Generation scheduling with thermal stress constraints

This paper describes a scheduling method for representing the thermal stress of turbine shafts as ramp rate constraints in the thermal commitment and dispatch of generating units. The paper uses Lagrangian relaxation for optimal generation scheduling. In applying the unit commitment, thermal stress over the elastic limit is used for calculating the ramping cost. The thermal stress contribution to generation cost requires the calculation of a set that includes thermal stress at the end of each time step; this requirement presents a complicated problem which cannot be solved by an ordinary optimization method such as dynamic programming. The paper uses an improved simulated annealing method to determine the optimal trajectory of each generating unit. Furthermore, the paper uses linear programming for economic dispatch in which thermal stress limits are incorporated in place of fixed ramp rate limits. The paper illustrates the economics of frequently ramping up/down of low cost generating units versus the cost of replacement of their turbine rotors with a shorter life span. The experimental results for a practical system demonstrate the effectiveness of the proposed method in optimizing the power system generation scheduling.     

考虑非凸曲线的电力市场交易计划方法

文中以二次规划算法解决了电力市场环境下考虑爬坡约束的短期发电计划制定问题，该方法的主要思想是将每台机组的报价曲线处理成一报价区域，从而将优化问题变成标准的二次规划形式，进而运用二次规划算法求解，这种方法还可以解决任意形状报价曲线给交易算法带来的困难，用一简单系统的实际计算验证了该方法的有效性。     

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     

The impacts of capabilities and constraints of generating units on simultaneous scheduling of energy and primary reserve

Frequency control, as an ancillary service, is usually provided by generation reserves. Modern generating units have special technical capabilities; e.g., their governor operation mode can be selected to be either active or passive, their ramp rate can be selected to be either normal or fast, etc. On the other hand, generating units have some technical constraints; e.g. some generating units cannot participate in primary frequency control at their capacity limits. In this paper, operational capabilities and constraints of generating units are incorporated in a “simultaneous scheduling of energy and primary reserve” problem. Furthermore, a heuristic iterative method (based on genetic algorithm) is proposed to obtain the optimal scheduling. The impacts of capabilities and constraints on scheduling are investigated through simulation studies. Simulation results depicts that taking these capabilities and constraints of generating units into account, not only reduces the total operational cost of generating units, but also will end up with a feasible solution for the system, even in cases where the previously proposed methods fail.     

Daily generation scheduling optimization with transmissionconstraints: a new class of algorithms

The authors describe a novel class of algorithm dealing with the daily generation scheduling (DGS) problem. These algorithms have been designed by adding artificial constraints to the original optimization problem; handling these artificial constraints by using a dual approach; using an augmented Lagrangian technique rather than a standard Lagrangian relaxation technique; and applying the auxiliary problem principle which can cope with the nonseparable terms introduced by the augmented Lagrangian. To deal with the DGS optimization problem these algorithms are shown to be more effective than classical ones. They are well suited to solve this DGS problem taking into account transmission constraints     

A new approach to security-constrained generation scheduling of large-scale power systems with a piecewise linear ramping model

This paper presents a new and efficient approach to determine security-constrained generation scheduling (SCGS) in large-scale power systems, taking into account dispatch, network, and security constraints in pre and post-contingency states. A novel ramp rate limit is also modeled as a piecewise linear function in the SCGS problem to reflect more practical characteristics of the generating units. Benders decomposition is applied to this constrained solution process to obtain an optimal SCGS problem based on mixed-integer nonlinear programming (MINLP). The formulation can be embedded in two stages. First, a MIP is formulated in the master problem to solve a unit commitment (UC) problem. This stage determines appropriate on/off states of the units. The second stage, the subproblem, is formulated as a NLP to solve a security-constrained economic dispatch (SCED) problem. This stage is used to determine the feasibility of the master problem solution. It provides information to formulate the benders cuts that connect both problems. The proposed approach is tested in the IEEE 118-bus system to show its effectiveness. The simulation results are more realistic and feasible, whilst assuring an acceptable computation time.     

