Dynamics and model analysis of hydropower systems

Globalization and growth in energy consumption in combination with climate challenges, make the use of sustainable energy production a necessity. Important sustainable energy sources (solar, wind) are intermittent in character, and hydropower from high head wa-ter reservoirs is a possible energy source for balancing out the variation in intermittent sources. The combination of several energy types as well as counteracting the intermittent energy production make energy management and control much more challenging; optimal energy production will require advanced control based on detailed system models. Another side of globalization is the possibility for everyone to contribute to solutions. This requires low-cost software tools. The combination of open-source software tools with the publication of models and methods provides transparency in research, and increases the possibility of developing optimal and reliable models and methods. In this thesis, a key contribution is the development of a library of mechanistic models for the waterway of hydropower production, using the modelling language Modelica with open-source tool OpenModelica. Another key contribution is the development of analysis methods using open-source languages Python and/or Julia. Mathematical models for various units of a hydropower system are presented and as-sembled in a hydropower Modelica library — OpenHPL. Detailed studies for modelling different hydropower units are demonstrated in this work, i.e., the study of different com-plexities of waterway models, and the study of a mechanistic Francis turbine model and its design algorithm. The library can be used in an open-source software OpenModel-ica, which makes it freely and widely available. In addition, the library also supports modelling and simulation in the commercial environment Dymola. The OpenHPL makes it possible to model different hydropower systems and connect them with models from other libraries, e.g., with models of the power system or other power gen-erating sources. This synergy of our library with other Modelica libraries makes it possible to model the hydropower system starting from precipitations/reservoir to final consumer of electricity. The application and validation of the developed library are presented for case study measurements from the real Trollheim hydropower plant. Various model analysis tools are implemented and tested for the OpenHPL hydropower models. These analysis tools are encoded in open-source scripting languages Python and Julia. The practical use of existing APIs for running and controlling simulations of OpenModelica models via Python or Julia is presented. One of the studied analysis tools is an automatic linearization that is provided by the APIs, and is tested for the hydropower models of different complexity. Opportunities to use the linearized hydropower models for control analysis and synthesis are demonstrated. Another studied analysis tool is a state estimation that provides the possibility to es-timate quantities in the hydropower system that are of interest and cannot be directly measured. The use of stochastic and deterministic approaches for the state estimation are demonstrated. Two types of nonlinear Kalman filters, UKF and EnKF, are studied and tested for the hydropower models for estimating the pressure and flow rate in vari-ous positions. Alternatively, the reduced order nonlinear observer is developed for the hydropower system. The last studied analysis tool is related to a structure analysis of the linearized hydropower models. This structure analysis is implemented based on directed graphs and provides structural observability/controllability, which in turn gives a necessary requirement for actual observability/controllability. It is also shown how the developed structure analysis of the linearized hydropower models can be used for analysis related to state estimation and control: observability is a requirement for state estimators to work properly, controllability is required for control design, and relative degree is important in the design of nonlinear feedback controllers