5 ms·

There are many layers of bad math in matters related to climate change, electric vehicles and renewable energy. Too many to list. One of my favorites is the u

There are many layers of bad math in matters related to climate change, electric vehicles and renewable energy. Too many to list. One of my favorites is the use of averages. This is self-evident to anyone who understands that the value of an average is highly dependent on the underlying distribution. However, most people --and certainly most politicians-- do not understand this at all. A typical example of this is calculating the additional power demand required in order to support a full transition to EVs. The bad calculation usually starts with a web search to get the average miles a person drives (about 30). That number is then applied to the entire population. A number comes out and Bob's your uncle. Except, he isn't. And that's nowhere close to a real number. Yet, it this sort of thing is used everywhere. Another one is solar panel output and solar installation power/energy production. This is so common, it has a name: The Flaw of Averages https://hbr.org/2002/11/the-flaw-of-averages https://hbr.org/2002/11/the-flaw-of-averages The greater point is that bad math is being used everywhere to drive narratives and make decisions that are just as flawed as the math used to justify or sell them to the public.

drdeca 4y ago
In the particular case of the "miles driven", what's wrong with the average? Is it because the amount of power used by an individual with an EV differs from being proportional to the distance they drive with it, in a way that matters when aggregated? Like, if the distance amount a randomly selected person drives has some distribution, then, if power use was proportional to distance traveled, then E[(energy use)] = E[k * (distance traveled)] = k * E[(distance traveled)], and, average energy use is total energy use divided by number of people, which is the same as the expectation of the energy use of a randomly selected person, so, total energy use would be (number of people) * k * E[(distance traveled)] . So, therefore, if that's not true, then one of the assumptions in the argument must not be true, so therefore, (energy use) must not be k * (distance traveled). Now, not being exactly the same, that's expected, yes. Like, there should be terms relating to e.g. "how long people are stopped at traffic lights", stuff associated with whether they use the car at all that week, etc. , but, nothing from that jumps out at me as something which obviously would make the shape of the distribution of "how much each person drives" beyond just "how much does a person drive on average", matter a whole lot. I'm not saying it doesn't. I'm saying, even considering it, nothing jumps out to me as a reason it should be obvious.
- robomartin 4y ago
  > I'm not saying it doesn't. I'm saying, even considering it, nothing jumps out to me as a reason it should be obvious. I'll ignore questions about the distribution and highlight what is perhaps the most egregious problem in EV estimates: Energy is the wrong metric. Using the average allows one to speak in terms of energy. Yet energy isn't what we need. We need power. Yes, of course, at the end of the day you are trying to store energy. However, what we need to know is what our power requirements might be. Here's a super-simple example. This isn't meant to be a full analytical model, it's just a simplified hypothetical used to illustrate the important difference between speaking in terms of energy and power. Ten EV's are driven the same number of average miles in a day. The number of miles does not matter. If those ten EV's are plugged-in for slow-charging all night, they receive a certain amount of energy. This energy is delivered slowly (at a low power level) over, say, twelve hours. On the other hand, if the same ten EV's where to simultaneously plug-in for rapid-charging in, say, one hour, the situation is much different. They would receive the same energy. However, this requires twelve times more power. The difference isn't trivial. It's the same energy, yet you need twelve times more power (and the ability to deliver that power) in the second case. Real-life hypothetical: Hurricane landing in Florida at some point in the future when EVs (from motorcycles to semi-trucks) have fully displaced internal combustion vehicles. A very large percentage of the population needs to rapid charge during a very narrow window of time. Everyone is on the road evacuating. The limiting factor is power generation capacity as well as power deliver capabilities (the "grid"). This is a highly simplified view into why using averages to broad-stroke estimates is in the realm of a fantasy. You don't have to look at natural disasters as the only drivers for this sort of peak demand. Holiday traffic and other events or local conditions alter the distribution. Regional differences have the same kind of influence. For example, where I live, most people have to drive 30 to 60 miles each way to go to work. That's hundreds of thousands of vehicles. Bad urban planning? No argument from me. Guess what? It isn't going to change. Anyone who thinks so has never had to pleasure of locking horns with the urban planning agencies where they live. Not going to happen. And it isn't just work. Entertainment, high-end restaurants, etc., are also 30 to 60 miles away. That's why using averages to calculate energy is only valid if we are OK with people not being able to charge their cars and being stranded when peak power demand exceed available generation and grid (transport) capacity. In CA we've had cases of people not being able to charge their EV's during evacuations and being asked to delay charging during periods of high heat. I have written simulation models to analyze this at a reasonably detailed level of granularity. My model predicted the need for additional (new, on top of what we currently have) power generation in the order of 900 GW to 1400 GW for the entire ground transportation fleet in the US going electric. I did this many years ago. I have since concluded that this range seems to be an accurate prediction. For a sense of proportion, this means we need to build a thousand nuclear power plants. No, solar and wind, individually or collectively, won't do it. I've done the math on that too.
tuatoru 4y ago
