The perfect solar design for a berkeley home

I E O R 1 6 0
F i n a l P ro j e c t

BERKELEYSOLAR

PREPARED FOR: BERKELEY CLIENT, PROFESSOR GLASSEY

PREPARED BY: NASSIM FARROKHZAD, REGINE LABOG, KENNETH LEE, RHONDA NASSAR,

MIRANDA ORTIZ, CHRISTINA YOU

University of California, Berkeley IEOR 160 FINAL PROJECT

Table of Contents

Executive Summary! 1

Objective! 1

Goals! 1

Solution! 2

Recommendations! 3

Task List! 4

PERT Chart! 5

Design Objectives - Solar System Batteries! 6

Solar System Batteries! 6

Maintenance Cost! 8

Acid Leakage and Durability! 9

Determining the Optimum Battery Capacity! 9

Minimizing the Lifetime Cost of the Battery System! 10

Battery Cost Optimization Results! 11

Conclusion! 12

Design Objectives - Solar System Panels! 13

Choosing the best solar panels! 13
U C B e r k e l e y! IEOR 160 Final Project

i

The Optimal Tilt Angle for Fixed Solar Panels! 15

Problem Analysis! 17

Determining the Monthly Demand! 17

Determining the Average Amount of Sunlight in Berkeley! 17

Models - Introduction! 19

Variables! 19

Parameters! 19

Model 1! 21

Introduction: Off-Grid, Solar Contractor (Buy/Sell Power)! 21

AMPL Model: Minimizing the Objective Function! 23

Constraints! 24

Model 2! 25

Introduction: On-Grid, Solar Contractor! 25

AMPL Model! 25

Model 3! 26

Introduction: Off-Grid, Solar Contractor (No Buy/Sell Power)! 26

AMPL Model! 27

Works Cited! 28

Appendix A - Battery Selection! 29

Appendix B - Demand Calculations! 30

Appendix C - Weather Calculations! 31

Appendix D - AMPL Model Outputs! 33

ii

Introduction! 33

Model 1! 33

Model 2! 36

Model 3! 38

Appendix E - Battery Cost Optimization! 41

Minimizing the Cost per Lifetime! 41

Appendix F - Solar Panel Cost Optimization! 42

Minimizing the Cost per Watt! 42

Appendix G - Solar Installation Costs! 43

Appendix H - Night Hours v Months! 44

Appendix I - kWh Bill for 25 Years! 45

Appendix J - Solar Power Calculator! 46


iii

Executive Summary
Objective

For this project, our goal was to provide our client with an optimal solar system design
for their Berkeley residence. Because every city has a different policy on solar panel in-
stallation and gets varying amounts of sunlight, we had to tackle many variables to
provide our client with his best options.

Goals

The owner outlined the following:

‣ Off the grid where he would have no connection to PG&E and would require a
self-sustainable solar panel system, even during consecutive cloudy days where
there would be little sunshine.

‣If possible, he would like to sell excess power and buy it if necessary.

‣The solar system must ﬁt the needs of his home with a working space of 1500 sq
ft of roof space.

Before even attempting to address the owner’s concerns, we needed to take multiple
variables out of the equation:

! How many hours of sunshine does the house get every day?

! How much energy does the owner need every month?

What kind of batteries and solar panels would serve the client’s needs while
minimizing the cost?

I E O R 1 6 0! BerkeleySOLAR

1

Solution

To answer these questions, we created five models 1:

1. Off grid but buying and selling power: This is not a feasible option for the user be-
cause the cost of the batteries needed to support the house during cloudy days exceeds
the payout from switching to solar.

2. On grid and selling excess power: In this situation, the user should install 103 solar
panels while selling to PG&E excess power during months when he doesn’t use as
much energy. After 25 years, the cost of the solar system panels would be $913. Also, be-
cause the cost of maintenance will be marginal compared to the cost of installation and
the lifetime of the solar panels are longer than what we outlined, the user would be
making revenue after 25 years. Also, we based our interest rate on 4% which could
change over time and did not factor the refinancing value of the home after switching to
solar.

3. Completely off grid getting nothing for excess power: This model was very difficult
to justify. Although it is possible to go off grid with the size of the roof and the amount
of sunshine Berkeley gets, we had to completely omit the budget constraint due to the
large costs.

4. Optimizing the battery’s cost over lifetime: To factor in key characteristics for our
ideal battery, we researched multiple batteries and created a model that used cost over
lifetime and added multiple constraints. After putting the batteries through this model,
we found that the Premium Surrette performed the best.

5. Minimizing the cost of solar panels: Before subjecting our choices through the model,
we limited our options to panels that fit four key characteristics that will be outlined
later. We finally settled on the Evergreen 210W panels due to it’s lower cost per watt,
but still decent efficiency and a low impact on the environment.

1 See appendix D-F for all models.

2

Recommendations

From our model, we found that the best option for our client would be to go with the
on-grid option and sell excess power to PG&E. Although the client can feasibly go off-
grid, it would be in his best interest to stick with the second model because it is the most
likely to ﬁt in his budget. The key issue with solar panels is that their cost does not jus-
tify their low efﬁciency and the main barrier in this is a lack of technological research in
solar panels. If the user goes on-grid, he will be able to get governmental aid in the form
of the California Solar Initiative as well as tax rebates. That way, he will reach his break-
even point sooner and can later invest in cheaper solar technology.


3

Task List
1. Research general solar power system background information to see what com-
ponents need to be considered.

2. Determine how much power the system needs to provide to be fairly certain that
he will not ever use more than this amount of power.

3. Research all things about batteries including information about their capacities,
lifetimes, sizes, brands, costs, etc.

4. Find optimal battery.

5. Research different panels including their wattage, size, efﬁciency, costs, etc.

6. Research costs projected by different contractors for the average home in Ber-
keley.

7. Research federal tax deductions and California Solar Initiatives.

8. Research variances in weather and sunlight availability in Berkeley.

9. Create models for different options:

1. Have contractor build your system design, on grid.

2. Build your own system, off grid

3. Have contractor build your system, off grid, but can buy and sell power

10. Solve models.

11. Write executive summary and recommendations.

12. Create PERT chart.


4

PERT Chart

Task # Time (in days) Corresponding Nodes Completed By:
1 1 Start, A Rhonda, Regine, Kenneth, Nas-
sim, Miranda
2 0.2 A,B Miranda
3 5 B,D Rhonda, Kenneth, Nassim
4 0.5 D,E Kenneth
5 2 B,C Regine
6 0.5 B,F Regine and Rhonda
7 0.2 B,G Regine, Miranda, and Rhonda
8 1 B,H Miranda
9 2 I,J Miranda and Regine
10 1 J,K Rhonda, Regine, Kenneth, Nas-
sim, Miranda
11 1 K,L All
12 0.2 L,M Miranda


