Cassandra has moved. Ugo Bardi publishes now on a new site called "The Seneca Effect."

Monday, May 28, 2012

Leverage points in energy storage.

This is a written version of a lecture that I gave to my students of the class of "Advanced Materials Technology." In this case, the subject of the lecture, energy storage, led me to develop some considerations that had to do with politics and with the typical human way of taking so often the wrong decision. I am not sure that there is a thermodynamic reason at the basis of this tendency, but this post gives some hint that it may be the case. The image of the waterfall above is used to indicate the flow resulting from an energy potential.

Hello, everyone, and welcome. Today, I would start by telling you of something that happened to me yesterday. I was giving a presentation on energy at a public meeting and several of the people attending were politically minded. During the debate, someone said something like, "You see, professor, I think if you were to be a candidate for the next elections, you would get exactly zero votes".

Let me say that it wasn't intended as an offense. No; it was a statement of fact and it  was correct. So, what did I say that made me so completely unelectable? Well, I had said that natural resources are limited, so that we should strive to consume less resources, not more. But, of course, you just can't run for a public office on a platform like that! There is something, I think, that makes impossible to connect physical reality with politics and that's why sometimes I have the impression that politics is the art of always taking the wrong decision.

Of course, politics is not the subject of our class, but I thought to mention to you the debate of yesterday because it think it is important to frame problems in a broad way; otherwise we might find ourselves in a situation where we spend a lot of effort and money to develop sophisticated technologies to solve the wrong problem. I think that is a very common situation, much more common than I would like it to be. And it may also be the case of energy storage. A lot of money and effort is spent in order to find technological solutions for storing the energy produced by renewables, but very little to understand what the real problem is. How much energy storage do we really need? And is it true that if we don't have 100% energy storage then renewables are useless, as some people say?

On this subject, I would like to start by mentioning something that was said some decades ago by Jay Forrester, the developer of system dynamics. He said that all complex systems have something that he called "leverage points;" that is, points on which you can act to control the system while expending very little effort. He added another concept: that people normally understand very clearly where the "levers" of the system are, but they often tend to pull the levers in the wrong direction; worsening the problem rather than solving it. Forrester's idea has been popularized by a rather famous paper by Donella Meadows titled "Leverage Points." It is a very interesting paper, highly suggested for you to read. But, today, we'll focus our discussion on energy storage. 

You surely remember from our previous lessons that system dynamics a curious way of drawing rectangles and little arrows. So, when we draw a rectangle we intend it as a "stock", an amount of something. Then, let me draw one on the white board.
This box represents a stock of resources and I marked it with the letter "R". Now, with "resources" we can mean anything, from money in your pocket to grain in a barn. The interesting thing, however, is when we intend these resources as energy.  So, we can call this box as stored energy.

You can think of this stored energy as, for example, a tank of gasoline. As long as this energy stays locked inside the tank, it doesn't do anything for us. In order for energy to be useful for something, we must use it and in order to use it we must have this energy flowing; to run an engine we must burn gasoline. That's very general and it is here that the laws of thermodynamics come into play. We know that energy must be conserved and also that it must be degraded. So, let me modify the diagram to make it show that energy flows. I'll do that by drawing some arrows and little clouds.

Let me explain. You see that there is a double edged arrow that goes from the "resources" box to a little cloud, at the bottom. We assume that the box has a higher thermodynamic potential than the cloud (which is another stock, just we don't bother to measure its size). So, energy flows from the box to the cloud and is degraded in the process. It could be gasoline being burned, water flowing downhill from a reservoir, and similar things. 

The downhill flow of energy is regulated by a valve represented by the butterfly-like thing in the drawing.  You can open and close the valve and this is represented in the model by changing the values of the constant "K1". That will regulate the flow, but that's not the only factor. Also the size of the reservoir will have an effect on the potential and hence on the flow. If you are drawing water from the bottom of a container, the speed of the flow will depend on how much water there is in the container. As you draw water out, the flow will gradually diminish. This is a common effect also for other types of systems, although not always. If we were thinking, instead, of a tank of gasoline then, obviously, the engine wouldn't slow down as there is less gas left!

I have also added another feature to the model: a way to fill the reservoir. Here we have another flow rate regulated by a valve. The energy flows into the reservoir from another stock, at a higher potential. Also this stock is represented as a little cloud - meaning that we don't care about its size. Here, I assume that there is no effect of the size of the stock on the rate of flow (think of rain filling a water reservoir) which is regulated simply by a constant called K0. So, we built a very schematic model of what we mean as energy storage.

