Model based control for run-of-river system. Part 1: Model implementation and tuning

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 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.

Semi-Discrete Scheme for the Solution of Flow in River Tinnelva

“…The assumed bottom topography of the river is illustrated in Figure 1. The section from 2.5 km to 3 km has a steeper bed compared to the other sections (Vytvytskyi et al, 2015). Due to different operational conditions, the volumetric outflow of water at the Årlifoss station is varying.…”

“…As several hydropower stations are installed at different locations along the same river length, water flow between different hydropower stations influence their operations. When the upstream station (first station) increases its power production, volumetric flow of water out from the first station increases, thus the downstream power station (second station) has to increase the power production in order to utilize the water resource efficiently (Vytvytskyi et al, 2015).…”

Second Order KP Scheme for the Solution of flow in a Venturi Channel

“…The Saint-Venant equation/Shallow Water Equation is a hyperbolic type PDE, which has versatile use in fluid dynamics: many different fluid dynamic applications such as fluid flows in open channels, water flow in the rivers to estimate wave propogation, compute tsunmai wave, etc. (Sharma, 2015;Vytvytskyi et al, 2015;Dissanayake et al, 2016). The Saint-Venant equation is given in Equation 3.…”

“…In the development of the KP scheme, the local speed of discontinuity propagation is taken into account [2]. Suitability of the KP scheme to simulate flows of water in a reach of a river has been tested by the authors of this paper (Sharma, 2015;Vytvytskyi et al, 2015;Dissanayake et al, 2016). Here, we consider the usefulness of the 2 nd order KP scheme to solve the Saint-Venant equation for fluid flow through a Venturi channel.…”

Use of Orthogonal Collocation Method for a Dynamic Model of the Flow in a Prismatic Open Channel: For Estimation Purposes

“…where H j± 1 2 (t) are the central upwind numerical fluxes at the cell interfaces (Kurganov and Petrova, 2007;Sharma, 2015;Vytvytskyi et al, 2015). More details in this scheme is included in (Kurganov and Petrova, 2007).…”