Emerging solution of large-scale unit commitment problem by Stochastic Priority List

This paper presents a new approach for unit commitment problem using Stochastic Priority List method. In this method, rapidly some initial unit commitment schedules are generated by Priority List method and priority based stochastic window system. Excess units are added with system dependent probability distribution to avoid overlooking a desired solution during repeated search. Constraints are not considered in this stage. Then schedules are modified gradually using the problem specific heuristics to fulfill constraints. To reduce calculations, heuristics are applied only to the solutions, which can be expected to improve. Besides, sign vector is introduced to reduce economic load dispatch (ELD) overhead recalculations. This process is repeated for optimal solution. The proposed method is tested using the reported problem data set. Simulation results for the systems up to 100-unit are compared to previous reported results. Numerical results show an improvement in solution cost and time compared to the results obtained from Genetic Algorithm and others.     

Large-scale decentralized unit commitment

A method for formulating and solving a decentralized unit commitment problem is presented in this work. The method, which extends the alternating direction method of multipliers (ADMM), is presented along with several heuristics and refinements to mitigate oscillations and traps in local optimality that result from the nonconvexity of unit commitment. We present and discuss the promising results from testing the method on large-scale systems of more than 3000 buses. The scalability observed so far suggests that this method is a practical option for use with large systems and may provide a significant benefit for computational speed.     

Stochastic Hopfield artificial neural network for unit commitment and economic power dispatch

This paper presents a Hopfield artificial neural network for unit commitment and economic power dispatch. The dual problem of unit commitment and economic power dispatch is an example of a constrained mixed-integer combinatorial optimization. Because of uncertainties in both the system load demand and unit availability, the unit commitment and economic power dispatch problem is stochastic. In this paper we model forced unit outages as independent Markov processes, and load demand as a normal Gaussian random variable. The (0,1) unit commitment-status variables and the hourly unit loading are modelled as sample functions of appropriate random processes. The problem variables over which the optimization is done are modelled as sample functions of random processes which are described by Ito stochastic differential equations. The method is illustrated by a simple example of a power system having three machines which are committed and dispatched over a four-hour period. In the method, unit commitment and economic dispatch are done simultaneously.     

Optimal generation scheduling with ramping costs

In this paper, a decomposition method is proposed which relates the unit ramping process to the cost of fatigue effect in the generation scheduling of thermal systems. The objective of this optimization problem is to minimize the system operation cost, which includes the fuel cost for generating the required electrical energy and starting up decommitted units, as well as the rotor depreciation during ramping processes, such as starting up, shutting down, loading, and unloading. According to the unit fatigue index curves provided by generator manufacturers, fixed unit ramping-rate limits, which have been used by previous studies, do not reflect the physical changes of generator rotors during the ramping processes due to the fatigue effect. By introducing ramping costs, the unit on/offstates can be determined more economically by the proposed method. The Lagrangian relaxation method is proposed for unit commitment and economic dispatch, in which the original problem is decomposed into several subproblems corresponding to the optimization process of individual units. The network model is employed to represent the dynamic process of searching for the optimal commitment and generation schedules of a unit over the entire study time span. The experimental results for a practical system demonstrate the effectiveness of the proposed approach in optimizing the power system generation schedule     

A Method for Solving the Fuel Constrained Unit Commitment Problem

The unit commitment problem involves finding the hourly commitment schedule for the thermal units of an electrical system, and their associated generation, over a period of up to a week. For some utilities, contractual or other factors limit the amount of fuel available to certain of the units or plants. This paper describes a new method which solves the unit commitment problem in the presence of fuel constraints. The method uses a Lagrangian decomposition and successive approximation technique for solving the unit commitment problem where the generation, reserve and fuel constraints are adjoined onto the cost function using Lagrange multipliers. All important operating constraints have been incorporated including minimum up and down times, standby operation, ramping limits, time-dependent start-up cost, spinning and supplemental reserve. The method is being applied to a production-grade program suitable for Energy Management Systems applications.     

