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With the expected rise in behind-the-meter solar penetration within thedistribution networks, there is a need to develop time-series forecastingmethods that can reliably predict the net-load, accurately quantifying itsuncertainty and variability. This paper presents a deep learning method togenerate probabilistic forecasts of day-ahead net-load at 15-min resolution, atvarious solar penetration levels. Our proposed deep-learning based architectureutilizes the dimensional reduction, from a higher-dimensional input to alower-dimensional latent space, via a convolutional Autoencoder (AE). Theextracted features from AE are then utilized to generate probabilitydistributions across the latent space, by passing the features through akernel-embedded Perron-Frobenius (kPF) operator. Finally, long short-termmemory (LSTM) layers are used to synthesize time-series probabilitydistributions of the forecasted net-load, from the latent space distributions.The models are shown to deliver superior forecast performance (as per severalmetrics), as well as maintain superior training efficiency, in comparison toexisting benchmark models. Detailed analysis is carried out to evaluate themodel performance across various solar penetration levels (up to 50\%),prediction horizons (e.g., 15\,min and 24\,hr ahead), and aggregation level ofhouses, as well as its robustness against missing measurements.

KPF-AE-LSTM: A Deep Probabilistic Model for Net-Load Forecasting in High Solar Scenarios