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.
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.
Estimation of unmeasured states plays an essential role in the design of control systems as well as for monitoring of hydropower plants. The standard Kalman filter gives the optimum state estimates for linear systems. However, this optimality is not relevant for nonlinear models and a choice between stochastic and deterministic approaches is not so obvious in this case. Thus the application of a nonlinear observer in a hydropower system is of interest here as an alternative to the widely used extended Kalman filter. This paper provides a study and design of a reduced order nonlinear observer to estimate the states of a hydropower system. Implementation of the nonlinear observer is done in OpenModelica and added to our in-house hydropower Modelica library-OpenHPL, where different models for hydropower systems are assembled. Simulations and analysis of the designed observer are done in Python using a Python API for operating OpenModelica simulations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.