Integral measures of electric power distribution networks: load–length curves and line-network multipliers

This paper describes an integral (macroscopic) approach to the evaluation and maximization of performance in the design of networks for the distribution of electric power. The method recognizes the hierarchical structure of tree shaped networks and accounts for all the consumption nodes, links (lines) and loads carried by each line. The lines that carry the same load form one group. The total length of the lines belonging to one group is calculated. The total length of all the lines is the sum of the total lengths calculated for each group. This analysis makes it possible to represent one network as a curve in the load–length plane. Next, the moment of the load at one consumption node is defined as the load times the direct distance from the source to the node. The global load moment is the sum of all the individual load moments. The global load moment is proportional to the area trapped above the load–length curve of the network. It is shown that this area must be minimized in order to minimize the discounted total cost of the network. Six competing distribution networks are compared on this integral basis. Networks that are tree shaped and sufficiently complex perform at nearly the same (high) level. The robustness exhibited by tree shaped power distribution networks is similar to the robustness of other tree flow structures (fluid, heat, goods, people) in animate, inanimate and engineered flow systems in accordance with constructal theory.