the perfect solar design for a berkeley home

BERKELEYSOLAR

PREPARED FOR: BERKELEY CLIENT, PROFESSOR GLASSEY

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

MIRANDA ORTIZ, CHRISTINA YOU

I E O R 1 6 0Final Project

U n i v e r s i t y o f C a l i f o r n i a , B e r k e l e y I E O R 1 6 0 F I N A L P R O J E C T

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! 13U C B e r k e l e y! I E O R 1 6 0 F i n a l P r o j e c t

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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! 33U C B e r k e l e y! I E O R 1 6 0 F i n a l P r o j e c t

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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

U C B e r k e l e y! I E O R 1 6 0 F i n a l P r o j e c t

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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! B e r k e l e y S O L A R

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Solution

To answer these questions, we created five models1:

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.


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1 See appendix D-F for all models.

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.


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Task List1. 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.


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PERT Chart

Task # Time (in days) Corresponding Nodes Completed By:1 1 Start, A Rhonda, Regine, Kenneth, Nas-

sim, Miranda2 0.2 A,B Miranda3 5 B,D Rhonda, Kenneth, Nassim4 0.5 D,E Kenneth5 2 B,C Regine6 0.5 B,F Regine and Rhonda7 0.2 B,G Regine, Miranda, and Rhonda8 1 B,H Miranda9 2 I,J Miranda and Regine10 1 J,K Rhonda, Regine, Kenneth, Nas-

sim, Miranda11 1 K,L All12 0.2 L,M Miranda


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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.


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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

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).

0

8

15

23

30

Marine Gelled Deep Cycle Industrial Deep Cycle

Years

Years (min)Years (max)


7

http://www.windsun.com


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


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2 www.solarinfo.com, www.rollsbattery.com, www.dcbatteries.com 3 For further detail on battery calculation refer to page 274 Based on Assumption 1

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 500Adjusted 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.


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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

http://www.vonwentzel.net


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.

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.

0

1250

2500

3750

5000

0 25 50 75 100

# of cycles

DOD (%)

500 Series400 Series


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

http://www.surrette.com


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-


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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.


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8 Assuming no recession for foreseeing future

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 I E O R 1 6 0! B e r k e l e y S O L A R

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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/PANEL

AREA (FT^2)

MAX # OF PANELS

PRICE/WATT

Evergreen 210W 180.7 $643 16.93 93 $3.49

Sanyo 195W 180.9 $915 12.47 125 $5.06


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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


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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


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http://www.powerfromthesun.net/Chapter6/Chapter6.htm

http://www.powerfromthesun.net/Chapter6/Chapter6.htm

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


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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.


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Models - IntroductionThese 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-sumermust purchase this much. If net[i] is positive in month i, then the system produced more thanneeded 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 notax 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 batteryI E O R 1 6 0! B e r k e l e y S O L A R

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*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


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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


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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.


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AMPL Model: Minimizing the Objective Function


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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., n.d. Web. 6 Dec 2010. <www.kyocerasolar.com>.

"How about Nickel-Cadmium Cells?" N.p., n.d. Web. 6 Dec 2010. <www.vonwentzel.net>.

"Life span of batteries used in "Deep Cycle Services" ." Web. 6 Dec 2010. <www.windsun.com>.

"My third letter." Von Wentzel Family Site. N.p., n.d. Web. 6 Dec 2010. <http://www.vonwentzel.net/>.

"Renewable Energy 2010 Design Catalog." 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>.

"Surrette Rolls are the crown jewels of DC batteries." N.p., n.d. Web. 6 Dec 2010. <www.dcbattery.com>.

"NASA Surface Meteorology and Solar En-ergy." NASA Langley Atmospheric Science Data Center (Distributed Active Archive Cen-ter). Web. 06 Dec. 2010. <http://eosweb.larc.nasa.gov/cgi-bin/sse/grid.cgi?>.

"Solar Calculator." Solar Power Facts and Helpful Info. Web. 06 Dec. 2010. <http://www.solartradingpost.com/calculate.php?name=5>."SOLAR RADIATION FOR FLAT-PLATE 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/nsrdb/redbook/sum2/23234.txt>.


