Transparent enhancement of active distribution network through FCA-based blind decomposition

Transparency is crucial for decision-making within an active distribution network (ADN). To enhance ADN’s transparency, this study develops a novel Blind Decomposition of Composite Events (BDCE) approach rooted in Free Component Analysis (FCA), with a detailed exploration of its related theorems, algorithms, and deductions. Notably, FCA employs non-commutative matrix variables instead of scalar variables, establishing a natural connection to Random Matrix Theory (RMT). By incorporating RMT, FCA-BDCE effectively utilizes spatial–temporal correlation—a matrix-derived spectrum statistic; it allows for the filtration of locally independent noises, such as individual-level measurement error, ubiquitous white noise, while retaining globally influential signals across some specified spatial–temporal span. This capability is particularly valuable when gaining insight into the complex ADN, a landscape with significant diversity and uncertainty. In general, our approach is model-free, theory-guided, and unsupervised, making it particularly suitable for ADN. A comprehensive case study validates the practical effectiveness of our FCA-BDCE approach, demonstrating its superiority over ICA-BDCE. • A novel FCA-based BDCE method enhances transparency in active distribution networks(ADN). • Non-commutative matrices and RMT capture spatial-temporal correlations in ADNs. • Our model-free and unsupervised approach provides insights for complex ADN dynamics. • FCA-BDCE outperforms ICA-BDCE in improving ADN decision-making via case studies.