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Design of optimal operation and control of a run-of-river hydro power plant depends on good models for the elements of the plant. River reaches are often considered to be shallow channels with free surface flow. A typical model for such reaches thus use the Saint Venant model, which is a 1D model based on the mass and momentum balances. This combination of free surface and momentum balance makes the problem numerically challenging to solve. Here, the finite volume method with staggered grid is used to illustrate the dynamics of the river upstream from the Grønvollfoss run-of-river power plant in Telemark, Norway, operated by Skagerak Energi. A model of the same river in the Grønvollfoss power plant has been studied previously, but here the geometry of the river is changed due to new information from Skagerak Energi. The numerical scheme for solving the model has been further developed. In addition, the behavior of the dynamic model is compared to data from experiments, carried out on the Grønvollfoss run-of-river power plant. The essence of the experiments is to consider the time taken from an increase in the input volumetric flow, to a measured change in level in front of the dam at Grønvollfoss. The model is manually tuned by changing the Strickler friction factor, the river length and the type of river slope/width (constant/varying) in order to fit the water level ahead of the Grønvollfoss dam from experimental data. Least squares model fitting is also used for the model with the constant slope and width of the river and this model shows good fitting after the manual tuning. The results of the improved model (numerically, tuned to experiments), is a model that can be further used for control synthesis and analysis.

Even though almost all processes in the real world are described by nonlinear models, nonlinear theory for analysis of these models is far less developed than the theory for linear models. Therefore model linearization is important in order to make efficient analysis tools for these models. This paper describes the possibility of automatic linearization in Python for a hydropower system modeled in OpenModelica using our in-house hydropower Modelica library OpenHPL. Linearization is made using a Python API. Simple uses of the linearized model for analysis and synthesis are indicated.

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 Grønvollfoss run-of-river power plant in Telemark, Norway, operated by Skagerak Energi AS. In an experiment on the Grønvollfoss run-of-river power plant, a step was injected in the upstream inlet flow atÅrlifoss, and the resulting change in level in front of the dam at the Grønvollfoss 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.

In this paper, a detailed overview of hydropower system components is given. Components of the system include intake race, upstream and downstream surge tanks, penstock, turbine and draft tube. A case study which includes a Francis turbine, taken from the literature, was used. The paper presents a case study hydropower system, with models implemented in Modelica. For simplicity, compressibility of water and elasticity of pipe walls were neglected. The main aims are to compare a turbine model based on the Euler equations vs. a table look-up model, and illustrate how the surge tanks influence the transients of the system.