هیبریداسیون بهینه سازی کلونی زنبور عسل و برنامه نویسی درجه دوم ترتیبی برای اعزام اقتصادی پویا

Dynamic economic dispatch deals with the scheduling of online generator outputs with predicted load demands over a certain period of time so as to operate an electric power system most economically. This paper proposes a hybrid methodology integrating bee colony optimization with sequential quadratic programming for solving dynamic economic dispatch problem of generating units considering valve-point effects. This hybrid method incorporates bee colony optimization as a base level search which can give a good direction to the optimal region and sequential quadratic programming as a local search procedure which is used to fine tune that region for achieving the final solution. Numerical results of a ten-unit system have been presented to demonstrate the performance and applicability of the proposed method. The results obtained from the proposed method are compared with those obtained from hybrid of particle swarm optimization and sequential quadratic programming and hybrid of evolutionary programming and sequential quadratic programming.

Static economic dispatch (SED) allocates the load demand for a given interval of time among the committed generating units economically while satisfying various constraints. Dynamic economic dispatch (DED) which is an extension of static economic dispatch, determines the optimal sharing of time varying load demand among the committed units. Power plant operators try to keep gradients for temperature and pressure inside the boiler and turbine within safe limits to avoid shortening the life of the equipments. This mechanical constraint imposes limit on the rate of increase or decrease of the electrical power output. This limit is called ramp rate limit which differentiates DED from SED problem. Thus, in DED the dispatch decision at one time period affects those at later time periods. DED is the most accurate formulation of the economic dispatch problem but it is the most difficult to solve because of its large dimensionality. As competition is increasingly introduced into the wholesale generation markets, there is a need to understand the incremental cost burden imposed on the system operation by the generator ramping rate limitations. Since the DED was introduced, several classical methods [1], [2], [3], [4], [5] and [6] have been employed for solving this problem. However, all of these methods may not be able to find an optimal solution and usually stuck at a local optimum solution. Classical calculus-based methods address DED problem with convex cost function. But in reality large steam turbines have a number of steam admission valves, which contribute nonconvexity in the fuel cost function of the generating units. Dynamic programming (DP) can solve such type of problems but it suffers from the curse of dimensionality. Recently, stochastic search algorithms [7], [8], [9], [10] and [11] such as simulated annealing (SA), Genetic algorithm (GA), evolutionary programming (EP), particle swarm optimization (PSO) and differential evolution (DE) have been successfully used to solve power system optimization problems due to their ability to find the near global solution of a nonconvex optimization problem. These methods use probabilistic rules and have a large possibility to explore the search space freely. These methods do not always provide global optimum solution but they often provide a fast and reasonable solution. Swarm intelligence [12], [13] and [14], a branch of natural inspired algorithms, focuses on the behavior of insect in order to develop some meta-heuristics algorithms. Bee colony optimization (BCO) algorithm [15] is a new member of swarm intelligence and it mimics the food foraging behavior of honey bees. This algorithm is simple, robust and capable to solve difficult combinatorial optimization problems. Hybrid methods [16], [17] and [18] combining probabilistic methods and deterministic methods are found to be very effective for solving DED problems. In hybrid methods, probabilistic method is used as a base level search which gives a good direction to the optimal global region and deterministic method is used to fine tune that region to get the final solution. In this paper a hybrid method which integrates bee colony optimization (BCO) and sequential quadratic programming (SQP) is proposed for solving DED problem. The proposed hybrid method uses the property of BCO which can give a good solution even when the problem has many local optimum solution at the beginning and SQP which has local search property is used to obtain the final solution. BCO-SQP method is divided into two parts. In the first part BCO is employed to obtain near global solution. In the second part SQP is employed to find the optimum solution. In order to show the effectiveness of the proposed hybrid method a 10-unit test system with nonsmooth fuel cost function is used in this paper. The results of the proposed hybrid BCO-SQP method are compared with those obtained from hybrid of particle swarm optimization and sequential quadratic programming (PSO-SQP) and hybrid of evolutionary programming and sequential quadratic programming (EP-SQP).

This paper presents a hybrid method by combining BCO with SQP for solving dynamic economic dispatch problem considering valve point effect. In the proposed method, probabilistic BCO explore the search space freely. Whenever a better valley is explored, deterministic SQP descends the valley quickly with gradient direction and guarantees a local optimum. The effectiveness of the proposed method is illustrated by using a 10-unit test system and compared with the results obtained from PSO-SQP and EP-SQP methods. It is evident from the comparison that the proposed BCO-SQP based approach provides better results than PSO-SQP and EP-SQP methods in terms of minimum production cost and computation time.