Introduction to the School Power Naturally Solar Learning Lab™
Virtual Array Tour: Lesson III in the Series
TEACHER INFORMATION
LEARNING OUTCOME
After experiencing the third and fourth routes through the Heliotronics SunViewer™
software application, students are able to interpret data displays and test hypotheses based
on those displays.
LESSON OVERVIEW
In this lesson, students investigate the following topic areas as they interpret data displays
and test hypotheses:
• Relationship between power and energy
• Photovoltaic system components and their function
• Efficiency and loss mechanisms
• Measurement units
• Quantitative terminology and perspective
GRADE-LEVEL APPROPRIATENESS
This Level II and III lesson is appropriate as an introduction to solar energy for students
in grades 5–12.
MATERIALS
Access to a computer or computer lab having Heliotronics SunViewer™ software
installed and receiving data from a Heliotronics Feynman™ data logger
Sufficient copies of Student Handouts One, Two, and Three.
SAFETY
No safety precautions are necessary while using this software, nor do the activities that
supplement this lesson raise safety issues.
www.SchoolPowerNaturally.org
ADDITIONAL SUPPORT FOR TEACHERS
There are 64 School Power Naturally (SPN) lessons available for downloading at
www.SchoolPowerNaturally.org. Some of the lessons that would mesh well with this
solar array tour are listed below, along with a brief description of content. (Note: In
addition to this new lesson (lesson III), three other new lessons that are closely related to
lesson III are described in the Teaching the Lesson section.)
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SPN Lesson #4, Energy Conversion Games (Students become acquainted with the
first law of thermodynamics, which concerns the conservation of energy as it is
transformed from one form to another. Students gain experience in identifying
forms of energy, and devices or processes that transform energy from one form to
another, within the context of a game format.)
SPN Lesson #9, How Photocells Work (In the context of a game format, students
learn how photovoltaic cells work. They are exposed to the p-n junction between
two types of semiconductors and learn how it relates to the production of
electricity in a photovoltaic cell.)
SPN Lesson #11, Junior Solar Sprint Series: Electrical Power (Students describe
how photovoltaic cells produce electricity, what voltage and amperage are, and
how each relates to electric power. They use ammeters and voltmeters and
mathematical formulas as they explore what electrical power means. Finally, they
examine their school’s solar collector to determine how the solar cells are
arranged to produce electrical output.)
SPN Lesson #24, Efficiency of Energy Conversion (After students become
familiar with the first and second laws of thermodynamics and gain experience in
reconverting electrical energy and determining efficiencies, they are able to
describe conversion efficiencies and factors affecting those efficiencies and relate
this to the school’s PV system.)
SPN Lesson #27, Allocating Energy from a Photovoltaic System (Students
describe how photovoltaic cells produce electricity, what voltage and amperage
are, and how each relates to electric power. They use ammeters and voltmeters
and mathematical formulas as they explore what electrical power means. Finally,
they examine their school’s solar collector to determine how the solar cells are
arranged to produce electrical output.)
TEACHING THE LESSON
This is the third in a series of three tour lessons that make use of the Heliotronics
SunViewer™ software application. (A separate fourth lesson makes use of inquiry
teaching and learning, using the online School Power Naturally database
[SunViewer.net™] developed by Heliotronics. This database presents and archives data
from your school’s solar array and that of other participating schools throughout New
York State.)
The first lesson in the series features a virtual array tour that includes screen shots and
commentary, and the second and third lessons feature pathways 2 through 4 and include a
projected set of images and pages that relate to data display. In the fourth lesson, such
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things as portions of the software application that display real time and stored operational
data are explored.
In advance, run copies of the Student Handouts for the students in your classroom. Note:
All three Handouts pertain to the “What Is It Doing?” part of the tour.
If you did not launch the Heliotronics SunViewer™ software application as part of the
initial tour, do so now. Find this icon (see figure 1):
Figure 1
Double-click it to launch the software application. Watch the Heliotronics SunViewer™
home page pop up (see figure 2):
Figure 2
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Locate the “end” button (see figure 3):
Figure 3
Click “end” to end the program now, or if you have time, follow the two pathways
suggested for this lesson and end the program at a later time by clicking the “home”
button and then “end.” Let’s go on. We see that there are four choices of buttons (see
figure 4) on this window:
Figure 4
These buttons are used to navigate the software. Clicking on any of them will take you to
other pages.
This lesson is limited to two pathways: “What Is It Doing?” and “How Well Is It
Working?” First, click “What Is It Doing?” and follow it in a sequential way to the
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locations designated, and later do the same for “How Well Is It Working?” Your first
click will bring up figure 5:
Figure 5
The display in figure 5 is intentionally designed to look like a speedometer in a car or
truck. Speed and distance have the same mathematical relationship as power and energy.
In other words, speed is the rate at which you traverse distance, while power is the rate at
which you consume or produce energy. (See figure 5.1 note, page 27.)
The equations below have been rewritten to show the units most commonly used.
