Free Surface Water Flows – Modeling, Simulation and Control

Abstract

Upstream and downstream channels are the key subsystems for the design of level/ flow control loops in run-of-river hydropower plants. Their dynamic response is notoriously complex, exhibiting low frequency resonance with weak damping, travelling waves, both sub- and supercritical flow, hydraulic jumps, etc. Part one of this report provides mathematical models derived from the basic physical conservation laws of mass and momentum (Reynolds averaged Navier Stokes partial differential equations (`pde')) for water flow and depth, using the `method of lines'/`compartment' approach (leading to models in discrete space, `continuous' time), first for long channels with constant or weakly changing cross section, then for wide channels with lateral extensions and finally for short channels such as spillways etc. where change of surface level is no longer small compared to water depth. All models are implemented in established industrial simulation packages, suitable for the engineering phases of preliminary control system design up to factory acceptance testing. Simulations are documented in detail and results for typical transients are discussed. Part two of the report develops the design of model-based level control for the linearized pde-model, basically using a notion from discrete control systems which leads to the impedance matching concept. Then this design approach is applied to a linearized state space model with floating coeffi cients, and finally to the nonlinear time domain models of Part one with large but slow dynamic variation of flow regime and including `controller gain scheduling'. Finally the model-based design method is verified on two typical application cases. This report is meant mainly for control engineers charged with design projects for control of hydrological and hydropower systems. The math needed is kept to the master/diploma level of university engineering graduates. To facilitate the access to small enterprises an `open source' system (Scilab/Xcos, see www.scilab.org) has been used. For further use the source code(s) for all cases are given in the connected `zip-container' . And all models are given as well in Matlab/Simulink source (using release `R2016b') in a second connected `zip-container'.