Some Further Observations on Photovoltaic Panels

by Oliver Seely

The text and photos on this page are in the public domain. Copying is encouraged!



Revised March 31, 2022

The following material was presented to the students in Professor Claudia Olivia Espinosa Villegas' class ME 418 Renewable Energy and Sustainability in the Mechanical Engineering Department at California State University Los Angeles on November 6, 2015. It is an updated version of the web page Some Observations on Photovoltaic Cell Panels

Introduction
When measured against the plane of its orbit about the sun, the polar axis of the earth is tilted by 23.4o. Los Angeles has a north latitude when measured from the equator of 34.05o. At noon on the winter solstice, in order to face the sun at a 90o angle with its surface, the plane of the surface would have to be tilted toward the south by the sum of these two numbers, or around 57.45o. At noon on the summer solstice, the surface would have to be tilted by the difference of these two values or around 10.65o. The average of these two numbers is the same as our northern latitude of 34.05o , which represents an average of the two extreme angles at noon on the winter and summer solstices. Suffice it to say that at any point on the earth, to achieve a maximum average energy from the sun using stationary panels, the panels ought to be tilted toward the equator at the angle of latitude.

























The decision to install photovoltaic panels hinges on where one lives. The amount of sunlight as determined by the climate of one's location and the ability to receive the direct rays of the sun when it is shining helps one to decide if it makes sense to install the panels. On the left and right are images showing available sunlight for the continental United States. The one on the right gives the zones in units of kilowatt hours per square meter per day. Although my home location in Lakewood, California would appear to be ideal because of the available sunlight per year, in actual fact our distance from the Pacific Ocean is only 12 km and coastal fog is a problem part of the year. On the average, the amount of sunlight we get is limited to between 5 and 8 hours per day throughout the year (see the blue strip along the coast in the left image in front of the arrow tip).
























A roof sloping toward the south at our angle of latitude in full view of the sky would be ideal. However, our roof line slopes toward the east and the west. There is a chimney near the peak, as you can see.








The panels have to be installed where there are no shadows during the day, so we installed our system, rated at 3 kilowatts, on the east-sloping roof with an additional tilt toward the south. There are 18 panels each rated at 165 watts which brings the system to a theoretical maximum power output of 2970 watts or 2.97 kilowatts. Maximum output occurs around 11 am each day that the sun shines.



















Even if one has a surface which slopes toward the north, things aren't hopeless. Here is a hill sloping northward near the Pasadena Freeway which has ground-mounted solar panels sloping south.














How much energy output can one expect?

Summary for Lakewood

Below is a table which shows the annual average consumption and the annual average generation. The average annual generated energy in kilowatt hours comes to 2905, which is a curious coincidence because for our 3 kilowatt (rated) system, with not at all the most advantageous tilt, our panels generate just under 3000 kilowatt hours of energy annually. Were the tilt a bit more advantageous, the energy production would likely exceed 3000 kilowatt hours. Were we a bit closer to the ocean, with more clouds and fog, the generated energy would be somewhat less. But it is a good value to remember for estimating your own needs.

Year Kilowatt hours consumed Kilowatt hours generated
2005-2006 3053 2818
2006-2007 3257 2945
2007-2008 3409 3048
2008-2009 3445 2915
2009-2010 3235 2993
2010-2011 2553 2782
2011-2012 3060 2760
2012-2013 3490 3005
2013-2014 3474 2881
2014-2015 3774 2732
2015-2016 3878 2683
2016-2017 3274 2722
2017-2018 3651 2558
2018-2019 3862 3814
2019-2020 2161 3062

A second installation of solar panels was approved by the utility in 2020 and the true-up period was restarted on January 1, 2020. Until we have good data on the excess solar energy generated and the $ credit actually received for it, we will not be able to plan whether, or how best to use, that energy.

Year Kilowatt hours consumed Kilowatt hours generated
2020 TBA TBA


At our vacation home near Yosemite National Park we have the same problem with the roof line as in Lakewood: it tilts east and west rather than north and south, but at this location there are high trees on the eastern side, as you can see, so it made more sense to put the panels on the west side so that they receive full sunlight earlier in the day. The tilt to the south is at about the same angle as the panels in Lakewood.


















On the basis of shading by trees on all three sides, east, south and west, and except for space heating, it is an all electric house, our installer recommended that we go for a 5 kw system. We have 21 panels rated at 245 watts each, or 21x245 = 5145 watts or 5.145 kw. What kind of annual output does that give us? The system was installed in July of 2013, so at this time we have just over one full year of output to measure. Note that from January 1, 2014 to January 1, 2015, the plot shows a total energy output from the panels of 6.00 megawatt hours, or 6000 kilowatt hours. So our 5145 watt system produces 6000 kilowatt hours of energy. The increased relative amount of energy generation over our panels in Lakewood is likely the result of higher elevation, more ultraviolet light and more sunny days in spite of the shading by the surrounding trees.

On the other hand, the shading produces random effects on the output of individual panels throughout the day and with the change of seasons. There are three banks of panels with seven panels each. Here is the energy output for each panel during the day of October 12, 2015 in watt-hours. The first seven numbers are for the north bank, the second seven for the middle and the final seven for the south bank.
840, 752, 574, 853, 944, 667, 582, 547, 747, 500, 971, 567, 905, 574, 753, 675, 643, 691, 862, 913, 536
Note the high output for one panel of 971 wH and a low output of another at 500 wH. A member of the PV Panel discussion group was alarmed enough to suggest that I look into the matter because he had seen a similar disparity in his installation because of a connection problem.

