tandem-solar

Python simulation toolkit for perovskite silicon tandem solar cell modules. Covers I V modelling, terminal configurations (2T/3T/4T), cell to module (CTM) loss analysis, and bypass diode protection under partial shading.

Based on work at the Solar Energy Research Institute of Singapore (SERIS), NUS, internship project on cell to module loss evaluation for next generation tandem solar technology (Summer 2025).

Related publication:

Devoto et al. (2024). Modelling the effects of tandem module circuit configurations. 41st EU PVSEC. doi:10.4229/EUPVSEC2024/2BV.1.41

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What this covers

Perovskite-Silicon Tandem Cell
  ├── Perovskite top cell   (Voc ≈ 1.3 V, high bandgap)
  └── Silicon bottom cell   (Voc ≈ 0.65 V, IBC technology)

Terminal configurations:
  2T  — monolithic, series-connected (current-matched)
  3T  — three terminals (3T-r recombination, 3T-s series)
  4T  — mechanically stacked, fully independent

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Modules

Module	Contents
cell_model.py	Single diode model (SDM): I V curves, parameter extraction, temperature/irradiance scaling
tandem.py	2T, 3T r, 3T s, 4T configuration models; end loss analysis
ctm_loss.py	CTM loss waterfall: optical, resistive, mismatch; Isc mismatch Monte Carlo
shading.py	Partial shading + bypass diode sweep, reproducing Devoto et al. Fig. 8

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Installation

git clone https://github.com/defnalk/tandem-solar.git
cd tandem-solar
pip install -r requirements.txt

Quick Start

from tandem import SolarCell, TandemModule, CTMLossAnalyser, ShadingAnalysis
from tandem.cell_model import SILICON_PARAMS, PEROVSKITE_PARAMS

# I-V curve for a silicon IBC sub-cell
si = SolarCell(SILICON_PARAMS)
V, I, P = si.iv_curve()
print(f"Silicon: Voc={SILICON_PARAMS.Voc:.2f} V, FF={SILICON_PARAMS.FF:.3f}")

# 11-cell tandem string — compare configurations
mod = TandemModule(n_cells=11)
comp = mod.compare_configurations()
for config, vals in comp.items():
    print(f"{config}: Pmpp={vals['Pmpp']:.1f} W  ({vals['rel_eff']*100:.0f}% of 4T)")

# CTM loss breakdown
ctm = CTMLossAnalyser(n_cells_series=11)
summary = ctm.loss_summary()
print(f"\nCTM ratio: {summary['ctm_ratio']:.3f}")
print(f"Cell sum → Module: {summary['P_cell_sum_W']:.1f} W → {summary['P_module_W']:.1f} W")

# Bypass diode sweep
sa = ShadingAnalysis(n_cells=22)
sweep = sa.bypass_diode_sweep()

Run the Full Simulation

python examples/full_simulation.py

Generates a 4 panel figure:

Panels:

• A: Normalised I V and P V curves for perovskite and silicon sub cells
• B: Configuration comparison: 2T / 3T r / 3T s / 4T Pmpp (11 cell string)
• C: CTM loss waterfall, 8.8% total loss, CTM ratio = 0.912
• D: Bypass diode sweep (reproducing Devoto et al. Fig. 8)

Running Tests

python -m pytest tests/ -v

31 tests, all passing.

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Physics Background

Single Diode Model

The standard SDM describes cell current implicitly:

I = I_ph − I_0·[exp((V + I·Rs)/(n·Vt)) − 1] − (V + I·Rs)/Rsh

Solved numerically using Brent's method at each voltage point.

Terminal Configurations

Config	Matching	End losses	Key property
2T	Current matched	None	Simplest; current mismatch penalising
3T r	Voltage matched	Low (1 cell)	Better than 3T s; BPD works like 2T
3T s	Voltage matched	High (3 cells)	No effective BPD implementation known
4T	Independent	None	Best efficiency; highest cost

CTM Loss Mechanisms

Cell Pmax sum (100%)
    − Optical reflection      (2.0%)
    − Encapsulant absorption  (1.5%)
    − Interconnect shading    (2.5%)
    − Interconnect resistance (1.0%)
    − Busbar resistance       (0.8%)
    − Isc mismatch            (1.5%)
    − Voc mismatch            (0.5%)
    + Light trapping gain    (+1.0%)
    ─────────────────────────────
    = Module power (CTM ratio ≈ 0.91)

Bypass Diode Protection (reproducing Devoto et al. 2024)

In a 22 cell 2T string with one shaded cell:

Cells under BPD	Power	vs STC
0 (no BPD)	~22 W	48%
1 cell	~44 W	95% ← best
3 cells	~40 W	86%
9 cells	~27 W	59%
10+ cells	~22 W	48% ← no improvement

Key finding: one bypass diode can protect up to 9 tandem cells in this module. Beyond that, the silicon bottom cell Vbd (≈ −3.7 V for IBC) is too low to prevent perovskite top cell reverse bias degradation before the diode activates.

Perovskite Stability Challenge

Perovskite sub cells have breakdown voltage Vbd ≈ −1 to −5 V, far lower than silicon PERC (Vbd > −20 V). This means:

• Standard bypass diode placement (1 per 20 cells) is insufficient for tandems
• IBC silicon's soft breakdown (Vbd ≈ −3.7 V) that benefits single junction modules becomes a disadvantage in 3T tandem bottom cells
• 3T s has no known effective bypass diode solution

References

• Devoto et al. (2024). Modelling the effects of tandem module circuit configurations. 41st EU PVSEC. doi: 10.4229/EUPVSEC2024/2BV.1.41
• McMahon et al. (2021). Homogenous voltage matched strings using three terminal tandem solar cells. IEEE J. Photovolt.
• Chu et al. (2015). Soft breakdown behavior of IBC silicon solar cells. Energy Procedia.
• Di Girolamo et al. (2024). Silicon/perovskite tandem solar cells with reverse bias stability down to −40 V. Adv. Sci.

Author

Defne Ertugrul, MEng Chemical Engineering, Imperial College London
Research internship: SERIS (Solar Energy Research Institute of Singapore), NUS, July 2025
Supervisor: Dr. Romika Sharma, Next Generation Industrial Solar Cells and Modules Cluster