ELEC 5564 Electric Power Generation by Renewable Sources - Electrical Characteristics of Solar PV

Electrical Characteristics of Solar PV

Equivalent Circuit of a Solar Cell

• A PV solar cell acts as a large area diode, comprising an n-type and p-type doped semiconductor, creating a space charge layer.

• The cell current $I$ depends on the terminal voltage $V$.

• Equation for cell current:
  $I = I<em>S(e^{\frac{qV}{nkT</em>c}} - 1)$

  • Where:
    • $I_D$ is the diode current.
    • $I_{SC}$ is the short-circuit current.
    • $V$ is the terminal voltage.
    • $k$ is the Boltzmann constant.
    • $q$ is the electron charge.
    • $A$ is the ideality factor (sometimes represented as $n$).
    • $T_C$ is the cell temperature (e.g., 25°C).
    • $I_S$ is the diode saturation current.
    • $V<em>T$ is the terminal voltage, $V = V</em>T$.

• The above equation represents a non-irradiated ideal solar cell (dark characteristics).

Mathematical Model for a Solar Cell

• For a practical solar cell, the terminal current $I$ is expressed considering series resistance ($R<em>S$) and shunt resistance ($R</em>{sh}$):

*Considering a practical solar cell, we have the terminal current I expressed as
$I = I<em>{SC} – I</em>D – I_{sh}$

• Equation for illuminated solar cell (in the presence of sunlight): $I = I<em>{sc} – I</em>D – I_{sh}$
  • Where:
    • $I<em>{SC}$ or $I</em>{ph}$ is the short circuit current (photocurrent).
    • $I_D$ is the diode current (solar cell dark characteristics).
    • $R_{sh}$ is the shunt resistance.
    • $R_S$ is the series resistance.
  • Also:
    $I<em>{sc} = I</em>D + I_{sh} + I$

Influence of Parallel Resistance ($R_{sh}$) on I-V Characteristics

• $R_{sh}$ describes the leakage current in the cell and is generally larger than 10 Ω in a full equivalent circuit model.
• The figure illustrates the I-V curve of a solar PV cell as a function of different $R_{sh}$ values under uniform radiation.

Influence of Series Resistance ($R_S$) on I-V Characteristics

• $R_S$ describes the ohmic loss through the junction and terminals and is typically less than 0.01 Ω.
• The figure illustrates the I-V curve of a solar PV cell as a function of different $R_S$ values under uniform radiation.

Two-Diode Model

• An extra diode is added for better curve-fitting.
• The number of parameters for modeling in the one-diode model is five:
  • Light generated current, $I_{ph}$(Isc)
  • Diode parameters: reverse saturation current, $I<em>0$ ($I</em>S$
  • Ideality factor, $n (k)$
  • Series resistance, $R_s$
  • Shunt resistance, $R_{sh}$
• In the two-diode model, the number of parameters becomes seven:
  • Reverse saturation currents $I<em>{01}$ and $I</em>{02}$
  • Ideality factors $n<em>1$ and $n</em>2$

Simplified Equivalent-Circuit Model

• A simplified equivalent-circuit model assumes that the effect of the large shunt resistance can be neglected (open circuit).

Three-Diode Model

• A three-diode model better explains the I–V characteristics of large-size industrial silicon solar cells.
• This model defines the different current components of the large-size industrial silicon solar cells more clearly.

Solar PV Modules - Parallel Connection

• A parallel connection of solar cells will give the output current:
  $I = I<em>{S1} + I</em>{S2} + … + I_{Sn}$

• The output voltage $V_O$ is equal to that of a single cell.

Solar PV Modules - Series Connection

• If the cells are connected in series, the output voltage is the sum of individual cell voltages:
  $V<em>o = V</em>1 + V<em>2 + … + V</em>n$
• The current equals that of a single cell:
  $I<em>{S1} = I</em>{S2} = I_{Sn} = IS$

Mathematical Model for a PV Module

• The PV model can be extended to represent a PV array with $n<em>p$ cells in parallel and $n</em>s$ cells in series.
• $V$ is the total voltage across the array, and $I$ is the total current out of the array.
• You can derive this starting with the single-cell model, and substituting $V arrow V/n<em>s$ and $I arrow I/n</em>p$, and then multiplying this expression by $n_p$.