Sunday, March 17, 2019

The Three Laws of Batteries (and a Bonus Zeroth Law)

The challenges posed by batteries aren't intractable but boy are they tough.
This fact is one of the reasons that, although there is some breakthrough or other announced just about every day of the year, be it a novel chemistry of a manufacturing technique or whatev, we don't post them.
Hard won experience says that as wonderful as things work in the lab, it just won't scale.
What follows is a great little overview of the parameters of the puzzle.

From GigaOm, March 2011:
Any field has to have laws that define it. Some of these will be real laws (think laws of thermodynamics or Newton’s laws) while others will be correlations that are not fundamentally true, but are true enough (think Tom Friedman’s First law of Petropolitics or Moore’s Law, or the ever popular Murphy’s law). Still others are laws that don’t (yet) have any practical use (like Issac Asimov’s Three laws of Robotics).

Suffice to say, you will need a few laws for batteries. Batteries are governed by the laws of thermodynamics and are made more complex by kinetics and transport. So any fundamental laws that define batteries are only derivatives of the laws in these other areas.

So instead of focusing on anything fundamental, I’ve decided to list my own laws of batteries that are observations on how batteries operate.

Here are my three laws for batteries. I will explain each as we go forward, and I have the bonus Zeroth law in the end, so stick around.

First law. In any battery, energy and power will play against each other; increasing one will lead to the loss of the other.

Second law. Any battery that is widely commercialized will operate at a voltage higher than its thermodynamic stability window.

Third law. Of the four metrics batteries are graded on for a given application (i.e., performance, cost, life, and safety), typically, only two can be simultaneously achieved. If the battery is designed to also perform satisfactorily on a third metric, it will fail spectacularly on the fourth.
Before I explain these laws, I should point out that some of the concepts in this blog post are based on previous posts have I made in my blog, This Week in Batteries. Click on the links to read the background.

The First Law
Let’s start with the first law, which states: In any battery, energy and power will play against each other; increasing one will lead to the loss of the other.

When a battery veteran gives an overview talk, there’s a customary slide that has to be shown; this plots specific energy on the x-axis and specific power on the y-axis. (Some flip this, but it is probably better to use the independent variable in the x-axis.) This is called a Ragone plot.
The picture below is an example of a Ragone plot.
Before we get to the law, it’s probably best that we understand the difference between energy and power. I find people use the two interchangeably. For example, they’ll say “my mobile phone lasts only 1 hour. I need a more powerful battery”.  What they really mean is they need a battery with more energy.
Power, on the other hand, is how quickly you use the energy.

Here’s one way to remember the difference: If you own an electric car (you probably don’t, but use your imagination), then having more energy means you can drive more miles before you have to recharge. Having more power means you can accelerate faster from, say, 0 to 60 mph.
So a Ragone plot captures how much energy the battery can give you at the power at which we use the energy.

Just so you know, the ratio of energy to power is the time of discharge of the battery. These are the diagonal lines you see in the figure.

What the first law states is that if you try to get the energy out quickly (at high power), then the energy will be lower than if you ask for the energy to come out slowly (at low power).
The reason for this is rooted in the losses inherent in a battery. When the power increases, the losses increase, and this in turn decreases the “effective” voltage of the battery.  The lower the voltage is, the lower the energy.

Hence the law that states that energy and power will play against each other.

But why is this the first law?

It’s because any battery design starts with understanding what the time of discharge requirements are. If you have a mobile phone, then you may say it’s three-hour continuous operation. If you need to use it in your Prius, you may come up with 10 seconds.

Once this is defined, a battery engineer can design the system around this requirement. In a mobile phone, the power requirement is minimal, so you find a way to get as much energy as you can in a small package.  In a Prius, your need a lot of power to get the car moving, so you’ll need to maximize the power.

Battery design is so rooted in this concept that the energy-power interplay is, in my mind, the first law of batteries.

The Second Law
On to the second law, which states: Any battery that is widely commercialized will operate at a voltage higher than its thermodynamic stability window.

Anyone who has worked on batteries will have, at some point in their career, experienced what alcoholics refer to as a moment of clarity (to quote Samuel L. Jackson in Pulp Fiction). The epiphany is that every battery we know of exists because of a freak of nature.  For me, the realization came when I was thinking about the Ni-MH battery, but a more glaring example is the lead-acid battery....MUCH MORE