Hal Yeager's Solar-Electric Home
          Hal Yeager's Solar-Electric Home

Section 1 -- Pictures and Commentary.
Section 2 -- Let's Talk Economics.
Section 3 -- Construction and Interconnection Pictures.
Section 4 -- Best Direction to Orient Arrays at the 38-th Parallel.
Section 5 -- Code Listing for Solar Calculation Program.
Section 6 -- Solar Links and Contact Me.
 
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Section 1 - Pictures and Commentary


 
Street view.  Can you see the solar panel array?  It's near the center, behind the smallest tree.
I had Light Energy Systems of Concord California install the array.  There might be less expensive contractors, but I wanted to use a contractor that had been in business for a long time and had experience with photo-voltaic systems.  With the energy crisis hitting all of a sudden, one has to be cautious of fly-by-night businesses.  A key factor that prompted me to put the array in was that I needed to have my roof totally redone after 47 years.  If the solar array is put in at the same time as a new roof, then a more reliable roof mounting system can be used.  But more importantly, you don't have to dis-assemble the array to re-do the roof at a later date.   Finding a roofer that will work with you and the solar contractor might be difficult.  I was lucky to find Steve Peters of Roof-Right in Pleasant Hill.  He came highly recommended from my friend Chris Wright, who is a home builder.

    My cost for the system was approximately $21,750 (which includes the fee of $277 to PG&E for time-of-use metering, see below)  The State of California contributed $10,548 to the system.  (Thus, the real cost of the system was $32,300.  There is legislation pending in the State Legislature which would give a tax credit to citizens who install solar systems like this.  I estimate that the tax credit for me would be around $750 if the legislation passes in 2001.

   I am fortunate to live in a non-rotating outage block, so my array will always be able to produce electricity.


 
Here is an East-looking view...from the top of the garage.

 
   While I discuss the economics in greater detail below, solar-electric arrays don't make economic sense for everyone, at least for now.  The cost per kilowatt hour can be as high as 33.5 cents for standard metering, and as low as 15.5 to 16 cents for time of use metering and an array with the best orientation for time of use metering.  This is not competative with the baseline rate of 13 cents for standard metering, but is competative with the costs of kiliowatts over 130% baseline, which start at 18 cents.

 Certainly, solar-electric arrays would make sense for more people if PG&E has to raise rates dramatically.  The cost of solar cells has been steady declining over the last decade.  If this trend continues, the economics will improve as well.

   If you are looking at solar-electric arrays as way to cut your electricity bill, and if you are near the baseline level on your usage, I would suggest that you first replace your incandescent lamps with compact fluorescents and that you buy an energy-efficient refrigerator.  I also recommend that you do not consider solar as an option unless you consume over 200% of baseline, or if you want to pay more for an environmentally friendly energy source.


 
Here is a view from the North looking to the South.

 
The Array is mounted on a mostly west facing roof facet (it has an 18-degree tilt to the West and a 3-degree tilt to the South). The array size is 29 ft by 9.25 ft, about 268 square feet.  It conforms to the tilt of the roof, and is spaced about 6 to 8 inches above the roof for ventilation.  It will produce 2.36 kilowatts of peak power under moderate to hot temperature conditions.  As an extra benefit, it will shade about 1/3 of the roof area that lies under the attic, helping to keep the attic and the house cooler for more hours of the day.

 
Here is a close up of a panel.

 
There are 24 panels, each of which is rated at 120 Watts of peak power (full sun, room temperature), but is expected to produce 105.7 to 110 watts of peak power under moderate to hot temperature conditions.  24x105.7 watts = 2,537 Watts of peak DC current.  DC-to-AC inverters typically have conversion efficiencies of around 93%.  Therefore, as a conservative estimate, we can expect that this system will produce a peak AC power output of about 2,359 Watts.  The output could go higher on a cool bright day, particularly if the array were oriented with a southern exposure.  However, this array has a western exposure (in order to maximized the time of use credit, discussed below), and so I do not expect this array will see very many cool bright days with full exposure (such would have to happen in June).

 
 
Here is a close up of a cell.

 
These are Kyocera solar cells, touted to be the longest lasting, most reliable, and highest power density cells in the industry(Download Specifications here, will open in another window).  Solar cells come in about three or four varieties.  First, there are single crystal cells, which are wafer-sized (made from 3 inch to 6 inch diameter wafers), and are of uniform color (dark blue to black).  There are also polycrystalline cells and amorphous cells.  The Kyocera panel shown about uses polycrystalline cells, each of which is a collection of relatively large "chunks" of silicon in crystal form, but with each chunk having its crystal axes oriented in a different direction, thereby causing the variations in color.  Amorphous cells use silicon which is relatively non-crystal form.  These are potentially less expensive to produce, but are still increasing in efficiency and reliability.
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Section 2 -- Let's Talk Economics.

