Solar PV Assignment

Serwaa Bekoe – 10022307 Natasha Ling-Leblanc – 10021264 Kaley Sheppard – 10022098

Group: 08_18_23

Introduction

It has been brought to our attention that the Kingston Memorial Hospital is considering the

implementation of a system of solar photovoltaic cells on its rooftop used to capture solar

electricity. In order to accurately determine whether this is a good idea that will benefit the

hospital in terms of energy as well as cost efficiency, several factors must be considered. We can

utilize data recorded that models the efficiency of a potentially similar system of photovoltaic

cells on the rooftop of Goodwin Hall at Queen’s University in Kingston. We can verify the

accuracy of our mathematical model designed to estimate the potential power produced by the

system on the hospital rooftop by comparing it to calculated values of energy production for

Goodwin Hall. There are several reasons why Kingston Memorial Hospital may want to

implement this program. Firstly, photovoltaic cells are environmentally friendly and provide a

good alternative source of energy. Secondly, these cells can provide an excellent potential for

education in the city as well as generate public interest in the actions of the hospital. One

potential reason the hospital would not decide to implement this project is that photovoltaic cells

tend to be very expensive and may not bring in the same amount of revenue in a given amount of

time as another project may. Solar panels tend to be only between 10 and 15% efficient at

capturing solar energy and using it to provide electricity. The rest of the solar energy is typically

lost in the form of heat. While recorded data of functioning solar arrays can be analysed, it is still

very difficult to accurately estimate energy production of another system because there are

factors like cloud cover or other obstructions that may decrease the panels’ efficiency

significantly.

Solar Photovoltaic Cell Technologies

There are several different technologies available when deciding which type of Solar

Photovoltaic cells to purchase and install. The fundamental function of Solar PV cells is to

harness solar energy and transform it to useful electrical energy. Some advantages to using these

systems are that “they are a safe, reliable, low-maintenance source of solar electricity”.1 In

addition to these benefits, solar photovoltaic cells produce no emissions or waste products,

making them a sustainable source of energy with very little environmental damage. The

1 Canada Mortgage and Housing

technology of photovoltaic cells is generally based upon Albert Einstein’s findings with regards

to the photoelectric effect. If a semiconductor is hit with incoming photons of a certain frequency

with energy greater than the work function, electrons are ejected from the metal and given a

kinetic energy equal to the photon energy minus the value of the work function. By attaching

conductors to the metal, electrons can be captured in the form of electricity. This is how solar

panels are able to capture energy from the light striking the earth from the sun. In order to

maximize the amount of energy captured by the cells, the effective area that is in contact with the

light must also be maximized. The single-axis and dual-axis tracking systems are designed so

that they are able to maximize the effective surface area for the longest amount of time

throughout the day as possible. The lifespan of an array of photovoltaic cells ranges although is

the longest for fixed panels because they present less opportunity for malfunction. The estimated

lifespan for an array of fixed solar panels is 20 years while the estimated lifespan for an array

with tracking systems is 10 years. Photovoltaic cell arrays require very little maintenance and are

designed so that material that accumulates on top of the panels is able to slide off due to the

elevation angle. Single and dual-axis tracking system technologies require more maintenance and

more frequent part replacement because they both have moving parts.

Fixed Angle System

A fixed angle system is comprised of an array of solar panels positioned at a fixed angle that is

determined with the purpose being to maximize solar energy intake. The ideal angle is

determined by using the longitude and latitude of the location at which the panels are placed. The

location of the panels leads to a change in solar radiation due to the position of the sun related to

the surface. In Kingston this angle of inclination is approximately 44° south of the vertical. By

positioning the panels at this angle, we can maximize the effective area for the longest time

interval in each day possible. This system, while the simplest, leads to the greatest loss of power

due to the solar energy that is not being directly taken in by the cell’s effective area. In a fixed

angle system, the panels are not able to recover any energy during times when the zenith angle of

the sun position is greater than 90° or when the azimuth angle is less than 90° or greater than

270°. Due to the fact that the fixed angle system has no moving parts, it is the least expensive to

install and requires the least amount of maintenance.

Single-Axis Tracking System

In a fixed panel system, energy is lost when the

angle of the sun is not perpendicular to the face of

the panel. In order to better orient the panels to the

position of the sun, tracking systems are used. In a

single-axis tracking system, panels face in a fixed

direction relative to the azimuth of the sun, but

their angle of elevation can be altered in order to

follow the sun across the sky throughout the course of a day. This increases the effective area of

the panels but still does not give a maximum level of electricity production because the sun

changes position in three dimensions as opposed to two. Unlike the fixed angle system, in a

single-axis tracking system, energy is able to be captured when the azimuth angle of the sun’s

position is less than 90° or greater than 270°, and also is able to capture energy for a greater

range of zenith angles.

