مسئله زمانبندی تولید با الگوریتم ژنتیک هوشمند

This paper presents a Genetic Algorithm (GA) solution to solve the Generation Scheduling (GS) problem with intelligent coding scheme. The intelligent coding scheme effectively handles minimum up/down time constraints of GS problem. GA with intelligent coding is called as Intelligent Genetic Algorithm (IGA). Penalty parameter-less constraint handling technique is used for satisfying power balance constraint. Performance of the IGA is tested on a 10-unit 24-h and 26-unit 24-h unit commitment test systems. The result obtained using IGA is compared with the results reported using Lagrangian Relaxation (LR), Enhanced Lagrangian Relaxation (ELR), LRGA, GA and Evolutionary Programming methods. Simulation results show the effects of intelligent coding scheme in obtaining feasible and minimum cost solution.

Generation Scheduling (GS) in a power system is to prepare the schedule of the generators with their output power in such a way that the total system production cost over the time period is minimized while meeting various plant and system constraints. In general, GS involves with the decisions with regards to unit status subjected to the loading levels, the amount of spinning reserve for each unit and satisfying Minimum Up-Time (MUT) and Minimum Down-Time (MDT) constraints over a given scheduling period. GS problem is a nonlinear, mixed-integer combinatorial optimization problem. The global optimal solution can be obtained by complete enumeration, which is not practicable to large power systems due to its excessive computation time [1]. A number of methods have been used previously for solving the above problem and each method has its own difficulties. The various traditional methods used for this problem are Priority List based method, Branch and Bound, Dynamic Programming and Lagrangian Relaxation [2] and [3]. In the Priority List method, an exhaustive enumeration of all unit combinations is performed at each load level. Hence, it is hard to handle if the dimension of the problem is large, whereas in the case of Branch-and-Bound method, finding the optimal solution is time consuming, because it can only be obtained by successive elimination of a set of inappropriate solutions [4]. Based on the “Principle of Optimality”, Dynamic Programming was suggested for GS problem. However, the main drawback of this is that it could not take into account the coupling time constraints and time dependent start-up costs [5]. Lagrangian Relaxation for GS problem is superior to Dynamic Programming due to its higher solution quality and faster computational time [6]. However, by using this, there is no guarantee to get an optimal solution. Many times the solution tend to be sub-optimal. In addition, it is difficult to handle the minimum up and down time constraints unless some heuristic methods are used. Hence, heuristic approaches like Genetic Algorithm (GA) [7], [8], [9] and [10], Evolutionary Programming (EP) [11], Simulated Annealing (SA) [12], Tabu Search (TS) [13], Fuzzy Logic/expert systems [14], [15] and [16], Artificial Neural Networks (ANN) [17], have been proposed to solve this problem. However, the results obtained by these methods required a considerable amount of computational time especially for a large system. Hence, recently, the traditional methods are integrated with these heuristic methods to solve this problem effectively. These hybrid methods are claimed to accommodate the constraints that are more complicated and claimed to have better quality solutions even though the system under consideration is very large [18], [19] and [20]. Later hybridization between two heuristic algorithms has been used to solve the GS problem [21], [22] and [23]. Recently, Particle Swarm Optimization approach inspired by quantum computing has also been introduced in [24]. GAs are having widespread application because of their aspects like simplicity, function independent and not being limited by the properties of the function such as continuity, existence of derivatives, unimodality, etc. In order to deal effectively MUT and MDT constraints of GS problem with GA, intelligent coding is used in this paper [25] and [26]. GA with intelligent coding is termed as Intelligent GA (IGA) in this paper. The other constraints are handled by integrating constraint violations into the fitness function, using penalty parameter-less constraint handling technique. Performance of the IGA approach is tested on 10-unit and 26-unit GS test systems. The remainder of the paper is organized as follows: Section 2 addresses the GS problem formulation. The GA for GS problem is described in Section 3, whereas, Section 4 explains the concepts of IGA and penalty parameter-less constraint handling scheme. Section 5 deals with the Economic dispatch and Section 6 discusses the numerical results followed by conclusion.

In this paper, MUT and MDT constraints of Generation Scheduling problem is easily handled using GA with intelligent coding scheme. MUT and MDT constraints are automatically satisfied by embedding into the intelligent coding scheme. For satisfying power demand constraints penalty parameter-less constraint handling scheme is used. Effectiveness of the approach is demonstrated on 10-unit and 26-unit test systems. GA with direct coding scheme, even after several iterations, fails to produce feasible solutions for higher order systems. However, the GA with intelligent coding produces the generation schedules without MUT and MDT constraint violations. Numerical results show that the total cost incurred over the scheduled period is less as compared to other reported methods. GA with intelligent coding scheme is an efficient tool to handle the GS problems having all constraints.