基于轨迹的最优潮流问题可行域计算方法

可行域对最优潮流问题求解具有至关重要的作用,然而如何构造最优潮流问题的可行域是一个具有挑战性的问题。本文基于一种非线性动力学系统提出了一种可行域计算方法。在指定空间中,该方法从已知可行解出发不断寻找其周围位置上的可行解,直到全部等间隔的可行解被找到,从而实现可行域的计算。利用所提出方法,本文研究了一个9节点及一个118节点系统的可行域。通过观察,得到了最优潮流问题在中载条件下最好解的启发性结论,并验证了可行域在较大规模算例中的非凸性。     

具有爬升约束机组组合的充分必要条件

在Lagrangian松弛框架下，很难确定机组组合问题的一个可行解是否可通过调整对偶机组组合而获得。对于具有爬升约束的机组组合调度问题来说，由于机组出力在连续的2个开机区间的耦合性，求解可行解就更困难。在Lagrangian松弛框架下，开发1个机组组合新方法的核心是如何获得1个可行的机组组合。文中采用Benders分解可行性条件严格证明了在给定时段，机组组合可行的充分必要条件：即在该时段一个相应于系统负载平衡约束和旋转各用约束的不等式组成立。该条件不需要求解经济分配问题，就可以判定机组组合的可行性。有了此条件，可在发电功率经济分配前知道机组组合是否可行，若不可行，则可通过调整机组组合状态而获得可行的组合。该条件对于构造一个求解机组组合问题的系统方法是重要且有效的。数值测试表明该条件是判定机组组合可行性的有效方法。     

变负荷条件下追踪电力系统安全最优运行轨迹的参数化方法

提出一种追踪线性约束下凸可分规划问题最优解轨迹的参数化方法。该参数优化算法可在对偶松弛凸可分规划算法的主循环之外,通过少量参数化扩展得到。参数分析表明最优解轨迹的性态是一条分段线性曲线,解轨迹上的破点和不可行现象存在密切关系。将这种方法应用到电力系统有功最优潮流问题中,得到一种统一经济调度和安全约束调度的参数化安全约束调度(security constrained economic dispatch,SCED)新算法,它可快速追踪变负荷条件下系统安全最优运行轨迹。算法在IEEE14-300节点测试系统及2个省级实际系统上通过测试,数值试验和几何分析表明了该方法的计算特性和物理内涵,同时清楚地显示了目前调度模式中存在的问题和改进方向。     

时滞不确定奇异系统的鲁棒H∞控制

针对带时滞的奇异系统,研究基于状态反馈的鲁棒H∞问题,系统的状态矩阵、状态滞后矩阵和输入矩阵均含有范数有界不确定项。采用Lyapunov泛函方法,给出了带时滞的不确定奇异系统鲁棒渐近稳定且具有H∞范数界γ充分条件;利用含等式约束的线性矩阵不等式（LMI）方法,给出了此类系统控制存在状态反馈的充分条件,该条件等价于严格线性矩阵不等式可解性问题,利用严格LMI的可行解,得到控制器矩阵的参数化表示。该鲁棒控制器的渐进稳定性条件宽松,克服了时滞奇异系统稳定性问题条件中的等式约束,控制器求解算法可行、高效,并通过一个数值实例说明了该方法的有效性。     

多智能体技术在机组组合运行与管理分析中的应用

电力系统机组组合问题是一个典型的大规模混合整数的非线性组合优化问题,很难得到理论上的最优解.该文提出了求解机组组合问题的多智能体体系结构,并且提出了自治与分级管理相结合的3层MAS系统体系结构,最终通过协调Agent、任务Agent、发电Agent的协商、谈判,获得了机组组合问题的一个较为满意的解.     

基于改进遗传算法的新建变电站中压配电网规划

针对新建变电站中压配电网规划未考虑负荷不确定性因素、遗传算法易产生不可行解的问题,对传统遗传算法的交叉、变异操作进行改进,对交叉、变异之后产生的线路跨越、孤环、孤链等不可行解提出了有效的修复方法,既保证了可行解的数量,又保留了不可行解中的优良基因.将负荷用区间数表示,利用区间潮流端点法考虑了负荷不确定因素,算例结果表明采用该方法获得的规划方案更合理,当负荷增长15%时规划方案仍然适用.     