Dual-Axis Tracking System

The dual-axis tracking system is able to maximize the effective area of the panels, therefore

maximizing the production of energy. This technology makes it possible for the photovoltaic

cells to rotate around a vertical axis as well

as change its angle of elevation which leads

to the sun’s rays always being perpendicular

to the panel. The effective area of a panel in

a dual-axis tracking system is essentially the

same as its true area because the incident

rays are always at 90 degrees to the surface.

The dual-axis tracking system is able to

capture energy when the sun’s position is given by any azimuth angle as well as any zenith angle

where the sun is above the horizon and the viewing plane of the surface on which the panels are

positioned. Although the dual-axis tracking system produces the most electricity, it is not always

the ideal option because of the significant increase in maintenance and installation costs.

Goodwin Hall

An array of 264 photovoltaic cells has been in operation on Goodwin Hall at Queen’s University

since the year 2002. This array of cells operates under a fixed panel system and so does not track

the movement of the sun. The system was

implemented primarily to serve “as a learning,

teaching, and research tool for Applied Science

students” and is able to provide sufficient power

for around five mid-sized homes.2 This

demonstrates one of many reasons for an

institution or franchise to use solar cells to

provide energy. Especially in the case of the

Kingston Memorial Hospital, the cells could

provide an excellent opportunity for education;

as well as generate the public’s interest in the

hospital’s other projects and functions. By using data collected from the Goodwin Hall array, we

are able to verify the accuracy of our own predictive model for power output of photovoltaic

cells over a given period of time in Kingston.

Technical Analysis

In order to predict the power output of each of the three different types of photovoltaic arrays

that may be viable selections for the hospital, we have developed a mathematical model using

MATLAB to comparatively analyse the potential output during one week of each season of the

year. In order to prove that these models are valid in predicting the possible power outputs for

the hospital, it is necessary to numerically compare our predicted values with real ones. In this

case, the power output data from Goodwin`s solar panels, provided from LiveBuilding data site,

is appropriate in validating our models. In addition to this, we have developed an initial, simple

model that predicts the output power for a full year but does not take into consideration the angle

2 LiveBuilding Data Site

of the sun in comparison to the panel. This means that in the simple model, the rays of the sun

are always completely perpendicular to the surface of the panel. The effective area is the true

area of the panel. The value for radiation used in this model is the average over the entire year,

and therefore includes night time, cloud coverage, and any other factors that could negatively

affect the solar radiation density. This model is clearly not very accurate, but is a good starting

point to predict the overall power output. In Kingston, radiation density is typically higher in the

winter than in the summer because the earth is in closer proximity to the sun for those months.

Our simplistic model has predicted that the power generated by a solar array covering 10000m2

of space, the approximate usable space for the hospital, is 773.3076kW. Due to the fact that solar

radiation varies throughout the year, we have taken into consideration one week per season in a

year. Even still, it is very difficult to predict cloud cover and solar radiation density over an

entire year. To determine the validity of our mathematical model, we have compared it to the

data collected from the Goodwin Hall solar array at Queen’s University. For each one week

sample, we determined the maximum solar radiation density using information from the

LiveBuilding Data site in order to improve the accuracy of the model. The average solar

radiation density varies from season to season.

Spring

During one week in spring of the year 2010, the Goodwin Hall solar array produced 917.24 kW

of power, as noted on the LiveBuilding Data site. Our predictive model for the power output of a

fixed panel system gives us an

approximate value of 1,214.5 kW. A

single-axis tracking system yields

2,438.5 kW and a dual-axis tracking

system yields 2,613.8 kW. As is

expected, the dual-axis tracking

system produced the most power

because it was able to maximize

effective area for the longest period of

time. Our predictive value for the

fixed panel system is very similar to Figure 1

the value that represents the power output of Goodwin Hall because there was not many

disturbances in terms of solar radiation density during that week. There was little cloud cover

and the solar radiation was strong for long periods of time. Figure 1 represents the Power Output

for one week in spring.

Summer

During one week during the summer in the

year 2010, the Goodwin Hall solar array

produced 862.7374 kW of power. Our model

has predicted an approximate output power

value of 720.3813 kW for a fixed panel

system, 2,501.0 kW for a single-axis tracking

system, and 2,703.8 kW for a dual-axis

tracking system. Once again, the dual-axis

tracking model has predicted the highest

output of power over one week. Goodwin

Hall produced more power during one week in spring compared to one week in summer. This

could be due to cloud cover or other variations in solar radiation, as well as the proximity of the

sun to the earth. Figure 2 depicts the Power Output for one week in summer.

Fall

During one week during the fall in

the year 2010, the Goodwin Hall

solar array produced 628.6224 kW.

