# Midterm Exam - Solution

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• ENEE498R Midterm Solution

October 17th

, Wednesday

Problem 1 (20 points): Given a PV module with 10 series solar cells, one of which is

(a) Describe the shading effect on I-V characteristics of a solar cell with and without

bypass diodes.

(b) Plot the corresponding I-V curve of the PV module without considering any bypass

diodes.

(c) Plot the corresponding I-V curve of the PV module assuming that the shaded cell has

a bypass diode. I S

C

VOC

Current ( I)

Single cell w/o shading

Single cell w/ shading

Fig. 1. I-V curves of single solar cell without bypass diode

Solution (a) Without the bypass diode, the current of the non-shaded PV cell will be blocked by the dark

diode of the shaded one. Without considering the parallel parasitic resistor, the current will go

down to zero. With the bypass diode, the current of the non-shaded PV cell pass through the

bypass diode of the shaded PV cell. The voltage goes down at around 9 times VOC of the non-

(6 points)

(b)

Voltage (V)

I SC

10 series non-shaded cells w/o

bypass diode

10 series cells one shaded w/o

bypass diode

10VOC9VOC (7points)

• (3)

Voltage (V)

I SC

10 series non-shaded cells w/

bypass diode

10 series cells one shaded w/

bypass diode

(7 points)

• Problem 2 (40 points): Given a PV module, the specifications are provided in table I.

Find I-V curve characteristics equation of this module at given operating condition, with

ambient temperature ( ) and irradiation ( ) to be 400C and 1200W/m

2, respectively.

Table I Datasheet of a PV module*

Electrical Data at STC Electrical Data at NOTC Constants

29.0 [V]

25.8 [V] 1.38 10-23 [J/0K]

7.6 [A]

6.1 [A] 1.60 10-19 [C]

36.2 [V]

32.9 [V] 20 0C

8.4 [A]

6.8 [A] 800 W/m2

Temperature Data Module Data 25

0C

47 [

0C] 1 1000 W/m

2

C3 -0.36 [%/0C] 60 1.2

Solution

First cell level data needs to be acquired. Cell short-circuit current and open circuit

voltage under STC can be calculated as,

(3 points)

(3 points)

Cell temperature can be found as,

(3 points)

( )

(3 points)

After finding cell temperature, open circuit voltage of the PV cell for operating condition

can be calculated as,

(

)

( ( ))

(3 points)

The short-circuit characteristic of the cell under operating condition can be found as,

• (3 points)

(3 points)

Normalized voltage of the PV cell is found as

(3 points)

From the normalized voltage, ideal fill factor can be found as,

( )

(4 points)

In order to find the series resistance, fill factor affected by the parasitic resistance should

be calculated. It can be determined using module parameters as,

(4 points)

The series resistance of a single PV cell can be determined as

(

)

(4 points)

The module current relation can be expressed as

[ (

)]

* (

)+

(4 points)

• Problem 3 (40 points): Design a Buck converter (figure 2) interface for a solar PV

system, to operate in continuous conduction mode (CCM) and to produce across a 10 load. The PV system generates 48V voltage. Assume , . Please determine following parameters for your design.

L

C R

PV panel

D

S

Fig 2. Buck converter cascaded with the pv panel

(a) Duty cycle D. (b) Inductance L, as well as capacitance C. (c) Voltage ratings of all the components (Switch, Diode, L and C). (d) Inductor RMS current.

Solution

(a) For the buck converter operating in CCM

(4 points)

(b) Since the dc current across the capacitor is zero,

(4 points)

( )

To ensure the circuit operate in CCM, >0, thus,

( )

(4 points)

To ensure CCM, we can choose

(4 points)

( )

• ( )

( )

(4 points)

(c) When the switch is off, the diode is on, maximum voltage Vin is applied to the switch, maximum voltage Vin-Vout is applied to the inductor

(4 points)

(4 points)

When the diode is off, the switch is on, maximum voltage Vin is applied to the

diode

(4 points)

For the filter capacitor, without considering the small ripple, the voltage is always

equal to Vout.

(4 points)

(d)

ILmax

IL

ILmin

ILmaxDIL/2

iL(t)

tT

( )

(

)

(4 points)