Analysis und Synthesis of Robustly Controlled Smart-Grid-Systems

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The energy sector is currently in the midst of a transition from centralized conventional power generation towards decentralized generation with a considerable share of renewable energy sources. This paradigm shift increases the complexity of the design, management, and control of the future power system due to the increase in the number of generating units, changing operating conditions, and uncertain prediction of renewable energy production. The control is challenging since smart grids are generally described by complex, nonlinear, differential-algebraic models with uncertain inputs and parameters. We propose new control and analysis methods to increase the operating region of smart grids and thus maximally exploit possible smart grid performance while maintaining grid stability under increasing variations in operating conditions and uncertainties. In order to address these challenges, compositional techniques will be developed to guarantee global properties by controlling and analyzing subsystems separately, while not ignoring the interdependencies or assuming that these are static. For power system control, a scheme combining principles of hierarchical and distributed robust control is envisaged: For an upper and coordinating control layer, the use of predictive control based on abstracted grid models is investigated to achieve an optimized load assignment online. On the lower layer, local feedback controllers are synthesized offline for the grid subsystems. To achieve robustness on this layer, the use of semi-definite programming for linear parameter-varying systems with explicit representation of the subsystem coupling will be investigated. In addition to the novelty arising from the two-layer control scheme, switching events as arising from abrupt faults in the transimission system will be considered and extend the state of the art in grid control.The proposed controller synthesis approach is verified by pioneering formal methods for guaranteeing grid stability in compliance with a given dynamic model and model uncertainties. Traditional simulation-based techniques cannot prove that all possible behaviors meet given specifications, since only a finite subset of infinitely many possible behaviors can be tested. The newly proposed method, however, can mathematically prove that all specifications are satisfied using reachability analysis. The formal approach also makes it possible to provide rigorous conditions under which a collection of verified subsystems meets global specifications, such that the application to system sizes relevant in the power systems industry becomes possible.The proposed methods will extend the state-of-the-art in controlling and analyzing large and distributed systems of nonlinear differential-algebraic and ordinary differential equations also beyond the domain of power systems.