Of course, when we go into the details, we see that the actual physical characteristics of the storage and of the valve will vary depending on the kind of system we have. Imagine you have a charge stored inside a capacitor (or maybe a battery). Then, you can you can regulate the flow of current by means of a variable resistor. If the resistor obeys Ohm's law, then the flow (the current) is directly proportional to the potential (the voltage). In the case of automotive batteries, a lot of effort is made to make sure that the potential remains constant as the battery discharges. This makes the system behave very differently than a dam, but it makes sure that your electric car keeps going with the same power available all the time. Otherwise, it would be like a big clockwork toy car, slowing down as it moves.

Whatever the details of the system could be, the point is that the energy cost related to controlling the valve is often very small in comparison to the amount of energy that can be stored in the system. So, you have this power of controlling the system potentials. Of course, you need to have the right technology, the equipment, the engineering and more. But once you have this capability - and often it is not that difficult - then controlling the flow becomes a decision that can be taken independently of thermodynamics. I think that now we can understand what Forrester had in mind with his "leverage points". The thermodynamic parameters of the system cannot be easily changed but large stocks of energy can be controlled by a relatively minuscule valve, such as the duct of a dam or the control rods in a nuclear reactor. It is a lot of power that you can have on these systems.

But, then, what does it mean what Forrester said, "pulling the levers in the wrong direction?" Well, this is the interesting part. Let's go back to the simple stock and flow model that we made before. Let's think of stored energy, this time, in terms of crude oil stored underground - in its natural deposits. Now, you know what most politicians say in this respect. They say that we should invest into increasing the production of national oil resources. They say that in this way we'll create jobs, restart economic growth and all the rest. But, in terms of a stock and flow diagram, what does it mean exactly? Well, something like this:

"R" is now oil fields. Obviously, there is no "rate0," that is there is no oil coming into the stock, since oil was created millions of years ago and no political activity will affect events that took place during the Jurassic. So, what has been happening is that, as we have been extracting (or producing, if you like) oil, the amount of oil remaining underground is going down. That has changed the "potential" of the wells. The amount of energy that you can get from a barrel of oil has not changed, but the total energy that you can get from the system is smaller, since it takes now more energy to extract the same amount of oil. This change of the thermodynamic parameters of the system appears in the form of economic parameters. It takes more and more money to get oil out, and that tends to reduce the flow marked as "rate1". We are crossing here the concept of "peak oil" but let's not go into the details right now.

Back to Jay Forrester, most people are perfectly able to understand where the "levers" are and our politicians are no exception. They say that we should act on the valve in the diagram. We should increase the coefficient K1 in order to compensate for the tendency of the system or slowing down its production rate. That's surely possible by means of investments, technology, and other things. But you understand that it is a mistake, don't you? By increasing the production rate we are running out of oil faster! It is what I called the "Seneca Effect" in a post where I took inspiration from the ancient Roman philosopher, Seneca, when he says that ruin is much faster than fortune. By pushing for extracting more oil from the remaining reserves we could perhaps enjoy a brief glut of oil, but then we would see it run out much faster than the "natural" rate of the depletion of the reserves. Unfortunately, it seems that not many politicians read my posts, alas....

So, you may understand why yesterday at that meeting I was told that I would get zero votes as a candidate for the next elections. See? Proposing to produce less oil means to increase gas prices and that's never very popular in a political context. I think it wouldn't be so unpopular as, say, proposing to abolish soccer, here in Italy. But it would surely come close.

That illustrates the mistake which comes from opening the valve too much. Of course, people can do the opposite mistake, even though this case is a bit more subtle. Let's go back to the case of a dam. If you don't let water flow, that is, you keep the valve closed, then, eventually the dam will overflow. You can see this as the "valve" behaving in a non linear way - having a threshold. Even worse, if there is too much potential in the basin, the dam may give way and that's another kind of threshold for the valve; a very bad one, of course. There are other examples; for instance, at the time of steam engines, people tended to increase the pressure in the water boiler by acting on the regulating valves. That gave them more power, surely, but, sometimes, the whole thing blew up. Think of controlling a nuclear reactor and you have exactly the same problem. It is what happened with the Chernobyl disaster. People had the means of controlling the flow of energy created by the reactor but they let too much potential accumulate. When they rushed in to stop the reactor, it was too late. So, the point is that whenever you have an energy potential, if you let it accumulate, it will try to release, or "vent" this potential in ways that may have nothing to do with a lever (or a valve) that you can control. A lot of accidents occur because of this effect. bad.

