Photovoltaic Modules (PVs), Ch. 5-9

 My name is Frank E. Orzechowski and I am an Engineering Consultant, here in Polk County, Florida. Over the last three years, several folks have contacted me about the application of photovoltaic (PV) modules for their home. I have come to realize, there is substantial misinformation and confusion pertaining to the use of this solar electric technology and its benefits. Upon request, I have produced a 16-part series providing the Homeowner with the basic information, necessary to determine whether it is practical to invest in this technology. It includes calculation tools the Homeowner can use, to obtain a, fairly accurate prediction of the cost of the required equipment, along with the length of time it will take to receive a total return on their investment. Below are chapter 5-9. To read chapters 1-4, see my post dated March 3.

Chapter 5–Understanding the Electric Bill

Electricity usage is measured in kilowatt-hours. A kilowatt is equal to 1000 watts and hours is the standard unit of time. The utility charges the Homeowner, based upon the (number of kilowatts of power) the appliance uses times the (number of hours) the appliance is operating. This value is the (kilowatt-hours) used for that particular appliance for any given time period.

The Homeowner can determine the amount of kilowatt-hours of electricity consumed from any appliance by multiplying the appliance’s (wattage rating) by the number of (hours) it was operated and then divide by (1000).

For example, if a 100 watt light bulb is operated for 10 hours, then (100 watts) times (10 hours) divided by (1000) gives us (1 kilowatt-hour) of electricity consumed. If a 1000 watt light bulb was operated for 1 hour, then (1000 watts) x (1 hour)/(1000) is (1 kilowatt-hour) of electricity consumed. Although these are two different applications, they consume the same number of kilowatt-hours.

If the wattage rating is not listed on the appliance, it can be approximated by multiplying the (voltage rating) by the (amps rating) located on the appliance label. For example, a blender is labeled 120 volts and 0.500 amps on the label. The wattage will be (120) x (0.500) = (60 watts). If we operated this appliance for one hour, then, (60 watts) x (1 hour)/ (1000) = (0.060 kilowatt-hours) of electricity consumed.

As a last example, let us look at a standard hot water heating element. Suppose it is rated at 4500 watts and it was heating the water in the tank for 2 hours. Then we would have (4500) x (2)/ (1000) to obtain (9 kilowatt-hours) of electricity consumed.

Although, there are differences between how, some appliances consume power, the homeowner can apply the aforementioned formula to determine the kw-hrs used by any appliance, with reasonable accuracy. All that is required to know is the value in watts, it consumes and the amount of time it operates. The Homeowner’s monthly electric bill is then, the complete sum of all the kw-hrs used, by all appliances for that given time period. The bill usually provides the total kilowatt-hour usage. Some bills, in addition, will show the average monthly use throughout the year. The abbreviation for kilowatt-hour is “kw-hr” or “kw-hrs” and will be used throughout the rest of this article.

So, how much do we pay for electricity? Each electric utility charges the homeowner for total kw-hrs used. The electric utility bill has become a somewhat, complex accounting of the Homeowner’s use of electricity. There are fuel charges, energy charges, state taxes, county taxes and customer service charges, which combine to become the total bill. As far as the Homeowner is concerned, the cost of electricity is a very simple calculation. It is the total dollar value from the bill divided by the total kw-hrs used for that billing period. For example, if a particular bill showed 1500kw-hrs used and the total bill was $200.00, then the cost per kilowatt-hour would be $200.00/1500kw-hrs =20000cents/1500kw-hrs=13.33cents/kw-hr.

In the next chapter, we will discuss how PV modules are combined to form a solar array.

Chapter 6–The PV Solar Array

A PV solar array is a combination of individual PV modules that, when added together, total the amount of power, in kilowatts per month, the Homeowner requires. They are normally, placed side by side on the Homeowner’s roof and electrically connected together by insulated cables and/or connectors. In general, the individual PV modules combined in the array are facing south. This is because the sun moves across the sky, from east to west, thus a south facing solar array will receive the most sunlight, respectively

There are several capacities, i.e., 0.150, 0.180, 0.190, 0.200, 0.220, 0.230 kilowatt modules etc. The contractor will utilize one or more of these together, to obtain the required array. The size of the roof and obstacles play an important role in this determination.

It should be noted, many of these modules undergo rigid testing by the Florida Solar Energy Center in conjunction with the University of Central Florida Research in Cocoa, Florida. Each manufacturer’s model is tested for safety, durability, output power vs. sunlight conditions and the amount the module degrades each year. These tests provide the public an opportunity to evaluate which modules have the best performance and which will provide the longest lifetime expectancy. The Homeowner can contact the FSEC via the web or by telephone for more information concerning the product they are interested in.

