Near-optimal execution policies for demand-response contracts in electricity markets

Demand side participation is essential for achieving real-time energy balance in today's electricity grid. Demand-response contracts, where an electric utility company buys options from consumers to reduce their load in future, are one of the important tools to increase the demand-side participation. In this paper, we consider the operational problem of optimally exercising the available contracts over the planning horizon such that the total cost to satisfy the demand is minimized. In particular, we consider the objective of minimizing the sum of the expected ℓβ-norm of the load deviations from given thresholds and the contract execution costs over the planning horizon. We present a data driven near-optimal algorithm for the contract execution problem. Our algorithm is a sample average approximation (SAA) based and we provide a sample complexity bound on the number of demand samples required to compute a (1 + ε)-approximate policy for any ε > 0. Our SAA algorithm is quite general and can be adapted to quite general demand models and objective function. For the special case where the demand in each period is i.i.d., we show that a static solution is optimal for the dynamic problem. We also conduct a numerical study to compare the performance of our SAA based DP algorithm. Our numerical experiments show that we can achieve a (1+ε)-approximation in significantly smaller number of samples than what is implied by the theoretical bounds. Moreover, the structure of the approximate policy also shows that it can be well approximated by a simple piecewise linear function of the state.