 
The Economics
     Here we are talking about grid-tie solar-electric array systems.  These systems convert the DC power of the PV arrays to AC power which is coupled directly onto the utility grid.  When operating, the system supplies your house's needs, and the excess is exported to the grid, for which you are given a credit (under Net metering).

    Solar-electric arrays are not for everyone, not unless PG&E has to start charging more than 34 cents per kilowatt hour.  With rebates from the State of California, they are, however, starting to make economic sense for some users.  There are, of course, good social and environmental reasons for having solar arrays.  This is partly my motivation.  My other motivation is a hedge against higher electricity costs over the next 25 years. 

     If you use more than about $80 a month in electricity, and use most of it during off-peak hours, then a solar array may start to make economic sense for you, particularly if you go over your baseline level by a large amount.  Off-peak hours are defined as before 12 noon and after 6 pm, Monday through Friday.  Stated another way, peak hours are 12 noon to 6 pm on weekdays. (At an average monthly bill of $80 per month, a 1.5 kw peak AC-power system would be an appropriate sized system.)

     If you fit this profile, you can sign up for Time-of-Use (TOU) metering with PG&E.  From May 1-st through October 31-st, the price of power under TOU metering is about 31.5 cents per kilowatt-hour during peak hours, and about 8.5 cents per kilowatt-hour during off-peak hours.  From November 1 to April 31, the price of power during peak hours is about 11.6 cents per kilowatt-hour during peak hours, and about 8.9 cents per kilowatt-hour during off-peak hours.  What this means is that, if your array is west facing or south-west facing, the TOU metering can effectively double the output of your PV system, and cut the effective cost per kilowatt-hour almost in half.

     There are many ways of computing the cost and payback of a solar array.  There are many factors to consider.  There is the initial cost of course, but over the 25-year life of the array, one has to consider the cost of borrowing money that pays for the initial cost.  One also has to consider that the cost of living will double or triple over the course of 25 years, so while $22,000 will look like a lot of money today, it will only look like $7,300 to $11,000 in 25 years.  Other factors that you have to consider is that PG&E will charge you $3.80 per month for the privilege of having the TOU metering service, and may charge you a minimum of $5 per month for electricity, even if you produce more than you use.  (However, I have gotten conflicting answers from PG&E on that last point; I really won't know until I get my first bill.) 

     Let's look at my system under standard metering and TOU metering.  My array will produce about 383 kwh per month on average with standard metering, and about 742 kwh per month under TOU metering.  I will compute the effective cost per kilowatt-hour of the solar array assuming that I have to fund it with a 25-year loan and pay only the real cost of money, which is an interest rate of around 3.5% to 4% per year (real cost of money is defined to be the current 30-year interest rate minus the inflation rate).  Using an interest rate reflective of the real cost of money is a simple way to take into account of effect of future inflation on what I would have had to pay PG&E if I did not have the solar array. 

    Financing on $21,500 at a real cost of money of 4% interest is $113.48 per month over the lifetime of 25 years.  The 4% interest rate is based on today's mortgage rate of 6.75% and a projected average inflation rate of 2.75% over the next 25 years.  We expect to replace the inverter after 12.5 years, and for this we will add a cost of $10 per month.

   $123.48 / 383 kwh = 32.2 cents per kwh

With time of use metering (TOU metering) the array effectively produces 742 kwh per month, but requires an additional financing of $1.46 per month for the $277 TOU fee and a monthly fee of $3.80, and so the cost is:

   $128.74 / 742 kwh = 17.3 cents per kwh

*1* If the State Legislature does pass a tax credit of $750 for residental solar systems, then these figures decrease to 31.2 cents and 16.8 cents per kwh, respectively.

*2* If the array produces 5% more than expected, then these figures decrease to 30.7 cents and 16.5 cents per kwh, respectively. 

*3* However, if PG&E does in fact charge a minimum of $5 per month if you do not buy more than $5 per month of electricity from them, then the above figures increase to 33.6 cents and 18 cents per kwh, respectively.

If each of the above three events *1* to *3* occurs, then these figures decrease to 31 cents and 16.7 cents per kwh, respectively. 

* * * * * * * * * * * * * * * * * * * *

If you took out that 6.75% loan today and the average inflation rate over the next 25 years actually turned out to be 3.25%, then your real cost of money is 3.5%, and financing costs are $107.63 per month for $21,500.  The cost are then:

  $117.63 / 383 kwh = 30.7 cents per kwh (std. met.)
  $122.69 / 742 kwh =  16.5 cents per kwh (TOU met.)

