There is a general need to change hydropower operational regimes to balance the growing contribution of variable renewable energy sources in power systems. Quantifying the burden on generation equipment is increasingly uncertain and difficult. Here, we propose a framework combining technical and economic indicators to analyze primary frequency control (PFC) on a timescale of seconds. We develop a model integrating hydraulic, mechanical, and electrical subsystems to characterize efficiency loss, wear and fatigue, regulation mileage, and frequency quality. We evaluate burden relief strategies under three idealized remuneration schemes for PFC, inspired by those used in Sweden, the USA, and China, respectively. We show how burden and compensation vary under future scenarios of renewable power systems. Our framework can be used by producers to develop favorable operation strategies that reduce burden and increase economic value, and by transmission system operators to provide insights on the relation between incentive structures and regulating performance.

This paper presents a mathematical model of hydro power units, especially the governor system model for different operating conditions, based on the basic version of the software TOPSYS. The mathematical model consists of eight turbine equations, one generator equation, and one governor equation, which are solved for ten unknown variables. The generator and governor equations, which are different under various operating conditions, are presented and discussed in detail. All the essential non-linear factors in the governor system (dead-zone, saturation, rate limiting, and backlash) are also considered. Case studies are conducted based on one Swedish hydro power plant (HPP) and three Chinese plants. The simulation and on-site measurements are compared for start-up, no-load operation, normal operation, and load rejection in different control modes (frequency, opening, and power feedback). The main error in each simulation is also discussed in detail. As a result, the model application is proved trustworthy for simulating different physical quantities of the unit (e.g., guide vane opening, active power, rotation speed, and pressures at volute and draft tube). The model has already been applied effectively in consultant analyses and scientific studies.