Table 2: Solar Panel Criteria

Efficiency
7
Availability
4
Manufacturing Carbon Footprint
2

Table 2: Solar Panel Criteria
We found cost per Watt to be the most important criterion because it is most directly related to the economic feasibility of the system. For this reason, we assigned cost per Watt a weight of ten. A system’s durability is also very important to its overall performance, as a greater system lifespan will
increase the amount of energy that it can produce. However, we decided that durability was less important than cost per Watt, giving it a weight of eight. Efficiency was not as important as the previous two criteria. In spite of this, it was still important that we meet a certain level of efficiency in order to generate enough power given the limited roof space. Therefore, we gave efficiency a weight of seven. The availability of a system was not very important due to the numerous solar panel options available, so it was given a weight of four. Finally, the carbon footprint was important from an environmental point of view, but weighting this category too heavily could lead us to selecting a solar power system that wasn't economically feasible, and therefore would not be implemented at all. For this reason, we gave the manufacturing carbon footprint a weight of only two. After performing this analysis on many different solar panels, we were left with a single number for each, representing how well each panel style met our criteria. We selected the top five as finalists for our recommended solar panel implementation.
3.3 Solar Panel Placement
Determining where to physically place the panels on the roof, as well as how to orient them, was important. This is because a panel’s orientation can have a large effect on the amount of solar energy it can gather and power it can generate. In order to decide how to optimally place the solar panels that were chosen, we created a number of placement scenarios. For each of our proposed scenarios, we determined a corresponding solar panel placement. Each placement has been carefully laid out attempting to meet the following criteria: maximum amount of power generation while still leaving room on the roof to walk. If at any point throughout the analysis, we felt that the given layout would not allow enough room to walk, we would remove the offending panels.
In order to generate the maximum amount of power, we wanted to place as many panels as possible at the optimal angle, without any of them being shaded between 9:00am and 3:00pm, the time
period of maximum sunlight.29. Aside from placing the panels outside of the shadowed area produced by the building, we also needed to ensure that the panels were not shaded by the row of solar panels in front of them. The minimum separation between the panels must be calculated using the worst case scenario sun position: when the sun is 30° above the horizon.
29 Lenardic, Denis. Solar radiation estimation and site analysis. http://www.pvresources.com/en/location.php.

30°

Θtilt
d
Solving for d in the above illustration yields the minimum separation distance between rows of solar panels without shading any of the panels at any point during the year. A solution for d can be found by using the equation below.
Figure 8: Depiction of the Sun Rays vs the Tilt of the Solar Panels
Calculating the minimum distance a row takes up is done using the following equation:

With this knowledge, we proceeded to break the roof up into a series of rectangles and determined the solar panel placement for each rectangle. We divided the width of each rectangle by the width of the solar panel and rounded down to get the number of solar panels for a given row. We then took the length of the rectangle and divided it by the minimum allowable distance for a row. This gave us the number of rows that we could have inside this rectangle. We did this for each rectangle, and then combined the results, making sure that there was enough walking space between the last row
of one rectangle and the first row of an adjacent rectangle. This process generated our optimal panel placement. To determine how we would wire the solar panels together, we followed the concept that we would wire solar panels in series that could potentially be shaded at the same time, and putting those rows in parallel with other rows. We calculated the maximum number of solar panels that could be placed in parallel by dividing the maximum current rating for the inverter by the peak current generated by the solar panels under ideal conditions. Rounding this number down gave us the maximum number of parallel rows.
Dividing the maximum voltage rating for the inverter by the peak voltage of the panels under ideal conditions and rounding down gave us the maximum number of solar panels that could be wired in series.
Based on the maximum number of panels that could be wired in series, we created rows of maximum length, going from north to south. This guaranteed that if there was shade, all of the panels in series would be shaded at the same time. We then placed as many adjacent rows in parallel as was allowed by the MAXparallel calculation, and wired them all to one inverter. We repeated this process until all solar panels were wired to an inverter. It is important to note that if shading occurs on a given solar panel, then current is unable to flow through it or any panels that are in series with this panel. This is important to consider when wiring up the panels, so that they are done in a way such that a small patch of shade won’t prevent multiple rows of panels from producing electricity.
3.4 Economic Feasibility of the Systems
The crux of this project was the determination of economic feasibility. In order to determine economic feasibility, one must do a thorough job of both understanding the mathematical analysis behind it and estimating the various parameters that are taken into account. This section will describe the mathematical analysis that we employed during our project as well as explain our methodology for the analysis. Later, during the economics section, we will present our choice of various parameters that go into the economic calculations along with our reasoning for their selection.
Initially, we gathered information about similar projects that have been done to determine economic feasibility. The Massachusetts Technology Collaborative (MTC) offers a Microsoft Excel spreadsheet that helps users determine the feasibility of solar panel installations.30 This spreadsheet was helpful because it accurately calculated the total rebates available in Massachusetts. It had a detailed depiction of cash flow analysis, and overall, cleanly presented the data. While being an excellent tool, we believed that there were many drawbacks to directly applying this economic analysis to Wesley United Methodist Church. The largest concern was that MTC’s analysis was specific to either a taxable commercial entity or a personal residence, while the Wesley United Methodist Church is neither, being a non-profit organization exempt from taxes. Rather than trying to modify what MTC had done, we decided to assume the relevant portions from their spreadsheet and use them as a basis for our own calculations. This allowed us to make a spreadsheet tailored specifically to the Wesley United Methodist Church. The spreadsheet that we made contained the following sections: Section 1: System Size and Cost Section 2: Installation and Fees
30 Non-Residential Rebate Calculator. Commonwealth Solar. http://www.masstech.org/SOLAR/Attachment%20A2-Non%20Residential%20Solar%20Rebate%20Calculator%20Only-070208.xls.
Section 3: System Life Expectancy
Section 4: Incentives and Rebates Section 5: Financing Section 6: Energy Generation and Usage Section 7: Worldwide Economic Factors Section 8: Results and Analysis The first section dealt with the scale of the system, the cost of the solar panels per Watt, and the cost of the inverter and other components. We chose to have the data entered in this way because by using cost per Watt as a primary variable, the economic analysis is more readily scalable to systems of various sizes. Until a company makes a final estimate, we feel it is best to analyze the data on a per Watt basis because other parameters can be changed to see how they affect the cost of the overall system. The end of Section 1 displays the total cost of the photovoltaic system components. The next section dealt with the cost of the installation and other associated fees. The largest contributor to this category was the installation cost per Watt. The most accurate way to determine an installation cost would be to get multiple estimates from different contractors. In the meantime, we have chosen to look at the installation cost on a per Watt basis because we can estimate it with a reasonable amount of certainty and because it is scalable to different system sizes. After taking into account electrical inspection costs and other fees, section two calculates the total cost of installation and fees.
Section three dealt with the system’s lifespan and maintenance costs. The system life expectancy is an important factor because it determines the amount of time the solar panel will be producing energy. A longer life expectancy generates a better net present value (the sum of future cash flows discounted to the present value) and a better return on investment. This section also deals with system degradation, as each year solar systems put out slightly less energy than they did before. This is
due to the system slowly breaking down. Maintenance costs, as well as a maintenance cost adjustor were also included in this section. The maintenance cost adjustor allowed us to predict how much maintenance costs will increase over the lifetime of the system. The next section, incentives and rebates, came primarily from MTC’s spreadsheets for determining economic feasibility. Its parameters are the system size, whether or not the building is a public building, and whether or not the components are manufactured in Massachusetts. It uses these factors to determine the total system rebate. This section also takes the Renewable Energy Credit (REC) price per Watt and an accompanying adjustor for this price and estimates the revenue that will be generated each year from renewable energy credits. At the end of this section, we were able to calculate the total cost of the solar panel system, by taking into account the cost of the components, the cost of installation and fees, and the total rebate received. The section on financing allows the user to input the down payment percentage, which is useful to help the church determine how the size of the down payment affects the system’s overall economic feasibility. The interest rate and loan period are also inputs in this section. With this data, we were able to calculate the size of the down payment and the monthly payment. The next section, energy generation and usage, allows us to calculate how much energy will be produced from the solar panels. There are fields to input the average daily insolation per m2 for each month. Using this data, along with the system efficiency, we can determine the total amount of energy expected to be generated in the system’s first year. Using the degradation factor from Section 3, we can then determine the expected energy generation for each year of the system’s life expectancy.
The last section, analysis, takes information from the previous sections to compute typical economic values such as net present value, the breakeven point, and cash flow. The yearly cash flow (a value which changes from year to year) is calculated by taking the amount of money saved in the year, from both RECs and saved energy costs, and subtracting the cost of the loan. Net present value is