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PROFESSOR: Final
presentations should
be very exciting--
fruits of your labor
over the entire
semester in reality.
The fundamentals
in the first third,
the technologies in the second,
gearing up toward the cross
cutting themes in the third.
I understand that we've
had an accelerated project
schedule this semester.
We've completed
the entire projects
over the duration of
about a month and a half,
so you are to be congratulated
for your hard work
in a very intense period of
time McKenzie tiger team style.
For that, I reward you
with doughnuts and coffee
over there.
I understand many of you
were up late last night,
so you're welcome to ingest
some shortchange carbohydrates
and some caffeine.
If you would like to
get some, get it now.
We're going to have another
minute of blah, blah, blah
before we dive into
the presentations
and the real fun begins.
I'd like to introduce
our panelists up here
in the front who will be
the evaluation criteria
a la American Idol style,
except that you're, of course,
a lot smarter and
equally well dressed.
Starting from right
to left in front of me
we have Dr. Jasmin Hofstetter,
who comes from IES, Spain.
That's the Institute for
Solar Energy in Spain.
That's where she did her
PhD with Antonio Luque.
Those who have been studying
intermediate band solar cell
materials may know
the name as one
of the fathers of the field.
She studied under Antonio
Luque's organization
with Carlos de Canizo and is the
winner of presentation awards
at scientific
conferences, among others,
so Jasmin is welcome here.
We have thought that Dr.
Mark Winkler, as well,
a PhD in Eric Mazur's
laboratory at Harvard.
Those who are familiar
with femtosecond laser
characterization may be familiar
with Eric Mazur, also one
of the fathers of the field.
Mark started the Harvard
Journal Energy Club,
which is Harvard's version of
the MIT Energy Club-- a lot
smaller and a lot less
dynamic than MIT's version,
but nevertheless to
be congratulated.
And of course, a very
good organization.
I kid.
There's a little bit
of MIT Harvard rivalry.
And of course, our
very own Joe Sullivan,
who has been with you
the entire semester.
For those who might
not be familiar as much
with this research as you
are with his teaching,
Joe is studying intermediate
band solar cell materials here
at MIT in the Media Lab
and has been working
for the last-- what is it now?
JOE SULLIVAN: Three and a half.
PROFESSOR: Three
and a half years--
focused on intermediate
band solar cell materials,
coming from a very broad
background in energy
from climate science.
So with that, I'd like to
welcome our first team down,
and the floor is yours.
STUDENT 1: Good morning, we are
the PV smart retrofit group,
and our project goal was
to assess whether or not
the there was an
electrical benefit
or loss from retrofitting an
old home with a PV system.
Now, in less lofty terms,
it essentially means
from an on site
energy perspective,
does it make sense to put
PV panels on my house?
You'd think that that's a
kind of an obvious question.
We'd all say, well, yeah.
We produce energy for
free, except that you
have to consider other
things, such as shading
from trees that you'd
have to cut down
or the color of the roof
that you might be changing
by adding a black panel.
These would both reduce the
thermal load of your house
in normal situation.
So by adding a PV panel and
increasing the thermal load,
you actually add the
energy to cool your house
during the summer.
We considered multiple
variables in this project.
One was location, which
has an effect on the amount
of sunlight you're receiving.
The PV panel's
presence and its size.
We had a couple of
situations where
there was no panel as
a kind of a baseline.
And then also different sizes
to figure out if a bigger
panel had a bigger effect.
We looked at two different
colors, black and white.
Those are the ends
of the spectrum,
and they give us
endpoints to look at,
and the color matters
because a darker
color will absorb more heat.
We looked at roof pitch.
The reason for this--
well, first off, roof pitch
is the angle of your roof.
And we looked at this because
we assumed that our panels were
fixed and parallel to
the roof, so this kind
of controlled what
angle your solar panel
was facing towards the sun.
And finally you had
your house footprint,
which is the area
that the house covers,
and when you combine
that with the roof pitch,
you get the area of the
roof, which is really
what we're concerned with.
We had five
scenarios, and as you
can see from our
cute little diagrams,
we have a black
roof, a white roof,
a white roof with the tree, a
white roof with a solar panel,
and a white roof with a
solar panel and a cut tree
so the solar panel is
getting plenty of sunlight.
In evaluating the
five scenarios,
we had three models of
increasing complexity from left
to right, which you
can note from the fact
that model one only
covers three of the five,
and these models all
had common assumptions.
The first was that
you had a single story
house in a suburban
locations, so you
didn't have shading from
other buildings, for example.
We had a common house size of
about 2000 square feet, or 186
square meters.
The roof pitch,
which in construction
is set usually at 5/12,
which means 5 inches of rise
for 12 inches of travel.
We had an unfinished
attic space,
which means that it's
sealed to the outside,
but you didn't make it
livable, a five kilowatt PV
system covering
36 square meters,
and we chose reflectance values
of 0.08 for black and 0.35
for white, and this, again,
reflects the effect that color
has on heat absorption.
With that, I will turn
you over to, Jordan.
JORDAN: So the first
one that we looked at
was basically using
most readily available
and simple models there can be.
So this is from the
Department of Energy
to measure-- well,
to get a gauge of how
the color of the roof
and the roof properties
affect the thermal
loads in the house.
This is a simple one
dimensional model
where you've got an inside
cavity of 65 Fahrenheit,
and you basically
input the location,
and from that it has a lookup
table of the average insulation
on the house, as well as the
number of heating degree days
and cooling degree days relative
to that 65 inside temperature.
The other parameters
are just at the roof,
so we insert the
reflectance, and we're
using values that represent
real tiles for an average house,
black and white, as well as the
thermal resistance and the heat
absorbance of the tiles--
from this model, the outputs
and the thermal loads
in terms of the heating
you need to put in, as well
as the cooling energy load.
So with the thermal
model assessed,
we can assess the
photovoltaic output.
And for this, we're just
using a simple model PVWatts.
This basically takes in
the location and the angle
of the panels, as well
as a derate factor
from converting to AC to DC.
It's quite a simple model,
and output from this
is the amount of
kilowatt hours per year
that you get from the panels.