As the sun comes up the shading of each panel attenuates the output of each panel according to the wind pattern on the branches, the time of day and the season. Here are two photos taken on October 16, 2015 of shading on the north and south banks around 11am.
























So as the shadows of the branches move across the panels one ends up getting a pretty large variation in output during the day. Whereas two single panels during one day might have a disparity of nearly 50% (971 vs. 500), the same isn't seen for a monthly output. Within an individual bank, the minimum to maximum output approaches 85% during the winter and around 90% during the summer. There is an expected trend for the banks during the winter, but opposite of what one expect during the summer..

Bank of Modules December, 2014, kwH July, 2015, kwH
North Bank 9.39 35.1
Middle Bank 8.31 35.8
South Bank 6.83 38.6
Total 171.67 766.7


In December, the south bank has the lowest output because of the shading by the trees on the south side of the property. Had we installed the southernmost bank where the installers first began to drill holes much nearer the south wall of the building, we would have seen an even greater attenuation during the winter. Curiously, the monthly output for July shows a slightly greater output for the south bank. However when one looks at the output of individual panels, any connection problem, if there is one, is masked by the random output due to daily shading.



It does snow from time to time at our elevation in the mountains and when I checked the histogram on December 7, 2013 from Lakewood, I went into a panic. It looked like my panels had stopped operating. We weren't planning to be up there for several more days so it was with some relief that each day the output progressed upward to give us the graph on the right after a week. When we arrived the snow had almost completely melted.















Tracking the Sun?

Here's a system of panels at the Fresno Yosemite International Airport. The point of view of the camera which took this photo is directly north. The banks of panels rotate east to west (right to left) during the day so as to achieve maximum output with the position of the sun. But the panels have a horizontal axis, so there is no advantage achieved by tilting at the angle of latitude. Note the cantilevered structure which seems to be attached to a structural member on the left bank of panels. It appears to be perpendicular to them and is the member which changes their tilt, either by movement of the cantilevered structure or a chain in a bed on top of it.














Structural modifications of any kind carry the risk of unintended consequences. Our installation in Lakewood caused a leak through the bathroom vent during heavy rain as a result of runoff onto the roof and subsequent splashing into the vent. The vent was modified by adding a shield, as shown. Ugly though it may be, it did the trick as demonstrated by another rainstorm shortly after its installation.







The Lakewood installation uses a single inverter, with direct current flowing to it and "inverted" using a variable oscillator controlled by the frequency of the grid, which averages 60 cycles per second or 60 Hertz. Each morning the controller goes through its countdown, synchronizing the inverter phase with that of the grid. When it locks into the phase of the grid the system goes online and electricity begins to flow from the panels. During the day I get the readout shown at the right which graphs my kilowatts of power during the day and logs the total energy produced at the lower left. We estimate that it will take 14 years to recoup our out of pocket expenses. Richard Corkish of the Photovoltaics Special Research Centre at the University of New South Wales estimates that it will take between 3 and 7 years to produce enough energy to equal that amount contained in the non-renewable fossil fuels used to fabricate the panels. That estimate can be found in his offering, Can Solar Cells Ever Recapture the Energy Invested in their Manufacture?













Panel Maintenance

The panels are guaranteed for 25 years. The good news is that the panels work silently with no moving parts, pumping excess electrical energy routinely into the electrical grid when we use less than that which is generated.


The bad news is that over time in an urban area where there is a lot of dustfall, the efficiency drops. In the Los Angeles area several months can go by without rain. These images show what happens after such a period. We have found it advisable to do a once-a-month rinsing of the panels to make them sparkling clean and to bring them back to maximum efficiency.









What happens to the energy output when the panels are rinsed? The data for the rinsing below were taken starting at 9:12 am on a cloudless midsummer morning, 2006. The cold water rinse was effected between readings taken at 9:26 and 9:33. The previous rinse had been done about a month before this one. There had been no rain between rinses.


When graphed, the extrapolated intersections with the time when the rinse was effected amounts to the difference between 1900 and 2000 kw, a power increase of around 5%. The initial high power output is caused by increased efficiency of the panels at the low temperature of the cold rinse water.
Time Power
output
(watts)
9:12 1838
9:19 1869
9:26 1896
cold
water
rinse		 xxxx
9:33 2157
9:40 2079
9:47 2070
9:54 2086
10:01 2124
10:08 2136
10:15 2160
10:22 2174
10:29 2177





Here's an image taken of the panels after two months without rain. My guess is that the drop in power output was somewhere around 10%.

















How much water?

I was asked recently about water needs for panels installed in some of the desert regions of California. The frequency of rinsing depends on the dustfall of the region, so any projection of needs requires a measurement of dustfall and a comparison with areas for which the dustfall and accompanying energy loss is known, but the rinsing frequency is a judgment call based on that energy loss which one is willing to tolerate. My once-per-month rinsing during the dry season in suburban Los Angeles seems to coincide with an energy loss of 5-10%. The "case study" rinsing frequency (below) seems to be based on an energy loss of 15% to trigger a rinse. A typical rinse of my 18 panels using the method shown in the photo above requires 1.21 cu. ft. of water. The rinse consists of a first pass "to soften up" the layer of dust and bird droppings followed by a second pass to remove the softened residue. 1.21 cu. ft. = 9.05 gallons (U.S., liq.) = 34.3 liters. A careful measurement of volume needed and the noble expectation that one will be able to claim that the runoff will go into one's garden is shattered when one observes the runoff lying in the rain gutter behind a pile of leaves and evaporating slowly. I leave it to the reader to make the calculations needed for his or her application. Suffice it to say that my method is just about the most inefficient one could use. An industrial operation would have an advantage of scale and recycling potential.

