Wednesday, August 17, 2005


Evaluating the performance of fuel cells

Posted by ben @ 5:53 PM | Permanent Link

At first I was planing to make this post very long and technical, but then I thought: "neh...". I think it would be much more useful if I keep it simple, and to the point. Basically, when we want to compare the performace of a fuel cell, we want to know the voltage that the fuel cell generates at a given current load. The load by the way would be whatever the fuel cell is powering, something like a computer, or a house, or the grid. The reason we want to know the voltage and the current is so that we can calculate the power being generated by the fuel cell:

Power (W/cm2) = Voltage (V) x Current (A/cm2)
Note: The cm2 is the area of the fuel cell, if there's a larger area, then the fuel cell will generate more power.

The figure on the right is a cartoon of a typical fuel cell performance curve (sometimes called a polarization curve). The blue line is the maximum theoretical voltage that can ever be generated by the fuel cell. But because nothing is 100% efficient, the fuel cell can never actually reach that voltage. The red line is the voltage that the fuel cell generates, and it depends on how much current is required by the load (the load would be whatever your fuel cell is powering, like a computer, a house or the grid). The more current that the load requires, the higher are the voltage losses. The reasons why voltage decreases can get a little tricky, I'll explain it quickly.

There are 3 main causes:
  1. The electrochemical reactions are too slow (technical term: activation losses)
  2. The resistance of the fuel cell is too big (Ohmic losses)
  3. The gasses (oxygen and the fuel) can't get to the reaction site fast enough (technical term: mass transfer losses)

Causes 1 and 3 are sometimes bulked together and are called the "overpotential". In the first figure, you see the η+iR term. η is the overpotential, iR is the Ohmic loss. So, the operating voltage of a fuel cell can be expressed by the following equation:

V = E0 - ηcathodeanode-iR

The cathode and the anode have overpotential losses (the overpotential of the anode is different than the overpotential of the cathode) and the entire fuel cell has the iR loss. E0 is the maximum theoretical voltage, typically around 1.2V for fuel cells.

Looking at figure 2 with the red and green line now, the fuel cell that generates the green performance curve will have a higher power output than the fuel cell that generates the red line because for every current, the voltage is higher. Each of the 3 causes mentioned above contributes to the voltage loss for every current load, but they do not all have the same contribution to voltage loss at all current loads. So I'll explain based on this second polarization curve.

The electrochemical reactions are too slow (Region #1):
When current loads (same thing as current density by the way) are small, then the voltage losses are dominated by the slowness of the electrochemical reactions. Comparing the fuel cell that generates the red performance curve to the fuel cell that generates the green performance curve in region #1, the green curve has faster electrochemical reactions than the red curve, this could be caused for many reasons like: a) the green curve is operating at a hotter temperature, b) the green curve has a better catalyst to promote the electrochemcial reactions, c) the green curve is operating on a fuel that is "easy" to react.

The resistance of the fuel cell is too big (Region #2):
Region number 2 also has "activation losses" but it is dominated by the fact that the fuel cell has a high resistance. If a fuel cell has a high resistance, then electrons will travel more slowly through that fuel cell and more heat will be lost (heat generated = i2R). That's bad. This is called Ohmic loss because the loss can be described by Ohm's law (V=iR). The difference between the fuel cell with the green curve and the fuel cell with the red curve is that the green curve has a lower resistance. So, how can we minimize the resistance? Well we can: a) make the fuel cell thinner (the thicker the material, the more resistance it offers) or b) try and find another material that has a higher electronic conductivity

The gasses can't get to the reaction site fast enough (Region #3):
If we can't supply the gass molecules to the reaction site fast enough, then the rate of the electrochemical reactions is limited. Gasses have to diffuse through a porous network (that makes up the electrode) until they reach the reaction site. At very high current loads, then a lot of gas has to be supplied so that a lot of electrons can be generated, but sometimes the gas can't get to the reaction site fast enough, and so the performance of the fuel cell is reduced. There could be a couple of differences between the fuel cell that generates the green curve and the fuel cell that generates the red curve: a) the green curve has an electrode that is more porous than the red curve, and so the gasses can travel through the electrode more easily b) the green curve could be using 100% oxygen for example, instead of air which is composed of oxygen and nitrogen.

So then, ready to see what a "real" performance curve looks like?

This comes from a solid oxide fuel cell from the company previously known as Global Thermo Electric (they were bought out by Fuel Cell Energy). The red curve is the best performance, the blue curve is the worst performance. On this graph you also see the power density as well, that's just the voltage * current density.

And that's it! Take home message: You want the highest voltage possible for any given current density.

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