Forecasting of Power Injected by DERs in Microgrid using Delay Embedded Dynamic Mode Decomposition

Temporal series forecasting is challenging due to the lack of persistence of excitation conditions imposed by William's lemma, which makes the system identification task very difficult. This work presents the delay embedded dynamic mode decomposition (DeDMD) technique to eliminate the persistence of excitation problems and to make accurate forecasting even with limited training data set. The existing DMD algorithm is enhanced to make it more relevant for the data which is not persistently excited by artificially expanding the dimensions of spanned subspace through embedding with Hankel matrix. The methodology is tested in a case study for forecasting the power injected by distributed energy resources (DERs) in the microgrid. Stability analysis for different Hankel rank conditions in addition to error analysis for both training and testing data is also performed to support the adequacy of DeDMD. The observed results suggest that the proposed method gives results with minimum error for temporal series prediction. The critical contribution of the paper is to extend the DMD technique's applicability for the data that is not persistently excited.