Unit Commitment Incorporating Histogram Control of Electric Loads With Energy Storage

This paper addresses the challenge of scheduling a large population of electric water heaters (EWHs) by incorporating a physically-based aggregate model of the population into the day-ahead unit commitment (UC). This goal has been accomplished via several innovations: (i) consideration of a large controllable temperature range over which random distributions of heaters can take many different shapes; (ii) modeling the random nature of the heater population and its dynamics via histograms and their transition equations; (iii) for varying levels of energy stored in the EWH population, finding the specific shapes of stationary EWH histograms that have minimum overlaps with the uncontrollable temperature zones; (iv) from such histograms, computing the bounds on the number of heaters that can be turned on/off in terms of the energy stored in the population; (v) incorporating the aggregate EWH power consumed and energy stored and their constraints into a modified UC; (vi) developing a scheme whereby individual EWHs self-dispatch to meet the scheduled histograms along with their aggregate energy and power levels. Numerical simulations illustrate the applicability and benefits of the approach, which, with minor extensions, can be extended to other forms of electric loads with energy storage such as space heating and cooling systems and electric vehicles.