Particulate matter

All kinds of stuff falls routinely from the sky: meteorites, cosmic dust and used satellites for starters. At our house in southern California and near an airport we get little spots of yellow gunk which produces opaque spots on the solar panels. It has the consistency of dust particles mixed with oil judging from the way it scrapes off the panels. There is a web page which claims the spots are bee poop. I don't know. Maybe so. Fortunately the ultraviolet light breaks enough of the chemical bonds in whatever binds the particles together to allow them finally to sluff off during repeated rinsings. Still, they do represent a potential fall-off of energy generated by one's installation.







There are other perils, of course. On Independence Day, July 4, there is a proliferation of private fireworks displays. Rockets with exploding displays are illegal in our community. What goes up has to come down and this year some residue landed on a panel but evidently it had burned and cooled. The image on the left is as I found it. The pile of ashes were brushed away (center) and then cleaned with Windex (right). But notice that after the spot was cleaned with Windex, ten years of residue appeared at the right, the smudge of which begins between the arrows.














Rate Games

When our system in Lakewood was first installed we were billed at a flat rate and that rate was close to 13 cents per kilowatt hour. The meter had an old fashioned spinning disk which reversed direction when the amount of energy generated exceeded that which was being consumed. We have since switched to "time of use" or TOU metering. It turns out that Southern California Edison (Lakewood) has a handful of rate schedules. TOU-D2 is for big users. TOU-D1 is for regular residential, or small, users. TOU-D8 is the schedule applied to the electricity use on the university campus where I taught for many years. Our home in Lakewood is billed on the TOU-D1 schedule.

TOU-D1 has four rates: two for summer and two for winter. For each they are on-peak and off-peak. On-peak is higher than off-peak.
Period Cost per
kwh ($ U.S.)
Winter On Peak 0.202
Winter Off Peak 0.142
Summer On Peak 0.504
Summer Off Peak 0.147


Note that the winter on-peak rate is about 50% more than the off-peak rate, but that the summer on-peak rate is about 250% more than the off-peak rate. The high value of the on- peak rate is not typical. It generally hovers around $0.43 per kilowatt hour or 200% more than the off-peak rate. The typical bill has a number of add-ons, such as "Transmission Owners Tariff Charge," the "Nuclear Decommissioning Charge," the "Public Purpose Programs Charge," the "The Public Utilities Commission Reimbursement Fee", and the "California Alternate Rates for Energy Surcharge, where applicable." All of these fees are charged by the kilowatt hour and although I have been told by a representative of the utility that there is variability from one month to the next as to which are applied to a specific customer's bill so that even if the customer wanted to create a private spreadsheet, it would be impossible because the rates change slightly from month to month owing to which of the above charges apply. On the other hand, an approximate rate can be determined by using simultaneous equations between pairs of months in which only one rate "season" was involved: winter or summer. Since on-peak and off-peak rates are different, one can then calculate each rate for that particular pair of months. When the crossover between winter and summer occurs, one is faced with four variables: summer on- and off- and winter on- and off-peak. My approach then is to fudge things by taking earlier values and then varying things in the spreadsheet until the value established by the utility matches the result of my equations. It isn't exact, but it is close. The long and the short of it is that with Time-of-use metering (TOU), our rates vary from one month to the next regardless of which utility is providing the service. If you pay a flat rate you still have to pay the squishy add-ons, listed above.

Net Metering

Get a check from the electric company?
Here are two histograms, one for August 21, 2012 on the left and one for April 24, 2015 on the right from Southern California Edison in Lakewood. The negative direction represents net generation and the positive direction net consumption. The red columns are at on-peak times and the green columns at off-peak times. Look carefully and tell me the difference between the two. Do you see that the on-peak times are not the same? Starting in January, 2011, in California, people who generate excess electricity are allowed to sell it to their electric utility. That is, for the first time in history, the tops of our roofs began to have profit potential, but a customer must have both a $ credit at the end of the year and have generated more kilowatt hours than were consumed to get a check from the electric company. Moreover, since the advantages of rebates and tax credits are forsaken if an installation greatly exceeds one's need for electricity, very few customers will ever see a check at the end of the year because there is no incentive for the customer to load up a roof with unneeded solar panels. Still, a customer might decide forego the rebates and tax credits to install far more panels than are needed.

Year kwH consumed kwH generated SCE bill
2000 7926
2005-2006 3053 -2818 -$107.19
2006-2007 3257 -2945 -$134.00
2007-2008 3409 -3048 -$68.06
2008-2009 3445 -2915 -$22.22
2009-2010 3235 -2993 -$64.20
2010-2011 2553 -2782 -$198.79
2011-2012 3060 -2760 -$29.63
2012-2013 3490 -3005 -$48.17
2013-2014 3474 -2881 $73.85
2014-2015 3774 -2732 $124.60
2015-2016 3878 -2683 $187.68
2016-2017 3274 -2722 $15.51
2017-2018 3651 -2558 $139.89


