Modeling of a Residential Photovoltaic System and Model Validation Using Measured Data

Incident Solar Radiation
The south facing roof gets the maximum exposure of sun during the day, so this is where the solar panels can be mounted. The incident solar radiation (KW/m2) that the roof will get changes with the time of the day and the month of the year and the inclination of the roof. Figure 3 provides the incident solar radiation data for Philadelphia which can be used in Malvern as well.

Shading
The roof is partially shaded from the surrounding trees this shading does vary somewhat by season. The percentage of the shade on the actual site is shown in Figure 4. The shading of the site corresponds to shading of the solar panels. For example, in January the system output will be 60% of its actual power output due to the shading.

Figure 4: Solar Obstruction Data of the site

Calculation
The house has an energy usage of 15,800 KWh/year with a peak power of 2,393 KWh/month. Bases on the available panel area and the incident solar radiation, we have calculated that the installation of a 6KW PV system will generate around 6600 KWh/year. Thus a 6 KW system will provide just over 40% of the house’s anual consumed energy. The total cost of the system without any incentives is approximately $43,056.

Financial Analysis
The following factors determine whether the investment in a PV system provides a reasonable rate of return or not:

1. The federal tax incentives and subsidies available
2. The state tax incentives and subsidies available
3. The tax bracket that the owner’s property falls under
4. The rate structure and percentage of rate increases of the local utility

For the system under study, figure depicts the relation between the first three factors mentioned above.

The initial cost of the system is $43,056 (based on the estimation that the cost of the purchasing and installing the panels is $7/KW). Pennsylvania’s 2009 Sunshine grant is expected to provide rebates 35% of the installed system costs to help defy the cost of installation. Accordingly for this model, the owner could receive approximately $10,450 in rebate from the state. The 35% rebate is calculated on the costs after the federal tax credit. The federal tax credit is calculated on the base installed cost.  Based on the system mentioned above the homeowner can get $12,917 as incentives from the government. Thus the total cost of the system to the owner will be $19,674.

The rate structure that will be considered is a charge of $0.1781/KWh. This is based on the charge rate from the owner’s utilities grid in January 2010. The rate structure is not fixed it can increase or decrease with time. However, the current trend is the increase in the price. Also the rate structure can be different from one region to another. For example, in 2008 Peco customers in West Chester were charged $0.148/KWh for the first 600 KWh used and $0.0729/KWh for the rest. This is important because it means that the solar power is competing with the lower charge. This means that when the financial analysis is done to calculate savings or profit, the analyst should use the correct values accordingly.The rate structure that will be considered is a charge of $0.1781/KWh. This is based on the charge rate from the owner’s utilities grid in January 2010. The rate structure is not fixed it can increase or decrease with time. However, the current trend is the increase in the price. Also the rate structure can be different from one region to another. For example, in 2008 Peco customers in West Chester were charged $0.148/KWh for the first 600 KWh used and $0.0729/KWh for the rest. This is important because it means that the solar power is competing with the lower charge. This means that when the financial analysis is done to calculate savings or profit, the analyst should use the correct values accordingly.

Results
The solar power output of the system was predicted based on the insolation data presented in the earlier section. The predicted solar power output is higher than the actual data. This can be a result of shading that the solar panels where getting or very cloudy days. The owner mentioned that in the month of December the solar panels were covered in snow. This can explain part of the low actual solar power obtained as shown in Figure 6. The actual power obtained in December was 68 KWh. The system in that season should have an output of 250 KWh. The same applies for the month of January. In the months of April, May and June the predicted solar power is close to the generated actual solar generated. For the month of July we don’t have any available readings yet. We will keep a close monitoring of the system performance every month.

Figure 7 shows the predicted usage and the actual usage of the residence under study. In August 2010 the actual usage was higher than the predicted usage. In September this fact changes because the owner decides to change the old hot water heater and replace it with an efficient one. This results in a decrease of actual usage by around 300 KWh. The effect of the new hot water heater is also reflected in the months of January and February where the consumption is much lower than what has been predicted. Figure 8 shows the predicted savings on the electric bill that the solar system contributes to. From the month of August 2010 till January 2011 the predicted savings are higher than the actual savings. This trend changes in the following months when the owner replaced the inefficient heaters in his house. From February till May the actual savings is higher than the predicted savings. In June the savings is the highest where there is $100 in savings on the electrical bill. The predicted savings per year is $1193. So far the actual savings are $1,118 without adding the savings of the month of July. If the savings of July are the same as June the actual savings will be $1,348 which is higher than the predicted savings. Based on this year’s actual savings the pay-back period of the system is 15 years ( $19,674/$1,348). After 15 years the owner of the house will start making money on the solar investment.

It is also noted that installing a solar power system increases the value of the house as the house would be considered energy efficient. According to the study “Evidence of Rational Market Valuations for Home Energy Efficiency” published in the Appraisal Journal, residential real estate markets assign to energy efficient homes an incremental value that reflects the discounted value of annual fuel savings. The capitalization rate used by homeowners was expected to be 4%-10%, reflecting the range of after-tax mortgage interest rates during the 1990s and resulting in an incremental home value of $10 to around $25 for every $1 reduction in annual fuel bills(3). Let’s consider that the value of the house under study will increase by $10 for every $1 of energy saved. By installing a solar power system the house will save around $1,300 on the annual electrical bill. That means the annual incremental increase of the home value will be approximately $13,000. With this consideration the payback period of the system is reduced to be 4 years.

Conclusion
A comprehensive engineering and financial analysis of installing a solar power system on a residential house was discussed. The location and incident solar radiation of the unit under study is very favorable for installing the system. The house has minimal shading which makes it ideal for a solar power system. The house has ample roof area for installing such a system as well. Studying the energy consumption of the unit showed that consumption peaks in the summer, which adds to the advantages of installing a solar power system. Finally a financial analysis was conducted that took into account  increasing in utility rates and financing option available for the owner. The results obtained were compared to actual data. The actual savings were higher than the predicted savings and that is mainly due to changes that the owner did at the consumption level. The payback period is around 15 years and only after this time the owner will be able to generate profit. The value of properties with renewable energy systems increases according to a market study. If this was taken into account the payback period of the house would be only 4 years. Finally, this analysis is based on current market predictions. A key issue in the successful implementation of residential solar PV systems is the contribution of state and federal rebates and tax incentives.

This may seem to be an artificial input to the market value of solar PV, but such inputs are not without precedent and over time, the installed cost will come down and PV panel costs come down.