Short-term hydrothermal scheduling using clonal selection algorithm

An efficient optimization procedure based on the clonal selection algorithm (CSA) is proposed for the solution of short-term hydrothermal scheduling problem. CSA, a new algorithm from the family of evolutionary computation, is simple, fast and a robust optimization tool for real complex hydrothermal scheduling problems. Hydrothermal scheduling involves the optimization of non-linear objective function with set of operational and physical constraints. The cascading nature of hydro-plants, water transport delay and scheduling time linkage, power balance constraints, variable hourly water discharge limits, reservoir storage limits, operation limits of thermal and hydro units, hydraulic continuity constraint and initial and final reservoir storage limits are fully taken into account. The results of the proposed approach are compared with those of gradient search (GS), simulated annealing (SA), evolutionary programming (EP), dynamic programming (DP), non-linear programming (NLP), genetic algorithm (GA), improved fast EP (IFEP), differential evolution (DE) and improved particle swarm optimization (IPSO) approaches. From the numerical results, it is found that the CSA-based approach is able to provide better solution at lesser computational effort.     

电力市场环境下解决机组组合问题的新方法

机组组合问题是电力市场环境下编制短期发电计划所面临的主要问题,在满足各种约束条件的情况下,如何合理地开、停机组、以及负荷如何在运行的发电机组之间经济地分配是一个比较困难的问题,特别是由于发电机组出力上升、下降速度的限制,使这个问题一直没有很好的解决方法。提出一种组合优化方法解决这一问题,即用启发式方法确定机组组合,用分段线性规划算法分配功率,并满足各种约束条件,特别是可以处理发电机组出力上升、下降速度约束、经实际系统检验是一种非常有效的算法。     

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.     

Flexible generator maintenance scheduling based on subjective relaxation of constraints

This paper presents a fuzzy-based method for determining a flexible generator maintenance scheduling by means of subjective relaxation of constraints imposed on the maintenance scheduling problem. The constraints are divided into hard (crisp) constraint set and soft (fuzzy) constraint set according to reflecting conditions which surround power systems. The problem is formulated as a fuzzy mathematical programming problem and solved with the fuzzy branch-and-bound method using Bellman-Zadeh maximizing decision. The proposed approach provides not only a new flexible concept of planning problems in power systems, but also natural expansion of conventional approaches based on crisp set theory. The effectiveness and feasibility of the proposed approach are demonstrated on two typical power system models which consist of 15 generators and 60 generators, respectively.     

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     

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.     

计及风电考虑离散化发电调节约束的在线滚动调度方法

在线滚动调度是消纳大规模接入风电的重要环节,需要考虑包括机组调节次数以及出力离散化的发电调节约束。含这些发电调节约束的在线滚动调度模型是一个大规模的非线性混合整数规划问题,难以在有效的时间内完成严格的求解。文中提出一种考虑离散化发电调节约束的在线滚动调度的三阶段算法,其核心是一种具有多项式计算复杂度的前推-回推式动态规划算法。最后在IEEE 31节点系统和264节点系统上进行算例测试,以验证算法的高效性和实用性。     

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.     

Long‐Term Generation Scheduling Method with Constrained Numbers of Unit Commitment and Fuel Constraints on Thermal Units

The long‐term generation scheduling in power utilities is aimed at maintaining power supply sufficiency and estimating fuel consumption. Multiperiod constraints, such as the allowable number of unit commitments of thermal units and fuel consumption with a given total amount of fuel, must be taken into appropriate consideration for practical economic scheduling in the long‐term scheduling horizon. Due to the large size and complexity of such scheduling problems, it is difficult to obtain solutions collectively in terms of stability and processing time in operational situations. We propose a new scheduling method which consists of “preparative processing” and “detailed optimization processing.” The former acts to divide the long‐term problem with multiperiod constraints into time units of a week according to quick and simplified scheduling results, and the latter acts to minimize the total operation cost on the basis of those weekly partitioned problems. The processing starts with an optimal scheduling result excluding the aforementioned two multi‐period constraints and proceeds to sequentially resolve the violation of each constraint with quantitative consideration of interrelationships between them. This paper describes the validation and effectiveness of the proposed method through the real world example of Chubu Electric Power Company.     