Speed (miles per hour) = Distance (miles) / Time (hours) Î Distance (miles) = Speed
(miles per hour) x Time (hours)
Power (kilowatts) = Energy (kilowatt-hours) / Time (hours) Î Energy (kilowatt-hours)
= Power (kilowatts) x Time (hours)
(See figure 5.2 note, page 28.)
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This speedometer display has a broad range of applicability. In the lower grades, the
qualitative similarities between it and a speedometer offer the student a starting point and
open the door to the more advanced distinctions between power and energy. The aim is to
make the concepts easier to understand as they are studied in depth in later grades, when
the display can facilitate quantitative discussions (e.g., discussions of fractions and
algebra, the calculus discussion of rates [derivatives] and infinitesimal summation of
continuous functions [integration]).
The figure 5 display is intended to serve as a catalyst for discussion of power and energy
concepts and their relationships. First, have the students observe this display on the
computer. Then facilitate a discussion on the display. (See figure 5.3 note, page 28.)
In small group work, or as individuals, challenge the students to describe a way to predict
how long it will take to generate 0.1 kWh of energy. Have them record, in the spaces
provided under “Relating Power and Energy” on Student Handout One, such things as:
• ideas of how to establish how long it would take to generate the energy cited in
the challenge
• an answer based on their calculations (see figure 5.4 note, page 29)
• responses to the remaining items up to the place where it alerts the students that
they will return to this section later on.
Discuss their ideas, and help them use the DAS system to test their ideas and come up
with a response to the challenge.
When you are ready to continue the tour, click “Monitoring Center,” figure 6:
Figure 6
This brings up figure 7:
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Figure 7
This window presents the items measured by the Solar Learning Lab™. As you proceed
on the “What Is It Doing?” pathway, other graphics feature these components and their
interactions. Have the students use figure 7 as their source as they list the quantities that
the system monitors on Student Handout Two.
Click “back,” and then click the “Current Weather” button, figure 8:
Figure 8
This brings up figure 9:
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Figure 9
This window displays the environmental quantities that make the greatest impact on the
power output of the solar array. Remind the students that they practiced formulating
hypotheses in lesson I of this series. (See figure 9.1 note, page 29.)
When you are ready to have the students test hypotheses (see Student Handout Three),
caution them that just because a hypothesis seems logical doesn’t necessarily make it
true. Hypotheses really do need to be tested. For example, consider this hypothesis: If
ambient temperature is 70°F, then the module temperature will be the same. This
hypothesis would probably be found to be inconsistent with the results observed, so it
would need to be modified to match the cases observed, or else it would have to be
rejected entirely.
Prompt students to:
• formulate a hypothesis having to do with relationships among the environmental
factors displayed in figure 9
• provide a rational explanation stating why they think the hypothesis is likely to be
accepted
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test their hypotheses
display their work on Student Handout Three.
The procedure students devise to test a hypothesis might include using the “Current
Weather” display in figure 9 and seeing what the difference is between module
temperature and ambient temperature for different wind speeds. Ideally the solar radiation
should be roughly the same in each of the tests in order to hold that variable constant.
(See figure 9.2 note, page 29.) Some other areas you might suggest for hypothesis
formation include:
• the impact of irradiance on module temperature
• the effect of clouds on irradiance
• the effect of time of year on irradiance
• the effect of clouds on power output
• the effect of clouds on steadiness of power (puffy clouds will cause the array
output to fluctuate somewhat)
• the effect of power output on efficiency.
Along with students testing their hypotheses, see that they make decisions as to which
hypotheses should be rejected and which ones they believe they have affirmed
sufficiently to be accepted. (See figure 9.3 note, page 29.)
Let the students know that hypotheses are typically affirmed or rejected on the basis of
statistical evidence. A good discussion of the process of hypothesis forming and testing
can be found at http://www.stats.gla.ac.uk/steps/glossary/hypothesis_testing.html, should
you need help with the use of statistics in affirming or rejecting hypotheses.
Consider having the students develop short reports to document their findings. The
student report might describe what they wanted to find out, how they went about testing
that, and what they did find out. (See figure 9.4 note, page 30.)
In addition to offering a way to make and test hypotheses, this activity offers an
opportunity to see how two physical phenomena can be present, yet one dominates in a
certain set of conditions, while the other dominates in an alternate set of conditions.
When you are ready to continue the tour, click “back,” and then click figure 10:
Figure 10
This brings up figure 11:
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Figure 11
This window provides perspective to students who may not have an intuitive grasp of the
amount of electricity a kilowatt represents. The box at the upper left shows the power
production of the solar array, while each of the boxes to the right shows the number of
appliances that could be run with that much power. For example, if the solar array is
producing 1 kilowatt, it could run five computers or one air conditioner.
Click figure 12,
Figure 12
to bring up figure 13:
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Figure 13
This window provides some detailed information on the power consumption required to
run an oven and an oven’s typical energy use.
When you are ready to return to the tour, click “close” and then figure 14,
Figure 14
bringing up figure 15:
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Figure 15
An air conditioner is thermostatically controlled, and as a result its compressor does not
remain on at all times. It cools the room and then turns off; when the room heats up
again, it turns back on—and it repeats this cycle over and over. This is reflected in the
fact that an air conditioner typically consumes 100 kWh per month rather than the 720
kWh it would consume if it ran all of the time.
