求解机组组合问题的改进混合整数二次规划算法

混合整数二次规划(MIQP)算法求解机组组合问题具有全局优化能力,但是针对大规模优化问题,其计算速度和计算精度将受影响.文中提出了求解机组组合问题的改进MIQP算法.该算法的核心思想是引入了松弛和解耦2种改进策略.通过求解松弛整数变量的二次规划模型,首先获得机组组合的下界空间,然后再通过拉格朗日解耦算法获得机组组合的上界空间,进而在上下界确定的寻优空间内采用MIQP算法进行再优化.不同测试算例表明,改进的MIQP算法快速且有效,可以降低优化问题的复杂度,显著减少计算时间.     

系统分解协调算法的抽水蓄能电站优化调度

建立了包含抽水蓄能电站的电网统一调度优化模型,即以调度周期内火电燃料成本为最小目标函数,满足系统及各机组约束条件。利用系统分解协调思想,开发了一个结合拉格朗日松弛方法和粒子群优化算法的混合算法,将原优化问题分解为两层优化问题。上层拉格朗日算子优化利用次梯度算法求解,下层各子问题利用粒子群优化算法求解,经过迭代寻优得到最优对偶解后,利用一个启发式算法求得满足系统约束及各机组运行约束的原问题的可行解。最后通过算例验证了模型的合理性及算法的有效性。     

机组组合问题的两阶段优化算法

针对电力系统机组组合问题(UC)高维、非凸、非线性的特点,提出了一种两阶段优化方法(LR-DE).利用拉格朗日松弛算法(LR)对UC问题进行解耦,将多机优化问题转化为单机优化问题的重复计算,使模型简化,利用动态规划法和次梯度法求出对偶解对应的拉格朗日乘子;根据对偶解信息设定拉格朗日乘子更新空间,并利用微分进化算法(DE)进行搜索,全面考虑所有约束条件,不断缩小对偶间隙,求出最优的机组组合状态.算例分析表明,该算法优化效果好,搜索能力强,能较好解决大规模机组组合优化问题.     

利用拉格朗日松弛法解决SIS中的负荷经济分配问题

利用拉格朗日松弛法对火力发电厂厂级监控信息系统(SIS)中的负荷经济分配问题进行了求解。该方法以发电费用为目标函数,用拉格朗日乘子将系统的负荷约束松弛,并将得到的拉格朗日函数分解为一个上下两层的优化问题分别进行求解,保证了算法的快速有效性。与混沌优化及遗传算法进行了仿真比较,结果表明所提出的方法收敛速度快,求解精度高,易于掌握,是解决电力系统负荷经济分配问题的有效手段。     

改进的拉格朗日松弛法求解机组组合问题

提出了一种求解机组组合问题的改进拉格朗日松弛算法。与现有此类方法相比,此算法进行了以下三个方面改进：基于启发式排序法得到较优的拉格朗日乘子初值;改进了动态规划求解单机问题时的累计费用以获得更优的机组启停决策;采用自适应性次梯度法结合集结投影次梯度法的联合优化策略加快算法收敛速度。10机到100机的6个算例表明,自适应性次梯度法和集结投影次梯度法的联合优化策略更易跳出其单一策略时的振荡现象,从而加快收敛。     

改进的拉格朗日松弛法求解机组组合问题

提出了一种求解机组组合问题的改进拉格朗日松弛算法.与现有此类方法相比,此算法进行了以下三个方面改进:基于启发式排序法得到较优的拉格朗日乘子初值;改进了动态规划求解单机问题时的累计费用以获得更优的机组启停决策;采用自适应性次梯度法结合集结投影次梯度法的联合优化策略加快算法收敛速度.10机到100机的6个算例表明,自适应性次梯度法和集结投影次梯度法的联合优化策略更易跳出其单一策略时的振荡现象,从而加快收敛.     

一种求解机组组合问题的快速拉格朗日松弛法

提出一种求解机组组合问题的快速拉格朗日松弛算法。与现有此类算法比较,此算法在以下两个方面进行了改进：采用启发式逆排序法对机组的启停决策进行修正,解决了松弛因子步长过大导致多余机组启动的问题,加快了收敛速度;提出一种基于二分法的经济调度算法,在每步迭代中得到机组的最优有功出力后,对单台机组不满足爬坡约束的相邻时段建立出有功出力调整模型并求解,有效地处理了爬坡约束。通过对10机到100机6个算例计算分析,本算法的计算时间远远小于其他算法,且可获得较好的计算结果。     

消纳大规模风电的热电联产机组滚动调度策略

首先,对热电联产机组的特性进行了分析,建立了考虑背压式和抽凝式热电联产机组以及并网风电的滚动调度模型。然后,针对热电联产机组的特性,基于拉格朗日对偶松弛算法框架,提出了考虑风电以及其他各类机组的联合优化滚动调度算法。一方面,提出了主问题的迭代步长自适应修正方法以提高算法收敛速度,子问题则采用一种高效的逆推回代动态规划方法进行求解;另一方面,针对抽凝式热电联产机组的热电耦合约束难题,将其分解为供热出力优化及有功出力优化2个子问题,提出了2个子问题的交替迭代优化算法。某省级电网的实际算例结果证明了该方法的有效性。     