Our model has predicted an

approximate output power value of

1426.8 kW for a fixed panel system,

2231.7 kW for a single-axis tracking

system, and 2413.6 kW for a dual-

axis tracking system. During this

week, the power output for Goodwin

Figure 2

Figure 3

Hall was fairly low in comparison to our predictive model. This shows that the solar radiation

density varies more in the fall than in the spring or summer. This could be because there is a

more dense cloud cover during the fall months. Figure 3 shows the Power Output for one week

in the fall.

Winter

During one week during the winter in the year 2010, the Goodwin Hall solar array produced

471.4917 kW. Our model has predicted an approximate output power value of 1594.6 kW for a

fixed panel system, 1923.2 kW or

a single-axis tracking system, and

2223.4 kW for a dual-axis

tracking system. There is a larger

difference between the predictive

values and the Goodwin Hall data

than in other monthly models. By

looking at Figure 4, we are able to

see that during the chosen week

we extracted our Goodwin Hall

data from, there were three days

in which there was a very low

quantity of solar radiation. Our predictive model for power output of a fixed panel system is the

closet to the real data for Goodwin Hall. This is to be expected because the photovoltaic cell

technology on Goodwin Hall is a fixed panel system. Figure 4 shows the Output Power over one

week in the winter.

Annual Power Generation

In addition to considering the power generated in each season, it is important to look at the

power output as a whole. In 2010, the photovoltaic solar array on Goodwin Hall generated 35115

kW of power. Our simple model predicted an annual power output of 18559 kW. This is an

inaccurate value because of the simplicity of the model. Our predictive models give a value of

38071 kW for a fixed system, 72721 kW for a single-axis tracking system, and 79251 kW for a

Figure 4

dual-axis tracking system. Once again, of our predictive values, the closet number to the data for

Goodwin Hall is the fixed panel model.

After the technical analysis, we can conclude that our fixed model is an appropriate method to

predict the power output of the Goodwin hall. With that being said, we can also validate the

single and dual-axis models because the follow a similar form. With these predictive models, we

can find possible values for power generation, annual revenue and net present value which we

will discuss in the next section.

Economic Analysis

Due to the fact that solar energy is still one of the most expensive forms of alternative energy

compared to its power generation, it is very important to consider the net present value as well as

the capital cost for each type of photovoltaic cell array technology. One issue with solar energy

is that although solar radiation is an unlimited resource, solar panel arrays are fairly inefficient

and typically very expensive. To purchase and install a system for the rooftop of the Kingston

Memorial Hospital, the total area covered and whether or not tracking systems and mounts need

to be installed must be considered. For our simple economic model, we used an average radiation

value over the year. This value included night time and cloud coverage and so was not very

accurate. Our simple model predicted an energy generation of 1,314,000 kWh and a predicted

annual revenue of $936,882. The predicted capital cost in our simple model was $3,700,000 and

the net present value after ten years of operation was predicted to be $2,056,700. Although this

information may be useful to consider, it is more beneficial to analyse the more sophisticated

models for each type of photovoltaic cell technology.

For our three different solar panel array technology models, we determined the average solar

radiation to be approximately 615.7 W/m2. This value was found by using the average between

the maximum and the minimum radiations throughout the year when the zenith angle of the sun

position was less than 90 degrees – the times at which the panel is able to absorb the solar

energy. This change significantly improves the accuracy of the mathematical model. Our

predictive model for a fixed panel system gave us values of 1,311,000 kWh annual energy

production, $934,740 annual revenue, $4,961,300 capital cost, and a net present value after ten

years of operation of $782,280. Our single-axis tracking system model gave us values of

2,504,200 kWh annual energy production, $1,785,500 annual revenue, $4,987,300 capital cost,

and net present value after ten years of operation of $5,983,600. Our dual-axis tracking system

model gave us values of 2,732,500 kWh annual energy production, $1,948,300 annual revenue,

$5,534,000 capital cost, and net present value after ten years of operation of $6,437,200. As is

expected, the dual-axis tracking system produces the most energy and therefore the most

revenue, but also has the highest capital cost. The fixed panel model returns the lowest quantity

of money, but also is the least expensive system to implement. It is difficult to make sense of

these numbers and use them in order to make a decision. These values are important to determine

in order to come to an appropriate decision as to which type of photovoltaic cell array to use for

Kingston Memorial Hospital, but certain tools can be used in order to determine which factors

are more important to consider than others. In certain situations, the financial viability may be

much more important than the technological viability and vice versa.

