  This paper develops a risk-aware controller for grid-forming inverters (GFMs)
to minimize large frequency oscillations in GFM inverter-dominated power
systems. To tackle the high variability from loads/renewables, we incorporate a
mean-variance risk constraint into the classical linear quadratic regulator
(LQR) formulation for this problem. The risk constraint aims to bound the
time-averaged cost of state variability and thus can improve the worst-case
performance for large disturbances. The resulting risk-constrained LQR problem
is solved through the dual reformulation to a minimax problem, by using a
reinforcement learning (RL) method termed as stochastic gradient-descent with
max-oracle (SGDmax). In particular, the zero-order policy gradient (ZOPG)
approach is used to simplify the gradient estimation using simulated system
trajectories. Numerical tests conducted on the IEEE 68-bus system have
validated the convergence of our proposed SGDmax for GFM model and corroborate
the effectiveness of the risk constraint in improving the worst-case
performance while reducing the variability of the overall control cost.
