Thyristor in a choppercircuit
Question: Can I do this also using power instead of energy?


Yes, you can convert switching energy losses to power losses by multiplying the energy loss (per cycle) by operating frequency fc. This produces watts numerically and is independent of duty cycle.

So, those fixed switching losses are ever present and can be subtracted from the target power loss (P\$_{hs}\$) leaving just the power value that is based only on duty cycle.

Given that you have numbers for on_power loss and off_power loss this would appear to be the easier route to take.