This document provides an analysis of optimal solar system battery and panel choices for a client's home in Berkeley. Key points:
1. The analysis evaluates different battery types and selects the Premium Surrette battery as the optimal choice due to its lower lifetime cost despite higher initial cost.
2. When choosing solar panels, the analysis selects Evergreen 210W panels due to their lower cost per watt and environmental impact while still maintaining decent efficiency.
3. The recommendations conclude that the best option for the client is an on-grid system that sells excess power to PG&E, as it is the most feasible option within the client's budget. Going off-grid would require prohibitively expensive batteries.
This document provides specifications for the SOLON Black 230/15 monocrystalline solar module. Key details include:
- Modules have high efficiency rates of up to 14.3% with excellent low light response.
- Modules come with a 10-year product guarantee and 25-year performance guarantee.
- Technical features include highly efficient monocrystalline cell technology, 0.16 inch solar glass, and an aluminum frame.
- Electrical data is provided for maximum power, voltage, current, and temperature coefficients under standard test conditions.
This report provides an overview of the global solar photovoltaic (PV) market. It outlines key industry data like global solar capacity, production figures, and forecasts for future growth. It also examines major country markets and discusses the advantages, challenges, and components of the solar PV industry. The report analyzes factors such as government incentives, technology developments, and manufacturing trends that are shaping the future of the solar industry.
This presentation discusses energy efficient LED lighting products from Minda NexGenTech Ltd. It notes that LED lights consume 30-50% less electricity than traditional lights and have significant savings in operation and maintenance. LED lights do not contain mercury or emit hazardous chemicals. The presentation provides technical specifications and benefits of LED street lights, home lighting systems, and lights for corporate use. It highlights opportunities to reduce energy consumption and costs by replacing existing lighting with LED options and using LEDs in new buildings. Customers of Minda NexGenTech are also mentioned.
Jcup 3 (2012) Presentation: Lexichem, a new Era. By Ed Cannon Ed Cannon
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This document provides a final report on the design of a solar powered lead acid battery charger. The report describes the hardware, power train, and software design of the system. The system uses a microprocessor to control charging of batteries from solar panels in order to optimize power transfer and efficiency. It improves on a previous prototype by adding isolation circuits, new sensors and meters, additional buck regulators, and a more advanced microprocessor for control. The overall goal is to develop a household-scale system for storing solar energy in batteries.
The document discusses a research project to create a magnetic field that protects astronauts from radiation in space. The researchers plan to build a prototype using a superconductor such as MgB2 wire cooled with liquid nitrogen to generate the magnetic field. By spring 2016, they aim to have finalized their research, designed a prototype, and potentially built and tested an initial tokamak device to evaluate the magnetic field effectiveness. Key components needed include a superconductor wire, liquid nitrogen, and sensors to measure the magnetic field strength generated.
The impact of technology in the gaming industryRegine Labog
This document provides an overview of gaming-on-demand and the video game industry. It discusses the history of video games and how the technology, society, and economy around gaming has changed over time. Currently, the largest businesses in the gaming market are general retailers, online retailers, specialty brick-and-mortar stores, and specialty online stores. Gaming-on-demand would allow users to stream high-end games over the internet to any device, eliminating the need for dedicated gaming hardware. However, issues around latency, bandwidth constraints, and piracy present barriers to the success of this business model.
This document provides specifications for the SOLON Black 230/15 monocrystalline solar module. Key details include:
- Modules have high efficiency rates of up to 14.3% with excellent low light response.
- Modules come with a 10-year product guarantee and 25-year performance guarantee.
- Technical features include highly efficient monocrystalline cell technology, 0.16 inch solar glass, and an aluminum frame.
- Electrical data is provided for maximum power, voltage, current, and temperature coefficients under standard test conditions.
This report provides an overview of the global solar photovoltaic (PV) market. It outlines key industry data like global solar capacity, production figures, and forecasts for future growth. It also examines major country markets and discusses the advantages, challenges, and components of the solar PV industry. The report analyzes factors such as government incentives, technology developments, and manufacturing trends that are shaping the future of the solar industry.