Figures 13 and 15 invite a discussion of the relationship between power and energy.
Discuss the text in these figures and tease from the students the difference between
kilowatts and kilowatt-hours. (See figure 15 note, page 30.)
If you would benefit from a review of the terms power, work, and energy, go to
http://www.findarticles.com/p/articles/mi_qa3726/is_199609/ai_n8752259.
When you are ready, click “close” and then figure 16,
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Figure 16
bringing up figure 17:
Figure 17
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This window explains the power consumption of a computer and reveals how that power
consumption can be reduced.
After reading the text, encourage your students to discuss computers and energy use. The
website http://www.greencampus.harvard.edu/cerp/documents/brochure_small.pdf
describes energy use and carbon dioxide avoidance, plus common myths about computers
and energy consumption.
To resume the tour, click figure 18,
Figure 18
bringing up figure 19:
Figure 19
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When you are through with figure 19, click “close.” Then click “close” in the
“Computer” window; this will bring you back to the “What Is It Doing?” window. There
you will find figure 20:
Figure 20
Click “Incandescent” in figure 20, bringing up figure 21:
Figure 21
When you activated the “click me” command by clicking “Incandescent,” you brought up
“Compact Fluorescent” (see figure 21 above). Now, click “Compact Fluorescent,” and
you will in turn bring up “Incandescent.” Continue to click “Incandescent” and “Compact
Fluorescent” alternately. As you do this, elicit responses from the students describing the
differences in power use by these two kinds of bulbs.
You may want to have your students research the use of fluorescent bulbs versus
incandescent bulbs in relationship to energy conservation. Go to
http://www.lightsofamerica.com/light-cfl.htm for lighting energy conservation
comparisons.
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LED lighting is even more efficient than incandescent or fluorescent, but it is not yet cost
effective for room lighting. (See figure 21 note, page 31.)
Click the bulb seen in figures 20 and 21.
This will bring up figure 22:
Figure 22
After clicking “Answers” and reading the text that appears in “Light Bulb Answers,”
click “close.” Then click “close” in figure 22. Next, click “back” and figure 23,
“Plotting”:
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Figure 23
This brings up figure 24:
Figure 24
This window displays plots for several interrelated measurements over a 24-hour period.
Walk students through the four graphs in figure 24: solar intensity, system output power,
module temperature, and system efficiency. Have students state what is being plotted for
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each axis for all four graphs. There are numerous relationships that exist among this data.
(See figure 24 note, page 31.)
For motivated classes, invite a discussion. In other circumstances, you may want to point
out the relationships more explicitly. Observing the interrelationships will be least
confusing if done on a clear day when the plots are smooth.
Point out the drop-down combo box (see figure 25) found on the left side of the
“Plotting” window:
Figure 25
This control allows the students to select data from the current day or any of the prior six
days. Have the students look at the data from earlier in the week. Compare data from
different days and have students describe why they believe the results are different.
Click “back” and then click figure 26,
Figure 26
bringing up figure 27:
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Figure 27
The “Data Capture” window allows simultaneous capture of several data points so that
they remain correlated. It is much like a camera that enables the user to freeze the action.
Point out to students that the columns on the left, “Real Time” and “Data Capture,”
continue on the right side of the figure. The data in the first column, “Real Time,” is
updated every second. The second column displays the “captured” data. Have the
students check several of the boxes and then click the “Data Snapshot” button (see figure
28 below):
Figure 28
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A copy of the “Real Time” data that was displayed in the checked rows will be displayed
in the “Data Capture” column. This data was obtained in the same moment so it is
correlated. Now click “Data Snapshot” again, and notice that the data is refreshed. This is
a useful way to acquire data manually. See Student Handout One. Click on the “clear”
button to see what happens. Try checking and unchecking boxes and clicking the “Data
Snapshot” button and the “clear” button until you are comfortable with the operation of
this page.
To get further information, you can access a help window by clicking on the “help”
button, figure 29:
Figure 29
This brings up figure 30:
Figure 30
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You can click “close” to get back to figure 27 to practice capturing data.
As you practice, be aware that you can click the “clear” button (see figure 31 below),
at any time to clear data you have previously selected.
Figure 31
Now, use the “Data Capture” window to further illustrate the power–energy relationship.
You can show how power and energy are related using real-world data. Before reading
further, review the instructions in the Data Capture section (pages 4 and 5) of Student
Handout One. (See figure 30.1 note, page 32.)
You will soon notice that if you carry out this activity on a clear day, the results will be
quite consistent. However, should you do it on a partly cloudy day, when the power is
fluctuating appreciably during the time intervals over which data is being accumulated,
the results will be somewhat inconsistent. (See figure 30.2 note, page 32.)
Look again at Student Handout One. If you are working on a clear day, your students
should take five or six data points spaced 2 or 3 minutes apart. If it is overcast but the
power is not fluctuating much, then take five or six data points separated by about 5
minutes each.
