A theoretical model for the determination of the optimal design of a power transportation and distribution system with several voltage levels

The paper presents an optinization model for the problem of electricity transportation and distribution. In most of the work in the field the attention is restricted to a single voltage level and the problem is presented as a network capacity expansion model. In this paper we capitalize on notions used in standardization studies of electrical networks to arrive at an optimization model of the global transportation and distribution system. Several voltage levels are considered simultaneously. The system is modeled using aggregate variables such as the density of lines and transformers at each voltage level, the number of neighbouring substations… The aim of the model is to simultaneously determine several important characteristics of the system such as the section and the length of the lines at each voltage level, the rated power of the transformers and their number at each substation. The resulting model is a nonlinear program: more specifically it is first written as an algebraic program which is then transformed to a signomial problem of the order of thirty constraints and variables. The problem is solved using a generalized reduced gradient code.