Hydro-thermal unit commitment problem using simulated annealing embedded evolutionary programming approach

This paper presents a new approach to solve the hydro-thermal unit commitment problem using Simulated Annealing embedded Evolutionary Programming approach. The objective of this paper is to find the generation scheduling such that the total operating cost can be minimized, when subjected to a variety of constraints. A utility power system with 11 generating units in India demonstrates the effectiveness of the proposed approach; extensive studies have also been performed for different IEEE test systems consist of 25, 44 and 65 units. Numerical results are shown comparing the cost solutions and computation time obtained by conventional methods.     

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     

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.     

Cutting plane methods for Lagrangian relaxation‐based unit commitment algorithm

In this paper, we study cutting plane methods for a Lagrangian relaxation‐based unit commitment algorithm. In the algorithm, nondifferentiable optimization methods can be applied to optimize the dual function, and a subgradient method which needs parameter tuning and has some drawbacks such as computational inefficiency and oscillating behavior is commonly used. The cutting plane method and the central cutting plane method are applied to the algorithm and implemented using reoptimization techniques. A numerical example shows that both methods are accelerated by the reoptimization techniques and have good convergence without parameter tuning. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 141(3): 17–29, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10066     

Monte Carlo based unit commitment procedures for the deregulated market environment

The unit commitment problem, originally conceived in the framework of short term operation of vertically integrated utilities, needs a thorough re-examination in the light of the ongoing transition towards the open electricity market environment. In this work the problem is re-formulated to adapt unit commitment to the viewpoint of a generation company (GENCO) which is no longer bound to satisfy its load, but is willing to maximize its profits. Moreover, with reference to the present day situation in many countries, the presence of a GENCO (the former monopolist) which is in the position of exerting the market power, requires a careful analysis to be carried out considering the different perspectives of a price taker and of the price maker GENCO. Unit commitment is thus shown to lead to a couple of distinct, yet slightly different problems. The unavoidable uncertainties in load profile and price behaviour over the time period of interest are also taken into account by means of a Monte Carlo simulation. Both the forecasted loads and prices are handled as random variables with a normal multivariate distribution. The correlation between the random input variables corresponding to successive hours of the day was considered by carrying out a statistical analysis of actual load and price data. The whole procedure was tested making use of reasonable approximations of the actual data of the thermal generation units available to come actual GENCOs operating in Italy.     

基于免疫算法的机组组合优化方法

机组组合是改善传统电力系统运行经济性和电力市场出清的重要手段。基于群体进化的智能优化算法存求解过程中存在计算效率低和易于早熟收敛等缺点。提出机组组合的免疫算法，利用免疫算法保持种群多样性的内在机制和免疫记忆特性改进既有的智能优化方法。新算法扩展了约束处理技术，能更好地对可行解空间搜索，采用一种由后向前、由前及后、双向迂回推进的精简程序改善个体可行解的局部最优性，同时利用优先级顺序法产生能较好反映问题先验知识的初始种群。典型算例证实新算法能获得更优的结果，具有更快的收敛速度，且在系统规模扩大时有大致线性的计算复杂性，是一种新的高效的机组组合智能优化算法。     

Studies on stochastic unit commitment formulation with flexible generating units

In recent years, restructured power system has emerged and renewable energy generation technology has developed. More and more different unit characteristics and stochastic factors make the unit commitment (UC) more difficult than before. A novel stochastic UC formulation which covered the usual thermal units, flexible generating units and wind generation units is proposed to meet the need of energy-savings and environment protection. By introducing a UC risk constraint (UCRC), many stochastic factors such as demand fluctuations, unit force outages, variety of energy price, even the stochastic characteristics of wind generation can be dealt with. Based on the theory of chance constrained programming (CCP), the UCRC, a probabilistic constraint is changed into a determinate constraint, and then the presented formulation can be solved by usual optimization algorithms. Numerical simulations on 4 test systems with different scales show that different UC schedules can be determined according to different stochastic factors and its calculation time is acceptable in the view of practical engineer.     

电力系统机组组合问题的系统进化算法

提出了一种适用于解决大规模电力系统机组组合问题的新型优化算法－－系统进化算法,与常规的优化算法相比该方法具有更强的适应性和鲁棒性,能处理高维数、非凸、离散、非一的实际系统化问题。系统进化的思想具有方法论的意义,根据实际问题的不同特征可以设计不同的系统进化算法。这种方法的提出可以为复杂系统的优化规划、运行决策提供新的途径。     

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.     

适用于不同电价机制的统一机组组合算法

现有电力市场中存在两种结算电价机制：按机组报价结算(一机一价)和按市场出清价格结算(统一电价)。不同市场之间的结算方式也有所不同,例如,双边交易中采用一机一价结算方式,而实时市场中采用边际电价结算方式。不同结算电价机制下,机组组合的目标函数不同,传统机组组合方法必须根据电价机制的不同进行调整。通过研究发现,两种结算方式下机组组合问题的最优条件具有类似的数学表达形式。基于这一统一的最优条件表达形式,提出了一种新的机组组合算法。与传统拉格朗日松弛法相比,新算法能够有效地求解两种电价机制下的机组组合问题。     