基于移动用户接入控制的5G通信基站需求响应

第五代蜂窝通信(5G通信)基站的能耗增长迅猛,将成为未来重要的电力负荷。优化基站的用能模式,尤其是通过多基站集群的协调运行来对移动用户进行接入控制,能在降低基站用能费用的同时,为电网提供可观的需求响应能力,注入新灵活性资源,实现通信运营商和电网的双赢。该文探究了5G通信规模化应用背景下,基于移动用户接入控制的5G通信基站需求响应。具体地,该文建立根据集群中各基站实时电价差异来调整用户与基站连接关系的基站群成本优化模型,并为快速求解该优化模型,提出一种启发式算法,将原问题分解为能量优化子问题和通信连接优化子问题,并基于实际的基站覆盖范围和信道特征阐明求解问题的稀疏性特征,降低模型的求解复杂度。两个子问题之间相互迭代求解直至收敛,以此获得局部最优解。最后通过算例验证了模型和算法的可行性。     

基于多核并行的中期火电开机优化算法

以指定时间段内参与计算电站的装机利用小时数相等为目标建立中期火电开机优化模型.针对问题的多状态、多阶段决策优化的特点,结合基于分治策略的Fork/Join框架,提出了多核并行的中期火电开机优化算法.该算法将原问题划分为规模较小的多个子问题分别进行求解,每个子问题从启发式搜索获得的初始可行解出发,采用逐步优化算法(POA...     

A decoupled solution of hydro-thermal optimal power flow problem bymeans of interior point method and network programming

This paper presents a new decoupled model together with a very efficient coordination algorithm to solve a hydrothermal optimal power flow (HTOPF) problem over a certain time horizon. Based on the Lagrange relaxation at the level of the KKT (Karush-Kuhn-Tucker) conditions of the primal problem, the HTOPF is decomposed into thermal plant subproblems formulated as OPF and hydroplant subproblems. To solve efficiently the thermal OPF subproblems, the warm-starting scheme has been incorporated into interior point quadratic programming (IPQP). As to the hydroplant subproblems, a united network flow model is presented in which a fixed head plant is treated as a special case of a variable head plant. The hydroplant subproblem can be formulated as a minimum-cost maximum-flow problem for which unit cost functions of hydroplants are defined exactly. A proposed variant of the partitioning shortest path algorithm has brought about a great speed up in the computation of the subproblems. The validity of the proposed method has been examined by solving the IEEE test systems and a Chinese power system consisting of 13 thermal plants and 12 hydro power plants; the last system is a large size problem such that it has 107712 primal and dual variables. Simulation results obtained are quite convincing     

Ramp rate constrained unit commitment by improved priority list and augmented Lagrange Hopfield network

This paper proposes an improved priority list (IPL) and augmented Hopfield Lagrange neural network (ALH) for solving ramp rate constrained unit commitment (RUC) problem. The proposed IPL-ALH minimizes the total production cost subject to the power balance, 15 min spinning reserve response time constraint, generation ramp limit constraints, and minimum up and down time constraints. The IPL is a priority list enhanced by a heuristic search algorithm based on the average production cost of units, and the ALH is a continuous Hopfield network whose energy function is based on augmented Lagrangian relaxation. The IPL is used to solve unit scheduling problem satisfying spinning reserve, minimum up and down time constraints, and the ALH is used to solve ramp rate constrained economic dispatch (RED) problem by minimizing the operation cost subject to the power balance and new generator operating frame limits. For hours with insufficient power due to ramp rate or 15 min spinning reserve response time constraints, repairing strategy based on heuristic search is used to satisfy the constraints. The proposed IPL-ALH is tested on the 26-unit IEEE reliability test system, 38-unit and 45-unit practical systems and compared to combined artificial neural network with heuristics and dynamic programming (ANN-DP), improved adaptive Lagrangian relaxation (ILR), constraint logic programming (CLP), fuzzy optimization (FO), matrix real coded genetic algorithm (MRCGA), absolutely stochastic simulated annealing (ASSA), and hybrid parallel repair genetic algorithm (HPRGA). The test results indicate that the IPL-ALH obtain less total costs and faster computational times than some other methods.     

Optimization-based scheduling of hydrothermal power systems withpumped-storage units

This paper presents an optimization-based method for scheduling hydrothermal systems based on the Lagrangian relaxation technique. After system-wide constraints are relaxed by Lagrange multipliers, the problem is converted into the scheduling of individual units. This paper concentrates on the solution methodology for pumped-storage units. There are, many constraints limiting the operation of a pumped-storage unit, such as pond level dynamics and constraints, and discontinuous generation and pumping regions. The most challenging issue in solving pumped-storage subproblems within the Lagrangian relaxation framework is the integrated consideration of these constraints. The basic idea of the method is to relax the pond level dynamics and constraints by using another set of multipliers. The subproblem is then converted into the optimization of generation or pumping; levels for each operating state at individual hours, and the optimization of operating states across hours. The optimal generation or pumping level for a particular operating state at each hour can be obtained by optimizing a single variable function without discretizing pond levels. Dynamic programming is then used to optimize operating states across hours with only a few number of states and transitions. A subgradient algorithm is used to update the pond level Lagrangian multipliers. This method provides an efficient way to solve a class of subproblems involving continuous dynamics and constraints, discontinuous operating regions, and discrete operating states     

