Design of I.v. distributors from standard cable sizes

An analytical study is made with the aid of a digital computer of the economic design of uniformly loaded a.c. distributors under balanced-phase loading conditions. The optimum profile of a continuously tapered distributor is obtained by an application of the calculus of variations, and the method is developed to cover the corresponding practical problem of designing a stepped distributor from standard cable sizes by introducing Lagrangian multipliers. Optimisation is carried out with respect to conductor volume and also with respect to costs over the life of the cable, taking energy losses into consideration. In the latter case, Kelvin´s law is shown to hold below a certain critical length. It is demonstrated that significant savings may be achieved by incorporating these methods in practical design work for new housing estates.