# What size of a solar system do you need and how to pay or it

## Solar Powered: Part 3 of 4

This is the third article from the series on how to choose the best solar pv system and financing.

### How much solar do you need?

Two key values that describe a pv systems are peak capacity, in kWp (kilowatt peak) and annual energy production per peak capacity, in kWh/kWp (kilowatt hour per kilowatt peak).

KWp is the value that describes the energy output of a system achieved under full solar radiation (under set Standard Test Conditions). Solar radiation of 1,000 watts per square meter is used to define standard conditions. A 200 Wp panel can generate a energy output of 200W. A 250Wp panel can generate 250W, and so on.

The hourly or daily amount of sunshine is different for every location throughout the day and the year, obviously. Therefore, a pv system generates a different amount of power output, ranging from 0 at night, when there is no sun, up to its peak capacity in full sunshine. Each day the energy output varies dependent mostly on the amount of sunshine.

Because weather conditions are somewhat similar over the years, it is possible to predict the average monthly and annual energy production of a system using historic, standardized weather data. There are maps available of solar resources showing how much energy reaches the surface of panels. The data is presented in standardized form. Maps show how many ‘standard’ sunshine hours can be exacted over a month or a year. For example, in Malta there are 5.7 ‘standard’ hours per day, on average, or 5.7h x 365 = 2,080h per year. This is useful because it allows you to calculate the energy generation of your solar system.

### Annual energy production

First, let’s calculate the annual production per peak capacity. Solar maps show how much sunlight reaches the panels. Depending on the pv system, the sunshine is converted into electricity at different efficiencies. The efficiency depends on the system’s configuration (tilt and azimuth of panels) and the equipment used (panels, cables, inverters). Currently available systems allow for 80% efficiency. So, the total amount of sunshine hours times the efficiency factor (80%) equals the annual energy production per peak capacity.

Again, taking Malta as an example: 5.7kWh/day x 365 = 2,080 kWh / year x 80% = 1,664 kWh/kWp per year.

To calculate your systems expected output, you multiply the peak capacity of the system (in kWp) by the energy production per peak capacity (kWh/kWp). You will get the total energy generated by a system each year. For a 2.5 kWp system in Malta, it would be 2.5 x 1,664 = 4,161 kWh per year.

There are websites with free solar energy output calculators. A very good, highly recommended one can be found here: http://pvwatts.nrel.gov/

Why is this important? This allows you to calculate the system size you will need in order to meet your energy demand. Check your electricity bills. See how many kWh of electricity you consume each year. Divide that number by the energy production per peak capacity and you will know what size pv system you need. An average household uses 10–20 kWh daily. As an example, let’s say you consume 10kWh. Multiply 10 by 365 for annual production, or 3,650 kWh. Divide that number (3,560) by energy production per peak capacity for your location. The result is the system capacity that would generate all the energy you need for the entire year. (Continuing the Malta example: 3,650kWh / 1,664 kWh/kWp= 2.19 kWp.)

Keep in mind that this is average energy consumption and production over a year. The data from the maps will not tell you if you will be able to meet your energy consumption for every given hour or at night. However, if you have a grid connected system, you can use the energy grid as a free storage and take back from it when needed and deliver it back when there is a production surplus.

### How much space do you need?

Say you have x sq m ( or y sq ft ) of roof space. You can assume that it takes about 1 sq m or 10 sq ft* to install around 0.10 kWp of a pv system. Or, to install 1kWp of a system, you need about 10 sq m, or 100 sq ft, of space. You can also calculate the maximum system size possible and the maximum energy output. Divide the roof size in sq m by 10 or, in sq ft, by 100 to get the system peak capacity. Then, multiply your result by the annual energy production per peak capacity.

Knowing this, you are able to estimate:

• How big the solar system should be to handle your energy consumption (using the last example): 2.19kWp x 10 sq m/kWp = 21.9 sq m or x 100 sq ft / kWp = 219 sq ft.

• How much energy your roof can generate: Assuming you have 150 sq m or 1,500 sq ft of available space: 150 sq m / 10 sq m /kWp or 1,500 sq ft / 100 sq ft / kWp = 15 kWp. Multiplied by the annual energy production per kWp: 15 kWp x 1,664 kWh = 24,966 kWh per year.

