### “Model based control for run-of-river system. Part 2: Comparison of control structures”

**Authors:**Liubomyr Vytvytskyi, Roshan Sharma and Bernt Lie,

**Affiliation:**Telemark University College

**Reference:**2015, Vol 36, No 4, pp. 251-263.

**Keywords:**Run-of-river hydropower, Saint Venant Equations, Modeling, Simulation

**Abstract:**Optimal operation and control of a run-of-river hydro power plant depend on good knowledge of the elements of the plant in the form of models. Both the control architecture of the system, i.e. the choice of inputs and outputs, and to what degree a model is used, will affect the achievable control performance. Here, a model of a river reach based on the Saint Venant equations for open channel flow illustrates the dynamics of the run-of-river system. The hyperbolic partial differential equations are discretized using the Kurganov-Petrova central upwind scheme - see Part I for details. A comparison is given of achievable control performance using two alternative control signals: the inlet or the outlet volumetric flow rates to the system, in combination with a number of different control structures such as PI control, PI control with Smith predictor, and predictive control. The control objective is to keep the level just in front of the dam as high as possible, and with little variation in the level to avoid overflow over the dam. With a step change in the volumetric inflow to the river reach (disturbance) and using the volumetric outflow as the control signal, PI control gives quite good performance. Model predictive control (MPC) gives superior control in the sense of constraining the variation in the water level, at a cost of longer computational time and thus constraints on possible sample time. Details on controller tuning are given. With volumetric inflow to the river reach as control signal and outflow (production) as disturbance, this introduces a considerable time delay in the control signal. Because of nonlinearity in the system (varying time delay, etc.), it is difficult to achieve stable closed loop performance using a simple PI controller. However, by combining a PI controller with a Smith predictor based on a simple integrator + fixed time delay model, stable closed loop operation is possible with decent control performance. Still, an MPC gives superior performance over the PI controller + Smith predictor, both because the MPC uses a more accurate prediction model and because constraints in the operation are more directly included in the MPC structure. Most theoretical studies do not take into account the resulting time delay caused by the computationally demanding MPC algorithm. Simulation studies indicate that the inherent time delay in injecting the control signal does not seriously degrade the performance of the MPC controller.

PDF (826 Kb) DOI: 10.4173/mic.2015.4.5

**DOI forward links to this article:**

[1] Prodromos Daoutidis, Michael Zachar and Sujit S. Jogwar (2016), doi:10.1016/j.jprocont.2016.06.002 |

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**BibTeX:**

@article{MIC-2015-4-5,

title={{Model based control for run-of-river system. Part 2: Comparison of control structures}},

author={Vytvytskyi, Liubomyr and Sharma, Roshan and Lie, Bernt},

journal={Modeling, Identification and Control},

volume={36},

number={4},

pages={251--263},

year={2015},

doi={10.4173/mic.2015.4.5},

publisher={Norwegian Society of Automatic Control}

};