Dr. Matthias Voigt

mvoigt@math.tu-berlin.de


Projects as a project leader

  • SE21

    Data Assimilation for Port-Hamiltonian Power Network Models

    Dr. Raphael Kruse / Prof. Dr. Volker Mehrmann / Dr. Matthias Voigt

    Project heads: Dr. Raphael Kruse / Prof. Dr. Volker Mehrmann / Dr. Matthias Voigt
    Project members: Riccardo Morandin
    Duration: -
    Status: running
    Located at: Technische Universität Berlin

    Description

    In this project we will study the modeling of power networks by employing the port-Hamiltonian framework. Energy based modeling with port-Hamiltonian descriptor systems has many advantages, e. g., it accounts for the physical interpretation of its variables, it is best suited for the modular structure of the network, since coupled port-Hamiltonian systems form again a port-Hamiltonian system and it encodes these properties in algebraic and geometric properties that simplify Galerkin type model reduction, stability analysis, and also efficient discretization techniques. To improve the predictions that one obtains from such models we suggest to employ data assimilation and state estimation techniques by incorporating the measurement data. These would allow to take the uncertainty in the measurements and the presence of unmodeled dynamics as well as data and modeling errors into account. The improved predictions can then be used to control the network such that (the expected value of) the load is kept as constant as possible. To control the network we propose to use techniques of model predictive control (MPC) which solve a sequence of finite horizon optimal control problems. The method uses predictions of the state and computes a local optimal control which is then used for the model simulation in the next iteration. This framework is very flexible, since it allows control in real time and the incorporation of nonlinear dynamics and/or inequality constraints. It has already been used successfully within other areas of energy network control. Our new ansatz will also incorporate the stochastic effects into the model predictive control framework using data assimilation. Our vision is to develop numerical methods for network operators that allows the incorporation of model uncertainities for improving simulation and control of power networks.

    http://www3.math.tu-berlin.de/numerik/NumMat/ECMath/SE21/

Projects as a member

  • SE1

    Reduced order modeling for data assimilation

    Prof. Dr. Volker Mehrmann / Dr. Christian Schröder

    Project heads: Prof. Dr. Volker Mehrmann / Dr. Christian Schröder
    Project members: Dr. Matthias Voigt
    Duration: -
    Status: completed
    Located at: Technische Universität Berlin

    Description

    One of the bottlenecks of current procedures for the generation and distribution of green (wind or solar) energy is the accurate and timely simulation of processes in the ocean and atmosphere that can be used in short term planning and real time control of energy systems. A particular difficulty is the real time construction of physically plausible model initializations and 'controls/inputs' to bring simulations into coherence with available observations when observation locations and observations are coming in at variable times and locations.

    The currently best approach for fixed observation times and locations are variational data assimilation techniques. These methods use a four dimensional model that is adapted to the incoming observations using a combination of different filtering techniques and numerical integration of the dynamical system. In order to make these methods efficient in real time data assimilation they have to be combined with appropriate model order reduction methods. A major difficulty in these techniques is the combination of approximate transfer functions and approximate initial and boundary conditions as well as the construction of guaranteed error estimates and the capturing of essential features of the original model. The so-called representer approach formulates the data assimilation problem as the numerical solution of a large-scale nonlinear optimal control problem and incorporates the assimilation of the model to the observations, via an extended ensemble Kalman filter, and the adaptation of the initial data in one approach. Adding further assumptions and linearization this optimization problem usually reduces to a linear quadratic optimal control problem which is solved via the solution of a boundary value problem with Hamiltonian structure.

    http://www3.math.tu-berlin.de/numerik/NumMat/ECMath/SE1/

Projects as a guest