The voltage and current at the maximum power point in a 200 W solar panel are listed in Table 10.5, along with the maximum power for various level of solar insolation.

Calculate the internal resistance of the panel for each level of solar power, the duty cycle of the buck converter for impedance matching with a load resistance of 8 Ω operating at 20 kHz. Calculate the minimum inductance for continuous conduction.

Question

The voltage and current at the maximum power point in a 200 W solar panel are listed in Table 10.5, along with the maximum power for various level of solar insolation.

Calculate the internal resistance of the panel for each level of solar power, the duty cycle of the buck converter for impedance matching with a load resistance of 8 Ω operating at 20 kHz. Calculate the minimum inductance for continuous conduction.

Accepted Answer

The internal resistance is given by Equation 10.39:

[latex]-r=-\frac{\Delta V}{\Delta I}=R_{L R}=\frac{V_P}{I_P}[/latex] (10.39)

[latex]r=\frac{V_P}{I_P}=\frac{41.3}{4.1}=10.07 \Omega[/latex]

The remaining values are 13.35, 20.80, and 41.60 Ω.

The duty cycle is given by Equation 10.40:

[latex]R_{L R}=\frac{1}{D^2} R_L[/latex] (10.40)

[latex]D=\sqrt{\frac{R_L}{r}}=\sqrt{\frac{8.0}{10.07}}=0.89[/latex]

The remaining values are 0.77, 0.62, and 0.44.

The minimum value of inductance to ensure continuous conduction is given by Equation 10.42:

[latex]L_{\min }=\frac{D^2(1-D) V_P}{2 f_s I_P}=\frac{(0.89)^2(1-0.89)(41.3)}{(2)\left(20 imes 10^3 ight)(4.1)} imes 10^6=21.9 \mu H[/latex]

The remaining values are 45.5, 76.0, and 112.8 μH.

Table 10.5 Parameters under different load conditions
Insolation (W/m²)	$V_{P} (V)$	$I_{P} (A)$	Maximum output power (W)
800	41.3	4.1	169
600	41.4	3.1	128
400	41.6	2.0	83.2
200	41.6	1.0	41.6

Question 10.7: The voltage and current at the maximum power point in a 200 ...

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