The amount which a customer gets from the utility for excess electricity generated is called the feed-in tariff which turns out to be, in California, an amount right around the wholesale rate for electricity. On the one hand, the feed-in tariff, which is a schedule regulated by the Public Utilities Commission, requires the utility to credit the customer (not to write him a check) for excess electricity at the rate charged for consumption at that time. That is, one kilowatt hour of consumed electricity is worth the same amount as one kilowatt hour of generated electricity, on-peak or off-peak, summer or winter. On the other hand, one does not get a check from the utility unless the total generation of energy exceeds the total consumption. The table above shows that even though eight years out of the 10 I ran up a $ credit with the utility, only during one, 2010-2011, did I generate more electricity than I consumed and the check at the end of that fiscal year was $8.42, amounting to 3.7 cents per kilowatt hour, so the on-peak rates which we pay may be as high as $0.50 per kilowatt hour and as low as $0.13 per kilowatt hour, but if you get a check from your utility, it will be at the wholesale rate. Before we go on, notice in the table that every year from 2005 to 2013 we had a $ credit, but no check was received until the total generation exceeded the total consumption. Note that even though I had a credit of $198.79 during 2010-2011, the check I received was $8.42, calculated at the wholesale rate for the net energy generated. Note also, that the first year we had to pay a utility bill was the year that on-peak times were changed. Finally, note that in 2000, about three years before we made the decision to install solar panels we consumed 7926 kilowatt hours of energy. Over the next three years we converted to compact fluorescent lights which brought our consumption down to around 6600 kilowatt hours, not nearly enough to break even after the panels were installed. What happened? We bought the vacation home near Yosemite and ended up staying in both about 50% of the time. The original estimate for my needs in sustainable energy was off by around 3600 kilowatt hours or more than 50%. Why? Presumably because I underestimated the number of cloudy days in a year and overestimated the energy available when the sun is low in the sky but our 50% occupancy pretty well took care of the problem. In any case, there's no match for real data, and a good relationship to remember is that the number of watts of rated power ends up being close to the annual kilowatt hours of generated electricity. The two numbers are coincidentally close to each other but may be off by 10-20%. Those numbers are in any case a good place to start. For any critic who complains (correctly) that watts are not the same as kilowatt hours, your answer ought to be, "No, but the two numbers are coincidentally close to each other and therefore easy to remember." A different location and a different slant will produce a different result. A friend in the greater Lakewood area asked me to estimate how many panels he would need with an annual consumption of 10,000 kilowatt hours. With the same tilt that I have, for 10,000 kwh, in order to break even he would need 10 rated kw, or 10,000 watts of panels. At a rated power output of 165 watts per panel, he'd need 10000/165 = 61 panels. At a rated power output of 245 watts per panel, he'd need 10000/245 = 41 panels.

In 2008-2009 we consumed 3445 kwH and generated 2915 kwH energy. An estimate of the number of panels needed to bring our generation up to the level of consumption for that 12- month period would be (3445-2915)/3445 x 18 = 2.77, or 3 panels. Although our credit would balloon up to around the level we enjoyed in 2010-2011 there would be no monetary advantage of doing so if our generated energy remained below that of our consumed energy. That is, there would be no check from the utility.

When you finally make the big decision, a jolly young technician will arrive with a hand held computer containing an appropriate app and will walk around on your property to figure the best place to put the panels. When that happened to us in the Yosemite cabin, I didn't tell the technician that we occupied the place only 50% of the time. His app told him to install 5kw of panels which ended up producing (for the first full year) 6000 kilowatt hours of energy. But that was what he would have recommended assuming 100% occupancy! At 50% occupancy it has worked out just fine, but beware! Have the numbers in front of you and tell the jolly technician that you'll need your estimated number of panels to break even.

How many panels do you REALLY need?

Do you want to generate 50% of the energy you consume? 100%? Would you be satisfied to reach a $ break-even point with fewer panels but by taking advantage of the rate differences offered by net metering?

One would expect that if one panel with a particular power rating in watts in one orientation generates x kilowatt hours of energy over one year, then two panels each having the same power rating as the first and mounted in the same orientation adjacent to each other will generate 2x kilowatt hours of energy over one year. Such an assumption allows us to apply a ratio of kilowatt hours of energy generated annually divided by the total rated watts of the panels. With the understanding that some installations are going to collect the sun's energy more effectively than others, the ratio gives us a range of expectations, but the data are real and offer a spectrum of what one might expect from one's own installation.

The three entries from Morristown, Tennessee, Madison, Wisconsin and Redding, California were contributed by a representative of Enphase after I expressed skepticism over other high values contributed by members of a solar energy discussion group.

Notwithstanding all of the possible disadvantages posed by privately owned rooftop systems such as shading by trees and other structures and bad placement and tilting, these ratios, from 0.97 to 1.71 offer good food for thought for intended owners of rooftop and other PV installations. I would add that the values of 0.97 and the one following that, 1.32, are panels on the roof of the same dwelling, the first with a compound tilt toward the south but mounted on an east-facing roof; the second panels are mounted flat on a west facing roof. Moreover, there are 5 panels without shading, but four are shaded by a chimney part of each day (see photo below). Yet, the second set has a B/A ratio (see table below) of 1.32, whereas the first has B/A=0.97. Why the difference? Possibly morning coastal fog for the location which diminishes the output of the panels on the east side..

Here are the data:

