  Inverter-based distributed energy resources provide the possibility for fast
time-scale voltage control by quickly adjusting their reactive power. The
power-electronic interfaces allow these resources to realize almost arbitrary
control law, but designing these decentralized controllers is nontrivial.
Reinforcement learning (RL) approaches are becoming increasingly popular to
search for policy parameterized by neural networks. It is difficult, however,
to enforce that the learned controllers are safe, in the sense that they may
introduce instabilities into the system.
  This paper proposes a safe learning approach for voltage control. We prove
that the system is guaranteed to be exponentially stable if each controller
satisfies certain Lipschitz constraints. The set of Lipschitz bound is
optimized to enlarge the search space for neural network controllers. We
explicitly engineer the structure of neural network controllers such that they
satisfy the Lipschitz constraints by design. A decentralized RL framework is
constructed to train local neural network controller at each bus in a
model-free setting.
