A comparison of linear interpolation and spline interpolation for turbine efficiency curves in short-term hydropower scheduling problems

Abstract

The purpose of short-term hydropower scheduling (STHS) in a competitive electricity market is to maximize the profit in the near future while adapting to the mid-term strategies for system operation. To ensure a realistic and feasible operation for STHS, it is crucial to accurately represent the hydropower production function (HPF). The turbine efficiency can be represented by a two-dimensional table provided by the turbine manufacturers or measured by the hydropower producers on-site with some given efficiency values for a set of net water head and discharge values. In literature, the actual efficiency value for any working point is usually linearly interpolated from the given efficiency values. To the best of authors' knowledge, no study has been done so far to investigate how a nonlinear interpolation for the turbine efficiency, i.e. spline interpolation, may contribute to the application of STHS. In this paper, we compare the performance of linear interpolation and spline interpolation for turbine efficiency curves in the STHS problem and the bidding strategy in intraday market. The interpolation methods are tested on an operational hydro-power scheduling model, Short-term Hydro Optimization Program (SHOP), which is used by most large hydropower producers in the Nordic countries. Numerical tests demonstrate superior behavior of spline interpolation for the estimation of turbine efficiency between measured points. Compared to linear interpolation, spline interpolation for turbine efficiency curves gives smoother discharge transitions in day-ahead scheduling and is vital for obtaining continuous marginal cost curves in intraday trading. Based on the results in this paper, spline interpolation is a promising alternative to linear interpolation for turbine efficiency curves in STHS.

A comparison of linear interpolation and spline interpolation for turbine efficiency curves in short-term hydropower scheduling problems