STUDENT 2: So I'll be talking
about a couple thermal electric
model.
This is the model that
we built in our group,
and we developed
this model based
on two sets of
individual parameters
and individual models.
I would say that one comprises
of the thermal model,
and there is the electric model.
So what we need to note
from this model here
is it's a further
step in complexity
when compared to the module
one that Jordan just discussed.
And it takes into account
various input parameters
that the model one
doesn't take into account.
So the basic structure of
this model is as follows.
We have a thermal model
which takes into account
several input conditions, such
as the insulation and shading,
and it outputs a living
space temperature,
which is this temperature of
the living room in our house.
And then this temperature is fed
into an electric model, which
calculates the cost
and energy values,
and thus we can compare an
energy production and energy
consumption.
Going to the thermal
model in detail,
I've just shown a picture here.
So it considers
basically when we
start from the top of the house,
we use insulation and shading
as the input parameters.
We then calculate the
temperature of the PV panel,
and then the
temperature of the roof
using two different
energy balance models.
And these two energy
balance models
are pretty robust in the
sense that they consider
all these physical phenomenon
which are realistic,
such as the
convection, radiation,
and PV electrical output.
And based on these
energy balance equations,
we can calculate the PV
panel temperature and then
the roof temperature.
And once we get these
two temperatures,
we get the heat flux
that goes into the roof
and that enters the attic.
And once you get
this, we find out
the attic temperature,
which then determines what
is the ceiling temperature.
And then we consider the
convection via ceiling,
and then finally we end up with
the living space temperature.
And then the couple this
living space temperature
with another electric model,
which I'll discuss now.
So the electric model is
basically based on an ideal gas
assumption.
So it basically--
what it does is
it calculates the energy
needed by the AC, which
could be the heating
or cooling, in order
to maintain the living space
at a particular temperature.
And we use this formula,
m dot Cp delta T,
which is an ideal
gas formula, which
gives out the energy
needed by the cooler.
And then so the electrical model
uses the power consumption,
and then we know the power
production through PV output.
So comparing these
two, we can really
assess whether PV installation
is favorable or not.
And this is just
the model in making.
What we want to signify
here is we actually
made this model on
our own, and this
is the MATLAB code we wrote.
And the model not only just
predicts energy values,
but it also can do
a lot more things,
such as predicting temperature.
And what I've shown
here is the PV output,
and then the cooling
load that is required,
so it can do a lot of
other things, as well.
This is the
temperature of the roof
in terms of direct sunlight
and diffuse sunlight.
So if anyone is
interested, I'd be
happy to discuss with them more.
Thank you.
And I'll now pass
it on to Heidi.
HEIDI: So I take over
from here talking
about the third and most
complex model that we used.
For this model, we used
two different softwares--
one called BEopt from
NREL, and the second,
called EnergyPlus,
which you'll see later,
developed by the
Department of Energy.
So what we did in this model
was we took into account
the 3D effects of these
thermal and electric loads
that have been talked about
in the other two models.
The first thing we did was to
actually model the 3D house,
as you can see right over here.
BEopt allows for a very nice
interface, where you can easily
model the house and easily
and put a whole bunch of input
parameters for the house.
And for these input
parameters, we
consulted with an experienced
building inspector
for the construction inputs
and used BEopt default values
for the rest of the inputs.
Once this model of
the house was done,
we had to actually
export it into EnergyPlus
because EnergyPlus gives us
a much more detailed look
into all these different
parameters, I guess.
And you can actually go in
and modify different things.
For the materials, we can
modify every single material
property-- conductivity,
density, specific heat--
and we actually did
that for the roof.
And we also removed
a whole bunch
of other miscellaneous loads
that BEopt had included.
So this is how we modeled
the trees and the panels
that we talked about in
our scenarios before.
For the trees, we modelled
them as these really large 5
by 20 meter rectangles that
act as shading for the house.
So the trees are located on
the south side of the house,
and we modelled them
as deciduous trees,
so we set up a transmitting
schedule so that they
have a higher transmittance in
the winter when the leaves have
fallen and a low
one in the summer.
And for the case of scenario
E in which the trees are cut,
we modelled the trees as
being five meters tall.
On the other hand,
for the PV panel,
we modeled it as being
fixed on the roof.
We actually had to completely
change the model from BEopt,
because they modeled
it as being decoupled
from the entire system, placed
30 meters away from the house.
So we completely changed
that, and we read extensively
into EnergyPlus literature and
found this particular object--
I guess you could call
it-- called the integrated
exterior vented cavity object.
And what this does is it
models a surface as being,
in our case, 0.5 meters
away from the roof,
and it models the convection
and radiation between these two
surfaces.
We also considered
the solar panel
to have a solar
absorbance of 0.92
and thermal emissivity of 0.9.
STUDENT 3: And so
we actually got
a lot of results, as
you might imagine,
from all those different
models, but just
for the purposes of comparison
for the presentation,
we're just going to show
you-- just summarize results.
And basically what we're
showing you here is specifically
for Boston, and this
figure that we're showing
is the y-axis is the
relative energy gain.
So in order to compare them,
we decided within each model
compare it to a
common situation.
So we decided to say
that, if we're in Boston,
let's say we start with
a white roof and a tree,
so that's scenario C there,
so that's why it's 0.
So everything is in
comparison to that.
And right off, we could see
that, as we might expect,
putting a PV on makes
sense energetically.
And specifically
scenario D, which
is where you completely remove
the tree instead of just
cutting it, in Boston at least,
is what makes the most sense.
And this is for both
models-- actually,
for all the models-- although
model one can't really
model a tree necessarily.
So that's why it basically
doesn't apply for that.
In terms of comparing the
results between the models,
model one actually does a
pretty decent job in Boston
in getting close to model
three, which is impressive,
because model one is
significantly more crude, much
simpler than model three, which
required many, many inputs.
And the reason we believe the
discrepancy is between models
two and three is that
model two-- the way
that we basically treated the
solar insulation-- it doesn't
treat diffuse
sunlight differently,
whereas basically the models
PVWatts and EnergyPlus will
take all that into
account, so we
think that's a larger
reason for that.
