Optimal Policies for Simultaneous Energy Consumption and Ancillary   Service Provision for Flexible Loads under Stochastic Prices and No Capacity   Reservation Constraint
  Flexible loads, i.e. the loads whose power trajectory is not bound to a specific one, constitute a sizable portion of current and future electric demand. This flexibility can be used to improve the performance of the grid, should the right incentives be in place.   In this paper, we consider the optimal decision making problem faced by a flexible load, demanding a certain amount of energy over its availability period, subject to rate constraints. The load is also capable of providing Ancillary Services (AS) by decreasing or increasing its consumption in response to signals from the Independent System Operator. Under arbitrarily distributed and correlated Markovian energy and AS prices, we obtain the optimal policy for minimizing expected total cost, which includes cost of energy and benefits from AS provision, assuming no capacity reservation requirement for AS provision. We also prove that the optimal policy has a multi-threshold form and can be computed, stored and operated efficiently. We further study the effectiveness of our proposed optimal policy and its impact on the grid.   We show that, while optimal simultaneous consumption and AS provision under real-time stochastic prices is achievable with acceptable computational burden, the impact of adopting such real-time pricing schemes on the network might not be as good as suggested by the majority of the existing literature. In fact, we show that such price responsive loads are likely to induce peak-to-average ratios much more than what is observed in the current distribution networks and adversely affect the grid. 
Mahdi Kefayati and Ross Baldick
math.OC cs.SY