计算机辅助工程优化设计的一种新的有效算法

一、引言七十年代初期,对非线性有约束的优化问题求解,流行的算法之一是序贯无约束极小化方法SUMT~([1])。这一方法是将目标函数变换为包含约束信息的罚函数,将求解一个有约束问题的过程变换为连续求解若干个无约束问题的过程,最后收敛于有约束问题的解,得到位于可行域内的(局部)极小点。     

电压无功功率优化控制中不可行问题的研究

分析了电力系统电压无功实时优化控制中出现的不可行问题,通过引入模糊约束,从一个新的角度对不可行问题进行了处理,最终获得尽量靠近原不等式约束空间的解。中结合原对偶内点法的特点提出了不可行问题的探测和中结合原对偶内点法的特点提出了不可行问题的探测和处理方法,并用模型系统和华东电力系统的实际数据进行了验算。结果表明,中所提的方法可以有效地探测和处理优化过程中的不可行问题,快速获得合理解。     

用遗传算法求解离散变量优化问题

遗传算法是一种新的优化算法,它模拟生物进化机理,对可行解优胜劣汰,最终获得问题的最优解。遗传算法全局搜索能力强,这是其它算法无法比拟的,并且直接对可行解编码操作,所以它更适合离散变量优化问题。     

用遗传算法求解离散变量优化问题

遗传算法是一种新的优化算法，它模拟生物进化机理，对可行解优胜劣汰，最终获得问题的最优解。遗传算法全局搜索能力强，这是其它算法无法比拟的，并且它直接对可行解编码操作，所以它更适合离散变量优化问题。     

The conditions for obtaining feasible solutions to security-constrained unit commitment problems

The core of solving security-constrained unit commitment (SCUC) problems within the Lagrangian relaxation framework is how to obtain feasible solutions. However, due to the existence of the transmission constraints, it is very difficult to determine if feasible solutions to SCUC problems can be obtained by adjusting generation levels with the commitment states obtained in the dual solution of Lagrangian relaxation. The analytical and computational necessary and sufficient conditions are presented in this paper to determine the feasible unit commitment states with grid security constraints. The analytical conditions are proved rigorously based on the feasibility theorem of the Benders decomposition. These conditions are very crucial for developing an efficient method for obtaining feasible solutions to SCUC problems. Numerical testing results show that these conditions are effective.     

具有相同机组水火电调度问题的新算法

对Lagrangian松弛法求解水火电调度问题时由机同机级引起解震荡现象进行了研究。通过一个例子分析了震荡产生的根本原因。对此，在松弛函数中引入了惩罚项并采用了伪次梯度法来修正乘子。新算法在求解低层子问题时并不同时求解，使震荡现象在很大程度上得以克服，同时可大幅度地降低偶解对约束的违反程度。通过简单的例子和对一个包含两组机同机组的短期发电调度问题的计算表明，对偶解的约束违反程度明显地降低，解震荡明显地减弱且最后可行解的质量有显著的改善。     

A solution for unit commitment using Lagrangian relaxation combined with evolutionary programming

This paper proposes an approach which combines Lagrangian relaxation principle and evolutionary programming for short-term thermal unit commitment. Unit commitment is a complex combinatorial optimization problem which is difficult to be solved for large-scale power systems. Up to now, the Lagrangian relaxation is considered the best to deal with large-scale unit commitment although it cannot guarantee the optimal solution. In this paper, an evolutionary programming algorithm is used to improve a solution obtained by the Lagrangian relaxation method: Lagrangian relaxation gives the starting point for a evolutionary programming procedure. The proposed algorithm takes the advantages of both methods and therefore it can search a better solution within short computation time. Numerical simulations have been carried out on two test systems of 30 and 90 thermal units power systems over a 24-hour periods.     

