A Branch and Cut Search for the Deterministic Optimization of the Thermal Unit Commitment Problem. Part I: Methodology

This two-paper series proposes a novel deterministic optimization approach for the Unit Commitment problem (UC), more specifically for the Security Constrained Unit Commitment problem (SCUC) addressing thermal generating units. In the first part, a suitable mathematical programming model is presented, which contemplates all the inherent constraints and a single set of binary variables, i.e. the on/off status of each generator at each time period, leading to a convex Mixed Integer Quadratic Programming (MIQP) formulation. This gives rise to a very difficult optimization problem, hard to solve through deterministic approaches for high-dimensional instances. To overcome this challenge, an effective solution methodology based on valid integer cutting planes is proposed, and implemented through a Branch and Cut search for finding the optimal solution. In the second of this two-paper series, the application of the model and proposed approach is illustrated with several examples of different dimensions and characteristics.