Designing a 3-phase pure sine inverter. Where do I start?
How do I filter the output of the H-bridge to get a sine wave without losing power? (I'm trying to keep the efficiency as high as possible)


An ideal filter doesn't lose power, a filter built with lossy components does. So you have a classic cost/performance tradeoff, expensive low loss components or cheaper higher loss components.


  What's a good frequency for the SPWM? (I suppose the higher the better for smaller filter components as long as I keep an eye on the switching losses)


It should be at least above 20kHz, so you can't hear it. As you raise it further, the switching losses in the switches increases linearly with the switching frequency, but the components in the filter can shrink. You have another design tradeoff, losses in the switches versus size of the filter components. It's likely that filter component losses increase with frequency as well. Remember you're only trying to make 50/60 (maybe 400?) Hz out of this thing, so there's no need to go up to the frequencies that class D audio amplifiers do. One benefit of using very high frequencies is the potential for miniaturisation, do you need the smallest possible size? The answer to the size might allow you to choose between 30kHz and 300kHz.


  How do I get 3 phases and a neutral (wye) out of this? At first I thought I'd just build 3 separate, 120° shifted, inverters and connect them all to 1 point (neutral). But now that I'm thinking about it, that's probably not a great idea since they won't be electrically insulated


There are two alternatives. Run three half-bridge generators from the same supplies of +/- 400V, so you'd need two sets of batteries. Or, run three full bridge single phase bridge-tied load generators from three independent 400V batteries, connect them together at the neutral point.