Recommendation

After analysing the data using our predictive models for power output and net present value, we

have come to the conclusion that it would be most beneficial for Kingston Memorial Hospital to

implement a dual-axis tracking system of photovoltaic cells. This system is able to capture the

most solar energy because the effective area of the panels is the same as the true area. Although

these panels are the most expensive to install and maintain, and have a slightly shorter lifespan,

we believe that the significantly higher value of output power and revenue is more important to

consider, especially in this situation. In order to verify our decision, we have created a decision-

making matrix designed to help us to determine which factors are most important when deciding

what system is the best. Our decision-making matrix is in agreement with our decision. Many

benefits to implementing a system of photovoltaic cells will be present regardless of which

tracking system is chosen like the potential for education, safety, and public interest in the

project and so these are a constant factor. In order to come to our decision, we have used several

decision-making tools and considered several different factors. Decision matrices are a beneficial

tool to determine which option is the best for the situation.

Fixed Panel

Single Axis Tracking

Dual Axis Tracking

Criteria Weight Score Weighted Score Weighted Score Weighted

Cost 4 5 20 4 16 3 12

Revenue 5 2 10 4 20 5 25

Efficiency 5 3 15 4 20 5 25

Durability 3 5 15 4 12 3 9

Safety 2 3 6 3 6 3 6

Maintenance 2 4 8 3 6 2 4

Total (sum) 74 80 81

Although the three options scored similarly when compared to each other, we feel that the

benefits of the dual-axis tracking system make it the best choice for the hospital.

Conclusion

As we continue into the future, alternative forms of energy are becoming more and more

important. Photovoltaic solar array energy is a useful method of capturing energy from the sun.

Although solar energy is relatively expensive compared to other alternative forms of energy and

is not particularly efficient, it is 100% renewable as opposed to many other forms of energy.

Kingston Memorial Hospital is looking into implementing a system of photovoltaic cells for their

rooftop. By creating a predictive mathematical model for economics and technology, we have

determined that the best option for the hospital is a dual-axis tracking system, a system which is

able to follow the exact position of the sun throughout all times when the zenith angle of the

sun’s position is less than 90°.

Works Cited

Knier, Gil. "How do Photovoltaics Work? - NASA Science." NASA Science. N.p., n.d. Web. 2

Dec. 2011. <http://science.nasa.gov/science-news/science-at-nasa/2002/solarcells/>.

"Photovoltaic (PV) Systems | CMHC." Canada Mortgage and Housing | Société canadienne

dhypothèques et de logement. N.p., n.d. Web. 2 Dec. 2011. <http://www.cmhc-

schl.gc.ca/en/co/maho/enefcosa/enefcosa_003.cfm>.

"Solar Array | Live Building." Live Building. N.p., n.d. Web. 2 Dec. 2011.

<http://livebuilding.queensu.ca/green_features/solar_array>.

"Solar Tracking Application." Rockwell Automation. N.p., n.d. Web. 2 Dec. 2011.

<samplecode.rockwellautomation.com/idc/groups/literature/documents/wp/oem-

wp009_-en-p.pdf>.

"The Code of Ethics of Professional Engineers Ontario." Professional Engineers Ontario:

Welcome to PEO's website. N.p., n.d. Web. 2 Dec. 2011.

<http://www.peo.on.ca/Ethics/code_of_ethics.html>.

Appendix A Date: October 30, 2011

From: Energy Consulting Services

Subject: Rooftop Assessment

To: Reginald Lewis

Dear Mr. Lewis,

In response to your email concerning the photovoltaic solar panel installation on the rooftop of the

Kingston Memorial Hospital, it is with great interest that we will partake in the consulting and

analysis of the implementation of these solar panels. Thank you for considering the Energy

Consulting Services for the assessment of Kingston Memorial’s Hospital solar panels. From the brief

information gathered through your email we would like to confirm that the hospital is, currently

looking into the dual-axis solar panels and would wish for us to give our impartial recommendations

on which type of solar panel (fixed, single or dual) would be the most profitable to the hospital. We

shall take into consideration the many factors that affect the overall effectiveness of a solar panel

before making any recommendations and will return with the information promptly. It is vital that we

gather exact data for our analysis, thus we will need access to the rooftops of the hospital to collect

information. We the engineers have a duty to the public and our client. So it will be necessary for us

to look further into the asbestos quantity on the rooftop to inspect the harms of working on the roof.

It is our primary objective to get our clients the top product on the market and through a thorough

analysis of the various photovoltaic panels available we shall recommend a product that will best suit

your situation. We must also regrettably decline Kingston Solar PV Inc. invitation to further discuss

the assessment at a hockey game at the Rogers Centre in Toronto. We simply wish to maintain an

impartial position during this research and evaluation period, and so therefore must not consider any

pre-existing notions. The Energy Consulting Services will strive to offer you the best possible

selection for you solar endeavours. We would like to meet with you on a future date to discuss the

results and proceed with the solar panel installation.

Thank you for your time!

