  Load serving entities with storage units reach sizes and performances that
can significantly impact clearing prices in electricity markets. Nevertheless,
price endogeneity is rarely considered in storage bidding strategies and
modeling the electricity market is a challenging task. Meanwhile, model-free
reinforcement learning such as the Actor-Critic are becoming increasingly
popular for designing energy system controllers. Yet implementation frequently
requires lengthy, data-intense, and unsafe trial-and-error training. To fill
these gaps, we implement an online Supervised Actor-Critic (SAC) algorithm,
supervised with a model-based controller -- Model Predictive Control (MPC). The
energy storage agent is trained with this algorithm to optimally bid while
learning and adjusting to its impact on the market clearing prices. We compare
the supervised Actor-Critic algorithm with the MPC algorithm as a supervisor,
finding that the former reaps higher profits via learning. Our contribution,
thus, is an online and safe SAC algorithm that outperforms the current
model-based state-of-the-art.
