Control and optimization meet the smart power grid: scheduling of power demands for optimal energy management

The smart power grid harnesses information and communication technologies to enhance reliability and enforce sensible use of energy through effective management of demand load. We envision a scenario with real-time communication between the grid operator and the consumers. The operator controller receives consumer power demand requests with different power requirements, durations, and deadlines by which they are to be activated. The objective of the operator is to devise a power demand task scheduling policy that minimizes the grid operational cost over a time horizon. The cost is a convex function of total instantaneous power consumption and reflects the fact that each additional unit of power needed to serve demands is more expensive as the demand load increases. First, we study the off-line demand scheduling problem, where parameters are known a priori. If demands can be scheduled preemptively, the problem is a load balancing one, and we present an iterative algorithm that optimally solves it. If demands need to be scheduled non-preemptively, the problem is a bin packing one.

Next, we devise a stochastic model for the case when demands are generated continually and scheduling decisions are taken online, and we focus on long-term average cost. We present two types of demand load control based on current power consumption. In the first one, the controller may choose to serve a new demand request upon arrival or postpone it to the end of its deadline. The second one, termed Controlled Release (CR) activates a new request if the current power consumption is less than a threshold, otherwise the demand is queued. Queued demands are activated when their deadlines expire, or if consumption drops below the threshold. We derive a lower performance bound for all policies, which is asymptotically achieved by the CR policy as deadlines increase. For both types above, optimal policies are of threshold nature. Numerical results validate the benefit of our approaches compared to the default policy of serving demands upon arrival.