Sincerely,

Energy Consulting Services

Engineering Code of Ethics

Within the email it comes to the attention of the engineering firm that there is an unknown

quantity of asbestos on 10m2 of the rooftop of the hospital that must be kept confidential. This

raises certain ethical issues that are seen in the Professional Engineers of Ontario (PEO) code of

ethics. As stated in the PEO code of ethics engineers have a “duty to the public, to the

practitioner's employer, to the practitioner's clients, [and] to other licensed engineers of the

practitioner's profession.”(section77:1) It is because of this code that in this situation it would be

necessary before any further action on the hospitals roof took place, to look further into the

asbestos on the roof. According to the code of ethics “public welfare is

paramount,”(section77:2:i) however it also states that engineers must act in, “professional

engineering matters for each employer as a faithful agent or trustee and shall regard as

confidential information obtained by the practitioner as to the business affairs.”(section77:3)

Thus in regards to the asbestos quantity on the rooftop, the engineering firm must take into

consideration the safety of the public but also maintain the confidentiality of the client. To

publicly announce the possibility of an unknown asbestos substance accumulating on the rooftop

of the hospital, would go against ones duty to their client but maintain the public`s welfare. The

ethical issue regarding the asbestos would be best solved if the firm privately approached the

client with the issue and request solutions to the problem. Both the duty to the public and the

client would be preserved. The firm would need to ask the client for leave to collect the

substance and determine the species of the asbestos and its harm to the public. Once that data

was determined the client would need to be approached with the information and, methods of

removing the asbestos would need to be discussed so that the solar panels could be installed

safely.

Appendix B

Serwaa Bekoe – Report writing and engineering ethics

Natasha Lebling – Mathematical modelling and report writing

Kaley Sheppard – Report writing and analysis

Appendix C

%~[THIS SCRIPT WAS MADE BY SERWAA BEKOE, NATASHA LING-LEBLANC & KALEY

SHEPPARD]~

clear; clc; [Current1,Date]=GetBuildingData('PV Current_halfhr_average_2010.txt'); [Voltage1,Date]=GetBuildingData('PV Voltage_halfhr_average_2010.txt'); [Density1,Date]=GetBuildingData('Solar.Array_halfhr_average_2010.txt'); [Current2,Date]=GetBuildingData('PV.Current_halfhr_average_week_January.txt'); [Voltage2,Date]=GetBuildingData('PV.Voltage_halfhr_average_week_January.txt'); [Density2,Date]=GetBuildingData('Solar.Array_halfhr_average_week_January.txt'); [Current3,Date]=GetBuildingData('PV.Current_halfhr_average_week_April.txt'); [Voltage3,Date]=GetBuildingData('PV.Voltage_halfhr_average_week_April.txt'); [Density3,Date]=GetBuildingData('Solar.Array_halfhr_average_week_April.txt'); [Current4,Date]=GetBuildingData('PV.Current_halfhr_average_week_July.txt'); [Voltage4,Date]=GetBuildingData('PV.Voltage_halfhr_average_week_July.txt'); [Density4,Date]=GetBuildingData('Solar.Array_halfhr_average_week_July.txt'); [Current5,Date]=GetBuildingData('PV.Current_halfhr_average_week_October.txt'); [Voltage5,Date]=GetBuildingData('PV.Voltage_halfhr_average_week_October.txt'); [Density5,Date]=GetBuildingData('Solar.Array_halfhr_average_week_October.txt'); E=0.1; %~~~~~~~~~~[[[[[[[[[[[SCRIPT FOR SIMPLE SOLAR PV MODEL]]]]]]]]]]]~~~~~~~~~~ Area=145.2; %in m2 Radiation1=mean(Density1)/1000; %in kW/m2 PowerSimple=Area*Radiation1*E*365 PowerSimpleGenerated1=PowerSimple*24 %~~~~~~~~~~~~~~[FIXED, SIMPLE AND DUAL MODEL FOR FULL YEAR]~~~~~~~~~~~~~~~~

location.longitude = -(76+30/60); % Kingston's longitude location.latitude = 44+(16/60); % Kingston's latitude location.altitude = 80; % Kingston's altitude time.UTC = -4; % 5 for EDT, 4 for EST time.year = 2010; time.sec = 00; i=1; for month=1:12 for day=1:eomday(2010,month) for hour=0:23 for minute=0:30:59 time.month=month; time.day=day; time.hour=hour; time.min=minute; sun=sun_position(time,location); datestring1(i)=datenum(time.year,time.month,time.day,time.hour,time.min,time.sec); azimuth1(i)=sun.azimuth; zenith1(i)=sun.zenith; if sun.zenith>90 %sun is below the horizon lightfactorone1(i)=0; else lightfactorone1(i)=1; end if ((sun.azimuth<90) || (sun.azimuth>270)) %sun is behind the panels lightfactortwo1(i)=0; else lightfactortwo1(i)=1; end i=i+1; end end end end ValidRadiation1=Density1'.*lightfactorone1; Radiation1=(max(ValidRadiation1)-min(ValidRadiation1))/(2*1000) %Radiation1=0.700; %in kW/m2 % Goodwin real data PowerGoodwin1=(Current1.*Voltage1)/1000; PowerGoodwinGenerated1=sum(PowerGoodwin1) %in kW % Fixed panel AreaFixed1=145.2.*cosd(abs(46-zenith1)).*cosd(abs(180-azimuth1)); %in m2 PowerFixed1=Radiation1.*E.*AreaFixed1.*lightfactortwo1.*lightfactorone1; PowerFixedGenerated1=sum(PowerFixed1) %in kW

