kruskal wallis power
for lots of information on the power of the test.
A fundamental part of a power analysis is 'against what' alternative. The Kruskal Wallis test has more power than an ANOVA if the alternative is not normal, but less if the alternative is normal. If you want to dig deeper, the "pitman relative efficiency" of the power comes to mind as a search term.
As far as actually computing the power, you could use the large sample theory or do simulations for specific scenarios.