We study the problem of minimizing the long-term average power grid operational cost through power demand scheduling. A controller at the operator side receives consumer power demand requests with different power requirements, durations and time flexibilities for their satisfaction. Flexibility is modeled as a deadline by which a demand is to be activated. The cost is a convex function of total power consumption, which reflects the fact that each additional unit of power needed to serve demands is more expensive to provision, as demand load increases. We develop a stochastic model and introduce two online demand scheduling policies. In the first one, the Threshold Postponement (TP), the controller serves a new demand request immediately or postpones it to the end of its deadline, depending on current power consumption. In the second one, the Controlled Release (CR), a new request is activated immediately if power consumption is lower than a threshold, else it is queued. Queued demands are activated when deadlines expire or when consumption drops below the threshold. These policies admit an optimal control with switching curve threshold structure, which involves active and postponed demand. The CR policy is asymptotically optimal as deadlines increase, namely it achieves a lower bound on average cost, and the threshold depends only on active demand. Numerical results validate the benefit of our policies compared to the default one of serving demands upon arrival.
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