An improved PSO technique for short-term optimal hydrothermal scheduling

This paper presents a new approach to the solution of optimal power generation to short-term hydrothermal scheduling problem, using improved particle swarm optimization (IPSO) technique. The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydraulic network, water transport delay and scheduling time linkage that make the problem of finding global optimum difficult using standard optimization methods. In this paper an improved PSO technique is suggested that deals with an inequality constraint treatment mechanism called as dynamic search-space squeezing strategy to accelerate the optimization process and simultaneously, the inherent basics of conventional PSO algorithm is preserved. To show its efficiency and robustness, the proposed IPSO is applied on a multi-reservoir cascaded hydro-electric system having prohibited operating zones and a thermal unit with valve point loading. Numerical results are compared with those obtained by dynamic programming (DP), nonlinear programming (NLP), evolutionary programming (EP) and differential evolution (DE) approaches. The simulation results reveal that the proposed IPSO appears to be the best in terms of convergence speed, solution time and minimum cost when compared with established methods like EP and DE.     

A Simulated Annealing based approach to solve the generator maintenance scheduling problem

The scheduling of maintenance actions of generators is not a new problem but gained in recent years a new interest with the advent of electricity markets because inadequate schedules can have a significative impact on the revenues of generation companies. In this paper we report the research on this topic developed during the preparation of the MSc Thesis of the second author. The scheduling problem of generator maintenance actions is formulated as a mixed integer optimization problem in which we aim at minimizing the operation cost along the scheduling period plus a penalty on energy not supplied. This objective function is subjected to a number of constraints detailed in the paper and it includes binary variables to indicate that a generator is in maintenance in a given week. This optimisation problem was solved using Simulated Annealing. Simulated Annealing is a very appealing metaheuristic easily implemented and providing good results in numerous optimization problems. The paper includes results obtained for a Case Study based on a realistic generation system that includes 29 generation groups. This research work was proposed and developed with the collaboration of the third and fourth authors, from EDP Produção, Portugal.     

A solution method using neural networks for the generator commitment problem

This paper studies the feasibility of applying the Hopfield-type neural network to unit commitment problems in a large power system. The unit commitment problem is to determine an optimal schedule of what thermal generation units must be started or shut off to meet the anticipated demand; it can be formulated as a complicated mixed integer programming problem with a number of equality and inequality constraints. In our approach, the neural network gives the on/off states of thermal units at each period and then the output power of each unit is adjusted to meet the total demand. Another feature of our approach is that an ad hoc neural network is installed to satisfy inequality constraints which take into account standby reserve constraints and minimum up/down time constraints. The proposed neural network approach has been applied to solve a generator scheduling problem involving 30 units and 24 time periods; results obtained were close to those obtained using the Lagrange relaxation method.     

Optimal Scheduling of Spinning Reserve with Transmission Constraints

An effective method is proposed to schedule spinning reserve optimally. The method considers the transmission constraint in the whole scheduling process. To get the feasible solution faster, transmission line limits are first relaxed using the Lagrangian Relaxation technique. In the economic dispatch, after unit generation and spinning reserve are allocated among the committed units to satisfy the system andunit constraints, the schedule is then modified by a linear programming algorithm to avoid line overloads. The schedule is then updated by a probabilistic reserve assessment to meet a given risk index. The optimal value of the risk index is selected via a cost/benefit analysis based on the tradeoff between the total Unit Commitment (UC) schedule cost and the expected cost of energy not served. Finally, a unit decommitment technique is incorporated to solve the problem of reserve over-commitment in the Lagrangian Relaxation–based UC. The results of reserve scheduling with the transmission constraint are shown by the simulation runs performed on the IEEE reliability test system.     

