Use of the Method of Branches and Boundaries to Optimize the Development of Electrical Networks of Complex Energy Systems

Abstract

The issues of development and use of methods and algorithms for optimizing the development of electrical networks of power systems that provide an effective solution to the problem of development, implementation of technical and resource constraints in the form of equalities and inequalities are considered. The essence of the proposed method of branches and boundaries is to break down the set of options for network development into disparate subsets and the consistent exclusion of subsets of unpromising solutions. Thus, to each subset external and internal estimations are put in accordance. At the decision of a problem of a choice of an optimum variant of development of a network of fragmentation of subsets is carried out on a sign of presence or absence in the considered subset of this or that branch. To determine the external and internal estimates at each optimization step, the shortest electrical networks must be found and the transport problems with intermediate traffic for the subsets of comparable electrical network development options must be solved. It should be noted that since the number of subset fractions depends on the order of consideration of acceptable branches of the electrical network, the efficiency of using the method of branches and boundaries depends significantly on the efficiency of the branch selection algorithm at each optimization step. Since the number of possible options for the development of the electrical network is a finite number, after performing a number of steps of fragmentation of the set of remaining options, the development will be so small that the exact lower limit of change in the cost function of each of the remaining subsets can be determined. The variant of network development that corresponds to the smaller of the lower limits is optimal. The proposed algorithm, which uses the method of branches and boundaries, has a fairly high level of convergence, resistance to the choice of initial approximations.