A genetic algorithm solution to the unit commitment problem

This paper presents a genetic algorithm (GA) solution to the unit commitment problem. GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms such as natural selection, genetic recombination and survival of the fittest. A simple GA algorithm implementation using the standard crossover and mutation operators could locate near optimal solutions but in most cases failed to converge to the optimal solution. However, using the varying quality function technique and adding problem specific operators, satisfactory solutions to the unit commitment problem were obtained. Test results for power systems of up to 100 units and comparisons with results obtained using Lagrangian relaxation and dynamic programming are also reported     

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     

机组优化组合的人工神经网络拉格朗日混合方法

本文提出了一种求解电力系统组合优化问题的混合神经网络－拉格朗日方法，至今，拉格朗日枪驰法－直被记是机组优化组合近解的实用方法，这样，基于神经网络的监督学习和自适应识别概念，我们用神经网络来推测负荷需求与拉格朗日乘子的非线性关系，并且采用了优化的学习速率和势态项来加速网络的收敛，数值计算的结果表明本文的方法是可行的。     

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     

考虑多种约束条件的机组组合新算法

提出了考虑系统降出力备用约束、机组出力变化速率、线路潮流约束和断面传输功率约束的机组组合新算法。算法没有引入任何乘子,计算单调收敛,速度快,并且不需要初始可行解。用ＩＥＥＥ ２４母线系统对算法进行了验证,结果表明,算法对各种约束条件的处理正确,解的质量好。     

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.     

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.     

考虑交流潮流约束的机组组合并行解法

针对传统机组组合模型的种种不足,该文提出了一种考虑交流潮流约束及静态安全约束的机组组合模型,并给出了一种完整的并行化解法。该法借助于扩展拉格朗日松弛法和变量复制技术,将原问题转换为其对偶问题,并利用附加问题原理将对偶问题分解为动态规划和最优潮流(OPF)子问题。对于OPF子问题,采用鲁棒性好、收敛速度快的预测校正内点法求解,同时在求解过程中,采用并行处理技术。IEEE118节点及IEEE300节点仿真结果表明,该方法收敛性好,非常适合并行处理。     

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     

有抽水蓄能电站的联合电力系统优化调度模型和算法

本文介绍了一组有抽水蓄能电厂的电力系统优化调度的模型和算法，包括机组的最优起停。用Ｌａｇｒａｎｇｉａｎ松弛法将问题问题分解为多个子系统，对协调级建议一种灵敏系数法代替常规的次梯度法、速度快适应性好；火电机组组合彩分解的方法；对抽水蓄能电厂的模型作了详细的描述，考虑了上、下游水库水位变化的影响，提出一种最大增益网的算法，可最优选择日抽水量。相应的模型和算法已成功地用于实际系统，并用于运行计划及效益分     

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.     

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.     

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     

A combination of the genetic algorithm and lagrangian relaxation decomposition techniques for the generation unit commitment problem

Unit commitment involves the scheduling of generators in a power system in order to meet the requirements of a given load profile. An analysis of the basis for combining the genetic algorithm (GA) and Lagrangian relaxation (LR) methods for the unit commitment problem is presented. It is shown that a robust unit commitment algorithm can be obtained by combining the global search property of the genetic algorithm with the ability of the Lagrangian decomposition technique to handle all kinds of constraints such as pollution, unit ramping and transmission security.     

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.     

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     

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.     

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。     

考虑输电网络影响的火电机组优化组合的一种实用算法

提出一种考虑输电网络损耗及线路过负荷的火电机组优化组合的实用算法。用动态规划法建立一个初始解,运用启发式手法对初始解进行修正,使之逐个满足各约束条件,得到运行可能解,并通过更新发电机起动优先顺序使此过程反复进行直至得到(准)最佳解。在求解过程中引入最优潮流计算,使考虑输电网络损耗及线路过负荷等网络因素对发电机组优化组合的影响成为可能,并提出一种调节发电机出力和改变发电机组合相结合的消除线路过负荷的方法。在IEEE-118母线(36机)系统上对所提出的算法进行了各种条件下的仿真计算,考察了网络损耗及线路过负荷对发电机组优化组合的影响,验证了所提算法对解决考虑输电网络因素影响的发电机组优化组合问题的有效性。     

Cooperative coevolutionary algorithm for unit commitment

This paper presents a new cooperative coevolutionary algorithm (CCA) for power system unit commitment. CCA is an extension of the traditional genetic algorithm (GA) which appears to have considerable potential for formulating and solving more complex problems by explicitly modeling the coevolution of cooperating species. This method combines the basic ideas of Lagrangian relaxation technique (LR) and GA to form a two-level approach. The first level uses a subgradient-based stochastic optimization method to optimize Lagrangian multipliers. The second level uses GA to solve the individual unit commitment sub-problems. CCA can manage more complicated time-dependent constraints than conventional LR. Simulation results show that CCA has a good convergent property and a significant speedup over traditional GAs and can obtain high quality solutions. The "curse of dimensionality" is surmounted, and the computational burden is almost linear with the problem scale