Daily integrated generation scheduling for thermal,pumped‐storage,and cascaded hydro units and purchasing power considering network constraints

We have developed an innovative power generation scheduling method using quadratic programming (QP). The advantage of using our method is that it simultaneously solves unit commitment and economic load dispatch. We relax the binary variables of the unit state into continuous variables to apply QP to this problem. We also add a penalty term to converge the value of those variables to 0 or 1 to the objective function: the sum of the fuel costs and the start‐up costs. This penalty term depends on the per‐unit fuel cost. The possibility of its variable converging to zero increases as the cost increases. This method was applied to a test system of daily generation scheduling that consisted of 29 thermal units, two pumped‐storage units, four cascaded hydro units, and one transmission. The schedule satisfied all constraints, that is, load‐power balance, operation reserve, power flow, minimum up/down‐times, and fuel consumption. This result shows that the proposed method is effective. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 175(1): 25–34, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21014     

Unit commitment by genetic algorithm with specialized search operators

An approach for solving the unit commitment problem based on genetic algorithm with new search operators is presented. These operators, specific to the problem, are mutation with a probability of bit change depending on load demand, production and start-up costs of the generating units and transposition. The method incorporates time-dependent start-up costs, demand and reserve constraints, minimum up and down time constraints and units power generation limits. Repair algorithms or penalty factors in the objective function are applied to the infeasible solutions. Numerical results showed an improvement in the solution cost compared to the results obtained from genetic algorithm with standard operators and other techniques.     

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     

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.     

发电厂热备用容量的优化分配和成本分析

在竞争的发电市场环境下，备用作为一种重要的辅助服务，其成本分析是一个急待解决的问题，对发电厂热备用容量进行优化分配和成本分析，采用电能收益和备用容量收益总和最大化的目标函数。解算方法首先是根据发电厂总的发电负荷约束获得机组的经济组合，其次是将负荷在各机组间进行经济分配实现热备用容量的优化分配，热备用容量的成本采用其机会成本等值，方法简单，计算结果符合工程实际，研究结果表明，发电厂在计及备用收益和满足发电机组最低出力约束的条件下开机台数越多总收益也越大；在给定的时段和相应的电能电价下，备用容量成本随发电厂出力的增加而增加，在给定的时段和相应的发电出力下，备用容量成本随电价的增加而有较大的增加。     

改进整数变量辨识方法在机组组合问题中的应用

如何辨识待定整数变量,是机组组合问题中的难点,为此在综合考虑机组不同出力水平对成本的影响、系统时段耦合、系统备用以及网络安全等约束的情况下,提出了待定整数变量辨识方法.首先对各线性化目标函数进行安全约束机组组合松弛计算,根据所得结果按给定规则确定所有在全时段机组状态出现启停的机组集合,有效缩小了机组组合的寻优空间.在不影响最优解的前提下,利用负荷曲线特异性截取技术,加速了待定整数集合识别过程,提高了计算效率.算例结果验证了该方法的有效性     

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     

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.     

Thermal unit commitment using binary/real coded artificial bee colony algorithm

This paper presents a binary/real coded artificial bee colony (BRABC) algorithm to solve the thermal unit commitment problem (UCP). A novel binary coded ABC with repair strategies is used to obtain a feasible commitment schedule for each generating unit, satisfying spinning reserve and minimum up/down time constraints. Economic dispatch is carried out using real coded ABC for the feasible commitment obtained in each interval. In addition, non-linearities like valve-point effect, prohibited operating zones and multiple fuel options are included in the fuel cost functions. The effectiveness of the proposed algorithm has been tested on a standard ten-unit system, on IEEE 118-bus test system and IEEE RTS 24 bus system. Results obtained show that the proposed binary ABC is efficient in generating feasible schedules.     

Adaptive simulated annealing schedule to the unit commitment problem

This paper presents an approach for solving the unit commitment problem based on a simulated annealing algorithm with an adaptive schedule. The control parameter, temperature, is adapted to the cost levels on which the algorithm operates during the annealing process. This shortens the time taken to find a good solution meeting all constraints and improves the convergence of the algorithm. The operators specific to this problem, mutation and transposition, are used as the transition operators. The method incorporates time-dependent start-up costs, demand and reserve constraints, minimum up and down time constraints and unit power generation limits. There are different definitions of the objective function for the feasible and infeasible solutions. Test results showed an improvement in effectiveness compared to results obtained from simulated annealing with a static schedule, genetic algorithm and other techniques.     

