大规模机组组合问题计及网络约束的线性化求解方法

为了提高求解机组组合问题计算效率,给出线性化方法,将目标函数分段线性化,将启机费用作为约束并将其线性化,同时将网络安全约束通过直流潮流模型进行线性化,从而建立较完备的混合整数线性规划的机组组合模型。采用世界上广为流行的CPLEX优化求解器求解,在对偶间隙设定为较合理的情况下,求解速度快。不同测试算例表明,该方法速度快,精度较高,能够求解较大规模的机组组合问题。     

基于线性化潮流的安全约束机组组合方法

在安全约束机组组合(security-constrained unit commitment, SCUC)问题中,通常需要考虑N-1条件下的网络安全约束。由于支路开断分布系数(line outage distribution factor, LODF)良好的计算效率,学者常将其应用于N-1故障分析中。但是利用LODF并不能计算故障后的电压与无功分布。因此文中基于一种线性化潮流模型推导了与其对应的改进支路开断分布系数,并将该系数应用于SCUC中。算例结果表明,所提出的模型较传统基于LODF的模型能提供更加安全的发电计划。而对于绝大多数(95%以上)的N-1故障,得到的发电计划能在使用交流潮流进行安全校验时保证可行性。     

基于奔德斯算法的安全约束机组组合方法

针对采用混合整数规划算法直接求解安全约束机组组合,将使计算效率大幅度降低,而利用奔德斯算法求解则存在着算法振荡和受系统规模制约求解效率下降的问题,提出了一种基于奔德斯算法的安全约束机组组合新方法。该方法在奔德斯算法的基础上,通过纳入新增越限约束校正环节,控制了奔德斯割的寻优方向,通过增加起作用约束识别环节,缩小了奔德斯算法的寻优空间,进而提高了安全约束机组组合优化问题的求解效率。6机3节点和54机118节点算例验证了所提方法的有效性。     

基于启发式混合整数规划法求解大规模机组组合问题

为了改进单纯的混合整数规划法在求解大规模机组组合问题时难以在合理时间内求得满意优化解的问题,提出了一种基于启发式的混合整数规划算法。该算法根据机组开停的内在机理,通过综合分析机组开停特性与负荷曲线特性,基于改进优先顺序法以确定部分整数变量,以此为基础结合混合整数规划法求解大规模机组组合问题,达到提高计算速度、扩大计算规模的目的。将所提算法应用于多个标准算例并与现有文献进行参照对比,验证了所提算法的正确性与高效性。将该算法应用于某实际电网,验证了该算法的实用性。     

月度安全约束机组组合建模及求解

月度发电计划的复杂性和求解规模,使得月度机组组合方案的制订变得十分困难.文中基于兼顾计算性能和月度计划关键需求的原则,通过时段简化和电力电量解耦,建立了以电量进度偏差最小为目标的月度安全约束机组组合(SCUC)模型,并采用混合整数规划(MIP)算法加以求解.实际系统算例测试验证了该模型的有效性.     

含抽水蓄能电网安全约束机组组合问题的混合整数线性规划算法

抽水蓄能机组的投运对电网发电调度计划的制定具有很大影响,建立了含抽水蓄能机组电网的安全约束机组组合模型。以考虑了抽水蓄能机组启停费用的所有机组总运行费用为目标函数,根据抽水蓄能机组的不同运行工况给出旋转备用容量的解析表达式,同时在系统功率平衡约束中考虑了网络损耗的影响,并考虑了抽水蓄能机组的运行调度约束及网络安全约束。为了保证模型求解的可靠性和提高模型求解的计算效率,将目标函数进行分段线性化,并根据抽水蓄能机组的运行特点将其旋转备用容量约束等价转化为线性表达式。同时采用一种动态分段线性化方法近似逼近网络损耗,从而将机组组合模型转化为混合整数线性规划模型,并采用成熟的数学优化求解器CPLEX进行求解。对某实际23机306节点电网算例的计算结果表明,所提出的混合整数线性规划调度模型的网损逼近效果合理正确,算法求解速度快,具有较好的工程实用价值。     

