  Let $\A$ be a ring with local units, $\E$ a set of local units for $\A$, $\G$
an abelian group and $\alpha$ a partial action of $\G$ by ideals of $\A$ that
contain local units and such that the partial skew group ring $\A\star_{\alpha}
\G$ is associative. We show that $\A\star_{\alpha} \G$ is simple if and only if
$\A$ is $\G$-simple and the center of the corner $e\delta_0 (\A\star_{\alpha}
\G) e \delta_0$ is a field for all $e\in \E$. We apply the result to
characterize simplicity of partial skew group rings in two cases, namely for
partial skew group rings arising from partial actions by clopen subsets of a
compact set and partial actions on the set level.