Enhanced techniques on sequential unit commitment with interchangetransactions

This paper presents two enhanced techniques for improving the solution optimality and computation performance of the sequential unit commitment (SC) method with interchange transactions. The conventional SC method, although often presenting superior performance over other methods, can lead to nonnear-optimal solutions in some circumstances due to the use of a local decision scheme to identify the best unit to be committed at each stage. The proposed technique, instead, uses a global-like decision scheme. It defines a small set of locally advantageous units which are individually examined globally by generating tentative commitment schedules to identify the globally best unit to commit at each stage. Studies have shown that the global-like decision scheme can effectively improve the solution optimality. Meanwhile, while an interchange transaction is incorporated with the unit commitment study, the constant transaction price often causes solution oscillation during iterations. A varying-λ technique is proposed in this paper. This technique properly models the impact of the interchange transactions on the power system hourly energy prices and, hence, successfully overcomes the oscillation problem such that the loading level of a transaction can be optimally determined similarly as for a generating unit     

Unit commitment using hybrid models: a comparative study for dynamic programming, expert system, fuzzy system and genetic algorithms

Hybrid models for solving unit commitment problem have been proposed in this paper. To incorporate the changes due to the addition of new constraints automatically, an expert system (ES) has been proposed. The ES combines both schedules of units to be committed based on any classical or traditional algorithms and the knowledge of experienced power system operators. A solution database, i.e. information contained in the previous schedule is used to facilitate the current solution process. The proposed ES receives the input, i.e. the unit commitment solutions from a fuzzy-neural network. The unit commitment solutions from the artificial neural network cannot offer good performance if the load patterns are dissimilar to those of the trained data. Hence, the load demands, i.e. the input to the fuzzy-neural network is considered as fuzzy variables. To take into account the uncertainty in load demands, a fuzzy decision making approach has also been developed to solve the unit commitment problem and to train the artificial neural network. Due to the mathematical complexity of traditional techniques for solving unit commitment problem and also to facilitate comparison genetic algorithm, a non-traditional optimization technique has also been proposed. To demonstrate the effectiveness of the models proposed, extensive studies have been performed for different power systems consisting of 10, 26 and 34 generating units. The generation cost obtained and the computational time required by the proposed model has been compared with the existing traditional techniques such as dynamic programming (DP), ES, fuzzy system (FS) and genetic algorithms (GA).     

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。     

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 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     

An interior-point/cutting-plane method to solve unit commitmentproblems

An interior-point/cutting-plane method for nondifferentiable optimization is used to solve the dual to a unit commitment problem. The interior-point/cutting-plane method has two advantages over previous approaches, such as the sub-gradient and bundle methods: first, it has better convergence characteristics; and second, does not suffer from the parameter-turning drawback. The results of a performance testing using systems with up to 104 units confirm the superiority of the interior-point/cutting-plane method over previous approaches     

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 solution method of unit commitment by artificial neural networks

The authors explore the possibility of applying the Hopfield neural network to combinatorial optimization problems in power systems, in particular to unit commitment. A large number of inequality constraints included in unit commitment can be handled by dedicated neural networks. As an exact mapping of the problem onto the neural network is impossible with the state of the art, a two-step solution method was developed. First, generators to be stored up at each period are determined by the network, and then their outputs are adjusted by a conventional algorithm. The proposed neural network could solve a large-scale unit commitment problem with 30 generators over 24 periods, and results obtained were very encouraging     

市场竞争条件下发电机组启停机计划优化研究

探讨市场竞争条件下的发电机组启停机计划问题有助于发电厂制定发电机组安全经济运行方案。文章以发电厂收益最大化为目标函数,考虑了无功和备用收益的影响,以机组本身的可用状态、发电功率限制、爬坡速率以及系统备用容量和电力市场交易等为约束条件,构造了市场竞争条件下发电机组启停机计划问题的数学模型,并提出了一种综合了二次规划、遗传算法、模拟退火算法的优点的混合优化方法进行解算。对某8机系统进行的算例分析表明:市场竞争条件下考虑了备用收入影响的发电厂启停机计划发生了一些变化;发电厂为了追求更大的收益更加注重生产成本问题;其通过竞争获得的发电功率直接影响发电机组启停计划及其功率分配;文中提出的混合优化算法较适用于求解市场条件下的启停机计划等优化问题。     

A solution for unit commitment using Lagrangian relaxation combined with evolutionary programming

This paper proposes an approach which combines Lagrangian relaxation principle and evolutionary programming for short-term thermal unit commitment. Unit commitment is a complex combinatorial optimization problem which is difficult to be solved for large-scale power systems. Up to now, the Lagrangian relaxation is considered the best to deal with large-scale unit commitment although it cannot guarantee the optimal solution. In this paper, an evolutionary programming algorithm is used to improve a solution obtained by the Lagrangian relaxation method: Lagrangian relaxation gives the starting point for a evolutionary programming procedure. The proposed algorithm takes the advantages of both methods and therefore it can search a better solution within short computation time. Numerical simulations have been carried out on two test systems of 30 and 90 thermal units power systems over a 24-hour periods.     