Lagrangian relaxation hybrid with evolutionary algorithm for short-term generation scheduling

Short-term generation scheduling is an important function in daily operational planning of power systems. It is defined as optimal scheduling of power generators over a scheduling period while respecting various generator constraints and system constraints. Objective of the problem includes costs associated with energy production, start-up cost and shut-down cost along with profits. The resulting problem is a large scale nonlinear mixed-integer optimization problem for which there is no exact solution technique available. The solution to the problem can be obtained only by complete enumeration, often at the cost of a prohibitively computation time requirement for realistic power systems. This paper presents a hybrid algorithm which combines Lagrangian Relaxation (LR) together with Evolutionary Algorithm (EA) to solve the problem in cooperative and competitive energy environments. Simulation studies were carried out on different systems containing various numbers of units. The outcomes from different algorithms are compared with that from the proposed hybrid algorithm and the advantages of the proposed algorithm are briefly discussed.     

Hydroelectric generation scheduling with an effective differentialdynamic programming algorithm

An effective multiplier method-based differential dynamic programming (DDP) algorithm for solving the hydroelectric generation scheduling problem (HSP) is presented. The algorithm is developed for solving a class of constrained dynamic optimization problems. It relaxes all constraints but the system dynamics by the multiplier method and adopts the DDP solution technique to solve the resultant unconstrained dynamic optimization problem. The authors formulate the HSP of the Taiwan power system and apply the algorithm to it. Results demonstrate the efficiency and optimality of the algorithm for this application. Computational results indicate that the growth of the algorithm's run time with respect to the problem size is moderate. CPU times of the testing cases are well within the Taiwan Power Company's desirable performance; less than 30 minutes on a VAX/780 mini-computer for a one-week scheduling     

Constraint programming for nurse scheduling

Nurse scheduling is a difficult, multifaceted problem. Here, the authors have presented the efficiency of Constraint Programming for solving this problem. The results obtained are very satisfactory for response time and for flexibility. The advantages of implementing this method are multiple: 1) it saves much time for the head nurse in the generation of schedules (the authors met head nurses for whom the task of scheduling takes a full working day); 2) the proposed system is not a rigid tool for schedule generation, but it is designed to help the decision maker in decisions and negotiations; 3) the proposed system is a flexible tool with respect to individual requests and for overcoming unforeseen absences; 4) it is very easy to manage constraints whether, for example, to define new constraints, activating or deactivating particular constraints, or modifying an already defined constraint. Ilog-Solver is a powerful tool for constraint programming. It provides the user with several types of variables, and the possibility of defining a specific constraint for the problem. The integration of object programming provided by Ilog-Solver allows better representation and saves much memory     

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.     

确定机组组合的一种改进的动态规划方法

提出了一种确定机组组合的改进动态规划方法,称为插值动态规划算法。这是一种启发式方法,可以和其他的经济调度算法相结合,用以解决多种约束条件下的机组组合问题,特别是可以处理机组功率上升、下降速度约束,且考虑了机组的开、停机特性、并有效避免了“维数灾”问题,经实践检验是一种简单、有效的实用算法。     

应用粒子群优化算法求解市场环境下的电力系统动态经济调度问题

在竞争性的电力市场环境下,为了获得最大化的社会利润,提出了基于竞价机制的动态经济调度模型,该模型综合考虑了发电机组的爬坡约束、输电线路的容量约束和污染气体排放量的约束。针对该模型,提出了一种新的求解方法:粒子群优化算法(PSO)。算例的结果表明,PSO算法能够有效地得到一个高性能的优化调度结果     

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     

Optimum short-term hydrothermal scheduling with spinning reservethrough network flows

Optimizing the thermal production of electricity in the short term in an integrated power system when a thermal unit commitment has been decided means coordinating hydro and thermal generation in order to obtain the minimum thermal generation costs over the time period under study. Fundamental constraints to be satisfied are the covering of each hourly load and satisfaction of spinning reserve requirements and transmission capacity limits. A nonlinear network flow model with linear side constraints with no decomposition into hydro and thermal subproblems was used to solve the hydrothermal scheduling. Hydrogeneration is linearized with respect to network variables and a novel thermal generation and transmission network is introduced. Computational results are reported     