Go over figures 2 and 3 of Handout One ahead of time with your students. Have the
students calculate the exact time interval between points and record the results in column
C of figure 3. This is done by taking the time just recorded and subtracting the prior time
measurement. Notice that the first box in column C is x’d out. This is because there is no
time data point prior to the first to subtract. Similarly the first boxes in E, G, and H are
x’d out.
Now, calculate the energy using the measured power. In column E, multiply the numbers
in the same row in columns C and D to get the energy generated over this time interval.
This was calculated using the following formula:
E=PxT
Next, calculate the power using the measured energy. In column G, calculate the change
in energy over the previous time interval. Subtract the current cumulative system energy
in column E from the prior and record it in column G. Divide this by the calculated time
interval from column C. Compare this amount to the measured power in the same row in
column D.
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This was calculated using the above equation algebraically rearranged as shown here:
P=E/T
Have the students compare the results. You may wish to have them do this alone, in small
groups, or as a class. (See figure 30.3 note, page 32.)
When you have finished taking data snapshots and clearing data, click “back” and you
will see that you have run out of options to click. Then click “home” to return to the
home page (see figure 32). Now you have completed the third of four routes through the
Heliotronics SunViewer™ software application.
Figure 32
When you are ready, go on to the fourth route by clicking the “How Well Is It Working?”
button (see figure 33):
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Figure 33
This will bring up figure 34:
Figure 34
This window provides access to several data windows that show how efficiently the solar
array converts sunlight into electricity.
Here you examine the efficiency of the solar array and its primary subsystems. After
calling attention to each of the subsystems and their names, click the “Inverter
Efficiency” button (see figure 35):
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Figure 35
Clicking figure 35 brings up figure 36:
Figure 36
This window shows the efficiency of the inverter and the power flows used to calculate it.
Let the students know that the system installed in your district probably has a single
inverter, whereas this photo shows two inverters. (See figure 36 note, page 33.)
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Spend sufficient time on the pictorial equation presented in figure 36 so that students see
that in the transformation, some energy is lost to the environment, and that inverter
efficiency is a measure of that relationship. The form in which the energy is lost is heat.
Click “back,” and then click figure 37,
Figure 37
bringing up figure 38:
Figure 38
This window shows the efficiency of the entire PV system and the power flows used to
calculate it.
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System efficiency describes how well the whole system converts the power in the
incident sunlight into the AC current (electricity) that the school uses. It shows the
relationship between the sunlight incident on the array and the electrical output energy
measured as it emerges from the inverter. Once again, go through the pictorial equation
and continue to stress that transformations of energy always result in some loss of energy
to the environment. Have the students write the equation. (See figure 38.1 note, page 33.)
Flip back and forth and have the students compare the efficiency scale in figure 38 to the
efficiency scale in figure 36. (See figure 38.2 note, page 33.)
Click “back,” and then click figure 39:
Figure 39
bringing up figure 40:
Figure 40
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Once again you are dealing with a pictorial equation. Have the students develop the
equation:
DC Power / Incident Solar Power = PV Module Efficiency
Incident solar power is calculated by multiplying the irradiance by the solar array area.
This relationship verifies what you mentioned to the students earlier about energy loss to
the environment and the fact that not much solar energy ends up as electricity. This
window shows what percentage of the Sun’s energy is converted to DC electricity by the
photovoltaic modules themselves.
Click “back” to return to the “How Well Is It Working?” window, and click “home” to
return to the home page. Then click “end.” This will complete your exploration of the
fourth pathway, which addressed the following topic areas:
• Relationship between power and energy
• Photovoltaic system components and their function
• Efficiency and loss mechanisms
• Measurement units
• Quantitative terminology and perspective.
In particular, this lesson is intended to bring focus on real-world use of energy concepts
and to explain how the language of science is useful in describing and understanding
things that are important and relevant to student lives and to society at large.
BACKGROUND INFORMATION
Virtual Tour Notes for the Teacher
Figure 5.1 Note: Typically students find the relationship between power and energy a
daunting one. A familiar visual, such as a speedometer, can be a helpful analogy for them
as they build mental models.
Speed = Distance / Time
Î
Distance = Speed x Time
Î
Energy = Power x Time
Similarly:
Power = Energy / Time
Here speed is a rate and distance is a sum or something that increases cumulatively.
Similarly power is a rate, whereas energy is the quantity that increases cumulatively.
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In the United States, we generally talk about distance in terms of miles and speed in
terms of miles per hour. Worldwide, including in the United States, electrical power is
discussed in terms of watts. Typically a prefix is added to scale to an appropriate level.
For example, your solar array output is measured in kilos (thousands) of watts, or
kilowatts. Power plant output is usually measured in mega (million) or giga (billion)
watts. For example, the output of a typical nuclear power plant is between 500 and 1,000
megawatts or, equivalently, 0.5 and 1.0 gigawatts. One watt describes energy being
produced or consumed at a rate of 1 joule / second.
A joule is a unit used to describe energy. However, when talking about the electricity
going to your school or home, electrical power engineers find it more convenient to talk
about kilowatt-hours. A kilowatt-hour is the amount of energy delivered if your electrical
service is drawing 1 kilowatt for one hour. Note also that 1 kilowatt-hour = 3,600,000
joules. High school physics students should be able to explain that equivalency.
