Using immune genetic algorithm based hybrid techniques for short-term unit commitment problem

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 shut-down 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 CS and the FS 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 immune genetic algorithm (IGA) combined with the CS and FS was carried out. The results show that the CS and FS all make substantial contributions to the IGA. The result demonstrated the accuracy of the proposed CIGAFS approach.     

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 new genetic-based tabu search algorithm for unit commitment problem

This paper presents a new algorithm based on integrating the use of genetic algorithms and tabu search methods to solve the unit commitment problem. The proposed algorithm, which is mainly based on genetic algorithms incorporates tabu search method to generate new population members in the reproduction phase of the genetic algorithm. In the proposed algorithm, genetic algorithm solution is coded as a mix between binary and decimal representation. A fitness function is constructed from the total operating cost of the generating units without penalty terms. In the tabu search part of the algorithm, a simple short term memory procedure is used to counter the danger of entrapment at a local optimum by preventing cycling of solutions, and the premature convergence of the genetic algorithm. A significant improvement of the proposed algorithm results, over those obtained by either genetic algorithm or tabu search, has been achieved. Numerical examples also showed the superiority of the proposed algorithm compared with two classical methods in the literature.     

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.     

An implementation of harmony search algorithm to unit commitment problem

This paper presents a harmony search algorithm (HSA) to solve unit commitment (UC) problem. HSA was conceptualized using the musical process of searching for a perfect state of harmony, just as the optimization process seeks to find a global solution that is determined by an objective function. HSA can be used to optimize a non-convex optimization problem with both continuous and discrete variables. In this paper it is shown that HSA, as a heuristic optimization algorithm, may solve power system scheduling problem in a better fashion in comparison with the other evolutionary search algorithm that are implemented in such complicated issue. Two case studies are conducted to facilitate the effectiveness of the proposed method. One is a conventional 10-unit test system and its multiples while the other is a 26-unit system, both of which are with a 24-h scheduling horizon. Comparison of the obtained results with other approaches addressed in the literature shows the effectiveness and fastness of the proposed method.     

A genetic algorithm solution to the unit commitment problem

This paper presents a genetic algorithm (GA) solution to the unit commitment problem. GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms such as natural selection, genetic recombination and survival of the fittest. A simple GA algorithm implementation using the standard crossover and mutation operators could locate near optimal solutions but in most cases failed to converge to the optimal solution. However, using the varying quality function technique and adding problem specific operators, satisfactory solutions to the unit commitment problem were obtained. Test results for power systems of up to 100 units and comparisons with results obtained using Lagrangian relaxation and dynamic programming are also reported     

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.     

A matrix real-coded genetic algorithm to the unit commitment problem

An approach to solving the unit commitment (UC) problem is presented based on a matrix real-coded genetic algorithm (MRCGA) with new repairing mechanism and window mutation. The MRCGA chromosome consists of a real number matrix representing the generation schedule. Using the proposed coding, the MRCGA can solve the UC problem through genetic operations and avoid coping with a suboptimal economic dispatch (ED) problem. The new repairing mechanism guarantees that the generation schedule satisfies system and unit constraints. The window mutation improves the MRCGA searching performance. Numerical results show an improvement in the solution cost compared with the results obtained from other algorithms.     

Cooperative coevolutionary algorithm for unit commitment

This paper presents a new cooperative coevolutionary algorithm (CCA) for power system unit commitment. CCA is an extension of the traditional genetic algorithm (GA) which appears to have considerable potential for formulating and solving more complex problems by explicitly modeling the coevolution of cooperating species. This method combines the basic ideas of Lagrangian relaxation technique (LR) and GA to form a two-level approach. The first level uses a subgradient-based stochastic optimization method to optimize Lagrangian multipliers. The second level uses GA to solve the individual unit commitment sub-problems. CCA can manage more complicated time-dependent constraints than conventional LR. Simulation results show that CCA has a good convergent property and a significant speedup over traditional GAs and can obtain high quality solutions. The "curse of dimensionality" is surmounted, and the computational burden is almost linear with the problem scale     

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.     

