  Transient stability of power systems is becoming increasingly important
because of the growing integration of renewable resources. These resources lead
to a reduction in mechanical inertia but also provide increased flexibility in
frequency responses. Namely, their power electronic interfaces can implement
almost arbitrary control laws. To design these controllers, reinforcement
learning (RL) has emerged as a powerful method in searching for optimal
non-linear control policy parameterized by neural networks.
  A key challenge is to enforce that a learned controller must be stabilizing.
This paper proposes a Lyapunov regularized RL approach for optimal frequency
control for transient stability in lossy networks. Because the lack of an
analytical Lyapunov function, we learn a Lyapunov function parameterized by a
neural network. The losses are specially designed with respect to the physical
power system. The learned neural Lyapunov function is then utilized as a
regularization to train the neural network controller by penalizing actions
that violate the Lyapunov conditions. Case study shows that introducing the
Lyapunov regularization enables the controller to be stabilizing and achieve
smaller losses.
