Determining the Effects of Practical Model Parameters on Output Voltage and the Output Power of PV Cells

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 the output voltage $v_L$ and output power $P_L$ of the PV cell when the load draws $i_L = 0.6 A$ , the series resistance is $R_s = 20 mΩ$ , and the parallel resistance is $R_p = 2 kΩ$ .

Question

Determining the Effects of Practical Model Parameters on Output Voltage and the Output Power of PV Cells

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 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], the series resistance is [latex]R_s = 20 mΩ[/latex], and the parallel resistance is [latex]R_p = 2 kΩ[/latex].

Accepted Answer

[latex]I_C = 1.2 A, I_S = 10 nA, i_L = 0.6 A, R_s = 20 mΩ, R_p = 2 kΩ, T = 30°[/latex] Using Eq. (2.2),

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

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. For n = 1, Eq. (16.28)

[latex]i_L = I_C - i_D - i_P = I_C - I_S\left(e^{\upsilon _D/\eta V_T} -1 ight) -\frac{\upsilon _D}{R_p}[/latex] (16.28)

gives the condition for PV voltage [latex]v_D[/latex]

[latex]0.6 - 1.2 + 10 × 10^{-9} ×(e^{\frac{\upsilon _D}{25.8 imes 10^{-3}} }-1)+\frac{\upsilon _D}{R_p}=0[/latex]

which, after solving by an iterative method by using Mathcad or Mathlab software, gives the voltage [latex]v_D = 0.467 V[/latex].

For n = 1, Eq. (16.29) gives the load voltage [latex]v_L[/latex]

[latex]\upsilon _L=\upsilon _D - R_si_L= \upsilon _D - R_s \left[I_C-I_S(e^{v_D/\eta V_T}-1)\frac{\upsilon _D}{R_p} ight][/latex] (16.29)

[latex]\upsilon _L=0.467 - 20 imes 10^{-3} imes \left[1.2-10 imes 10^{-9} imes (e^\frac{0.467}{25.8 imes 10^{-3}}-1 )-\frac{0.467}{2 imes 10^3} ight]=0.455 A[/latex]

The output load power is [latex]P_L = v_L i_L = 0.467 × 0.455 = 0.273 W[/latex].

Question 16.3: Determining the Effects of Practical Model Parameters on Out...

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