考虑大规模可再生能源接入的输电设备检修计划

随着可再生能源的快速发展,对于高电压等级(500 kV及以上和部分220/330 kV)的输电设备检修计划编制,必须考虑可再生能源输送能力的保障。为此,提出了一种大电网输电设备检修计划编制方法。利用等效负荷的概率密度函数和日最小开机出力计算弃风电量,作为检修计划的优化目标之一;针对光伏、水电的特性分别提出适合其外送通道设备检修的时段。考虑输电断面运行安全,建立了基于多约束条件的大电网检修计划模型,采用混合整数规划方法对该模型进行求解。以实际电网的年度检修计划编制作为算例进行了验证。     

A solution to the ramp rate and prohibited operating zone constrained unit commitment by GHS-JGT evolutionary algorithm

Unit commitment (UC) problem on a large scale with the ramp rate and prohibited zone constraints is a very complicated nonlinear optimization problem with huge number of constraints. This paper presents a new hybrid approach of ’Gaussian Harmony Search’ (GHS) and ’Jumping Gene Transposition’ (JGT) algorithm (GHS-JGT) for UC problem. In this proposed hybrid GHS-JGT for UC problem, scheduling variables are handled in binary form and other constants directly through optimum conditions in decimal form. The efficiency of this method is tested on ten units, forty units and hundred units test system. Simulation results obtained by GHS-JGT algorithm for each case show a better generation cost in less time interval, in comparison to the other existing results.     

Optimal power scheduling of thermal units considering emission constraint for GENCOs’ profit maximization

In this paper, authors propose a novel method to determine an optimal solution for profit based unit commitment (PBUC) problem considering emission constraint, under a deregulated environment. In a restructured power system, generation companies (GENCOs) schedule their units with the aim of maximizing their own profit by relaxing demand fulfillment constraints without any regard to social benefits. In the new structure, due to strict reflection of power price in market data, this factor should be considered as an important ingredient in decision-making process. In this paper a social-political based optimization algorithm called imperialist competitive algorithm (ICA) in combination with a novel meta-heuristic constraint handling technique is proposed. This method utilizes operation features of PBUC problem and a penalty factor approach to solve an emission constrained PBUC problem in order to maximize GENCOs profit. Effectiveness of presented method for solving non-convex optimization problem of thermal generators scheduling in a day-ahead deregulated electricity market is validated using several test systems consisting 10, 40 and 100 generation units.     

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.     

Feasible solution for dynamic economic load dispatch using feasible operation region

High penetration of renewable energy in the future power system will pose a big problem to the load dispatch operation. The large disturbance and high forecast error must be considered when scheduling a limited number of controllable generators to follow rapid change in load. This paper proposes a dynamic economic load dispatch (DELD) problem approach based on the concept of a feasible operation region (FOR). FOR is defined as the region that committed generators may operate in to match the load profile without violating the ramp‐rate constraints. The DELD problem is solved in two stages. In the first stage, FOR of each generator is computed using recent real‐time forecasted load as well as renewable energy generation. In the second stage, a generation schedule is determined by solving the DELD problem interval by interval while considering ramp‐rate constraints and FOR constraints. The method can gives feasible solution for feasible load and specify the amount of compensation required for feasible solution for infeasible load. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

考虑服务配置的细粒度电力任务云边协同优化调度策略

新型电力系统的建设促使电力业务范围向用户侧深入,业务种类及数量不断增加。边设备资源有限,只能配置有限数量的服务,任务的时延能耗需求与设备资源有限的矛盾日益突出。为实现云边资源协同与任务的优化调度,提出了一种考虑服务配置的细粒度电力任务云边协同优化调度策略。通过建立微服务的时延与能耗模型,并对任务调度中的约束条件进行分析,将时延与能耗的优化决策问题转化为带约束的多目标优化问题,采用NSGA-Ⅱ算法求解。然后通过基于模糊逻辑的多准则决策方法为任务选择调度方案。仿真结果表明,所提策略在时延和能耗方面的性能优于其他策略,能够适应不同的任务场景并做出最优决策,提高了任务的完成率。