The science behind pvSpline
pvSpline’s engine implements published, peer-reviewed models from irradiance to AC power. Below is the model chain with its primary-literature references, and the accuracy-validation study against measured plants.
Papers
Two papers describe pvSpline’s engine and its validation: the validation study is published as a technical report, and the paper on the 3-D subsystem is still a working draft. Each links to its PDF, which reports the results.
Technical report · October 2026
Validation of the pvSpline photovoltaic simulation engine against 49 grid-connected systems in three climates: a no-calibration protocol
A validation of the pvSpline engine against measured AC production from 49 grid-connected systems across three climates, benchmarked against pvlib-python, NREL PVWatts and PVGIS. No model parameter is calibrated against the validated series, and all four measurement datasets are public.
Download PDF ↓Working draft · in preparation
Geometry in the renderer, radiometry in the solver: a deterministic GPU-measured factor-table architecture for 3-D near shading, shade-driven electrical mismatch, anisotropic diffuse masking, and bifacial rear irradiance in the pvSpline photovoltaic simulator
The 3-D subsystem: a deterministic, GPU-measured factor-table architecture for near-shading, shade-driven electrical mismatch, anisotropic diffuse masking, canopy transmittance, terrain horizon and bifacial rear-side irradiance. It accompanies the validation paper.
Download PDF ↓Model chain and references
Each stage of the irradiance-to-AC chain implements a specific published model. Defaults follow PVsyst conventions, with peer-reviewed alternatives selectable per site.
| # | Stage | Model | Reference |
|---|---|---|---|
| 1 | Solar position | NREL SPA | Reda & Andreas (2004) |
| 2 | Tracker orientation | Astronomic / irradiance-optimized, backtracking, wind-stow | Geometric calculation |
| 3 | GHI → DHI/DNI decomposition | Erbs (default); Engerer2 (option) | Erbs et al. (1982); Engerer (2015) |
| 3a | Clear-sky reference (Engerer2) | Ineichen–Perez | Ineichen & Perez (2002) |
| 4 | Transposition GHI → POA | Hay–Davies (default); Perez (option) | Hay & Davies (1980); Perez et al. (1990) |
| 5 | Incidence-angle modifier | Martín–Ruiz (beam); fixed diffuse/ground | Martín & Ruiz (2001) |
| 6 | Air mass | Kasten–Young | Kasten & Young (1989) |
| 7 | Spectral correction | Lee–Panchula AM polynomial + PWAT | Lee & Panchula (2016); Gueymard (1994) |
| 8 | Cell temperature | Faiman | Faiman (2008); IEC 61853-2 |
| 9 | DC power | Linear-γ (default); De Soto / PVsyst single-diode (options) | De Soto et al. (2006); Mermoud & Lejeune (2010) |
| 10 | DC ohmic + mismatch losses | Load-aware quadratic I²R; flat mismatch | PVsyst convention |
| 11 | Inverter | Tabulated CEC-shape η-curve + AC clip | CEC (2005) protocol |
| 12 | Soiling | Kimber deposition + continuous exponential wash | Kimber et al. (2006); Coello & Boyle (2019) |
| 13 | Degradation | Two-parameter linear (+ optional Arrhenius climate scaling) | Jordan & Kurtz (2016); Hülsmann et al. (2014) |
Primary-literature references
The works below are the original authors’; pvSpline implements them.
- California Energy Commission (2005). Performance Test Protocol for Evaluating Inverters Used in Grid-Connected Photovoltaic Systems.
- Coello, M., & Boyle, L. (2019). Simple model for predicting time series soiling of photovoltaic panels. IEEE Journal of Photovoltaics, 9(5), 1382–1387.
- De Soto, W., Klein, S. A., & Beckman, W. A. (2006). Improvement and validation of a model for photovoltaic array performance. Solar Energy, 80(1), 78–88.
- Engerer, N. A. (2015). Minute resolution estimates of the diffuse fraction of global irradiance for southeastern Australia. Solar Energy, 116, 215–237.
- Erbs, D. G., Klein, S. A., & Duffie, J. A. (1982). Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation. Solar Energy, 28(4), 293–302.
- Faiman, D. (2008). Assessing the outdoor operating temperature of photovoltaic modules. Progress in Photovoltaics: Research and Applications, 16(4), 307–315.
- Gueymard, C. (1994). Analysis of monthly average atmospheric precipitable water and turbidity in Canada and Northern United States. Solar Energy, 53(1), 57–71.
- Hay, J. E., & Davies, J. A. (1980). Calculation of the solar radiation incident on an inclined surface. Proc. First Canadian Solar Radiation Data Workshop, 59–72.
- Hülsmann, P., & Weiss, K.-A. (2014). Simulation of water ingress into PV-modules: IEC-testing versus outdoor exposure. Solar Energy, 115, 347–353.
- IEC 61853-2 (2016). Photovoltaic (PV) module performance testing and energy rating — Part 2.
- Ineichen, P., & Perez, R. (2002). A new airmass independent formulation for the Linke turbidity coefficient. Solar Energy, 73(3), 151–157.
- Jordan, D. C., Kurtz, S. R., VanSant, K., & Newmiller, J. (2016). Compendium of photovoltaic degradation rates. Progress in Photovoltaics: Research and Applications, 24(7), 978–989.
- Kasten, F., & Young, A. T. (1989). Revised optical air mass tables and approximation formula. Applied Optics, 28(22), 4735–4738.
- Kimber, A., Mitchell, L., Nogradi, S., & Wenger, H. (2006). The effect of soiling on large grid-connected photovoltaic systems in California and the Southwest US. Proc. IEEE 4th World Conf. on Photovoltaic Energy Conversion, 2391–2395.
- Lee, M., & Panchula, A. (2016). Spectral correction for photovoltaic module performance based on air mass and precipitable water. Proc. IEEE 43rd Photovoltaic Specialists Conference, 1351–1356.
- Martín, N., & Ruiz, J. M. (2001). Calculation of the PV modules angular losses under field conditions by means of an analytical model. Solar Energy Materials and Solar Cells, 70(1), 25–38.
- Mermoud, A., & Lejeune, T. (2010). Performance assessment of a simulation model for PV modules of any available technology. Proc. 25th European Photovoltaic Solar Energy Conference, Valencia.
- Perez, R., Ineichen, P., Seals, R., Michalsky, J., & Stewart, R. (1990). Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy, 44(5), 271–289.
- Reda, I., & Andreas, A. (2004). Solar position algorithm for solar radiation applications. Solar Energy, 76(5), 577–589.
- Spencer, J. W. (1971). Fourier series representation of the position of the sun. Search, 2(5), 172.