28

http://www.kyocerasolar.com






http://www.vonwentzel.net/

http://www.vonwentzel.net/

http://www.aeesolar.com

http://www.aeesolar.com



http://www.pureenergysystems.com

http://www.pureenergysystems.com



http://www.dcbattery.com

http://www.dcbattery.com

http://eosweb.larc.nasa.gov/cgi-bin/sse/grid.cgi?




http://www.solartradingpost.com/calculate.php?name=5




http://rredc.nrel.gov/solar/old_data/nsrdb/redbook/sum2/23234.txt




Appendix A - Battery SelectionThe 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

Battery VoltageAmpere- hours

Hour rating Current Power Max KWH DOD KWH

# to buy Lifetime Price Total Cost

Cost per Lifetime

Lifeline AGM (8D)

12 225 20 11.25 135 2.7 0.5 1.35 64 1000 $387.00 $24,768.00 $24.77

West Marine Gel (8D)

12 225 20 11.25 135 2.7 0.5 1.35 64 500 $449.00 $28,736.00 $57.47

Inexpensive Trojan (2xT105)

12 225 20 11.25 135 2.7 0.5 1.35 64 500 $152.00 $9,728.00 $19.46

Premium Surrette 400 (HT8DM)

12 221 20 11.05 132.6 2.652 0.5 1.32 65 1250 $246.00 $15,990.00 $12.79

Premium Surrette 500 (12CS11PS)

12 342 20 17.1 205.2 4.104 0.5 2.05 42 3200 $683.00 $28,686.00 $8.96

2-KS-33PS (Surrette 500 series)

2 1750 20 87.5 175 3.5 0.5 1.75 50 3300 $1,184.00 $59,200.00 $17.94


4 1104 20 55.2 220.8 4.416 0.5 2.20 39 3300 $1,703.00 $66,417.00 $20.13


4 1350 20 67.5 270 5.4 0.5 2.7 32 3300 $2,130.00 $68,160.00 $20.65

6-CS-17PS (Surrette 500 series)

6 546 20 27.3 163.8 3.276 0.5 1.63 53 3300 $1,316.00 $69,748.00 $21.14


6 683 20 34.15 204.9 4.098 0.5 2.04 42 3300 $1,643.00 $69,006.00 $20.91


6 820 20 41 246 4.92 0.5 2.46 35 3300 $1,905.00 $66,675.00 $20.20

Surrette S-460 (Sur-rette 400 series)

6 350 20 17.5 105 2.1 0.5 1.05 82 1300 $484.00 $39,688.00 $30.53

Surrette S-530 (Sur-rette 400 series)

6 400 20 20 120 2.4 0.5 1.2 72 1300 $550.00 $39,600.00 $30.46


29

Appendix B - Demand CalculationsMonth KWH

Billed This Year

KWH Billed Previous year

Average Variance Standard De-‐via1on

Average KWH+2σ

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

InsolaFon with 15˚ Tilt

InsolaFon at 90˚ Tilt

Slope of Line Found From Two Points

Projected Insola-‐Fon at 37.87 ˚

Average -‐ 2σ

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)Minimum Solar Insola1on (In KWH/m^2/day)Minimum Solar Insola1on (In KWH/m^2/day)Minimum Solar Insola1on (In KWH/m^2/day)Minimum Solar Insola1on (In KWH/m^2/day) InsolaFon with 15˚

TiltInsolaFon at 90˚

TiltSlope of Line Found From Two Points

Projected InsolaFon at 37.87 ˚

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


31

Maximum Solar Insola1on (In KWH/m^2/day)Maximum Solar Insola1on (In KWH/m^2/day)Maximum Solar Insola1on (In KWH/m^2/day)Maximum Solar Insola1on (In KWH/m^2/day)Maximum Solar Insola1on (In KWH/m^2/day) InsolaFon with 15˚

TiltInsolaFon at 90˚

TiltSlope of Line Found From Two Points

Projected InsolaFon at 37.87 ˚

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


32

Triangular Distribu1on Variance

Standard Devia1on

0.101968495 0.3193250610.37795151 0.614777610.318089166 0.5639939420.210061512 0.458324680.129163585 0.3593933570.131089127 0.3620623240.064049466 0.253079960.114099774 0.337786580.139465118 0.3734502890.168693588 0.410723250.124776307 0.35323690.281501183 0.530566851

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 14605.39498Nonlin evals: constrs = 6, Jac = 5.: _varname _var :=1 'net[1]' -8702 'net[2]' -7023 'net[3]' -762.54 'net[4]' -663.55 'net[5]' -5536 'net[6]' -524.57 'net[7]' -556.58 'net[8]' -490.59 'net[9]' -59310 'net[10]' -568.511 'net[11]' -71912 'net[12]' -78813 np 014 nb 015 LI 016 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


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 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 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;