And then similar
thing in Phoenix.
And basically we see a
slightly different case here.
Actually scenario E, where
you just-- you install the PV,
but you cut the tree
instead of completely
removing it-- gives you a
slightly better increase
in net energy gain.
In terms of-- and
this is, again,
just in terms of energies.
There could be rounding errors.
This is ignoring the fact
that, if you cut a tree down,
the net greenhouse gas emissions
would be changed and altered,
and this is ignoring
all those other effects.
This is just in terms of net
energy gain of the house.
And just to point out the
discrepancy between model one
here, we think that model
one is actually, again--
that's using PVWatts to
get your energy output.
And that's basically assuming
peak solar insulation,
whereas our models basically
use more empirical formulas
to get the estimates
for your PV output.
And then the last thing we
did to do the sensitivity--
or to compare the models, was do
a sort of sensitivity analysis.
So basically on
your y-axis, what
you have is your percent change
in your relative energy gain--
relative, again, to
that scenario C--
divided by the percent
change in your parameters.
So we just considered
four parameters.
The x-axis is a rough
estimate of how difficult
it would be to actually change
that parameter in your house.
So the far left
one is the PV size.
We just assumed if you went--
instead of a five kilowatt
to a 5.5 kilowatt, so that's
why the price is roughly $3,000.
We assumed about a $5 to $6
per watt installation cost
for that.
So that's basically
the easiest one to do,
and you get various significant
change in your thermal energy
gains because of that.
And then just
because of time I'm
going to rush through these, but
basically a lot of the models
follow similar trends in
terms of the sensitivities.
The last one is the roof pitch.
You obviously wouldn't
really want to change that.
It's very expensive to do.
Luckily, for most
of the models, it's
not actually that
sensitive to it,
at least within a close amount
to where you start with.
So in conclusion,
in all three models,
it makes sense to
install a PV system.
It's kind of what we
expected from the beginning,
but it's nice to get
that sort of conclusion.
For models one and
two, we actually
were able to get pretty
reasonable results,
but they're limited in
terms of what you can
consider within those models.
The advantage of looking
at this basically
is that, if you have
a user that isn't
as familiar with EnergyPlus
in model three, which
is very sophisticated-- it
requires a lot of inputs--
they can still get a
rough estimate, which
is relatively close, using
these much simpler models.
And model three--
again, we were taking
that to be the more
realistic case,
but you'd have to compare
it to real life data
and do an empirical analysis
to see how close it actually
does correlate.
And then just,
again, to summarize
the results we got from
model three-- in Boston,
it makes sense to
install the PV,
but completely remove the tree.
And your payback period
is about 24 years.
In Phoenix, the best scenario
is to install the PV,
cut the tree, and
it's about 51 years.
And interestingly, the maximum
of that relative energy gain
was essentially
the same in both,
even though the
scenarios were different.
So we'd just like to
acknowledge Professor Buonassisi
for helping assist
us and guiding
the direction of the project,
and Bryan Urban at Fraunhofer
and other members at Fraunhofer
for giving us guidance.
And with that, we would like
to ask you for questions.
[APPLAUSE]
AUDIENCE: My
question is I grew up
in a neighborhood that
has a lot of trees,
and so cutting
down all the trees
wouldn't be very practical,
but do you at all consider
PV systems that
could handle shading
at different times of the day?
So somehow decoupling
different parts
of it knowing that some of them
will be in sunlight for part
of the day, some of them will
be shaded, and that will change?
STUDENT 3: So you could
make the model-- especially
in EnergyPlus, you could make
it as complex as you want.
We just did this for simplicity,
just to put boundaries
around what are problem is
that we were considering,
but you could definitely-- yeah,
you could definitely add that
to the model if you wanted to.
STUDENT 1: Cutting
the tree was not
worrying about the output of
the actual cell in terms of
whether or not some shading
was going to bring down
the rest of the cell.
The reason we
would cut the trees
is to increase the maximum
amount of sunlight per day
hitting the panel.
And it's because we were looking
mostly at endpoints, trying
to get the spectrum ends.
That was why we went
to such extremes.
Cutting down selective trees
and just parts of trees
would be kind of in between.
It's a little bit more
difficult to assess.
STUDENT 2: Cutting down trees
is actually [INAUDIBLE].
It's not [INAUDIBLE] because
we found that the shading
factor doesn't play a much
bigger role if you look
at the relative [INAUDIBLE].
So you would as
well have increased
the-- there will be objectively
small loss in the energy gain,
but that shouldn't matter much.
AUDIENCE: Sort of a
philosophical question.
If the payback period in Phoenix
is 51 years, is it worth it?
That's a long time period
for-- I guess economically
you could say that you could do
other things with that capital
instead that would have
a shorter payback period.
JORDAN: Well, 51
years-- then the answer
is probably not if you're
looking at the benefit of cost
money-wise.
We did analysis
about the energy.
So we found an estimate for the
embedded energy of the panel.
This is from-- I can't
remember the source,
but they change quite a bit.
But this example says it's
1,500 kilowatt hours per meter
squared, so that equivalents
to nine years payback.
Pretty much nine
years in Boston.
I think it turned out to
be eight years in Phoenix.
So there is a
benefit energy-wise,
but in this example,
perhaps not cost-wise--
perhaps not the most
advantageous to do per dollar.
MARK WINKLER: A related
question, actually.
Can you back to your
two slides back maybe?
JORDAN: Yeah.
MARK WINKLER: Your look
at the net energy gain
was quite similar.
So why the large difference
in yearly savings
and payback period.
STUDENT 3: Just the cost of
electricity in each location.
We estimated it as about $0.07
per kilowatt hour in Phoenix
and $0.17 in Boston
for residential.
STUDENT 1: Which is why you
would get a shorter payback
period for Boston-- is because
the cost of the electricity
that you're [INAUDIBLE].
MARK WINKLER: So I would have
assumed that the generation
mix is sort of similar.
Is that regulatory,
or-- I would assume
they're coal/gas centric
generation mixes.
