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.     

A new unit commitment method

This paper introduces a new unit commitment method based on a decommitment procedure for solving the power system resource scheduling problem. From an initial schedule of all available units committed over the study period, a `one-at-a-time' unit decommitment is accomplished by dynamic programming according to some specified economic criteria. The decommitment process continues until no further reduction in total cost is possible, or the unit schedules of two consecutive iterations over the time period remain unchanged without any violation of the spinning reserve constraint. Two criteria for decommiting a unit are introduced and described in detail. Comparisons of the proposed unit commitment method with the Lagrangian relaxation (LR) approach and Fred Lee's sequential unit commitment method (SUC) demonstrate the potential benefits of the proposed approach for power system operations planning     

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.     

Scheduling of hydrothermal power systems

The authors present a method for scheduling hydrothermal power systems based on the Lagrangian relaxation technique. By using Lagrange multipliers to relax system-wide demand and reserve requirements, the problem is decomposed and converted into a two-level optimization problem. Given the sets of Lagrange multipliers, a hydro unit subproblem is solved by a merit order allocation method, and a thermal unit subproblem is solved by using dynamic programming without discretizing generation levels. A subgradient algorithm is used to update the Lagrange multipliers. Numerical results based on Northeast Utilities data show that this algorithm is efficient, and near-optimal solutions are obtained. Compared with previous work where thermal units were scheduled by using the Lagrangian relaxation technique and hydro units by heuristics, the new coordinated hydro and thermal scheduling generates lower total costs and requires less computation time     

基于粒子群修正策略的机组组合解耦算法

机组组合问题是电力系统优化运行的一个难点,理论上难以得到最优解。提出了一种基于粒子群修正策略的解耦算法。首先采用集结投影次梯度的拉格朗日松弛算法得到机组组合的对偶解;然后依据对偶信息中的备用乘子及对偶组合状态建立粒子群优化空间;而后利用无约束的标准粒子群优化算法实现拉格朗日乘子的局部更新,通过粒子的调整和粒子间信息的传递改变机组启停,进而修正拉格朗日对偶解,最终得到机组组合问题的近似最优解。6个系统的仿真计算验证了该方法的求解速度及计算精度。     

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     

基于改进拉格朗日乘子修正方法的逆序排序机组组合

机组组合与经济调度是两个不同范畴的优化决策问题,其优化过程在概念上有本质的区别。用经济调度中的拉格朗日乘子对机组组合中的乘子进行修正有概念含混的误区。文章在阐明机组组合与经济调度中拉格朗日乘子的差异及作用机理的基础上,提出了一种新的逆序排序机组组合中拉格朗日乘子的修正方法,并对机组的搜索范围及机组运行的经济指标作了相应的改进,使原有算法在精度和计算速度上均得到了显著提高。20机、26机及110机测试系统的计算结果表明了文中的改进方法是有效的,进一步增强了机组组合对大规模系统的适应性。     

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.     

一种求解机组组合问题的新型改进粒子群方法

将电力系统中机组组合这一复杂的多约束混合整数规划问题分解为具有整型变量和连续变量的两个优化子问题,提出采用改进离散二进制粒子群算法和标准粒子群算法相结合的双层嵌套方法,分别对外层机组的启、停状态变量和内层功率经济分配进行交替迭代优化求解。同时在算法中引入基于机组优先顺序的变异技术和修补策略,能有效地处理机组最短启、停时间约束,并提高算法的全局寻优能力和计算效率。通过对10机系统的算例计算,并同其他算法的结果进行比较分析,仿真结果表明新方法求解精度高、收敛速度快,从而验证了新方法的可行性和有效性。     

Unit commitment using a hybrid model between Lagrangian relaxation and genetic algorithm in competitive electricity markets

This paper presents a hybrid model between Lagrangian relaxation (LR) and genetic algorithm (GA) to solve the unit commitment problem. GA is used to update the Lagrangian multipliers. The optimal bidding curves as a function of generation schedule are also derived. An IEEE 118-bus system is used to demonstrate the effectiveness of the proposed hybrid model. Simulation results are compared with those obtained from traditional unit commitment.     

基于蚁群优化算法的机组最优投入

机组最优投入问题（optimal Unit Commitment,UC)是寻求1个周期内各个负荷水平下机组的最优组合方式及开停机计划，使运行费用为最小。该问题是一个高维数、非凸的、离散的、非线性的优化问题，很难找出理论上的最优解，但由于它能带来显著的经济效益，所以受到了国内外很多学者的广泛关注。作者尝试采用一种新型的模拟进化优化算法－－蚁群优化算法（ACO）来求解该问题。首先，利用状态、决策及作者提出的路径概念把UC设计成类似于旅行商（TSP）问题的模式，从而可以方便地利用ACO来求解。其次，由于ACO处理的是无约束优化问题，对于UC这一约束优化问题，提出了不同的方法来处理各种约束。用tabu表限制不满足旋转备用约束和机组最小启／停时间约束的状态；通过附加惩罚项来处理线路N安全性约束。数值算例验证了此算法的可行性和有效性。     

面向启发式调整策略和粒子群优化的机组组合问题

提出一种启发式调整策略和粒子群优化相结合的新方法求解电力系统中的机组组合(UC)问题.算法将UC问题分解为具有整型变量和连续变量的两个优化子问题,采用离散粒子群优化和等微增率相结合的双层嵌套方法对外层机组启、停状态变量和内层机组功率经济分配子问题进行交替迭代优化求解.同时构造了关机调整和替换调整两个启发式搜索策略对优化结果进行进一步局部微调以提高算法解决UC问题的全局寻优能力和计算效率,从而有效改善解的质量.以10～100台机组组成的5个测试系统为算例,通过与其他算法结果进行比较分析,验证了该方法的可行性和有效性.仿真结果表明该方法解决大规模机组组合问题具有求解精度高和收敛速度快的优势.     