Rated Watts (A) Annual kwh generated (B) Details Location B/A Comments
5145 6090 Av. for 2013, 2014 Oakhurst, Calif. 1.18 Less than ideal tilt
2970 (18 x 165w) 2888 10-yr. average Lakewood, Calif. 0.97 Compound tilt on east-facing roof
2835 (9 x 315w) 3751 (2020,2021 av) annual average Lakewood, Calif. 1.32 Flat on west-facing roof
4600 6345 3-yr. av. Tennessee 1.38 Ground mounted, ideal tilt.
7500 8570 3-yr. av. Michigan 1.14 N.A.
5280 5842 2-yr. av. Tacoma, WA 1.11 N.A.
2250 3400 7-yr. av. Northern California, 37 deg. north. 1.51 N.A.
22560 26524 3-yr. av. Central Illinois 1.18 N.A.
1125 1570 5-yr. av. SW Wisconsin 1.40 N.A.
6500 9230 Jan 1, 2015 - Jan 1, 2016 Morristown, Tennessee 1.42 Azimuth 180 deg., reported
8400 9500 Jan 1, 2015 - Jan 1, 2016 Madison, Wisconsin 1.13 Azimuth 180 deg., reported
7500 12800 Jan 1, 2015 - Jan 1, 2016 Redding, Calif. 1.71 Azimuth 180 deg., reported
2000 2084 1 year High Littleton near Bristol, UK. 1.042 Due south, 40 deg. elevation
14850 16199 Aug 1, 2015 - July 31, 2016 Oakhurst, Calif. 1.091 Azimuth 170 deg., reported; shade trees east and west.
2760 4566 Annual average over seven years Long Beach, Calif. 1.65 No shade, due south, ideal tilt
3660 5962 One year output Carlsbad, Calif. 1.63 Azimuth 255 deg., ideal tilt
6110 9148 One year output Mar Vista, Calif. 1.50 Azimuth 180 deg., ideal tilt
9100 11700 Four year average Bitterroot Valley, Montana 1.29 Latitude 46.0 deg N, array facing 152 deg (SSE)
3375 5498 One year output Pleasanton, Calif. 1.62 Latitude 37.4 deg N, array facing 160 deg (SSE)


Without putting too fine a point on it, for starters one could estimate, based on real data, the number of rated watts needed to produce an annual quantity of energy in kilowatt hours with the simple equation

(Rated Watts) = (Annual energy to be generated in kilowatt hours)/(B/A)

An appropriate value of (B/A) could be taken from one of the values deemed to be appropriate in this table, or calculated from a known installation similar to that which is desired.

Out-of-pocket costs for your panels.

For what it's worth, I have three numbers for $ per rated watt for our first and second installations and one for a future installation now being planned. Here they are:
Installation 1, 2004: 18 165-watt panels, $13175 after State of California tax credit and rebate. That comes to 13175/(18x165)=$4.44 per rated watt.
Installation 2, 2014: 21 245-watt panels, $15304 after State of California tax credit (no more rebates). That comes to 15304/(21x245) = $2.97 per rated watt.
Installation 3, 2018: 9 315-watt panels, $8990 after State of California tax credit. That comes to 8990/(9x315) = $3.17 per rated watt.

If you are advising a group responsible for management of a large organization, there is always the possibility of "slippage" where good, hard judgment on the part of board members is needed. A board member of a local church asked me to take a look at a proposal received by a solar panel installer. The bottom line: The cash purchase price of $172,159 (including all applicable credits and discounts) for a system of 28,100 rated watts comes out to $172,159/28,100 = $6.13 per watt. So the advice I gave them was that the price was high and that they must get competitive bids on the purchase.

More Panels?


In the United States there are around 3,300 electric utilities of which approximately 200 supply a majority of citizens their electrical energy; the rules governing the generation of solar energy can vary considerably from one state to the next. In California the utilities enforce the "120% Rule". Until I decided to put in a second set of panels at the location of the first installation, I thought erroneously that the "120% Rule" limited one's energy generation to 120% of one's energy consumption. Most amusingly, not so. The 120% Rule is a safety regulation set up so that one does not overload the busbar of the main circuit breaker panel. A busbar rated at 100 amperes with the main circuit breaker at the top and allowing current to pass into the bus from the grid at that point can, according to the rule, accommodate solar energy sources which generate up to 20% of the rated capacity, the current from which then passes into the busbar at the bottom through separate circuit breakers. So the worry that I would be denied an installation of the second set of panels turned out to be groundless. On the other hand, the new installation may be judged just to exceed that which is allowed under the 120% rule, even though my projection to the summer solstice predicts 18.64 amperes at maximum output. If I'm unable to make my case, either I will have to upgrade the circuit breaker panel at an estimated cost of $2,200 or do a "side tap" which would be to connect the new installation, through a separate circuit breaker, directly to the meter at an estimated cost of $600. Most unfortunately, the interpretation of the "120% rule" varies by jurisdiction, utility and State, so it isn't at all clear that my case for no upgrade will be approved. San Diego, for example, interprets the "120% rule" as follows: Add up the current rating of all inverters feeding the grid, then multiply by 1.25. That value becomes the 20% beyond which one's circuit breaker panel is rated. I may be accurate about my system not exceeding 20 measured amperes, but the foregoing calculation leads to a value of just over 30 amperes, which would demand a circuit breaker panel of at least 150 amperes. A decision has yet to be made on my case for no upgrade.

Companies which install solar panels don't want to fool around with installations of three panels or so, just what I needed to pass through the gap between $ break-even and energy (kwh) break even, but they were ready, willing and able to install nine panels for me! So, among the options I will have producing considerably more energy than I consume will be each year to receive a check after the completion of the annual true-up cycle, albeit at the wholesale rate of around 3.7 cents per kwh. For a period of about 7 years after the first installation I showed a $ credit, though my consumption of energy was greater than the generation of energy, but the $ credit was based on the "on-peak" rate when consumption was generally less than generation. But in 2011, the on-peak period was changed from 10am-6pm to 11am-6pm which put me just below the $ break- even point. Looking toward the future when the on-peak rate may change even further, I decided to install a sufficient number of panels to arrive at a kwh break-even. The new installation, with nine panels, has six more than would be needed to reach kwh break-even. In addition to receiving a check at the wholesale rate there are some other possibilities which may prove to be even more advantageous. Watch this space!

How about the loss of output over the years?