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。     

A multi‐agent approach to unit commitment

This paper proposes a multiagent system to power system unit commitment problems. Multiagent is a new paradigm for developing software applications. Coordinating the behavior of autonomous agents is a key issue in agent‐oriented programming techniques today. Recently, agents are being used in an increasingly wide variety of applications, ranging from comparatively small systems such as E‐mail filters to large, open, complex systems such as air traffic control. Though some agent frameworks have been proposed in the power system field, the number of studies is limited. In this paper, we developed a power system unit commitment application by multiagent architecture. Our multiagent system has the following characteristics: (1) The system consists of a single facilitator agent, two mobile agents, and one or more generator agents which are elements of power system network. (2) The facilitator agent is developed to act as a manager for the process by using the singleton design pattern. The mobile agents migrate to generator‐agents to increase or decrease their power generations. The generator agents have their operational data. (3) Message object is developed to communicate between the agents using KQML‐like object. The proposed approach is applied to a simple model system, and the results show that the multiagent system is an efficient decentralized approach for solving power system unit commitment problems. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 141(2): 41–47, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10057     

A method for unit commitment with transmission losses and flow constraint

Researches on the unit commitment with transmission network have been reported recently. However, most of these researches mainly discussed the security constrained unit commitment, while the relationship between unit commitment and transmission losses was not considered. However, from the standpoint of operating reserve for ensuring power supply reliability, a unit commitment considering transmission losses is required. Further, under the deregulation and liberalization of the electric power industry, not only the line's security but also transmission losses are expected to play an important role in calculating the network access charge, and unit commitment taking into account transmission losses is also desired from this viewpoint. In this paper, a unit commitment approach with both transmission losses and line flow constraint is presented. Based on a heuristic iterative optimization method, first, an initial schedule is created by using a successively decommitting unit approach that is proposed in this paper. Then, we determine constraints included in the unit commitment schedule by a heuristic iterative optimization approach, in which an algorithm able to get rid of line overload by DC optimal power flow is developed. Through numerical simulations on two test power systems, the effectiveness of the proposed method is shown. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 142(4): 9–19, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10116     

基于自适应系统优化算法的机组组合

算法采用系统分解理论将系统约束松弛,把机组组合问题分解为2层优化问题.上层通过拉格朗日乘子的自适应调整来协调单个机组的子系统,下层采用遗传算法求解单个机组独立的子系统优化问题.对拉格朗日乘子的自适应调整明显减少了对偶间隙的振荡现象,对遗传算法中交叉变异算子自适应的调整有效地克服了早熟现象.算例表明可行解的质量高、收敛速度快,与传统算法相比具有更高的自适应性,适用于大规模、复杂系统的机组组合问题的求解.     

具有相同机组水火电调度问题的新算法

对Lagrangian松弛法求解水火电调度问题时由机同机级引起解震荡现象进行了研究。通过一个例子分析了震荡产生的根本原因。对此，在松弛函数中引入了惩罚项并采用了伪次梯度法来修正乘子。新算法在求解低层子问题时并不同时求解，使震荡现象在很大程度上得以克服，同时可大幅度地降低偶解对约束的违反程度。通过简单的例子和对一个包含两组机同机组的短期发电调度问题的计算表明，对偶解的约束违反程度明显地降低，解震荡明显地减弱且最后可行解的质量有显著的改善。     

Frequency security constrained short-term unit commitment

In island grids and weakly interconnected power systems, a loss of a large proportion of generation will cause the system frequency to fall dramatically. In order to ensure a stable operation with the lowest impact on the system, the disturbed power balance must be equalized within a short specified time by activating the seconds reserve of on-line units or by load shedding or both. This paper presents a frequency security constrained short-term scheduling. The procedure commits and optimizes units, calculates necessary seconds reserve capability, and allocates them among the available on-line units to provide emergent frequency regulation following a loss of generation. By means of the low-pressure pre-heater interruption (LPHI) implemented into thermal power plants, seconds reverse provision is increased. Thus, load shedding caused by insufficient availability of seconds reserve can be avoided. A case study on typical island systems with a large number of different units is demonstrated using the proposed procedure. Results from the study validated robust performance of the proposed procedure that minimizes fuel costs while maintaining frequency security condition.     

兼顾经济和环保效益的机组组合

在节能减排背景下,提出了同时兼顾经济和环保效益的多目标机组组合模型,基于拉格朗日松弛法的思想,将该问题分解为单机子问题,在子问题中利用并列选择遗传算法对经济和环保效益进行双目标优化。分别以发电费用最小、排放最小和综合最小为目标建立模型,对6机30节点算例进行了计算和比较,验证了算法和模型的有效性,实现了综合考虑经济和环保因素的机组组合问题的求解。     

基于拉格朗日松弛及子问题解耦动态规划的周机组组合快速求解方法

当前逐渐增大的电力系统规模和逐渐拓展的模拟周期使得快速求解机组组合问题面临巨大挑战。提出一种基于拉格朗日松弛和子问题解耦动态规划的周机组组合快速求解方法,以提高周机组组合计算效率。引入拉格朗日对偶乘子对原始问题中的耦合约束进行松弛,并分解得到若干单机组子问题;构建单机组子问题的状态转移图及状态转移成本,利用动态规划算法计算单机组最优状态转移,以获得单机组子问题最优解;对问题进行迭代求解直至收敛,从而快速得到周机组组合结果。将所提方法应用于IEEE 118节点系统、IEEE 300节点系统和贵州电网,验证其优异的计算效率。     

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