Impact of White-Light LED Color Temperature and CRI on Indoor Photovoltaic Efficiency

2.1 Detailed-Balance Calculations

The study employs detailed-balance calculations based on Shockley-Queisser theory to determine theoretical maximum efficiency limits for IPVs under various LED conditions. This approach considers the spectral mismatch between LED emission and photovoltaic material absorption characteristics.

2.2 LED Spectrum Analysis

Commercial white-light LEDs with varying CT (2200K to 6500K) and CRI values (70, 80, 90) were analyzed. The spectral power distribution of each LED was measured and used to calculate available photon flux for photovoltaic conversion.

3.1 Color Temperature Effects

Lower color temperatures (2200-3000K) consistently yielded higher theoretical efficiencies (up to 45% improvement over 6500K LEDs) and required lower optimal bandgap energies (approximately 0.2-0.3 eV reduction). This aligns with the increased red spectral content in warm-white LEDs.

3.2 CRI Impact Analysis

Contrary to previous assumptions, high-CRI LEDs (CRI 90) necessitate significantly lower bandgap materials (1.4-1.6 eV) compared to low-CRI counterparts (1.7-1.9 eV). The broader spectral distribution in high-CRI LEDs extends further into the red region, changing the optimal material requirements.

3.3 Material Performance Comparison

While optimal IPV performance requires wide-bandgap materials under low-CRI lighting, mature technologies like crystalline silicon (c-Si) and CdTe show improved performance under high-CRI illumination due to better spectral matching with their absorption profiles.

4.1 Mathematical Framework

The detailed-balance calculations are based on the Shockley-Queisser limit formalism adapted for indoor conditions:

$\\eta_{max} = \\frac{J_{sc} \\times V_{oc} \\times FF}{P_{in}}$

Where $J_{sc} = q \\int_{\\lambda_{min}}^{\\lambda_{max}} EQE(\\lambda) \\Phi_{photon}(\\lambda) d\\lambda$

The optimal bandgap energy $E_g^{opt}$ is determined by maximizing the efficiency function $\\eta(E_g)$ for each LED spectrum.

4.2 Code Implementation

import numpy as np
import pandas as pd

def calculate_ipv_efficiency(led_spectrum, bandgap_energy):
    """
    Calculate theoretical IPV efficiency for given LED spectrum and bandgap
    
    Parameters:
    led_spectrum: DataFrame with columns ['wavelength_nm', 'irradiance_w_m2_nm']
    bandgap_energy: Bandgap energy in eV
    
    Returns:
    efficiency: Theoretical maximum efficiency
    """
    h = 6.626e-34  # Planck's constant
    c = 3e8        # Speed of light
    q = 1.602e-19  # Electron charge
    
    # Convert wavelengths to energies
    wavelengths = led_spectrum['wavelength_nm'].values * 1e-9
    energies = (h * c) / wavelengths / q
    
    # Calculate photon flux
    photon_flux = led_spectrum['irradiance_w_m2_nm'] * wavelengths / (h * c)
    
    # Calculate current density (assuming perfect EQE above bandgap)
    usable_photons = photon_flux[energies >= bandgap_energy]
    j_sc = q * np.sum(usable_photons)
    
    # Simplified efficiency calculation
    input_power = np.sum(led_spectrum['irradiance_w_m2_nm'])
    efficiency = (j_sc * 0.7 * 1.0) / input_power  # Assuming typical Voc and FF
    
    return efficiency

# Example usage for different CRI conditions
bandgaps = np.linspace(1.0, 2.5, 100)
efficiencies_cri70 = [calculate_ipv_efficiency(led_cri70, eg) for eg in bandgaps]
efficiencies_cri90 = [calculate_ipv_efficiency(led_cri90, eg) for eg in bandgaps]