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Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and known nonlinear extensions of the fundamental lemma. Applying a transformation to the usual linear equation in Hankel matrices, we arrive at an alternative implicit kernel representation of the system trajectories while keeping the requirements on persistency of excitation. We show that this representation is equivalent to the solution of a specific kernel regression problem. We explore the possible structures of the underlying kernel as well as the system classes to which they correspond.

The integration of distributed energy resources (DERs) into the electrical grid causes various challenges in the distribution grids. The complexity of smart grids as multi-domain energy systems requires innovative architectures and algorithms for system control. While these solutions are good on paper, several testing methods are required to test the applicability of components, functions and entire systems to the existing energy grids. In this paper, a full-scale low-voltage test setup in the Smart Grid Technology Lab (SGTL) at TU Dortmund University is used to evaluate the capability of an Optimal Power Flow Algorithm (OPF) to support voltage control, congestion management, and to provide redispatch to the higher grid levels. While conventional redispatch is commonly done preemptively, this paper analyses the possibility of providing redispatch to the higher voltage levels without taking the future grid state into consideration. The importance of this implementation is that the smart grid application used to execute the OPF is configured based on IEC 61850 data models, making the software independent of the hardware. Such standardised control algorithms are interoperable and can be implemented on any hardware that suits the requirements., Comment: 10 pages, 9 figures, 6 tables, currently in submission for IEEE Transactions on Power Systems