Optimal dispatch of electric power with ambient air quality constraints

A method is given for allocating power loads for a system of electric generating units in a way which meets the time-dependent demand and minimizes the sum of the fuel cost and a penalty function for pollution. The method takes into account explicitly the dynamic nature of ambient air pollution which depends on the topography of a region and on the past performance of the system. With suitable and reasonably realistic approximations, the problem is reduced to a linear-quadratic optimal control problem for which a linear feedback control rule is obtained. In addition, a discrete version of the problem is given which has the form of a quadratic programming problem, and thus can accommodate, in a straightforward manner, additional constraints such as fuel limitations and upper bounds on emission.