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**Home Solar PV System: Actual and Calculated Outputs**

by U. Bonne, ulrichbonne@msn.com, Kailua-Kona, Hawaii, 7 December 2009

**The installed PV system**, of nominal 2.1 kW peak DC power (2.0 kW AC power), consists of 12 SolarWorld SW-175 panels[1], and was installed on a South-facing roof, see Fig.1. Each panel has its own micro-inverter (Enphase M190-72-240-S11/2/3)[2]. The micro-inverters came with a display and Ethernet link to the Enphase website (Envoy Communication Gateway[3]), which collects and transmits performance information from each solar panel/module to the Enphase website for use by the customer. This “EnlightenEnphase” software and web monitors and manages the connected solar power systems and is available 24 hours a day. It stores the data taken of each panel every 5 minutes[4]. The system was installed in one day by Cano Electric[5] at a total installed cost of 7.95 $/kW AC, tax included. It was officially approved by the County Inspector 12 days after installation, and after submitting that Notice with the PV Engineering Plan and the signed Net Energy Metering (NEM) agreement, HELCO installed their special meter about a month after that. -- Note that the PV system is not officially accepted nor are generated kWh credited by HELCO until completion of that last step.

**The PV simulation model** set up to calculate its performance, presently runs on Excel spreadsheets, after doing some quick cramming of spherical trigonometry. It was validated by proving that it

1) Reproduces the minute-by-minute PV system output,

2) Length of day at any latitudes, compared to web data and

3) Length of day at any time of year, also compared to web data.

It also has built-in the dependence of roof slope and orientation.

Figure 2 below shows a composite graph of data vs. time of day, with the PV system watts output data in blue, the sun’s orientation in terms of the azimuth angle in green, the sun’s elevation angle in red, and the calculated watts output in pink. The calculated data do not include VOG or cloud cover effects and thus match only the best PV outputs. Note that in the morning, the PV output start is delayed until the sun rises from behind the mountain, which is not considered in the model.

Future plans: Besides now being able to predict PV output performance vs. time of day, day of year, latitude, and roof slope and orientation, the next step will be to determine the effect of roof slope and orientation of annual output for Hawaii and other latitudes. For example, the same installation moved to a latitude of 45 degrees (as for Minneapolis, MN) the PV model predicts a 33% drop in output.

An effect worth further study is that the used PV spectral sensitivity and output is such that it does not seem to depend on the increasing atmospheric (mostly UV) attenuation of the power of the sun, as its elevation changes.

**Performance data:** Lets compare actual with expected performance based on outputs of 1) Energy and 2) Power; and 3) The resulting pay-back period:

1) Energy: The PV system of Fig.1 puts out 31% more actual kWh than the energy output I had expected from a 2.1-kW system: A total of 238.6 kWh generated over 24 days was equivalent to a capacity factor of (238.6/24)/(2.1*24)*100 = 19.7%[8] or 31% higher than the expected 15% for South Kona with its usual ½-day cloud cover, low November sun elevation and VOG, while the best actual outputs exceed the expected kWh output by close to 60%.

Compared to the listed web of 5.6 “winter peak-sun hours” for Hawaii in the Winter[6], which is equivalent to a capacity factor of (5.6/24)*100 = 23.3%, we underperformed by 11%.

However, even on a cloudy and rainy day such as Dec 6 in Kailua-Kona, it generated 4.2 kWh, vs. 11.0 kWh the day before that, corresponding to capacity factors of 8.7 and 22.9%, respectively.

2) Peak power: I had expected a power output of 2 kW AC on clear days, before allowing for sun elevation and roof slope. The best data collected during relatively clear days in the 20-26 Nov. week, were noon-time peak powers of a little over 1.8 kW, as shown by the data and simulation on Fig.2 (right-hand y-scale for the total of 12 panels). The 20-deg. roof slope at that time of year (second half of Nov.) in Hawaii (20-deg latitude) should not cause more than a 4% loss. However, the normal 23% atmospheric attenuation at equinox noon on the equator used to rate the panels, should now have grown by 8.71% to 31.7%[7]. So, we should expect a peak AC power output of 2.0(100 - 4 - 8.71)/100 = 1.74 kW, which we did obtain and exceed at times, even without making allowances for VOG attenuation.

3) Economics: If we make the conservative assumptions that

a) The annual average energy PV output would be no worse that he one described above for November,

b) Its output would not decrease by more than 0.5%/year,

c) The cost of residential electricity would stay around the present rate of R = 0.40 $/kWh,

d) We can recover all applicable tax credits (30% Federal + 35% State, so that our capital investment is decreased by a factor F = (1-0.3)*(1-0.35) = 0.4550. and

e) All PV output is bought by HELCO under the Net Energy Metering agreement,

then our C = $15,895.13 capital investment, producing at a rate of Q = 238.6/24 *365 = 3628 kWh/year or 3456 kWh/year if we include the above 0.5%/year decrease, would pay off in C*F/(R*Q) = 11.5 years w/o tax rebates or cost of capital; 5.23 years with tax credits and no cost of capital, and ~6 years with a loan costing 5%/year interest for that time.

.

**Conclusions:** The PV system of Fig.1 put out 31% more actual **energy** (kWh) than my expected energy output (averaged over a week) corresponding to 3.6 "peak sun hours" or 15% capacity factor associated with the low November sun elevation plus VOG and cloud cover, while the best actual outputs exceed the nominal kWh output by 60%. The latter are assumed to have minimal or no output reductions due to VOG and cloud cover. Even on a cloudy and rainy day such as Dec 6 in Kailua-Kona, it generated 4.2 kWh, vs. 11.0 kWh the day before that. **Peak power** outputs (kW) were close to and a few times exceeded the 1.74 kW for this time of the year, roof orientation and at the Kona latitude. Therefore, as a customer of a newly installed PV system, I am very satisfied.

**References**

- SolarWorld SW175, 175 Watt 24V PV Module, listed at $826 or 4.72 $/W, at shttp://www.ecodirect.com/SolarWorld-SW175-p/solarworld-sw175.htm
- Enphase Energy Inc, Microinverter System at http://enphaseenergy.com/
- Enphase Energy Inc, http://enphaseenergy.com/products/products/envoy.cfm
- Enphase Energy Inc, https://enlighten.enphaseenergy.com/login
- John Cano, Cano Electric Inc #19101, 308 Kamehameha St Suite 211, Hilo, Hi 96721, office phn.: 808-969-1595, cano.jg@gmail.com
- http://www.solar4power.com/solar-power-insolation-window.html “peak-sun hours” are numerically the same as kWh/m2/day because “peak sun” is 1000 Wh/m2/day.
- Increased atm. attenuation by (1/cos((lat.+ 23.44)/57.3) -1)*23 = 8.71% for Hawaii on Dec.21
- The average capacity factor from mid Nov. 2009 to mid Jan.2010 (67 days) was 20.1%

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