5

Design Objectives - Solar System Batteries
Solar System Batteries

Since we have decided to go off the grid, a battery backup system is required to save the
excess energy gained during the day for nights and cloudy days. This means the batter-
ies would be deeply discharged on regular basis. For a solar system, the following bat-
teries are offered by different vendors:

• Lead-acid Batteries are made of lead electrode plates submerged in dilute sulfuric
acid as an electrolyte. They are readily available in the market and have low ini-
tial cost. These batteries can be designed for either shallow or deep cycle usage.
oShallow cycle batteries are designed to supply a large amount of current for
a short time but they cannot tolerate being deeply discharged frequently.
oDeep cycle batteries are designed to be repeatedly discharged by as much as
80% of their capacity (Depth of Discharge, DOD).
• Marine batteries are made of lead sponge electrodes and considered to be a “hy-
brid” of starting and deep cycle battery.
• Gelled Deep Cycle contains an acid gel which means if it’s broken, the acid does
not leak. But, this type of batteries must be charged at a slower rate and lower
voltage to prevent excess gas from damaging the cells.
• Absorbed Glass Mat (AGM) Batteries are made of ﬁne ﬁber Boron-Silicate glass
mats which contains the acid. These batteries also don’t leak acid if broken.


6

Fig. 1 demonstrates the life span of these batteries if they are used in deep cycle service.
According to this plot, “Industrial Deep Cycle” battery demonstrates the longest life

30 Years
(max)
Years
(min)

23
Years

15

8

0
Marine Gelled
Deep
Cycle Industrial
Deep
Cycle

span, followed by “Rolled Surrette® Deep Cycle”.

Figure 1: Life span of batteries used in "Deep Cycle Services" (Source:
www.windsun.com, deep cycle battery FAQ)

Choosing the Best Battery

In general, Lead-acid batteries are cheaper and last longer than Marine, AGM
and Gelled batteries, but they are not as safe as the latter ones. So, in order to make the
right selection, ﬁrst we need to make some assumptions for our problem:

Assumption 1) The batteries will be used in an off-grid, full-time home for an indeﬁ-
nitely long time, therefore, capacity and long term cost will be the most important fac-
tors.

Assumption 2) The batteries will be placed in the resident’s home and not in a remote
site; therefore, maintenance is not much of a concern in our choice of batteries. Price
and lifetime is valued over maintenance in our research.

Assumption 3) The batteries are stored in a place where the temperature does not fell
under 50°F below which the batteries capacity starts to decline.

Assumption 4) Nickel-Cadmium batteries were not considered in our analyses because
they are “extremely toxic to the environment and require very expensive disposal” (3).

7

Therefore, the user will most probably not want to store them in his house and they will
end up costing more to dispose of than buying new lead-acid batteries.

Assumption 5) We do not consider Lithium ion batteries because they are extremely ex-
pensive for this specific type of application.

Assumption 6) The user have no constrains on his/her initial capital investment and
has enough and appropriate space to store the batteries and the solar panels.

Within different brands of lead-acid batteries, Surrette® repeatedly is reported as the
most efficient and economical choice by vendors and contractors.2 Our initial calcula-
tion for lifetime cost has confirmed3. In particular, Premium Surrette 500 (12CS11PS)
excels over all the other batteries in an economic sense. The initial up front expense may
be out of reach for some customers, but given its lifetime, it is the cheapest.4

In contrary to “sealed” batteries, Surrette® batteries require frequent maintenance,
which after researching and discussing in detail below does not alter our choice of bat-
tery.

Maintenance Cost

As mentioned earlier, AGM and Gel batteries are almost maintenance free. There are
also so-called Lead-Acid “Sealed” batteries which needs to be replaced every 5-7 years
in the exchange of no maintenance throughout these years. These batteries are not eco-
nomically suited for our purpose.

The maintenance of Flooded Lead Acid-Surrette 500 batteries require “watering, equal-
izing charges and keeping the top and terminals clean” (7). One of the websites our
group researched that supported AGM batteries, conducted numerical analyses of the
price difference between Surrette® and AGM. Even after adding the electrolyte mainte-
nance costs, the Surrette Premiums 500® still remained the cheapest. (8)
Their calculation costs were based on some assumptions:

1) Cycle once a day

2
www.solarinfo.com,
www.rollsbattery.com,
www.dcbatteries.com

3
For
further
detail
on
battery
calculation
refer
to
page
27

4
Based
on
Assumption
1

8

2) Hiring someone and paying him“$20/hr” for maintenance chores

3) Each battery requires ¼ hour maintenance each month

4) Each cell requires ¼ qt of $ 1/qt distilled water that equates to
$0.000583/(Ah*cycle) for Surrette 400 and $0.00049 (Ah*cycle) for Surrette 500
Table 1: Maintenance cost per cycle for various batteries (Source: www.vonwentzel.net)

Lifeline
AGM Surrette
400 Surrette
500
Adjusted
Cost($) 0.0015 0.00147 0.00108

Acid Leakage and Durability

The Premium Surrette 500 (12CS11PS) utilizes the new generation “dual container
modular construction” (6). This feature eliminates breakage and subsequently acid
leakage due to rough handling or abuse. Even if the outer container were to break, the
battery would still operate without any acid spills (7). Therefore, Premium Surrettes are
safe for our user to store in his garage or a battery room in his house. In addition, these
batteries can be installed without any special skills or tools. Therefore, our user is going
to highly value this option, since he wants to save as much money as possible.

Our analyses and assumptions show that Premium Surrette 500 (12CS11PS) cells
are unsurpassed in the qualities they offer. Their higher cycle lives compared to their
budget competition, their durability, their thick lead plates and not having to replace
them every few years makes them an attractive economic choice, even if their up-front
price is not the most economical (4).

Determining the Optimum Battery Capacity

In order to ﬁnd the optimum battery capacity, ﬁrst we looked at customer’s average
daily usage based on Kwh-hr. In order to be in safe side, we decided to design a storage
system that would provide up to 5 times of this capacity in case of an emergency. This
number is an industry standard. Next, given their ampere-hour5, depth of discharge6,
and the cost of the batteries, we calculated the lifetime cost of different batteries.

5
Ampere-hour
is
a
measure
of
a
battery’s
capacity
(e.g.
6
Amp-hr
battery
can
maintain
a
current
of
1
Ampere

for
6
hours)

6
Depth
of
Discharge
(DOD)
is
the
extend
at
which
a
battery
is
being
discharged

9

The depth of discharge affects the lifespan of batteries. For example, Fig. 2 demonstrates
the effect of DOD on the lifecycle of Surrette 400 and 500 series.

