One big regulation force in the EU at the moment is to integrate the markets of countries with one another. If more capacity is traded, the combined social welfare should increase, as buyers find more sellers and the other way around. A second assumption is that prices for electricity should decrease, as suppliers would need to give way from their current position of strong market power.

This blog post reports on empirical results from the last decade, where it is shown that the second assumption does not seem to hold: Prices were not significantly lower when two markets (e.g. the German and the French market) were coupled (note: the definition of "coupled" is that prices between the markets at the same time were within 5% of one another).

http://www.bruegel.org/nc/blog/detail/article/898-market-coupling-does-not-lo...

The author and also commentators speculate on why that might be and possible reasons are manifold - the electricity markets are influenced by many outside factors. However, one idea of the author is worth mentioning: "One possible explanation could be the sometimes unusual shapes of electricity cost curves. (...)This possibly needs to involve supply function equilibria to address the effects of oligopolistic competition in market integration."

I have been using supply functions in my papers as well, for their smooth state transition behaviour during market clearing and their usefulness in multi-unit auctions when market outcomes are uncertain.