An algorithm for combined heat and power economic dispatch

This paper presents a new algorithm for combined heat and power (CHP) economic dispatch. The CHP economic dispatch problem is decomposed into two sub-problems: the heat dispatch; and the power dispatch. The sub-problems are connected through the heat-power feasible region constraints of cogeneration units. The connection can be interpreted by the unit heat-power feasible region constraint multipliers in the Lagrangian function, and the interpretation naturally leads to the development of a two-layer algorithm. The outer layer uses the Lagrangian relaxation technique to solve the power dispatch iteratively. In each iteration, the inner layer solves the heat dispatch with the unit heat capacities passed by the outer layer. The binding constraints of the heat dispatch are fed back to the outer layer to move the CHP economic dispatch towards a global optimal solution     

相同机组调度与竞标问题研究

本文在对利用拉格朗日松驰法解决大型电力市场综合资源的调度与竞标时所碰到的相同机组问题进行了讨论,认为改进电力市场竞标模式并不是解决相同机组调度与竞标问题的根本方法。     

Unit commitment using Lagrangian relaxation and particle swarm optimization

Unit commitment (UC) is a NP-hard nonlinear mixed-integer optimization problem. This paper proposes ELRPSO, an algorithm to solve the UC problem using Lagrangian relaxation (LR) and particle swarm optimization (PSO). ELRPSO employs a state-of-the-art powerful PSO variant called comprehensive learning PSO to find a feasible near-optimal UC schedule. Each particle represents Lagrangian multipliers. The PSO uses a low level LR procedure, a reserve repairing heuristic, a unit decommitment heuristic, and an economic dispatch heuristic to obtain a feasible UC schedule for each particle. The reserve repairing heuristic addresses the spinning reserve and minimum up/down time constraints simultaneously. Moreover, the reserve repairing and unit decommitment heuristics consider committing/decommitting a unit for a consecutive period of hours at a time in order to reduce the total startup cost. Each particle is initialized using the Lagrangian multipliers obtained from a LR that iteratively updates the multipliers through an adaptive subgradient heuristic, because the multipliers obtained from the LR tend to be close to the optimal multipliers and have a high potential to lead to a feasible near-optimal UC schedule. Numerical results on test thermal power systems of 10, 20, 40, 60, 80, and 100 units demonstrate that ELRPSO is able to find a low-cost UC schedule in a short time and is robust in performance.     

Implementation of a Lagrangian relaxation based unit commitmentproblem

An effort is made to provide an understanding of the practical aspects of the Lagrangian relaxation methodology for solving the thermal unit commitment problem. Unit commitment is a complex, mixed integer, nonlinear programming problem complicated by a small set of side constraints. Until recently, unit commitment for realistic size system has been solved using heuristic approaches. The Lagrangian relaxation offers a new approach for solving such problems. Essentially, the method involves decomposition of the problem into a sequence of master problems and easy subproblems, whose solutions converge to an ϵ-optimal solution to the original problem. The authors concentrate on the implementation aspects of the Lagrangian relaxation method applied to realistic and practical unit commitment problems     

考虑发电机组输出功率速度限制的最优机组组合

本文对发电机组输出功率速度限制条件下的电优机组组合问题进行了研究，提出了基于拉格朗日松弛原理的协调求解方法，构造在了构弛功率平衡约束的情况下的分离单机子问题的简单的网络模型，从而利用最短路径算法求出可行的组合方案。在此基础，利用动态优化调度的新算法－积留量法进行调整，从而达到机组组合与运行的良好协调，算例的试算，获得了较满意的效果。     

Sequential Lagrangian-MILP approaches for Unit Commitment problems

The short-term Unit Commitment (UC) problem in hydro-thermal power generation is a fundamental problem in short-term electrical generation scheduling. Historically, Lagrangian techniques have been used to tackle this large-scale, difficult Mixed-Integer NonLinear Program (MINLP); this requires being able to efficiently solve the Lagrangian subproblems, which has only recently become possible (efficiently enough) for units subject to significant ramp constraints. In the last years, alternative approaches have been devised where the nonlinearities in the problem are approximated by means of piecewise-linear functions, so that UC can be approximated by a Mixed-Integer Linear Program (MILP); in particular, using a recently developed class of valid inequalities for the problem, called “Perspective Cuts”, significant improvements have been obtained in the efficiency and effectiveness of the solution algorithms. These two different approaches have complementary strengths; Lagrangian ones provide very good lower bounds quickly, but they require sophisticated heuristics—which may need to be changed every time that the mathematical model changes—for producing actual feasible solutions. MILP approaches have been shown to be able to provide very good feasible solutions quickly, but their lower bound is significantly worse. We present a sequential approach which combines the two methods, trying to exploit each one’s strengths; we show, by means of extensive computational experiments on realistic instances, that the sequential approach may exhibit significantly better efficiency than either of the two basic ones, depending on the degree of accuracy requested to the feasible solutions.