Figure 5.2 Note: The formula Distance = Rate x Time expresses one of the most
frequently used relationships in algebra. Try
http://mathforum.org/dr.math/faq/faq.distance.html to further explore this formula.
Figure 5.3 Note: You might want to bring out the following points during the discussion:
• Have you seen other gauges, dials, or measuring displays that look like this one?
(speedometer and odometer in a car)
• What does a speedometer display? (speed) What does an odometer display?
(distance)
• How are speed and distance related? (Speed is the rate at which you traverse
distance.)
o Can a slow car and a fast car go the same distance? (yes) What then is the
important difference for the two cars? (It takes longer for the slow car to
go the same distance.)
o When each has arrived at its destination, will the change in their odometer
readings be the same or different? (same)
o During the trip, will the speedometer reading be the same or different?
(different) Why? (A higher speed gets you there faster. It is this rate of
change of distance that is indicated by the speedometer; the faster you go,
the higher a number it displays while en route.)
• Have your students come up with related analogies. (For example, how much
energy is required to bake a cake? At what power level is the energy delivered?
How much energy is required to dry your hair with a hair dryer? How long does
it take? At what rate is the energy delivered to the hair dryer? There are many
other similar analogies; invite a discussion of them.)
• What does this have to do with power and energy? (Power is a rate just like
speed. Distance is a cumulative quantity just like energy. In other words, though
they represent different physical properties, their mathematical description is
identical.)
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•
•
•
•
How is power indicated on your school’s display? (The needle points to the
number of kilowatts being produced by our solar array, just as the speedometer
needle points to the number representing the speed of a car.)
How is energy displayed and how is this similar to the odometer in a car? (It is
displayed in the bottom text box, just as distance is displayed in the digital
odometer in a car.)
What about the middle text box? What is it for? (Notice that it changes in
synchronization with the pointer. It provides the numerical value of power. This is
the one aspect of the display that is not an exact analogy to a speedometer.)
Assuming that this display is sized and calibrated properly for our system, what is
the highest power output we would expect to see? (This is somewhat tricky. Your
array is rated for 2 kilowatts; however, under unusual circumstances, it might put
out a bit more. Just as it is highly unusual to “bury” the speedometer on your car
[most people don’t ever drive their car as fast as the highest number on their
speedometer], this display shows a maximum value somewhat higher than your
array will produce.)
Figure 5.4 Note: With some help, eighth graders and above should be able to solve the
power energy equation for time and use the displayed power output to calculate the time
required. They can test their prediction by recording the cumulative energy in kilowatthours and seeing how long it takes for it to increase by 0.1 kWh. This is best done on a
sunny day since it would take a while on an overcast day. On a partly cloudy day, the
power may fluctuate. Such an observation might invite a discussion of statistical
distributions and averages among more advanced students.
Figure 9.1 Note: You may want to finish going through all of the windows with the
students before looking at Student Handout Three and testing hypotheses. Or you might
want to take a break now and work on hypotheses before returning to the tour. Whenever
you decide to work on hypotheses, remember that a quick way to help students make a
statement in a hypothesis format is to suggest that they use the “If…then…” format. For
instance, if ambient temperature is 70°F, then the module temperature will be the same.
Figure 9.2 Note: Best results will be obtained if this activity is carried out on clear days
and at about the same time each day. In that way, the modules will have had time to
reach equilibrium with the ambient temperature.
Figure 9.3 Note: For some classes, you may need to present a situation to test and then
walk them through it before they begin to work on Student Handout Three. The following
set of examples would be appropriate for Level II students:
•
•
•
If the module temperature is higher than the ambient temperature, then the Sun is
shining on the array.
If the module temperature is the same as the ambient temperature, then the Sun is
shining on the array.
If the ambient temperature is higher than the module temperature, then the Sun is
shining.
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Ask students to pick the hypothesis they believe is closest to the actual situation and to
back up their claim. They might say, “I think the first hypothesis would be accepted as
correct because if the Sun were shining, it would make the array hotter than the air since
the array will absorb the Sun’s energy in much the same way that asphalt absorbs the
Sun’s energy and heats up. I think the second hypothesis would be rejected as incorrect
because the array and the air will absorb the Sun’s energy at different rates. I believe the
third hypothesis would be rejected as incorrect because the array will absorb the Sun’s
energy more than the air will.”
Here is a situation that might be appropriate for Level III students:
Hypothesis: If the day is windy, then the speed of the wind is greater, and the difference
between ambient and module temperatures is smaller.
Backup explanation: The more air that is moving across the array, the more that the
energy that the array has absorbed from the Sun will be transferred to the cooler air
flowing across the array.
Alternate hypothesis: The faster the wind, the larger the difference in temperature
between ambient temperature and module temperature. To back this claim up, the student
might point to the space shuttle and the high-tech heating tiles that are designed to keep
the shuttle from burning up in the atmosphere due to air friction.
