Determining the Output Voltage and Power of a PV Cell

The reverse saturation current of a PV cell operating at $30°$ C is 10 nA. The solar current at $30°$ C is 1.2 A. Calculate (a) the output voltage $v_L$ and output power $P_L$ of the PV cell when the load draws $i_L = 0.6 A$ , and (b) the load resistance $R_L$ at the maximum output power $P_{\max}$ .

Question

Determining the Output Voltage and Power of a PV Cell

The reverse saturation current of a PV cell operating at [latex]30°[/latex]C is 10 nA. The solar current at [latex]30°[/latex]C is 1.2 A. Calculate (a) the output voltage [latex]v_L[/latex] and output power [latex]P_L[/latex] of the PV cell when the load draws [latex]i_L = 0.6 A[/latex], and (b) the load resistance [latex]R_L[/latex] at the maximum output power [latex]P_{\max}[/latex].

Accepted Answer

[latex]I_C = 1.2 A, I_S = 10 nA, i_L = 0.6 A, T = 30°[/latex]

Using Eq. (2.2),

[latex]V_T=\frac{kT}{q}[/latex] (2.2)

the thermal voltage is

[latex]V_T=\frac{1.38 imes 10^{-23} imes (273 + 30)}{1.602 imes 10^{-19}}= 25.8 mV[/latex]

a. Equation (16.19)

[latex]i_L = I_C - i_D = I_C - I_S(e^{v_D/\eta V_T - 1})[/latex] (16.19)

gives the PV voltage

[latex]\upsilon _D=V_T imes ln\left(\frac{I_C - i_L}{I_s}+1 ight)= 25.8 imes 10^{-3} imes \left(\frac{1.2 - 0.6}{10 imes 10^{-9}}+1 ight)=0.467 V[/latex]

b. Equation (16.23)

[latex]\left(1+\frac{V_{mp}}{V_T} ight)e^{V_{mp}/\eta V_T}=\left(1+\frac{I_C}{I_S} ight) [/latex] (16.23)

gives the condition for voltage[latex] V_{mp}[/latex]

[latex]\left(1+\frac{V_{mp}}{V_T} ight)e^\frac{V_{mp}}{V_T}-\left(1+\frac{I_C}{I_S} ight)=0[/latex]

which, after solving by an iterative method using Mathcad or Mathlab software, gives the voltage [latex]V_{mp }= 0.412 V[/latex].

Equation (16.19) gives the corresponding load current [latex]I_{mp}[/latex]

[latex]I_{mp }= 1.2 - 10 imes 10^{-9} imes (e^{\frac{0.412}{25.8 imes 10^{-3}} }-1)=2.128 A[/latex]

The maximum output power is [latex]P_{\max} = V_{mp} I_{mp }= 0.412 × 2.128 = 0.877 W[/latex].

The load resistance [latex]R_L = V_{mp}/I_{mp} = 0.412/2.128 = 0.194 Ω[/latex].

Question 16.2: Determining the Output Voltage and Power of a PV Cell The re...

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