  Based on stochastic differential equations (SDEs), we analyse the overall
performance of heterogeneous power systems network, subject to spatially
distributed and correlated noise with random initial conditions. We determine
bounds on the H_2 norm of the heterogeneous system based on a closed-form of
the norm of the homogeneous power system. Then, we formulate possible scenarios
for performance optimization and link these to applications for network design
and control problems in power systems. Our results are corroborated by
numerical simulations from Kundur's four-machine two-area network after
adaption to our setup.
