In the subproject B02 of the Collaborative Research Center/Transregio CRC/TRR 391 Spatio-temporal Statistics for the Transition of Energy and Transport, we construct and investigate statistical methods for aggregation and decomposition to tackle the complexity of energy distribution networks, which can involve easily several 100 individual items with corresponding storage dynamics, e.g. electrical vehicles, controllable loads in households, and energy storage systems. Our analysis takes the perspective of upper-level energy transmission networks towards the statistical behavior of lower-level distribution grids at the vertical grid coupling between both layers. Aggregation of the storage dynamics of energy distribution networks can improve system operation on the transmission system via temporal couplings. Control actions decided upon on the transmission level in turn need to be mapped to the individual items composing the distribution systems. In other words, it is necessary to ensure that the action computed for aggregated abstractions can be disaggregated, i.e., control actions can be assigned in a feasible manner to the individual devices.

We thus aim to construct aggregations which admit statistical guarantees (a) on the temporal evolution of aggregated non-stationary statistics at the coupling, especially with respect to energy demand and active and reactive power fluctuations, and (b) for feasible disaggregation.

Optimal Power Flow (OPF) problems are of crucial importance for the operation of electrical energy grids. A prime indicator are the steadily increasing costs for generator redsipatch and curative grid actions in Germany –cf. the monitoring report by the German grid authority (Bundesnetzagentur BNA)– as these operational decisions are based on the solution of OPF problems. In this context, we investigate novel numerical methods including stochastic OPF formulations and distributed solution algorithms. The former is driven by the increasing share of volatile renwables in the energy mix, which have to be modelled by non-Gaussian distributions. We use Polynomial Chaos Expansions to achieve a tractable reformulation. The modelling of such uncertainties is one of our research topics in the Collaborative Research Center/Transregio CRC/TRR 391 Spatio-temporal Statistics for the Transition of Energy and Transport.

We also investigate distributed optimization algorithms to solve optimal power flow problems in stationary and time coupled multi-stage formulations as well as the application of design of experiments to enable in-operation estimation of parameters.