5000

3750
#
of
cycles

2500

1250

0
0 25 50 75 100
DOD
(%)

500
Series
400
Series

Figure 2: Surrette(R) batteries’ lifecycle vs. %DOD (Source: www.surrette.com)

Since we will have batteries for 5 times of the user’s average usage, we assume the bat-
teries rarely go beyond DOD of 50%. Now, our goal is to ﬁnd which battery would offer
the minimum lifetime cost.

Minimizing the Lifetime Cost of the Battery System7

Given
the
ampere-‐hour
and
the
hour
rating,
we
were
able
to
determine
the
maxi-‐
mum
current
that
would
be
pulled
from
the
battery
to
last
for
20
hours.

Then,
with
the

given
voltage
and
the
calculated
current,
we
were
able
to
calculate
the
maximum
energy
in

Kilowatt-‐hours
by
multiplying
the
voltage
and
current
and
dividing
by
1000
to
convert
it
to

the
correct
units.

7 Refer to the appendix for the numerical results of the model

10

In
order
to
determine
the
number
of
batteries
to
buy,
it
was
necessary
to
make
the

deJinition
of
the
number
of
batteries
to
buy
be
a
function
in
terms
of
the
depth
of
discharge.

Because
each
battery
had
a
different
maximum
energy,
a
different
depth
of
discharge
had
to

be
used
for
each
battery.

Also,
the
chosen
depth
of
discharge
for
each
battery
would
affect

the
number
of
batteries
bought,
with
lower

requiring
more
batteries
due
to
the
low
level
of

drain
on
the
battery.

The
numerator
of
that
function
was
obtained
by
Jinding
the
average

daily
energy
usage
of
the
household
which
ended
up
being
approximately
20KWH.

The
av-‐
erage
daily
energy
usage
was
used
because
that
would
reJlect
the
average
amount
of
energy

drained
from
the
battery
each
day,
which
would
give
a
more
realistic
analysis
of
the
cost
per

cycle
through
a
more
accurate
cost
and
lifetime
determination.

Because
there
are
some

days
where
the
sun
will
not
shine,
and
the
battery
will
not
charge,
the
battery
energy
capac-‐
ity
should
be
greater
than
the
average
daily
discharge.

Five
times
the
average
daily
usage

was
used
because
the
probability
of
having
Jive
days
of
no
sunshine
is
very
small.

There-‐
fore
the
number
of
batteries
required
was
determined
using
the
total
energy
required,
mul-‐
tiplied
by
Jive
and
dividing
it
by
the
total
energy
of
the
battery
that
will
be
taken
from
each

battery
at
that
depth
of
discharge
and
rounding
up.

Total
cost
was
then
determined
by
multiplying
the
number
of
batteries
by
the
price

given.

The
lifetime
in
cycles
is
determined
by
using
a
function
which
is
different
for
each

battery,
and
the
depth
of
discharge,
which
determined
the
lifetime
of
the
battery.

The
cost

per
cycle
of
each
battery
was
then
found
and
the
battery
with
the
lowest
cost
per
cycle
is

the
one
chosen
to
be
the
most
optimal,
with
an
optimal
battery
capacity
equal
to
the
com-‐
bined
capacity
of
the
battery
chosen
and
the
number
of
batteries
bought.

Battery Cost Optimization Results

As it was discussed earlier, we can safely assume that the batteries rarely would
be discharge above 50% of their capacity since the user stores electricity five times of
his/her average daily usage. Based on manufacturers’ data on corresponding number of
lifecycles to DOD, we found the minimum cost per cycle that is required for the resi-
dence to completely supply his own energy, for approximately four days without re-
charging. The cheapest battery cost per cycle according to our calculation is $8.96. It
means that we need to buy 42 of the Premium Surrette® 500 (12CS11PS) batteries.

We need to mention, there are also some aspects of the battery selection that can
affect our final decision but not easy to incorporate into the model. The saving of using
500 series battery is $120 per year which for twenty-five years translates to $1080 (as-
suming 10% discount rate). The resident can save on the front cost of batteries by buy-


11

ing Surrette® 400 series and invest the difference in the market. Hopefully, 8 he is able to
at least earn twice as this future saving. That decision is based on the customer’s per-
sonality and lifestyle.

The model also doesn’t take into the account the energy loss by the wires. By having
more wiring, there is more energy loss during transportation. So a battery of a larger
voltage, say 6V, would lose less energy than several batteries of smaller voltage, say
three 2V’s. So, the user may want to consider using the same series of the batteries our
model suggest but pick the one with higher voltage. Also there is energy lost during the
conversion of DC to AC and that is not taken into account our model either.

Conclusion

The total storage capacity would then be 172 KWH with a Depth of Discharge of 50%. It
is feasible to go completely off the grid but it is an ill advice based on the battery costs
alone. If one chose to go off grid, one would have to pay at least $8.96 dollars per cycle.
Each cycle is one day, so the cost per month would be 268.8 dollars, much more than the
price of electricity from PG&E. Also the weight and volume demand for storage of
batteries would exceed the typical free space in a typical household. The volume
required for all of the batteries is 110 Cubic feet and would weigh 11,424 lbs., a space of
which one would be hard pressed to ﬁnd in Berkeley.

8
Assuming
no
recession
for
foreseeing
future

12

Design Objectives - Solar System Panels
Choosing the best solar panels

Every square meter of the Earth’s surface receives approximately 164W of solar energy
from the sun. If we could cover 1% of the Sahara desert with solar panels, we could
generate enough electricity to power the entire world. Although we could potentially
harness the sun’s energy to satisfy all of our needs, the technology currently available
can only harness, at most, 20% of that power. As is frequently said in the solar industry,
“not all solar panels are created equal.” Therefore, we based our choice in solar panels
on the following four criterions:

1. Minimum warranted power rating - This is the amount of power guaranteed by the
manufacturer that the solar panel can generate. In some solar panel specification
sheets, this was also known as the negative tolerance rating. Generally, a good solar
panel would have a negative tolerance rating at 5% or less.
2. PVUSA Test Conditions (PTC): PVUSA is an independent lab that releases a PTC rat-
ing for all solar panels listed under the California Solar Initiative. Compared to the
STC (Standard Test Conditions) rating that manufacturing companies use, the PTC
tests the panels under more extreme, real-world conditions.
3. Efficiency Rating: This is the most well-known rating since researchers are focused on
creating a low-cost high-efficiency solar panel. The higher this efficiency, the more
power attainable per square inch of the panel surface.
4. UL Listing: Underwriters Laboratories is a product rating company that tests the
safety of products. They test solar panels for their mounting method, weather resis-
tance, performance, as well as other safety considerations and have a large photovol-
taic testing site in Silicon Valley. Products that pass UL’s harsh tests are often adver-
tised as UL Listed.

After passing the four constraints, we narrowed our options to two solar panels which
excelled in either efficiency, or environmental impact and affordability.