This is one of the points made in the "Empirically grounded technology forecasts" paper that Noah's article is based on. The authors define things stochastically and run their model thousands of times to come up with likely ranges: a PDF, not a single number. Doing things stochastically, policy can be made that is robust to uncertain numbers.
- robomartin 4y ago
  The only times a stochastic model works is if the reality you are trying to simulate aligns well with this approach. Poking fun at the oversimplifications we make in Physics just to be able to put some numbers on paper, I often say that a cow is never a uniform sphere of milk one meter in diameter. We can do math with such a simplified model, however, believing this to always match reality would be a mistake. In another comment I gave the example of hurricane evacuation day/week in Florida. This is a clear case of the distribution not being anywhere close to normal. The average, in that and other cases, is absolutely meaningless and useless for peak power demand prediction. The median might be better. Or, better yet, doing the math with thousands of data points picked from a reasonably similar distribution. In business forecasting this flaw of the averages has gained deeper understanding as something that could result in seriously flawed predictions (for example: inventory or capital requirements). Those who have gained this insight will usually resort to the use of suitably distributed multiple data point calculations to drive forecasts. This isn't different at all in the case of EV's and related fields. Well, it shouldn't be.
Schroedingersat 4y ago
> A typical example of this is calculating the additional power demand required in order to support a full transition to EVs. The bad calculation usually starts with a web search to get the average miles a person drives (about 30). That number is then applied to the entire population. A number comes out and Bob's your uncle. > Except, he isn't. And that's nowhere close to a real number. What's the real number then, and what prevents us from solving the problem of moving people around with 10kWh/day of electricity * the number of people (especially if we grow up and stop demanding a personal 4t climate controlled 100mph pod)? > Another one is solar panel output and solar installation power/energy production. What prevents us replacing the first 30% of fossil fuels in the areas 90% of people live with PV with <50% curtailment then? What prevents another 30% being replaced with wind? What rational reason is there to think that a strategy that has provided a solution to half the problem with a miniscule fraction of the cumulative resources spent on the existing monopolists wouldn't make further progress? What are you proposing we do instead except build PWRs which will run out of fuel in less than a year if we actually try to use them to replace a meaningful portion of primary energy?
- robomartin 4y ago
  > What's the real number the First, we need to understand that the problem is power, not energy, generation and transport. The difference between the two is massive. Second, we need to understand that we need power over and above the currently installed capacity. This should be self-evident; we consume the power we generate today. We don't have enough excess capacity. I live in California, we have blackouts and the government has asked our insignificant number of EV owners to alter their charging behavior during period of peak demand. We need more power. Third, in the US, we need approximately 1200 GW in new power generation and transport capacity. Of course, this would be distributed non-uniformly according to regional requirements. The grid needs to be able to move this power as well. The current infrastructure cannot. For context, the entire power generation system in the US is good for about 1200 GW today. In other words we, conceptually, need to create a full duplicate of the US power generation and transport system. This isn't trivial. We can't even build a high speed train and now we are talking about doubling our power generation and transport capacity in just a few years. CA wants a major transition to EV's in eight years. This is demented. I don't even want to imagine the power problems and fires we are going to have to live through. > What prevents us replacing the first 30% of fossil fuels in the areas 90% of people live > What prevents another 30% being replaced with wind? Let's start with this: Solar and wind are unreliable. To illustrate, here's an example from about one month ago from my own 13 kW solar array: https://i.imgur.com/A0u4I0R.png https://i.imgur.com/A0u4I0R.png First thing to notice is that the peak is nowhere near 13 kW. In other words, you don't get twelve hours of power at the peak power rating of the panels. The most I have seen is a 10 kW to 11 kW peak for a few minutes around April/May. What are those horrendous dips? Clouds. Yup. Now imagine an entire city relying on this for power? Wind is similar. Here's today so far. It's horrible. Again, clouds. https://i.imgur.com/breTHQd.png https://i.imgur.com/breTHQd.png We actually went from a potential peak of 8 kW down to 0.792 kW around noon. Once again, imagine an entire town with this problem. Batteries? Sure. So, you build one array to supply power during the day. And then a full duplicate of that array to charge the batteries you will need to provide power at night. However, it isn't that simple. If you notice, the power generation output curve is an inverted parabola. The integral of that parabola over time is 2/3 the area of the enclosing constant power rectangle. This means you have to build an array 1.5 times larger in order to fill the voids, store that energy and be able to provide constant power even when the sun is up. If we continue to analyze and compensate for deficiencies and reliability problems, it is very easy to show that a solar system capable of replacing a fossil fuel or nuclear power source has to be built 7 to 15 times larger than the required steady-state output. This includes an absolutely massive amount of batteries, of course. The only real solution I see is a large amount of new nuclear power generation and, yes, some solar and wind. I don't think there's another way to do it. Part of me think that manufacturing, transporting and installing that many panels and batteries is likely to create a far greater ecological disaster than most people imagine. Just a hunch, haven't done the numbers on that one.