One hears the value of 0.5% per year bandied about. That is, for each year in operation the output of energy of solar panels diminishes by 0.5%. How close is that to reality? The first installation described here has now operated for over 13 years. The data showing annual generation of energy are given in kilowatt hours in the table above, showing the full years from 2005-2006 to 2017-2018. Using a regression line calculator on the web, we get the trend shown in the figure:

Note that just glancing at the data points, dispersed though they are, one can see a very definite downward trend. Thirteen dispersed points don't make a lot of sense to produce a regression line which offers much confidence, but it's the only thing we have, so the equation comes out to be y= -25.74x + 3014.19, so at year zero, y=3014.19 kwh and at year 15, y= -25.74*15+3014.19=2628.09 kwh, a loss of 3014.19-2628.09=386.1 kwh, or a percentage drop of 386.1/3014.19*100=12.8%. The percentage drop per year would then be 12.8/15=0.85%. Considering that the 0.5% figure probably is a representation of the aging of clean panels, the 0.85% per year drop in energy output is not surprising if one takes into account the buildup of dust layers month by month and periodic rinsing of dirty panels. The figure is in the right ball park in any case, in my opinion.















The Down Side of Photovoltaic Panels on Your Roof

You're the owner of your own private utility, for better or for worse. Most people won't be interested in assuming that role, just as most people aren't interested in being ham radio operators, hang glider pilots or deep sea divers. As an owner of your own private utility, it is your job to keep it operating, so you have to have a system which will give you a "heads up" when things go wrong.

In the beginning, our system had a window in the inverter which showed the alternating current power being produced during the day (left). That meant that in order to make sure everything was operating properly, I had to go outside and look at the readout in the window. A push of a button cycled between kilowatts of power, voltage, daily energy, total energy and total hours of operation. One day, with no discernable motive, I took a look and saw a blank readout (right).











Suddenly one's attitude changes abruptly. You are the CEO of your private utility and when your panels don't work, that means money out of your pocket. While waiting for the repairman to arrive, I took a look in the junction box where the wires from the panels connect to the wire which leads to the inverter. The removal of the inspection plate and a brief investigation revealed the damage you see here. The plastic shield of the twist connector had melted, leaving the conical compression connector which holds the wires together. The single red wire leading out of the connector to the inverter had melted close to its entrance in the connector. The twisted wires had evidently slowly corroded, the resistance went up, heat was generated and finally the single wire to the inverter melted. The problem was corrected after about three days.
Fortunately, an upgrade by the manufacturer uses bluetooth to transmit the panels' generation from the inverter into the house where it sits in my study.





















Solar Silliness

It isn't difficult to see installations of PV panels with problems. Sometimes people step into it innocently owing to lack of experience. Others look at a spread sheet detailing expense and make bad decisions. Take shading as an example. At the left and right one sees a panel fully exposed to sunlight (left) and then with the shade of a wooden dowel falling diagonally across the panel (right). Look at the change in current for that small dowel!
When we installed the panels on our house roof I had the expectation that we could allow them to sit there without a worry or care and to generate electricity during daylight hours for the next twenty-five years when the guarantee runs out. That they ought to be exposed to unshaded sunlight was obvious, but my early discovery that in order to achieve maximum output they need also to be rinsed periodically was an early lesson in the maintenance of solar panels. I have been more recently surprised that these two points are not fully appreciated by everyone, not even some "experts."

Here's a house in our neighborhood with panels mounted in a manner which are shaded by a nearby telephone pole during a part of each day when the sun is low in the sky.























As more people install PV systems it stands to reason that some will make informed choices and others will not. It is with more than a little amusement then that one can find some rather large but ill-conceived installations carried out by people one would think should know better. Here is an ambitious private installation of approximately 35 kW on an apartment house in Santa Monica, California, consisting of both vertically and horizontally mounted panels. The vertical panels face southwest and do not receive direct sunlight until late each morning. Moreover, neither the vertical panels nor the horizontal panels at the right are tilted toward the south at the angle of latitude. The shadows cast by the 3 palm trees and the eucalyptus tree (right) for the better part of the day almost certainly will have an attenuating effect on the energy output; how much would be a function of the internal series/parallel circuitry but could be determined with a simulated equivalent unshaded system. There does seem to be a cleaning schedule in place judging from the blue crystalline appearance of the panels' surfaces, at left.

The shading of one's solar panels by a neighbor's trees can rise to a litigious level if one lives in California. The Solar Shade Control Act, signed by the governor in 1978, bans trees or shrubs from shading more than 10 percent of a neighbor's solar panels between 10 a.m. and 2 p.m. and includes shading on panels installed after the trees were planted if the trees grow to such a height to produce shade which exceeds that which is allowed by the law. A recent celebrated case invoking that law involves neighbors in a community near San Francisco. Neighbor A planted eight redwood trees, B, between 1997 and 1999. Neighbor C installed a 10 kW photovoltaic solar panel system, C, in 2001. Redwood trees, B, grew until their shade, D, exceeded that which is allowed by the Solar Shade Control Act. In December 2007, Santa Clara County Superior Court Judge Kurt Kumli ruled that six of the trees can remain and that the two generating the most shade must be removed. It was reported on July 23, 2008 by KGO-TV that Governor Schwarzenegger has settled the conflict by signing a bill which states that a tree which casts a shadow onto a neighbor's solar panel will no longer have to be cut down, as long as the trees were planted before the panels were installed.













The California Department of Transportation building in Los Angeles (right) has a system of panels sandwiched in a casing of bullet-proof glass on the south face, but notice in the close-up that each rank of panels shadows the one below. Moreover, there is no cleaning schedule for the glass surface. If one could depend on frequent inundations blowing from the south then these panels would be periodically cleaned, but that kind of weather doesn't often happen in southern California. We have lengthy periods without rain and when the storms do come they're more often in the form of vertical drizzles which will very definitely clean the uppermost rank of panels but do little good for the ones below.











