Implementation and validation of virtual clones of coloured building-integrated photovoltaic facades

Abstract

A newly introduced colour correction transmittance factor (CCTF) and an innovative probabilistic-to-deterministic approach were applied to create virtual clones of coloured building-integrated photovoltaic (BIPV) systems. These virtual clones calculate the current at maximum power point ($I_{mpp}$) by adjusting the plane-of-array irradiance according to the transmittance properties of the coloured layer, which are governed by the CCTF. An ensemble of 200 randomly combined physical photovoltaic model chains was implemented (probabilistic approach), and the median of the diverse outputs was calculated to provide a deterministic $I_{mpp},$ estimations. The virtual clones were validated against observations from two BIPV facades located in Zwolle (The Netherlands), where black (CCTF=1.00), light-grey (CCTF=0.89), and terracotta (CCTF=0.70) photovoltaic modules were mounted. Hourly $I_{mpp}$ data were collected from June 2023 to May 2024. The performance of different regression techniques was evaluated for the calibration of the virtual clones. The non-calibrated virtual clones showed similar accuracy throughout the year, with the determination coefficient ($R^2$) that ranged from 0.594 (light-grey) to 0.613 (terracotta). Although the models generally overestimated $I_{mpp}$, the results demonstrated that such a tendency was accentuated during overcast days. Consistent biases were also observed for solar elevations greater than 30°. Finally, the façade orientation influenced the simulation performance. Indeed, the non-calibrated models overestimated by circa 150 $A$ the annual $I_{mpp}$ from the south-facing façade, and by more than 700 $A$ the annual $I_{mpp}$ from the façade oriented south-west, regardless of the colour. However, calibration, particularly with Random Forest and Gradient Boosting, consistently reduced cumulative error across all scenarios.