Integrating genetic algorithms, tabu search, and simulatedannealing for the unit commitment problem

This paper presents a new algorithm based on integrating genetic algorithms, tabu search and simulated annealing methods to solve the unit commitment problem. The core of the proposed algorithm is based on genetic algorithms. Tabu search is used to generate new population members in the reproduction phase of the genetic algorithm. A simulated annealing method is used to accelerate the convergence of the genetic algorithm by applying the simulated annealing test for all the population members. A new implementation of the genetic algorithm is introduced. The genetic algorithm solution is coded as a mix between binary and decimal representation. The fitness function is constructed from the total operating cost of the generating units without penalty terms. In the tabu search part of the proposed algorithm, a simple short-term memory procedure is used to counter the danger of entrapment at a local optimum, and the premature convergence of the genetic algorithm. A simple cooling schedule has been implemented to apply the simulated annealing test in the algorithm. Numerical results showed the superiority of the solutions obtained compared to genetic algorithms, tabu search and simulated annealing methods, and to two exact algorithms     

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%。     

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。     

A genetic algorithm solution to a new fuzzy unit commitment model

This paper proposes a new fuzzy model for the unit commitment problem (UCP). A solution method for the proposed UCP model based on the genetic algorithms (GAs) is presented (FZGA). The model treats the uncertainties in the load demand and the spinning reserve constraints in a new fuzzy logic (FL) frame. The proposed FL model is used to determine a penalty factor that could be used to guide the search for more practical optimal solution. The implemented fuzzy logic system consists of two inputs: the error in forecasted load demand and the amount of spinning reserve, and two outputs: a fuzzy load demand and a penalty factor. The obtained fuzzy load demand is more realistic than the forecasted crisp one; hence the solution of the UCP will be more accurate.In the proposed FZGA algorithm, coding of the solution is based on mixing binary and decimal representation. The fitness function is taken as the reciprocal of the total operating cost of the UCP in addition to penalty terms resulted from the fuzzy membership functions for both load demand and spinning reserve.Results show that the fuzzy-based penalty factor is directly related to the amount of shortage in the committed reserve; hence will properly guide the search, when added to the objective function, in the solution algorithm of the UCP. Accordingly, acceptable level of reserve with better-cost savings was achieved in the obtained results. Moreover, the proposed FZGA algorithm was capable of handling practical issues such as the uncertainties in the UCP. Numerical results show the superiority of solutions obtained compared to methods with traditional UCP models.     

Modified cuckoo search algorithm for short-term hydrothermal scheduling

This paper proposes a modified cuckoo search algorithm (MCSA) for solving short-term hydrothermal scheduling (HTS) problem. The considered HTS problem in this paper is to minimize total cost of thermal generators with valve point loading effects satisfying power balance constraint, water availability, and generator operating limits. The MCSA method is based on the conventional CSA method with modifications to enhance its search ability. In the MCSA, the eggs are first sorted in the descending order of their fitness function value and then classified in two groups where the eggs with low fitness function value are put in the top egg group and the other ones are put in the abandoned one. The abandoned group, the step size of the Lévy flight in CSA will change with the number of iterations to promote more localized searching when the eggs are getting closer to the optimal solution. On the other hand, there will be an information exchange between two eggs in the top egg group to speed up the search process of the eggs. The proposed MCSA method has been tested on different systems and the obtained results are compared to those from other methods available in the literature. The result comparison has indicated that the proposed method can obtain higher quality solutions than many other methods. Therefore, the proposed MCSA can be a new efficient method for solving short-term fixed-head hydrothermal scheduling problems.     

火电机组启停机经济调度新算法

合理的开停机方案能带来经济效益，提出一种混合模拟退火－遗传算法模型进行火电机组的优化启停计划调度，采用十进制编码，无需解码，可减少计算误差的时间，由于引入了模拟退火算法，使得这种算法能接受新特性，不仅改进了忆部收敛性且能加速寻优过程，最终可得到近于全局最优的解，经算例验算表明，该算法可以满足安全可靠的多种约束条件下，较好地改善机组启停计划的经济性，是安排火电机组启停机计划的一种可行方法。     

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.     

Solving the unit commitment problem with a genetic algorithm through a constraint satisfaction technique

This paper proposes a genetic algorithm (GA) in conjunction with constraint handling techniques to solve the thermal unit commitment problem. To deal effectively with the constraints of the problem and prune the search space of the GA in advance, the difficult minimum up- and down-time constraints are embedded in the binary strings that are coded to represent the on-off states of the generating units. The other constraints are handled by integrating penalty factors into the cost function within an enhanced economic dispatch program. The proposed GA approach has been tested on a practical Taiwan Power (Taipower) thermal system over a 24-hour period for different utility factors and GA control parameters. Test results reveal that the features of easy implementation, fast convergence, and a highly near-optimal solution in solving the UC problem can be achieved by the proposed GA approach.     

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。     

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。