  We analyze the dynamics of the power grid with a high penetration of
renewable energy sources using the ORNL-PSERC-Alaska (OPA) model. In particular
we consider the power grid of the Balearic Islands with a high share of solar
photovoltaic power as a case study. Day-to-day fluctuations of the solar
generation and the use of storage are included in the model. Resilience is
analyzed through the blackout distribution and performance is measured as the
average fraction of the demand covered by solar power generation. We find that
with the present consumption patterns and moderate storage, solar generation
can replace conventional power plants without compromising reliability up to
$30\%$ of the total installed capacity. We also find that using source
redundancy it is possible to cover up to $80\%$ or more of the demand with
solar plants, while keeping the risk similar to that with full conventional
generation. However this requires oversizing the installed solar power to be at
least $2.5$ larger than the average demand. The potential of wind energy is
also briefly discussed