A typical phenomenon, here, is that even though you may think that you are in control; that is your "lever" works well, you will not be able to manage the system the way you would like to. If there are time delays in the system, humans will have a hard time in understanding it and the result will be wide oscillations; extremely difficult to control and which can cause a lot of damage. This phenomenon has been studied by - guess by whom!  - Jay Forrester who dubbed it the "bullwhip effect." It is normally applied to business systems, but even business systems must obey the laws of thermodynamics. Systems can oscillate and collapse even without human intervention. This is the case of the so-called "self organized criticality". You may have heard of it in terms of the "sandpile model". It is a different kind of model, but the avalanches in the sandpile are, in the end, caused by the gravitational potential acting on the grains.

So, I think we got to the point I wanted to make with this presentation. Levers or valves are ways to create potentials and let them accumulate. It is good to have such valves, but we have to be very careful with what we do. Sometimes we squander the accumulated potential and sometime we may create high potentials which then we can't control so well. The results may be uncontrollable oscillations.

Now, let's go back to the problem we had started with: energy storage for renewables. What people often say in this case - especially politicians - is that we should build a big energy storage system that would allow us to have energy "on demand" whenever we want it. But, because it would be so expensive, the problem is often considered as the definitive reason why renewables will never be of any use.

But let's analyze the question more in depth. Energy "on demand" means that we want stable prices and full availability at any time. But storage, in itself, is not a guarantee of stability. Consider crude oil: there is no problem in storing it; surely we don't have the problem of having to use it before it disappears - as it is the case with wind or sunlight. But oil prices fluctuate a lot nevertheless; as we all know. We attribute what we call "price volatility" to market factors. But we can also see it as a manifestation of the "bullwhip effect" that Forrester described long ago. So, storage doesn't, in itself, guarantee price stability - on the contrary it may well increase the amplitude of fluctuations!

Let me explain. If there is little storage space available producers must reduce prices to sell the energy they produce before they have to throw it away. It is exactly the opposite when producers have lots of storage space. With oil safely stored inside wells, producers may be tempted to keep it there and wait for customers to become desperate and willing to pay any price for it. I am afraid that something like that may have been happening more than once in the world's oil market. That may become more and more frequent as producers understand that their resources are gradually running out.

So, Forrester's idea turns out to be correct once more. In calling for more and more storage for renewable energy, we are pulling the levers in the wrong direction. If we want to reduce price volatility we should do exactly the opposite; we should reduce storage instead of increasing it. Of course, don't make me say that we don't need storage at all. We do need energy on demand for many practical purposes and for essential services, say for hospitals and the like. We need to be able to turn lights on even in a windless night. What we don't really need is a system that aims to provide energy at any moment, at constant prices. It would be atrociously expensive and we would have big troubles in keeping it stable.

Instead, the best compromise in terms of cost would be a system with limited storage that uses prices as a way to manage demand. With such a system you can have as much energy as you want, at any moment, but you must be prepared to pay for it. That may be seen as a problem, but also as an opportunity. You may have to pay a lot for energy at some moments, but you may also have it very cheap in other periods  - that's an opportunity if you can be flexible. It is a little like with air travel. If you are flexible about your schedule, you can travel at low costs. Otherwise, you must be prepared to pay a lot of money for your ticket. By the way, these techniques of "demand management" used by the airline industry give the possibility of traveling even to people who, otherwise, couldn't even dream to afford a plane ticket. In a sense, in such a system the rich are subsidizing the ticket of the poor. Something similar could happen for energy in the future - limiting the amount of storage could make energy more affordable even for the poor.

So, you see that the lack of a complete storage system is not the death sentence for renewables. Instead, it is a feature that allows for a better distribution of low cost energy. Incidentally, it works the same also for nuclear energy. Nuclear plants are not storing energy; normally they are running at near full power all the time. That doesn't match the market demand as it is nowadays and that means there are moments - overnight for instance - when you can have lots of energy at low prices from nuclear plants. Unfortunately, nuclear plants have plenty of different problems, as we all know.

