DigitalF: Europan Campus Rottal-Inn
R. Brandenberg, Matthias Huber, M. Silbernagl
The summed start-up costs in a unit commitment problem
EURO Journal on Computational Optimization, vol. 5, no. 1-2, pp. 203-238
We consider the sum of the incurred start-up costs of a single unit in a Unit Commitment problem. Our major result is a correspondence between the facets of its epigraph and some binary trees for concave start-up cost functions CU, which is bijective if CU is strictly concave. We derive an exponential H-representation of this epigraph, and provide an exact linear separation algorithm. These results significantly reduce the integrality gap of the Mixed Integer formulation of a Unit Commitment Problem compared to current literature.
DigitalNachhaltigF: Europan Campus Rottal-Inn
M. Silbernagl, Matthias Huber, R. Brandenberg
Improving Accuracy and Efficiency of Start-Up Cost Formulations in MIP Unit Commitment by Modeling Power Plant Temperatures
IEEE Transactions on Power Systems, vol. 31, no. 4, pp. 2578-2586
This paper presents an improved mixed-integer model for the thermal unit commitment problem. By introducing new variables for the temperature of each thermal unit, the off-time-dependent start-up costs are modeled accurately and with a lower integrality gap than state-of-the-art formulations. This new approach significantly improves computational efficiency compared to existing formulations, even if they only model a rough approximation of the start-up costs. Our findings were validated on real-world test cases using CPLEX.