This paper seeks to consider the design of small, naturally cooled, and high‐frequency (in excess of 10 kHz) inductors. Its purpose is to show that the design of such inductors can be obtained from the solution of a signomial program. In its most general form, the signomial program calls for minimising the total mass (or cost) of the inductor whilst ensuring the satisfaction of the inductance value together with constraints imposed by the copper fill‐factor, the allowed temperature rise, Kirchhoff's mmf law, and the core flux density.
The signomial program is solved using a sequential geometric programming (SGP) approach specifically tailored to the inductor design problem. In essence, SGP seeks a constrained minimum mass (or cost) solution by optimally setting the inductor geometry parameters, the air‐gap length, and the relevant electrical and magnetic quantities.
Design results reveal that including the inductor geometry parameters in the set of problem variables leads to significant savings in the inductor mass (or cost).
In cases where there are restrictions on the inductor weight, the optimal solution of the signomial program can be used for manufacturing inductors having cores with non‐standard sizes. In other applications where core dimensions are chosen from the manufacturer's database, the SGP approach can be used to complete the design by either maximising the inductance value or minimising the total loss whilst enforcing a given inductance value.
This work presents a first attempt to optimise an inductor design via signomial programming. The proposed solution methodology is based on SGP, but specifically adapted to the inductor design problem.