If the array lasts an extra 5 years, then the cost can be paid over 30 years, and the cost per month of financing $21,500 at a real cost of money of 4% interest is $102.64.  The computations are then

  $112.64 / 383 kwh = 30.9 cents per kwh (std. met.)
  $117.64 / 742 kwh =  15.9 cents per kwh (TOU met.)
 

If you want to ignore the real cost of money over 25 years, then the cost of $21,500 would be divided over 25 years ($860 per year, $71.67 per month).

  $81.67 / 383 kwh = 21.3 cents per kwh (std. met.)
  $82.50 / 742 kwh = 11.1 cents per kwh (TOU met.)

If you presume that you would be paying 13.5 cents per kwh to PG&E, then the payback time would be 39.5 years for standard metering (including $3,000 for one replacement inverter), and 18 years for TOU metering.

Editorial
     In 1996, I thought that the deregulation of the electricity market in California was a bad idea and would lead to higher prices to consumers in the end.  I still think it will lead to higher prices despite the recent drop in wholesale prices in May 2001.
    In practice, a regulated electric utility only builds enough power plants to meet the demand.  That was the case in 1996.  Building any more plants would decrease profits.  The idea that the State would then force PG&E to sell off its power plants to a handful of energy companies and then expect these companies to sell the power back to us at lower prices was naïve.  With so few companies controlling the State's power on the open market, it only takes one company to without 5% of the total demand (or one quarter of its supply) to cause prices to rise dramatically.  If each of the five major companies withheld 5% of their supply, they could then cut total supply to the State and force prices up.
     To truly have low rates, the State needs to have a supply capacity that is approximately 150% to 200% of the maximum demand, with the supply capacity being provide by 10 or more major energy companies.
     But will we have new energy companies start up and save us?  Well, if you though that it was difficult for a start-up airline to break into the airline market and compete against the major airlines, starting a new electric company is harder yet.  It cost about $300 million to $400 million to build a 500 Megawatt generating plant.  You can start three start-up airlines the size of JetBlue for that amount.  And you will need 10% to 20% of your revenue just to pay the debt service on your new power plant. The Big Five will have the financial wherewithal to under cut you when you try to get your new plant on line.  With the State signing long term contracts with the big five energy companies at roughly twice the price paid in 1998, the Big Five can use this windfall to fund their losses on the spot market and in future long-term contracts, if they need to drive prices down in order to put a start up on the financial ropes.
   For the record, I do not work for PG&E, a power company, the State of California, or a solar-related company.
 
 
 
 
 
 
 

The State legislature could help these economics if they eliminated PG&E's monthly service charge for TOU metering, and PG&E's $5 monthly minimum service charge.
 
 
 

Do you have Suggestions or Corrections to these calculations, then email me at hyeager@flash.net.
 

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Section 3 -- Construction and Interconnection Pictures.

Click here to view pictures of the construction and the inverter.
 

Section 4 -- Best direction to orient arrays at the 38-th parallel.

 
The table below provides the equivalent hours of full sun exposure for an average day of the year for various
tilt angles of the array.  If your system produces an output of 2.5 kwh at full sun exposure, then you multiply the number from the table by 2.5 to find the average kilowatt-hours produced per day by your system.  The yearly hours and kilowatt-hours can be found by multiplying the numbers by 365.25 days (the 0.25 accounts for leap years over the course of 25 years).  Average equivalent hours of full sun with 

Time of Use metering (TOU metering) are shown in Parenthesis().

The area of 80% to 100% of maximum hours for standard metering are shown in varying degrees of blue font.
The area of 80% to 100% of maximum hours for TOU metering are shown in varying degrees of red font.
The numbers for my array are show in green font.

