Mixed-integer minimization of the cost function of the Unit Commitment problem for isolated power systems

Abstract

Unit Commitment (UC) is a minimization problem that aims to schedule the required generating units in a power system over some time horizon to meet the demand based on minimizing the production cost. In this paper, we present a novel technique to minimize such functions based on Mixed-integer formulation, neglecting the time horizon and most of the constraints. This technique can be considered as a first step in a better and tighter mixed-integer formulation of the unit commitment problem, especially for isolated power systems that contain a small number of generating units. Data from isolated power systems on marine vessels are used to test this technique. The proposed technique requires more constraints and binary variables. However, the numerical results presented in this work, show that the proposed method gives more efficient results for low demand, and close results to those obtained from local minimizers when the demand is high. The computational time of the suggested method does not seem to be explicitly longer than the time taken by the local minimizers, especially for small isolated power systems.

Dynamic formulation of the unit commitment and economic dispatch problems

“…In previous work by the present authors [12], the piecewise linear (PWL) approximation of the this function was discussed. Multiplying (31) by the binary indicator α j (k) to drive the power to zero when the unit is off, and by using the auxiliary variable Z pα j (k), defined as before, the fuel consumption function is obtained to be:…”

“…subject to the difference equations in (8), (11), (14), (21) and the constraints in (7), (12), (13) (1),…”