Question

这两句话都对吗？为什么？？

I finished my article yesterday evening when the light went out. 这句对吗？？

I was going to finish my article yesterday evening when the light went out.

Answer 1

从句是瞬时性动作，主句应该用进行时或完成时，强调从句动作发生的一瞬间，主句主语正在做什么或已经做完什么。
I have finished my article yesterday evening when the light went out. 当电灯熄灭时我已经做完了作业。
I was going to finish my article yesterday evening when the light went out. finish 没有进行时态，所以用将来时（实际也是进行的结构be going to，不能换成would)
当电灯熄灭时，我正要完成作业（快要完成了）。

类似的语句还有：
I was doing my homework when she came in.
她进来时我正在做作业。
I have arrived home when the rain stated.
下雨时我已经赶回家。

Answer 2

上对下错。