Volker Mehrmann, Caren Tischendorf, Matthias Voigt
Lena Scholz (TU)
01.01.2019 – 31.12.2021
Modern power systems need to be controlled and optimized as dynamical systems in real time, rather than as stationary systems as is the case today. To properly deal with strong decentralization, new long distance DC transmission lines, and the increased randomness in power generation, a complete model hierarchies of different modeling granularity should be set up that can be used for different simulation, control, and optimization tasks. As basis we use energy-based models (or port-Hamiltonian systems) of (partial) differential-algebraic equations that also allow the appropriate treatment of stochasticity and time-delay.
Within the project a new port-Hamiltonian formulation of power systems has been constructed that has many improved properties. The new compact port-Hamiltonian form derived in [Nedialkov, Pryce & Scholz 2021] has remarkable simplicity and symmetry, is proven to be always structurally amenable, and gives rise to a differential-algebraic equation system that always has an index at most 1. Moreover, the modeling framework of port-Hamiltonian descriptor systems has been extended to include under- and over-determined systems and arbitrary differentiable Hamiltonian functions [Mehrmann & Morandin 2019].
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