Optimal packing of transformer coil via dynamic programming

One of the transformer major design elements is its core design. The good performance of the transformer requires its coil core to be laminated and composed of different widths – stepped layers of specific steel packed together. For optimum design, the cross sectional shape of the core must be as circular as possible. So, an optimal packing can be attained by maximizing the steel core coverage. The number of different widths of steel plates n is selected to compose the packed core for a coil of diameter d. Then, an optimum sequence of decisions, for the n widths as well as the number of thin plates of each, is required. Dynamic programming is concerned with these optimum sequential decisions. An adequate forward recursive equation is formulated, because there isn't a standard dp model for sequential decision making problems. To implement the recursive computations, a FORTRAN program is developed. Assuming that d is given the values 150, 200, 250, 300, 400 and 500 mm., while giving n the values from 2 to 15, the program is run at different combinations of n and d. It is found that maximum core coverage is sensitive to changing of n but it is slightly affected by changing of d.