电力系统优化调度模型与算法研究.doc

作者姓名：翟桥柱论文题目：电力系统优化调度模型与算法研究作者简介：翟桥柱，男， 1972年6月出生，1999年9月师从于西安交通大学系统工程研究所管晓宏教授，于2005年12月获博士学位。中 文 摘 要电力系统优化调度是有巨大潜在经济效益的一类优化问题。它的主要目标是在确保电力正常供应的前提下合理利用发电资源，减少能源消耗和环境污染，降低发电总成本，提高发电厂在电力市场中的竞争力。随着主要发电用燃料煤、石油和天然气等资源的日渐消耗和世界范围内电力市场化改革的推进，如何进一步提高电力系统优化调度水平成为迫切需要研究的一个课题。Lagrange松弛法是目前公认的求解电力系统优化调度问题最有效的方法之一。本文主要研究了Lagrange松弛法框架下一些多年遗留问题以及电力市场环境下与调度有关的一些新问题。具体包括以下几个方面：对电力系统优化调度问题进行了概述，特别分析了电力市场环境下对调度问题的新要求，介绍了我国电力系统优化调度现状。Lagrange松弛框架下的同构振荡是一个多年未获解决的难题，同构振荡是指在松弛法框架下，乘子每次修正后，相同机组对应的子问题的解始终保持同步变化。虽然从对偶问题角度看，同构振荡是自然的，但由于受系统负载需求的制约，在可行解和最优解中相同机组的开关状态及生产情况一般不同，所以同构振荡会使构造可行解变得异常困难。本文通过分析同构振荡产生的根源，指出只有通过合理的途径将对偶优化中的相同子问题化为不同才能从根本上消除同构振荡。由于正是系统负载需求约束导致相同机组的解可能不同，所以本文提出采用增广Lagrange函数引入对负载需求约束的惩罚项，且在解子问题时提出了序贯求解算法以克服可分性被破坏后给求解带来的困难，理论分析和实例测试均表明这是一种能彻底克服同构振荡的有效算法，同时这种方法还可以解决相同机组市场竞标中的公平性问题。(参见：Qiaozhu Zhai, Xiaohong Guan, Jian Cui. Unit Commitment with Identical Units: Successive Subproblems Solving Method Based on Lagrangian Relaxation J. IEEE Transactions on Power Systems, Vol.17, No. 4, pp.1250-1257. 2002. X.H. Guan, Q.Z. Zhai, F. Lai. New Lagrangian Relaxation Based Algorithm for Resource Scheduling with Homogeneous SubproblemsJ. Journal of Optimization Theory and Applications, Vol. 113, No.1, pp.65-82, 2002.)电力系统优化调度中机组的爬升约束会给求解带来极大困难，引起困难的根本原因在于离散量与连续量的密切耦合，本文通过深入分析提出了一种新的状态定义及阶段划分方法，基于新的状态定义实现了离散量与连续量的解耦，以此为基础设计了一种双动态规划算法，在低层用连续动态规划求解最优的连续决策，在高层用离散动态规划求解最优的离散决策，其中离散决策费用与低层的最优连续决策有关。双动态规划法可以迅速获得具有爬升约束机组子问题的最优解，理论分析及数值计算均表明了算法的有效性，从而彻底改变了长期以来该问题难以有效求解的局面，解决了遗留多年的又一个难题。(参见：翟桥柱，管晓宏，郭燕，孙岚. 具有混合动态约束的生产系统优化调度新算法J. 自动化学报，Vol. 30, No. 4, pp.539-546, July 2004. Wei,Fan, Xiaohong Guan, Qiaozhu Zhai. A New Method for Unit Commitment with Ramping ConstraintsJ. Electric Power Systems Research, Vol.62, pp.215-224, 2002.)目前文献中广泛采用的机组煤耗曲线是凸二次曲线，然而实际的煤耗曲线是非常复杂的非凸函数，凸二次曲线仅是一种近似。本文提出的子问题求解算法可以处理更为精确的非凸煤耗特征，理论分析和实例测试验证了相关方法的有效性，从而在模型的精确性和解的性能两方面均取得了重要突破，新方法在日益重视节能降耗和环保指标的电力市场环境下具有重要意义。(参见：Qiaozhu Zhai, Xiaohong Guan, Feng Gao. Production Scheduling with Hybrid Dynamics and ConstraintsC. 43rd IEEE Conference on Decision and Control, December 2004, Atlantis, Paradise Island, Bahamas, 0476-THA01.6, 2004.)本文深入分析、总结了各种不同的水电调度模型。在Lagrange松弛框架下，不考虑水头影响时针对独立水系子问题建立了一个线性混合整数规划模型，考虑水头影响时，证明了水电转换关系可用一个三元非线性函数表示，接着研究了如何在线性混合整数规划模型中考虑非线性水电转换关系的问题，通过适当的数学变换再次得到一个线性混合整数规划模型。有关结果对于提高模型精度有重要意义。Lagrange松弛框架下最后一步是基于对偶解构造可行解。本文明确提出了构造可行解的两阶段思想，同时提出了离散可行解的重要概念。离散可行解本身不是可行解，但仅需调整其中部分连续变量的取值即可得到可行解。文中提出并证明了一个解成为离散可行解的充分必要条件，利用该条件将获得离散可行解的问题转化为求解一个纯整数规划，通常该整数规划问题极易求解。以上工作使得构造可行解不再无章可循而是一个系统化的过程。(参见：Xiaohong Guan, Sangang Guo, and Qiaozhu Zhai. The Conditions for Obtaining Feasible Solutions to Security-Constrained Unit Commitment Problems J. IEEE Transactions on Power Systems, Vol.20, No. 4, pp.1746-1756. 2005. 吴 磊，翟桥柱，管晓宏. 发电经济调度可行解判据及其求解方法J. 电网技术，Vol.28, No.1, pp. 1-4, 2004.)长期以来，求解电力系统优化调度的Lagrange松弛框架下一些重要概念如对偶间隙、乘子意义等常被曲解，本文首次给出了一个具有正对偶间隙的调度例子，同时深入分析了乘子的经济意义，相关结论指出有些长期流传的解释需要纠正。针对按统一边际价格结算的电力市场，提出并证明了关于最优竞标策略的基本定理，该定理明确指出了调度与竞标的重要关系。基于文中提出的所有方法，已开发出一套调度软件系统，该系统目前已在国内一些电厂中得到初步应用。关键词： 电力系统优化调度；机组组合；经济分配；混合整数规划；Lagrange松弛法；电力市场Research on the Model and Algorithms for Hydrothermal SchedulingZhai QiaozhuABSTRACTHydrothermal scheduling (HTS) is a class of optimization problems with significant potential benefits. Definitely considering the stability of power supply, the goal of HTS is to optimize the allocation of power generation resources, to minimize the environment pollution and the consumption of fuel, and to minimize the generation cost which is very important to generation corporations in the deregulated electric power market. With the shortage of coal, petroleum, natural gas and with advances in the reform of electric power market, it has been an urgent research topic to adopt some more accurate models and more efficient algorithms for HTS. Lagrangian Relaxation (LR) is one of the most successful algorithms for HTS. In this paper, some difficult problems in the LR framework are studied, for which few effective methods were proposed in the past. Some important new problems in the deregulated electric power market are also discussed. These problems include: A brief introduction to HTS and a summary of the current algorithms are presented. Especially, new demands for the model and algorithms for HTS in the deregulated electric power market and the state of art of HTS in china are analyzed. When the Lagrangian relaxation based methods are applied to solve power