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.