% Single Axis AreaSingle1=145.2.*cosd(abs(46-zenith1)); %in m2 PowerSingle1=Radiation1.*E.*AreaSingle1.*lightfactorone1; PowerSingleGenerated1=sum(PowerSingle1) %in kW % Dual Axis AreaDual1=145.2; %in m2 PowerDual1=Radiation1.*E.*AreaDual1.*lightfactorone1; PowerDualGenerated1=sum(PowerDual1) %in kW %~~~~~~~~~~~~~~~~~[SEASONAL FIXED, SINGLE AND DUAL MODEL]~~~~~~~~~~~~~~~~~ %~~~~~~~~~~~~~~~[FOR WINTER (using first week of January)]~~~~~~~~~~~~~~~~~ location.longitude = -(76+30/60); % Kingston's longitude location.latitude = 44+(16/60); % Kingston's latitude location.altitude = 80; % Kingston's altitude time.UTC = -4; % 5 for EDT, 4 for EST time.year = 2010; time.sec = 00; time.month= 1; i=1; for day=1:7 for hour=0:23 for minute=0:30:59 time.day=day; time.hour=hour; time.min=minute; sun=sun_position(time,location); datestring2(i)=datenum(time.year,time.month,time.day,time.hour,time.min,time.sec); azimuth2(i)=sun.azimuth; zenith2(i)=sun.zenith; if sun.zenith>90 %sun is below the horizon lightfactorone2(i)=0; else lightfactorone2(i)=1; end if ((sun.azimuth<90) || (sun.azimuth>270)) %sun is behind the panels lightfactortwo2(i)=0; else lightfactortwo2(i)=1; end i=i+1; end

end end Radiation2=max(Density2)/1000; %in kW/m2 % Goodwin real data PowerGoodwin2=(Current2.*Voltage2)/1000; PowerGoodwinGenerated2=sum(PowerGoodwin2) %in kW % Fixed panel AreaFixed2=145.2.*cosd(abs(46-zenith2)).*cosd(abs(180-azimuth2)); %in m2 PowerFixed2=Radiation2.*E.*AreaFixed2.*lightfactortwo2.*lightfactorone2; PowerFixedGenerated2=sum(PowerFixed2) %in kW % Single Axis AreaSingle2=145.2.*cosd(abs(46-zenith2)); %in m2 PowerSingle2=Radiation2.*E.*AreaSingle2.*lightfactorone2; PowerSingleGenerated2=sum(PowerSingle2) %in kW % Dual Axis AreaDual2=145.2; %in m2 PowerDual2=Radiation2.*E.*AreaDual2.*lightfactorone2; PowerDualGenerated2=sum(PowerDual2) %in kW %~~~~~~~~~~~~~~~[FOR SPRING (using first week of APRIL)]~~~~~~~~~~~~~~~~~~~ location.longitude = -(76+30/60); % Kingston's longitude location.latitude = 44+(16/60); % Kingston's latitude location.altitude = 80; % Kingston's altitude time.UTC = -4; % 5 for EDT, 4 for EST time.year = 2010; time.sec = 00; time.month= 4; i=1; for day=1:7 for hour=0:23 for minute=0:30:59 time.day=day; time.hour=hour; time.min=minute; sun=sun_position(time,location); datestring3(i)=datenum(time.year,time.month,time.day,time.hour,time.min,time.sec); azimuth3(i)=sun.azimuth; zenith3(i)=sun.zenith; if sun.zenith>90 %sun is below the horizon