(*) 1 sq m is not exactly 10 sq ft. 1 sq m is exactly 10.7639104 sq feet. For simplicity’s sake, assume 10 ft per 0.1kWp in the calculations. Each system and each roof is different, so the actual area covered by the pv system will vary depending on the size, shape, type of a roof and its location. Taking 1 sq m or 10 s ft per 0.10 kWp is a useful approximate.

### How much your space is worth?

Knowing how much energy your rooftop or ground space can generate, you can also calculate the revenue it can produce. Simply multiply the annual energy production by the energy price. Using the Malta example: 24,966 kWh x 0.16 EUR/kWh = 3,994 EUR. Over 20 years, that’s 79,891 EUR. Assuming the pv system costs 2,300 EUR/kWp, the installation costs would be 34,500 EUR. So, 150 sq m of space is worth, in this case, 45,391 EUR in profit or 79,891 EUR in revenue.

### Which financing offer is best for you?

You have calculated your needs and now know the size pv system you want. Now you can confidently ask around for offers. You can receive offers for a turn key installation, where it’s up to you to finance the system (with cash, a bank loan, etc.) and offers for a PPA, where you enter into a long term contract for solar energy purchase.

Look at the pv system as a bank deposit or the purchase of company stock. An investment is required in the beginning (the system installation) that will give you a number of payouts in the future (generated solar energy). The payouts in the future can bear a certain risk. Different financing and ownership solutions for solar systems have different risk profiles. Being able to calculate the relation between the initial investment and the future payouts allow you to compare different solar solutions and decide if the return on investment compensates for the risks involved.

Two indicators will give you an idea about the profitability of the investment and allow for comparing different options: the payback period and the internal rate of return.

The payback period indicates how long will it take get the invested money back. Say there is an opportunity that requires an investment (a solar systems cost) of 1,000. For the next 10 years, it will pay back 163, each year (solar energy revenues). By dividing 1,000 (the investment) by 163 (annual return) you calculate the payback period, in this case, 6.13 years. This means that after 6.13 years, you get all of your invested money back. During the remaining 3.87 years of the project, all other revenues are profit.

The internal rate of return (IRR) is a number to describe the equivalent interest rate on a bank deposit required to match the profitability of the investment. It takes into consideration the value of money in time: cash now vs. cash in the future. Basically, the same amount of money now is worth more now than it would be in the future. Using the example above, the investment of 1,000 now, gives payouts of 163 each year, for the next 10 years. That’s 1,630 in total. But the value of that money NOW is greater than it will be in 10 years. The IRR shows the equivalent interest of a one year deposit. In this case, the IRR is 10%. In other words, the analyzed investment is equivalent to a one year deposit with 10% interest. 1,630 over the next 10 years is equivalent to receiving 1,100 next year, when investing 1,000.

The IRR for any investment can be calculated using a formula in a spreadsheet. All it needs is a series of time organized data about the investment and payouts. The investment should be input as a negative number and payouts are entered as positive numbers. The formula does the rest for you. It will give you a single value, an interest rate in percentage. It should be noted that if you enter data related to annual payments, the interest rate will be annual. If the data relates to monthly payments, the formula will give you a monthly interest rate.

IRR is very handy when comparing different types of investments within different time frames. You can use it to compare a one year bank deposit, a 15 year PPA and a 20 year cash investment into solar.

### How to calculate a rate of return on a solar system with a PPA?

You want to install a 2.19 kWp solar system in Malta that costs 5,037 EUR and generates 3,645kWh per year. Instead of buying it directly, you have an offer from a solar company to enter into a PPA (a power purchase agreement). The company offers you a 20 year contract, with a fixed price of solar energy at 0.15 EUR/kWh. They require a 10% upfront payment. Your current grid energy price is 0.16 EUR/kWh. Is this a good deal?

Your investment is the 10% upfront payment: 503 EUR. What are the payouts? The pv system will offset 3,645 kWh of electricity you consume per year. Your annual revenue will be:

3,645 kWh x 0.16 EUR/kWh (the current price of electricity) = 583 EUR.

The payment made to the solar company will be your annual costs. Under a PPA, you buy solar energy from a system installed on your roof. In this example, the annual production of 3,645 kWh will be bought by you at 0.15 EUR/kWh. So, in the first year, your revenues equals 583.20 EUR, and your costs equal 546.75 EUR. Therefore, a profit of 36.45 EUR will be yours in the first year.

