This research is carried out in the framework of Matheon supported by Einstein Foundation Berlin.

Project SE21:
Data Assimilation for Port-Hamiltonian Power Network Models

## Duration: | June 2017 - December 2018 |

## Project leaders: | R. Kruse, V. Mehrmann, M. Voigt, |

Department of Mathematics, Technical University of Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany | |

email: kruse(at)math.tu-berlin.de Tel: +49 (0)30 314 - 23 354 (office) - 28 579 (secretariat) | |

email: mehrmann(at)math.tu-berlin.de Tel: +49 (0)30 314 - 25 736 (office) - 21 264 (secretariat) | |

email: mvoigt(at)math.tu-berlin.de Tel: +49 (0)30 314 - 24 767 (office) - 21 264 (secretariat) | |

## Responsible: | R. Morandin, |

Department of Mathematics, Technical University of Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany | |

email: morandin(at)math.tu-berlin.de Tel: +49 (0)30 314 - 23 439 (office) - 21 264 (secretariat) | |

## Support: |
Einstein Center for Mathematics (ECMath) |

## ECMath project website: |
Project SE21 |

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## Background

The increased share of renewable energy sources, and the demand for the construction of new power lines, lead to major mathematical and computational challenges for the layout and operation of large scale power networks.
Classical power networks are usually top-down structured, where only a medium number of larger power plants distribute the energy they produce to the consumers.
In recent years, an increasing number of smaller producers, such as solar photovoltaic panels, wind turbines, or local power plants, are incorporated into the power network.
Often, these producers are at the same time consumers ("*prosumers*").
To store the produced energy, the smaller units are often equipped with a battery, that can be charged if more energy than needed is produced, and otherwise discharged.
These units of production, consumption, and storage devices are called *residential energy systems*.

This change in the network structure results in a high demand for fast communication between grid operator and energy suppliers who run the power plants. The distributed strategy allows to produce the energy only when it is needed, and to keep the load of the network as constant as possible. The residential energy systems can also be used in order to reduce load peaks, which are currently causing a large overhead in the infrastructure, which is constructed to compensate for them. To deal with these challenges, there is a large demand in (automatic) optimal and robust control techniques, to reduce the need for large infrastructure and to save costs on the side of the grid operator. These controllers typically work using real-time measurements within the network (such as state information of producers, consumers, or distribution substations). Another increasingly popular tool for regulating the load is by using real-time pricing, e.g., if there is a high demand on energy, the prices go up. This effect can be used to control consumer behavior, such that they may consume the energy later, when the load of the network and thus the prices are lower.

Furthermore, it is in the nature of many renewable energy producers that the energy production is highly volatile and uncertain, e.g., in solar or wind energy. Thus it is of great interest not only to measure the state information of certain devices in the network, but also to make predictions such that the grid operator can properly react on changes of the network load. The predictions are obtained by simulating a dynamical system which represents a model of the complete power network, with all its local and global components.

back to top## The Goal

In this project we will study the modeling of such 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. In practice, this results in charging or discharging the energy storage devices of the residential energy systems or in a regulation of the energy production in the generators of the power plants.

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 simultaion 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.

## Benefit to Innovation Area

The outcome of this project will be very beneficial for the grid operators, for the installation and operation of new power production units and net power connections. Using port-Hamiltonian systems will improve the current modeling of power networks and account for the physical properties of its variables. Data assimilation techniques as well as specific discretization and model reduction techniques will allow to get better estimates for the future production and demand (and thus the network load). It will enable the grid operator to optimize energy production by using these improved predictions. By incorporating the statistics of the measurement devices it will also improve the prediction of statistical quantities, e.g., averages and standard deviations of the network load which then allows an estimation of the uncertainty in the future loads.

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