How can we calculate optimal dimensions for volume of transformer?
I understand that your question is about &quot;how to optimize the design of a transformer with a specific set of constraints in order to minimize the function Volume&quot;.
I have tried several methods of design optimization. Methods such as Gradients are generally not applicable, as variables (such as wire gauge) are not continuous functions, moreover, it is not your case, but often the optimization needs to be multi-objective. In my experience, stochastic methods such as genetic algorithms are more effective and easy-to-implement.
Anyway, unfortunately there will be no single answer to your question. If you don't want to spend too much time developing a tool for this, you can try various design configurations manually with the core models available on the market. After a few tries, you can already get an idea of how the optimization algorithms would work on your problem.