pvfit5 — Estimation of the Five Parameters of the PV Single-Diode Model

Version: 1.2.0 | Date: 2026-04-23 | Author: Valerio Lo Brano

pvfit5 estimates the five parameters of the single-diode model (SDM) of a photovoltaic module at Standard Test Conditions (STC: 1000 W/m² irradiance, 25 °C cell temperature) using only commercial datasheet values.

A genetic algorithm (DEAP) coupled with the CEC model implementation in pvlib minimises a weighted combination of relative errors on Voc, Isc, Vmp, and Imp — plus a stationarity constraint at the maximum power point — and reconstructs the full I–V curve via the Lambert W method.

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Paper

Lo Brano, V. (2026). Open and Reproducible Estimation of PV Single-Diode Parameters from Datasheet Data. Energy Reports (Open Access, CC-BY).

DOI: 10.1016/j.egyr.2026.109280

A copy of the paper is included in this repository: paper/LoBrano2026_EnergyReports.pdf

See also CITATION.cff for machine-readable citation metadata.

If you use this software in your research, please cite the article above.

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Background

The single-diode model describes the I–V characteristic of a PV cell as:

I = I_L - I_0 [exp((V + I·R_s) / (n·N_s·V_th)) - 1] - (V + I·R_s) / R_sh

The five unknown parameters to be estimated are:

Parameter	Symbol	Unit	Description
Photocurrent	I_L_ref	A	Light-generated current at STC
Saturation current	I_o_ref	A	Diode reverse saturation current at STC
Ideality factor	a_ref	—	Modified diode ideality factor (n · N_s · V_th)
Series resistance	R_s	Ω	Accounts for ohmic losses in contacts and bulk
Shunt resistance	R_sh	Ω	Accounts for leakage current paths

These parameters are estimated at STC (Standard Test Conditions):

• Irradiance: 1000 W/m²
• Cell temperature: 25 °C

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Required Inputs

The algorithm needs only the values that appear on a standard PV module datasheet at STC:

Input	Symbol	Unit	Description
Open-circuit voltage	Voc	V	Voltage when no current flows
Short-circuit current	Isc	A	Current when terminals are short-circuited
Maximum power	Pmax	W	Maximum power at the MPP
Voltage at MPP	Vmp	V	Voltage at the maximum power point
Current at MPP	Imp	A	Current at the maximum power point

Optional inputs (advanced users):

Input	Unit	Default	Description
α_sc (alpha_sc)	A/°C	0.05	Short-circuit current temperature coefficient
EgRef	eV	1.121	Band gap energy at reference (crystalline Si)
dEgdT	eV/K	−0.000267	Temperature coefficient of band gap

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Output

The algorithm returns:

1. The five SDM parameters (I_L_ref, I_o_ref, a_ref, R_s, R_sh) at STC, which fully characterise the PV module.
2. Simulated key points (Voc, Isc, Vmp, Imp, Pmp from the fitted model) compared against the datasheet values.
3. Total relative error — the weighted objective function value (lower is better), including individual errors on Voc, Isc, Vmp, Imp, and a stationarity residual at the maximum power point.
4. I–V curve plot — a publication-quality figure showing the reconstructed curve with both the datasheet key points and the fitted maximum power point, so any discrepancy is immediately visible.
5. Summary text file — <MODULE_NAME>_CEC.txt with all parameters and errors.

See example_output/Gruposolar_GS601456P-218.txt for a complete text output example.

Example plots

Graph 1 — Live adaptation (updates during GA evolution, auto-closes):

Graph 2 — Final I–V curve (publication-quality, stays open):

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Requirements

• Python ≥ 3.10
• pip

The following Python packages are required and are installed automatically by pip install pvfit5:

Package	Min version	Purpose
pvlib	0.10	CEC single-diode model and I–V solver (Lambert W)
DEAP	1.4	Genetic algorithm framework
NumPy	1.24	Numerical arrays
Matplotlib	3.7	Live and final I–V plots
SciPy	1.10	Statistical analysis
pandas	2.0	Dataframe handling and Excel I/O
openpyxl	3.1	Excel reading (.xlsx)
XlsxWriter	3.1	Excel writing (.xlsx)
seaborn	0.12	Statistical plots (batch analysis)
tqdm	4.60	Progress bar for the GA evolution

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Installation

Using pip

From PyPI:

pip install pvfit5

From GitHub (latest development version):

pip install git+https://github.com/valeriolobrano/pvfit5.git

For local development (editable install):

git clone https://github.com/valeriolobrano/pvfit5.git
cd pvfit5
pip install -e .

