Demand response for contingency management via real-time pricing in Smart Grids

In this paper, we investigate real-time pricing for a power grid operator that sells electric power to a set of self-interested aggregators within a particular day, named actual day. We propose a real-time pricing scheme for the grid operator to manage demand response (DR) of aggregators upon a contingency of supply deficiency. Under our scheme, the grid operator offers real-time discounted electricity prices to aggregators in order to incentivize them to reschedule their day-ahead demands over time. We formulate a bilevel optimization problem, named bilevel discount pricing problem (BDPP), to design discounted electricity prices for the grid operator so as to minimize its residual cost, defined as the sum of operational costs from the contingency up to the end of the actual day. We further derive the equivalent one-level optimization problem of BDPP, named one-level discount pricing problem (ODPP). Since both BDPP and ODPP are non-convex optimization problems, it is difficult to solve them globally optimally. Alternatively, we develop a sequential convex programming (SCP) based algorithm to solve ODPP locally optimally. We also propose a randomized search (RS) based algorithm to heuristically solve BDPP. Last, we compare performances of algorithms using a numerical example based on the Singapore power grid data, from which we observe that the residual cost of the grid operator reduces remarkably while aggregators pay less bills after rescheduling. Moreover, algorithms converge in an efficient time, e.g., a couple of minutes. Hence, our pricing scheme can manage DR of aggregators in real time to provide a cost-efficient secondary reserve service.