I very much value your presence here, since you are the future. From what I can tell, you are a very fine young person. It is very important that people in the future understand how numbers are used and how they are misused.
Here is a presentation prepared for The California Energy Commission describing the current state of affairs for solar energy in the "Sunshine State:"
http://www.solarelectricpower.org/ewebeditpro/items/O63F5151.pdfAccording to this presentation (last slide) which apparently is germane to the current hoopla, we have the following figures:
Current California Solar Capacity: 88 Megawatts.
Proposed Capacity in 2018 if this bill, unlike it's many predecessors actually delivers on it's promise: 3000 Megawatts.
Now, solar hype types often make statements like these: "The cost of solar capacity has fallen by 50 percent since {plug in year here}! Installed solar capacity has increased by 1000 percent since {plug in year here}. The key word, of course, in these sentences is "percent."
This is very much like the statement "Measured thyroid cancer rates after Chernobyl increased by 1000 percent." This statement is approximately true and it sounds very, very dramatic. However, if one learns that only 10 or so thyroid cancer cases had been identified in the area in a given year before Chernobyl, and that thyroid cancer isn't particularly fatal, and that almost no screening for thyroid cancer was done before Chernobyl, and almost everyone in the area is now having themselves screened for this cancer, one quickly sees that the actual case is very different than what is being
advertised.
Now let's turn to percent business and solar power.
Solar hype types will sometimes make a statement like this: "Solar power is growing exponentially!"
OK, let's take them at their word. What does it mean?
I do not know how much math you know as a young person, but I will nonetheless offer the following explanation:
Typically when one says that something is growing exponentially one can use a formula that looks like this N(t) = No*exp(rt) where N(t) is the value at some time, t, and No is the value at time zero, which we will take to be the end of 2004, as described in the presentation. r is the rate at which the power is growing, t is the time and the exp refers to the function that raises the irrational number, e, to the power in the parentheses. Thus, dividing both sides of the equation by No, we have N(t)/No = exp(rt). Taking the natural logarithm of both sides we have ln(N(t)/No) = rt.
Now, according to the presentation, N(t) is 3000 Megawatts and No is 88 Megawatts. t is 2018-2004 = 14. Plugging these values in the last equation in the last paragraph and solving for r we see that r is roughly equal to 0.252.
Now, the current peak energy demand, were it to stay constant forever, which it won't, in California is about 55,000 Megawatts roughly, if all the hyped up breathless news articles about this wonderful bill to be signed by Governor Schwartzenhummer are to be believed. Typically, on most grids one has to have excess capacity built in case of burn-outs, failures, either in the grid or in the generating station. If this excess capacity is 20% then we would need 55,000*1.2 = 66,000 Megawatts of power to address California's electrical needs.
Now given our discovered "exponential" rate above, how long would it take to provide all of California's electricity needs from solar power? (In the day. When the sun is shining. When it isn't raining. When there is no snow on the ground. When the smog isn't too bad. When there are no Santa Anna driven dust storms. When the smoke from chaparral fires isn't blocking out the sun.)
From our equation we now have ln(66,000/88) = 0.252*t. Solving for t we see that the value is 26 years. This sounds reasonable but it isn't.
Why not?
Because the sun shines only one half of the day on average.
OK, let's double the capacity to 130,000 Megawatts, and store half the power we make in daylight, in magic batteries. Then how many years? 29 years. But then again, in December the daylight doesn't shine for half the time, but more like a third of the time. So really, if we want to light our Christmas displays, we really have to have three times the capacity. Now we're up to 31 years.
But wait. Batteries really aren't magical, are they? All of them have internal Resistance and lose power both on charging and discharging. Let's up the daylight power requirement by a factor of 5 overall to account for this business. Now we're up to 33 years, and can have this wonderful system by 2038, when you'll probably be my age, assuming humanity isn't wiped out by climate change before then.
Still not too bad though, is it?
Well the problem is that this is after all, an exponential relationship. As such all of the other factors also rise exponentially; the cost of the system rises exponentially; the resources required to build it rises exponentially; the land area covered rises exponentially, etc, etc.
Most people who know something about mathematical modeling, understand that most systems do not follow the same functions over broad ranges of conditions. When for instance, one is learning this stuff, the classic example is bacterial growth. The growth of bacteria in a medium follow exponential functions quite nicely when the colony is small and the medium is much larger than the colony. If the function held over all ranges, it is usually easy to calculate the amount of time that it would take for the colony to have the mass of the earth. But of course colonies never actually do reach that mass. Generally the depletion of the medium changes the modeling function into some other type of function.
In our example of the miraculous growth of solar power, lets calculate how much power needs to be installed between year 33 and year 32 in order for solar power to grow exponentially as solar hype types want you to believe it will. We have N(32) = 88*exp(0.252*32) = 280,000 megawatts and N(33) = 88*exp(0.252*33) = 361,000 Megawatts. The difference is 361,000-280,000 = 81,000 Megawatts.
According to this website, the price per watt of a solar panel is $5.10 as of this month:
http://www.solarbuzz.com/moduleprices.htmNote that the price has been rising recently, not going down as promised by our solar hype types.
Be that as it may, let's say that the price falls by a factor of 5, though, in the next 33 years, just to give our solar hype types their fantastic nonsensical assumptions. Then the price will be 1 dollar per watt. Remember though we need 81,000 MEGAwatts or 81,000
million watts. The cost of the last year's (year 32) installation is thus $81,000,000,000.00. I really don't think that the Californians of 2038 are going to want to spend 81 billion dollars for new solar capacity. Shit, this is a state where they won't even pay for their schools. For that amount of money they could invade Mexico, kill their children, rape their women and steal their energy. Given the level of American ethics and extrapolating it forward some thirty years, they'd probably prefer the Mexican option to the silicon option.
In short: It's bullshit, pure and simple.
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