STUDENT 3: Yeah.
You mean in terms of
how the houses are--
MARK WINKLER: This is a
little outside the scope
of what you guys did.
I was just curious
if you guys had
any sense of why
the big difference
in wholesale electricity
price is between Boston--
STUDENT 3: I think part of it
is just how plentiful energy is.
I guess Boston is at the very
end in the corner of the US.
It's more difficult to get fuel,
oil, gas shipped over here.
I think Arizona--
I think they're
relatively close to a nuclear
power plant over there.
Oil-- I think it's
just location--wise.
JOE SULLIVAN: There's
a lot of coal there.
They actually ship a
lot of the electricity
to California because they
can't [INAUDIBLE] in California.
One quick question, though.
The relative energy gains
are the same for both.
Do you have different
sized panels,
or is heating that much?
That's a big deal.
STUDENT 3: Heating, yeah.
JOE SULLIVAN: OK.
So if you--
HEIDI: Also for Phoenix.
For Phoenix, you can see
this is the cooling over here
and heating on the
right over there,
and for Phoenix, you can
just look at the values
and see that there's a lot more
cooling than heating compared
to the Boston case, where
there's a lot more heating
by many orders of
magnitude more.
And so that kind
of balances it out.
JOE SULLIVAN: And so that's
only in a cutting down
a tree case if you were already
well shaded or not shaded
at all?
HEIDI: These are
actually all the curves
for all the scenarios, and--
JOE SULLIVAN: I see.
OK.
HEIDI: So it does matter
just because of location.
So if you're not
cutting down a tree,
then there's no
decrease in shading.
Or is it just the panel
itself that's heating up more?
STUDENT 3: Well, actually
if you go back to--
JOE SULLIVAN: Sorry, I
think I missed something.
STUDENT 3: Actually,
in Boston it actually
makes more sense to have a
black roof than a white roof.
So you actually want--
shading isn't necessarily
good in Boston, just because
there's so much heating
that you need in the winter.
It seems to be the
dominant effect in Boston,
and in Phoenix,
it's the opposite.
The cooling is the
dominant effect.
PROFESSOR: Did you
consider the possibility
that snow also
insulates the house
once it falls on the roof?
STUDENT 3: No.
We did not.
I don't know if-- is
that built into-- I
don't know what would happen.
No, I don't think we did,
but that's a good point.
AUDIENCE: Along
those lines, do you
have any intuition
as to why in one case
it's better to cut down a
tree other than remove it,
and then the other is better to
remove it rather than just cut
it down?
Are you expecting it
to grow back and then
have to incur more
costs because you're
going to have to cut it down
again, or-- what's going on?
STUDENT 3: Well, just
in terms of pure energy,
it was very, very
slightly better
in this case to have
the tree just cut
just in terms of the balance
between heating and cooling
[INAUDIBLE].
STUDENT 1: I may be able
to help clarify that.
The idea is in Boston
we're relatively cold most
of the year, so the more
sunlight that hits your house
is going to add more
heat to your house,
and that's less energy
that you have to pay for.
So the reason that it's
beneficial to cut down
the tree completely in Boston is
because it allows more sunlight
to hit your house, whereas
in Phoenix, you don't want
the sunlight to hit your house.
If you cut down the
tree completely,
that's more you have to
pay for AC in the summer.
So the--
AUDIENCE: [INAUDIBLE] the
difference between cutting down
the tree and removing it?
STUDENT 1: So--
STUDENT 3: So-- go ahead.
STUDENT 1: Cutting
the tree is assuming
that you're going to maintain
it at that certain level.
So by cutting the tree,
you keep a certain amount
of shading on the lower
part of your house,
but you still allow sunlight
to hit your solar panel.
Cutting down the
tree completely means
there's no shading
on your house at all.
AUDIENCE: I guess I have
a philosophical question.
So I think there are
a lot of people--
motivation for the solar panels
is not just the [INAUDIBLE],
but rather the desire
to do something
good for the
environment, and to lower
carbon emissions, et cetera.
But when you cut down trees,
that increases your carbon
emission because you're
reducing the plant,
that reduces your carbon output.
So given that you won't have a
tree there for like 50 years,
does that offset the
carbon emission gains
that you get by--
STUDENT 1: Just my two cents.
If you really want
to go in depth,
you can look at
how much carbon is
going to be produced
by the coal power plant
to give you the energy that
you're going to be using for 50
years and compare that
to the amount of carbon
that one tree was going to save
you, or you could ask yourself,
am I planning to have a child
during those 50 years, which
will produce so much more CO2
than that tree will take out?
Either way, it's
relatively a small value.
However, we do
acknowledge that there
was a lot of
philosophical questions
that we argued
amongst ourselves,
but we realized we didn't have
the time to try to evaluate,
or the materials, and scope.
PROFESSOR: One more
question, and then we're
going to have to switch groups.
Jasmin?
JASMIN HOFSTETTER: Do
you have any real data
to compare your
model results to.
From your results,
it seems that it
doesn't make any
sense to install
solar panels ins Phoenix.
Is that right?
That's the impression?
STUDENT 3: Financially.
Just purely financially, yeah.
In terms of the PV
output, it seemed
to be pretty close
in comparison to what
we got from other sources.
So it seems like the net gain
in energy is roughly right,
but obviously people still
install panels there.
So either, I'm guessing,
subsidies, or larger
installations, or
something else, or just the
desire to install it
just for installing it--
not necessarily for financial
reason-- in Phoenix.
JASMIN HOFSTETTER: What was the
temperature that you assumed?
I suppose you assumed a constant
temperature in the house that
was like the--
STUDENT 3: Yes, that
would also change it.
JASMIN HOFSTETTER: What
was this temperature?
STUDENT 3: The set
points for our model
was-- the cooling
set point was 71.
HEIDI: 76.
Yeah, 76.
And then the heating
set point was 71.
STUDENT 3: Yes.
JASMIN HOFSTETTER: Can you
say that again, please?
HEIDI: The cooling set point
was 76 degrees Fahrenheit,
and the heating was 71.
STUDENT 3: For both locations.
