In the development of a digital twin (DT) for hydropower turbines, dynamic modeling of the system (e.g., penstock, turbine, speed control) is crucial, along with all the necessary data interface, virtualization, and dashboard designs. Since the DT must mimic the actual dynamics of the hydropower turbine accurately, adaptive learning is required to train these dynamic models online so that the models in the DT can effectively follow the representation of the actual hydropower turbine dynamics accurately and reliably. This study presents an adaptive learning method for obtaining the hydropower turbine models for DT development of hydropower systems using the recursive least squares algorithm. To simplify the formulation, the hydropower turbine under consideration was assumed to operate near a fixed operating point, where the system dynamics can be well represented by a set of linear differential equations with constant parameters. In this context, the well-known six-coefficient model for the Francis turbine was formulated as the starting point to obtain input and output models for the turbine. Then, an adaptive learning mechanism was developed to learn model parameters using real-time data from a hydropower turbine testing system. This led to semi-physical modeling, in which first principles and data-driven modeling are integrated to produce dynamic models for DT development. Applications to a pilot system at the Norwegian University of Science and Technology (NTNU) were made, and the models learned adaptively using the data collected from the university’s pilot system. Desired modeling and validation results were obtained.

In the development of a digital twin (DT) for hydropower turbines, dynamic modeling of the system (e.g., penstock, turbine, speed control) is crucial, along with all the necessary data interface, virtualization, and dashboard designs. Since the DT must mimic the actual dynamics of the hydropower turbine accurately, adaptive learning is required to train these dynamic models online so that the models in the DT can effectively follow the representation of the actual hydropower turbine dynamics accurately and reliably. This study presents an adaptive learning method for obtaining the hydropower turbine models for DT development of hydropower systems using recursive least squares algorithm. To simplify the formulation, the hydropower turbine under consideration was assumed to operate near a fixed operating point, where the system dynamics can be well represented by a set of linear differential equations with constant parameters. In this context, the well-known six-coefficient model for the Francis turbine was formulated as the starting point to obtain input and output models for the turbine. Then, an adaptive learning mechanism was developed to learn model parameters using the real-time data from a hydropower turbine testing system. This led to a semi-physical modeling in which the first principles and data-driven modeling are integrated to produce dynamic models for the DT development. Applications to a pilot system at the Norwegian University of Science and Technology (NTNU) were made, and the models learned adaptively using the data collected from the university’s pilot system. Desired modeling and validation results were obtained.

In traditional short-term hydropower scheduling problems, which usually determine the optimal power generation schedules within one week, the off-design zone of a hydraulic turbine is modeled as a forbidden zone due to the significantly increased risk of turbine damage when operating within this zone. However, it is still plausible to occasionally operate within this zone for short durations under real-world circumstances. With the integration of Variable Renewable Energy (VRE) into the power system, hydropower, as a dispatchable energy resource, operates complementarily with VRE to smooth overall power generation and enhance system performance. The rapid and frequent adjustments in output power make it inevitable for the hydraulic turbine to operate in the off-design zone. This paper introduces the operating zones associated with various production costs derived from fatigue analysis of the hydraulic turbine and calculated based on the turbine replacement cost. These costs are incorporated into a short-term hybrid scheduling tool based on Mixed Integer Linear Programming (MILP). Including production costs in the optimization problem shifts the turbine’s working point from a high-cost zone to a low-cost zone. The resulting production schedule for a Hydro-Solar hybrid power system considers not only short-term economic factors such as day-ahead market prices and water value but also lifetime hydraulic turbine cost, leading to a more comprehensive calculation of the production plan. This research provides valuable insights into the sustainable operation of hydropower plants, balancing short-term profits with lifetime hydraulic turbine costs.