شبکه های عصبی Hopfield محاسبات سریع مبتنی بر برنامه ریزی پویا برای تعهد واحد و توزیع اقتصادی

This paper develops a new dynamic programming based direct computation Hopfield method for solving short term unit commitment (UC) problems of thermal generators. The proposed two step process uses a direct computation Hopfield neural network to generate economic dispatch (ED). Then using dynamic programming (DP) the generator schedule is produced. The method employs a linear input–output model for neurons. Formulations for solving the UC problems are explored. Through the application of these formulations, direct computation instead of iterations for solving the problems becomes possible. However, it has been found that the UC problem cannot be tackled accurately within the framework of the conventional Hopfield network. Unlike the usual Hopfield methods which select the weighting factors of the energy function by trials, the proposed method determines the corresponding factor using formulation calculation. Hence, it is relatively easy to apply the proposed method. The Neyveli Thermal Power Station (NTPS) unit II in India with three units having prohibited operating zone has been considered as a case study and extensive study has also been performed for power system consisting of 10 generating units.

The unit commitment problem schedules the available generators to meet the required load subject to various constraints. The UC plays a major role in power systems operation and control. The unit commitment has commonly been formulated as non-linear, mixed integer, large-scale combinatorial problem for providing the best generating unit schedule and minimizing the operating cost of power system. The economic dispatch problem (EDP) optimally allocates the load demand among the running units while satisfying the power balance equations and unit operating limits [1]. Reviews of unit commitment problem (UCP) may be found in Ref. [2]. The solution methods being used to solve the unit commitment problem can be divided into three categories. • Optimization method such as dynamic programming [3] and [4] mixed integer programming, branch and bound [5] and Lagrangian relaxation [6] and [7]. • Heuristic methods such as priority list [8]. • Artificial intelligence methods such as neural networks [9] genetic algorithms [10] and [11], expert systems [12], simulated annealing [13], evolutionary programming [14] and [15] and Tabu search [16]. The dynamic programming method [3] and [4] based on a priority list is flexible, but the computational time suffers from dimensionality. The shortcoming of branch and bound method [5] is that the execution time increases rapidly for large-scale UC problem. The Lagrangian relaxation (LR) method [6] and [7] provides a fast solution but it suffers from numerical convergence and solution quality. The priority list method [8] is simple and fast, but the quality of final solution is quite far from the optimum. With the advent of artificial intelligence approaches, genetic algorithm (GA), evolutionary programming (EP), simulated annealing (SA), Tabu search (TS) and expert systems (ES) have been proposed to solve the UC problem. GA, EP and TS require a considerable amount of computational time, especially for a large system. One draw back of SA is that it takes much of CPU time to reach a near global minimum. Due to the use of the sigmoidal function in the conventional Hopfield method to solve UC problems, the numerical iteration method is inevitably applied though the numerical iteration method often suffers from large amount of computational requirement [17]. Further, adopting the modified sigmoidal function causes incorrect generation dispatch and selecting shape constant is troublesome. To avoid the aforementioned problems, a linear model describing the input–output relationship is proposed. The proposed method is different from all Hopfield methods previously reported. All previously presented Hopfield methods apply the iterative procedures requiring a large quantity of computation to arrive at accurate solutions. However based on the formulations developed the proposed method computes its solutions analytically and no iteration is needed in the solving process. Consequently, computational efforts are greatly reduced. Determination of weighting factors is relatively simple for the proposed analytic method, because the value of the corresponding factor is determined using straightforward calculation. It can be determined regardless of the power mismatch and converging speed selected. The proposed dynamic programming based Hopfield neural network (DPHNN) is a hybrid of intelligence system and traditional mathematical programming. With its two steps processing, the algorithm can benefit from the advantages of both the methods. The proposed DPHNN method has been applied to NTPS 7 unit system and 10 unit system. Computational results from the proposed method are compared with other methods.

The paper develops a hybrid dynamic programming based Hopfield neural network approach to unit commitment problem which is extremely different from the hybrid methods previously reported. From the results of the example, it is obvious that the proposed analytic method is far superior to other methods previously presented. The proposed method is relatively simple, straightforward and efficient. It also exhibits the ability to attain power match to any extent required. The computational results show that the saving in cost for DPHNN is superior and takes less CPU time. Further, because the determination of the weighting factors of the energy function is unnecessary, the proposed method is very easy to apply. The proposed model unlike other neural network requires no training. The paper essentially aims at proposing a new method for the UC problem of generation system, and it has been successfully achieved. In addition, the proposed DPHNN could be extended to solve ramp rate or security constrained UC problems. To resolve the ramp rate and security constrained problem by the proposed method some endeavors still have to be made and are worth pursuing in the future.