Spectral Clustering and Multi-Modal Stable Matching for Enhanced Management of Photovoltaic Stations and Virtual Power Plants

As renewable energy sources like photovoltaic (PV) stations expand, efficient management and operation are becoming increasingly important for maintaining grid stability and optimizing resource allocation. In this paper, we introduce a novel framework that integrates spectral clustering and multi-modal stable matching to enhance the coordination of PV stations and Virtual Power Plants (VPPs). We begin by applying spectral clustering to group PV stations based on geographic locations and key weather conditions. Our custom-built similarity matrix for PV stations, combined with our theoretical insights, suggests that using fewer eigenvectors in spectral clustering not only reduces computation time but also improves clustering accuracy. This method ensures that each cluster of PV stations shares similar environmental conditions, allowing for more effective collective management. In the second stage, we utilize multi-modal stable matching to assign these PV clusters to VPPs. Unlike traditional stable matching, the multi-modal approach considers multiple factors, such as energy demand, geographic proximity, and VPP capacity, resulting in a more balanced and stable allocation. We validate our approach through experiments on both synthetic and real-world PV station data. The results demonstrate that our framework leads to more accurate grouping of PV stations, facilitating more effective decision-making across multiple criteria. This also enhances work offloading when tasks become intensive on certain nodes. Our work presents a promising solution for managing large-scale renewable energy resources in future power systems, improving both efficiency and stability.