## Description

Problem 1. [5 points] Gallium Arsenide has a band gap of 1.42 eV. What maximum wavelength

can a photon have to create electron-hole pairs?

Problem 2. [20 points] Let us explore the design of a PV system for Las Vegas, NV to deliver

4000 kWhr/yr. Las Vegas is known to receive 6.4 kWhr/m2day of average annual insolation and it

has an average ambient temperature of 26.9

◦C. Answer the following questions:

1. What should the AC rated power of the system be?

2. Estimate the DC power of the system under standard test conditions given the following information: i) The modules operate nominally at 45◦C and the maximum power of the modules

drops by 0.36%/

◦C above 25◦C, ii) Losses due to dirt are 3%, losses due to mismatched modules

are 3%, and the inverter efficiency is 92%.

3. If the PV modules are 13% efficient, what is the required area for the system?

4. Suppose the installed cost of the system is $6 per DC Watt, and the system is paid for with a

30-year loan at 6% interest rate. Las Vegas offers a renewable energy credit that pays the owner

$0.05/kWhr generated. What is the cost of electricity generated in year 1?

Problem 3. [8 points] The figure below shows the I − V curves for two cells. Answer the following

questions:

1. Estimate Rs for the cell with I − V curve labelled as Rs =?

2. Estimate Rp for the cell with I − V curve labelled as Rs = 0.

3. Estimate the maximum power that can be delivered by the cell with I − V curve labelled as

Rs = 0.

4. Consider the cell with I − V curve labelled as Rs = 0. Sketch the I − V curve that would be

obtained by connecting 5 parallel strings each with 10 series-connected cells of this type.

Problem 4. [2 points] We wish to deliver maximum power to a 12 V battery from a PV resource with

the following characteristics: Open-circuit voltage 41 V, short-circuit current 6 A, maximum-power

point voltage 40 V, and maximum-power point current 5 A. Pick a DC-DC converter topology to accomplish this and indicate the duty cycle at which the converter would have to be operated for the task.

Problem 5. [5 points] A grid-connected PV array consists of sixteen Shell SP150 modules that can

be arranged in a number of series (S) and parallel (P) configurations: (16 S, 1 P), (8 S, 2 P), (4 S,

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EE 8744: Modeling, Analysis, and Control of Renewable Energy Systems Spring 2021

4 P), (2 S, 8 P), (1S, 16 P). The array delivers power to a Sunny Boy SB2500 inverter. Using the

specifications of the PV modules in Table 1 (a), and the specifications of the inverter in Table 1 (b),

what series-parallel configuration of modules would deliver maximum power to the inverter?

Circle the right answer and provide an explanation for your choice:

1. (16 S, 1 P)

2. (8 S, 2 P)

3. (4 S, 4 P)

4. (2 S, 8 P)

5. (1S, 16 P)

6. None of the above.

[Note. To clarify the notation, (2 S, 8 P) corresponds to the case that the array is built with 8 parallel

strings and each string has 2 modules connected in series.]

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