Effect of models uncertainties on the emission constrained economic dispatch. A prediction interval-based approach

Although electricity is a clean and relatively safe form of energy when it is used, the generation and transmission of electricity have severe effects on the environment. An alternative to diminish the polluting emissions released by the generating units is the Emission Constrained Economic Dispatch (ECED). This is an optimization problem where the total fuel cost is minimized while treating emissions as a constraint with a pre-specified limit. Usually, the fuel cost and emission functions of the generating units must be experimentally derived, introducing then uncertainties in the obtained models. However, these uncertainties are often neglected and the ECED problem is solved considering the coefficients of the functions involved as exact (totally known) values. In this investigation we analyzed the effect of the uncertainties associated to the experimental derivation of the input-output curves of thermal power plants. Particularly, when polynomial models are fitted through multiple linear regression, we proposed an approach that, based on the respectively prediction intervals, can provide solutions immunized, in some sense, against variability in the coefficients estimates. We tested the proposed approach in a real system from the Chilean electrical power network. For the analyzed system we noted that, when uncertainties are not considered, the deterministic optimal solutions can be environmentally infeasible in some scenarios; whereas solutions obtained through the proposed approach, can significantly diminish the risk of environmental violations. The robustness of the prediction interval-based solutions was obtained with a negligible increase of the total fuel cost in all the cases studied.