lightfactorone3(i)=0; else lightfactorone3(i)=1; end if ((sun.azimuth<90) || (sun.azimuth>270)) %sun is behind the panels lightfactortwo3(i)=0; else lightfactortwo3(i)=1; end i=i+1; end end end Radiation3=max(Density3)/1000; %in kW/m2 % Goodwin real data PowerGoodwin3=(Current3.*Voltage3)/1000; PowerGoodwinGenerated3=sum(PowerGoodwin3) %in kW % Fixed panel AreaFixed3=145.2.*cosd(abs(46-zenith3)).*cosd(abs(180-azimuth3)); %in m2 PowerFixed3=Radiation3.*E.*AreaFixed3.*lightfactortwo3.*lightfactorone3; PowerFixedGenerated3=sum(PowerFixed3) %in kW % Single Axis AreaSingle3=145.2.*cosd(abs(46-zenith3)); %in m2 PowerSingle3=Radiation3.*E.*AreaSingle3.*lightfactorone3; PowerSingleGenerated3=sum(PowerSingle3) %in kW % Dual Axis AreaDual3=145.2; %in m2 PowerDual3=Radiation3.*E.*AreaDual3.*lightfactorone3; PowerDualGenerated3=sum(PowerDual3) %in kW %~~~~~~~~~~~~~~~~[FOR SUMMER (using first week of JULY)]~~~~~~~~~~~~~~~~~~~ location.longitude = -(76+30/60); % Kingston's longitude location.latitude = 44+(16/60); % Kingston's latitude location.altitude = 80; % Kingston's altitude time.UTC = -4; % 5 for EDT, 4 for EST time.year = 2010; time.sec = 00; time.month= 7; i=1;

for day=1:7 for hour=0:23 for minute=0:30:59 time.day=day; time.hour=hour; time.min=minute; sun=sun_position(time,location); datestring4(i)=datenum(time.year,time.month,time.day,time.hour,time.min,time.sec); azimuth4(i)=sun.azimuth; zenith4(i)=sun.zenith; if sun.zenith>90 %sun is below the horizon lightfactorone4(i)=0; else lightfactorone4(i)=1; end if ((sun.azimuth<90) || (sun.azimuth>270)) %sun is behind the panels lightfactortwo4(i)=0; else lightfactortwo4(i)=1; end i=i+1; end end end Radiation4=max(Density4)/1000; %in kW/m2 % Goodwin real data PowerGoodwin4=(Current4.*Voltage4)/1000; PowerGoodwinGenerated4=sum(PowerGoodwin4) %in kW % Fixed panel AreaFixed4=145.2.*cosd(abs(46-zenith4)).*cosd(abs(180-azimuth4)); %in m2 PowerFixed4=Radiation4.*E.*AreaFixed4.*lightfactortwo4.*lightfactorone4; PowerFixedGenerated4=sum(PowerFixed4) %in kW % Single Axis AreaSingle4=145.2.*cosd(abs(46-zenith4)); %in m2 PowerSingle4=Radiation4.*E.*AreaSingle4.*lightfactorone4; PowerSingleGenerated4=sum(PowerSingle4) %in kW % Dual Axis AreaDual4=145.2; %in m2 PowerDual4=Radiation4.*E.*AreaDual4.*lightfactorone4; PowerDualGenerated4=sum(PowerDual4) %in kW %~~~~~~~~~~~~~~|[FOR FALL (using first week of OCTOBER)]~~~~~~~~~~~~~~~~~~

location.longitude = -(76+30/60); % Kingston's longitude location.latitude = 44+(16/60); % Kingston's latitude location.altitude = 80; % Kingston's altitude time.UTC = -4; % 5 for EDT, 4 for EST time.year = 2010; time.sec = 00; time.month= 10; i=1; for day=1:7 for hour=0:23 for minute=0:30:59 time.day=day; time.hour=hour; time.min=minute; sun=sun_position(time,location); datestring5(i)=datenum(time.year,time.month,time.day,time.hour,time.min,time.sec); azimuth5(i)=sun.azimuth; zenith5(i)=sun.zenith; if sun.zenith>90 %sun is below the horizon lightfactorone5(i)=0; else lightfactorone5(i)=1; end if ((sun.azimuth<90) || (sun.azimuth>270)) %sun is behind the panels lightfactortwo5(i)=0; else lightfactortwo5(i)=1; end i=i+1; end end end Radiation5=max(Density5)/1000; %in kW/m2 % Goodwin real data PowerGoodwin5=(Current5.*Voltage5)/1000; PowerGoodwinGenerated5=sum(PowerGoodwin5) %in kW % Fixed panel AreaFixed5=145.2.*cosd(abs(46-zenith5)).*cosd(abs(180-azimuth5)); %in m2 PowerFixed5=Radiation5.*E.*AreaFixed5.*lightfactortwo5.*lightfactorone5; PowerFixedGenerated5=sum(PowerFixed5) %in kW % Single Axis

