  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.
