人工免疫算法在水电机组优化组合中的应用

针对水电机组优化组合问题提出一种模拟生物免疫系统的人工免疫算法,给出算法的基本步骤,构造几种人工免疫算子,并对一个有12台机组的水电系统作仿真计算.计算结果表明:人工免疫算法比遗传算法具有更好的全局收敛性和收敛速度.     

Hybrid chaos search genetic algorithm and meta-heuristics method for short-term load forecasting

A hybrid chaos search genetic algorithm (CGA) /fuzzy system (FS), simulated annealing (SA) and neural fuzzy network (NFN) method for load forecasting is presented in this paper. A fuzzy hyper-rectangular composite neural networks (FHRCNNs) was used for the initial load forecasting. Then, we used CGAFS and SA to find the optimal solution of the parameters of the FHRCNNs, instead of back-propagation (BP) (including parameters such as synaptic weights, biases, membership functions, sensitivity factor in membership functions and adjustable synaptic weights). First, the CGAFS generates a set of feasible solution parameters and then puts the solution into the SA. The CGAFS has good global optimal search capabilities, but poor local optimal search capabilities. The SA method on the other hand has good local optimal search capabilities. We combined both methods to try and obtain both advantages, and in doing so eliminate the drawback of the traditional artificial neural networks (ANN) training by BP (where the weights and biases are always trapped into a local optimum, which then leads the solution to sub-optimization). Finally, we used the CGAFS and SA combined with NFN (CGAFSSA–NFN) to see if we could improve the quality of the solution, and if we actually could reduce the error of load forecasting. The proposed CGAFSSA–NFN load forecasting scheme was tested using the data obtained from a sample study, including 1 year, 1 week and 24-h time periods. The proposed scheme was then compared with ANN, evolutionary programming combined with ANN (EP–ANN), genetic algorithm combined with ANN (GA–ANN), and CGAFSSA–NFN. The results demonstrated the accuracy of the proposed load-forecasting scheme.     

A solution to unit commitment problem using fire works algorithm

This paper presents a new approach using swarm intelligence algorithm called Fireworks Algorithm applied to determine Unit Commitment and generation cost (UC) by considering prohibited operating zones. Inspired by the swarm behaviour of fireworks, an algorithm based on the explosion (search) process and the mechanisms of keeping the diversity of sparks has been developed to minimize the total generation cost over a given scheduled time period and to give the most cost-effective combination of generating units to meet forecasted load and reserve requirements, while adhering to generator and transmission constraints. The primary focus is to achieve better optimization while incorporating a large and often complicated set of constraints like generation limits, meeting the load demand, spinning reserves, minimum up/down time and including more realistic constraints, such as considering the restricted/prohibited operating zones of a generator. The generating units have certain ranges where operation is restricted based upon physical limitations of machine components or instability, e.g., due to steam valve or vibration in shaft bearings. Therefore, prohibited operating zones as a prominent constraint must be considered. In this paper the incorporating of complicated constraints of an optimization problem into the objective function is not considered by neglecting the penalty term. Numerical simulations have been carried out on 10 – unit 24 – hour system.     

遗传粒子群混合算法在电厂机组负荷组合优化中的应用

粒子群优化算法应用于火电厂机组组合问题中存在早熟收敛等现象,提出3方面改进的遗传粒子群混合算法:改进粒子群初始化方法,提出粒子初始化机组运行状态组合合理性判据,并初始化一定比例的粒子使其机组负荷随机在对应机组负荷上限附近赋值;采用部分解除约束结合惩罚函数的约束处理方法,对粒子进行机组负荷平衡操作,使大部分粒子满足约束条件;通过引入遗传算法中的交叉和变异操作增加了粒子的多样性,减小了算法陷入局部极值的可能性。采用改进的遗传粒子群混合算法对3机及5机火电厂机组负荷组合进行优化,仿真结果表明,优化成功率能达到100%。     

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.     

电力系统机组组合中Kuhn-Tucker最优性条件的扩展应用

机组组合(ED)是电力系统规划中常见的混合整数非线性组合优化问题.结合电力系统机组组合问题的特点,将经典数学规划理论中的Kuhn-Tucker最优性条件与现代优化计算方法中的启发式算法相结合,实现机组组合问题中的整数变量优化部分与连续变量优化部分的信息融合,使主问题与子问题的求解信息同时影响全局优化的搜索过程.提出了一种随机的启发式越限处理方法,该方法突破了K-T最优性条件在电力系统中的传统应用规则.最后,通过仿真计算,说明提出的方法的优越性.     

基于搜索+调整的两阶段萤火虫算法求解机组组合问题

提出了一种新颖的基于搜索+调整的两阶段萤火虫算法求解机组组合问题。算法将机组组合求解流程分解为具有离散变量和连续变量的两个优化问题,通过二进制编码的萤火虫算法求解含离散变量的机组启停主问题,利用改进的实数编码萤火虫算法解决连续变量的负荷经济分配子问题,采用调整策略校核和修复约束,实现主子问题的交替迭代求解。算法通过启发式的约束调整策略,以及两种编码方式实现了离散变量和连续变量的分解优化,提高了机组组合问题求解的效率和精度。通过对6个不同规模算例的计算及与其他经典算法的对比,验证了所提算法的有效性和优越性。     

Hybrid Taguchi-Immune Algorithm for the thermal unit commitment

In this paper, a Hybrid Taguchi-Immune Algorithm (HTIA) is presented to deal with the unit commitment problem. HTIA integrates the Taguchi method and the Traditional Immune Algorithm (TIA), providing a powerful global exploration capability. The Taguchi method (TM) is incorporated in the crossover operations in order to select the better gene for achieving crossover consequently, enhancing the TIA. It has been widely used in experimental designs for problems with multiple parameters. The effectiveness and efficiency of HTIA are demonstrated by presenting several cases, and the results are compared with previous publications. Our results show that the proposed method is feasible, robust, and more effective than many other previously developed computation algorithms.     

