Graphical Estimation of Optimum Weights of Iron and Copper of a Transformer

Transformer may be designed to make one of the following quantities as minimum, (i) total volume (ii) total weight (iii) total cost (iv) total losses. In general these requirements are contradictory and it is normally possible to satisfy only one of them in a transformer. However the conditions for all the above quantities end in terms of the ratio of weight of iron and copper. In particular, the ratio is unity for optimum weight design of a transformer. Once we obtain optimum weights, optimum requirement for other quantities can easily be estimated. The design equations are modified so as to have only two variables in the equation. Necessary objective function and constraint equations are formed with two variables. Graphical method is adopted and optimum values are estimated separately and simultaneously. A 5 kVA single phase core type distribution transformer is taken and the condition for optimum weight design is verified and analysed.