Solar Cell Equivalent Circuit and Characteristics

Jul 16, 2024

Lecture Notes: Solar Cell Equivalent Circuit and Characteristics

Ideal Solar Cell

  • Definition: A solar cell with no losses (no resistances).
  • Equivalent Circuit:
    • Current source (iph) in parallel with a diode.
    • Current source 'iph' represents photon-generated current.
    • iph is proportional to the irradiance (solar radiation intensity).
    • Diode represents the junction diode.
    • Output Current (i) equation: i = iph - id
    • Id (diode current) equation: i0 * (e^(qv / αkt) - 1)
      • i0: Reverse saturation current (dark current).
      • q: Electron charge = 1.602 x 10^(-19) C.
      • v: Voltage across the diode.
      • α: Diode ideality factor.
      • k: Boltzmann constant.
      • T: Temperature (Kelvin).

Practical Solar Cell

  • Resistances: Practical cells have parasitic resistances.
  • Series Resistance (rs): Represents metallic contacts, metal grids, and internal resistances of p and n layers.
  • Shunt Resistance (rsh): Represents leakage current across the junction.
    • rs: Small value, rsh: High value.
  • Output Current (i) in practical cell: i = iph - id - irsh
    • Adjustments in diode current equation: v + i * rs instead of v.
    • Current through rsh: (v + i * rs) / rsh

Solar Cell Characteristics

IV Characteristics (Current vs Voltage)

  • Short Circuit Current (isc): Maximum current when output is short-circuited.
    • Voltage = 0 at short circuit, current = isc.
  • Open Circuit Voltage (voc): Maximum voltage when terminals are open-circuited.
    • Current = 0 at open circuit, voltage = voc.
  • Graph: Combination of isc and voc points with forward-biased diode curve.

PV Characteristics (Power vs Voltage)

  • Power Calculation: Power (P) = Voltage (V) * Current (I).
  • Power Curve: Derived from IV curve, showing maximum power point (MPP).
    • vmp: Voltage at MPP.
    • imp: Current at MPP.

Performance Parameters

Short Circuit Current (isc)

  • Definition: Maximum current under short-circuit conditions.
  • Dependence:
    • Solar irradiance level.
    • Area of the solar cell.
    • Material characteristics.
  • Proportional to iph: isc ≈ iph - id - irsh
  • Temperature: Slightly dependent, often neglected.

Open Circuit Voltage (voc)

  • Definition: Maximum voltage under open-circuit conditions.
  • Dependence:
    • Material quality.
    • Strong function of temperature.
    • Weak function of irradiance.
  • Equation: voc = vt log(isc / i0 + 1)
    • vt: Voltage equivalent of temperature.

Fill Factor (FF)

  • Definition: Ratio of maximum power (vmp * imp) to product of voc and isc.
    • FF = (vmp * imp) / (voc * isc)
  • Indicator: Quality of solar cell.
  • Typical Values: 0.7 to 0.8

Conversion Efficiency

  • Definition: Ratio of electrical power output to solar power input.
    • Efficiency = (Electrical power output) / (Solar radiance power input)
  • Typical Values: 10% to 12%

Summary

  • Understanding the equivalent circuit and characteristics of ideal and practical solar cells is crucial for evaluating their performance.
  • Key parameters such as isc, voc, fill factor, and conversion efficiency help in assessing the quality and efficiency of solar cells.