South Tilt
(Degrees)
  West Tilt (Degrees) 
  -20.00    -15.00   -5.00    0.00    5.00    10.00    15.00    20.00    25.00    30.0
-20 3.73 (6.44) 3.77 (6.65) 3.79 (6.84) 3.81 (7.15) 3.81 (7.27) 3.79 (7.35) 3.76 (7.40) 3.72 (7.42) 3.67 (7.41) 3.60 (7.36)
-15 4.14 (7.03) 4.17 (7.27) 4.20 (7.49) 4.21 (7.82) 4.20 (7.96) 4.20 (8.07) 4.17 (8.14) 4.13 (8.16) 4.07 (8.15) 4.00 (8.10)
-10 4.50 (7.56) 4.54 (7.83) 4.56 (8.06) 4.56 (8.43) 4.56 (8.58) 4.56 (8.71) 4.54 (8.79) 4.49 (8.82) 4.43 (8.81) 4.35 (8.75)
 -5 4.82 (8.02) 4.87 (8.32) 4.87 (8.56) 4.87 (8.96) 4.87 (9.13) 4.87 (9.27) 4.86 (9.37) 4.82 (9.41) 4.75 (9.39) 4.65 (9.31)
  0 5.11 (8.41) 5.15 (8.74) 5.15 (8.99) 5.16 (9.44) 5.15 (9.61) 5.16 (9.76) 5.16 (9.88) 5.09 (9.90) 5.02 (9.88) 4.92 (9.81)
  5 5.34 (8.72) 5.40 (9.08) 5.40 (9.36) 5.40 (9.83) 5.40 (10.0) 5.40 (10.2) 5.39 (10.3) 5.33 (10.3) 5.25 (10.3) 5.15 (10.2)
10 5.54 (8.98) 5.59 (9.35) 5.61 (9.66) 5.61 (10.2) 5.61 (10.4) 5.61 (10.5) 5.59 (10.6) 5.53 (10.7) 5.44 (10.7) 5.34 (10.6)
15 5.70 (9.17) 5.74 (9.54) 5.77 (9.89) 5.77 (10.4) 5.77 (10.6) 5.77 (10.8) 5.74 (10.9) 5.69 (11.0) 5.60 (10.9) 5.49 (10.8)
20 5.80 (9.28) 5.85 (9.66) 5.88 (10.0) 5.90 (10.6) 5.90 (10.8) 5.88 (11.0) 5.85 (11.1) 5.80 (11.1) 5.71 (11.1) 5.60 (11.0)
25 5.87 (9.33) 5.92 (9.72) 5.95 (10.1) 5.98 (10.7) 5.97 (10.9) 5.95 (11.1) 5.92 (11.2) 5.86 (11.2) 5.78 (11.2) 5.67 (11.1)
30 5.89 (9.31) 5.95 (9.70) 5.98 (10.1) 6.01 (10.7) 6.00 (10.9) 5.98 (11.1) 5.94 (11.2) 5.88(11.2) 5.81 (11.2) 5.70 (11.1)
35 5.87 (9.23) 5.93 (9.61) 5.97 (9.98) 6.00 (10.6) 5.99 (10.8) 5.96 (11.0) 5.92 (11.1) 5.86 (11.1) 5.79 (11.1) 5.68 (11.1)
40 5.81 (9.07) 5.87 (9.46) 5.91 (9.82) 5.94 (10.5) 5.93 (10.7) 5.90 (10.8) 5.86 (10.9) 5.80 (11.0) 5.72 (11.0) 5.62 (10.9)
45 5.70 (8.85) 5.76 (9.23) 5.80 (9.59) 5.84 (10.2) 5.83 (10.4) 5.80 (10.6) 5.75 (10.7) 5.69 (10.7) 5.62 (10.7) 5.52 (10.6)
50 5.55 (8.57) 5.61 (8.93) 5.66 (9.29) 5.69 (9.90) 5.68 (10.1) 5.65 (10.3) 5.60 (10.4) 5.54 (10.4) 5.47 (10.4) 5.37 (10.3)
55 5.37 (8.22) 5.42 (8.57) 5.47 (8.91) 5.50 (9.50) 5.49 (9.73) 5.46 (9.90) 5.41 (9.98) 5.36 (10.0) 5.28 (10.0) 5.19 (9.94)
60 5.14 (7.81) 5.19 (8.15) 5.24 (8.47) 5.27 (9.03) 5.26 (9.26) 5.23 (9.42) 5.19 (9.51) 5.13 (9.55) 5.05 (9.53) 4.96 (9.47)
65 4.87 (7.35) 4.93 (7.67) 4.96 (7.96) 5.00 (8.50) 4.98 (8.70) 4.96 (8.87) 4.92 (8.96) 4.86 (9.00) 4.79 (8.99) 4.70 (8.93)
70 4.57 (6.83) 4.62 (7.13) 4.66 (7.41) 4.69 (7.90) 4.68 (8.09) 4.65 (8.24) 4.61 (8.35) 4.56 (8.39) 4.49 (8.38) 4.41 (8.32)
A negative value for the West Tilt means that the array is tilted to the East.
A negative value for the South Tilt means that the array is tilted to the North.
Click Here for a page Explaining the West and South Tilts (will open in another window).
The computation takes into account an approximate cloud cover mode for fall, winter, and early spring as follows:
25% average cloud cover for the last 6 weeks of fall
50% average cloud cover for winter
25% average cloud cover for the first 6 weeks of spring.
If any one knows where average daily cloud coverage statistics are kept, please e-mail me.
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Section 5 -- Code Listing for Solar Calculation Program

Click here to view the code for the program that calculated the above table.
Let me know if you find errors.
 

Section 6 - Solar Links and Contact me.

Links to Additional Information.

http://www.energy.ca.gov/links/solar.html

http://www.ttcorp.com/upvg/pv_othr.htm

Got Comments, Corrections, Questions, drop me an e-mail at homesolar1@yahoo.com.
Please understand that I may not be able to get back to you immediately.
 
 
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