HEIDI: For both locations.
JASMIN HOFSTETTER: Thank you.
AUDIENCE: [INAUDIBLE].
JOE SULLIVAN: Are we out of--
PROFESSOR: No, that's it.
You guys are done.
Congratulations.
[APPLAUSE]
[INAUDIBLE] coming up, PV grid.
What happens when you install
loads, and oodles, and oodles,
and oodles of solar
onto the grid?
We're going to hear all about.
And take it away.
Knock it out of park, guys.
IBRAHIM: So as
[? Tony ?] mentioned,
we're the PV grid project.
I'm Ibrahim.
MARY: I'm Mary.
RITA: I'm Rita.
ASHLEY: I'm Ashley.
JARED: I'm Jared.
IBRAHIM: All right,
so I'm just going
to start with the motivation
behind our project.
So as we discussed in
class, PV installations
have witnessed very
significant growth rates
over the last few years.
Last year alone PV installation
growth rates were around 17%.
Around 18 gigawatts
globally were installed.
As the cost of PV
approaches grid parity,
more investors and
consumers are going
to want to adopt PV systems.
However, one lingering
or major obstacle
preventing the further or
high penetration levels
of PV systems is intermittency.
So as we discussed
in class, there's
variability in terms
of the solar resource,
both on a long-term scale and
a short-term scale seconds
to minutes.
So on a long-term
scale, we're talking
about the position of the
sun relative to the Earth
and so on.
So in that respect,
that's predictable
and can be planned for.
When we define or talk
about intermittency,
it's the short-term
unpredictable effects
that change the power
output significantly.
So what we have here is
the fractional change
in power output over
the course of one day.
So as you can see, between
the two consecutive seconds,
the power output
can almost double,
and it can at other
times drop by half.
So from a system
operator perspective,
that's obviously
a major challenge
because demand should
match supply at all times.
So again, these effects, or
these intermittency issues,
arise due to regional weather
patterns that can be predicted
and also due to local
weather patterns that
are less predictable.
So in our project, what
we tried to address is,
can the weather report be
used to predict the power
output from an ensemble
of smaller distributive PV
systems?
That is, can we average out
these local less predictable
intermittency effects?
I'll give it to Mary to
discuss our approach.
MARY: So our goal
of this project
was to design a model
that could quantitatively
analyze a PV grid and determine
its robustness in terms
of variability.
And our main components were
meantime between failure--
which is the average
time between two system
failures, which Rita
will define and discuss
later-- number of
systems in the grid,
and geographic
dispersion, which we
measured through
geometric mean distance.
Our data set was from
the Oahu airport,
which is part of the National
Renewable Energy Laboratory.
There are 17 systems all
within about a kilometer
of each other, so it's a very
small, very dense system,
but there was second interval
data for a year, which we used.
So there's a fair amount
of data to give us
an estimate of how
intermittency varies
over the course of a system
and the number of systems
and density.
RITA: So our first
step was to define
what was a PV system failure.
In order to do so, we
accessed the CAISO website--
that is, the California
Independent System Operator--
and we took that data from
one week of the actual demand
and hour hand demand forecast.
They give this value
for every hour,
so we took the value for
every hour of the week,
and then we plotted
in this graph
that we have a line for
each day of the week,
and can see that both the
magnitudes and the shapes
throughout the week
are almost the same.
We can also see that the
values are almost all positive.
This means that they
usually underestimate.
They usually think
that the demand
is going to be under
what it really happens.
And so what we defined was
that, if this estimation is
OK for CAISO, if
they can manage that
the grid with this
variation, then they
could also manage the grid with
this variation in a PV output.
And so we looked at 5:00 PM.
That is the hour that
we have the biggest
variation between the two,
and we averaged the value,
and we got to 6%.
So this means that, if our
intermittency is above 6%,
we are going to have
a PV system failure.
If the variation is below
6%, then the intermittency
is not going to be a failure.
Then we could define the
mean time between failures--
that is, the mean time between
two intermittencies higher
than 6%.
JARED: OK, now that we
have some context of what
the problem is, and we have an
idea of what variability is,
and we have a data
set to work with,
I'm going to talk about how
we actually solve the problem.
We use coding in MATLAB to
handle this huge data set.
NREL had 17 systems out
there for every second
of an entire year.
And so we took all
the files from NREL
and put them all
into one huge matrix.
You can imagine it
was-- it ended up
being about 23 fields
by several million,
and it's about 677 megabytes.
So actually handling the
data was an issue in itself.
I don't recommend it
with an old computer.
And we also the GPS
coordinates for each
of those locations
and the variability
from the California
ISO, so with that data
we could begin to build
our code to figure out
a quantitative description
of mean time between failure
and our idea of density.
So once everything was
loaded into one big matrix
that we could work
with, we moved on
to use the GPS coordinates.
And of those 17
systems, we found
every single combination
of 17 choose 2,
17 choose 3-- every possible
way that you could connect
these systems-- and
came up with something
like 60,000 different
ways of connecting these,
and then for each
possible connection,
we had a function
that would calculate
this geometric
mean distance that
would give you an
idea of the density
of that particular connection.
And so to compare our
mean time between failure
for these systems while
holding the density constant,
we then searched through
those possible combinations
and found this magic
number that kind of
existed for each of those
possible combinations of two,
of three, or four,
all the way through.
And it kind of lined up
for geometric mean distance
of 400 meters.
So using that set,
we could then go on
and see how increasing
the number of systems
helped the mean time
between failure.
And then for a given set,
we ended up using eight.
17 choose 8 gave us like 24,000
possible ways to connect them.
We searched through and
found varying densities
for one set number.
Then finally we
wrote a function that
calculated the mean time
between failure that
went through our data
from NREL and said--
looked at the fractional
difference and said,
OK, each time it's about
6%, that's a failure,
and then measured that distance,
took the average of that,
and that was our mean
time between failure.
And then finally,
once we had all
that together, we
crunched all the numbers,
took a long time on my computer.
We were able to plot it together
and get some very nice trends.
