  Volt-var control (VVC) is the problem of operating power distribution systems
within healthy regimes by controlling actuators in power systems. Existing
works have mostly adopted the conventional routine of representing the power
systems (a graph with tree topology) as vectors to train deep reinforcement
learning (RL) policies. We propose a framework that combines RL with graph
neural networks and study the benefits and limitations of graph-based policy in
the VVC setting. Our results show that graph-based policies converge to the
same rewards asymptotically however at a slower rate when compared to vector
representation counterpart. We conduct further analysis on the impact of both
observations and actions: on the observation end, we examine the robustness of
graph-based policy on two typical data acquisition errors in power systems,
namely sensor communication failure and measurement misalignment. On the action
end, we show that actuators have various impacts on the system, thus using a
graph representation induced by power systems topology may not be the optimal
choice. In the end, we conduct a case study to demonstrate that the choice of
readout function architecture and graph augmentation can further improve
training performance and robustness.
