WHY THERMAL MODEL?

The starting point of any machine optimization even today, starts with a super reliable empirical formula of the slot temperature relating to the permissible current density. For example, a naturally cooled slot can have 4.5 A/sq mm and a liquid cooled can have up to 9 A/ sq mm( these values of course vary slightly with machine topology). But anyhow, while doing the design optimization, thats how we put the constraint of the current in the winding. And this is flawed with the empirical limitation and especially in this generation when we have so much computation power, it makes no sense ( ok!! this is exaggerated, it still makes sense). But at least you will agree, that one primary goal of the machine design is to utilize the iron to its full capacity, and this is very important in the analysis of the cost vs efficiency curve. If you are downplaying ampere's equation with limited current, then you have never used it to its full extent. So let the machine decide how much current it can withstand in its winding through your favourite optimization algorithm.

WHAT SHOULD WE DO?

Well, to start with, do not limit your current in the slot while optimizing your machine. Instead couple a thermal model to determine what limit you can reach while respecting the temperature of your winding. So now the question comes, do we need a finite element model or an easy analytical model. And this is again quite tricky my friend, as finite element model can take so much extra time ( in optimization even millisecond maters) to produce a reliable result. Look at this nice 3D model of temperature distribution of a reluctance machine.

In an optimization problem, we definitely don't need the above. A lot of researchers these days have shown a very promising analytical thermal model that shows a very good agreement with the finite element model. You need to remember that, a thermal model is not as complicated as respecting maxwell equations. So it is possible to reach very good accuracy with a reluctance network.

EASY FIX

For example check this one, exactly the same analytical model of the previous finite element model. The biggest challenge is however to know the convection coefficient. But if you are working in a company or any lab with a prolonged history of thermal measurement, you will get those coefficients. If not, you can make a good educated guess from the literature.

The models are based on the super nice work of my colleagues

CONCLUSION

You can always use a simple analytical thermal model when you are optimizing your machine, at least make a couple of rounds of the 'optimization run' with a thermal model. It is anyhow a good start to understand the machine you are designing. Let me know what do you think in the comment section, and if you have used a thermal model in optimization.