Clustering Rooftop PV Systems via Probabilistic Embeddings

TL;DR

This work tackles the scalability and missing-value challenges of clustering large, spatially distributed rooftop PV time-series by introducing probabilistic entity embeddings that map each PV system to a Dirichlet distribution parameterized by concentration vectors $\gamma_u$. The approach combines profiling, wording via word-like clustering, and Latent Dirichlet Allocation to produce compact, uncertainty-aware embeddings, enabling distance-based clustering with symmetric KL and Bhattacharyya measures and agglomerative fusion into $C$ clusters. The authors validate the method on a 4-year dataset of 175 Utrecht households, showing superior representativeness and robustness over a physics-based baseline and providing quantile-based cluster summaries for effective data condensation and missing-value imputation. A leave-one-out sensitivity score is proposed to guide hyperparameter tuning, and a comprehensive hyperparameter study offers practical guidance for balancing performance and robustness, with implications for grid planning and distributed energy resource management. Future work extends the framework to other multi-site power-data contexts and downstream tasks like optimal bidding and state estimation to assess real-world impact.

Abstract

As the number of rooftop photovoltaic (PV) installations increases, aggregators and system operators are required to monitor and analyze these systems, raising the challenge of integration and management of large, spatially distributed time-series data that are both high-dimensional and affected by missing values. In this work, a probabilistic entity embedding-based clustering framework is proposed to address these problems. This method encodes each PV system's characteristic power generation patterns and uncertainty as a probability distribution, then groups systems by their statistical distances and agglomerative clustering. Applied to a multi-year residential PV dataset, it produces concise, uncertainty-aware cluster profiles that outperform a physics-based baseline in representativeness and robustness, and support reliable missing-value imputation. A systematic hyperparameter study further offers practical guidance for balancing model performance and robustness.

Figures (6)

• Figure 1: Our entity-based clustering method groups PV systems with similar characteristics (or behavior) into representative clusters.
• Figure 2: The flow diagram of our probabilistic entity-based clustering. Long time series $\{\mathbf{x}_u\}_{u=1}^U$ of the PV systems are first mapped onto a probabilistic embedding that is characterised by concentration parameters $\{\gamma_u\}_{u=1}^U$ that parameterize $K$-dimensional topic distributions $\theta\sim\text{Dir}(\gamma_u)$. Then, the pair-wise distances between these profiles are calculated using a proper statistical distance, and, finally, $C$ clusters are formed using agglomerative clustering.
• Figure 3: Summarizing clusters with quantiles. Each point represents a different PV system. In this case, the full profile length of each system is $T$=2.
• Figure 4: The effect of the number of clusters on the dispersion and sensitivity scores for physics- and entity embedding-based clustering methods. Each green dot corresponds to a distinct hyperparameter setting. The white circles on the violin plots represent the quartiles of the given setting populations.
• Figure 5: The effects of number of topics, wording granularity, and statistical distance and linkage criterion choices on the dispersion and sensitivity score for entity embedding-based clustering. The white circles represent the quartiles of their respective population.