1st Workshop: Integration of local energy systems

We consider the problem of optimal and constrained control for unknown systems. A novel data-enabled predictive control (DeePC) algorithm is presented that computes optimal and safe control policies using real-time feedback driving the unknown system along a desired trajectory while satisfying system constraints. Using a finite number of data samples from the unknown system, our proposed algorithm uses a behavioral systems theory approach to learn a non-parametric system model used to predict future trajectories. We show that, in the case of deterministic linear time-invariant systems, the DeePC algorithm is equivalent to the widely adopted Model Predictive Control (MPC), but it generally outperforms subsequent system identification and model-based control. To cope with nonlinear and stochastic systems, we propose salient regularizations to the DeePC algorithm. Using techniques from distributionally robust stochastic optimization, we prove that these regularization indeed robustify DeePC against corrupted data. We illustrate our results with nonlinear and noisy simulations and experiments from autonomous energy systems. 

Modern power systems are experiencing a deep transformation related to the massive integration of renewable generation, the electrification of mobility and the restructuration of the entire energy system. The presentation will summarize the electrical power system state and future prespectives and will introduce some challenges and opportunities related to how modern power systems can be understood, designed and engineered. The presentation will include some considerations on electric power system design, operation, protection and control in order to set the scene to further discussion on these topics.

The paper considers the synchronisation of dynamical subsystems by interactions. Asymptotic synchronisation means that all subsystem outputs asymptotically follow the same trajectory. Literature has considered this problem mainly for linear or nonlinear subsystems with diffusive couplings, which appear as physical couplings among the subsystems or as digital couplings among the local subsystem controllers.

A basic assumption requires the subsystems to have identical dynamics. After reviewing the main results for the synchronisation of linear subsystems, the presentation investigates the robustness of synchronised systems with respect to deviations of the subsystems or the couplings from the assumptions mentioned above.

It shows that for oscillator networks even infinitesimally small changes of the agent parameters make the overall system to become  asymptotically stable and, hence, not synchronisable with respect to a non-trivial synchronous trajectory. An investigation of this phenomenon shows why the property of synchrony is so sensitive with respect to the subsystem parameters. Consequently, the synchronisation theory of linear multi-agent systems is not applicable because no-one can produce identical agents. Research on synchronised systems has to be directed to a larger class of systems, for example, to affine subsystems like Kuramoto oscillators or to more general nonlinear subsystems like limit-cycle oscillators.

Most real world dynamical systems consist of a network of subsystems from different physical domains, modeled by partial-differential equations, ordinary differential equations, algebraic equations, combined with input and output connections. To deal with such complex systems, in recent years, the class of dissipative port-Hamiltonian (pH) descriptor systems has emerged as a very efficient modeling methodology.

The main reasons are that the network based interconnection of pH systems is again pH, Galerkin projection in PDE discretization and model reduction preserves the pH structure and the physical properties are encoded in the geometric properties of the flow as  well as the algebraic properties of the equations. Furthermore, dissipative pH system form a very robust representation under structured perturbations and directly indicate Lyapunov functions for stability and passivity analysis. We discuss dissipative pH systems and describe, how many classical models can be formulated in this class. We illustrate some of the nice properties and illustrate the results by some real world examples, arising in energy networks or energy conversion.

Modern model-based control methods are important keys to cope with the operational challenges of large scale systems as the European power network with its decreasing robustness. Linear models enable very performant design methods but have the drawback of modeling errors which increase with the distance to the operating point, where critical situations are often inherently located.

Nonlinear modeling is able to overcome this, but in general at the price of lower performance and generalizability. At the Fraunhofer Application Center for Integration of Local Energy Systems ILES, research on multilinear models shows that these offer an intermediate way to get best of both worlds, i.e. better accuracy in larger operating regions as well as generalized, reduced, efficient, and performant models. The talk will recap main results and show the application of the modeling framework in the power systems context.