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.     

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     

A solution to the ramp rate and prohibited operating zone constrained unit commitment by GHS-JGT evolutionary algorithm

Unit commitment (UC) problem on a large scale with the ramp rate and prohibited zone constraints is a very complicated nonlinear optimization problem with huge number of constraints. This paper presents a new hybrid approach of ’Gaussian Harmony Search’ (GHS) and ’Jumping Gene Transposition’ (JGT) algorithm (GHS-JGT) for UC problem. In this proposed hybrid GHS-JGT for UC problem, scheduling variables are handled in binary form and other constants directly through optimum conditions in decimal form. The efficiency of this method is tested on ten units, forty units and hundred units test system. Simulation results obtained by GHS-JGT algorithm for each case show a better generation cost in less time interval, in comparison to the other existing results.     

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.     

基于改进的逆序排序法的机组组合优化算法

文章提出了改进的逆序排序法来求解机组组合优化问题.该算法从可用机组全投入运行这一可行解出发,在每次迭代过程中优化一台机组在整个调度周期内的开停状况,以最小化总生产成本或总购电成本,直到连续两次迭代的目标函数值不再减小为止.该方法的显著优点在于计算不会振荡,迭代不会发散,且每次迭代的结果均为可行解.该算法在单机组优化过程中,以机组的最小启停区间而不是单个时段为研究调度对象,缓解了组合爆炸问题,明显地加快了计算速度.     

应用MAS解决基于利润的机组组合问题研究

电力系统引入放松管制的市场运行机制之后,形成一种基于利润的机组组合问题:①优化目标从费用最小转为利润最大;②各发电公司从自身利益出发,可以不完全满足中心调度的要求。针对以上特点,提出一种基于多Agent系统的解决方法。仿真结果表明,该方法能够适应解决现代电力系统机组组合问题的新需要,能够获得更大的经济效益。     

电力市场环境下可靠性机组组合机制

完善的双边现货市场是实现电力市场优化资源配置功能的关键,可靠性机组组合是双边现货市场环境下满足日内发电容量充裕度等可靠性要求的重要手段。探讨集中式市场环境下可靠性机组组合的组织方式、出清模型与结算机制。总结国内外各典型电力市场中可靠性机组组合相关机制设计,得到可靠性机组组合机制设计的一般思路。通过算例分析对比各可靠性机组组合出清模型下的市场绩效。基于数值仿真与理论分析结果为中国可靠性机组组合机制设计提供建议。     

风电与储能系统互补下的火电机组组合

针对具有风电和火电机组的电力系统,在储能系统配置给定的前提下,提出通过储能尽量消除风电不确定性并部分以备用形态出现的研究思路,建立了火电机组组合2层优化决策模型。上层问题以火电机组组合成本最小为目标,下层问题以储能系统对电网中电能时空平移和提供备用所得收益最大为目标,以储能系统消除不确定性程度为满足对象,其中计及了自动发电控制(AGC)机组和非AGC机组的特性,以及系统频率调节效应的作用。基于分解协调的原理,通过上、下层问题的交替迭代对该模型予以求解,决策储能系统充/放电功率、调控范围及机组启停方案。该方法可在减少火电机组备用容量的同时,提升系统应对不确定性的能力,通过10机组系统验证了模型和方法的有效性。     

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.     

基于改进约束序优化方法的带安全约束的不确定性机组组合问题研究

为快速有效地求解考虑间歇性可再生能源接入的SCUC问题,在现有约束序优化的基础上,提出了一种适用于不确定性SCUC问题求解的改进约束序优化算法。该方法针对序优化的粗糙模型和精确模型分别融入了离散变量识别策略和无效安全约束削减策略。相比于传统求解方法,提出的改进约束序优化算法在充分发挥传统序优化计算效率方面优势的同时,进一步增强了算法的紧凑性,降低了计算冗余度,有效提升了算法的求解效率。基于IEEE-118节点标准算例的仿真验证了所提算法的正确性和有效性。     

机组组合问题的罚函数法

机组组合问题是一个大规模的非线性、0、1变量混合整数规划问题 ,是一个难问题。以罚函数方法解决0、1变量整数规划问题是一个新的尝试。文中考虑包括发电机爬坡约束和时间约束等动态约束在内的多种约束条件 ,对机组组合问题的 0、1变量进行松弛 ,并在目标函数中增加一个惩罚函数项 ,将问题变换成一个非线性连续变量的规划问题 ,以SQP法求解。本算法经过一个简单的算例检验 ,说明是行之有效的。     

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。     

Stochastic unit commitment problem considering risk constraints and its improved GA‐based solution method

This paper proposes a model of the stochastic unit commitment (SUC) problem, which takes account of the uncertainty of electric power demand and its resulting risk, and its solution method based on an improved genetic algorithm (IGA). The uncertainty of electric power demand is modeled using a set of scenarios which are introduced by scenario analysis. The variance, which measures the dispersion of generation costs of unit commitment schedule under each scenario around the expected generation cost, is used as a measure of risk. Based on the expected returns–variance of returns (E–V) rule in the theory of portfolio analysis, a utility function is devised by appending the variance of the expected generation cost into the original expected generation cost function, with consideration of the risk attitude of the generation companies and power exchange centers. The objective of this optimization problem is to minimize the utility function. The proposed IGA is used to solve this NP‐hard optimization problem. Based on numerical examples, the superiority of the IGA‐based solution method is verified through comparison with a traditional GA‐based solution method. Optimal schedules of SUC, as well as the expected costs and variances, are compared with/without risk constraints, and with different risk attitudes. Test results show that, in solving the SUC problem, it is necessary to consider the electric power demand uncertainty and its resulting risk, as well as the risk attitude of the decision maker. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

基于优化Kriging代理模型的场景分析法求解机组组合问题

由于风电具有很强的波动性和不确定性,为机组组合(Unit Commitment, UC)问题带来许多问题和挑战。因此,提出了一种基于优化Kriging代理模型的场景分析法来处理风电的不确定性。首先通过“预测箱”方法生成大量场景,然后由序列优化的Kriging代理模型估计各场景所对应的经济成本。同时,根据风电不确定性及运行成本对系统的影响,采用重要性采样法削减场景。通过考虑功率平衡和风电爬坡约束的随机机组组合(Stochastic Unit Commitment, SUC)模型验证了该方法的有效性。算例分析结果表明,序列优化Kriging代理模型可以使用较少的场景预测场景运行成本。与Kantorovich 距离法相比,该方法的削减结果选择了较为重要的场景,其求解结果具有更好的经济性和可靠性。     

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.     

适合于机组组合问题的扩展优先顺序法

针对传统PL（Priority List）方法采用单一排序指标,即平均满负荷费用AFLC（Average Full-Load Cost）不能全面反映机组优先顺序的不足,提出一种扩展优先顺序法EPL（Extended Priority List）解决机组组合问题。在分析PL方法特点的基础上,定义μ-Load Cost反映机组在不同出力范围内的经济指标,形成不同μ值的机组组合的邻域,而后定义机组的效用系数UUR（Unit Utilization Ratio）优化机组的优先顺序。此外,引入参数控制机组组合邻域的规模并采取策略对机组组合进行调整使其满足所有约束,从而提高计算效率。最后采用26机组、38机组以及45机组24时段等3个系统的测试结果来验证该方法的有效性。     

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。