> Can someone who understands the subject matter better than I do please explain
> to me how "cents per watt" is an applicable comparative metric for fossil fuels and solar cells
The price of electricity is basically the total money you put into running the plant over its lifetime divided by the total amount of power you get out of it during that lifetime. That's called the "levelized cost of electricity" or LCoE.
For plants that don't use fuel - wind, hydro, PV - the total amount of money is basically the price of the plant, the price of repairs and operations, and the price of borrowing the money to pay for the first two. For systems that go up in a short time, like wind and PV, the costs are utterly dominated by the price of the equipment.
For other sources the total cost of operations varies. Nuclear plants use fuel, but so little of it that it's not a major factor. However, these plants have enormous up front costs and decades long building cycles, so their LCoE tends to be utterly dominated by the prevailing interest rate. Coal and natural gas plants cost about 1/4 that of a nuclear plant and are therefore more heavily dominated by fuel costs, so their cost of operations goes up and down with the cost of the fuel.
So when you're trying to compare the price of a PV plant to a coal plant, for instance, the key metric in the case of PV is the cost of the panels. That's because there's no fuel cost and almost zero maintenance (had mine 5 years, done exactly $0 work on them so far).
Since the amount of sunlight shining in a particular area is averaged over long periods and available online, you can then predict the amount of power the plant will produce over its lifetime. For instance, in Toronto 1000 W worth of panels (i.e., a set of panels that will produce 1000 watts under specific conditions) will produce about 1200 kWh of power every year, after all conversion losses are factored in. We expect those panels to last about 25 years. So then
LCoE = (cost in cents/watt * size of system in watts) / (25 years * 1200 kWh * system size in KILOwatts)
So let's say the system, *all in*, costs you $3.50 a watt (about right these days). Then if you put up a system with 12 panels like mine, you get
LCoE = (3.50 * 3000) / (25 * 1200 * 3) = 11.66 cents/kWh
I think you'll find that is very comparable to what you are paying from your local utility, which is why PV is the fastest growing power source in the world today.
This same basic formula can be used with any power source, but the inputs will differ. For instance, the equivalent number for a nuclear power plant is about 7500 to 8000 kWh per kW of panels installed, because they run full out 24/7, or at apt 85% full power, or "capacity factor". But as you might expect, construction costs are much higher, about $8/W or more (that plant in Florida came in at about $11/W, which is why they cancelled it).
Likewise, wind turbines here in Ontario average about 30% "capacity factor" (CF), so that's about 2600 kWh/kW. That sounds bad until you consider they cost about $2/W installed. So when you compare the two head up it's something like (2 / 0.3) = 6.66 for wind vs. (8 / 0.85) = 9.41 for nuclear, which is why wind is the second fastest growing power source on the planet.
And that's why we measure everything in terms of cents per watt. If you know that (although dollars per watt is the typical figure) and the capacity factor, everything else sort of disappears. So you can get a *very* good idea of the economics simply by dividing the ($/W) by (CF).
If you'd like to do this on your own, with real numbers and more factors, you can. It's actually very easy and you can run through a given location in about 2 minutes: