A MILP model for hydro unit commitment with irregular vibration zones based on the constrained Delaunay triangulation method

Irregular Vibration Zones are common in the giant hydropower stations built during the past decade in southwest China. They significantly affect the safe operation of the hydropower station, and thus became a key issue for hydropower operations in southwest China. The irregular Vibration Zone (VZ) constraint leads to nonconvex, discrete safe operating zones even with holes, which exacerbates the difficulty of solving the Hydro Unit Commitment (HUC) problem. This paper presents a novel Mixed Integer Linear Programming (MILP) model for the HUC problem with the irregular VZ constraint. The method firstly aggregates the power generation performance function and the irregular VZ constraint into a single function, which is highly nonconvex and discrete. The constrained Delaunay triangulation method is then utilized to partition the irregular domain of the function and construct the MILP compatible constraints with the disaggregation convex combination method. The practical behavior of the model is then analyzed through two cases for a giant hydropower station located in southwest China, which suffers from irregular VZs. The results show the high efficiency and the high accuracy of our model. The major advantage of the proposed method is that it can automatically model the general irregular VZs with fewer integer variables.