Abstract
Optimal operation and control of a run-of-river hydro power plant depends on good knowledge of the elements of the plant in the form of models. River reaches are often considered shallow channels with free surfaces. A typical model for such reaches use the Saint Venant model, which is a 1D distributed model based on the mass and momentum balances. This combination of free surface and momentum balance makes the problem numerically challenging to solve. The finite volume method with staggered grid was compared with the Kurganov-Petrova central upwind scheme, and was used to illustrate the dynamics of the river upstream from the Gronvollfoss run-of-river power plant in Telemark, Norway, operated by Skagerak Energi AS. In an experiment on the Gronvollfoss run-of-river power plant, a step was injected in the upstream inlet flow at Arlifoss, and the resulting change in level in front of the dam at the Gronvollfoss plant was logged. The results from the theoretical Saint Venant model was then compared to the experimental results. Because of uncertainties in the geometry of the river reach (river bed slope, etc.), the slope and length of the varying slope parts were tuned manually to improve the fit. Then, friction factor, river width and height drop of the river was tuned by minimizing a least squares criterion. The results of the improved model (numerically, tuned to experiments), is a model that can be further used for control synthesis and analysis.
Highlights
1.1 BackgroundThere are in total over 1500 hydro power plants operating in Norway today, with a total capacity of more than 28 GW
The finite volume method with staggered grid (Vytvytskyi et al, 2015; Vytvytskyi, 2015; LeVeque, 2002) is compared with the Kurganov-Petrova central upwind scheme (Sharma, 2015; Kurganov and Petrova, 2007), and the chosen scheme compared to experiments on the system with the model tuned by changing the river bed, the friction factor, the width and the height drop of the river
The Finite Volume method with staggered grid was compared with the Kurganov-Petrova central upwind scheme and the latter was determined as better for discretizing the Saint Venant equations; the Kurganov-Petrova algorithm is a high resolution scheme with a less noisy result
Summary
There are in total over 1500 hydro power plants operating in Norway today, with a total capacity of more than 28 GW. The installed power in Grønvollfoss is 2x16 MW (i.e. two turbines), and the average annual production is 172 GWh. It is of interest to control the operation of the Grønvollfoss power plant in such a way that the level in front of the dam is as high as possible in order to maximize the available power, while variation in the level is minimized to avoid loss of water flowing over doi:10.4173/mic.2015.4.4 c 2015 Norwegian Society of Automatic Control. The level depends both on the power production/turbine flow and on the upstream inflow of water. It is of interest to develop a dynamic model for such a run-of-river system in a suitable form for control studies, which is solved efficiently with sufficient numerical accuracy, and which gives good representation of the real power plant
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