I wanted to conclude this talk with some even more general considerations about the whole economic system. We can see the economy as a machine that stores energy in the form of "capital" and gradually releases it in the form of waste (or "pollution" if you like). The interesting point is that here, too, Forrester's law applies; that is, we tend to pull the levers in the wrong direction. One of these wrong ways would be opening up too much the valve that connects the capital stock to the waste stock. It is what we call "consumerism." Of course, consuming something means to destroy it and I have this feeling that maybe we are doing that really too fast, don't you agree with me?  That's surely a problem. The other possible way to operate the valve in the wrong way is that sometimes we accumulate so much capital  - that is, so much potential - that we lose control of how it is dissipated. We may pass some threshold that makes dissipation very fast, actually disastrously fast. We call this kind of phenomenon "war," which is, by the way, another example of how politics normally manages so often to take the wrong decisions.

So, you see that there is something as too much storage and I think that you are gaining some idea of how system dynamics coupled with thermodynamics gives to you a wide ranging view of many kinds of phenomena; most of them very relevant for our life. Now, of course this class is not about economics and in the next lesson we'll go in more detail into the technology of energy storage; batteries, fuel cells and the like. But I thought that this introduction could be useful for you and I hope that it clarified, at least, that knowing about thermodynamics will not very helpful for your future political career, in case you were planning one!


  1. I'll dispute the claim that too much storage produces volatility.  Our current system has great "storage" but limited extraction rates; it's the limited rate which leads to price volatility as demand changes.

    1. But, the system limits (finite supply of the resource) mean that opening the tap all the way (i.e. unlimited extraction rates) would only defer price volatility - eventually the reservoir (stock) would deplete, leading to inequality between supply and demand and bringing in price bullwhipping.

      The only way to avoid price or demand volatility would be to have an infinite and unvarying supply of the resource - then you could have the tap on full, all the time. Unfortunately our world is small and finite.

      Perhaps a large enough reservoir could mimic infinite and unvarying supply, but that ignores the human factors that Prof Bardi worked in - it is humans who make the decisions about when, why and how to manipulate the taps (when there is enough in the reservoir for humans to be in control of the levers), and it is humans who will act selfishly to drive up prices or demand.

      I'm not sure that increasing extraction rates is wise or would lead to a decrease in price volatility, given that the things we are extracting are finite and the intergenerational need for them is just as great as our desire for them in the here and now.

    2. It is true, too. The fact that the rate of extraction is limited dampens oscillations. But oscillations can exist only because there is the possibility of storage, that is, it is possible to choose whether to extract and burn oil or keep it underground. Complex systems, as usually, behave as the result of the interplay of various factors

  2. Another problem is how does a society open the valve for capital that has accumulated in the hands of a few? The poor will not have the option of turning on lights and heat when it is needed the most under this type of renewable scheme. Who needs lights or as much heat when the sun is shining? And unfortunately the same people who can most pay also are closest to the valve of both energy and capital (not sure if that is the right word), so as to close the loop if energy becomes scarce. The beauty of fossil fuels is that the flow is currently too great for those near the valve to devour all the energy, which allows others to benefit from its flow. I think it was John Michael Greer who talked about the future being like the novel Dune, where there are a few with amazing technologies while the rest just scrape by.

  3. I read Donella Meadows paper and what struck me was that she says she goes into situations where people know exactly what the problem is but they are pulling the lever in the wrong direction. I was watching a PBS program in the US and it was praising how the most amazing country in the world (subtext) the US was born from property rights. They compared the US to South American countries and the difference or so they say is property rights. I talk to my right wing friends and my unbiased schooling and it is always property rights that directly leads to our amazing lives and it hit me why no one would vote for you (not even yourself apparently): While pricing schemes and taxation are a way to modify property rights, it is the property rights themselves that are at the heart of the destruction of our commons (atmosphere, species diversity, etc). People at the top do not want their property rights modified and people at the bottom have little property and are reliant on those who do have property. Pulling the lever the other way would suggest that to protect the commons it may be necessary to remove all property rights of individuals, corporations, and governments. Then again this is probably just as much a pipe dream as any.

