  Starting from the Hamilton-Jacobi-Bellman (HJB) equation, we derive an
optimal feedback controller that makes use of available phase angle
measurements to drive the phase angles of the DC/AC converters towards steady
state angles that are frequency synchronous. The unique optimal controller that
solves the HJB equations is the angular droop control, and it guarantees
exponential stability of the desired steady state angles. For the linearized
system, the angular droop control is locally optimal in the \mathcal{H}_2 sense
and has active power to phase angle droop behavior. Additionally, we conduct a
performance analysis using system \mathcal{H}_2 norm to show that the angular
droop improves significantly upon standard frequency droop control during
transients and has better scalability to large networks. Finally, we suggest a
practical implementation of the angular droop control and corroborate our
results numerically through two different test cases.