This presentation discusses energy efficient LED lighting products from Minda NexGenTech Ltd. It notes that LED lights consume 30-50% less electricity than traditional lights and have significant savings in operation and maintenance. LED lights do not contain mercury or emit hazardous chemicals. The presentation provides technical specifications and benefits of LED street lights, home lighting systems, and lights for corporate use. It highlights opportunities to reduce energy consumption and costs by replacing existing lighting with LED options and using LEDs in new buildings. Customers of Minda NexGenTech are also mentioned.
Jcup 3 (2012) Presentation: Lexichem, a new Era. By Ed Cannon Ed Cannon
Lexichem is introducing a new version with improved performance in generating chemical names from structures and vice versa. The new version achieves 98.71% accuracy in "round tripping" structures compared to 60.02% for the previous version. It also offers faster processing speeds. New features include generating names that distinguish stereochemistry, support for ring templates, and the Lexichem Workbench desktop application for structure/name conversion and substructure searching. The performance enhancements and new tools provide chemists with more robust naming and structure conversion capabilities.
This document provides a final report on the design of a solar powered lead acid battery charger. The report describes the hardware, power train, and software design of the system. The system uses a microprocessor to control charging of batteries from solar panels in order to optimize power transfer and efficiency. It improves on a previous prototype by adding isolation circuits, new sensors and meters, additional buck regulators, and a more advanced microprocessor for control. The overall goal is to develop a household-scale system for storing solar energy in batteries.
The document discusses a research project to create a magnetic field that protects astronauts from radiation in space. The researchers plan to build a prototype using a superconductor such as MgB2 wire cooled with liquid nitrogen to generate the magnetic field. By spring 2016, they aim to have finalized their research, designed a prototype, and potentially built and tested an initial tokamak device to evaluate the magnetic field effectiveness. Key components needed include a superconductor wire, liquid nitrogen, and sensors to measure the magnetic field strength generated.
The impact of technology in the gaming industryRegine Labog
This document provides an overview of gaming-on-demand and the video game industry. It discusses the history of video games and how the technology, society, and economy around gaming has changed over time. Currently, the largest businesses in the gaming market are general retailers, online retailers, specialty brick-and-mortar stores, and specialty online stores. Gaming-on-demand would allow users to stream high-end games over the internet to any device, eliminating the need for dedicated gaming hardware. However, issues around latency, bandwidth constraints, and piracy present barriers to the success of this business model.
The effect of pdms based microdevice channel width on plasmid dna transformat...Regine Labog
The document summarizes an experiment that studied the effect of microdevice channel width on plasmid DNA transformation efficiency in E. coli. Four PDMS microdevices with channel widths of 50 μm, 100 μm, 250 μm, and 500 μm were fabricated and used in chemical transformation trials. While transformation was successful, the data showed high variability and no clear relationship between channel width and transformation efficiency. Future work is needed to improve device design and experimental methods to better study the potential influence of channel width.
Engineering a bioartificial kidney utilizing a decellularized matrixRegine Labog
This document proposes engineering a bioartificial kidney using a decellularized donor kidney matrix that is then recellularized. Specifically:
1) A donor kidney would be decellularized using detergents to remove all cellular material while keeping the extracellular matrix intact.
2) Bone marrow-derived stem cells would be differentiated into kidney cell types then seeded sequentially onto the matrix to repopulate it.
3) The recellularized kidney would be cultured in a bioreactor to mimic physiology and test waste removal efficiency before potential transplantation.
4) Characterization of stem cell contribution and kidney function would be done through immunostaining and waste clearance measurements. The goal is to engineer a
Continuum biomechanics modeling of homologue proteinsRegine Labog
This document summarizes a study that used COMSOL modeling to compare the biomechanical properties of actin and mreB proteins. The researchers modeled actin's helical twist and mreB's parallel structure to apply forces and measure displacement. The results showed mreB had significantly lower maximum displacement than actin, likely due to actin's flexibility from its twisted structure. This difference supports actin's role in eukaryotic cells requiring flexibility, while mreB provides rigid structure for bacterial cells.