Using uv

uv is a fast Python package manager that can replace pip and virtualenv.

Add to an existing project:

uv add pvfit5

From GitHub:

uv add git+https://github.com/valeriolobrano/pvfit5.git

Run directly without installing (ephemeral):

uvx --from pvfit5 pvfit5 \
    --voc 36.3 --isc 8.19 --pmax 218.95 --vmp 29.0 --imp 7.55

Create a new project with pvfit5:

uv init my_pv_project
cd my_pv_project
uv add pvfit5
uv run pvfit5 --voc 36.3 --isc 8.19 --pmax 218.95 --vmp 29.0 --imp 7.55

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Usage

Command line

After installing pvfit5, run it from the terminal with your module datasheet values:

pvfit5 --voc 36.3 --isc 8.19 --pmax 218.95 --vmp 29.0 --imp 7.55

All five datasheet values are required. Optional arguments:

Argument	Description	Default
--name	Module name (for output files)	PVModule
--error-target	GA early-stop threshold	1e-2
--alpha-sc	α_sc in absolute units (A/°C)	0.05
--alpha-sc-rel	α_sc in relative units (1/°C); overrides --alpha-sc	—
--egref	Band gap energy at reference conditions (eV)	1.121
--degdt	Temperature coefficient of band gap (eV/K)	-0.000267
--no-plot	Disable live and final plots	—

Full example:

pvfit5 --voc 36.3 --isc 8.19 --pmax 218.95 --vmp 29.0 --imp 7.55 \
       --alpha-sc 0.05 --egref 1.121 --name MyModule

Python library

from pvfit5.find_pv_parameters import fit_parameters, PVModuleData, STC, GAConfig

nd  = PVModuleData(voc=36.3, isc=8.19, pmax=218.95, vmp=29.0, imp=7.55)
stc = STC()                       # default: EgRef=1.121, dEgdT=-0.000267
ga  = GAConfig(error_target=1e-2)

results, summary = fit_parameters(nd, stc, ga, module_name="MyModule")
print(summary)

# Access individual results
print("R_s  =", results["best_individual"]["R_s"], "Ω")
print("R_sh =", results["best_individual"]["R_sh"], "Ω")

Plots

The script opens two plots:

• Graph 1 (live): I–V curve updating during GA evolution (auto-closes after 3 s).
• Graph 2 (final): publication-quality I–V curve with annotated errors (stays open). Use --no-plot to suppress both.

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Batch Validation (optional)

Run the algorithm on a large set of modules from the pvlib CEC database:

# Analyse 100 modules in alphabetical order
pvfit5-batch -n 100 --selection alpha

# Analyse 200 random modules (reproducible with --seed)
pvfit5-batch -n 200 --selection random --seed 42 --output my_results.xlsx

Results are saved to an Excel file. Run pvfit5-batch --help for all options.

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Analysing Batch Results (optional)

After running pvfit5-batch, analyse the output Excel file:

# Analyse the default output file
pvfit5-analysis

# Analyse a specific file
pvfit5-analysis my_results.xlsx

# Suppress figure output
pvfit5-analysis my_results.xlsx --no-figures

The script produces:

• PDF and CDF plots for RMSE and runtime.
• Dominance analysis of partial errors.
• results_summary.xlsx with descriptive statistics.

For per-technology statistics:

pvfit5-parametric

# Or with a specific input and output file
pvfit5-parametric my_results.xlsx --output my_statistics.xlsx

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License

Released under the BSD-3-Clause License. Free to use, modify, and redistribute, provided the original copyright notice is retained. The software is provided without warranty of any kind.