit outages in generation maintenance scheduling. The inclusion of network constraints in generating unit maintenance will increase the complexity of the problem, so we decompose the global generator scheduling problem into a master problem and sub-problems using Benders decomposition. At the first stage, a master problem is solved to determine a solution for maintenance schedule decision variables. In the second stage, sub-problems are solved to minimize operating costs while satisfying network constraints and generators’ forced outages. Benders cuts based on the solution of the sub-problem are introduced to the master problem for improving the existing solution. The iterative procedure continues until an optimal or near optimal solution is found.     

基于随机规划的含风电场的电力系统节能优化调度策略

含风电场的多电源电力系统优化调度是一个新的具有重要经济和社会效益的复杂非线性问题.针对传统的水火经济调度模型以及新兴的火风互补经济调度模型,提出了基于随机规划的水、火、风混合系统短期优化调度模型,利用机会约束描述目标函数和约束条件,并给出不同置信水平下的调度方案.同时考虑水电站耗水量最小、火电煤耗量最小以及氮氧化物排放...     

Simulation of Optimal Medium-Term Hydro-Thermal System Operation by Grid Computing

This paper presents a model for the simulation of the optimal medium-term operation of a hydrothermal system. System stochastic parameters are modeled by Monte Carlo scenarios, which are solved on distributed processors. For each scenario a yearly hydro-thermal scheduling (HTS) problem with hourly time resolution is formulated and solved as a large mixed integer linear program (MILP). HTS modeling includes unit commitment, start-up costs and minimum up/down time constraints. The model is applied to the Greek Power System, comprising 29 thermal units and 13 hydroplants; 100 simulation scenarios are generated and solved on 18 distributed processors. Test results include both medium-term objectives, such as reservoir water management, and short-term decisions such thermal unit start-up decisions.      

Clonal selection algorithm for power generators maintenance scheduling

This paper introduces a technique based on the one of the artificial immune system (AIS) technique known as the clonal selection algorithm (CSA) to obtain the optimal maintenance schedule outage of generating units. Based on a weekly load profile, the proposed technique provides the optimal maintenance window and calculates the optimal output power from each generator over a one year horizon. The maintenance scheduling problem is decoupled into two interrelated sub-problems namely, the maintenance scheduling and the power system sub-problems. The CSA is used to solve the maintenance scheduling subproblem to obtain the optimal maintenance outage of each unit. Based on the schedule generated by the CSA, the economic dispatch iterative lambda technique is used to find the optimal output power from each unit. Due to the search nature of the CSA, infeasible solutions may be introduced during the solution process. Therefore, a local search technique is used to watch the feasibility of the new solutions. The paper reports test results of the proposed algorithm to find the optimal maintenance schedule of the IEEE 30 bus system with 6 generating units and the IEEE 118 bus system with 33 generating units. Results are compared against the results obtained by complementary decision variables structure (CDV) and the evolutionary programming based techniques. Results are encouraging and indicate the viability of the proposed CSA technique.     

Power generation scheduling for multi-area hydro-thermal systemswith tie line constraints, cascaded reservoirs and uncertain data

The authors propose an approach to the short-term generation scheduling of hydro-thermal power systems (GSHT). The objective of GSHT is to minimize the total operation cost of thermal units over the scheduling time horizon. To solve the problem within a reasonable time, the problem is decomposed into thermal and hydro subproblems. The coordinator between these subproblems is the system Lagrange multiplier. For the thermal subproblem, in a multi-area power pool, it is necessary to coordinate the area generations for reducing the operation cost without violating tie limits. A probabilistic method is employed in considering load forecasting errors and forced outages of generating units to satisfy system reliability requirements. For the hydro subsystem, network flow concepts are adopted to coordinate water use over the entire study time span and the reduced gradient method is used to overcome the linear characteristic of the network flow method to obtain the optimal solution. Three case studies for the proposed method are presented     

Short-term hydrothermal generation scheduling model using a genetic algorithm

A new model to deal with the short-term generation scheduling problem for hydrothermal systems is proposed. Using genetic algorithms (GAs), the model handles simultaneously the subproblems of short-term hydrothermal coordination, unit commitment, and economic load dispatch. Considering a scheduling horizon period of a week, hourly generation schedules are obtained for each of both hydro and thermal units. Future cost curves of hydro generation, obtained from long and mid-term models, have been used to optimize the amount of hydro energy to be used during the week. In the genetic algorithm (GA) implementation, a new technique to represent candidate solutions is introduced, and a set of expert operators has been incorporated to improve the behavior of the algorithm. Results for a real system are presented and discussed.     

