  In this paper we derive fundamental limitations on the levels of $H_2$ and
$H_\infty{}$ performance that can be achieved when controlling lossless
systems. The results are applied to the swing equation power system model,
where it is shown that the fundamental limit on the $H_2$ norm scales with the
inverse of the harmonic mean of the inertias in the system. This indicates that
power systems may see a degradation in performance as more renewables are
integrated, further motivating the need for new control solutions to aid the
energy transition.