Dual programming methods for large-scale thermal generationscheduling

The problem of thermal generation scheduling is considered in the framework of the short-term hydro-thermal coordination problem. Dual programming methods are applied to the large-scale problem deriving from a fine subdivision of the daily optimization horizon for networks with hundreds of thermal units. The starting point for the dual approach is obtained from the solution of a thermal scheduling problem with discarded generation ramp-rate constraints. The relaxed daily scheduling decouples into as many smaller dispatch problems as the number of subintervals. Two dual programming methods are implemented: the former is the dual active set algorithm by Goldfarb and Idnani while the latter is based on the application of continuation method techniques. These approaches are extensively tested with reference to both a small sample system and to the daily thermal generation scheduling of the Italian (ENEL) system (over 100 thermal units and 96 quarter hour subintervals). Incorporating the dual programming approach within the ENEL hydro-thermal coordination procedure is also considered     

基于连续线性规划的梯级水电站优化调度

梯级水电站优化调度是一个多时段、多变量和多约束条件的大规模优化问题,其求解过程非常复杂。文章尝试采用连续线性规划的优化方法来解决梯级水电站长期优化调度问题。通过采用泰勒级数一阶描述形式,对优化调度目标函数和约束条件中的非线性约束进行线性化处理,建立了基于连续线性规划算法的优化调度数学模型,提出了用连续线性规划技术求解梯级水电站优化调度问题的算法,并采用迭代步长的动态比例缩减因子保证算法能快速准确地收敛到优化问题的最优解。利用Matlab7.0编制连续线性规划梯级水电站优化调度程序,一个两级梯级水电站群的仿真分析结果表明,该算法可用于求解梯级水电站优化调度问题,并可快速得到非线性问题的最优解。     

Optimal short-term scheduling for a large-scale cascaded hydrosystem

This paper describes a short term hydro generation optimization program that has been developed by the Hydro Electric Commission (HEC) to determine optimal generation schedules and to investigate export and import capabilities of the Tasmanian system under a proposed DC interconnection with mainland Australia. The optimal hydro scheduling problem is formulated as a large scale linear programming algorithm and is solved using a commercially-available linear programming package. The selected objective function requires minimization of the value of energy used by turbines and spilled during the study period. Alternative formulations of the objective function are also discussed. The system model incorporates the following elements: hydro station (turbine efficiency, turbine flow limits, penstock head losses, tailrace elevation and generator losses), hydro system (reservoirs and hydro network: active volume, spillway flow, flow between reservoirs and travel time), and other models including thermal plant and DC link. A valuable by-product of the linear programming solution is system and unit incremental costs which may be used for interchange scheduling and short-term generation dispatch     

Further developments in LP-based optimal power flow

The authors describe developments that have transformed the LP (linear programming) approach into a truly general-purpose OPF (optimal power flow) solver, with computational and other advantages over even recent nonlinear programming (NLP) methods. it is pointed out that the nonseparable loss-minimization problem can now be solved, giving the same results as NLP on power systems of any size and type. Coupled formulations, where for instance voltages and VAr become constraints on MW scheduling, are handled. Former limitations on the modeling of generator cost curves have been eliminated. In addition, the approach accommodates a large variety of power system operating limits, including the very important category of contingency constraints. All of the reported enhancements are fully implemented in the production OPF software described here, and most have already been utilized within the industry     

含海上风储联合发电系统的韧性调度策略

为应对台风诱发的海上风电机组高风停机(high wind-speed shutdown, HWSS)事件,提出了一种含风储联合发电系统的多时间尺度协调调度方法。首先,基于历史和即时信息进行台风全生命周期模拟,得到强度时变的台风轨迹集合;基于台风轨迹和风电出力曲线,进一步计算该台风轨迹集合下风电场的可用出力,并纳入所提出的模糊集合中。其次,考虑风电出力波动对各类型备用需求的影响,提出了多类型备用需求的次小时级调度框架,以避免机组小时阶跃变化造成调度方法不可行的风险。然后,在此基础上,通过确定性转化形成可求解的混合整数线性规划问题。最后,在增加了2个海上风电场的IEEE-RTS系统上进行了仿真实验。实验结果表明,所提出的调度策略能够在台风极端天气下,充分利用风储联合发电系统的灵活性,通过预调度提升系统韧性。     

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CCHP的工业大用户综合能源系统扩展规划

工业大用户是一个多能源综合供给系统,传统的工业大用户综合能源系统(integrated energy system,IES)规划忽略了多种能源的参与.计及冷热电联供系统(combined cooling,heating and power,CCHP),考虑多能梯级利用及其与可转移生产任务的耦合关系,文章建立了工业大用户...