基于外逼近方法的中期机组组合问题

利用外逼近方法（OAM）提出一种求解机组组合（UC）问题新的确定性方法。OAM是一种分解方法,它把UC问题分解为一系列的混合整数线性规划（MILP）主问题和非线性规划（NLP）子问题。应用分支割平面方法求解MILP,应用新的零空间内点法求解NLP。54机组168时段等多个系统的数值仿真表明,OAM具有快速的收敛速度,能有效处理爬坡约束,为大规模安全约束机组组合问题的有效求解提供了一条新途径。     

基于辅助优化问题的安全约束机组组合约束削减方法

安全约束机组组合(Security-constrained Unit Commitment, SCUC)问题作为制定发电计划的核心环节,在电力系统优化调度等方面具有十分重要的意义。针对考虑故障态约束后SCUC问题规模庞大、难以求解的情况,提出了一种基于辅助优化问题的故障态安全约束削减方法。首先引入与具体故障态安全约束相关的辅助优化问题,从而建立判别相应故障态安全约束是否冗余的充分必要条件。然后探究冗余故障态安全约束辨识过程的具体加速方法,包括松弛辅助优化问题方法,使用可行性判据进行故障态安全约束预分类方法,以及多线程并行计算方法。最后,在IEEE118测试系统上对所提方法的正确性和有效性进行了仿真验证。     

考虑多时间尺度灵活性的含大规模风电电力系统机组组合研究

考虑机组多时间尺度启停约束,建立系统多时间尺度灵活性供给模型;考虑风电预测误差分布时变性,建立多时间尺度灵活性需求分析模型;基于混合整数线性规划方法,提出考虑多时间尺度灵活性的含大规模风电电力系统机组组合模型。模型能够充分反映含大规模风电电力系统多时间尺度灵活性供需平衡关系,在保证灵活性和安全性的前提下,提高运行经济性。通过混合整数线性规划建模能降低模型计算复杂性,为大规模系统的应用提供基础。     

求解安全约束机组组合问题的混合整数规划算法性能分析

安全约束机组组合(SCUC)是当前国外电力生产和调度中应用的先进优化软件.简要介绍了SCUC的发展背景,给出了SCUC的完整数学模型和优化算法.基于混合整数规划算法开发了SCUC优化程序.以IEEE RTS标准系统进行500台机组系统和中国某省级实际电网(161台机组,109个安全断面)的分析计算,结果验证了该算法和程序的有效性和实用性.     

A study of a unit commitment problem with transmission constraints

Unit commitment problem is an optimization problem to determine the start‐up and shut‐down schedule of thermal units while satisfying various constraints, for example, generation‐demand balance, unit minimum up/down time, system reserve, and so on. Since this problem involves a large number of 0–1 type variables that represent up/down status of the unit and continuous variables expressing generation output, it is a difficult combinatorial optimization problem to solve. The study at present concerns the method for requiring the suboptimum solution efficiently. Unit commitment method widely used solves the problem without consideration of voltage, reactive power, and transmission constraints. In this paper, we will propose a solution of unit commitment with voltage and transmission constraints, based on the unit decommitment procedure (UDP) method, heuristic method, and optimal power flow (OPF). In this method, initial unit status will be determined from random numbers and the feasibility will be checked for minimum start‐up/shut‐down time and demand‐generation balance. If the solution is infeasible, the initial solution will be regenerated until a feasible solution can be found. Next, OPF is applied for each time period with the temporary unit status. Then, the units that have less contribution to the cost are detected and will be shut down based on the unit decommitment rules. This process will be repeated until suboptimal solution is obtained. The proposed method has been applied to the IEEE 118‐bus test system with 36 generating units with successful result. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 144(3): 36–45, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10187     

The challenges of the unit commitment problem for real-life small-scale power systems

Small-scale power systems mainly present two particular problems when it comes to their modeling and solution. Due to their size, it is important to consider and meet various types of reserve requirements in order to have a reliable operation of the power system. It is also important to consider variable start-up costs in order to obtain a more accurate unit commitment. In this paper six different types of reserve requirements are considered for the unit commitment problem: spinning reserve, regulation reserve (AGC per unit), ten-minute reserve, ten-minute non-synchronized reserve, ten-minute operational reserve, and ten-minute distributed reserve. Additionally, a Mixed Integer Programming formulation is introduced to represent variable start-up costs. The model introduced here is currently in use by the Baja California (México) power system operator.     