system unit commitment, the identical solutions to the subproblems associated with identical units may cause the dual solution to be far away from the optimal solution and serious solution oscillations. As a result, the quality of the feasible solution obtained may be very unsatisfactory. This issue has been long recognized as an inherent disadvantage of Lagrangian relaxation based methods. In this paper, the homogeneous solution issue is identified and analyzed through a simple example. Based on this analysis, a successive subproblem solving method is developed. The new method combines the concepts of augmented Lagrangian relaxation and surrogate subgradient to produce a good search direction at the high level. The low level subproblems including those corresponding to the identical units are solved successively so that the commitments of the identical units may not be homogeneous in the dual solution. Compared with the standard Lagrangian relaxation method, the new method can obtain better dual solutions and avoid the solution oscillations. Numerical testing shows the new method is efficient and the quality of the feasible solution is greatly improved. (Qiaozhu Zhai, Xiaohong Guan, Jian Cui. Unit Commitment with Identical Units: Successive Subproblems Solving Method Based on Lagrangian Relaxation J. IEEE Transactions on Power Systems, Vol.17, No. 4, pp.1250-1257. 2002. X.H. Guan, Q.Z. Zhai, F. Lai. New Lagrangian Relaxation Based Algorithm for Resource Scheduling with Homogeneous SubproblemsJ. Journal of Optimization Theory and Applications, Vol. 113, No.1, pp.65-82, 2002.)Ramp-rate constraints make the problem very complex and there are only different kinds of approximation approaches to handle the constraints up to present. A double-level dynamic programming algorithm is presented in this paper to solve the subproblem with ramp-rate constraints. It is based on a novel formulation of the discrete states so that the problem is decomposed into solving continuous and discrete problems separately. By employing the features of piecewise linear functions, break points of cost-to-go are mapped across time, and the production levels of a consecutive running span are determined efficiently by dynamic programming without discretization. Dynamic programming is also applied to determine the optimal discrete operating states across time. The new method can not only find the exact global optimal solution with much less computation efforts, but also requires no convex hypothesis on the fuel cost characteristics of thermal units. The complexity analysis and numerical testing results of the new method show the method is very efficient and effective. Since the demand for high quality solution becomes more urgent in the deregulated electric power market, the new method will doubtless be adopted quickly and universally. (Wei,Fan, Xiaohong Guan, Qiaozhu Zhai. A New Method for Unit Commitment with Ramping ConstraintsJ. Electric Power Systems Research, Vol.62, pp.215-224, 2002. Qiaozhu Zhai, Xiaohong Guan, Feng Gao. Production Scheduling with Hybrid Dynamics and ConstraintsC. 43rd IEEE Conference on Decision and Control, December 2004, Atlantis, Paradise Island, Bahamas, 0476-THA01.6, 2004. )Different models for hydro power plants scheduling are summarized. Under the framework of LR, a mixed integer linear programming formulation is founded without considering the head-dependant power energy production. Then, the head-dependant power energy production is studied in a mixed integer linear programming formulation. It is proved that the head-dependant power energy output can be treated as a nonlinear function of three independent variables. Some transformations are introduced and once again a mixed integer linear programming formulation is set up. The result model is therefore more accurate than all the models adopted heretofore. The final step in LR framework is to construct a feasible solution based on the dual solution. A Two-Step scheme is devised for this purpose. An important definition of Discrete-Feasible-Solution is introduced. A Discrete-Feasible-Solution is usually not a feasible solution but a feasible solution can be obtained by simply adjusting the continuous variables in the Discrete-Feasible-Solution. The necessary and sufficient condition for a solution to be Discrete-Feasible is given. A simple integer programming problem is set up in