Two variable approach for optimum design of a distribution transformer

Abstract

In Power Systems, distribution transformers are found in large numbers at the consumer end. The transformers are generally to satisfy one of the objectives, viz. cost, weight, volume or losses depending upon the need of the consumer and their circumstances to be minimum or optimum. The transformer may be said accordingly as optimum cost, weight, volume or loss transformer. The above objectives are governed by many variables. It is the general practice that some variables are assumed as known and fixed and other variables are treated as independent or free variables. The optimization is finding optimum values for these independent variables and making the objective optimum or minimum. Hence it is difficult to arrive at an optimum design. At the same time, in computer based optimizing method, the steps involved are (i) synthesis (ii) analysis and (iii) an optimizing routine. In this method the optimum value of a variable, which appear in design equation, is achieved, which in turn is used to minimize or maximize a quantity of interest in the calculation subsequently. The transformer is made up of basically iron and copper. The objectives indicated above are directly related to iron and copper. The transformer is supposed to deliver its rated kVA as output and so the output of the transformer itself is taken as constraint. It is therefore necessary that the output equation is to be modified substituting the known values for the variables in the equation and finally obtaining an equation in terms of two variables as they appear in the objective function. Thus the objective function and constraint equation are formed only with the help of two variables depending upon the objective in mind, where the requirements for any optimizing problem are fulfilled. Voltage regulation is calculated from the results obtained by the proposed method and presented. A new algorithm for overall optimum design of a distribution transformer is presented using two variable approach.