Short-term generation scheduling of cascade hydropower plants with strong hydraulic coupling and head-dependent prohibited operating zones

A lot of large hydropower plants have been built in China in the past few decades. Large-capacity hydropower units usually have multiple prohibited operating zones (POZs) varying with the net head. Many cascade hydropower plants are hydraulically coupled because the distance between the upstream and downstream reservoirs is so small that the forebay water level of the downstream reservoir will influence the tailwater level of its immediate upstream reservoir. The integrated consideration of the strong hydraulic coupling between cascade hydropower plants, the head-dependent POZs of individual units, and other operation constraints make the daily operation of cascade hydropower plants very challenging for both operators and researchers. Therefore, this paper has developed an accurate optimization model for determining the hourly generation scheduling of cascade hydropower plants with strong hydraulic coupling and head-dependent POZs. The objective is to maximize the total profits of the cascade hydropower plants from selling electricity in the day-ahead market. To solve such a complicated mathematical model with non-convex and nonlinear features, the model is converted into a mixed-integer linear programming (MILP) formulation using multiple linear approximation techniques so as to take full advantage of the effective and mature commercial solvers. The MILP formulation focuses mainly on addressing two nonlinearities, namely the three-dimensional tailwater level curves and head-dependent POZs, which are approximated through the piecewise linear interpolations based on the meshing and triangulation technique. The developed model is applied to the optimal operation of the Tianshengqiao cascade hydropower plants which are located on the Hongshui River, China. The optimization results demonstrate that the proposed model is able to be applied in the short-term generation scheduling of cascade hydropower plants in different hydrological conditions, and the optimized total profits for the cascade hydropower plants on typical days in dry season and flood season are 1,809,842 USD and 1,856,964 USD, respectively. Moreover, the developed model is computationally efficient and produces more realistic and executable generation scheduling than the state-of-the-art optimization model which only considers the head-dependent characteristics of POZs without considering the strong hydraulic coupling.