36



OUTPUT: MINOS 5.51: optimal solution found.2 iterations, objective 913.0905062Nonlin evals: constrs = 15, Jac = 14.: _varname _var :=1 'net[1]' 1276.382 'net[2]' 1230.073 'net[3]' 1829.224 'net[4]' 2169.615 'net[5]' 2440.256 'net[6]' 2252.097 'net[7]' 2670.378 'net[8]' 2845.889 'net[9]' 2755.86


37

10 'net[10]' 2578.0611 'net[11]' 1570.0912 'net[12]' 1000.6513 np 102.70214 LI 9354.8415 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



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 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>=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 blah: p=if np=0 then 0 else 1;




39

output: MINOS 5.51: optimal solution found.3 iterations, objective 1260743.679Nonlin evals: constrs = 4, Jac = 3.: _varname _var :=1 'net[1]' 75.62 'net[2]' 149.1853 'net[3]' 379.2964 'net[4]' 584.6425 'net[5]' 765.6946 'net[6]' 698.7427 'net[7]' 865.1168 'net[8]' 979.3619 'net[9]' 882.3610 'net[10]' 817.73711 'net[11]' 289.47412 'net[12]' 013 np 45.245914 nb 71915 LI 9354.8416 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 + msubject to x <= 1500 ft2/area of 1 solar panel

max wattage > demand

x is an integerx = number of panels

y = price per panelm = 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, IncAkeena Solar, Inc.

Albion Power Company, Inc.Alliance Solar Services

Alter Systems, LLCAmerican Solar Corp.

Applied Star Energy SystemsBorrego 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

Com

pan

y


43

Appendix H - Night Hours v Months

11.600

11.825

12.050

12.275

12.500

1 2 3 4 5 6 7 8 9 10 11 12

Nig

ht H

ours

Months (JAN-DEC)


44

Appendix I - kWh Bill for 25 YearsMonth kWH

billed Cur-rent Year

$ Billed Cur-rent Year

$/kWh Cur-rent Year

kWH billed Previ-

ous Year

$ Billed Previ-

ous Year

$/kWh Previ-

ous Year

Ave. kWH

for next 25 Years

kwh/day

$ Billed

for next 25 Years

$/kWh for

next 25 Years

JanFebMarAprMayJunJulAugSepOctNovDecTotalAver-age

795.00 $188.00 $0.24 645.00 $128.00 $0.20 720.00 30 $158.00 $0.22686.00 $145.00 $0.21 654.00 $132.00 $0.20 670.00 27.917 $138.00 $0.21646.00 $129.00 $0.20 413.00 $55.00 $0.13 529.50 22.063 $89.00 $0.17374.00 $46.00 $0.12 567.00 $100.00 $0.18 470.50 19.604 $72.00 $0.15421.00 $67.00 $0.16 509.00 $93.00 $0.18 465.00 19.375 $79.00 $0.17507.00 $92.00 $0.18 472.00 $81.00 $0.17 489.50 20.396 $86.00 $0.18465.00 $79.00 $0.17 526.00 $100.00 $0.19 495.50 20.646 $88.00 $0.18396.00 $59.00 $0.15 459.00 $78.00 $0.17 427.50 17.813 $69.00 $0.16557.00 $112.00 $0.20 485.00 $85.00 $0.18 521.00 21.708 $98.00 $0.19566.00 $116.00 $0.20 561.00 $114.00 $0.20 563.50 23.479 $115.00 $0.20665.00 $136.00 $0.20 701.00 $151.00 $0.22 683.00 28.458 $144.00 $0.21784.00 $184.00 $0.23 776.00 $181.00 $0.23 780.00 32.5 $182.00 $0.236,862.00 6,768.00 6,815 $1,318.00571.83 $0.19 564.00 567.92 $109.83


45

Appendix J - Solar Power Calculator

System Specifications Berkeley, CA

Solar Radiance (kWh/sqm/day)Ave. Monthly Usage (kWh/month)System Size (kWh)Roof Size (sq. ft)Estimated CostPost Incentive Cost

IncentivesFederal IncentivesTax Credit

State IncentivesProperty Tax

Local InventivesRebate (for PG&E)

SavingsEstimated CostPost Incentive CostAve. Monthly Savings25 Year Savings25 Year ROIBreak Even

Carbon EmissionsAnnual Carbon Dioxide Usage (pounds)Driving EquivalentOffset by planting:

5.43390129.822981

208,708.60140,252.18

30%

Exempt

.35/W AC

208708.60140,252.18

570284,858.01

203.10%15.27 Years

70,20977,800 miles176 trees/year


46