Aristotle vs plutarch a comparison of solonian reformRegine Labog
Plutarch and Aristotle provide different but complementary accounts of Solon's reforms in ancient Athens. Both describe Solon establishing property classes, canceling debts, and granting new political powers to the lower classes. However, Plutarch includes more details on specific laws and emphasizes the chronology, while Aristotle focuses on the constitutional framework. Overall, their accounts agree on the major reforms but take different approaches reflecting their separate literary goals. Solon's poetry is also analyzed, with some passages used to corroborate historical events while others expressed his personal feelings.
A review on microfluidic immunoassays as rapid saliva based clinical diagnosticsRegine Labog
This document describes research on developing a microfluidic immunoassay device to rapidly detect and quantify levels of matrix metalloproteinase-8 (MMP-8), a biomarker for periodontal disease, in human saliva samples. The device, called a microchip electrophoretic immunoassay (μCEI), uses microfluidic channels to enrich and separate the MMP-8 antigen from saliva via competitive immunoassay and capillary electrophoresis. The μCEI shows potential for point-of-care diagnosis and monitoring of periodontal disease through a small, portable device that analyzes saliva, which could enable more frequent disease assessment.
A novel microfluidic device for rapid melanoma diagnosisRegine Labog
This document describes a proposed microfluidic device for rapid melanoma diagnosis. The device uses cell lysis with SDS to extract mRNA from skin samples. Molecular beacons anchored in the device wells are used to detect five relevant melanoma genes from the extracted mRNA. If fluorescence is detected in the wells, it indicates the presence of those genes and suggests a positive melanoma diagnosis. The portable, quantitative device aims to improve current melanoma diagnostics by providing faster, less invasive results compared to standard pathological analysis methods. The microfluidic design incorporates mixing channels and molecular detection to analyze skin samples for potential melanoma markers at the point-of-care.
- Zara is a major clothing brand owned by Spanish company Inditex that operates a unique fast fashion business model. Unlike other brands, Zara produces small quantities of clothing and replenishes stores frequently based on real-time customer feedback.
- Zara maintains control over its entire supply chain from design to manufacturing to distribution. This vertical integration allows it to produce and deliver new designs to stores within 2 weeks.
- For the US market, Zara should start with an aggressive online presence to test demand before opening physical stores focused on major coastal cities. An initial online-focused strategy allows it to learn customer preferences at lower cost and risk.
Storytelling For The Web: Integrate Storytelling in your Design ProcessChiara Aliotta
In this slides I explain how I have used storytelling techniques to elevate websites and brands and create memorable user experiences. You can discover practical tips as I showcase the elements of good storytelling and its applied to some examples of diverse brands/projects..
Connect Conference 2022: Passive House - Economic and Environmental Solution...TE Studio
Passive House: The Economic and Environmental Solution for Sustainable Real Estate. Lecture by Tim Eian of TE Studio Passive House Design in November 2022 in Minneapolis.
- The Built Environment
- Let's imagine the perfect building
- The Passive House standard
- Why Passive House targets
- Clean Energy Plans?!
- How does Passive House compare and fit in?
- The business case for Passive House real estate
- Tools to quantify the value of Passive House
- What can I do?
- Resources
Explore the essential graphic design tools and software that can elevate your creative projects. Discover industry favorites and innovative solutions for stunning design results.
PDF SubmissionDigital Marketing Institute in NoidaPoojaSaini954651
https://www.safalta.com/online-digital-marketing/advance-digital-marketing-training-in-noidaTop Digital Marketing Institute in Noida: Boost Your Career Fast
[3:29 am, 30/05/2024] +91 83818 43552: Safalta Digital Marketing Institute in Noida also provides advanced classes for individuals seeking to develop their expertise and skills in this field. These classes, led by industry experts with vast experience, focus on specific aspects of digital marketing such as advanced SEO strategies, sophisticated content creation techniques, and data-driven analytics.