The Los Angeles Convention Center has a system which was installed by the L.A. Department of Water and Power. The panels were placed around the periphery of the building well below the roof line (I would estimate 4-7 meters). The panels which are mounted on the east and west sides receive no direct sunlight for about half of each day. The ones mounted on the west side and shown in the photograph at the right are in the shade until early afternoon.




On the other hand, a student recently asked me if possibly the installation was set up to overcome the architectural limitations of the building and to take advantage of sunlight during certain hours of the day. PV panels in the early days were expensive and such an installation would hardly have made sense, but one reads that there has been a 50% drop in the price of PV panels so people more and more may simply be of a mind to put the panels wherever there is space, regardless of disadvantages of tilt or shading. Here is an installation in Lakewood, California where panels are placed flat against eastern and southern sloping roof surfaces, where each set of panels will produce electrical energy at highest yield at different times. The leaves of the tree on the southern side in the foreground will likely produce problems of shading at certain hours.




A system consisting of 3872 300 watt panels (Schott ASE-300-DGF/50) yielding a rated power output of 1162 kilowatts was recently installed on the campus of CSU Fresno over Parking Lot V. The general contractor for this installation was Chevron Energy Solutions. The owner of the panels is MMA Renewable Ventures with which the campus has entered into a 20-year power purchase agreement at a starting rate of $0.16 per kilowatt hour and a 2% annual inflation adjustment. An examination of current rates paid by big users of electricity makes a rate of $0.16 per kilowatt hour appear to be a bit pricey. Note that there seems to be a slight tilt toward the south of 1-2 degrees, possibly with drainage in mind.





However, in the image at the right which has had its brightness reduced and contrast increased, the effect of such drainage where morning dew and occasional drizzles are the only sources of precipitation for several months running is a distinct residue which builds up over the cells at the lowest elevation of each set of panel segments. It is not clear at this writing if there is a program of routine rinsing in place.









Here's one worth mentioning. This 205 kilowatt array is in Washington, D.C. and is said to comprise 891 230 W solar panels. Sure enough, 891 x 230 / 1000 = 204.93 kilowatts. But Washington, D.C. is at latitude 38 o 53' north which means that at the very best, the rated power output of horizontal panels will be attenuated by an average factor of
cosine(38 o 53') = 0.78 , decreasing the figure above to 159.6 kilowatts. Judging from the image at the right, it would appear that there isn't the slightest indication of tilt so as to allow the panels to self-clean in the annual rainfall of 39.3 inches. (100 cm). The average solar energy in Washington, D.C. is about 73% that of southern California, so it could be argued that horizontal panels will gain a little from the diffuse sunlight through the frequent cloud cover over Washington, D.C., but most likely the gain will be more than offset by the loss due to the lack of tilt on sunny days. Moreover, one would expect the dustfall on these panels to turn to mud on the surface, not unlike some of the other examples in this section, until the panel guys arrive to give them a power rinse. Where is this ill-conceived installation, I hear you ask? It is on the roof of the headquarters of the . . . wait for it . . . U.S. Department of Energy.






This installation may be found above the top level of a parking structure on Holliston Avenue at Caltech in Pasadena, California. It consists of 1404 170 watt Suntech STP170S-24/Ab-1 panels, giving a total rated power output of 238.68 kilowatts. The sign in the photo at the driveway claims 199 kilowatts. It was installed by EI Solutions. Note that the panels are mounted horizontally. What is not clear from the image is that the only practical access to the panels for periodic rinsing would have to be by hydraulic lift on the east and west sides. The installation runs nearly the length of the structure and the limited access to the panel surface at the north and south ends would make periodic rinsing of the entire panel surface impractical from those access points. A representative of Suntech Energy Solutions points out that where the realization of installations such as this, including the execution of "power purchase agreements" by investor groups, are concerned, optimizing energy output is only one of a variety of considerations. The others are the level and conditions of any production rebate, time-of-use energy tariffs by the electrical utility, financing requirements for the area available and the stated objectives of the client. That is, given the sometimes conflicting agendas encountered when putting together an investor group to realize an installation such as this, other exigencies have to be considered.


A Case Study

A large system (557 kW) was recently installed on the campus of CSU Dominguez Hills by Sun Edison. There are 3279 panels, each rated at 170 watts, bringing the maximum rated power output to 557,430 watts or 557.43 kilowatts. The panels have been mounted nearly horizontally over Parking Lot 1. At our latitude of 34 degrees north they ought to have been tilted toward the south by 34 degrees if the objective is to maximize the generation of energy. At noon at our latitude on the summer solstice the sun is 10.5 degrees from the vertical. At noon on the winter solstice it is 57.5 degrees from the vertical. Assuming 0% loss if the panels are pointing directly at the sun, horizontal panels suffer a power loss of 1.7% and 46.3% at noon on the summer and winter solstices, respectively, for an average annual loss of 24%. On the other hand, under Time of Use (TOU) billing (discussed above), the On-peak period is from 10am to 6pm when the rate charged is higher and if the objective is to maximize one's $ credit the panels ought to be tilted appropriately in a southwesterly direction. Even though we often get brilliant sunlight in southern California from 7am to 10am, that time period still falls in the category of Off-peak.