It is difficult to provide a simple, all variable encompassing formula to allow the Homeowner to calculate the exact power received from a given set of modules or an array. Factors such as, latitude, temperature, season, available sunlight, equipment, orientation, module quality, years of operation and installation practices, all determine the actual power output over time. However, the FSEC has developed a fairly, accurate formula that would apply for most homes in central Florida, for the purpose of calculating the power required to meet their needs and the number of modules needed to accomplish this. The actual formula is derived from the physics of the PV module technology and the incident radiation from the sun at a given latitude. It is fairly complex, however a consumer friendly form of it is incorporated in the calculation process in chapter’s 7, 8 and 9, so the Homeowner can easily determine their requirements without the need to engage in complex mathematics.

Each homeowner can look at their electric bill and observe their monthly usage. For example, suppose, for one calendar year, the electric consumption averages 1500kw-hrs/month, which is typical for a 3BR-2B home with four residents. The decision can now be made to choose application #1, #2 or #3 for their home. If the first or second application is desired, the solar array must produce, at least, 1500kw-hrs/month, simply to break even. In practice, the Homeowner would install a larger array, let us say, a 1600kw-hr/month system, to account for unusual losses or sunless days. If the third application is desired, the Homeowner may choose a percentage of the total requirement. This might be 25% of the 1500kw-hr/month, which is about 375kw-hr/month. In order to obtain whatever value of kw-hrs/month is needed, the correct number of PV modules must be incorporated.

In the next chapter, we will look at the cost calculation for application #1.

Chapter 7–Solar Array Cost Calculation for Application #1

Assume the installation of a 1600kw-hr/month array utilizing 0.200kw PV modules.

Step 1 Calculate the total kilowatt output required of the array.

Array kilowatts required = (Homeowner’s monthly kw-hr requirement) /(133.76)

Array kilowatts required = (1600)/(133.76) = 11.9617 kilowatts

The array kilowatts required is thus, rounded off, about 12 kilowatts

Step 2 Calculate the number of modules needed to obtain the 12 kilowatts. For our demonstration, we will utilize a standard 0.200 kilowatt module.

Number of modules = (required kilowatts)/(module kilowatt rating)

Number of modules = (12)/(0.200)

Number of modules = 60

Step 3 Calculate the approximate area these modules will occupy when placed on the Homeowner’s roof. We will assume a square for our demonstration, however, several configurations are acceptable.

For a typical 0.200 kilowatt module, the dimensions measures about 4.3 ft x 2.9 ft or about 12.47 square feet for the area of one module.

Approximate Total Array Area = (number of modules) x (module area)

Approximate Total Array Area = (60) x (12.47)

Approximate Total Array Area = 748.2 sq ft

Taking the square root of the approximate total array area will provide the dimensions of a square which would represent the required square space on the roof to accommodate the array. In this case, the square root of 748.2 sq ft is about 27.35 ft, so the array system would be about 27.35 ft by 27.35 ft, if it was shaped in the form of a square.

Step 4 Calculate the cost for the entire array system, including all equipment installation, testing and required permits.

There are several licensed contractors and solar equipment providers throughout the U.S. and it would be impossible to list them all. However, at the present time, most have come up with a dollar figure for quotation purposes. If the homeowner requires special equipment or installation, it may be more. At this time, the Homeowner can assume the Total Cost to be about $8000.00 per kilowatt with respect to their array. In our example, the array required 12 kilowatts total, therefore, the cost of the system will be $8000.00 x 12 = $96,000.00 and this assumes a licensed contractor performs the installation. The cost of the Battery Bank is about $9000.00 for this system, which gives us a total of $105,000.00. If the Homeowner feels competent enough to do the installation without the use of the contractor and purchases the equipment direct from the distributor, then the cost is reduced to about $6000.00 per kilowatt with respect to their array. In this case, the system would cost $6000.00 x 12 = $72,000.00, however, the cost of the battery bank remains the same, $9000.00, so the total cost would now come to $81,000.00. I will address the issue of “Do it yourself installation” in chapter 16, however, it should be noted, the Homeowner will not receive any rebates or credit from the State or Federal Government if they install their own equipment. A licensed contractor is required to be eligible for the rebates and credit.

In the next chapter we will calculate the cost for application #2.

Chapter 8–Solar Array Cost Calculation for Application #2

Assume the installation of a 1600kw-hr/month array utilizing 0.200kw PV modules.

Step 1 Calculate the total kilowatt output required of the array.