Augmented Lagrange Hopfield network based Lagrangian relaxation for unit commitment

This paper proposes an augmented Lagrange Hopfield network based Lagrangian relaxation (ALHN-LR) for solving unit commitment (UC) problem with ramp rate constraints. ALHN-LR is a combination of improved Lagrangian relaxation (ILR) and augmented Lagrange Hopfield network (ALHN) enhanced by heuristic search. The proposed ALHN-LR method solves the UC problem in three stages. In the first stage, ILR is used to solve unit scheduling satisfying load demand and spinning reserve constraints neglecting minimum up and down time constraints. In the second stage, heuristic search is applied to refine the obtained unit schedule including primary unit de-commitment, unit substitution, minimum up and down time repairing, and de-commitment of excessive units. In the last stage, ALHN which is a continuous Hopfield network with its energy function based on augmented Lagrangian relaxation is applied to solve constrained economic dispatch (ED) problem and a repairing strategy for ramp rate constraint violations is used if a feasible solution is not found. The proposed ALHN-LR is tested on various systems ranging from 17 to 110 units and obtained results are compared to those from many other methods. Test results indicate that the total production costs obtained by the ALHN-LR method are much less than those from other methods in the literature with a faster manner. Therefore, the proposed ALHN-LR is favorable for large-scale UC implementation.     

A decentralized scheduling method for flowshop problems with resource constraints

In this paper, we propose a decentralized scheduling method for flowshop scheduling problems with resource constraints using the Lagrangian decomposition and coordination approach. When a flowshop scheduling problem with resource constraints is decomposed into machine‐level subproblems, the decomposed problem becomes very difficult to solve so as to obtain the optimal solution, even when the production sequence of operations is given. In this study, the decomposed subproblems are solved by a simulated annealing algorithm combined with dynamic programming. By decomposing the problem into single machine subproblems, the changeover cost can easily be incorporated in the objective function. In order to reduce the computation time, a heuristic algorithm for calculating the starting times of operations is also proposed. The performance of the proposed method is compared with that of the simulated annealing method by which the schedule of the entire machine is successively improved. Numerical results have shown that the proposed method can generate better solutions than the conventional method. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 149(1): 44–51, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10364     

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     

A genetic algorithm approach to short‐term scheduling of crude oil operations in refinery

As a type of process plant, a refinery is characterized by the interaction of discrete events and continuous processes. To schedule crude oil operations in a refinery, it is necessary to define and schedule the jobs simultaneously such that heuristics and meta‐heuristics cannot be directly applied. It is very challenging to schedule crude oil operations. To solve this problem, it is decomposed into two subproblems hierarchically. At the upper level, a refining schedule is found, while at the lower level a detailed schedule is obtained to realize the refining schedule. Given a refining schedule at the upper level, this paper studies the detailed scheduling problem at the lower level. Based on a control‐theoretic perspective, the problem is innovatively transformed to a problem of assigning charging tanks to distillers such that meta‐heuristic methods can be applied. Then, a genetic algorithm (GA) approach is developed to solve the problem. In realizing the proposed GA, based on a set of existence conditions of a feasible schedule, methods are presented to guarantee that each chromosome corresponds to a feasible schedule. An industrial case study is used to show the application of the proposed method. It shows that the method works well and is applicable to real‐life problems. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

考虑发电机阀点效应的改进拉格朗日松弛有功调度策略

发电机阀点效应导致的非凸非光滑特性增加了有功经济调度模型的复杂度,从而增大了求解难度.文中提出一种考虑发电机阀点效应影响的改进拉格朗日松弛有功调度算法.首先,提出一种二次多项式分段拟合算法,从而将发电机阀点效应成本分解为多个分段二次多项式形式;其次,将拟合后的表达式代入拉格朗日松弛子问题中,从而将原问题转化为分段二次规划问题,并采用比较对称轴及优化变量上下限的方法快速求解,避免了引入整数变量造成的求解效率偏低问题.同时,为防止多个局部最优解导致的优化过程不收敛问题,提出一种基于近端梯度法的增广求解策略,通过在目标函数中引入辅助变量及惩罚项来加强子问题的凸性,加快收敛速度.最后,基于40机和48机测试系统对所提方法的有效性进行了测试.     

配电网络电容器实时优化投切的逐次线性整数规划法

并联补偿电容器组是配电网络无功优化的重要设备。本文从实时控制的角度研究电容器优化投切的台数问题，推导了其逐次线性整数规划模型，并提出了适合配电网电容器投切特点的对偶松弛解法和逐次归整解法。所得模型简洁，求解过程无振荡现象，收敛快，计算量小，且所得优化整数解不易偏离最优整数解。