Improving Accuracy and Efficiency of Start-Up Cost Formulations in MIP Unit Commitment by Modeling Power Plant Temperatures

Abstract

Abstract-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. Start-up costs [cost] NOMENCLATURE Indices and Sets

Column generation for the discrete UC problem with min-stop ramping constraints

“…Arroyo and Carrion (2006); Morales-España et al (2015) and Gentile et al (2017) provided efficient MILP formulation to model start-up and shut-down trajectories when a thermal production is in the domain [0, P min u ]. Silbernagl et al (2016) and Brandenberg et al (2017) provided efficient models to compute start-up costs and curves. Frangioni et al (2008) presented different types and formulations for ramping constraints when a thermal production is in the domain [P min u , P max u ], ensuring physical modulation constraints.…”

The summed start-up costs in a unit commitment problem

“…This result is important, both from the theoretical and practical point of view, since • the BTIs, and in particular the proof of Lemma 15, strengthen our understanding of the start-up costs, • the existing start-up cost models are extended formulations of conv(epi(DCU Σ i )), and may therefore be analyzed and tightened using the BTIs, and • separated in a cutting plane approach, the BTIs reduce the integrality gap of the current state-of the art models (Carrión and Arroyo (2006); Simoglou et al (2010)) to match those of the the temperature model (Silbernagl et al (2014)).…”

“…This section mainly compares the integrality gap of a Unit Commitment problem which models epi(LCU Σ i ) using binary tree inequalities (BTI) to a Unit Commitment problem using the start-up cost formulations presented in Carrión and Arroyo (2006) (1-Bin), Simoglou et al (2010) (3-Bin), and Silbernagl et al (2014) (1-Bin* and Temp).…”

“…1). In Silbernagl et al (2014) we present how to exploit the exponential definition of the start-up costs. Here however, we only need CU i to be non-negative, increasing, and concave, with CU i (0) = 0.…”

An approach to optimize the cycling operation of conventional combined heat and power plants

“…However, there are scientific papers where the significant attention is devoted to the features of transient modes. For instance, in [14][15][16] the start-ups are considered taking into account the preceding offline time of the unit. It was complicated by limiting the temperature increase and the heating speed [17], ramping constraints, including start-up, shutdown production trajectory, ramp rate and ramp down constraints [18][19][20], and the change of thermal stress of the main equipment [21].…”