MODWT-Based Multi-Timescale Coupling Correlation Analysis of Source and Load Nodes

A single correlation coefficient computed directly from an undecomposed power time series may obscure coupling patterns associated with short-term fluctuations, stage-wise variations, and long-term trends among heterogeneous source and load nodes. To address this issue, this study proposes a multi-timescale source–load coupling correlation analysis method based on the maximal overlap discrete wavelet transform (MODWT). MODWT is first used to decompose multi-node power time series into high-, medium-, and low-frequency components. Within each frequency band, pairwise correlations are calculated over separate time windows and aggregated in Fisher z-space using effective-sample-size-based reliability weights. The resulting scale-specific correlation matrices are then fused according to the fluctuation-energy contributions of the reconstructed components. A case study using one year of 5 min measurements from 12 source–load nodes shows clear scale-dependent coupling patterns: the two photovoltaic (PV) nodes remain strongly correlated across scales, whereas PV–load correlations are generally weak and load–load correlations decrease from the high-frequency scale toward longer time scales. As an illustrative downstream application, the proposed matrices are further used as fixed graph priors in a common joint forecasting model. The proposed graph achieves the lowest training-stage mean squared error (MSE) in 7 of 8 reported configurations and reduces training-stage MSE by approximately 1.1–9.3% relative to the conventional Pearson-correlation graph. Additional test-set results show a similar comparative trend, indicating that the benefit of the proposed multi-timescale correlation information is not confined to the training data and remains evident on unseen samples.