With a few known inputs, we can calculate important values that indicate how beneficial solar installation is in both the short term and the long term. Variables to consider include cost of installation, the energy load size, peak sun hours in a given location, cost of utility power, net metering rates, and many others.

### Levelized Cost of Energy

In St. Louis, residents pay approximately 9.7c/kWh for residential electricity. Since solar energy costs nothing once arrays are implemented, the cost must be levelized to see what the per-kWh cost would be over the lifetime of a solar array. The levelized cost of solar energy was calculated as follows:

The calculated LCOE values for solar do include the 30% federal tax credit.

Annual production factors in the array size, average peak sun hours in St. Louis, average derate factor of a panel and panel efficiency:

The following assumptions were made in the calculation:

• Peak sun hours per day[i] = 4.8
• Derate factor[ii]: 0.77

Installation costs are per-watt quotes given by Straight Up Solar, a St. Louis-based solar company. Figure 7 shows what the LCOE for four different array sizes would be. The levelized cost for a 5 kW and 6 kW array is less than 8c/kWh. This is actually lower than current grid prices, but the upfront cost is still a barrier to most people and companies interested in solar installation.

Figure 7: LCOE for different solar array sizes.

### Cost Savings

To simulate further scenarios, the MATLAB model looks at factors that could improve the cost of solar. All cost and energy calculations were made under the assumption that a single-family home uses 12,720 kWh annually, which is the Missouri average. Since homes built by Habitat incorporate energy efficiency, it is possible that the actual value is lower than the average.

This model calculates energy production over the whole year, rather than looking at seasonal, monthly, or even daily house load and solar resource. Since solar resource varies throughout the day and year, looking at discrete time intervals can show the benefits of solar power more clearly.

Most residential energy consumption in the St. Louis region follows the trend shown in Figure 8. Note that the data in the figure indicates annual consumption of 6000-65000 kWh, which is significantly lower than the Missouri average used in simulation. As expected, demand is higher in the summer months when cooling is needed. The trends may look different based on what systems are used. For example, many homes use natural gas for heating and electric cooling. An electric heating system would significantly increase the demand in the winter months.

Figure 8: Load profile of a typical single-family home in St. Louis, MO (Jason Trobaugh, 2017-2018 data)

Solar production of an array closely follows the pattern of consumption shown above. More solar can be generated in the summer months because there are more peak hours of sunlight. Figure 9 shows how much solar a 6 kW array would produce over the year along with the percentage of total consumption this 6 kW array could cover.

Figure 9: Monthly energy consumption graphed with predicted monthly generation of a 6 kW solar array.

As shown, solar production cannot accommodate the high demands in the summer, but a 6 kW array meets the house demand in the spring, fall, and winter months. As smaller increments of time are analyzed, more accurate cost and savings calculations can be made.

A monthly load profile can give more accurate net-metering predictions than looking at annual production and consumption. With Missouri’s current net metering policy, the above overproduction would accumulate \$66 in savings annually. However, day-to-day production will give more accurate results since a home’s electricity load changes throughout the day.

Ameren Missouri’s net metering rate[iii] does not offer the same benefits as it does in other states. Calculations under different net metering conditions simulate how the cost of solar could become more competitive under policy changes. With a net metering rate that is twice what it currently is, (5.2c/kWh) the homeowner would obtain \$132/year from net metering. If power sent back was priced at utility cost (9.7c/kWh), the net metering benefits would increase to \$186.

### Projected Costs

As panel efficiency improves and solar becomes more incentivized, the cost of solar panels will decrease over time. The cost of solar has shown a decreasing trend, while utility costs steadily climb. Using NREL data on utility costs by zip code, it was found that St. Louis utility costs appear to be increasing by 1.6% per year. On the other hand, solar costs are decreasing by 3.6% per year. Figure 10 shows the projected trend of different sized solar arrays and utility power.

Figure 10: Projected LCOE over time for solar and utility power in St. Louis, MO.

As shown in the figure, the cost of utility power is grid competitive and the gap between solar and utility power will only continue to increase. This model assumes the rates will remain constant, but factors such as carbon taxing, improved solar efficiency, or tariffs on solar panels could alter the rate of growth/decline.

### Carbon Emissions

The model converts energy savings from a solar array to emissions savings as a means to show how many tons of CO2 can be saved by reducing dependence on the grid. The equation is as follows:

The annual load was estimated at 12,720 kWh, the Missouri average.[iv] According to calculated values, a 5 kW array would save 20 tons of CO2 emissions per year in a single family home. To put this in context, the average carbon emissions per capita in St. Louis is 22.9 metric tons per year, meaning the addition of solar cuts a sizable portion of an individual’s carbon footprint.

Two different theoretical carbon taxes were simulated. As this paper does not focus on environmental policy, assumptions were made to simplify calculations. The first taxes emissions at \$40/ton, with a 5% increase each year. Assuming residents would be taxed directly and pay this amount and the load remains the same each year, the emissions tax would add up to \$75,856 over 25 years. A 5 kW solar array would save \$40,226 over this time period.

In a second model, carbon emissions are taxed at \$12.50/ton, with a \$12.50 increase each year. Representative Jim McDermott proposed this tax[v] in 2012, with the idea that consumption would drop rapidly with such an aggressive tax. Assuming no change in consumption, the tax would result in \$153,733 lost over 25 years. The solar array would save \$72,211.

With both proposed carbon taxes, we can use the same conversion equation above to convert \$/ton to \$/kWh and predict the price increase in utility power. The equations for utility price increase would be as follows:

• \$40/ton tax with 5% increase each year:
• \$12.50/ton tax with \$12.5 increase each year:

The projected cost of utility electricity with the added carbon taxes can be seen in Figure 11 below. With these moderate and aggressive taxes, solar becomes grid competitive in 5-10 years rather than 30. The values can be altered to accommodate other carbon tax policies. Should a policy be implemented, there will be an even greater incentive to install solar arrays.

Because the focus of this report is on low-income residents and making renewable energy more affordable, it is important to consider how a carbon tax will affect those below the poverty line. The simplified model above assumes each individual pays the tax on their emissions and no tax credits or subsidies are included.

A study[vi] done at the University of Illinois points out low-income families spend a higher percentage of their earnings on electricity and a federal carbon tax that is equal to all would disproportionately burden different income levels. Additionally, those living in the middle of the country rather than the coasts experience more severe winters and summers. Thus, someone in St. Louis would spend more on heating and cooling than someone in northern California. In order to make a federal carbon tax equitable, it could not follow the simple model above.

Figure 11: Cost projections with added carbon tax.

[i] Turbine Generator, 2018. https://www.turbinegenerator.org/solar/missouri/

[ii] Guide to PVWatts Derate Factors for Enphase Systems When Using PV System Design Tools. PVWatts, 2014.

[iv] Electricity Local, “Saint Louis, MO Electricity Statistics”.

[v] “Carbon Tax Effectiveness: Estimated CO2 Reductions from a Briskly Rising Task”, Carbon Tax Center, 2012.

[vi] Fullerton D. et al. Does a carbon policy really burden low-income families? University of Illinois: Climate Change Policy Initiative (2017), 1-9.