Tut 4 solutions - Page 1 of 7 SOLA2540& SOLA9001 Applied...

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Page 1 of 7 SOLA2540 & SOLA9001 Applied Photovoltaics Tutorial 4 Solutions Question 1 (Assuming T = 300 K) V oc 1 = 0.55 V , I sc 1 = 1.3 A , V oc 2 = 0.60 V , I sc 2 = 1.0 A , n = 1 I 01 = I sc 1 exp qV oc 1 kT ! " # $ % &− 1 = 1.3 A exp 0.55 V 0.026 ! " # $ % & 1 = 8.45 × 10 10 A I 02 = I sc 2 exp qV oc 2 kT ! " # $ % &− 1 = 1.0 A exp 0.60 V 0.026 ! " # $ % & 1 = 9.50 × 10 11 A (a) In parallel 1 2 01 1 02 2 1 2 01 02 10 11 1.3 1.0 2.3 exp exp 0 ln 1 2.3 0.026 ln 1 8.45 10 9.50 10 0.562 sc com sc sc oc com sc sc sc sc oc com I I I A A A for V qV qV I I I I kT kT I I kT V q I I A V A A V = + = + = + = + = + + = × + × + × = Q (b) In series 1 2 1.0 0.55 0.6 1.15 sc com oc com oc oc I A V V V V V V = = + = + = Question 2 V OC = 620 mV; I SC = 2.5 A; ideality factor, n = 1; T = 300K; and nkT/q = 26 mV (a) I = I L I 0 exp qV nkT " # $ % & ' 1 " # $ % & ' when I = I MP ; V = V MP Therefore, I MP = I L I 0 exp qV MP nkT " # $ % & ' 1 " # $ % & ' I L I MP I 0 + 1 = exp qV MP nkT " # $ % & ' qV MP nkT = ln 1 + I L I MP I 0 " # $ % & ' Therfore, V MP = nkT q ln 1 + I L I MP I 0 " # $ % & '
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Page 2 of 7 Given I MP = 2.38 A I = I L I 0 exp qV nkT " # $ % & ' 1 " # $ % & ' At V OC ; I = 0 and I L = I SC Therefore, I 0 = I SC exp qV OC nkT " # $ % & ' 1 = 2.5 exp 0.620 0.026 " # $ % & ' 1 = 1.10 × 10 10 A and V MP = nkT q ln 1 + I L I MP I 0 " # $ % & ' = 26 × 10 3 ln 1 + 2.5 2.38 1.10
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