Friday, February 4, 2011

For those who like numbers—doing the math


Here are my calculations for zeroing out our PG&E bill (Pacific Gas & Electric is our local utility) and figuring out how much the electricity actually costs. One feature that is really nice with the Volt is that you can program it with the daily and weekend rate schedule. We have it programmed so it only charges during off-peak hours—12 Midnight to 7 AM and most of the day on weekends.

If you want to skip the math, the bottom line is that the solar electricity is estimated to cost us about 11.4 cents per kilowatt hour--i.e. less than the lowest household rate PG&E now offers.

Assumptions:
The web site PVwatts ver 1, see: http://rredc.nrel.gov/solar/calculators/PVWATTS/version1/ predicts that our 3.24 kilowatt system (18 panels rated at 180 watts each) with a 15 degree tilt, oriented in a southwest direction will generate 64% of its annual energy in the summer, and will generate 43% of that summer energy in the peak hours of 2 – 9 PM. PVWatts also estimates that the system will generate 4436 kilowatt hours (kwh). However, since there is some shading due to an apartment building behind our house,I am inclined to stick with the more conservative estimate of 4265 kwh given to us by Super Solar, our contractor. (By the way, they did a super job, and I am happy to recommend them: http://www.supersolar.us/ )
Combining those assumptions with the following PG&E - E9 rate schedule for the Pacific coastal region:
Summer rate schedule (Peak is 2-9PM M-F, off peak is 12 AM – 7 AM M-F and weekends except 5 – 9 PM): (sorry about the numbers not lining up---I'm still trying to get the hang of this)
Rate Structure
    Baseline (KWH)                           
        130%
       Baseline
         200%
      Baseline
          300%
       Baseline
Territory T
249.0
323.7
498.0
747.0
Peak ($/kwh)
0.28741
0.30470
0.44575
0.55420
    
Partial Peak
0.09406
0.11135
0.25240
0.36207
Off Peak
0.03565
0.05294
0.13998
0.18172
Winter rate schedule: No Peak time, off peak is the same as summer—12AM – 7AM M-F and weekends except 5 – 9 PM
Rate StructureBaseline 130%
Baseline
200%
Baseline
300%
Baseline
Territory T
294.0
382.2
588.0
882.0
Partial Peak
0.09394
0.11123
0.25227
0.36194
Off-Peak
0.04457
0.06186
0.13998
0.18172
The car will use about 300 kwh/month if we drive about 1000 miles per month on the electricity.
The house uses about 300 kwh/month based on past electricity bills.
From reading our meter reports online we use about 35% of our electricity between 2 and 9 PM, and we use about 10% in the off-peak.
Calculations:
PG&E Payment for solar electricity in the summer:
  • 43% is generated on 5 days at 28.7¢per kwh: .43 x .287 x 5/7 =      0.088
  • 57% is generated in partial peak at 9.4¢ per kwh: .57 x .094 x 5/7 =      0.038
  • The weekend uses 2/7 of the power at about 4.76¢ per kwh: .0476 x 2/7 = .013
    Total summer payment per KWH of solar produced:             0.136
Now there are two credits that accrue due to the solar panels:
1. We use less energy in the peak than we produce with the solar. So even if the solar produced the same total number of kwh that we use—300 kwh per month—the solar would produce more of these in the peak hour, and generate a credit. Our cost of electricity in the summer is projected to be:
  • 35% peak hour x .287 x 5/7 =         $ 0.072
  • 55% partial peak x .094 x 5/7 =          0.037
  • 10% off peak x .05     =         .005 (note that I am assuming Tier 2 pricing for the off-peak)
    Summer charges for electricity:        $ 0.114 per kwh
    The monthly charge would be 300 kwh x .114 = $34.20
    The monthly credit in the summer would be: .136 payment x 300 kwh = $40.80 per month
    Net credit = $6.60 for the six summer months = $39.60 per year
2. There is also a credit because the solar system produces more than the house consumes. The solar system produces 4265 kwh, but the house only uses 3600. This excess is produced in the summer, when the payment is 13.6¢ per kwh. 4265 – 3600 = 665 kwh extra. Multiply that by 13.6¢ = $90.44.
Therefore the total credit for the solar is $39.60 plus 90.44 = $130.04.
From this we have to subtract the cost of charging the car. For a year this would be 300 kwh/month x 12 months x 4¢ per kwh (average winter and summer) = $144.00.

This leaves a total PG&E bill of $13.96, (say $14) about one dollar per month, although I understand that PG&E charges a minimum of $6 per month to tie to the grid.
Stay tuned to see if these calculations all turn out to be correct.

Also in the realm of numbers is the question as to the actual cost of electricity with the solar system. For us, the 3.24 kw cost $17,010 minus an instant rebate of $948 from PG&E for an upfront cost of $16,062. This is eligible for a 30% tax credit (I'll start on that in a few days) so that brings the cost down to $11,243. For our 1927 house, we had to do quite a bit of electrical work--$3,860 minus 30% tax credit = $2700. This brings the total cost to right around $14,000.

Fortunately, we were able to refinance our house at 4% for 30 years to pay for this. That comes to $809.62 per year (say 810). Dividing the $810 by 4265 kwh comes to 19 cents per kwh. However, because of the rates discussed above we are covering the electricity for the house (3600 kwh per year) plus the electricity for the car (3600 kwh per year) = 7200 kwh for the $810 plus $14 = $824. Dividing $824 by 7200 kwh = 11.4¢ per kwh. The lowest PG&E household rate is now 11.9¢ per kwh, and that goes up quickly after the first tier, so the solar cost is very competitive.

Now to be honest, you don't need solar panels to qualify for the electric car charging rate. If you pay to have a second meter installed (I'm not sure of the cost of that) you can pay the regular household rate for your home and the E9 rates for your car. If you can keep your home in the baseline 11.9¢ rate, and charge your car for 4¢, then your average rate comes out to about 8¢ per kwh—so you save even more money without solar panels. But why be greedy? The solar rate is cheaper than you are paying now, and it is inflation proof—unlike the regular PG&E rates. And it helps reduce CO2, air pollution, and all the downsides of fossil fuels and nuclear. So, to me, it's worth it.

One last point—you may have noticed that interest rates have gone up since last Fall when we financed this. They are now closer to 5% than 4%. But also note that I didn't count the mortgage interest tax deduction that homeowners get. So even the current 5% is more like 4% if you itemize deductions.
   

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