AreaSingle5=145.2.*cosd(abs(46-zenith5)); %in m2 PowerSingle5=Radiation5.*E.*AreaSingle5.*lightfactorone5; PowerSingleGenerated5=sum(PowerSingle5) %in kW % Dual Axis AreaDual5=145.2; %in m2 PowerDual5=Radiation5.*E.*AreaDual5.*lightfactorone5; PowerDualGenerated5=sum(PowerDual5) %in kW %~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[PLOTS]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ figure(1) plot(datestring2,PowerGoodwin2,'b',datestring2,PowerFixed2,'g',datestring2,PowerSingle2,'r',datestring2,PowerDual2,'c'); xlabel('Date'); ylabel('Power (kJ/s)'); title('Power Output from Solar Panels for a Week in Winter'); datetick('x','dd-mmm','keepticks'); legend('Measured (Goodwin)','Simulated-fixed panels','Simulated-single axis tracking','Simulated-dual axis tracking') figure(2) plot(datestring3,PowerGoodwin3,'b',datestring3,PowerFixed3,'g',datestring3,PowerSingle3,'r',datestring3,PowerDual3,'c'); xlabel('Date'); ylabel('Power (kJ/s)'); title('Power Output from Solar Panels for a Week in Spring'); datetick('x','dd-mmm','keepticks'); legend('Measured (Goodwin)','Simulated-fixed panels','Simulated-single axis tracking','Simulated-dual axis tracking') figure(3) plot(datestring4,PowerGoodwin4,'b',datestring4,PowerFixed4,'g',datestring4,PowerSingle4,'r',datestring4,PowerDual4,'c'); xlabel('Date'); ylabel('Power (kJ/s)'); title('Power Output from Solar Panels for a Week in Summer'); datetick('x','dd-mmm','keepticks'); legend('Measured (Goodwin)','Simulated-fixed panels','Simulated-single axis tracking','Simulated-dual axis tracking') figure(4) plot(datestring5,PowerGoodwin5,'b',datestring5,PowerFixed5,'g',datestring5,PowerSingle5,'r',datestring5,PowerDual5,'c'); xlabel('Date'); ylabel('Power (kJ/s)');

title('Power Output from Solar Panels for a Week in Fall'); datetick('x','dd-mmm','keepticks'); legend('Measured (Goodwin)','Simulated-fixed panels','Simulated-single axis tracking','Simulated-dual axis tracking') %~[REVENUE FOR SIMPLE, FIXED, SIMPLE AND DUAL MODEL FOR FULL YEAR FOR KGH]~ AreaRoof=10000; %in m2 Radiation=Radiation1; %in kW/m2 Tarrif=0.713; %in $/kWh PanelCost=370; %in Canadian dollars/m2 n=1:1:10; %for 10 years %SIMPLE REVENUE RadiationSimple=0.150; %in kW/m2 PowerSimple=AreaRoof*RadiationSimple*E; EnergySimpleGenerated=PowerSimple*24*365 RevenueSimple=EnergySimpleGenerated*Tarrif CapitalCostSimple=AreaRoof*370 NPVSimple= -CapitalCostSimple+sum(RevenueSimple./1.10.^n) %FIXED REVENUE AreaFixed=AreaRoof.*cosd(abs(46-zenith1)).*cosd(abs(180-azimuth1)); %in m2 PowerFixed=Radiation.*E.*AreaFixed.*lightfactortwo1.*lightfactorone1; PowerFixedGenerated=sum(PowerFixed); %in kW EnergyGeneratedFixed=trapz(datestring1,PowerFixed)*(86400/3600) %in kWh RevenueFixed=EnergyGeneratedFixed*Tarrif FixedPanelArea=3.9; %m2 FixedPanelCost=(491.892+PanelCost*FixedPanelArea); %Canadian dollars CapitalCostFixed=(AreaRoof/FixedPanelArea)*FixedPanelCost NPVFixed=-CapitalCostFixed+sum(RevenueFixed./1.10.^n) %SINGLE REVENUE AreaSingle=AreaRoof.*cosd(abs(46-zenith1)); %in m2 PowerSingle=Radiation.*E.*AreaSingle.*lightfactorone1; PowerSingleGenerated=sum(PowerSingle); %in kW EnergyGeneratedSingle=trapz(datestring1,PowerSingle)*(86400/3600) %in kWh RevenueSingle=EnergyGeneratedSingle*Tarrif SingleAxisArea=3.9; %in m2, (holds two panels) SingleAxisCost=(502.043+SingleAxisArea*PanelCost); %in Canadian Dollars CapitalCostSingle=(AreaRoof/SingleAxisArea)*SingleAxisCost %in Canadian Dollars NPVSingle= -CapitalCostSingle+sum(RevenueSingle./1.10.^n) %DUAL REVENUE AreaDual=AreaRoof; %in m2 PowerDual=Radiation.*E.*AreaDual.*lightfactorone1;

PowerDualGenerated=sum(PowerDual); %in kW EnergyGeneratedDual=trapz(datestring1,PowerDual)*(86400/3600) %in kWh RevenueDual=EnergyGeneratedDual*Tarrif %in Canadian Dollars DoubleAxisArea=3.9; %m2 (hold two panels) DoubleAxisCost=(715.250+DoubleAxisArea*PanelCost); %Canadian Dollars CapitalCostDual=(AreaRoof/DoubleAxisArea)*DoubleAxisCost NPVDual=-CapitalCostDual+sum(RevenueDual./1.10.^n)