Figure 9.4 Note: The reports might include:
• an introduction that describes the hypothesis and the rationale for the testing
• a description of the experimental method for verifying the hypothesis
• a discussion of what conditions are ideal and if the experiment cannot be done
under ideal conditions, then what assumptions are being made
• a description of the data acquisition methodology
• a brief discussion of results (what was measured)
• a conclusion.
The report might also include ideas for testing further questions that arise from the work.
Figure 15 Note: Questions that could prompt such a discussion include:
• How many hours are there in a month, assuming there are 30 days in a month?
(30 days / month x 24 hours / day = 720 hours)
• Given that the oven requires 2.6 kW to operate, why does it only use 9.8 kWh of
energy per month? (The oven is on only intermittently; most of the time it is off.
Even when it is on, the heating elements are on only part of the time. Accordingly,
the energy consumed over the course of the month is far less than what is implied
by the power consumption of 2.6 kW.)
• Typically, the air conditioner requires 1 kW to operate. In the summertime, an air
conditioner is often left on 24 / 7. Why isn’t its energy consumption something like
720 kWh? (Air conditioners are thermostatically controlled. Most of the power
Virtual Array Tour: Lesson III
30
Levels II and III
•
consumption results from the compressor in the air conditioner being on. When
the room temperature reaches the thermostat set point, the compressor shuts off.
The result is that much of the time, the air conditioner is consuming far less than
1 kW.)
If a typical air conditioner uses 1 kW compared to a typical oven’s 2.6 kW, how
do you account for the oven using far less energy than an air conditioner in
August? (The air conditioner uses less power than the oven while running, but in
August, with its relatively high ambient temperatures, people tend to run the air
conditioner frequently or all of the time.) Remind students that kilowatt-hours
measure energy consumed, whereas kilowatts are a measure of power, which is
the rate of energy consumption. You could talk about how this is analogous to the
tortoise and the hare. Again, you are working with the analogy between speed
and power (rates) and energy and distance (cumulative quantities).
Figure 21 Note: You might want to have students investigate LED lighting and respond
to some of the following questions:
• What are some of the advantages of LED lighting? (rugged, extremely efficient,
very long lifetime)
• What are some applications in which the new ultrabright LEDs are being used?
(flashlights, brake lights, traffic lights, exit signs)
• What are the advantages for these applications that make the added cost
worthwhile? (It is costly to change lightbulbs in traffic lights; LEDs greatly
reduce the frequency of replacing lightbulbs; flashlight batteries are a very
expensive form of electricity; the long lifetime of LEDs combined with energy
efficiency makes them desirable for flashlights.)
Figure 24 Note: Some of the things to look for include:
• The output power curve is shaped almost identically to the solar intensity curve.
(This is because the power output is almost directly proportional to the incident
radiation.)
•
Module temperature is shaped similarly to solar intensity. (The incident radiation
heats the modules and though not exactly proportional, the module temperature is
strongly correlated to the incident radiation.) As the module temperature
increases, the voltage drops due to properties of the semiconductor materials. The
current increases somewhat, but not as fast as the voltage drops (recall that
Power = Current x Voltage or P = I x V), so there is some reduction in module
efficiency as a result of heating. This also will impact the overall system
efficiency, but much less so than the inverter efficiency described below.
•
The system efficiency increases with system output power to a point and then
begins to decrease. This odd behavior is due primarily to two loss mechanisms in
the inverter. The first is called semiconductor switching and it remains
approximately constant for all inverter power levels. The second is ohmic heating
(often referred to as [I^2] x R losses or “I squared R” losses in the inverter).
These losses increase as the square of the current increases. Since the switching
Virtual Array Tour: Lesson III
31
Levels II and III
losses are constant at low power levels, much of the power from the PV array is
lost through the switching losses and the efficiency is poor. As the power level
increases, the losses remain roughly the same, but the power is increasing so the
efficiency increases. The second loss mechanism results from resistive losses in
the inverter’s internal wiring and components. Power dissipated in a resistor goes
as (I^2) x R or P = R x I^2, where I is the current, R is the circuit resistance, and
P is the power dissipated (in this case, wasted). Plotting this function, you find
that at low values of I, the (I^2) x R losses are quite small. However, this function
grows rapidly and becomes large for high values of I. It therefore becomes the
dominant loss mechanism and increases faster than the power increases. As a
result, the efficiency of the inverter begins to drop off at higher power levels.
Increasing module temperature also has an impact on the PV system efficiency
but less than that caused by the inverter.
Figure 30.1 Note: Recall that:
P = E / T, where
P = power
T = time period over which the energy was generated or used
E = energy used over the time interval during which measurements are being taken
When you measure the energy generated over several time intervals and record the
power during each of those intervals, you can then calculate:
• the power using the energy and time data, and
• the energy using the power and time data.
Figure 30.2 Note: A complete explanation of why that is so is beyond the scope of this
lesson. If it is unclear to you why power fluctuations would add inconsistency to the
results, then wait for a clear day to carry out this activity. But if you are comfortable with
the explanation of why the results might come out inconsistently, then the activity
presents an excellent opportunity for classroom discussion and deeper understanding of
power, energy, and experimental procedures.