The Sanyo 195W PV module, compared to the average 12% efficiency of most panels,
surpasses them with a 19.7% cell efficiency. They do this with a patented HIT (hetero-
junction w/ intrinsic thin layer) technology that allows the PV module to obtain max

13

power within a fixed space. This creates a lower de-rating related to temperature. In
other words, as the temperature increases, these solar panels produce 10% or more elec-
tricity than conventional crystalline silicon modules. The PV design reduces recombina-
tion loss of the charged carrier by surrounding the energy generation layer of single thin
crystalline silicon with high-quality ultra-thin amorphous silicon layers. The solar pan-
els operate silently with no moving parts and are among the lightest per watt in the in-
dustry. They have a PTC rating of 180.9W and its packing density reduces the transpor-
tation, fuel, and storage cost per installed watt.

Evergreen’s 210W PV modules are ideal for grid-tied solar systems and feature anti-
reflective glass, an anodized aluminum frame, 108 cells per panel, and watertight junc-
tion boxes that require zero maintenance. All panels have a minimum warranted power
of -0/+5W, have a PTC rating of 180.7W, and are independently tested by four labs that
regularly check panel power so the power given is the power promised. The anti-
reflective glass delivers 2-3% more electricity than panels containing standard glass and
maintains 4% higher output than most other crystalline silicon panels under hot condi-
tions. The amount of time it takes for the environmental footprint of the manufacturing
process to be offset by the clean energy created by the PV module is called the “low en-
ergy payback.” Evergreen’s products can recoup the environmental impact in a year
with a combination of efficiency and environmentally responsible manufacturing proc-
esses. The Evergreen Spruce PV module produces 30g of CO2 per equivalent kWh as
well as uses less lead than other panels thanks to lead-free solder.

BRAND PTC PRICE/ AREA MAX # OF PRICE/
PA N E L (FT^2) PA N E L S WAT T

Evergreen 210W 180.7 $643 16.93 93 $3.49

Sanyo 195W 180.9 $915 12.47 125 $5.06


14

The Optimal Tilt Angle for Fixed Solar Panels

The optimal orientation for solar panels would be to align the face of the solar
panel with the sun. However, that would require continuous adjustments of the solar
panel. It is too expensive to purchase the equipment to adjust it continuously and, there-
fore, changing the tilt angle to its daily and monthly optimal values is not practical, if
the panels are mounted on the roof, or economical for our user. As professor Glassey at
the Industrial Engineering and Operations Research department at UC Berkeley sug-
gested and many solar panel websites our group consulted, tilting the ﬁxed plate by an
angle equal to the latitude seems to be the most practical solution. At this tilt, if the col-
lector is facing south, our case, since the user lives in the Northern Hemisphere, the sun
will be “normal to the collector at noon twice a year” at the “equinoxes”, when day and
night are equal length. The noontime sun will only vary “above and below this position
by a maximum angle of 23.5 degrees”.8

Our group research presents the results of a study that was conducted on two
south facing sites in Albuquerque, New Mexico and Madison Wisconsin. Figure 2.4
shows that by titling at the latitude, the user will only be slightly below the maximum
yearly irradiation optimal position. The ﬁgure shows that variations in the tilt angle do
not affect the irradiation received by much and therefore, given the amount of money
and work the user has to invest in order to reach an optimal tilt angle each day, it is not
worth his/her effort or money, because the amount of irradiation difference is
minimal.8


15

Hence, the user should tilt the ﬁxed panel at the latitude angle, which is 37.87 from
horizontal, because it is easiest, cheapest and will maximize annual performance.

Figure 2.4 Total irradiation south-facing tilted surfaces

_________________

8. http://www.powerfromthesun.net/Chapter6/Chapter6.htm#6.3.1%20Orientation


16

Problem Analysis
Determining the Monthly Demand

In order to determine how much demand the client would need monthly, our group
ﬁrst assumed that the given KWH billed for this year and last year have a normal dis-
tribution. Using this assumption, the average and standard deviation of the two data
sets were calculated. More data would have made the data sets more accurate, but our
group was only given two, so we worked with what we had. According to the normal
distribution, approximately 95% of data is located within two standard deviations of the
mean. Thus, we made our target demand for each month equal to the average plus two
times the standard deviation, so that we could be 97.5% sure that his demand would
never exceed this value.

Determining the Average Amount of Sunlight in Berkeley

In order to determine the average amount of sunlight that was available (kWh/m^2/
day) to the solar panels in Berkeley, we used the triangular distribution presented in


17

class. The Renewable Resource Data Center website provided us with information
about the available solar insolation in Berkeley, taking into account cloudy days and
monthly temperature variations. Since we were only given one set of averages, maxi-
mums, and minimums for each month, we used the triangular distribution to find the
standard deviation of the data.

Firstly, the website only provided us with the solar insolation values for a 15 degree tilt
and a 90 degree tilt. Since our optimal design required an approximately 38 degree tilt,
we had to extrapolate the data. Upon making the assumption that the data was ap-
proximately linear, we used the degree of tilt as our x value and the solar insolation as
our y value and calculated a line for each month passing through the two points (15, in-
solation[i]) and (90,insolation[i]). First, the slopes were calculated. Next, using the
equation , plugging in the point (15, insolation[i]) for (x1,y1), and then plugging in x=38,
we obtained the insolation (y) value for a tilt of 38 degrees. We performed this iteration
for each month’s average, maximum, and minimum insolation values. Next, in order to
find the standard deviation, we assumed that the average given was equivalent to the
mode, and we found the standard deviation formula on Wikipedia. Using this formula,
the averages, the maximums, and the minimums, we calculated the standard deviation
for each month. Adding and subtracting 2*standard deviation from the average, we ob-
tained a 95% confidence interval. To be safe, we assumed that the available amount of
sunlight would be equal to the lower bound of this confidence interval. In taking the
lower bound of the confidence interval to be our assumed solar availability for each
month, we are 97.5% sure that the amount of available solar insolation will never be less
than this value. Thus, we are 97.5% sure that there will always have enough sunlight to
provide an adequate amount of power to our system.


18

Models - Introduction
These are the variables and parameters that show up in our models. The ones with an
asterisk next to them (*) are the variables/parameters that don’t show up in every
model

Variables

*net[i]= If negative, the system did not produce enough energy in month I and the con-
sumer
must purchase this much. If net[i] is positive in month i, then the system produced more
than
needed and the consumer will sell it.

np = number of panels>=0

*nb = number of batteries>=0

p = If 0, then no panels were produced and therefore no installation costs were incurred
and no
tax can be deducted. If p=0 then they can.

