Based on 12 months of solar data, it is recommended that solar panels should be installed for Michigan homeowners versus solar shingles. The rate of return on investment for solar panels (IRR) at a 95% confidence is 3.391% to 3.914%. The IRR for solar shingles at a 95% confidence is 1.410% to 1.953%. However, this report will show that solar arrays in Michigan do not provide a desirable return on investment.

The panels that were analyzed in this report were installed in Fall of 2016 at Floyd Hall in Kalamazoo, Michigan. These solar arrays consist of solar panels and solar shingles. The power output of these solar arrays are being collected in a server in Floyd Hall Lab A-216. Because panels and shingles have an expected life of 25 years, this report uses a life value for the solar arrays at 25 years. The specifications for both the solar panels and solar shingles were taken from the data sheets from their respective manufactureâ€™s website. The cost of kWh was projected from the data taken from the U.S. Energy Information Administration (EIA). The installation cost was based on estimates from multiple sources including the installation cost of the solar arrays at Floyd Hall. Power generated for the first 12 months was 5722.4 kWh and 3769.484 kWh for the solar panels and solar shingles respectively. To determine the future output in kWh for the remaining years a normal distribution was used. The mean of this distribution was the initial value with a 10% of the mean as standard deviation. Crystal Ball and OptQuest were used in order to simulate 10,000 trials for this analysis.

First the life cycle cost of the solar arrays was calculated. The life cycle cost represents the total cost of owning and maintaining an asset over its lifetime. The life cycle cost is calculated as follows:

Life cycle cost=Initial cost+present value of maintenance cost+present value of energy cost+present value of repair and replacement+present value of salvage value

The present value of repair and replacement does fluctuate depending on each system. This analysis recognizes this fluctuation, however, this analysis does not require this parameter because its impact to IRR is minimal.

This report analyzed the ideal example for a homeowner wishing to install enough solar energy to cover 100% of their energy bill. An ideal example requires several assumptions that must be made (see Table 1 below). This analysis includes a 12-hour sunlight period with zero cloud coverage which also includes a 2.5hr solar noon period. Based on the data sheets the standard testing conditions (STC) power rating was used. With these assumptions one can then calculate the amount of solar panels and solar shingles that are needed.

This report also analyzes the IRR for a 6kWh solar array. This takes into account government subsidies, various weather conditions that effect power output, and maintenance costs. A normal distribution was used in order to determine the future values of the power generated from the solar arrays. This was done because weather varies year-to-year and behaves as a random variable. Therefore, having power generated as a random variable provides a realistic analysis. As mentioned above, the cost of kWh was projected from the data taken from the EIA based on trends in electricity prices in the last 30 years.

See Table 2 for the results for the life cycle cost for each solar array.

For a homeowner to achieve enough solar energy to cover 100% of their energy needs, the homeowner will need 9 solar panels or 131 solar shingles based on the assumptions in Table 1. The reason for the drastic difference between the amount of panels versus shingles is the STC power rating. More shingles are needed to make up for this difference. The maximum IRR for solar panels based off of the assumptions in Table 1 is 12.841%. For solar shingles the maximum IRR is 6.084%. To reiterate, these IRR values are based off of non-realistic conditions.

However, the results for a realistic analysis that accounts for variability determined the following figures below:

FIGURE 1

FIGURE 2

Figure 1 shows the Crystal Ball results of IRR assuming that the power generated is a normal distribution. From here, one can see that with 95% certainty the IRR is expected to be between 3.391% and 3.914%. Likewise, in Figure 2, one can see that with 95% certainty the IRR is expected to be between 1.410% and 1.953%.

This report analyzed the life cycle cost of maintaining both solar panels and solar shingles. Also, for a homeowner to achieve 100% of their energy bill through solar energy it was calculated to have an IRR of 12.841% for solar panels and 6.084% for solar shingles. A more realistic analysis was achieved with Crystal Ball and OptQuest performing MonteCarlo simulation. Based on the results from Figure 1 and Figure 2 from the Crystal Ball simulation, one can see that the IRR for panels is higher than the IRR for shingles. This is not surprising because the power rating for the panels is significantly higher than the power rating for shingles.

If a Michigan homeowner was trying to choose between solar panels versus solar shingles this report has shown that the IRR for panels is higher than shingles. However, the IRR for panels is too low to recommend an initial investment even with the governmentâ€™s subsidies. A future analysis can be improved upon with more data collected and improvements to solar arrays efficiency.