Fuel cell anode stoichiometry control
A system and method for controlling an anode exhaust gas bleed valve in a fuel cell system that includes estimating the gas composition in the anode exhaust gas, using an inverse valve model to calculate a desired valve flow coefficient, and bleeding the anode exhaust gas at a flow rate that results in the desired valve flow coefficient. The method includes determining the partial pressure of nitrogen in the anode exhaust gas, calculating the partial pressure of water vapor and hydrogen in the anode exhaust gas, and calculating the gas mole fraction of the nitrogen, water vapor and hydrogen in the anode exhaust gas. The method also includes using the gas mole fraction of nitrogen, water vapor and hydrogen to determine the desired valve flow coefficient, and using the desired valve flow coefficient to determine when to open and close the bleed valve.
1. A fuel cell system comprising:
a fuel cell stack including an anode input and an anode output;
a bleed valve for periodically bleeding anode exhaust gas from the anode output; and
a controller for controlling the bleed valve, said controller determining the partial pressure of nitrogen in the anode exhaust gas, calculating the partial pressure of water vapor and hydrogen in the anode exhaust gas, calculating the gas mole fraction of the nitrogen, the water vapor and the hydrogen in the anode exhaust gas using the partial pressure of the nitrogen, the water vapor and the hydrogen, determining a desired valve coefficient using the gas mole fraction of the nitrogen, the water vapor and the hydrogen in the anode exhaust gas, and determining when to open and close the bleed valve using the desired valve flow coefficient.
2. The system according to claim 1 wherein the controller determines the desired valve flow coefficient using the gas mole fractions and an inverse valve model.
3. The system according to claim 2 wherein the controller uses one inverse model for sub-critical flow and one inverse valve model for critical flow.
4. The system according to claim 3 wherein the equation:
Q
=
1360
C
v
P
1
Y
x
S
g
T
is used for the sub-critical flow, and the equation:
Q
=
1360
C
v
P
1
2
3
x
t
S
g
T
is used for the critical flow, where Q is flow and standard cubic feet per hour, C v is the valve flow coefficient, P l is an upstream pressure, Y is the expansion factor, x is the pressure drop ratio, x t is the terminal pressure drop ratio, S g is the specific gravity of the gas through the bleed valve and T is the temperature of a gas.
5. The system according to claim 1 wherein the controller further calculates a flow rate of nitrogen into the anode exhaust gas, and integrating the flow rate of the nitrogen to update the partial pressure of the nitrogen.
6. The system according to claim 5 wherein the controller determines the nitrogen flow rate in the anode exhaust gas using the equation:
V
N
2
=
P
N
2
A
Δ
p
N
2
t
where V N2 is the volume flow of nitrogen in the anode exhaust gas, P N2 is a permeation coefficient, A is the area of a membrane, Δp N2 is the partial pressure differential of nitrogen permeation across the membrane and t is the thickness of the membrane.
7. The system according to claim 1 wherein the controller assumes that the recirculation gas has a 100% relative humidity to determine the partial pressure of the water vapor, and determines the partial pressure of the hydrogen using the partial pressure of the nitrogen and the water vapor, wherein the combination of the partial pressure of the nitrogen, the water vapor and the hydrogen is the total static pressure in the anode exhaust gas.
8. The system according to claim 1 wherein the bleed valve is a pulse width modulated solenoid valve having a known full valve flow coefficient, and wherein the controller sets the duty cycle of the solenoid valve as the ratio of the desired valve flow coefficient to the full valve flow coefficient.
9. The system according to claim 1 wherein the fuel cell system is on a vehicle.