Let’s face it, lots of people aren’t very good at math, even rather basic math. On the other hand, some people are quite good at it. If you aren’t very good at math, there are plenty of other things for you to do in life. My own field of law practice mostly does not require much skill at math, and there a plenty of math-challenged people who are nevertheless very good lawyers.

But some big societal decisions require a certain level of math competence. Some of these decisions can involve multi-hundreds of billions of dollars, or even multi-trillions of dollars. For example, consider the question of whether proposed electricity generation system X has the capability to deliver the amount of electricity a state or region needs, and at the times it is needed. Answering this question is just a matter of applied basic arithmetic. Given the dollars involved, you would think that when a question like this is being addressed, it would be time to call in some people who could do the arithmetic, or who at least would be willing to try.

Yet when the issue is replacing generation of electricity by fossil fuels with generation by “renewables,” it seems that the need to believe that the renewables will work and be cost effective is so powerful that all efforts to do the arithmetic get banished. I last considered this issue in a post last week titled “California’s Zero Carbon Plans: Can Anybody Here Do Basic Arithmetic?” The answer for the California government electricity planners was a resounding “NO.” Today, the Wall Street Journal joins the math-challenged club with a front page story headlined “Batteries Challenge Natural Gas As America’s No. 1 Power Source.” (probably behind pay wall)

The theme of the story is that “renewable” energy sources, such as solar, paired with batteries to balance periods of low production, are rapidly becoming so cheap that they are likely to “disrupt” natural gas plants that have only recently been constructed:

[T]he combination of batteries and renewable energy is threatening to upend billions of dollars in natural-gas investments, raising concerns about whether power plants built in the past 10 years—financed with the expectation that they would run for decades—will become “stranded assets,” facilities that retire before they pay for themselves. . . . But renewables have become increasingly cost-competitive without subsidies in recent years, spurring more companies to voluntarily cut carbon emissions by investing in wind and solar power at the expense of that generated from fossil fuels.

To bolster the theme, we are introduced to industry executives who are shifting their investment strategies away from natural gas to catch the new renewables-plus-batteries wave. For example:

Vistra Corp. owns 36 natural-gas power plants, one of America’s largest fleets. It doesn’t plan to buy or build any more. Instead, Vistra intends to invest more than $1 billion in solar farms and battery storage units in Texas and California as it tries to transform its business to survive in an electricity industry being reshaped by new technology. “I’m hellbent on not becoming the next Blockbuster Video, ” said Vistra Chief Executive Curt Morgan.

But how does one of these solar-plus-battery systems work? Or for that matter, how does a wind-plus-battery system work? Can anybody do the arithmetic here to demonstrate how much battery capacity (in both MW and MWH) it will take to balance out a given set of solar cells at some particular location so that no fossil fuel backup is needed? You will not find that in this article.

Here’s something that ought to be obvious: solar panels at any location in the northern hemisphere will produce less power in the winter than in the summer. The days are shorter, and the sun is lower in the sky and consequently weaker. Therefore, any system consisting solely of solar panels plus batteries, where the batteries are seeking to balance the system over the course of a year, will see the batteries drawn down continuously from September to March, and then recharged from March to September. Do batteries that can deal with such an annual cycle of seasons even exist? From the Journal piece:

And while batteries can provide stored power when other sources are down, most current batteries can deliver power only for several hours before needing to recharge. That makes them nearly useless during extended outages. . . . Most current storage batteries can discharge for four hours at most before needing to recharge.

OK, then, so if solar-plus-battery systems are about to displace natural gas plants, what’s the plan for winter? They won’t say. The fact is, the only possible plans are either fossil fuel backup or trillions upon trillions of dollars worth of batteries. But the author never mentions any of that. How much fossil fuel backup? That’s an arithmetic calculation that is not difficult to make. But the process of making the calculation forces you to actually propose the characteristics of your solar-plus-battery system, which then makes the costs obvious. How much excess capacity of solar panels and batteries do you plan to build to minimize the down periods? Do you need solar panel capacity of four times peak usage, or ten times? Do you need battery capacity of one week’s average usage (in GWH) or two weeks or a full month?

The simple fact is that wind/solar plus battery systems would not need any government subsidies if they were cost effective. The Biden Administration is proposing to hand out many, many tens of billions of dollars to subsidize building these systems. They are clearly not cost-effective, and not even close. But no one in a position to know will make the relatively simple calculations to let us know how much this is going to cost. Even the Wall Street Journal can’t seem to grasp the math involved. And President Biden? It’s embarrassing even to ask the question.