Economic Dispatch of a Single Micro-Gas Turbine Under CHP Operation with Uncertain Demands

This work considers the economic dispatch problem for a single micro-gas turbine, governed by a discrete state-space model, under combined heat and power (CHP) operation and coupled with a utility. If the exact power and heat demands are given, existing algorithms can be used to give a quick optimal solution to the economic dispatch problem. However, in practice, the power and heat demands can not be known deterministically, but are rather predicted, resulting in an estimate and a bound on the estimation error. We consider the case in which the power and heat demands are unknown, and present a robust optimization-based approach for scheduling the turbine's heat and power generation, in which the demand is assumed to be inside an uncertainty set. We consider two different choices of the uncertainty set relying on the $\ell^\infty$- and the $\ell^1$-norms, each with different advantages, and consider the associated robust economic dispatch problems. We recast these as robust shortest-path problems on appropriately defined graphs. For the first choice, we provide an exact linear-time algorithm for the solution of the robust shortest-path problem, and for the second, we provide an exact quadratic-time algorithm and an approximate linear-time algorithm. The efficiency and usefulness of the algorithms are demonstrated using a detailed case study that employs real data on energy demand profiles and electricity tariffs.