5.13 Consider a single 87.5 W, First Solar CdTe module (Table 5.3) used to charge a 12-V battery.

a. What duty cycle should be provided to a maximum-power-point, buck-boost converter to deliver 14-V to the battery when the module is working at standard test conditions (STC)? How many amps will it deliver to the battery under those conditions?

b. Suppose ambient temperature is 25°C with 1-sun of insolation. Recalculate the amps delivered to the battery.

TABLE 5.3 Examples of PV Module Performance Data Under Standard Test Conditions (1 kW/m2 , AM1 .5, 25°C Cell Temperature) I

Mam1fo~turer Sun Power Yingli First Solar NanoSolar Sharp

1\'Iodcl E20/•U5 Ym: 1·+5 l-S Serie~ 3 Utility 230 NS- l-'IJ:"G5

:vlaterial c-Si me-Si CdTc CIGS a-Si Panel i..'.rlkicm:y 20.1(;: l:"N.i- 12 .21:i I IN. ~ lJ . (11.i

Rated puwcr /\11'1' (W11 ) ... JJ.:i 24) 87.5 23() 135 Rati..'.d \oliagc \!\11'1' <V > 72.9 .2,0.2 49.2 ...J0.2 ..J.7 Rated currcm /\11'1' <Al 5.97 8. 11 1.78 6 2.X8 Opcn-cin.:uit \'oltagc Voe (VI X:\6 37.8

... (iJ 50.7 61 .. ~

SlmrH:irniiL i:urrcn1 /o..,c (A) 6A> X.<13 1.98 6.7 :)Al

NUCT( C) 45 .+6 -t'i -i7 45 Temp. Cncff. pf Pm.ix ( <.; /K) - (Ug - 0.-l-5 - 0.25 - 03l) - 0.2...J. T~mp . Cocff. \/()(.· (<,( / K) - 0.27 - 0 ... 2.> - 0.:!7 - lUO - (UO

Tcrnp. Codi'. /sc(',U KJ 0.05 0.06 o.o .. i 0.00 ().()7

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6.1 A clean, 1m2,15% efficient module (STC) has its own 90o/c ff . . NOCT is 45oc d 't d ' o e lClent mverter Its

an Is rate power degrades by 0.5%/oc above the z5oc STC ..

a.

b.

~ l~m'l .,lck/1_;wh=? 6kWh/m2 PV ~

90%

Figure P 6.1

What is its standard test condition (STC) rated power of the module?

For a day w~th 6 kWh/mZ of insolation, find the kWh that it would deliver if it operates at its NO.CT temperature. Assume the only deratings are due to temperature and mverter efficiency.

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6.6 A grid-connected PV array consisting of sixteen 150-W modules can be arranged in a number of series and parallel combinations: (16S, 1P), (8S, 2P), ( 4S, 4P), (2S, 8P), (1S, 16P). The array delivers power to a 2500-W inverter. The key characteristics of modules and inverter are given below.

INVERTER

Maximum AC power 2500 W Input voltage range for MPP 250 V - 550 V Maximum input voltage 600 V Maximum input current 11 Amp

Table P 6.6

MODULE

Rated power Pdc,STC Voltage at MPP Open-circuit voltage Current at MPP

150 w 34 v

43.4 v 4.40 A

Short-circuit current 4.8 A

Using the input voltage range of the inverter maximum power point tracker and the maximum input voltage of the inverter as design constraints, what

series/parallel combination of modules would best match the PVs to the inverter? Check the result to see whether the inverter maximum input current is satisfied. For this simple check, you don't need to worry about temperatures.

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Additional Problems: Use the logic used to develop buck and boost DC-DC converters in class to develop duty cycle relationship for the buck-boost converter shown in Figure 5.52.

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2. Define levelized cost of ene g (LCOE) · · . r Y usmg a mathematical expression. What is LCOE used £ · power system plannmg? . or m

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3. You have a project that returns $1000 and $2000 at the end of years 1 and 2 respectively. Your ini­tial investment is $2400 at the outset. Assume a 103 discount rate.

a. Draw the cash flow diagram. b. What is the net present value?

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4. You want to borrow $2000 at 63 rate to be repaid back in equal payments over 5 years. a. Compute the annual payment. b. Draw the cash fl.ow diagram.

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