  The power domination problem focuses on finding the optimal placement of
phase measurement units (PMUs) to monitor an electrical power network. In the
context of graphs, the power domination number of a graph $G$, denoted
$\gamma_P(G)$, is the minimum number of vertices needed to observe every vertex
in the graph according to a specific set of observation rules. In
\cite{ZKC_cubic}, Zhao et al. proved that if $G$ is a connected claw-free cubic
graph of order $n$, then $\gamma_P(G) \leq n/4$. In this paper, we show that if
$G$ is a claw-free diamond-free cubic graph of order $n$, then $\gamma_P(G) \le
n/6$, and this bound is sharp. We also provide new bounds on $\gamma_P(G \Box
H)$ where $G\Box H$ is the Cartesian product of graphs $G$ and $H$. In the
specific case that $G$ and $H$ are trees whose power domination number and
domination number are equal, we show the Vizing-like inequality holds and
$\gamma_P(G \Box H) \ge \gamma_P(G)\gamma_P(H)$.