Revolutionizing the Digital Landscape: Web Development Companies in Indiaamrsoftec1
Discover unparalleled creativity and technical prowess with India's leading web development companies. From custom solutions to e-commerce platforms, harness the expertise of skilled developers at competitive prices. Transform your digital presence, enhance the user experience, and propel your business to new heights with innovative solutions tailored to your needs, all from the heart of India's tech industry.
Architectural and constructions management experience since 2003 including 18 years located in UAE.
Coordinate and oversee all technical activities relating to architectural and construction projects,
including directing the design team, reviewing drafts and computer models, and approving design
changes.
Organize and typically develop, and review building plans, ensuring that a project meets all safety and
environmental standards.
Prepare feasibility studies, construction contracts, and tender documents with specifications and
tender analyses.
Consulting with clients, work on formulating equipment and labor cost estimates, ensuring a project
meets environmental, safety, structural, zoning, and aesthetic standards.
Monitoring the progress of a project to assess whether or not it is in compliance with building plans
and project deadlines.
Attention to detail, exceptional time management, and strong problem-solving and communication
skills are required for this role.
Technoblade The Legacy of a Minecraft Legend.Techno Merch
Technoblade, born Alex on June 1, 1999, was a legendary Minecraft YouTuber known for his sharp wit and exceptional PvP skills. Starting his channel in 2013, he gained nearly 11 million subscribers. His private battle with metastatic sarcoma ended in June 2022, but his enduring legacy continues to inspire millions.
The effect of pdms based microdevice channel width on plasmid dna transformat...Regine Labog
The document summarizes an experiment that studied the effect of microdevice channel width on plasmid DNA transformation efficiency in E. coli. Four PDMS microdevices with channel widths of 50 μm, 100 μm, 250 μm, and 500 μm were fabricated and used in chemical transformation trials. While transformation was successful, the data showed high variability and no clear relationship between channel width and transformation efficiency. Future work is needed to improve device design and experimental methods to better study the potential influence of channel width.
Engineering a bioartificial kidney utilizing a decellularized matrixRegine Labog
This document proposes engineering a bioartificial kidney using a decellularized donor kidney matrix that is then recellularized. Specifically:
1) A donor kidney would be decellularized using detergents to remove all cellular material while keeping the extracellular matrix intact.
2) Bone marrow-derived stem cells would be differentiated into kidney cell types then seeded sequentially onto the matrix to repopulate it.
3) The recellularized kidney would be cultured in a bioreactor to mimic physiology and test waste removal efficiency before potential transplantation.
4) Characterization of stem cell contribution and kidney function would be done through immunostaining and waste clearance measurements. The goal is to engineer a
Continuum biomechanics modeling of homologue proteinsRegine Labog
This document summarizes a study that used COMSOL modeling to compare the biomechanical properties of actin and mreB proteins. The researchers modeled actin's helical twist and mreB's parallel structure to apply forces and measure displacement. The results showed mreB had significantly lower maximum displacement than actin, likely due to actin's flexibility from its twisted structure. This difference supports actin's role in eukaryotic cells requiring flexibility, while mreB provides rigid structure for bacterial cells.
Aristotle vs plutarch a comparison of solonian reformRegine Labog
Plutarch and Aristotle provide different but complementary accounts of Solon's reforms in ancient Athens. Both describe Solon establishing property classes, canceling debts, and granting new political powers to the lower classes. However, Plutarch includes more details on specific laws and emphasizes the chronology, while Aristotle focuses on the constitutional framework. Overall, their accounts agree on the major reforms but take different approaches reflecting their separate literary goals. Solon's poetry is also analyzed, with some passages used to corroborate historical events while others expressed his personal feelings.
