Flow estimation based on anode pressure response in fuel cell system

1. A method for determining a flow of anode gas out of an anode sub-system of a fuel cell system, said method comprising:

defining a time period for determining the flow where the time period is between injection events when hydrogen gas is injected into an anode side of the fuel cell stack;

providing a measurement of the pressure in the anode sub-system at a plurality of predetermined time intervals during the time period;

calculating a slope of a pressure line representing changes in the pressure in the anode sub-system during the time period using the pressure measurements; and

determining the flow of anode gas out of the anode sub-system using the slope of the pressure line, wherein determining the flow of anode gas out of the anode sub-system also includes using a volume of the anode sub-system and a temperature of the anode sub-system.

2. The method according to claim 1 wherein determining the flow of anode gas out of the anode sub-system includes determining flow through a bleed valve that bleeds anode exhaust gas from the anode sub-system.

3. The method according to claim 1 wherein determining the flow of anode gas out of the anode sub-system includes determining a flow through a drain valve that drains water out of the anode sub-system.

4. The method according to claim 1 wherein determining the flow of anode gas out of the anode sub-system includes determining if there is a leak in the anode sub-system.

5. The method according to claim 1 wherein providing a measurement of the pressure at predetermined time intervals includes measuring the pressure at about every three milli-seconds during the time period.

6. The method according to claim 1 wherein the anode sub-system includes a recirculation line that directs an anode exhaust gas from an output of a fuel cell stack to an anode input of the fuel cell stack.

7. The method according to claim 1 wherein the fuel cell system includes a fuel cell stack, and wherein determining the flow out of the anode sub-system also includes using an ideal gas constant, fuel cell stack current, and the number of fuel cells in the stack.

8. The method according to claim 7 wherein determining the flow includes using the equation:

n

.

=

P

.

·

V

R

·

T

-

I

·

N

cell

2

·

F

where {dot over (n)} is the flow (moles/sec), {dot over (P)} is the slope of the pressure line, V is the anode sub-system volume in liters, R is the ideal gas constant (8.315 kPa-L/mol-K), T is the anode sub-system temperature (K), I is the stack current, N cell is the number of cells in the stack and F is Faraday's Constant (96485 A-s/mole).

9. The method according to claim 1 wherein calculating the slope of a pressure line includes using the equation:

P

.

=

∑

i

=

1

n

⁢

(

t

i

-

t

_

)

⁢

(

P

i

-

P

_

)

∑

i

=

1

n

⁢

(

t

i

-

t

_

)

2

where t i is the time that a pressure measurement is taken, £ is an average of the sample times, P i is a pressure measurement at a particular sample time and is the average of all of the measured pressures during the sample period.

10. The method according to claim 1 wherein determining the flow of anode gas out of the anode sub-system using the pressure line slope includes determining if the pressure line fits to a straight line within a predetermined threshold.

11. The method according to claim 10 wherein determining if the pressure line fits to a straight line includes using the equation:

r

2

=

(

∑

i

=

1

n

⁢

(

t

i

-

t

_

)

⁢

(

P

i

-

P

_

)

∑

i

=

1

n

⁢

(

t

i

-

t

_

)

2

⁢

∑

i

=

1

n

⁢

(

P

i

-

P

_

)

2

)

2

where t i is the time that a pressure measurement is taken, £ is an average of the sample times, P i is a pressure measurement at a particular sample time and P is the average of all of the measured pressures during the sample period.

12. The method according to claim 1 wherein defining a time period for determining the flow includes defining the time period between injection events when hydrogen gas is injected into an anode side of a fuel cell stack.

13. A method for determining a flow of anode gas out of an anode sub-system of a fuel cell system, said fuel cell system including a fuel cell stack, said method comprising:

defining a time period for determining the flow where the time period is between injection events when hydrogen gas is injected into an anode side of the fuel cell stack;

providing a measurement of the pressure in the anode sub-system at a plurality of predetermined time intervals during the time period;

calculating a slope of a pressure line representing changes in the pressure in the anode sub-system during the time period using the pressure measurements;

determining if the pressure line fits to a straight line within a predetermined threshold; and

determining the flow of anode gas out of the anode sub-system using the slope of the pressure line, a volume of the anode sub-system and a temperature of the anode sub-system.

14. The method according to claim 13 wherein determining the flow of anode gas out of the anode sub-system includes determining flow through a bleed valve that bleeds anode exhaust gas from the anode sub-system or a drain valve that drains water out of the anode sub-system.

15. The method according to claim 13 wherein determining the flow of anode gas out of the anode sub-system includes determining if there is a leak in the anode sub-system.

16. The method according to claim 13 wherein calculating the slope of a pressure line includes using the equation:

P

.

=

∑

i

=

1

n

⁢

(

t

i

-

t

_

)

⁢

(

P

i

-

P

_

)

∑

i

=

1

n

⁢

(

t

i

-

t

_

)

2

where t i is the time that a pressure measurement is taken, £ is an average of the sample times, P i is a pressure measurement at a particular sample time and P is the average of all of the measured pressures during the sample period.

17. The method according to claim 13 wherein determining the flow includes using the equation:

n

.

=

P

.

·

V

R

·

T

-

I

·

N

cell

2

·

F

where {dot over (n)} is the flow (moles/sec), {dot over (P)} is the slope of the pressure line, V is the anode sub-system volume in liters, R is the ideal gas constant (8.315 kPa-L/mol-K), T is the anode sub-system temperature (K), I is the stack current, N cell is the number of cells in the stack and F is Faraday's Constant (96485 A-s/mole).

18. The method according to claim 13 wherein determining if the pressure line fits to a straight line includes using the equation:

r

2

=

(

∑

i

=

1

n

⁢

(

t

i

-

t

_

)

⁢

(

P

i

-

P

_

)

∑

i

=

1

n

⁢

(

t

i

-

t

_

)

2

⁢

∑

i

=

1

n

⁢

(

P

i

-

P

_

)

2

)

2

where t i is the time that a pressure measurement is taken, £ is an average of the sample times, P i is a pressure measurement at a particular sample time and P is the average of all of the measured pressures during the sample period.

19. A method for determining a flow of gas out of a closed system, said method comprising:

defining a time period for determining the flow where the time period is between injection events when hydrogen gas is injected into an anode side of the fuel cell stack;

providing a measurement of the pressure in the closed system at a plurality of predetermined time intervals during the time period;

calculating a slope of a pressure line representing changes in the pressure in the closed system during the time period using the pressure measurements; and

determining the flow of the gas out of the closed system using the slope of the pressure line, wherein determining the flow of anode gas out of the anode sub-system also includes using a volume of the anode sub-system and a temperature of the anode sub-system.