Abstract Electricity dispatch is a difficult optimisation problem that aims at minimising total fuel cost while satisfying system power demand and certain thermal unit constraints. Modelling valve point effects, multiple fuel options or transmission losses brings non-convexity and non-smoothness into the mathematical models. This paper proposes mathematical programming-based models for valve point effects, multiple fuel options and transmission loss problems respectively. Mathematical programming leads to robust and rigorous optimisation methods for these problems. The applicability of the proposed methods is demonstrated through a number of case studies. For all the case studies, the corresponding methods identify power schedules at least as good as or better than the best known in literature.