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.     

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.     

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.     

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。     

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 solution to the unit commitment problem considering LNG fuel constraints

In this paper, an algorithm is proposed for finding a quasi-optimal schedule for the short-term thermal unit commitment problem taking LNG fuel constraints into account. In recent years, LNG fuel has been used increasingly. As a result, LNG fuel constraints should be considered in making a unit commitment schedule. Generally, unit commitment is a nonlinear combinatorial problem including discrete variables. To solve the problem, a two-step algorithm is developed using mathematical programming methods. First a linear programming problem is solved to determine the amount of LNG fuel to be consumed by each LNG unit, then a Lagrangian relaxation approach is used to obtain a unit commitment schedule. This two-step algorithm simplifies the problem and thus has good convergence characteristics. To test the effectiveness of the proposed algorithm, a numerical simulation was carried out on a 46-unit thermal system over a 24-hour period. A result with a dual gap of 0.00546 was obtained. © 1998 Scripta Technica, Electr Eng Jpn, 125(3): 22–30, 1998     

Decision analysis solution of the unit commitment problem

The topic of unit commitment has been and continues to be of interest to many researchers and to many utilities. Much of the past research has utilized integer programming, dynamic programming, linear programming, gradient directed search, and heuristic techniques. This research combines both linear programming and dynamic programming to solve the unit commitment problem as a decision analysis problem. The result provides most of the advantages of linear programming and dynamic programming with less stringent requirements on the pre-solution information needed for unit transition sequences.     

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.     

A combination of the genetic algorithm and lagrangian relaxation decomposition techniques for the generation unit commitment problem

Unit commitment involves the scheduling of generators in a power system in order to meet the requirements of a given load profile. An analysis of the basis for combining the genetic algorithm (GA) and Lagrangian relaxation (LR) methods for the unit commitment problem is presented. It is shown that a robust unit commitment algorithm can be obtained by combining the global search property of the genetic algorithm with the ability of the Lagrangian decomposition technique to handle all kinds of constraints such as pollution, unit ramping and transmission security.     

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.     

A genetic algorithm solution approach to the hydrothermal coordination problem

In this paper, a genetic algorithm solution to the hydrothermal coordination problem is presented. The generation scheduling of the hydro production system is formulated as a mixed-integer, nonlinear optimization problem and solved with an enhanced genetic algorithm featuring a set of problem-specific genetic operators. The thermal subproblem is solved by means of a priority list method, incorporating the majority of thermal unit constraints. The results of the application of the proposed solution approach to the operation scheduling of the Greek Power System, comprising 13 hydroplants and 28 thermal units, demonstrate the effectiveness of the proposed algorithm.     

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.     

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 Heuristic algorithm to solve the unit commitment problem for real-life large-scale power systems

One of the main needs that power system operators around the world have is to solve complex Unit Commitment models for large-scale power systems in an acceptable computation time. This Paper presents an alternative Heuristic algorithm that successfully addresses this need. The Heuristic algorithm makes use of various optimization techniques such as Mixed Integer Linear Programming (MILP), Quadratic Programming (QP), Quadratically Constrained Programming (QCP), and Dynamic Programming (DP). CPLEX 12.2 is used as the main optimization engine for MILP, QP, and QCP. DP is an in-house algorithm used to obtain the commitment of Combined Cycle Plants (CCPs) when represented with the component-based model. This Heuristic algorithm combines the global optimality capabilities of MI (L) P formulations with the highly detailed models available for CCPs using LR–DP formulations. The Heuristic algorithm introduced in this Paper is capable of solving up to 1-week scenarios with a 1-hour time window for the complex Mexican Power System.     

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     

A combinatorial artificial intelligence real-time solution to the unit commitment problem incorporating V2G

Plug-in hybrid electric vehicles (PHEVs) have been the center of attention in recent years as they can be utilized to set up a bidirectional connection to a power grid for ancillary services procurement. By incorporating Vehicle to Grid (V2G), this paper proposes a real-time solution to a non-convex constrained unit commitment (UC) optimization problem considering V2G parking lots as dispersed generation units. V2G parking lots can be considered as virtual power plants that my decrease dependency to small expensive units in a UC problem. In this paper, firstly a probabilistic attendance model of PHEVs in a parking lot is investigated, while expected number of PHEVs as well as the equivalent generation capacity of the parking lot is obtained using a radial basis neural network. Secondly, a particular UC problem considering V2G parking lot is solved using GA-ANN as a hybrid heuristic method. A real-time estimation of PHEVs number in the V2G parking lot and real-time solution to UC–V2G problem associated with load variation makes this work distinguished, while the proposed method is applied to a standard IEEE 10-unit test system with promising results.     

基于自适应粒子群优化算法的机组组合

机组组合是一个大规模、非线性混合整数优化问题,求解比较困难,为了提高粒子群算法的全局和局部搜索能力,提出一种惯性权值自适应调整的粒子群算法.该算法按照适应度的大小将粒子群分成两个子群,然后根据适应度的进化速度和进化停滞系数动态调整惯性权值.通过对典型函数的测试以及10台机组24小时的优化调度,计算结果表明该方法收敛精度较高.     

发电机组组合的混合蚁群优化算法

电力系统中的机组组合作为一个非确定型多项式困难问题,一直难以获得其理论最优解.针对算法的精度和速度这一矛盾,提出了一种结合启发式算法和蚁群算法的混合优化算法.用优先级排序法获得次优解,并在附近形成一个搜索邻域;采用蚁群算法在此邻域内寻优,减小了蚁群算法的空间复杂度.同时,在蚁群算法中引入了人工鱼群算法的拥挤度概念.拥挤度阈值在迭代过程中是自适应变化的,从而增强了算法的遍历寻优能力,也保持了较快的收敛速度.经济负荷分配采用简化梯度法.对一个10机系统算例仿真计算,验证了所提算法对解决机组组合问题具有很强的搜索能力和快速收剑性.     

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.     

Emerging solution of large-scale unit commitment problem by Stochastic Priority List

This paper presents a new approach for unit commitment problem using Stochastic Priority List method. In this method, rapidly some initial unit commitment schedules are generated by Priority List method and priority based stochastic window system. Excess units are added with system dependent probability distribution to avoid overlooking a desired solution during repeated search. Constraints are not considered in this stage. Then schedules are modified gradually using the problem specific heuristics to fulfill constraints. To reduce calculations, heuristics are applied only to the solutions, which can be expected to improve. Besides, sign vector is introduced to reduce economic load dispatch (ELD) overhead recalculations. This process is repeated for optimal solution. The proposed method is tested using the reported problem data set. Simulation results for the systems up to 100-unit are compared to previous reported results. Numerical results show an improvement in solution cost and time compared to the results obtained from Genetic Algorithm and others.