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.     

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。     

Projected mixed integer programming formulations for unit commitment problem

The thermal unit commitment (UC) problem is a large-scale mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. This paper presents a projected reformulation for UC problem. After projecting the power output of unit onto [0,1], a novel MIQP reformulation, denoted as P-MIQP, can be formed. The obtained P-MIQP is tighter than traditional MIQP formulation of UC problem. And the reduced problem of P-MIQP, which is eventually solved by solvers such as CPLEX, is compacter than that of traditional MIQP. In addition, two mixed integer linear programming (MILP) formulations can be obtained from traditional MIQP and our P-MIQP of UC by replacing the quadratic terms in the objective functions with a sequence of piece-wise perspective-cuts. Projected MILP is also tighter and compacter than the traditional MILP due to the same reason of MIQP. The simulation results for realistic instances that range in size from 10 to 200 units over a scheduling period of 24 h show that the projected reformulation yields tight and compact mixed integer programming UC formulations, which are competitive with currently traditional ones.     

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.     

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).     

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.     

Binary fireworks algorithm for profit based unit commitment (PBUC) problem

The deregulation of electricity markets has transformed the unit commitment and economic dispatch problem in power systems from cost minimization approach to profit maximization approach in which generation company (GENCO)/independent power producer (IPP) would schedule the available generators to maximize the profit for the forecasted prices in day ahead market (DAM). The PBUC is a highly complex optimization problem with equal, in equal and bound constraints which allocates scheduling of thermal generators in energy and reserve markets with no obligation to load and reserve satisfaction. The quality of the solution is important in deciding the commitment status and there by affecting profit incurred by GENCO/IPPs. This paper proposes a binary coded fireworks algorithm through mimicking spectacular display of glorious fireworks explosion in sky. In deregulated market GENCO/IPP has the freedom to schedule its generators in one or more market(s) based on the profit. The proposed algorithm is tested on thermal unit system for different participation scenarios namely with and without reserve market participation. Results demonstrate the superiority of the proposed algorithm in solving PBUC compared to some existing benchmark algorithms in terms of profit and number of iterations.     

竞争机制下基于改进遗传算法的火电机组启停

电力市场正逐步引入厂网分开竞价上网的竞争机制,而发电厂的发电情况与电网的经济运行有极大的关系。在这种运行模式下,火电机组的优化启停数学模型需要进一步改进。本文从发电厂利润最大化角度出发,建立火电机组启停的数学模型,并提出用优化遗传算法确定火电机组启停的方法。该方法能有效克服一般遗传算法在机组优化组合中的不足,提高了收敛速度,对发电机组优化组合问题具有实用价值。     

A rolling-horizon unit commitment framework with flexible periodicity

In this work, we develop a mathematical model and framework to represent rolling-horizon unit commitment (UC) processes with multiple periodicities. In control center operations, UC is solved repeatedly to adjust device commands based on new information about load, generation availability, renewable energy production, and other aspects of system state as uncertain conditions are realized. We develop a three-level model including 24-h UC, rolling-horizon UC (RHUC), and economic dispatch (ED) and give formulations for the three problems including interdependencies. This framework allows for evaluation of, among other things, different periodicities of the rolling horizon problem and the benefits of more accurate forecasting information. Experimental results are shown for a 6-bus system and a 3012-bus system with wind generation in two wind scenarios. Although the generation costs are very similar, the deviation between RHUC schedules and actual deployment is noted to be superior for a 20-min periodicity compared to a 30-min periodicity. Additionally, less reserve is deployed in the 20-min RHUC case.     

A fuzzy chance-constrained program for unit commitment problem considering demand response,electric vehicle and wind power

As a form of renewable and low-carbon energy resource, wind power is anticipated to play an essential role in the future energy structure. Whereas, its features of time mismatch with power demand and uncertainty pose barriers for the power system to utilize it effectively. Hence, a novel unit commitment model is proposed in this paper considering demand response and electric vehicles, which can promote the exploitation of wind power. On the one hand, demand response and electric vehicles have the feasibility to change the load demand curve to solve the mismatch problem. On the other hand, they can serve as reserve for wind power. To deal with the unit commitment problem, authors use a fuzzy chance-constrained program that takes into account the wind power forecasting errors. The numerical study shows that the model can promote the utilization of wind power evidently, making the power system operation more eco-friendly and economical.     

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。     

基于遗传禁忌混合算法的静态电压稳定裕度计算

提出一种基于遗传禁忌混合算法的静态电压稳定裕度计算的新方法.该方法将全局搜索能力强的遗传算法和局部搜索能力强的禁忌搜索算法结合在一起,通过改进的连续潮流法计算,可快速而准确地获取系统最大静态电压稳定裕度,并在一定程度上弥补遗传算法和禁忌搜索算法单独使用的不足.应用该混合算法对IEEE14节点系统进行仿真计算,验证了该方法可行且有效.