Constructal tree shaped networks for the distribution of electrical power

In this paper, we extend to the design of electric power distribution networks the constructal method of deducing the multiple dimensions of the network from the maximization of global system performance. Unlike earlier constructal designs of tree shaped networks, where the global objective was minimization of flow resistance and exergy destruction, in the present study, the global objective is minimization of the present worth total cost. The first half of the paper is a detailed account of all the components of the distribution system (hierarchy, voltage levels, lines, transformers) and the associated cost components that make up the global cost function. Emphasis is placed on the relations between length scales (radii, or reaches) at every voltage level and the costs of components and assemblies of components at every level and, ultimately, at the global level. It is shown that the global cost depends on multiple length scales, the load density (power consumption per unit of territory served) and the operating and economic characteristics of the voltage lines and transformers. Tradeoffs between the costs of lines and transformers exist at every voltage level, and this permits the multiple minimization of the global cost function. The optimized radii for each voltage level of the network are reported: they decrease at their own rates as the load density increases.