Parameters

ce= cost to purchase electricity/price to sell back electricity

cp = cost of each solar panel

LI = labor and installation cost (equal to $7-$9 dollars per watt)

nmc = number of miscellaneous costs (inverter, controller, maintenance)

LT[j] = lifetime of each of the miscellaneous components

mc[j] = cost of each miscellaneous component

Budget = maximum initial budget

d[i] = demand for each month

*bc = cost of each battery

*ltb = lifetime of each battery

19

*E = maximum useable energy within battery

*dod = depth of discharge of battery

sun[i] = sunlight availability per day per m^2 in month i

sigmas[i] = standard deviation of available sunlight in month i

sigmad[i] = standard deviation of demand in month i

A = area of one panel in m^2

Eff = efﬁciency of the panels


20

Model 1
Introduction: Off-Grid, Solar Contractor (Buy/Sell Power)

In this model, the consumer is off grid but can buy/sell power that he needs/has over-
produced. The objective function is to minimize the net present value of the costs in-
curred over a 25 year project lifetime.

The term is a summation of the consumer’s costs from buying extra energy that he
needs and the revenues from selling power in the months he has excess. If in month i
net[i]>0 then this means that he has produced excess power and will sell it at price “ce”
(we are making the assumption that the price to sell energy is equal to the price to buy
it). Thus, if net[i]>0 then the cost is subtracted, whereas if net[i]<0 then the cost is added
to the total cost.

The term is the annuity formula, where “ ” is the money that we dis-
count back each year for the duration of 25 years at a rate of 4%. In order to simplify our
calculations, we assumed that the interest was compounded at the end of each year, so
that the fact we discounted the sum of the payments at the end of each year rather than
discounting them each month does not make a difference.

The term represents the total discounted cost of both the initial batteries and their re-
placements over the 25 year period. We made the assumption that you have to buy new
batteries every “ltb” years. So, if the lifetime of the battery is 10 years then we have to
buy a battery every 10 years (i.e. in year 0, 10, and 20). Ceil(25/ltb) is equivalent to 25
divided by ltb rounded to the next highest integer (i.e. ceil(25/10)=ceil(2.5)=3). This de-
termines, based upon the lifetime of each battery (ltb) in years, how many times you
will have to buy new batteries throughout the project lifetime of 25 years, assuming that


21

you have to buy them every “ltb” years. We start at time t=0 because you must buy
parts for the installation now.

The term is a summation of the j miscellaneous parts, such as controllers, inverters,
mounting systems, and switches. The parameter LT[j] is the respective lifetime of mis-
cellaneous cost j; here we assume again that we must buy a new miscellaneous part
every LT[j] years. Of course, there are more costs, but we are assuming that the rest are
negligible in comparison.

The term takes into account the Federal Tax Deduction of 30% of total costs (not includ-
ing batteries) for people who go “off the grid”. Unfortunately, when people go off the
grid, they do not qualify for the California Initiative, which compensates you for an ad-
ditional 13% of the total after tax rebate costs.

-1318*

Lastly, the term is the “revenue” that you save by not having to pay your monthly PGE bills. The

term -1318 is the average amount that Berkeley residents pay for their PG&E bill and
discounts this annual payment back at a 4% discount rate for the duration of the project lifetime.


22

AMPL Model: Minimizing the Objective Function


23

Constraints

Constraint #1 is the budget constraint, which says that the initial investment that the
consumer made on the solar power system does not exceed the amount (“Budget”)
available to him. This brings me to another assumption: in order to simplify our calcula-
tions we are assuming that this person has savings from which he can invest this
money, rather than having to deal with complications of a loan and loan payments.

Constraint #2 is binary and is determinant of whether or not certain costs associated
with actually installing the system will be incurred. In some of the models it was opti-
mal to not build the solar powered system, and to instead just stick with PGE bills, so
the installation and labor costs would not be incurred. Constraints and costs multiplied
by variable p are the constraints and costs that are only applicable if the system is actu-
ally built, and equal to zero if it is not.

Constraint #3 makes sure that your power demands are met. As explained earlier, net is
the variable which measures the amount that you must purchase in order to have an
adequate amount of power (if negative), and the amount by which you have exceeded
your power needs and can sell back (if positive).

Constraint #4 ensures that the panels do not exceed the available roof space.

Constraint #5 ensures that we have adequate battery capacity to store the energy we
need, and is explained further in the “Battery” section of our paper.

Constraint #6 is a measure of installation costs, which we have found is approximately
$8 per watt. Thus, constraint #6 ﬁnds the wattage of our system and multiplies it by 8
dollars to get total installation costs.


24

Model 2
Introduction: On-Grid, Solar Contractor

This model is essentially the same as Model #1, except now the person is connected to
PGE. We modeled the net again like revenue for two reasons. One, PGE gives you the
option of a plan where they do buy back your excess energy, and sell you energy in the
months that you do not have enough. Two, even if you choose to go with the plan in
which you buy extra energy and PGE credits you for future electricity (in this case you
would qualify for the California Solar Initiative), the electricity that you don’t have to
pay in the future is like revenue. For simplicity, we will assume that the person is selling
to PGE excess power and buying power that he did not make enough of himself.

Thus, everything is the same as in the previous model except batteries are not included
in the cost or the constraints because the consumer does not need them.

AMPL Model


25

Model 3
Introduction: Off-Grid, Solar Contractor (No Buy/Sell Power)

In this scenario, the person is completely off grid and does not have the means to buy or
sell to anyone; for this reason the variable “net” is not included in the objective function,
because whatever he makes extra is lost. Due to the fact that he must sustain himself
completely, we have added the constraint that all values of “net” must be greater than
or equal to zero. If during any month net<0, then he did not have enough energy and
his power went out. Lastly, since the panels must be built if he wants any electricity at
all, p will equal one no matter what.


26

AMPL Model


27

Works Cited
"Batteries Catalog." Kyocera Solar. N.p., "Surrette Rolls are the crown jewels of DC
n.d. Web. 6 Dec 2010. batteries." N.p., n.d. Web. 6 Dec 2010.
<www.dcbattery.com>.
<www.kyocerasolar.com>.

"How about Nickel-Cadmium Cells?" N.p., "NASA Surface Meteorology and Solar En-
n.d. Web. 6 Dec 2010. ergy." NASA Langley Atmospheric Science
<www.vonwentzel.net>. Data Center (Distributed Active Archive Cen-
ter). Web. 06 Dec. 2010.
<http://eosweb.larc.nasa.gov/cgi-bin/sse/grid.c
"Life span of batteries used in "Deep Cycle gi?>.
Services" ." Web. 6 Dec 2010.
<www.windsun.com>. "Solar Calculator." Solar Power Facts and
Helpful Info. Web. 06 Dec. 2010.
<http://www.solartradingpost.com/calcu
"My third letter." Von Wentzel Family Site. late.php?name=5>.
N.p., n.d. Web. 6 Dec 2010. "SOLAR RADIATION FOR FLAT-PLATE
<http://www.vonwentzel.net/>. COLLECTORS FACING SOUTH AT A
FIXED-TILT." Renewable Resource Data Cen-
ter (RReDC) Home Page. Web. 06 Dec. 2010.
<http://rredc.nrel.gov/solar/old_data/ns
"Renewable Energy 2010 Design Catalog."
rdb/redbook/sum2/23234.txt>.
N.p., n.d. Web. 6 Dec 2010.
<www.aeesolar.com>.