drdeca 4y ago

In the particular case of the "miles driven", what's wrong with the average? Is it because the amount of power used by an individual with an EV differs from being proportional to the distance they drive with it, in a way that matters when aggregated? Like, if the distance amount a randomly selected person drives has some distribution, then, if power use was proportional to distance traveled, then E[(energy use)] = E[k * (distance traveled)] = k * E[(distance traveled)], and, average energy use is total energy use divided by number of people, which is the same as the expectation of the energy use of a randomly selected person, so, total energy use would be (number of people) * k * E[(distance traveled)] . So, therefore, if that's not true, then one of the assumptions in the argument must not be true, so therefore, (energy use) must not be k * (distance traveled). Now, not being exactly the same, that's expected, yes. Like, there should be terms relating to e.g. "how long people are stopped at traffic lights", stuff associated with whether they use the car at all that week, etc. , but, nothing from that jumps out at me as something which obviously would make the shape of the distribution of "how much each person drives" beyond just "how much does a person drive on average", matter a whole lot. I'm not saying it doesn't. I'm saying, even considering it, nothing jumps out to me as a reason it should be obvious.

robomartin 4y ago
> I'm not saying it doesn't. I'm saying, even considering it, nothing jumps out to me as a reason it should be obvious. I'll ignore questions about the distribution and highlight what is perhaps the most egregious problem in EV estimates: Energy is the wrong metric. Using the average allows one to speak in terms of energy. Yet energy isn't what we need. We need power. Yes, of course, at the end of the day you are trying to store energy. However, what we need to know is what our power requirements might be. Here's a super-simple example. This isn't meant to be a full analytical model, it's just a simplified hypothetical used to illustrate the important difference between speaking in terms of energy and power. Ten EV's are driven the same number of average miles in a day. The number of miles does not matter. If those ten EV's are plugged-in for slow-charging all night, they receive a certain amount of energy. This energy is delivered slowly (at a low power level) over, say, twelve hours. On the other hand, if the same ten EV's where to simultaneously plug-in for rapid-charging in, say, one hour, the situation is much different. They would receive the same energy. However, this requires twelve times more power. The difference isn't trivial. It's the same energy, yet you need twelve times more power (and the ability to deliver that power) in the second case. Real-life hypothetical: Hurricane landing in Florida at some point in the future when EVs (from motorcycles to semi-trucks) have fully displaced internal combustion vehicles. A very large percentage of the population needs to rapid charge during a very narrow window of time. Everyone is on the road evacuating. The limiting factor is power generation capacity as well as power deliver capabilities (the "grid"). This is a highly simplified view into why using averages to broad-stroke estimates is in the realm of a fantasy. You don't have to look at natural disasters as the only drivers for this sort of peak demand. Holiday traffic and other events or local conditions alter the distribution. Regional differences have the same kind of influence. For example, where I live, most people have to drive 30 to 60 miles each way to go to work. That's hundreds of thousands of vehicles. Bad urban planning? No argument from me. Guess what? It isn't going to change. Anyone who thinks so has never had to pleasure of locking horns with the urban planning agencies where they live. Not going to happen. And it isn't just work. Entertainment, high-end restaurants, etc., are also 30 to 60 miles away. That's why using averages to calculate energy is only valid if we are OK with people not being able to charge their cars and being stranded when peak power demand exceed available generation and grid (transport) capacity. In CA we've had cases of people not being able to charge their EV's during evacuations and being asked to delay charging during periods of high heat. I have written simulation models to analyze this at a reasonably detailed level of granularity. My model predicted the need for additional (new, on top of what we currently have) power generation in the order of 900 GW to 1400 GW for the entire ground transportation fleet in the US going electric. I did this many years ago. I have since concluded that this range seems to be an accurate prediction. For a sense of proportion, this means we need to build a thousand nuclear power plants. No, solar and wind, individually or collectively, won't do it. I've done the math on that too.

tuatoru 4y ago

This is one of the points made in the "Empirically grounded technology forecasts" paper that Noah's article is based on. The authors define things stochastically and run their model thousands of times to come up with likely ranges: a PDF, not a single number. Doing things stochastically, policy can be made that is robust to uncertain numbers.

