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.

The air entrainment characteristics of three separate Froude number hydraulic jumps are investigated numerically using an unsteady RANS, realizable k-ε turbulence model, with a Volume of Fluid treatment for the free surface. Mean velocity profiles, average void fraction, and Sauter mean diameter compare favorably with experimental data reported in literature. In all simulations, time-averaged void fraction profiles show good agreement with experimental values in the turbulent shear layer and an accurate representation of interfacial aeration at the free surface. Sauter mean diameter is well represented in the shear layer, and free surface entrainment results indicate bubble size remains relatively unchanged throughout the depth of the jump. Several different grid resolutions are tested in the simulations. Significant improvements in void fraction and bubble size comparison are seen when the diameter to grid size ratio of the largest bubbles in the shear layer surpasses eight. A three-dimensional simulation is carried out for one Froude number jump, showing an improvement in the prediction of entrained air and bubble size compared with two-dimensional results at a substantial increase in computation time. An analysis of three-dimensional vorticity shows a complex interaction between spanwise and streamwise vortical structures and entrained air bubbles. The jump is similar to a turbulent mixing layer, constrained by the free surface, with vortex pairing and subsequent fluctuations in free surface elevation. Downstream fluctuations of the toe are associated with a roll up of the primary spanwise vortex, fluctuations of the free surface, and counter-rotating streamwise vortex pairs. The action of these flow structures is likely responsible for the improvement in three-dimensional results.

The authors would like to thank the many stakeholders with whom we have engaged to elicit feedback on the opportunities and challenges associated with developing and deploying standard modular hydropower technologies. Ongoing engagement with these technology innovators, commercial service/equipment providers, project developers, and environmental stewards has yielded insight into the myriad perspectives and experiences that shape the current hydropower landscape and inform standard modular hydropower research.

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