Figure 30.3 Note: You might want to have student groups consider the following
questions:
• What was the point of this exercise? (It was to see that power and energy are
related mathematically. If you measure power over time, you can calculate the
energy, and if you measure energy over time, you can calculate the power.)
• If this data was collected on a cloudy day, how might the results differ and why?
(On a cloudy day, the power might fluctuate over the time interval due to passing
clouds. This would change the amount of sunlight incident on the array, and
therefore it would change its power output. Under those circumstances, we would
not have enough data to correctly calculate the energy produced).
• How might you change things so that this would work? (If you could shorten the
time interval sufficiently so that the power fluctuations during the interval were a
small percentage of the total power, then the results would appear consistent.)
Virtual Array Tour: Lesson III
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Levels II and III
Figure 36 Note: The function of the inverter is to transform the direct current from the
PV modules to alternating current that is compatible with the utility grid. The display is
arranged to form the equation for efficiency, which is:
Output / Input = Efficiency
Figure 38.1 Note: The equation that students come up with should look something like
this:
System Output
Solar Input
= AC power from the inverter
= Power in the sunlight incident on the solar array
Figure 38.2 Note: Students might think that it is the inverter rather than the array that is
very inefficient. Actually, only about 10% of the solar energy incident on the array
becomes direct current. That current then goes into the inverter, where about 90% of the
direct current becomes alternating current as it leaves the inverter. Hence, the system’s
efficiency overall is about 9%, and most of the losses are in the solar module’s
inefficiency in converting sunlight to electricity. The efficiency of terrestrial solar
modules ranges from about 5% to about 22%.
SOURCE FOR THIS ADAPTED ACTIVITY
This activity is based on the Heliotronics SunViewer™ software that was provided to
SPN-participating schools.
LINKS TO MST LEARNING STANDARDS AND CORE CURRICULA
Standard 1—Analysis, Inquiry, and Design: Students will use mathematical analysis,
scientific inquiry, and engineering design as appropriate to pose questions, seek answers,
and develop solutions.
M1.1: Extend mathematical notation and symbolism to include variables and
algebraic expressions in order to describe and compare quantities and express
mathematical relationships.
S1.1: Formulate questions independently with the aid of references appropriate
for guiding the search for explanations of everyday observations.
S1.12a: Independently form a hypothesis.
S1.3: Represent, present, and defend their proposed explanations of everyday
observations so they can be understood and assessed by others.
S2.1c: Design and conduct an experiment to test a hypothesis.
S3.2: Interpret the organized data to answer the research question or hypothesis
and to gain insight into the problem.
S3.2a: Accurately describe the procedures used and the data gathered.
S3.2c: Evaluate the original hypothesis in light of the data.
Virtual Array Tour: Lesson III
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Levels II and III
Standard 4—The Physical Setting: Students will understand and apply concepts,
principles, and theories pertaining to the physical setting and living environment and
recognize the historical development of ideas in science.
S4.1c: Most activities in everyday life involve one form of energy being
transformed into another…. Energy in the form of heat is almost always one of the
products of energy transfer.
S4.1e: Power is the time-rate at which work is done or energy is expended.
S4.1p: Electrical power and energy can be determined for electric currents.
S4.2a: Heat moves in predictable ways, flowing from warmer objects to cooler
ones, until both reach the same temperature.
S4.4d: Electrical energy can be produced from a variety of energy sources and
can be transformed into almost any other form of energy.
S4.4e: Electrical circuits provide a means of transferring electrical energy.
S4.5b: Energy can change from one form to another, although in the process
some energy is always converted to heat. Some systems transfer energy with less loss of
heat than others.
Produced by the Research Foundation of the State University of New York with funding
from the New York State Energy Research and Development Authority (NYSERDA)
www.nyserda.org
Special thanks to Heliotronics, Inc. for their contribution
in developing the content for this lesson
Should you have questions about this activity or suggestions for improvement,
please contact Bill Peruzzi at billperuz@aol.com
(STUDENT HANDOUT SECTION FOLLOWS)
Virtual Array Tour: Lesson III
34
Levels II and III
Name __________________________________________
Date ___________________________________________
Introduction to the School Power Naturally Solar Learning Lab™
Virtual Array Tour: Lesson III in the Series
STUDENT HANDOUT ONE
Background Information
Your school, which participates in the School Power Naturally (SPN) program, has been
provided:
• a Solar Learning Lab™, which includes a solar array that generates electricity
from sunlight; a set of weather equipment; and software to treat, display, and
store data
• an educational data-monitoring system
• a site license for Heliotronics SunViewer™ educational data display software.
In addition, archived data has been displayed on the Internet for viewing by anyone in
the world.
Your teacher will introduce you to the Solar Learning Lab by conducting a virtual tour by
means of the Heliotronics SunViewer™ software application.
DEVELOP YOUR UNDERSTANDING
Materials
A computer or computer lab that has Heliotronics SunViewer™ software installed
Protractors
Sufficient copies of Student Handouts One, Two, and Three
Procedure
Use Student Handouts One, Two, and Three to record your responses and work.
