I have no idea, but I wonder if the equation is an "average" of some kind? here in CA for example, its extremely common for a system to generate way more than its kW rating on a yearly basis. My 8.6kW system (for example) generated 13.14 MWh last year (in its 7th year of existence) and has generated 9.4MWh already this year.
This is super common here in CA, so much so that until I joined this board and saw that in other parts of the US, a "9kW" system actually generated around 9-10kW (not 14 like I would expect), I was surprised. I know its because of the amount of sun we get here, etc, but it makes me think that the formula must be some sort of average or something.
At the time, being the EE nerd that I was, I did a lot of digging about solar panel systems, both in 2008 when we got the install, and in 2004 when we moved into the house. In 2004 there was this web site run by the NJ government. In it, one could put in the the numbers of appliances a house had, the square footage, the air conditioning systems and its efficiency, angle on the roof and how many square feet of roofing there was, one's longitude and latitude, and the model would suck in information from NASA on solar irradiation data for the site, including how much cloud cover on average one might have.
Included in all this were the solar panel types, how efficient they were as a function of temperature, and whether they were single crystal or amorphous.
The inverters get to be fun, too. At the time, one would hook up strings of panels, then put the strings in parallel, then connect the whole mess to the inverters. The inverters would "hunt" for the correct voltage and current that gave one maximum power from the panels. Early in the morning or late in the afternoon, there wouldn't be much power from the panels; at noon, there'd be more; but the inverters' efficiencies
varied with the power input, the ambient temperature, and so on.
In addition, one has to use copper wires to move the energy from the panels to the inverters.
Losses.. don't tell me about losses. If one has a single string of panels, there's no guarantee that, with a given solar input, that a particular panel's current and voltage will be the same as other panels' currents and voltages. This results in inefficiencies where one can't get the full advertised power from all the panels because the current and running through panel X results in less power than the same current running through panel Y. Then take a string of panels like that and parallel it with another batch of panels. Total power of the panels, if they could all have the same sun energy perpendicular to the surface of the panels, in my system, is 9.02 kW. The actual output power, max, is 7.8 kW. I've watched the power levels go up and down: There really is about 13.5% loss in wires, inbalances, and the inverters. Once or thrice a year the inverters would peak at their maximum output power for a half hour or so around noon, but mostly that never happened, the installers had it all sized about right.
So, when one is designing a system to meet that NJ requirement, one can find on-line designers. Input to the designer: Roof angle. Location, which gives where the sun is over time for the entire year. Average temperatures recovered from databases on Each Day throughout the year. Cloud cover and, throughout the year, on a daily basis, the percentages of days when the air is absolutely clear and when it's foggy.
And, interestingly, the make and model of the panels one is putting up! I've seen the manufacturer's data sheets for these panels. Temperature variations. Power vs. irradiation and, no, it's not linear.
Interestingly, modern setups aren't built like that any more. First off, the panels are monocrystalline: They're black, not mottled blue like mine. The mottled blue ones have amorphous silicon and are cheaper but aren't as efficient. The black ones cost more, but, partly because of economies of scale, the prices have dropped and, since they're more efficient, one needs fewer of them to reach a given power level.
The next huge difference is those power blocks. Like the ones I was talking about with regard to Tesla battery chargers earlier. A given panel is 250W-500W at about 20V or so. One places a DC-DC converter on each panel, then connects the outputs of the DC-DC converters on a string of, say, 10 panels in series. Each DC-DC converter fools around with the current/voltage level on its input until it maximizes the power draw from that particular panel. All the other DC-DC converters are doing the same thing.
So, the
output of each DC-DC converter in a string has a different amount of power, since the panels have manufacturing variations. Well, the outputs are all wired up in series, so each has the
same current. The modules communicate with each other; the entire string voltage is set to 300V, say; the higher power panels get more of that voltage, the lesser power panels get less of that voltage,
and all the panels make the maximum amount of power they're capable of.
Boom! My system has 15% losses: At least 10% of those losses would go bye-bye. There might be 1% loss in each of the DC-DC converters, but we're now 9% to the good, and a system could have 9% fewer panels for the same total output power level.
This also makes the inverters simpler, too. My inverters have to live with voltages that range from 150VDC to 450 VDC as a function of sunlight, and from that, they generate 240 VAC. It's not easy making them efficient over that wide a voltage range. With the individual DC-DC converters on the panels trick, one can keep the DC voltage into the inverters at 300 VDC for most of the range of sunlight intensity that one might run into, so the inverters get more efficient. There's 3% more efficiency, for a total of 12% fewer panels for a given power level.
And now, we get tricky. Do what Tesla does: Make the batteries in their Powerwalls 300V, the same as the panel string voltages. Suddenly, switching back and forth between city power and battery power, and charging batteries in general, gets to be more technically feasible.
Going back to your original question: The equations are complex and there was some flunky, or hired flunky, in NJ that designed and mandated that equation. I suspect that it wasn't reviewed by professionals. And, like I said, once the error was discovered.. what were they going to do? Tell people to put fewer panels on their houses? I mean, these were the people trying to
get people to go solar! Even the public utilities didn't raise a fuss.