Array kilowatts required = (Homeowner’s monthly kw-hr requirement) /(133.76)

Array kilowatts required = (1600)/(133.76) = 11.9617 kilowatts

The array kilowatts required is thus, rounded off, about 12 kilowatts

Step 2 Calculate the number of modules needed to obtain the 12 kilowatts. For our demonstration, we will utilize a standard 0.200 kilowatt module.

Number of modules = (required kilowatts)/(module kilowatt rating)

Number of modules = (12)/(0.200)

Number of modules = 60

Step 3 Calculate the approximate area these modules will occupy when placed on the Homeowner’s roof. We will assume a square for our demonstration, however, several configurations are acceptable.

For a typical 0.200 kilowatt module, the dimensions measures about 4.3 ft x 2.9 ft or about 12.47 square feet for the area of one module.

Approximate Total Array Area = (number of modules) x (module area)

Approximate Total Array Area = (60) x (12.47)

Approximate Total Array Area = 748.2 sq ft

Taking the square root of the approximate total array area will provide the dimensions of a square which would represent the required square space on the roof to accommodate the array. In this case, the square root of 748.2 sq ft is about 27.35 ft, so the array system would be about 27.35 ft by 27.35 ft, if it was shaped in the form of a square.

Step 4 Calculate the cost for the entire array system, including all equipment installation, testing and required permits.

At this time, the Homeowner can assume the Total Cost to be about $8000.00 per kilowatt with respect to their array. In our example, the array required 12 kilowatts total, therefore, the cost of the system will be $8000.00 x 12 = $96,000.00 and this assumes a licensed contractor performs the installation. If the Homeowner feels competent enough to do the installation without the use of the contractor and purchases the equipment direct from the distributor, then the cost is reduced to about $6000.00 per kilowatt with respect to their array. In this case, the system would cost $6000.00 x 12 = $72,000.00. Again, it should be noted, the Homeowner will not receive any rebates or credit from the State or Federal Government if they install their own equipment. A licensed contractor is required to be eligible for the rebates and credit.

In the next chapter we will calculate the cost for application #3.

Chapter 9–Solar Array Cost Calculation for Application #3

Now, let us take a look at application number three, where the Homeowner will elect to purchase less equipment to save on investment cost. We will assume, the chosen percentage of the monthly kw-hr use is 25%. This means, the array will be, just large enough to supply about 25% of the monthly electric need. The calculation process will be identical to the one performed in the last example and we will assume, the Homeowner utilizes about the same 1500 kw-hr/month from the Electric Utility.

In this case, 25% of 1500 kw-hrs is 375 kw-hrs. Thus, the array must be capable of supplying about 375 kw-hrs per month.

Step 1 Calculate the total kilowatt output required of the array.

Array kilowatts required = (Homeowner’s monthly kw-hr requirement) /(133.76)

Array kilowatts required = (375)/(133.76) = 2.804 kilowatts

The array kilowatts required is thus, rounded off, about 3 kilowatts

Step 2 Calculate the number of modules needed to obtain the 3 kilowatts. For our demonstration, we will utilize a standard 0.200 kilowatt module.

Number of modules = (required kilowatts)/(module kilowatt rating)

Number of modules = (3)/(0.200)

Number of modules = 15

Step 3 Calculate the approximate area these modules will occupy, when placed on the Homeowner’s roof. We will assume a square for our demonstration, however, several configurations are acceptable.

For a typical 0.200 kilowatt module, the dimensions measures about 4.3 ft x 2.9 ft or about 12.47 square feet for the area of one module.

Approximate Total Array Area = (number of modules) x (module area)

Approximate Total Array Area = (15) x (12.47)

Approximate Total Array Area = 187.05 sq ft

Taking the square root of the approximate total array area will provide the dimensions of a square which would represent the required square space on the roof to accommodate the array. In this case, the square root of 187.05 sq ft is about 13.68 ft, so the array system would be about 13.68 ft by 13.68 ft, if it was shaped in the form of a square.

Step 4 Calculate the cost for the entire array system, including all equipment installation, testing and required permits.

At this time, the Homeowner can assume the Total Cost to be about $8000.00 per kilowatt with respect to their array. In our example, the array required 3 kilowatts total, therefore, the cost of the system will be $8000.00 x 3 = $24,000.00 and this assumes a licensed contractor performs the installation. If the Homeowner feels competent enough to do the installation without the use of the contractor and purchases the equipment direct from the distributor, then the cost is reduced to about $6000.00 per kilowatt with respect to their array. In this case, the system would cost $6000.00 x 3 = $18,000.00, but again, no rebates or credits will be available.

This completes the cost calculation for each of the three applications. In the next chapter, we will discuss some of the misinformation about rebates and credits circulating around the state.