# EE 8744: Modeling, Analysis, and Control of Renewable Energy Systems Homework 1 solution

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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
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?