Unfortunately, this problem is known to be NP-hard by a reduction from the dominating set problem.
Given a graph G, a dominating set in G is a set of nodes D such that every node in the graph is either in D or is one hop away from D. The problem of finding the smallest dominating set in a graph is known to be NP-hard, and this problem easily reduces to the one you're trying to solve: given a graph G, produce a city (represented as a graph) that has the same structure as G, then give every power plant a radius of 1 (meaning that it can cover a node and all its neighbors). Finding the smallest set of power plants to cover the entire city then ends up producing a dominating set for the graph. Therefore, your problem is NP-hard.
As mentioned in this section of the Wikipedia page, it turns out that this problem is surprisingly hard to approximate. The Wikipedia page lists a few algorithms and approaches for approximating it, but it appears to be one of those NP-hard problems that resists polynomial-time approximation schemes.
Hope this helps!