Discrete state-space model to solve the unit commitment and economic dispatch problems

Abstract

The unit commitment (UC) and economic dispatch (ED) problems are the most important problems in managing and optimizing the operations of power systems. Mixed-integer programming (MIP) seems to be one of the most exact and reliable techniques to solve the traditional UC problem, in comparison to other techniques. The solutions of the UC problem, when formulated as a MIP, involves the solutions of the ED problem. Recently, the attention is drawn to formulating a state-space model for the power generation process that can be used to solve the UC problem, for several potential reasons. First, state-space models can be easier to implement the model predictive control (MPC) strategy. Besides, state-space models are more suitable to describe the power ramping process, should more complicated models than the linear first order models are sought. Further, state-space models can be more useful when different stages of the ramping process are considered. In this work, we present a mixed-integer state-space model to solve both the UC and ED problems by considering the output power level, status of the generating unit, and up and down time counters as state variables. The up and down time counters are expressed from equalities. Numerical experiments are provided to compare the proposed model with another MIP that is not described as state-space model. The numerical results show that the proposed model is competitive, and it gives even better results for small-sized problems, especially when Piecewise Linear (PWL) objective functions are considered.