Learning the Optimal Energy Supply Plan with Online Convex Optimization

In this paper, we propose an online learning approach, utilizing the framework of Online Convex Optimization (OCO) to tackle the problem of learning the optimal energy supply plan, in terms of total incurred cost, from the perspective of an electricity retailer that also owns power generators and renewable energy sources. The retailer does not have prior knowledge about key dynamic processes that affect the problem, such as future demand, renewable energy supply, and wholesale market prices. The retailer sequentially learns how to adjust the power generation plan so as to minimize the power generation cost plus the cost of buying additional power from the wholesale market, in case the planned generated amount is not enough to cover the demand. We use Online Mirror Descent (OMD) and Online Gradient Descent (OGD), and we verify that they both achieve sublinear static and dynamic regret, which compare the cumulative cost of each algorithm against that of the optimal offline static and dynamic solution respectively. In particular, dynamic regret appears to be well aligned with the considered setting since it captures the fact that a power generator can dynamically change its power output between consecutive time slots based on only small adjustments and not in an arbitrary fashion, due to ramp constraints. Our model can capture different settings of electricity markets. Simulations with real data verify that OMD precisely learns the optimal dynamic supply policy for small power adjustments between consecutive time slots.