The Power Dominating Set problem is a variant of the classical domination problem in graphs:

Given an undirected graph *G=(V,E)*, find a minimum
subset *P* of *V* such that all vertices in *V* are
"observed" by vertices in *P*.

Herein, a vertex observes itself and all its neighbors, and
if an observed vertex has all but one of its neighbors observed,
then the remaining neighbor becomes observed as well.
Answering an open question of Haynes et al., we show that
Power Dominating Set can be solved by "bounded-treewidth
dynamic programs". Moreover, we simplify
and extend several of their NP-completeness results, additionally
showing that Power Dominating Set remains
NP-complete for planar graphs, for circle graphs, and for split graphs.
In particular, our improved reductions imply that
Power Dominating Set parameterized by *|P|* is W[2]-hard
and cannot be better approximated than Dominating Set.