Energy Yield for Bifacial Tandem Solar Cell

Using spectral on-demand data from NREL and simulated EQE data from GENPRO4.

This example shows how to model the performance of a bifacial tandem solar cell, with different bandgaps and how it compares to a monofacial counterpart. It uses “spectral-on-demand” data from the NSRDB providded by NREL. For the absorptances of the subcells GENPRO4 simulated EQE curves are used originally createf for the following publication: .. [1] P. Tillmann, K. Jäger, A. Karsenti, L. Kreinin, C. Becker (2022)

“Model-Chain Validation for Estimating the Energy Yield of Bifacial Perovskite/Silicon Tandem Solar Cells,” Solar RRL 2200079, DOI: 10.1002/solr.202200079

First, the nessesary libraries and datasets (spectral irradiance for the front side, diffuse and direct irradiance and eqe data) are loaded. The meta data of the spectral irradiance data contains the direct and diffuse irradiance data needed for the bifacial model

from pv_tandem import (
    geo,
    utils,
    bif_yield,
    solarcell_models,
    irradiance_models,
)
import matplotlib.pyplot as plt
import numpy as np
import pvlib
import pandas as pd
import seaborn as sns

spec_irrad_ts = pd.read_csv(
    "./data/spec_poa_dallas_2020.csv", index_col=0, parse_dates=True
)

spec_irrad_ts.columns = spec_irrad_ts.columns.astype(float)
# converting spectral data from W/µ/m² to W/nm/m²
spec_irrad_ts = spec_irrad_ts.clip(lower=0) / 1000

eqe = pd.read_csv("./data/eqe_tandem_2t.csv", index_col=0)
eqe = utils.interp_eqe_to_spec(eqe, spec_irrad_ts)

meta_ts = pd.read_csv(
    "./data/meta_ts_dallas_2020.csv", index_col=0, parse_dates=True
)

coord_dallas = dict(latitude=32.8, longitude=-96.8)

Next we use the python library pvlib to calculate the solar position (zenith and azimuth angle), then the geometry of the bifacial soalr cell array is defined and the backside irradiance is calculated in the plane-of-array (poa). Further, the noct (nominal operating cell temperature) model of pvlib is used to calculated the cell temperature from irradiance, ambient temperature and wind speed

solar_pos = pvlib.solarposition.get_solarposition(
    meta_ts.index, **coord_dallas
)

illumination_df = meta_ts
illumination_df["zenith"] = solar_pos["zenith"]
illumination_df["azimuth"] = solar_pos["azimuth"]

illumination_df = illumination_df[["DNI", "DHI", "zenith", "azimuth"]]

# The

simulator = bif_yield.IrradianceSimulator(
    illumination_df,
    albedo=0.3,
    module_length=1.96,
    module_height=0.5,
)

irrad_poa = simulator.simulate(spacing=6, tilt=25, simple_results=True)

# pvlib is used to calculate the solar cell temperature

temperature = pvlib.temperature.noct_sam(
    spec_irrad_ts.sum(axis=1) * 1.15 + irrad_poa["back"],
    meta_ts["Temperature"],
    meta_ts["Wind Speed"],
    noct=45,
    module_efficiency=0.25,
)

cell_temps = pd.DataFrame({"pero": temperature, "si": temperature})


electrical_parameters = {
    "Rsh": {"pero": 1000, "si": 3000},
    "RsTandem": 3,
    "j0": {"pero": 2.7e-18, "si": 1e-12},
    "n": {"pero": 1.1, "si": 1},
    "Temp": {"pero": 25, "si": 25},
    "noct": {"pero": 48, "si": 48},
    "tcJsc": {"pero": 0.0002, "si": 0.00032},
    "tcVoc": {"pero": -0.002, "si": -0.0041},
}

tandem = solarcell_models.TandemSimulator2T(
    eqe=eqe,
    electrical_parameters=electrical_parameters,
    subcell_names=["pero", "si"],
)

Jsc_backside = (irrad_poa["back"] / 1000 * 35).rename("si").to_frame()
Jsc_backside["pero"] = 0

Jsc = tandem.calculate_Jsc(spec_irrad_ts)

Jsc["si"] = Jsc["si"] + irrad_poa["back"]

V_tandem = tandem.calc_IV(Jsc, cell_temps)

P = V_tandem.values * tandem.j_arr[None, :]
P_max = P.max(axis=1)
P_max = pd.Series(P_max, index=spec_irrad_ts.index)


# A dataset with simulated eqe data for several different perovskite bandgaps is
# loaded to scan the energy yield for the optimal bandgap

eqe_all_bgs = pd.read_csv("./data/eqe_tandem_all_bgs.csv")

P_stc = []
energy_yield_bif = []
energy_yield_mono = []
j_ph = []

for bandgap in eqe_all_bgs["bandgap"].sort_values().unique():
    eqe = eqe_all_bgs.loc[
        eqe_all_bgs["bandgap"] == bandgap, ["pero", "si", "wl"]
    ]
    eqe = eqe.set_index("wl").sort_index()
    eqe = utils.interp_eqe_to_spec(eqe, spec_irrad_ts)

    j0 = utils.calc_j0_RT(eqe["pero"], lqe_ele=0.01)

    electrical_parameters["j0"]["pero"] = j0

    tandem = solarcell_models.TandemSimulator2T(
        eqe=eqe,
        electrical_parameters=electrical_parameters,
        subcell_names=["pero", "si"],
    )

    j_ph.append(pd.Series(irradiance_models.AM15g().calc_jph(eqe) / 10))

    V_stc = tandem.calc_IV_stc()
    P_max_stc = V_stc.reset_index().eval("current*tandem").max()

    P_stc.append(pd.Series({bandgap: P_max_stc}))

    ey_bif = tandem.calc_power(
        spec_irrad_ts, cell_temps=cell_temps, backside_current=Jsc_backside
    )
    ey_bif = ey_bif.sum() / 1000 * 10

    energy_yield_bif.append(pd.Series({bandgap: ey_bif}))

    ey_mono = tandem.calc_power(spec_irrad_ts, cell_temps=cell_temps)
    ey_mono = ey_mono.sum() / 1000 * 10

    energy_yield_mono.append(pd.Series({bandgap: ey_mono}))


energy_yield_bif = pd.concat(energy_yield_bif)
energy_yield_mono = pd.concat(energy_yield_mono)
P_stc = pd.concat(P_stc)

fig, ax = plt.subplots(dpi=150)

ax2 = ax.twinx()

ax = energy_yield_bif.plot(ax=ax, c="C0", label="bif")
ax = energy_yield_mono.plot(ax=ax, c="C1", label="mono")
ax2 = P_stc.plot(ax=ax2, c="C2", label="stc")

ax.set_xlabel("Perovskite Bandgap (eV)")
ax.set_ylabel("Annual energy yield (kWh/m²)")
ax2.set_ylabel("Power density (kWh/m2)", color="C2")
ax2.tick_params(axis="y", colors="C2")

handles, _ = ax.get_legend_handles_labels()
handles2, _ = ax2.get_legend_handles_labels()

# Combine the handles from both axes
handles += handles2

ax.legend(
    handles,
    [
        "Energy yield bifacial",
        "Energy yield monofacial",
        "Standart test conditions",
    ],
)

<matplotlib.legend.Legend object at 0x7f31994336a0>

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