Photovoltaic
1. Figure 11.12 introduced the I-V curve for a photovoltaic module, including its
maximum power point. Suppose, for some strange reason (e.g. shading impacts), the IV curve for a small module looks like the following:
a. Write an equation for the output power as a function of the current delivered.
b. What would be the maximum power this module could deliver under these
circumstances? Show this Maximum Power Point (MPP) on the I-V curve.
2. Using the "peak hours" approach to system sizing, along with our estimate of 0.75 as
an appropriate "de-rating" factor, size a system to deliver 4000 kWh/yr to a home in
Austin, TX. Assume fixed, south-facing photovoltaics exposed to 5.2 kWh/m2
-day of
irradiance.
a. Find the rated power of the system (kW, dc,stc)
b. Assuming 15% system efficiency, how big would the array be (m2 and ft2
)?
c. Now go to the PVWatts website for Austin and compare their results with those
you just found. For starters, what tilt angle for those south-facing PV modules
would give you the same 5.2 h/day of full sun (5.2 kWh/m2
-day)?
d. How many kW would be needed to deliver that 4000 kWh/yr?
3. Suppose a commercial building has a rooftop area that can be covered with 2000 m2
of horizontal PVs. You are trying to decide between single-crystal silicon (X-Si) modules
with 20% efficiency that cost $1.00/W versus thin-film CIGS cells with 10% efficiency that
cost only $0.60/W. Suppose balance of systems (inverter, racking, etc.) cost $1/W, and
the cost of installing the system, including permits, labor, and profit is $500 per m2 of roof
area. For the system installed in Boulder, CO, which is the most cost effective system:
X-Si or CIGS?
Chapter 12 Questions
1. From Eq. 12.4, we know power in the wind is equal to . With density
in kg/m3
, area in m2
, and v in m/s, the power Pw will be in watts.
PW
1
2
Av
3
a. Using a standard density of 1.225 kg/m3
, what is the energy content of 100 hours
of steady 6 m/s winds blowing through a 10 m2 swept area?
b. Compare that to the kWh that would pass through this area if we had 50 hours
of 3 m/s winds plus 50 hours of 9 m/s winds. In other words, the same average
windspeed of 6 m/s. Comment on your result.
2. A GE wind turbine with 85 m blade diameter is rated at 1.5 MW in 12.5 m/s winds.
a. Assuming a standard air density of 1.225 kg/m3
, what is the efficiency of the
turbine when operating at its rated windspeed?
b. Using the correlation given in Eq. 12.6, estimate the kWh/yr delivered in
Rayleigh winds averaging 7 m/s.
3. Historically, it has been standard practice to install anemometers at a height of 10m
above ground. To estimate windspeeds at higher elevations, the following simple
relationship has often been used:
V
V0
H
H0
1/7
where V0 is the windspeed at height H0 (e.g. 10 m) and V is the expected windspeed at
another elevation H.
If the average windspeed at 10 m is 5.7 m/s, what would the above equation suggest is
the windspeed at the 80 m hub height of a fairly big turbine?
4. A wind turbine with 10-m diameter blades is to be used in a wind regime with average
wind speed 6 m/s. Assuming Rayleigh statistics and the Capacity Factor correlation given
in Eq. 12.6:
a. Estimate the Capacity Factor and the energy delivered (kWh/yr) if this turbine is
equipped with a 20 kW generator.
b. Estimate the Capacity Factor and the energy delivered if this turbine is equipped
with a 30 kW generator.
c. What would be the optimum rated power of the generator to deliver maximum
energy? (you need a bit of calculus)? What would be its CF and how much energy
would it deliver?
d. What can you conclude about how to interpret Capacity Factor? Can you provide a
qualitative description of why bigger CF isn't always better? For a given generator
size, will a bigger blade diameter always produce more energy?