One of the great things,
I think, about our code
is that it was only 525
lines, and if you've ever
built a programmer, a
big application, that's
really small.
It's very easy just to go in
and see exactly what's going on.
So it's very flexible.
We could hand it off
to another company,
to another research group,
and they go in and adapt
it to just about any data set.
If you are able to get data in
California, or from Germany,
or from somewhere else, and
bring it into our format,
it's very easy just to plug
it in and run the data.
Very, very minimal
changes within our code.
And then you could
also build on our code
to look at other problems.
So we have the change in the--
we have the variability data
as a function of time.
We also have the solar
output as a function of time.
So you could conceivably
go in and figure out
how your meantime
between failure changes
based on the time of day and
change your critical percentage
based on the time
of day, and there
are several other problems that
you could go, and launch off
of our code, and continue on.
And if you're interested
at all, I actually
put the code of my public space.
There's the link there.
Check it out.
It's pretty cool.
And then Ashley is going
to talk about our results.
ASHLEY: Cool, so the first
thing that we did in order
to try to see the trends in
these huge fields of data
was just to plot the data.
It was actually a
much bigger task
than I thought it
was going to be.
The plot on the left is for
one day's worth of data,
and the plot on the right
is one week's worth of data.
The y-axis is power density
in watts per square meter,
and the x-axis is
the time in seconds.
The blue is all 17 of
our systems together,
and the red is just
for one system.
So as you would assume,
the power output for all 17
together is clearly
a lot greater
than the output from
just one system,
but this give us a sense of
being able to see fluctuations
within one day, and
also were able to see
when the sun rose, and peaked,
and also fell each day.
And in order to quantify all
those different fluctuations,
we did the fractional change
in power density versus time,
once again, for one day,
and then for one week.
And red is the one system.
Blue is all 17 systems
together, and we can already
see just from plotting the
data that having all 17
systems together does
start to average out
the fluctuations of
individual systems
by a significant amount.
So then Rita earlier
mentioned that we use 6%
as our cut off for failure.
We actually went ahead and
did 6%, 12%, and 18% just
to see how sensitive our
analysis was to that threshold
value.
So here we have
plotted on the left
the meantime between failure
versus the number of systems,
and on the right,
meantime between failure
versus the geometric
mean distance.
I also calculated
these values for using
a week's worth of data,
a month's worth of data,
and a year's worth of data.
So the week would give
you more fluctuations,
but the year would give you the
more long-term overall system
behavior.
Relationship between the mean
time between failure and number
of systems is quadratic, and
we found a linear relationship
between the mean time
between failure and the GMD.
So this is four 6% cut off.
This is for 12% cut off,
and this is for 18% cut off.
And the mean time
between failure
increases dramatically
as you go from the 6% cut
off to the 18% cut off.
So a lot of this makes
sense, but it was
really cool to quantify that.
RITA: So after
applying those graphs
we could take our conclusions
and answer our question.
And so the first thing that we
noticed, but we were expecting,
is that a big data
sample should be
used if conclusions are going
to be used as a design tool.
As Ashley said, we used for
a week, a month, and a year.
And so we know that the
bigger the data set,
it's going to be--
it's not going
to be influenced by
abnormal things that
can happen in a given day.
And we also saw that
there is a linear relation
between mean time
between failure and GMD.
When GMD increases-- that
is, when density decreases--
we are going to have an increase
in mean time between failure.
This was also what
we were expecting
because the local
effects will not affect
systems that are further apart.
We also saw that there
was a quadratic relation
between mean time between
failure and number of systems.
Number of systems increased.
Mean time between
failures also increased.
This was also according
to what we expected
because we know that the
percentage and the total output
is going to be lower.
We also saw that the mean time
between failure is very low,
even when we can see
the 17 systems together,
we have about 900
seconds between failures.
This means that
some backup systems
should be used in order
to take over the load
when we have a failure.
And so now we're
running conditions
to ask our first question.
And so we conclude
that localized
predictable intermittency
do average out
and that this effect decreases
as the number of systems
and the GMD increase.
The data that we used
was for 17 systems,
and the biggest distance
between them was one kilometer.
So we believe that
it's important to run
our code for a bigger set of
data, because only in this way
we can confirm our
conclusions and guidelines
for the design of PV
systems can be defined.
Thank you, and we'll be happy
to answer your questions.
[APPLAUSE]
JOE SULLIVAN: So
a couple things.
First of all, you ended
at exactly 15 minutes.
I find that remarkable.
Additionally, just-- sorry.
Can you repeat what exactly
a failure mode is defined as?
Are you looking at 6%
intermittency varying
from second to second?
So if you look at the output
from one second to the next,
does that change by over 6%?
RITA: Mm-hm.
JOE SULLIVAN: It wasn't
average out over an hour.
RITA: No, no.
It was second by second.
JOE SULLIVAN: You got
the 6% from Cal ISO.
RITA: We said that if there--
in a given hour, we measured--
let me just--
JARED: They only had an
hour of data [INAUDIBLE].
RITA: Yeah, they only
gave hourly data.
So the difference
between the actual demand
and the hour-ahead
demand forecast.
So this is what they are
expecting, but the difference
between what they are expecting
and what the grid is really
asking them.
So if they can manage this
difference on a second base,
they can also manage this
difference on the PV grid.
JOE SULLIVAN: So you
took the worst case.
Is that how you got 6%?
RITA: Yeah, we took the
average of the worst case.
It's the 5:00 PM.
The 5:00 PM is always
the worst hour.
It's always when
they have that peak.
And in fact, all of the
base-- almost all of the base
were around 6%.
Our peak was like 6.8%, and
we averaged, and it was 6%.
MARK WINKLER: So
that's essentially
their peaking capacity?
RITA: Yeah.
ASHLEY: Also, so I
actually wrote down
the numbers for
6% function, 18%--
like our mean time
between failure.
For 6%, we had up to 15
minutes between failure.
So it's a pretty low amount
of time between failures.
And if you allow 12%
as your intermittency,
you can get up to
about half a day.
And then for 18% as your cut
off, you get about nine days.
So it is still
very intermittent,
and you would pretty often have
to have backup systems if you
had the small of a system.