A review on microfluidic immunoassays as rapid saliva based clinical diagnosticsRegine Labog
This document describes research on developing a microfluidic immunoassay device to rapidly detect and quantify levels of matrix metalloproteinase-8 (MMP-8), a biomarker for periodontal disease, in human saliva samples. The device, called a microchip electrophoretic immunoassay (μCEI), uses microfluidic channels to enrich and separate the MMP-8 antigen from saliva via competitive immunoassay and capillary electrophoresis. The μCEI shows potential for point-of-care diagnosis and monitoring of periodontal disease through a small, portable device that analyzes saliva, which could enable more frequent disease assessment.
A novel microfluidic device for rapid melanoma diagnosisRegine Labog
This document describes a proposed microfluidic device for rapid melanoma diagnosis. The device uses cell lysis with SDS to extract mRNA from skin samples. Molecular beacons anchored in the device wells are used to detect five relevant melanoma genes from the extracted mRNA. If fluorescence is detected in the wells, it indicates the presence of those genes and suggests a positive melanoma diagnosis. The portable, quantitative device aims to improve current melanoma diagnostics by providing faster, less invasive results compared to standard pathological analysis methods. The microfluidic design incorporates mixing channels and molecular detection to analyze skin samples for potential melanoma markers at the point-of-care.
- Zara is a major clothing brand owned by Spanish company Inditex that operates a unique fast fashion business model. Unlike other brands, Zara produces small quantities of clothing and replenishes stores frequently based on real-time customer feedback.
- Zara maintains control over its entire supply chain from design to manufacturing to distribution. This vertical integration allows it to produce and deliver new designs to stores within 2 weeks.
- For the US market, Zara should start with an aggressive online presence to test demand before opening physical stores focused on major coastal cities. An initial online-focused strategy allows it to learn customer preferences at lower cost and risk.
Storytelling For The Web: Integrate Storytelling in your Design ProcessChiara Aliotta
In this slides I explain how I have used storytelling techniques to elevate websites and brands and create memorable user experiences. You can discover practical tips as I showcase the elements of good storytelling and its applied to some examples of diverse brands/projects..
Connect Conference 2022: Passive House - Economic and Environmental Solution...TE Studio
Passive House: The Economic and Environmental Solution for Sustainable Real Estate. Lecture by Tim Eian of TE Studio Passive House Design in November 2022 in Minneapolis.
- The Built Environment
- Let's imagine the perfect building
- The Passive House standard
- Why Passive House targets
- Clean Energy Plans?!
- How does Passive House compare and fit in?
- The business case for Passive House real estate
- Tools to quantify the value of Passive House
- What can I do?
- Resources
Explore the essential graphic design tools and software that can elevate your creative projects. Discover industry favorites and innovative solutions for stunning design results.
PDF SubmissionDigital Marketing Institute in NoidaPoojaSaini954651
https://www.safalta.com/online-digital-marketing/advance-digital-marketing-training-in-noidaTop Digital Marketing Institute in Noida: Boost Your Career Fast
[3:29 am, 30/05/2024] +91 83818 43552: Safalta Digital Marketing Institute in Noida also provides advanced classes for individuals seeking to develop their expertise and skills in this field. These classes, led by industry experts with vast experience, focus on specific aspects of digital marketing such as advanced SEO strategies, sophisticated content creation techniques, and data-driven analytics.
Revolutionizing the Digital Landscape: Web Development Companies in Indiaamrsoftec1
Discover unparalleled creativity and technical prowess with India's leading web development companies. From custom solutions to e-commerce platforms, harness the expertise of skilled developers at competitive prices. Transform your digital presence, enhance the user experience, and propel your business to new heights with innovative solutions tailored to your needs, all from the heart of India's tech industry.
Architectural and constructions management experience since 2003 including 18 years located in UAE.
Coordinate and oversee all technical activities relating to architectural and construction projects,
including directing the design team, reviewing drafts and computer models, and approving design
changes.
Organize and typically develop, and review building plans, ensuring that a project meets all safety and
environmental standards.
Prepare feasibility studies, construction contracts, and tender documents with specifications and
tender analyses.
Consulting with clients, work on formulating equipment and labor cost estimates, ensuring a project
meets environmental, safety, structural, zoning, and aesthetic standards.