But it gets worse than that. The lack of tilt means that there is no natural gravity runoff for rain or rinse water. If it appears to you that from the acute angle of view in the photo above the surface color is something other than the typical metallic blue of a silicon photovoltaic cell, you would be right. It appears (at this writing in the fall of 2006) that there has been no rinsing service to maintain maximum output. The surface has been allowed to collect the dustfall of greater Los Angeles since installation around four months ago during which time there has been no rainfall. It is not clear at this writing what the dark spots in the middle of several of the panels represent, but the buildup of dirt certainly doesn't bode well for the overall output of the panel array. It is also not clear at this writing who suffers the greatest disadvantage (the university or the power company) if the power output drops significantly due to lack of maintenance. Only knowledge of the specific billing arrangement worked out in the contract would reveal that information.

Do real data support the depressing conclusion expressed above? Well, yes, generally. On February 28, 2007, a cloudless day from 10am to early afternoon, the system on our rooftop peaked at 10:51 am with an average power output of 2271 watts over the 15 minute interval (7 minutes on either side) which bracketed the maximum of 2284 watts. Taking the theoretical maximum power output specification of these panels, the 2271 watt average translates to [2271/(18 x 165)]x100 = 76.5%. On that same day the power of the university system peaked at 12:15 pm, showing a power output of 319,841 watts. Carrying out an equivalent calculation one gets [318,841/(3279 x 170)] x 100 = 57.4%, a value diminished, I would offer, by the lack of tilt of the panels at the angle of our latitude. We are stymied at this point from looking more closely at these figures and trying to establish how much the diminished value is caused by the lack of tilt and how much by dustfall because the tilt of the domestic roof-top system is itself not ideal. One would need to observe the output of at least one 170 watt panel the normal vector of which is pointing directly at the sun at the time of maximum power by the array of 3279 panels to establish a credible attenuation of power owing both to tilt as well as dustfall.

Here is the one-year line chart of energy generated vs. date for the university system.



Note the two discontinuities identified by the arrows. They represent the increased output following rinsing. That we are experiencing the driest year since records have been kept starting in the latter part of the nineteenth century, we've had many cloudless days. All maxima on the chart above are representative of energy output on cloudless days. Taking the highest adjacent maxima before and after cleaning, we have 10/27/2006 and 10/28/2006, 1644 kwh and 1930 kwh. The lower value is 85.2% of the upper value. Again on 3/15/2007 and 3/16/2007 we have 2222 kwh and 2599 kwh respectively. The low value is 85.5% of the higher value, suggesting that the event which triggers rinsing by the maintenance crew is a 15% drop from maximum expected value. The very low energy outputs and those at zero are unexplained. They are either outages of the panel system for part or all of the day or there was a failure of the data collection system. No explanation is available at this writing.

Photovoltaic Panels, a Game Changer?

In urban southern California it isn't unusual to see oil derricks pumping petroleum near private residences like the one shown here.

The owners of the pumped oil almost certainly are NOT the residents of any of the surrounding houses because the mineral rights of the neighborhood were bought decades ago. But how about a rooftop solar installation which produces energy whether you are at home, at work or on a holiday. It keeps pumping energy, just like the oil derrick but there is no drilling, no spills, no damage to the environment and no purchase of mineral rights are necessary. Give it some thought.



Things we haven't covered

1. Leasing arrangements.
We have one family member who has installed panels on a leasing arrangement. I asked him to give me a testimonial about his experience. I would offer that his approach probably points the way to the future. Very few folks want to be managers of their own private electric utility unless they can figure out a way to be compensated handsomely. Here is what he writes:

Leasing solar panels
This was an easy decision to make. Since I'm leasing them that means the company owns them and has to service them. If power drops below the specified minimum, it's up to them to figure out why. Sure, I could have taken on this responsibility and gotten a higher value from the panels but the cost was my time. And right now time is something I do not have much to spare, so I value it EXTREMELY highly. So far there have been no problems with my panels and they just keep churning out money.

2. Community solar farms. An estimated 85 percent of US residents can neither own nor lease systems because their roofs are physically unsuitable for solar or because they live in multi-family housing. If you are one of the 85% then a community solar farm may be for you. Read all about it at Community Solar Farm
3. Plug-in panels.
4. Microinverters
5. Disconnecting from the grid using battery-based energy storage.

Things we have covered only briefly.

1. Feed-in tariff. Search the web for an explanation.
2. Net metering. Search the web for an explanation.


Conclusion

So as to gain maximum advantage from an installed system of photovoltaic panels, the following preliminary conclusions can be made:

1. If you are connected to a grid, install a system sufficiently large to generate as much energy in kilowatt hours as you use during the entire year. Even that strategy might have to be modified if the on-peak rate changes to be highest at night. In any case, you need to start thinking about a Plan B to use up the energy credit you build up throughout the year and possibly to install more panels if you find yourself suddenly having to pay for electricity.
2. Tilt your panels toward the south (in the northern hemisphere) or toward the north (in the southern hemisphere) at the angle of your latitude.
3. Regularly rinse your panels to keep them clean and to maximize their output.
4. If the panels meet all of your electrical energy needs, that is, if energy consumption is close to energy generation, then the decision to switch to "Time of Use" metering makes sense only if the Winter Off Peak rate is so much lower than the Summer On Peak rate that some Plan B for using up the accrued credit becomes financially appealing.
5. Don't opt for "Time of Use" metering if your panels produce somewhat less than your electricity requirement during the winter, but more than you use during the summer because a slight change in rate of one period vs. another can make the difference between an annual energy credit and an unwelcome electricity bill.
6. If your panels produce only a small fraction of the electrical energy you use throughout the year then do NOT switch to TOU metering. Doing so would subject you to the inflated "Summer On Peak" rate which at this writing is on the order of three times the flat rate.

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