1
Name __________________________________________
Date ___________________________________________
RELATING POWER AND ENERGY
Figure 1
Look at the pointer in figure 1. What is the power output and what are the units?
Power_____________ Units_____________
Again using figure 1, predict how long it would take to generate 0.1 kWh of energy.
Show your work.
Time_____________
Lesson III: Student Handout One
2
Note: This lesson was designed with a 2 kW solar array in mind. If you have a larger
array, you might want to use a larger value for kWh.
Now, can you do the same thing using real data? Find the same image using the
SunViewer™ software. Notice that the pointer moves every second or so.
Does it move a lot or a little?
How might clouds play a role in how much and how often the pointer moves?
Make a prediction as to how long it will take to produce .1 kWh of energy, and describe
how you came up with that number.
Record the energy on the display and record the time.
Energy__________
What will the energy read when .1 kWh has been produced?
Energy after .1 kWh _____________
Time it took ______________
Could you perform this activity at nighttime? Why or why not?
(You are finished for now with this Handout, but you will return to it later on)
Lesson III: Student Handout One
3
Figure 2
Now, using the SunViewer™ software, find the page that looks like figure 2.
In the table that follows (see figure 3), the three columns having the heading “Measure”
are to be filled in using the “Data Capture” window (figure 2). The four columns having
the heading “Calculate” are to be filled in using the data taken to do the calculations
indicated in the column headings.
Using the computer, go to the “Data Capture” window (figure 2) and put check marks
next to the following rows: Time, System Output Power, and Cumulative System Energy.
Uncheck the rest of the boxes. Your teacher will suggest a time interval and a number of
data points. When you are prompted to begin, click the “Data Snapshot” button. Data will
appear in the “Data Capture” column. Record this data in the table below. Repeat this
process at the end of the next time interval and the data will refresh. Continue until you
have acquired the planned number of data points.
Lesson III: Student Handout One
4
A
B
Measure
C
Calculate
D
Measure
E
Calculate
F
Measure
n
Time = T
Delta T = DT
DT = Tn – Tn-1
System Output
Power = P
Energy = E
E = P x DT
Cumulative
System Energy
= CE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Figure 3
XXXXXX
XXXXXX
G
H
Calculate Calculate
Delta Energy =
DE
DEn = CEn –
Cen-1
Power PC
PC = DE / DT
XXXXXX
XXXXXXX
Notice that the energy E is calculated from the measured power and time. The energy DE
is calculated from the change in measured energy over the time interval. Compare the
two. How much do they differ?
Now compare the measured power P with the power PC calculated from the measured
energy. How close are they?
In the chart above, you showed that if you measure power over time, you can calculate
energy and, conversely, if you measure energy over time, you can calculate power.
In the space below, discuss the relationship between power and energy. Describe how
you might perform a similar set of measurements showing the relationship between speed
and distance. What measurement instruments would you use?
Lesson III: Student Handout One
5
Name __________________________________________
Date ___________________________________________
STUDENT HANDOUT TWO
USING THE MONITORING CENTER
The SunViewer™ software is designed to present the data in manageable chunks.
However, as students master their understanding of the photovoltaic system, they may
want to view the data in a more compact form. The monitoring center is designed for this.
Below, students are invited to familiarize themselves with the monitoring center and to
gain a deeper understanding of the information displayed.
Figure 4
Lesson III: Student Handout Two
6
After studying figure 4, list below the quantities that the photovoltaic system monitors. In
other words, what are each meter and each text box displaying?
Quantities the system monitors:
Dials and Gauges
Text Boxes
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
15
16
17
18
Lesson III: Student Handout Two
7
There are two extra text boxes that are not used in the School Power Naturally system.
Can you find them?
Bonus: How do the Electrical Measurements readings (current and voltage) relate to the
Array Output Power and System Output Power readings? Show the equations that relate
them.
Lesson III: Student Handout Two
8
Name __________________________________________
Date ___________________________________________
STUDENT HANDOUT THREE
MAKING AND TESTING HYPOTHESES
After studying figure 5 (see below), a student formulated this hypothesis:
1. HYPOTHESIS ONE:
If ambient temperature is 70°F, then the module temperature will be the same,
70°F.
Figure 5 (tour figure 26 in lesson I)
Lesson III: Student Handout Three
9
You have a choice: you can reformulate the hypothesis that the student formulated and
test it, or you can test the hypothesis as written (hypothesis one). So where it says
“hypothesis two,” record the hypothesis you are going to test.
2. HYPOTHESIS TWO:
Now, before testing this hypothesis, describe which data you will examine (from lesson
III) in conducting your test. Be sure to explain how you will use the data to “accept” or
“reject” the hypothesis.
3. PROCEDURE FOR TESTING THE HYPOTHESIS:
Collect the data and make a claim. Was your hypothesis affirmed or rejected?
4. CLAIM:
Now justify (back up) your claim. Tell why you have accepted or rejected the hypothesis.
5. CLAIM JUSTIFICATION:
Lesson III: Student Handout Three
10