"Solar Series 5000." Kyocera Solar. N.p.,
n.d. Web. 6 Dec 2010.
<www.kyocerasolar.com>.

"Solar Series 5000." Pure Energy Systems.
N.p., n.d. Web. 6 Dec 2010.
<www.pureenergysystems.com>.

"Surrette(R) batteries’ lifecycle vs. %DOD
." Web. 6 Dec 2010. <www.surrette.com>.

28

Appendix A - Battery Selection
The Premium Surrette® 500 (bold numbers in the table below) is our ﬁnal selection for the battery system

Table
2:
Summary
of
calculations
for
battery
selection
based
on
the
model

Ampere-
Hour
#
to
Cost
per

Battery Voltage Current Power Max
KWH DOD KWH Lifetime Price Total
Cost
hours rating buy Lifetime
Lifeline
AGM

12 225 20 11.25 135 2.7 0.5 1.35 64 1000 $387.00 $24,768.00 $24.77
(8D)
West
Marine

12 225 20 11.25 135 2.7 0.5 1.35 64 500 $449.00 $28,736.00 $57.47
Gel
(8D)
Inexpensive

Trojan
12 225 20 11.25 135 2.7 0.5 1.35 64 500 $152.00 $9,728.00 $19.46
(2xT105)
Premium

Surrette
400
12 221 20 11.05 132.6 2.652 0.5 1.32 65 1250 $246.00 $15,990.00 $12.79
(HT8DM)
Premium

Surrette
500
12 342 20 17.1 205.2 4.104 0.5 2.05 42 3200 $683.00 $28,686.00 $8.96
(12CS11PS)
2-KS-33PS

(Surrette
2 1750 20 87.5 175 3.5 0.5 1.75 50 3300 $1,184.00 $59,200.00 $17.94
500
series)
4-KS-21PS

(Surrette
4 1104 20 55.2 220.8 4.416 0.5 2.20 39 3300 $1,703.00 $66,417.00 $20.13
500
series)
4-KS-25PS

(Surrette
4 1350 20 67.5 270 5.4 0.5 2.7 32 3300 $2,130.00 $68,160.00 $20.65
500
series)
6-CS-17PS

(Surrette
6 546 20 27.3 163.8 3.276 0.5 1.63 53 3300 $1,316.00 $69,748.00 $21.14
500
series)
6-CS-21PS

(Surrette
6 683 20 34.15 204.9 4.098 0.5 2.04 42 3300 $1,643.00 $69,006.00 $20.91
500
series)
6-CS-25PS

(Surrette
6 820 20 41 246 4.92 0.5 2.46 35 3300 $1,905.00 $66,675.00 $20.20
500
series)
Surrette
S-
460
(Sur-
6 350 20 17.5 105 2.1 0.5 1.05 82 1300 $484.00 $39,688.00 $30.53
rette
400

series)
Surrette
S-
530
(Sur-
6 400 20 20 120 2.4 0.5 1.2 72 1300 $550.00 $39,600.00 $30.46
rette
400

series)


29

Appendix B - Demand Calculations
Month KWH KWH Billed Average Variance Standard
De-‐ Average
KWH+2σ
Billed Previous year via1on
This Year
12 784 776 780 16 4 788
11 665 701 683 324 18 719
10 566 561 563.5 6.25 2.5 568.5
9 557 485 521 1296 36 593
8 396 459 427.5 992.25 31.5 490.5
7 465 526 495.5 930.25 30.5 556.5
6 507 472 489.5 306.25 17.5 524.5
5 421 509 465 1936 44 553
4 374 567 470.5 9312.25 96.5 663.5
3 646 413 529.5 13572.25 116.5 762.5
2 686 654 670 256 16 702
1 795 645 720 5625 75 870


30

Appendix C - Weather Calculations

Average
Solar
Insola1on
(In
KWH/m^2/day)

InsolaFon
with
InsolaFon
at
Slope
of
Line
Found

Projected
Insola-‐ Average
-‐
2σ
15˚
Tilt 90˚
Tilt From
Two
Points Fon
at
37.87
˚

January 3.7 3.3 -‐0.005333333 3.578026667 2.939376544
February 4.4 3.6 -‐0.010666667 4.156053333 2.926498113
March 5.1 3.7 -‐0.018666667 4.673093333 3.54510545
April 5.6 3.4 -‐0.029333333 4.929146667 4.012497307
May 5.7 2.8 -‐0.038666667 4.815693333 4.096906619
June 5.6 2.5 -‐0.041333333 4.654706667 3.930582018
July 5.9 2.7 -‐0.042666667 4.924213333 4.418053413
August 6.1 3.3 -‐0.037333333 5.246186667 4.570613507
September 6.1 4.1 -‐0.026666667 5.490133333 4.743232755
October 5.5 4.3 -‐0.016 5.13408 4.312633499
November 4.1 3.6 -‐0.006666667 3.947533333 3.241059534
December 3.6 3.3 -‐0.004 3.50852 2.447386298

Minimum
Solar
Insola1on

(In
KWH/m^2/day)

InsolaFon
with
15˚
InsolaFon
at
90˚
Slope
of
Line
Found

Projected
InsolaFon
at

Tilt Tilt From
Two
Points 37.87
˚

January 2.8 2.5 -‐0.004 2.70852
February 3.1 2.4 -‐0.009333333 2.886546667
March 3.8 2.7 -‐0.014666667 3.464573333
April 4.2 2.6 -‐0.021333333 3.712106667
May 4.8 2.5 -‐0.030666667 4.098653333
June 4.7 2.3 -‐0.032 3.96816
July 5.6 2.6 -‐0.04 4.6852
August 5.3 3 -‐0.030666667 4.598653333
September 5.2 3.5 -‐0.022666667 4.681613333
October 4.3 3.4 -‐0.012 4.02556
November 3.2 2.8 -‐0.005333333 3.078026667
December 2.1 1.9 -‐0.002666667 2.039013333


31

Triangular
Distribu1on
Standard
Devia1on
Variance

0.101968495 0.319325061
0.37795151 0.61477761
0.318089166 0.563993942
0.210061512 0.45832468
0.129163585 0.359393357
0.131089127 0.362062324
0.064049466 0.25307996
0.114099774 0.33778658
0.139465118 0.373450289
0.168693588 0.41072325
0.124776307 0.3532369
0.281501183 0.530566851

