Answer:
(It had been a most unpleasant coincidence that the power outage had come when we had guests staying over; the entire house was full.)
Step-by-step explanation:
The sentences are sematically linked, so the semicolon is connecting the two sentences coherently. This means that the semicolon can be replaced by a connector: It had been a most unpleasant coincidence that the power outage had come when we had guests staying over since the entire house was full. The coherence is related to a known or evident reason.