So if you had a much wider
spread system and a lot more
systems in your grid,
then you could definitely
significantly increase the
mean time between failure.
Yeah, Joe?
JOE SULLIVAN: So you
have this awesome graph.
So if you go back to
the time between failure
number of systems.
The interesting takeaway
is how large of an area
do you have average over, right?
So 300 seconds on
a grid perspective
is unacceptable for
widespread PV developed point.
We need to be on
the order of years.
And so do you have an idea
of what that distance is?
ASHLEY: If we just
extrapolate it out?
JOE SULLIVAN: If you
extrapolate-- this is obviously
like we're taking the very, very
edge of that function and then
extrapolating [INAUDIBLE].
ASHLEY: So looking
at the numbers--
JOE SULLIVAN: But it looks like
it's going up exponentially,
or do you have an idea
of what that trend is?
ASHLEY: For 6% for
the one year, it
was almost exactly x squared.
It was like x squared plus
50, or 100, or whatever
that would be.
So if you want, you
could say, mean time
how many seconds are in a
year equals number squared.
So the square root of however
many number of seconds
there are in a
year would give you
your number of systems required
for a year between failures.
IBRAHIM: But this is for a
given geometric mean distance,
so you have two factors.
If you sort of
spread them out more,
probably going to
require less systems.
JARED: And if you
looked that map,
that's all at the end of a
runway at the Honolulu airport.
So if you have a huge
field in Arizona,
thousands of systems, your
mean time between failure
is going to be a lot better.
MARK WINKLER: So I'm actually
really surprised that there's
such a huge effect
from adding systems,
just because it seems as
though the relevant length
scales for weather
should be very large.
Do you guys say
anything about that?
JARED: I think the idea was
that, for long-term weather,
you can predict that.
So if you know
there's going to be
a storm front coming through,
you can add natural gas.
You can add coal to the system.
Back up--
ASHLEY: And that would
cover the entire system.
JARED: Our kind of variability
we're talking about
is say, if one cloud goes
over, or a flock of birds,
or something.
So we were thinking
that would be
on a few seconds
for a single module
for a cloud just go over
shade it for a short distance.
So if you add
thousands of modules,
the other modules wouldn't
be shaded while that one is.
MARK WINKLER: But
these fields-- I
mean, 100 meters on the
scale of cloud cover,
this still seems like a
somewhat small length scale.
Let me rephrase the question.
Do you think that the
graph on the right
would be a smooth
function of distance,
or do you think
there's some length
scale at which the
behavior on that plot
changes significantly?
JARED: That would be
interesting if we could find--
ASHLEY: The assumption
is definitely
evenly dispersed in an area.
JARED: That would be something
that, if we had another data
set that had wider
distances, it would
be very easy to plug it in.
I think our code's
really flexible.
It would show us
that relationship.
MARK WINKLER: What do
you guys think, though?
JARED: It's a good question.
ASHLEY: I wouldn't be surprised
if it was linear still.
I guess another
complexity we could do
would be you would
have-- right now we just
have one big field of
systems, but if you
had one set of systems that
was spaced x distances apart,
and then you had some
number of kilometers
away from another
one space-- I'm not
sure how exactly
would model that,
but I think that
at that point I'm
not sure what the
curve would look like,
but a continuing linear
trend seems reasonable to me.
IBRAHIM: So I guess another
thing to keep in mind
is we did not take into
account transmission costs,
so I guess you'd have to weigh
the cost of failure versus, I
guess, the added incurred
cost for transmission lines
and so on, so there's
sort of an optimum point
where you want to
space them and have
a certain number of
systems where I guess,
after a certain point, your
returns diminish and are not
equal to, I guess,
the cost of failure.
So that's something
where, I guess,
future people can
come in and expand on.
AUDIENCE: So all this
is data from Hawaii,
which has a very notable
climate and weather.
I've never been there, but--
[LAUGHTER]
Do you think that this is
really-- your code is flexible,
so I understand that, but do
you think the conclusions are
really extensible to
other parts of the world
with different weather
patterns or climate?
RITA: That's why we think
that the future mark is really
to do it for a different place
and for a bigger set of date
because we really want to be
sure that the conclusions are
going to be applicable, because
we had that same question.
We were talking just
about a small place.
We said that it's one kilometer
apart for the distance
that we have.
So we also want to run
for a bigger set of data
and for another place just to
be sure that our conclusions are
applicable everywhere.
JARED: And I would say the
relationship would probably
hold because if you have-- say,
if your regional weather is
very different, that
wouldn't show up
in the fractional second to
second difference that we had.
And so the timescale
that we measured it on I
think would be, say, small
clouds or intermittent events
that would occur over a wide
range of different climates.
The general regional
weather is predictable,
and it isn't investigated
in our study at all.
So I would say I think
the relation would hold.
ASHLEY: I think
that the big change
between different regions
would just be the total output
power that you can
get, but I think--
I wouldn't be surprised if the
fluctuation is still the same
or is similar.
And I think certainly that, as
you increase a number systems
and as you decrease the density
with which they're packed,
you should be able to
have a more robust grid.
I would be very surprised
if that weren't the case.
AUDIENCE: Do you see shading
for planes at the airport?
ASHLEY: There's no way
for us to determine
what causes the shading.
The raw data we
have is just output.
JOE SULLIVAN: Can you
see how they move?
[LAUGHTER]
ASHLEY: It's like
there is this line--
IBRAHIM: We actually
did that for one plot.
You could see the cloud
moving around the plot.
JOE SULLIVAN: That's cool.
IBRAHIM: And you see the
power output for [INAUDIBLE].
ASHLEY: Yeah, it was
on the order of-- we
had like two billion
data points, I think,
which was overwhelming.
But yeah, it was really cool.
Any more questions?
Yeah?
AUDIENCE: Can you describe
a little more what these PV
system failures entail?
And what happens,
and how long does it
take to get them
back up and running?
What has to be done to do that?
ASHLEY: You wanna get that one?
JARED: Sure.
So basically there
is a certain capacity
that the grid would have.