Monitoring the progress of a project to assess whether or not it is in compliance with building plans
and project deadlines.
Attention to detail, exceptional time management, and strong problem-solving and communication
skills are required for this role.
Technoblade The Legacy of a Minecraft Legend.Techno Merch
Technoblade, born Alex on June 1, 1999, was a legendary Minecraft YouTuber known for his sharp wit and exceptional PvP skills. Starting his channel in 2013, he gained nearly 11 million subscribers. His private battle with metastatic sarcoma ended in June 2022, but his enduring legacy continues to inspire millions.
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International Upcycling Research Network advisory board meeting 4Kyungeun Sung
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Visual Style and Aesthetics: Basics of Visual Design
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EASY TUTORIAL OF HOW TO USE CAPCUT BY: FEBLESS HERNANEFebless Hernane
CapCut is an easy-to-use video editing app perfect for beginners. To start, download and open CapCut on your phone. Tap "New Project" and select the videos or photos you want to edit. You can trim clips by dragging the edges, add text by tapping "Text," and include music by selecting "Audio." Enhance your video with filters and effects from the "Effects" menu. When you're happy with your video, tap the export button to save and share it. CapCut makes video editing simple and fun for everyone!
1. 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
2. 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
3. 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
U C B e r k e l e y! IEOR 160 Final Project
ii
4. 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! IEOR 160 Final Project
iii
5. 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
6. 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.
I E O R 1 6 0! BerkeleySOLAR
2
7. 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.
I E O R 1 6 0! BerkeleySOLAR
3
8. 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.
I E O R 1 6 0! BerkeleySOLAR
4
9. 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
I E O R 1 6 0! BerkeleySOLAR
5
10. 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.
I E O R 1 6 0! BerkeleySOLAR
6
11. 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).
I E O R 1 6 0! BerkeleySOLAR
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12. 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
I E O R 1 6 0! BerkeleySOLAR
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13. 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
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14. 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
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15. 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-
I E O R 1 6 0! BerkeleySOLAR
11
16. 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
I E O R 1 6 0! BerkeleySOLAR
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17. 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! BerkeleySOLAR
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18. 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
I E O R 1 6 0! BerkeleySOLAR
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19. 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
I E O R 1 6 0! BerkeleySOLAR
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20. 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
I E O R 1 6 0! BerkeleySOLAR
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21. 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
I E O R 1 6 0! BerkeleySOLAR
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22. 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.
I E O R 1 6 0! BerkeleySOLAR
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23. 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
I E O R 1 6 0! BerkeleySOLAR
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24. *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
I E O R 1 6 0! BerkeleySOLAR
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25. 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
I E O R 1 6 0! BerkeleySOLAR
21
26. 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.
I E O R 1 6 0! BerkeleySOLAR
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28. 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.
I E O R 1 6 0! BerkeleySOLAR
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29. 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
I E O R 1 6 0! BerkeleySOLAR
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30. 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.
I E O R 1 6 0! BerkeleySOLAR
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32. 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>.
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35. 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
I E O R 1 6 0! BerkeleySOLAR
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36. 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
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37. 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;
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38. 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;
I E O R 1 6 0! BerkeleySOLAR
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39. 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.
I E O R 1 6 0! BerkeleySOLAR
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40. Model 2
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 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;
I E O R 1 6 0! BerkeleySOLAR
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42. 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 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;
I E O R 1 6 0! BerkeleySOLAR
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43. 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;
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;
I E O R 1 6 0! BerkeleySOLAR
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44. output:
MINOS 5.51: optimal solution found.
3 iterations, objective 1260743.679
Nonlin evals: constrs = 4, Jac = 3.
: _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.
I E O R 1 6 0! BerkeleySOLAR
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45. 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
I E O R 1 6 0! BerkeleySOLAR
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46. 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
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47. 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
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48. 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)
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49. 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
I E O R 1 6 0! BerkeleySOLAR
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50. 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
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