Dynamic programming for scalable just-in-time economic dispatch with non-convex constraints and anytime participation

This paper considers two classes of dynamic programming frameworks for economic dispatch in power systems. The first framework is of classical continuous convex economic dispatch. We present recursive formulae for computing the parameters of value functions and show that the value functions are generalized quadratic and generalized piecewise quadratic for unconstrained and generation-capacity constrained convex economic dispatch, respectively. The second framework is of discrete dynamic programming for economic dispatch with non-convex cost functions and constraints. The discrete dynamic programming framework is computationally scalable and decentralized. The computations of the value table are scalable in the sense that any newcomers and seceders of generation units can be numerically efficiently taken care of, by not re doing the entire backward induction process but only computing the value tables of the successors. Extension of the discrete dynamic programming framework to dynamic economic dispatch with ramp constraints is also presented. We demonstrate the proposed algorithms by three numerical case studies. One is for non-convex economic dispatch with 15 generation units and prohibited operating zones. Another example of a larger scale system of 53 units with consideration of transmission losses is also studied. For a dynamic case, the proposed method is applied to a dynamic economic dispatch problem with non-convex ramp constraints.