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.     

Unit commitment solution methodology using genetic algorithm

Solution methodology of unit commitment (UC) using genetic algorithms (GA) is presented. Problem formulation of the unit commitment takes into consideration the minimum up and down time constraints, start up cost and spinning reserve, which is defined as minimization of the total objective function while satisfying the associated constraints. Problem specific operators are proposed for the satisfaction of time dependent constraints. Problem formulation, representation and the simulation results for a 10 generator-scheduling problem are presented     

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.     

Effects of ramp-rate limits on unit commitment and economicdispatch

The authors propose an algorithm to consider the ramp characteristics in starting up and shutting down the generating units as well as increasing and decreasing power generation. They consider the inclusion of ramping constraints in both unit commitment and economic dispatch. Since implementing ramp-rate constraints is a dynamic process, dynamic programming (DP) is a proper tool to treat this problem. To overcome the computational expense which is the main drawback of DP, this study initially employs artificial intelligence techniques to produce a unit commitment schedule which satisfies all system and unit operation constraints except unit ramp-rate limits. Then, a dynamic procedure is used to consider the ramp properties as units are started up and shut down. According to this adjustment, maximum generating capabilities of units will change the unit operation status instead of following a step function. Finally, a dynamic dispatch procedure is adopted to obtain a suitable power allocation which incorporates the unit generating capability information given by unit commitment and unit ramping constraints, as well as the economical considerations. Two examples are presented to demonstrate the efficiency of the method     

基于等风险约束的机组日运行调度

本文从一个新的角度探讨了电力系统机组日运行调度问题。以系统等运行风险度和机组投运前导时间为约束,旋转备用为目标函数,建立了求解机组日运行计划的动态规划数学模型并提出了相应的算法。该方法可与常规的机组最优投入方法结合,进一步研究大型发电系统的可靠、安全、经济运行。     

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     

电力市场下综合考虑系统可靠性和旋转备用效益的机组组合

通过对电力市场条件下机组组合问题的研究，提出了综合考虑发电系统可靠性和旋转备用效益的机组组合的模型和方法。该方法以旋转备用的比较效益最大为目标函数，通过概率评估方法，利用系统投运风险度确定机组投运台数，利用系统响应风险度确定旋转备用的合理分布，并提出了一种求解以上问题的启发式求解算法，给出了算例及结果。     

Reserve constrained multi-area economic dispatch employing differential evolution with time-varying mutation

For a power pool that involves several generation areas interconnected by tie-lines, the objective of economic dispatch (ED) is to determine the most economical generation dispatch strategy that could supply the area load demands without violating the tie-line capacity constraints. The objective of multi-area economic dispatch (MAED) is to determine the generation levels and the interchange power between areas which would minimize total fuel cost while satisfying power balance constraint, upper/lower generation limits, ramp rate limits, transmission constraints and other practical constraints. In reserve constrained MAED (RCMAED) problem inter-area reserve sharing can help in reducing the operational cost while ensuring that spinning reserve requirements in each area are satisfied. The tie-line limits too play a pivotal role in optimizing the cost of operation. The cost curves of modern generating units are discontinuous and non-convex which necessitates the use of powerful heuristic search based methods that are capable of locating global solutions effectively, with ease. This paper explores and compares the performance of various differential evolution (DE) strategies enhanced with time-varying mutation to solve the reserve constrained MAED (RCMAED) problem.The performance is tested on (i) two-area, four generating unit system, (ii) four area, 16-unit system and (iii) two-area, 40-unit system. The results are found to be superior compared to some recently published results.     

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。     

电力市场中考虑机组启停约束的购电策略

在电力市场环境下,电网以最小化购电费用为目标,而发电公司以最大化售电收益为目标,如何寻找二者之间的市场成交点是一项复杂而重要的工作。制定发电计划时,机组的启停是必须考虑的问题。基于此,文中对电力市场中考虑机组启停约束的购电策略进行了研究,并建立了相应的数学模型,提出了机组报价对电网总购电费用灵敏度的概念,以及考虑机组启停约束的购电算法,得出的结论对制定发电计划有一定的指导意义。