A multi-surface reflected irradiance model for pyranometer corrections and PV yield calculations in complex urban geometries

The need for research of PV system performance in urban areas is increasing as more and more PV systems are installed each year. To facilitate this research, a PV monitoring station is constructed on the campus of the TU Delft in a complex urban geometry. Unfortunately, the diffuse horizontal irradiance (DHI) measurements that are measured using a pyranometer are corrupted due to a non-free horizon and reflections from the environment. To correct the pyranometer measurements for this reflected irradiance, an accurate reflected irradiance model is required. The research described in this report proposes a reflected irradiance model that includes both the first and the second order of reflections. The model is worked out analytically and it was found that de-coupling of the contributions of direct and diffuse irradiance is possible. Due to this de-coupling, the correction of pyranometer measurements can be done using an analytical formula instead of an iterative process. Methods are developed to obtain all the required inputs for this reflected irradiance model. The first of these methods shows that a horicatcher picture taken in diffuse conditions can be used to obtain both the view factors and the reflectivities of all surfaces contributing to the reflected irradiance on any surface that is visible in the horicatcher picture. The second developed method shows that the amount of irradiance received by each surface at any time can be determined by constructing raised horizon profiles for each of the surfaces that contribute to the reflected irradiance using LiDAR data. Both developed methods are proven to be reliable for studies that aim to determine the amount or reflected irradiance. All required inputs to the reflected irradiance model are obtained for two receiving surfaces on the PVMD monitoring station, located at the campus of TU Delft. These two receiving surfaces correspond to the locations of two pyranometers. This way, the reflected irradiance as captured by a pyranometer can be modeled. For both of these receiving surfaces, the model gives two outputs. A diffuse reflectivity factor, a fixed factor that determines the amount of diffuse irradiance that is reflected to the receiving surface, and a direct reflectivity factor that determines the amount direct irradiance that is reflected onto the receiving surface. This direct reflectivity factor depends on the location of the sun and can be presented in a reflectance sensitivity image (RS-image), a new developed representation that shows how the environment contributes to the reflected direct irradiance, depending on the location of the sun. The diffuse and direct reflectivity factors can be used together with the measured irradiances to compute the reflected irradiance at any given time. The model was validated using KNMI DHI measurements. It was found that the proposed method for correcting pyranometer measurements results in 4 times more accurate results than the original measured data, reducing the %RMSE from 25.0% to 6.3% for a clear day in May. The reflected irradiance model was validated by comparing measured reflected irradiance to the modeled reflected irradiance. It was found that for a clear day, the second order reflected irradiance model can predict the reflected irradiance with a %RMSE of 4.39%, whereas a fixed albedo model and the first order reflected irradiance model both resulted in worse predictions with a %RMSE of 32.57% and 23.16%, respectively. It is thus concluded that introducing a second order of reflections in the reflected irradiance model reduces the %RMSE with a factor of 5 for a clear day. During the process it was found that designing a validation for the reflected irradiance model and for the pyranometer correction method was a difficult and complex problem on itself. Both the validations that were performed were found to be valid only under certain conditions. The isotropic sky assumption proved to be insufficiently accurate for predicting the irradiance on a vertical surface for overcast conditions or when there is a direct component on the vertical surface. This resulted in insufficiently accurate calculations of the reflected irradiance for these conditions. Validations was performed only for clear sky conditions. A validation method that works also for cloudy and overcast conditions should be designed for further validation of the reflected irradiance model and the pyranometer correction model. Besides that, also a uncertainty analysis should be performed for more insights in the obtained results.