Chebyshev based continuous time power system operation approach

There is a growing interest to increase temporal resolution in power system optimization models in order to improve representation of intermittent renewable generation and thus capture more variability and costs. This increase in temporal resolution, however, presents important modeling challenges since the optimization problem complexity grows with the higher number of variables and constraints needed to represent further (discrete) time periods. In this context, this paper proposes a modeling approach in continuous time, based on a pseudo-spectral representation of Chebyshev polynomials that can be applied to a variety of power system optimization problems. In particular, this paper illustrates a specific application of the proposed modeling approach to determine continuous time operation of a small-scale power system, highlighting its main advantages such as the continuous temporal resolution, straightforward implementation of differential and integral constraints needed to properly model flexibility, and reduction of computational burden. Comparison between continuous and discrete time power system operation solutions is also presented.