Is the information about the rain anecdotal, or has someone actually recorded the voltage on say a chart recorder for a year, and have meteorological records in the region for the same period.
If it is an accurate statement, then what might be happening in the region that changes during, or for a while after it has rained that could put a greatly increased load on the distribution system. I would assume that the distribution authority would know who all the large power users are, and when they put extra demands on the network, since they have to plan for peak demand(or in this case they can't plan, since they just don't have the capacity). The other possibility is that thousands of smaller users are for some reason placing greater demands on the system when it is not raining. What is your pattern of use, for example,
cheers,
Richard