A new method for unit commitment with ramping constraints

Unit commitment with ramping constraints is a very difficult problem with significant economic impact. A new method is developed in this paper for scheduling units with ramping constraints within Lagrangian relaxation framework based on a novel formulation of the discrete states and the integrated applications of standard dynamic programming for determining the optimal discrete states across hours, and constructive dynamic programming for determining optimal generation levels. A section of consecutive running or idle hours is considered as a commitment state. A constructive dynamic programming (CDP) method is modified to determine the optimal generation levels of a commitment state without discretizing generation levels. The cost-to-go functions, required only for a few corner points with a few continuous state transitions at a particular hour, are constructed in the backward sweep. The optimal generation levels can be obtained in the forward sweep. The optimal commitment states across the scheduling horizon can then be obtained by standard dynamic programming. Numerical testing results show that this method is efficient and the optimal commitment and generation levels are obtained in a systematic way without discretizing or relaxing generation levels.     

基于改进约束序优化方法的带安全约束的不确定性机组组合问题研究

为快速有效地求解考虑间歇性可再生能源接入的SCUC问题,在现有约束序优化的基础上,提出了一种适用于不确定性SCUC问题求解的改进约束序优化算法。该方法针对序优化的粗糙模型和精确模型分别融入了离散变量识别策略和无效安全约束削减策略。相比于传统求解方法,提出的改进约束序优化算法在充分发挥传统序优化计算效率方面优势的同时,进一步增强了算法的紧凑性,降低了计算冗余度,有效提升了算法的求解效率。基于IEEE-118节点标准算例的仿真验证了所提算法的正确性和有效性。     

A solution to the unit commitment problem considering LNG fuel constraints

In this paper, an algorithm is proposed for finding a quasi-optimal schedule for the short-term thermal unit commitment problem taking LNG fuel constraints into account. In recent years, LNG fuel has been used increasingly. As a result, LNG fuel constraints should be considered in making a unit commitment schedule. Generally, unit commitment is a nonlinear combinatorial problem including discrete variables. To solve the problem, a two-step algorithm is developed using mathematical programming methods. First a linear programming problem is solved to determine the amount of LNG fuel to be consumed by each LNG unit, then a Lagrangian relaxation approach is used to obtain a unit commitment schedule. This two-step algorithm simplifies the problem and thus has good convergence characteristics. To test the effectiveness of the proposed algorithm, a numerical simulation was carried out on a 46-unit thermal system over a 24-hour period. A result with a dual gap of 0.00546 was obtained. © 1998 Scripta Technica, Electr Eng Jpn, 125(3): 22–30, 1998     

适合于机组组合问题的扩展优先顺序法

针对传统PL（Priority List）方法采用单一排序指标,即平均满负荷费用AFLC（Average Full-Load Cost）不能全面反映机组优先顺序的不足,提出一种扩展优先顺序法EPL（Extended Priority List）解决机组组合问题。在分析PL方法特点的基础上,定义μ-Load Cost反映机组在不同出力范围内的经济指标,形成不同μ值的机组组合的邻域,而后定义机组的效用系数UUR（Unit Utilization Ratio）优化机组的优先顺序。此外,引入参数控制机组组合邻域的规模并采取策略对机组组合进行调整使其满足所有约束,从而提高计算效率。最后采用26机组、38机组以及45机组24时段等3个系统的测试结果来验证该方法的有效性。     

适合于机组组合问题的扩展优先顺序法

针对传统PL(Priority List)方法采用单一排序指标,即平均满负荷费用AFLC(Average Full-Load Cost)不能全面反映机组优先顺序的不足,提出一种扩展优先顺序法EPL(Extended Priority List)解决机组组合问题.在分析PL方法特点的基础上,定义μ-Load Cost反映机组在不同出力范围内的经济指标,形成不同μ值的机组组合的邻域,而后定义机组的效用系数UUR(Unit Utilization Ratio)优化机组的优先顺序.此外,引入参数控制机组组合邻域的规模并采取策略对机组组合进行调整使其满足所有约束,从而提高计算效率.最后采用26机组、38机组以及45机组24时段等3个系统的测试结果来验证该方法的有效性.     