A tabu search based hybrid optimization approach for a fuzzy modelled unit commitment problem

This article presents a solution model for the unit commitment problem (UCP) using fuzzy logic to address uncertainties in the problem. Hybrid tabu search (TS), particle swarm optimization (PSO) and sequential quadratic programming (SQP) technique (hybrid TS–PSO–SQP) is used to schedule the generating units based on the fuzzy logic decisions. The fitness function for the hybrid TS–PSO–SQP is formulated by combining the objective function of UCP and a penalty calculated from the fuzzy logic decisions. Fuzzy decisions are made based on the statistics of the load demand error and spinning reserve maintained at each hour. TS are used to solve the combinatorial sub-problem of the UCP. An improved random perturbation scheme and a simple method for generating initial feasible commitment schedule are proposed for the TS method. The non-linear programming sub-problem of the UCP is solved using the hybrid PSO–SQP technique. Simulation results on a practical Neyveli Thermal Power Station system (NTPS) in India and several example systems validate, the presented UCP model is reasonable by ensuring quality solution with sufficient level of spinning reserve throughout the scheduling horizon for secure operation of the system.     

基于改进离散粒子群算法的电力系统机组组合问题

提出一种新的离散粒子群算法。结合改进的自学习策略优化粒子群算法适用于求解电力系统中的机组组合（unit commitment,UC）问题。算法将UC问题分解为具有整型变量和连续变量的2个优化子问题,采用离散粒子群优化和原对偶内点法相结合的双层嵌套方法对外层机组启、停状态变量和内层机组功率经济分配子问题进行交替迭代优化求...     

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。     

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.     

Application embedded chaos search immune genetic algorithm for short-term unit commitment

This paper presents a Hybrid Chaos Search (CS) immune algorithm (IA)/genetic algorithm (GA) and Fuzzy System (FS) method (CIGAFS) for solving short-term thermal generating unit commitment (UC) problems. The UC problem involves determining the start-up and shutdown schedules for generating units to meet the forecasted demand at the minimum cost. The commitment schedule must satisfy other constraints such as the generating limits per unit, reserve and individual units. First, we combined the IA and GA, then we added the chaos search and the fuzzy system approach. This hybrid system was then used to solve the UC problems. Numerical simulations were carried out using three cases: 10, 20 and 30 thermal unit power systems over a 24 h period. The produced schedule was compared with several other methods, such as dynamic programming (DP), Lagrangian relaxation (LR), Standard genetic algorithm (SGA), traditional simulated annealing (TSA), and Traditional Tabu Search (TTS). A comparison with an IGA combined with the Chaos Search and FS was carried out. The results show that the Chaos Search and FS all make substantial contributions to the IGA. The result demonstrated the accuracy of the proposed CIGAFS approach.     

Using immune genetic algorithm based hybrid techniques for short-term unit commitment problem

This paper presents a hybrid chaos search (CS), immune algorithm (IA)/genetic algorithm (GA), and fuzzy system (FS) method (CIGAFS) for solving short-term thermal generating unit commitment (UC) problems. The UC problem involves determining the start-up and shut-down schedules for generating units to meet the forecasted demand at the minimum cost. The commitment schedule must satisfy other constraints such as the generating limits per unit, reserve, and individual units. First, we combined the IA and GA, then we added the CS and the FS approach. This hybrid system was then used to solve the UC problems. Numerical simulations were carried out using three cases: 10, 20, and 30 thermal unit power systems over a 24 h period. The produced schedule was compared with several other methods, such as dynamic programming (DP), Lagrangian relaxation (LR), standard genetic algorithm (SGA), traditional simulated annealing (TSA), and traditional Tabu search (TTS). A comparison with an immune genetic algorithm (IGA) combined with the CS and FS was carried out. The results show that the CS and FS all make substantial contributions to the IGA. The result demonstrated the accuracy of the proposed CIGAFS approach.     

Thermal power generation scheduling by simulated competition

This paper presents a new method for solving the unit commitment problem by simulation of a competitive market where power is traded through a power exchange (PX). Procedures for bidding and market clearing are described. The market clearing process handles the spinning reserve requirements and power balance simultaneously. The method is used on a standard unit commitment problem with minimum up/down times, start-up costs and spinning reserve requirement taken into account. Comparisons with solutions provided by Lagrangian relaxation, genetic algorithms and Chao-an Li's unit decommitment procedure demonstrate the potential benefits of this new method. The motivation for this work was to design a competitive electricity market suitable for thermal generation scheduling. However, performance in simulations of the proposed market has been so good that it is presented here as a solving technique for the unit commitment problem     

一种用于机组组合问题的改进双重粒子群算法

为了更经济快速地解决机组组合问题,提出一种改进双重粒子群优化(particle swarm optimization,PSO)算法,包含离散部分和连续部分。离散PSO分时段优化机组的启停状态,在种群更新时加入了临界算子,改进了可行解的判别条件,各机组出力最低值的和要在一定程度上低于负荷需求值,并考虑机组启停时间的向前继承和向后约束。连续PSO用于启停状态确定过程中和确定后的负荷分配,考虑功率平衡约束、热备用约束和机组的出力上下限约束。求解经济负荷分配时,利用罚函数的方法满足机组的爬坡速率约束,最后得到煤耗最小值。采用2个24时段的算例进行仿真,实验结果表明新算法减少了搜索量,提高了收敛速度,并为机组组合问题提出了新思路。