Gradient Search Technique Applied to Dual-Optimal Design of a 3-Phase Core Type Transformer

Abstract

Most of the power and distribution transformers in power system are 3-phase core type transformers. They are extensively used- as such their cost is a sizable proportion of the total system cost. Therefore they are to be designed cost-optimally. The optimality is with reference to an objective function, generally in presence of constraints. The design variables are to be varied within their given bounds and the optimal solution is to be reached in finite number of steps, satisfying the given constraints. The paper presents a method for optimizing the design, in presence of constraints specified by the customer and the regulatory authorities, through gradient search technique. The objective function is a weighted combination of the cost of the transformer and the running losses which is not a mathematically framed but obtained from the transformer design sub-routine through computer programme. The objective of this paper is to find out above objective function without mathematically framed function which leads to inaccuracy for approximation due to magnetic saturation and nonlinearity present in the system. Most of the objective function is framed by taking few terms from a polynomial to avoid complicacy of the function, such as core loss expression obtained from curve with the variation of flux densities. The starting point has been chosen within the allowable parameter space- the steepest decent path has been followed for convergence. The step length has been judiciously chosen. The hyper surface has been found to be concave. As such no local minima problem is faced. The method is best as it its convergence is quickest.