Stochastic unit commitment problem considering risk constraints and its improved GA‐based solution method

This paper proposes a model of the stochastic unit commitment (SUC) problem, which takes account of the uncertainty of electric power demand and its resulting risk, and its solution method based on an improved genetic algorithm (IGA). The uncertainty of electric power demand is modeled using a set of scenarios which are introduced by scenario analysis. The variance, which measures the dispersion of generation costs of unit commitment schedule under each scenario around the expected generation cost, is used as a measure of risk. Based on the expected returns–variance of returns (E–V) rule in the theory of portfolio analysis, a utility function is devised by appending the variance of the expected generation cost into the original expected generation cost function, with consideration of the risk attitude of the generation companies and power exchange centers. The objective of this optimization problem is to minimize the utility function. The proposed IGA is used to solve this NP‐hard optimization problem. Based on numerical examples, the superiority of the IGA‐based solution method is verified through comparison with a traditional GA‐based solution method. Optimal schedules of SUC, as well as the expected costs and variances, are compared with/without risk constraints, and with different risk attitudes. Test results show that, in solving the SUC problem, it is necessary to consider the electric power demand uncertainty and its resulting risk, as well as the risk attitude of the decision maker. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Solving unit commitment problems with general ramp constraints

Lagrangian relaxation (LR) algorithms are among the most successful approaches for solving large-scale hydro-thermal unit commitment (UC) problems; this is largely due to the fact that the single-unit commitment (1UC) problems resulting from the decomposition, incorporating many kinds of technical constraints such as minimum up- and down-time requirements and time-dependent startup costs, can be efficiently solved by dynamic programming (DP) techniques. Ramp constraints have historically eluded efficient exact DP approaches; however, this has recently changed [Frangioni A, Gentile C. Solving nonlinear single-unit commitment problems with ramping constraints. Oper Res 2006;54(4):767–75]. We show that the newly proposed DP algorithm for ramp-constrained (1UC) problems allows to extend existing LR approaches to ramp-constrained (UC); this is not obvious since the heuristic procedures typically used to recover a primal feasible solution are not easily extended to take ramp limits into account. However, dealing with ramp constraints in the subproblems turns out to be sufficient to provide the LR heuristic enough guidance to produce good feasible solutions even with no other modification of the approach; this is due to the fact that (sophisticated) LR algorithms to (UC) duly exploit the primal information computed by the Lagrangian Dual, which in the proposed approach is ramp feasible. We also show by computational experiments that the LR [approach] is competitive with those based on general-purpose mixed-integer program (MIP) solvers for large-scale instances, especially hydro-thermal ones.     

计及N-k网络安全约束的二阶段鲁棒机组组合

为提高调度决策的安全性以增强其应对偶发线路故障扰动的能力,文中提出一种计及N-k网络安全约束的二阶段鲁棒机组组合模型。首先,介绍了2种当前研究中采用的N-k不确定集合,并对集合特点进行了阐述;其次,基于2种N-k不确定集合,构建了一般形式的二阶段鲁棒机组组合模型。其中,第一阶段为线路故障前的机组启停决策;第二阶段为观测到线路故障最坏情况下的经济调度决策。所提模型可采用列与约束生成(CCG)算法将第一阶段、第二阶段问题分别对应转化为主问题与子问题进行迭代求解,并且运用对偶原理和线性化技术,可将主问题与子问题均转化为混合整数线性规划(MILP)模型。最后,通过对IEEE 14节点及IEEE 118节点系统的测试分析,验证了所提模型的有效性。