robomartin 4y ago
The only times a stochastic model works is if the reality you are trying to simulate aligns well with this approach. Poking fun at the oversimplifications we make in Physics just to be able to put some numbers on paper, I often say that a cow is never a uniform sphere of milk one meter in diameter. We can do math with such a simplified model, however, believing this to always match reality would be a mistake. In another comment I gave the example of hurricane evacuation day/week in Florida. This is a clear case of the distribution not being anywhere close to normal. The average, in that and other cases, is absolutely meaningless and useless for peak power demand prediction. The median might be better. Or, better yet, doing the math with thousands of data points picked from a reasonably similar distribution. In business forecasting this flaw of the averages has gained deeper understanding as something that could result in seriously flawed predictions (for example: inventory or capital requirements). Those who have gained this insight will usually resort to the use of suitably distributed multiple data point calculations to drive forecasts. This isn't different at all in the case of EV's and related fields. Well, it shouldn't be.

Schroedingersat 4y ago

> A typical example of this is calculating the additional power demand required in order to support a full transition to EVs. The bad calculation usually starts with a web search to get the average miles a person drives (about 30). That number is then applied to the entire population. A number comes out and Bob's your uncle. > Except, he isn't. And that's nowhere close to a real number. What's the real number then, and what prevents us from solving the problem of moving people around with 10kWh/day of electricity * the number of people (especially if we grow up and stop demanding a personal 4t climate controlled 100mph pod)? > Another one is solar panel output and solar installation power/energy production. What prevents us replacing the first 30% of fossil fuels in the areas 90% of people live with PV with <50% curtailment then? What prevents another 30% being replaced with wind? What rational reason is there to think that a strategy that has provided a solution to half the problem with a miniscule fraction of the cumulative resources spent on the existing monopolists wouldn't make further progress? What are you proposing we do instead except build PWRs which will run out of fuel in less than a year if we actually try to use them to replace a meaningful portion of primary energy?

robomartin 4y ago
> What's the real number the First, we need to understand that the problem is power, not energy, generation and transport. The difference between the two is massive. Second, we need to understand that we need power over and above the currently installed capacity. This should be self-evident; we consume the power we generate today. We don't have enough excess capacity. I live in California, we have blackouts and the government has asked our insignificant number of EV owners to alter their charging behavior during period of peak demand. We need more power. Third, in the US, we need approximately 1200 GW in new power generation and transport capacity. Of course, this would be distributed non-uniformly according to regional requirements. The grid needs to be able to move this power as well. The current infrastructure cannot. For context, the entire power generation system in the US is good for about 1200 GW today. In other words we, conceptually, need to create a full duplicate of the US power generation and transport system. This isn't trivial. We can't even build a high speed train and now we are talking about doubling our power generation and transport capacity in just a few years. CA wants a major transition to EV's in eight years. This is demented. I don't even want to imagine the power problems and fires we are going to have to live through. > What prevents us replacing the first 30% of fossil fuels in the areas 90% of people live > What prevents another 30% being replaced with wind? Let's start with this: Solar and wind are unreliable. To illustrate, here's an example from about one month ago from my own 13 kW solar array: https://i.imgur.com/A0u4I0R.png https://i.imgur.com/A0u4I0R.png First thing to notice is that the peak is nowhere near 13 kW. In other words, you don't get twelve hours of power at the peak power rating of the panels. The most I have seen is a 10 kW to 11 kW peak for a few minutes around April/May. What are those horrendous dips? Clouds. Yup. Now imagine an entire city relying on this for power? Wind is similar. Here's today so far. It's horrible. Again, clouds. https://i.imgur.com/breTHQd.png https://i.imgur.com/breTHQd.png We actually went from a potential peak of 8 kW down to 0.792 kW around noon. Once again, imagine an entire town with this problem. Batteries? Sure. So, you build one array to supply power during the day. And then a full duplicate of that array to charge the batteries you will need to provide power at night. However, it isn't that simple. If you notice, the power generation output curve is an inverted parabola. The integral of that parabola over time is 2/3 the area of the enclosing constant power rectangle. This means you have to build an array 1.5 times larger in order to fill the voids, store that energy and be able to provide constant power even when the sun is up. If we continue to analyze and compensate for deficiencies and reliability problems, it is very easy to show that a solar system capable of replacing a fossil fuel or nuclear power source has to be built 7 to 15 times larger than the required steady-state output. This includes an absolutely massive amount of batteries, of course. The only real solution I see is a large amount of new nuclear power generation and, yes, some solar and wind. I don't think there's another way to do it. Part of me think that manufacturing, transporting and installing that many panels and batteries is likely to create a far greater ecological disaster than most people imagine. Just a hunch, haven't done the numbers on that one.