Now, calculate the revenues and costs for years 2–20. Planning for future energy production, you have to take into consideration that solar panels age, just like every other technology. They lose efficiency. But not much. Good panels lose only about 0.5% efficiency each year. Knowing that, you should deduct 0.5% each year, if you bought the good panels, from the amount of energy generated. As for energy cost savings, we can assume quite conservatively as well, that grid energy will go up in price by 2% each year. Let’s be conservative for the sake of this example and use 0.8% as our efficiency loss.

Over the 20 year period, the profits (payouts) vary from 36 EUR in year 1, to 257 in year 20. The sum total on all payouts is 2,914 EUR with an initial investment of 504 EUR. Such a series of investment and payouts over 20 years has the IRR of 17.58%. In this example, this specific PPA offer is equivalent to an annual deposit with the interest rate of 17.58%.

Another investment possibility from a solar company is an offer that does not require an upfront payment. You receive the payouts with no initial investment. For example, you are offered a PPA with no upfront payment. You only pay for the energy delivered at a fixed price of 0.16 EUR/kWh. In this case, there is no IRR to calculate. The IRR is infinite. You can also see this as receiving free money. The total savings with this offer over the 20 year period amount to 2,241 EUR.

### How to calculate the rate of return for a solar system bought with cash?

When financing a pv system with cash, you buy, own and operate it yourself. While the revenues generated would be the same, the costs would differ. You would only pay for the monitoring, maintenance and insurance of the system while you own it. Monitoring and maintenance can be outsourced to a specialized company for a flat annual fee. Most likely, the company that installs your system would also offer monitoring and maintenance. Let’s assume those costs to be at 50 EUR/kWp per year with an insurance premium of 0.5%. This results in an annual cost of 109.5EUR and 25 EUR, respectively. By deducting these costs from annual revenues received from your system, you profit 448 EUR in year 1 and 585 EUR in year 20. The initial investment is equal to the total installation cost of the pv system: 5,037 EUR. This option has an IRR of 7.64%.

### How to calculate a rate of return on a solar system financed with loan?

In addition to the costs mentioned when purchasing with cash, there is additional cost related when financing. The amount of the debt service depends on your interest rate, the duration of a loan and the amount borrowed. Your bank or your solar company should give you an offer for your specific situation with a calculated payment schedule.

For this example, let’s assume an interest rate of 5%, a 10 year repayment plan and 80% financing (the loan will mount to 80% of the pv system value, 4,029 EUR in this case). This results in an annual payment of 522 EUR that has to be deducted from the profit previously calculated. Your profit, after financing, equals -73 EUR in year 1 and 585 EUR in year 20. In the first 10 years, profits are not high enough to cover financing costs. After an initial investment of 1,007 EUR (20% of the system value) there has to be additional ‘investments’ for the first 10 years of the project to service the loan. After repayment of the loan, all profits constitute investment payouts. The IRR for our example equals 10%, higher than paying with cash, but much lower than our previous example of over 17%.

Let’s do another comparison. This time, let’s finance the system using a mortgage on the property. Because you are using property equity, the loan can cover 100% of the installation costs with an interest rate of 3%. It can also be repaid over 20 years. This results in an annual debt service of 338 EUR. Profits after covering your monthly loan payment equal 109 EUR in year 1 and jump to 247 EUR in year 20. There is no initial investment, so it’s not possible to calculate the IRR. Once again, it’s an investment with no initial costs. The sum total of savings is 3,553 EUR.

### Comparing the financing options

To sum up, let’s compare all of our above examples: 2 PPA offers, one cash purchase and 2 loan offers.

• The IRRs equal:

PPA1=17.58%; PPA2 = infinite; Cash = 7.64%; Loan1 = 10%; Loan2 = infinite.

• The cash total (EUR) generated in each case equals:

PPA1=2,411; PPA2=2,241; Cash = 5,288; Loan1 = 4,099; Loan2 = 3,554

The decision is up to you, based on your preference and other factors involved. General rules that can be observed here are: (1) by owning the system yourself, you are able to generate more cash, (2) the biggest impact on the IRR is the amount of the initial investment. The lower the upfront payment, the higher the IRR.

Creator of Online Project Tracker. Web app solving problems with communication and data inconsistency issues when managing construction and O&M projects. http://www.hienergypeople.com/online-project-tracker/

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