Maximum
Solar
Insola1on

(In
KWH/m^2/day)

InsolaFon
with
15˚
InsolaFon
at
90˚
Slope
of
Line
Found

Projected
InsolaFon
at

Tilt Tilt From
Two
Points 37.87
˚

January 4.3 4.2 -‐0.001333333 4.269506667
February 6.1 5.4 -‐0.009333333 5.886546667
March 6.8 4.9 -‐0.025333333 6.220626667
April 6.9 3.8 -‐0.041333333 5.954706667
May 7.1 3 -‐0.054666667 5.849773333
June 7.1 2.6 -‐0.06 5.7278
July 7.2 2.8 -‐0.058666667 5.858293333
August 7.4 3.6 -‐0.050666667 6.241253333
September 7.3 4.7 -‐0.034666667 6.507173333
October 6.4 5.2 -‐0.016 6.03408
November 4.9 4.6 -‐0.004 4.80852
December 4.6 4.7 0.001333333 4.630493333


32

Appendix D - AMPL Model Outputs
Introduction

AMPL Assumptions

• In these ﬁles, sigmas are not included in the calculations because we used the
value of sun (calculated in our table) that already accounted for that
• We estimated/assumed that the total cost over the lifetime of inverter, controller,
mounting system would be approximately 3000
• We estimated/assumed that 1500 would be the initial cost of the inverter, control-
ler, mounting system
• Also assumed r=0.04 (i.e. 4%)
• Assumed sell back cost for electricity = cost to buy electricity which is approxi-
mately 12 cents

Model 1

param ProjectLife;
param sun {i in 1..12};
param d {i in 1..12};
param days {i in 1..12};
param ce;
param cp;
param A;
param budget;
param sigmad {i in 1..12};
param E;
param dod;
param eff;
param bc;

var net{i in 1..12};
var np>=0;
var nb>=0;


33

var LI>=0;
var p;

minimize cost: (sum{i in 1..12}
-net[i]*ce)*(1-1/(1+.04)^ProjectLife)/.04+cp*np+LI+bc*(365*ProjectLife)/3600*nb*+3000
*p- .3*(cp*np+LI+1500*p)-1318*p*(1-1/(1+.04)^ProjectLife)/.04;

subject to Budget: cp*np+bc*(365*ProjectLife)/3600*nb+LI+1500<=budget;
subject to MeetDemand {i in 1..12}: days[i]*(sun[i])*A*np*eff=d[i]+2*sigmad[i]+net[i];
subject to Roof: A*np<=1500/0.7894;
subject to Battery {i in 1..12}: nb>=if np=0 then 0 else ceil((d[i]+2*sigmad[i]+net[i])/
(E*dod));
subject to LabIns: LI = max {i in 1..12} ((d[i]+2*sigmad[i])/days[i])*(1000*8/24)*p;
subject to cool: p= if np=0 then 0 else 1;

data; ############ DATA STARTS HERE ############

param sun:= 1 2.94 2 2.93 3 3.55 4 4.01 5 4.10 6 3.93 7 4.42 8 4.57 9 4.74 10 4.31 11 3.24 12
2.45;
param d:= 1 720 2 670 3 529.5 4 470.5 5 465 6 489.5 7 495.5 8 427.5 9 521 10 563.5 11 683 12
780;
param days:= 1 31 2 28 3 31 4 30 5 31 6 30 7 31 8 31 9 30 10 31 11 30 12 31;
param ce:= 0.12;
param ProjectLife:= 25;
param cp:=868;
param A:=1.164;
param budget:= 100000;
param sigmad:= 1 75 2 16 3 116.5 4 96.5 5 44 6 17.5 7 30.5 8 31.5 9 36 10 2.5 11 18 12 4;
param E:=4.104;
param dod:=0.5;
param eff:=.197;
param bc:=683;


34

Output:
MINOS 5.51: optimal solution found.
1 iterations, objective 14605.39498
Nonlin evals: constrs = 6, Jac = 5.
: _varname _var :=
1 'net[1]' -870
2 'net[2]' -702
3 'net[3]' -762.5
4 'net[4]' -663.5
5 'net[5]' -553
6 'net[6]' -524.5
7 'net[7]' -556.5
8 'net[8]' -490.5
9 'net[9]' -593
10 'net[10]' -568.5
11 'net[11]' -719
12 'net[12]' -788
13 np 0
14 nb 0
15 LI 0
16 p 0
;

Therefore, if the user is off the grid, he/she has to pay a lot for batteries, so it would
be optimal for him to not invest in solar panels and buy all his electricity from PGE.


35

Model 2

param ProjectLife;
param ce;
param cp;
param A;
param budget;
param E;
param dod;
param eff;
param bc;

var net{i in 1..12};
var np>=0;
var LI>=0;
var p;

minimize cost: (sum{i in 1..12}
-net[i]*ce)*(1-1/(1+.04)^ProjectLife)/.04+cp*np+LI+3000*p-.3*(cp*np+LI+1500*p)-1318*
p*(1-1/(1+.04)^ProjectLife)/.04;

subject to Budget: cp*np+LI+1500<=budget;
subject to cool: p= if np=0 then 0 else 1;


36


param sun:= 1 2.94 2 2.93 3 3.55 4 4.01 5 4.10 6 3.93 7 4.42 8 4.57 9 4.74 10 4.31 11 3.24 12
2.45;
param d:= 1 720 2 670 3 529.5 4 470.5 5 465 6 489.5 7 495.5 8 427.5 9 521 10 563.5 11 683 12
780;
param days:= 1 31 2 28 3 31 4 30 5 31 6 30 7 31 8 31 9 30 10 31 11 30 12 31;
param ce:= 0.13;
param cp:=868;
param A:=1.164;
param sigmad:= 1 75 2 16 3 116.5 4 96.5 5 44 6 17.5 7 30.5 8 31.5 9 36 10 2.5 11 18 12 4;
param E:=4.104;
param dod:=0.5;
param eff:=.197;
param bc:=683;

OUTPUT:
: _varname _var :=
1 'net[1]' 1276.38
2 'net[2]' 1230.07
3 'net[3]' 1829.22
4 'net[4]' 2169.61
5 'net[5]' 2440.25
6 'net[6]' 2252.09
7 'net[7]' 2670.37
8 'net[8]' 2845.88
9 'net[9]' 2755.86


37

10 'net[10]' 2578.06
11 'net[11]' 1570.09
12 'net[12]' 1000.65
13 np 102.702
14 LI 9354.84
15 p 1
;

Therefore, the user can maximize his revenue by using 103 panels and producing ex-
tra and selling back what he doesn’t need. This way, the cost is only 913 dollars over
25 years. If he continued past 25 years his revenue would probably be positive. Also,
changes in interest rates over the years could also help.!