Experiences with mixed integer linear programming based approacheson short-term hydro scheduling

This paper describes experiences with mixed integer linear programming (MILP) based approaches on the short-term hydro scheduling (STHS) function. The STHS is used to determine the optimal or near-optimal schedules for the dispatchable hydro units in a hydro-dominant system for a user-definable study period at each time step while respecting all system and hydraulic constraints. The problem can be modeled in detail for a hydro system that contains both conventional and pumped-storage units. Discrete and dynamic constraints such as unit startup/shutdown and minimum-up/minimum-down time limits are also included in the model for hydro unit commitment (HUC). The STHS problem is solved with a state-of-the-art package which includes an algebraic modeling language and a MILP solver. The usefulness of the proposed solution algorithm is illustrated by testing the problem with actual hydraulic system data. Numerical experiences show that the solution technique is computationally efficient, simple, and suitable for decision support of short-term hydro operations planning. In addition, the proposed approaches can be easily extended for scheduling applications in a deregulated environment     

Short-term operation scheduling of a hydropower plant in the day-ahead electricity market

This paper presents a novel approach to solve the short-term operation scheduling problem of a hydropower plant that sells energy in a deregulated electricity market with the objective of maximizing its revenue. This paper proposes a nonlinear programming based scheduling model that determines both the optimal unit commitment (start-ups and shut-downs scheduling) and the generation dispatch of the committed units (hourly power output). The power generated by each hydro unit is considered as a nonlinear function of the water discharge and the volume of the associated reservoir. The dependence of the units’ operating limits (maximum and minimum water flows) on the actual gross head has been also taken into account in this model. The results from a case study are also presented to illustrate the application of the proposed approach in a real hydro plant.     

Hydro-thermal unit commitment problem using simulated annealing embedded evolutionary programming approach

This paper presents a new approach to solve the hydro-thermal unit commitment problem using Simulated Annealing embedded Evolutionary Programming approach. The objective of this paper is to find the generation scheduling such that the total operating cost can be minimized, when subjected to a variety of constraints. A utility power system with 11 generating units in India demonstrates the effectiveness of the proposed approach; extensive studies have also been performed for different IEEE test systems consist of 25, 44 and 65 units. Numerical results are shown comparing the cost solutions and computation time obtained by conventional methods.     

Mixed integer programming of generalized hydro-thermal self-scheduling of generating units

This paper presents the application of mixed-integer programming (MIP) approach for solving the hydro-thermal self scheduling (HTSS) problem of generating units. In the deregulated environment, the generation companies schedule their generators to maximize their profit while satisfying loads is not an obligation. The HTSS is a high dimensional mixed-integer optimization problem. Therefore, in the large-scale power systems, solving the HTSS is very difficult. In this paper, MIP formulation is adopted for precise modeling of dynamic ramp rate limits, prohibited operating zones, operating services, valve loading effects, variable fuel cost, non-linear start-up cost functions of thermal units, fuel and emission limits of thermal units, multi head power-discharge characteristics of hydro plants and spillage of reservoir. The modified IEEE 118-bus system is used to demonstrate the performance of the proposed method.     

Optimal short-term scheduling for a large-scale cascaded hydrosystem

This paper describes a short term hydro generation optimization program that has been developed by the Hydro Electric Commission (HEC) to determine optimal generation schedules and to investigate export and import capabilities of the Tasmanian system under a proposed DC interconnection with mainland Australia. The optimal hydro scheduling problem is formulated as a large scale linear programming algorithm and is solved using a commercially-available linear programming package. The selected objective function requires minimization of the value of energy used by turbines and spilled during the study period. Alternative formulations of the objective function are also discussed. The system model incorporates the following elements: hydro station (turbine efficiency, turbine flow limits, penstock head losses, tailrace elevation and generator losses), hydro system (reservoirs and hydro network: active volume, spillway flow, flow between reservoirs and travel time), and other models including thermal plant and DC link. A valuable by-product of the linear programming solution is system and unit incremental costs which may be used for interchange scheduling and short-term generation dispatch     

An improved PSO technique for short-term optimal hydrothermal scheduling

This paper presents a new approach to the solution of optimal power generation to short-term hydrothermal scheduling problem, using improved particle swarm optimization (IPSO) technique. The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydraulic network, water transport delay and scheduling time linkage that make the problem of finding global optimum difficult using standard optimization methods. In this paper an improved PSO technique is suggested that deals with an inequality constraint treatment mechanism called as dynamic search-space squeezing strategy to accelerate the optimization process and simultaneously, the inherent basics of conventional PSO algorithm is preserved. To show its efficiency and robustness, the proposed IPSO is applied on a multi-reservoir cascaded hydro-electric system having prohibited operating zones and a thermal unit with valve point loading. Numerical results are compared with those obtained by dynamic programming (DP), nonlinear programming (NLP), evolutionary programming (EP) and differential evolution (DE) approaches. The simulation results reveal that the proposed IPSO appears to be the best in terms of convergence speed, solution time and minimum cost when compared with established methods like EP and DE.