Say, you can compensate for a
6% drop in this case, or a 20%
drop, or something like that.
So if your system is
completely powered by PV,
which is not realistic,
and you have, say,
a 20% drop and
nothing to compensate
that, you have a blackout.
And so we investigated
18%, for instance.
So that would be,
say, if your grid
is a certain percentage
of PV and then has
natural gas, or
coal, or something
that you can bring
online quickly
to compensate a drop in PV.
That would be an idea
of what a failure is--
if you aren't able to
compensate that fluctuation
AUDIENCE: And how
long [INAUDIBLE]?
JARED: How long
would a failure last?
It depends.
If you can't meet the demand--
AUDIENCE: [INAUDIBLE].
JARED: For a PV system,
I think the problem is
the PV system would come back up
right after the cloud was over,
but if you can't
meet power demand,
you've got all kind
of protection systems
that would trip off,
and it would be mess.
So I don't think would
come back very quickly.
ASHLEY: That's a good
question, though.
JARED: That's a good question.
PROFESSOR: It's relevant because
you can envision back up power
that could kick in really
quick, but exhaust itself
within the period of
the delta t necessary.
AUDIENCE: For your
definition of intermittency,
did you look at the absolute
value or just the drop?
Because the grid can't deal with
excess power as well, and so
I was just wondering if
you had insight on that.
Like if you dumped 60%
more power in the demand,
there's no way for you to--
JARED: We did the
absolute value.
So 6% more, 6% less.
JASMIN HOFSTETTER: So I'm
going to ask you for real data.
So do you know where
more or less data points
would lie for, let's say,
PV systems on houses that
are like-- with a
typical distance
in some kind of neighborhood.
JARED: I think that
would just be you
would adjust your
geometric mean distance
to whatever the distance
from the houses are.
I don't think our data has to
be a solar farm, for instance.
I think it could be houses in
a neighborhood, for instance.
So if they're perfectly
connected to the grid,
I think that our code
would account for that.
ASHLEY: This was
for eight, right?
JARED: Uh-huh.
ASHLEY: The right-hand graphic
held the number of systems
at eight.
And so if you had eight
houses spread apart
by an average of 150
meters, then you would--
and if you considered a year's
worth of data-- is it like 250?
I just can't see it.
So you'd have meantime between
failure of 250 seconds, which
is four minutes?
Doing math under pressure.
JARED: Right, but if you
have a grid to back that up,
it's not big of a deal.
AUDIENCE: I'm confused about
the plot on the right here.
What it's suggesting is
that one week you picked
was significantly below the
year average [INAUDIBLE],
and you could have equally
picked another week that
was significantly above.
JARED: Right.
This was, I think,
just to give the trend.
The relationship between the
day, and a week, and a year
is just the day
that we-- I'm sorry.
A week, and a month, and a year
is just the week we picked,
the month we picked.
I think you see on
some of the other plots
that the week and the
month actually shift.
It's just the year was kind
of the average of those.
MARK WINKLER: I would
assume that areas,
or specifically countries, that
made large investments in solar
would have studied this
question in a detailed fashion.
Do you know if, for example,
Germany or Spain have looked
at this problem when it's spread
across hundreds of kilometers.
ASHLEY: Ibrahim, do
you know that one?
I think you might be--
IBRAHIM: I was actually
very-- we didn't find
a lot of literature actually.
For wind, there was a
lot of data out there,
I guess, because the high
penetration levels with PV.
There were very few studies.
Most of them actually
were addressing the US.
I didn't find any, actually,
on Germany or Spain.
Probably maybe they're
in Spanish or German,
so I don't know.
JOE SULLIVAN: So
what I find really
startling is that,
for a given system,
the time between failure
of the 6% intermittency
is on the order of a minute.
Do you have any the idea-- is
that vastly different for wind
and what that number is?
And this is outside
of your-- I'm
just wondering if in your
literature searching.
JARED: You probably
know the most about it.
ASHLEY: You would know from it.
JOE SULLIVAN: It seems like
you have this big rotor.
There's some momentum, and
that to slow that thing down
requires more time, but
I don't-- as opposed
to electrons.
JARED: I would say
wind would definitely
have a much longer time
scale than solar, I think.
There's a lot of momentum there.
RITA: But when wind stops,
the times that you have
intermittency is going
to be much bigger.
And there'd be
backup systems you
need to have to take over
for a long period of time.
JARED: And maybe
in high winds you
would have more of an issue,
because if the turbine is
spinning too fast, you
actually have to stop it.
So maybe there you'd run
into issues of variability
on the order of minutes.
AUDIENCE: So I
think-- and this is
kind of going back to location
data set-- comes from Hawaii,
which I would imagine has
mostly direct sunlight.
For locations such as
Boston, would the data
set change for,
say, diffuse light
and would that generally bring
in panels closer together
or require more panels at
the same geometric distance
to get the same results?
ASHLEY: Well, the raw data
that we have doesn't separate
direct and diffuse, so I think
that the first thing would
be we'd want to
look at a data set
and from whatever
other location you
wanted to know about and look at
how diffuse and direct differs.
I don't think we have a
sense here of that effect.
Does that answer your
question to some degree?
AUDIENCE: Some degree.
I don't know if someone
else wants to add more.
JOE SULLIVAN: [INAUDIBLE]
after you respond.
JARED: I think it's
interesting-- I was just
thinking about this.
Something that might be
interesting to investigate
is concentrated solar.
If it's easier to
shade, it would
look like a denser system.
So maybe that would be-- maybe
a concentrated solar farm
might be a bad idea if you
have lots of little clouds.
So that's something I
think that you could
expand into from this project.
IBRAHIM: And another thing, I
guess, to add to your point,
if you look at, I guess,
solar thermal systems
probably because of the diffuse
sunlight, the intermittency I
would expect is going
to be probably less.
You're going to have less,
or the mean time to failure
is going to be longer,
so you could maybe
add a solar thermal system, sort
of balance the power output,
and decrease your
intermittency even further.
JOE SULLIVAN: Any
last questions?
No?
All right, let's
thank our group.
[APPLAUSE]
