  We study operations of a battery energy storage system under a baseline-based
demand response (DR) program with an uncertain schedule of DR events.
Baseline-based DR programs may provide undesired incentives to inflate baseline
consumption in non-event days, in order to increase "apparent" DR reduction in
event days and secure higher DR payments. Our goal is to identify and quantify
such incentives. To understand customer decisions, we formulate the problem of
determining hourly battery charging and discharge schedules to minimize
expected net costs, defined as energy purchase costs minus energy export
rebates and DR payments, over a sufficiently long time horizon (e.g., a year).
The complexity of this stochastic optimization problem grows exponentially with
the time horizon considered. To obtain computationally tractable solutions, we
propose using multistage model predictive control with scenario sampling.
Numerical results indicate that our solutions are near optimal (e.g., within 3%
from the optimum in the test cases). Finally, we apply our solutions to study
an example residential customer with solar photovoltaic and battery systems
participating in a typical existing baseline-based DR program. Results reveal
that over 66% of the average apparent load reduction during DR events could
result from inflation of baseline consumption during non-event days.
