The global photovoltaic (PV) installed capacity, vital for the electric sector’s decarbonation, reached 1552.3 ${\mathrm{GW}}_p$ in 2023. In France, the capacity stood at 19.9 ${\mathrm{GW}}_p$ in April 2024. The growth of the PV installed capacity over a year was nearly 32% worldwide and 15.7% in France. However, integrating PV electricity into grids is hindered by poor knowledge of rooftop PV systems, constituting 20% of France’s installed capacity, and the lack of measurements of the production stemming from these systems. This problem of lack of measurements of the rooftop PV power production is referred to as the lack of observability. Using ground-truth measurements of individual PV systems, available at an unprecedented temporal and spatial scale, we show that by estimating the PV power production of an individual rooftop system by combining solar irradiance and temperature data, the characteristics of the PV system inferred from remote sensing methods and an irradiation-to-electric power conversion model provides accurate estimations of the PV power production. We report an average estimation error (measured with the pRMSE) of 10% relative to the system size. Our study shows that we can improve rooftop PV observability, and thus its integration into the electric grid, using little information on these systems, a simple model of the PV system, and weather data. More broadly, this study shows that limited information is sufficient to derive a reasonably good estimation of the PV power production of small-scale systems.

The global photovoltaic (PV) installed capacity, vital for the electric sector decarbonation, has reached 1,552.3 GWp in 2023. In France, the capacity stood in April 2024 at 19.9 GWp. The growth of the PV installed capacity over a year was nearly 32% worldwide and 15.7% in France. However, integrating PV electricity into grids is hindered by poor knowledge of rooftop PV systems, constituting 20% of France's installed capacity, and the lack of measurements of the production stemming from these systems. This problem of lack of measurements of the rooftop PV power production is referred to as the lack of observability. Using ground truth measurements of individual PV systems, available at an unprecedented temporal and spatial scale, we show that estimating the PV power production of an individual rooftop system by combining solar irradiance and temperature data, the characteristics of the PV system inferred from remote sensing methods and an irradiation-to-electric power conversion model provides accurate estimations of the PV power production. Our study shows that we can improve rooftop PV observability, and thus its integration into the electric grid, using little information on these systems, a simple model of the PV system and weather data.

In order to reach the supply/demand balance, electricity providers need to predict the demand and production of electricity at different time scales. This implies the need of modeling weather variables such as temperature, wind speed, solar radiation and precipitation. This work is dedicated to a new daily rainfall generator at a single site. It is based on a seasonal hidden Markov model with mixtures of exponential distributions as emission laws. The parameters of the exponential distributions include a periodic component in order to account for the seasonal behaviour of rainfall. We show that under mild assumptions , the maximum likelihood estimator is strongly consistent, which is a new result for such models. The model is able to produce arbitrarily long daily rainfall simulations that reproduce closely different features of observed time series, including seasonality, rainfall occurrence , daily distributions of rainfall, dry and rainy spells. The model was fitted and validated on data from several weather stations across Germany. We show that it is possible to give a physical interpretation to the estimated states.

In order to reach the supply/demand balance, electricity providers need to predict the demand and production of electricity at different time scales. This implies the need of modeling weather variables such as temperature, wind speed, solar radiation and precipitation. This work is dedicated to a new daily rainfall generator at a single site. It is based on a seasonal hidden Markov model with mixtures of exponential distributions as emission laws. The parameters of the exponential distributions include a periodic component in order to account for the seasonal behaviour of rainfall. We show that under mild assumptions , the maximum likelihood estimator is strongly consistent, which is a new result for such models. The model is able to produce arbitrarily long daily rainfall simulations that reproduce closely different features of observed time series, including seasonality, rainfall occurrence , daily distributions of rainfall, dry and rainy spells. The model was fitted and validated on data from several weather stations across Germany. We show that it is possible to give a physical interpretation to the estimated states.