Model 3

**We had to take out constraint for budget

param ProjectLife;
param ce;
param cp;
param A;
param budget;
param E;
param dod;
param eff;
param bc;


38

var net{i in 1..12}>=0;
var np>=0;
var nb>=0;
var LI>=0;
var p;

minimize cost:
cp*np+LI+bc*(365*ProjectLife)/3600*nb+3000*p-.3*(cp*np+LI+1500*p)-1318*p*(1-1/(1+.
04)^ProjectLife)/.04;

subject to Battery {i in 1..12}: nb>=ceil((d[i]+2*sigmad[i]+net[i])/(E*dod));
subject to blah: p=if np=0 then 0 else 1;


param sun:= 1 2.94 2 2.93 3 3.55 4 4.01 5 4.10 6 3.93 7 4.42 8 4.57 9 4.74 10 4.31 11 3.24 12
2.45;
param d:= 1 720 2 670 3 529.5 4 470.5 5 465 6 489.5 7 495.5 8 427.5 9 521 10 563.5 11 683 12
780;
param days:= 1 31 2 28 3 31 4 30 5 31 6 30 7 31 8 31 9 30 10 31 11 30 12 31;
param ce:= 0.12;
param cp:=868;
param A:=1.164;
param sigmad:= 1 75 2 16 3 116.5 4 96.5 5 44 6 17.5 7 30.5 8 31.5 9 36 10 2.5 11 18 12 4;
param E:=4.104;
param dod:=0.5;
param eff:=.197;
param bc:=683;


39

output:
: _varname _var :=
1 'net[1]' 75.6
2 'net[2]' 149.185
3 'net[3]' 379.296
4 'net[4]' 584.642
5 'net[5]' 765.694
6 'net[6]' 698.742
7 'net[7]' 865.116
8 'net[8]' 979.361
9 'net[9]' 882.36
10 'net[10]' 817.737
11 'net[11]' 289.474
12 'net[12]' 0
13 np 45.2459
14 nb 719
15 LI 9354.84
16 p 1
;

In Model 3, we had to omit the budget constraint because it is so expensive. There-
fore, it is ill advisable to go completely off the grid.


40

Appendix E - Battery Cost Optimization
Minimizing the Cost per Lifetime

The eventual model that we decided to use in order to minimize the cost per lifetime of
the battery was:

The depth of discharge is the decision variable.

Constraint# 1: The life time of the battery is equal to a function of the Depth of Dis-
charge

Constraint # 2: The total cost of batteries from one type = the number of batteries
needed to meet demand multiplied by the price of one battery of a speciﬁc type.

Constraint# 3: The number of batteries to buy is calculated by using the Ceiling of the
total energy required divided by the energy multiplied by the depth of discharge


41

Appendix F - Solar Panel Cost Optimization
Minimizing the Cost per Watt

min u = xy + m
subject to x <= 1500 ft2/area of 1 solar panel
max wattage > demand

x is an integer
x = number of panels
y = price per panel
m = maintenance costs for 25 years


42

Appendix G - Solar Installation Costs
A1 Sun Inc.
ACME Electric
Acro Energy Tech, Inc.
Advanced Alternative Energy Solutions
Advanced Conservation Systems, Inc
Akeena Solar, Inc.
Albion Power Company, Inc.
Company

Alliance Solar Services
Alter Systems, LLC
American Solar Corp.
Applied Star Energy Systems
Borrego Solar Systems, Inc.
CA Solar Systems, Inc.
Century Roof and Solar
Clean Solar, Inc.
Gary Plotner
Global Resource Options
$0 $12,500.00$25,000.00$37,500.00$50,000.00
Costs


43

Appendix H - Night Hours v Months

12.500

12.275
Night Hours

12.050

11.825

11.600
1 2 3 4 5 6 7 8 9 10 11 12
Months (JAN-DEC)


44

Appendix I - kWh Bill for 25 Years
Month kWH $ $/kWh kWH $ $/kWh Ave. kwh/ $ $/kWh
billed Billed Cur- billed Billed Previ- kWH day Billed for
Cur- Cur- rent Previ- Previ- ous for for next 25
rent rent Year ous ous Year next 25 next 25 Years
Year Year Year Year Years Years
Jan 795.00 $188.00 $0.24 645.00 $128.00 $0.20 720.00 30 $158.00 $0.22
Feb 686.00 $145.00 $0.21 654.00 $132.00 $0.20 670.00 27.917 $138.00 $0.21
Mar 646.00 $129.00 $0.20 413.00 $55.00 $0.13 529.50 22.063 $89.00 $0.17
Apr 374.00 $46.00 $0.12 567.00 $100.00 $0.18 470.50 19.604 $72.00 $0.15
May 421.00 $67.00 $0.16 509.00 $93.00 $0.18 465.00 19.375 $79.00 $0.17
Jun 507.00 $92.00 $0.18 472.00 $81.00 $0.17 489.50 20.396 $86.00 $0.18
Jul 465.00 $79.00 $0.17 526.00 $100.00 $0.19 495.50 20.646 $88.00 $0.18
Aug 396.00 $59.00 $0.15 459.00 $78.00 $0.17 427.50 17.813 $69.00 $0.16
Sep 557.00 $112.00 $0.20 485.00 $85.00 $0.18 521.00 21.708 $98.00 $0.19
Oct 566.00 $116.00 $0.20 561.00 $114.00 $0.20 563.50 23.479 $115.00 $0.20
Nov 665.00 $136.00 $0.20 701.00 $151.00 $0.22 683.00 28.458 $144.00 $0.21
Dec 784.00 $184.00 $0.23 776.00 $181.00 $0.23 780.00 32.5 $182.00 $0.23
Total 6,862.00 6,768.00 6,815 $1,318.00
Aver- 571.83 $0.19 564.00 567.92 $109.83
age


45

Appendix J - Solar Power Calculator
System Speciﬁcations Berkeley, CA
Solar Radiance (kWh/sqm/day) 5.43
Ave. Monthly Usage (kWh/month) 3901
System Size (kWh) 29.82
Roof Size (sq. ft) 2981
Estimated Cost 208,708.60
Post Incentive Cost 140,252.18

Incentives
Federal Incentives
Tax Credit 30%

State Incentives
Property Tax Exempt

Local Inventives
Rebate (for PG&E) .35/W AC

Savings
Estimated Cost 208708.60
Post Incentive Cost 140,252.18
Ave. Monthly Savings 570
25 Year Savings 284,858.01
25 Year ROI 203.10%
Break Even 15.27 Years

Carbon Emissions
Annual Carbon Dioxide Usage (pounds) 70,209
Driving Equivalent 77,800 miles
Offset by planting: 176 trees/year


46

The perfect solar design for a berkeley home

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The perfect solar design for a berkeley home