机组组合随机模型及其算法简介

电力系统中的机组组合问题是在满足系统负荷和备用要求以及机组运行的技术条件约束的情况下,确定未来一段时期内的各机组的开、停机时间并在机组间分配负荷,以使系统总成本达到最小,获取最大的经济效益.文章给出在不确定的荷载需求下机组组合问题的一些常见的随机规划模型和算法的综述.     

Unit commitment using Lagrangian relaxation and particle swarm optimization

Unit commitment (UC) is a NP-hard nonlinear mixed-integer optimization problem. This paper proposes ELRPSO, an algorithm to solve the UC problem using Lagrangian relaxation (LR) and particle swarm optimization (PSO). ELRPSO employs a state-of-the-art powerful PSO variant called comprehensive learning PSO to find a feasible near-optimal UC schedule. Each particle represents Lagrangian multipliers. The PSO uses a low level LR procedure, a reserve repairing heuristic, a unit decommitment heuristic, and an economic dispatch heuristic to obtain a feasible UC schedule for each particle. The reserve repairing heuristic addresses the spinning reserve and minimum up/down time constraints simultaneously. Moreover, the reserve repairing and unit decommitment heuristics consider committing/decommitting a unit for a consecutive period of hours at a time in order to reduce the total startup cost. Each particle is initialized using the Lagrangian multipliers obtained from a LR that iteratively updates the multipliers through an adaptive subgradient heuristic, because the multipliers obtained from the LR tend to be close to the optimal multipliers and have a high potential to lead to a feasible near-optimal UC schedule. Numerical results on test thermal power systems of 10, 20, 40, 60, 80, and 100 units demonstrate that ELRPSO is able to find a low-cost UC schedule in a short time and is robust in performance.     

A practical hydro, dynamic unit commitment and loading model

We describe the dynamic unit commitment and loading (DUCL) model that has been developed for use in real-time system operations at BC Hydro (BCH) to determine the optimal hydroelectric unit generation schedules for plants with multiple units and complex hydraulic configurations. The problem is formulated and solved with a novel procedure that incorporates three algorithms. First, an expert system is used to eliminate infeasible and undesirable solutions. Second, dynamic programming is used to solve the optimal static unit commitment problem for a given plant loading, feasible unit combinations, and current hydraulic conditions. Third, the DUCL problem is formulated and solved as a large-scale network problem with side constraints. Output from the model includes DUCL schedules, spinning and operating reserve, and trades curves such as that between water usage and the number of unit switches. The innovative use of the procedure allows the model to effectively schedule hydro units for the energy and capacity markets in real-time. Application of the method is demonstrated by determining the 24-time-step DUCL schedule for a 2700 MW plant with ten units of four different unit types     

计及风电不确定性的多场景多时段安全约束机组组合解耦求解方法

为了加速求解计及风电不确定性的安全约束机组组合问题,提出计及风电不确定性的多场景多时段安全约束机组组合解耦求解方法。将原问题解耦为多个场景的安全约束机组组合问题;通过将各场景的调度时段分为多个子时段对各场景安全约束机组组合问题进行解耦,形成多个并行的子问题;为了确保多场景解耦和多时段解耦解的可行性,利用一致性约束耦合不同的子问题,并在目标函数中添加惩罚项。通过算例分析验证了所提方法的有效性。结果表明,在可接受的精度下,所提方法比传统集中式方法显著缩短了多场景安全约束机组组合问题的求解时间。     

Unit commitment scheduling by Lagrange relaxation method taking into account transmission losses

Since the application of the Lagrange relaxation method to the unit commitment scheduling by Muckstadt in 1979, many papers using this method have been published. The greatest advantage of applying the Lagrange relaxation method for the unit commitment problem is that it can relax (ignore) each generator's output dependency caused by the demand–supply balance constraint so that a unit commitment of each generator is determined independently by dynamic programming. However, when we introduce the transmission loss into the demand–supply balance constraint, we cannot decompose the problem into the partial problems in which each generator's unit commitment is determined independently and have to take some measures to obtain an optimal schedule by the Lagrange relaxation method directly. In this paper, we present an algorithm for the unit commitment schedule using the Lagrange relaxation method for the case of taking into account transmission losses. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 152(4): 27–33, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20119