    1. Brian, it is curious this American point of view about South America. I have been traveling a lot in South America, especially in Brazil, and I can tell you that there's hardly any other place in the world where property rights are so clearly, and sometimes violently, marked. Take any bus heading to the vast Brazilian countryside and look out of the window from time to time. But don't focus on the beatiful landscape. Just look at the road side: you will notice miles upon miles of uninterrupted barbed wire that delimts huge farming properties (the "fazendas"). There is hardly a single square inch of ground not privately owned and duly enclosed by barbed wire. A true nightmare for a European! So it's definitely not the property rights that make the difference.

  4. Ugo, thank you for the great article - you might smile - but I AM planning a political move, trying to bring systems-thinking and the "limits to growth" to the public in Germany.

    I have been talking with a lot of people lately and the latent feeling that something is not quite right can be found with a lot of people, regardless of their upbringing and intellectual background. I owe it to myself to try and see whether the "systematic aknowledging of limits" approach really fails at the political level. I have the feeling it might go both ways. If we look at the Occupy movement, they had it partially right. There was the emotional upsettlement, but they had no unified intellectual framework around which to state their woes and which would have helped formulate specific ideas for change.

    I believe that if scientists in in each country would found a political party, based on the current scientific findings in social science (for example humans have an innate sense of fairness, that is being trampled in the current system), climate science and biophysical economics / steady state economy, they might have a fighting chance. The very least this feat would accomplish, would be to bring the critical issues closer to public discourse.

    Current parties are mostly run by career politicians, many of them being lawyers, which has made historical sense - as when there is "enough" for everyone, the biggest problem is the distribution. Now that we enter a different age, based on limits - it´s the engeneers and scientists, that have to come to the front and lead based on their expertise of dealing with relationships of stocks and flows, the need to account for upkeep and structural integrity of systems etc.

    What do you think of this weird idea? :-)

    (I an a repentant economist, studying medicine at the Charité in Berlin)

    1. Well, Maxim, when you say "scientists would form a political party" you are surely ambitious! I tried politics a little, years ago, at the beginning it is lots of fun; then - if you really want to pursue a career in it - it becomes a job. I don't know, right now, as I said in my post, bringing to the debate subjects such as "the limits to growth" it is utterly impossible. But, in the future, who knows.....?

    2. Thank you for your reply Ugo, considering the odds I am probably not just ambitious, but weirdly and utterly insane ;-) Let´s see what the future brings.

  5. Uh, I think you're being over-enthusiast about "yield management" and its supposed social positive consequences.

    What I observe is that it brings a lot of complexity to the booking system, and that people who often take the plane (ie the rich) learn faster how to deal with this complexity and organize to get the cheap fares. While those who travel once every two or three years keep paying high fares...

    Plus, yield management was only a part of the move of air travel pricing to a totally liberal philosophy, which widened the gap between fares on competitive and uncompetitive routes (by competitive, I mean that you can choose between several airlines to fly it). London to NY, or NY to Miami fligths are probably among the cheapest in terms of price per unit distance ; and it's also on those routes that you find the people who could afford to pay more !!

    You can also add the frustration of ruminating on the idea that you could have bought your place cheaper. (people are what they are !)

    The same effects of yield management (advantage to the rich who use the service regularly ; cheaper fares on routes between major city, which happen to have the wealthier inhabitants ; frustration generated) are conspicuous if you take the train in France... (and probably in other places !)

    Last point, about flying : above a given threshold (more than 150 persons per day and per airline) on a route, there are almost no economies of scale for the airline, which means that on all important routes, the airline has no reason to sell a ticket for much less than the mean cost. More exactly, the only reason for this can be that the airline has "over-capacities" because of a push to growth and cannot afford the cost of reducing its size. This is the only reason why you can sometimes buy your ticket for less than its (monetary) cost, and this has almost nothing to do with the guy seated next to you who bought his ticket for twice the price...

    (By the way, I almost never take the plane !)

    And this was about a detail, thank you for your blog in general !

    1. Thanks for the info, MG. Indeed, I may have over-simplified a little (perhaps more than a little). I think, however, that the points you make don't change the main point I wanted to make, that is if you have an oversupply of something, then there is a chance even for the poor to get a little of it. Then, life is always more complicated than one would think!

  6. I definitely think that our BIGGEST problem is that we try to solve every problem!




Ugo Bardi is a member of the Club of Rome, faculty member of the University of Florence, and the author of "Extracted" (Chelsea Green 2014), "The Seneca Effect" (Springer 2017), and Before the Collapse (Springer 2019)