210 and 220 may include a hydrogen nozzle pressure sensor 210 and a hydrogen low-pressure sensor 220. The controller 600 determines a hydrogen supply amount based on a pressure measured through the hydrogen nozzle pressure sensor 210 and the hydrogen low-pressure sensor 220. The controller 600 may be provided with a flow rate conversion map using, as an input thereof, a pressure measured through the hydrogen nozzle pressure sensor 210 and the hydrogen low-pressure sensor 220, and as an output thereof, a hydrogen supply amount corresponding to the measured pressure. Using the flow rate conversion map, the controller 600 may determine a hydrogen supply amount. Furthermore, the controller 600 may determine the hydrogen supply amount by substituting the pressure measured through the hydrogen nozzle pressure sensor 210 and the hydrogen low-pressure sensor 220 into a flow rate conversion formula.

Meanwhile, the controller 600 may estimate a gas discharge amount in a state of reflecting not only the hydrogen supply amount, but also a hydrogen consumption amount and a residual gas amount. The gas discharge amount may be estimated as a value obtained by deducting the hydrogen consumption amount and the residual gas amount from the hydrogen supply amount. In an exemplary embodiment of the present disclosure, the hydrogen concentration estimation system for the fuel cell 100 may further include a current sensor 400 and a cooling water temperature sensor 500. The controller 600 may measure electricity generation current of the fuel cell 100 through the current sensor 400, and may determine a hydrogen consumption amount based on the measured electricity generation current. Referring to the related art, an amount of hydrogen consumed per minute in the fuel cell 100 may be determined through the following Expression 1:

Hydrogen Consumption Amount per Minute=(Stack Current*Number of Stack Cells*R*T_s*60)/(2*F) [Expression 1]

In Expression 1, “R” represents an ideal gas constant, “T_s” represents an absolute temperature corresponding to 0° C., and “F” represents a Faraday constant. The stack current represents electricity generation current of the fuel cell 100 measured by the current sensor 400, and the number of stack cells represents the number of cells forming the fuel cell 100. The controller 600 may determine the hydrogen consumption amount consumed in the fuel cell 100, through Expression 1 as described above.

Furthermore, the controller 600 may measure a cooling water temperature at an outlet side of the fuel cell 100 through the cooling water temperature sensor 500, and may determine a residual gas amount based on the measured outlet-side cooling water temperature and a pressure variation amount of the fuel cell 100 measured by the hydrogen low-pressure sensor 220. Referring to the related art, the residual gas amount remaining in the fuel cell 100 may be determined through the following Expression 2:

Residual Gas Amount=(Hydrogen Electrode Pressure Variation Amount*Hydrogen Electrode Volume*T_s)/(Stack Temperature*P_s) [Expression 2]

In Expression 2, “T_s” represents an absolute temperature corresponding to 0° C., and “P_s” represents 100 kPa. The fuel cell hydrogen electrode pressure variation amount represents a pressure variation amount of the fuel cell 100 measured by the hydrogen low-pressure sensor 220, and the stack temperature represents a temperature of the fuel cell 100 measured through the cooling water temperature sensor 500. The controller 600 may determine the residual gas amount remaining in the fuel cell 100 through Expression 2 as described above. Accordingly, the controller 600 may estimate a gas discharge amount based on the hydrogen supply amount, the consumed hydrogen amount and the residual gas amount.

Thereafter, the controller 600 determines a reduction amount reduced from the estimated gas discharge amount for a reference time after cut-off of the discharge valve 310, and then determines whether or not degradation of the fuel cell 100 has occurred, based on the determined reduction amount. The controller 600 cuts off the discharge valve 310 after completion of estimation of the gas discharge amount. When the controller 600 cuts off the discharge valve 310, the fuel cell hydrogen electrode of the fuel cell 100 does not communicate with the exterior of the fuel cell 100, and the discharge amount of gas discharged through the discharge line 300 should be maintained to be an amount estimated before cut-off of the discharge valve 310. However, a crossover phenomenon may occur between the fuel cell hydrogen electrode and the air electrode in the fuel cell 100 after cut-off of the discharge valve 310.

When hydrogen present at the fuel cell hydrogen electrode of the fuel cell 100 crosses over to the air electrode after cut-off of the discharge valve 310, the estimated gas discharge amount may be reduced due to a reduction in hydrogen concentration of the fuel cell hydrogen electrode. Furthermore, when degradation of the fuel cell 100 has occurred, the amount of hydrogen crossing over from the fuel cell hydrogen electrode to the air electrode in the fuel cell 100 is increased, as compared to a normal state, and, accordingly, the estimated gas discharge amount is further reduced. For the present reason, it is necessary to set a reference time and to determine a reduction amount reduced from the estimated gas discharge amount for the reference time after cut-off of the discharge valve 310. Furthermore, the controller 600 checks whether or not degradation of the fuel cell 100 has occurred, using the reduction amount of the gas discharge amount.

The controller 600 determines a difference between the reduction amount of the gas discharge amount and a reference reduction amount of the gas discharge amount as a reduction variation amount, and then determines that degradation has occurred in the fuel cell 100, when the determined reduction variation amount is greater than a reference reduction variation amount. The controller 600 determines a difference between the determined reduction amount of the gas discharge amount and the refence reduction amount of the gas discharge amount as a reduction variation amount. The reference reduction amount of the gas discharge amount represents a reduction amount of the gas discharge amount for the reference time in an initial state in which the fuel cell 100 is not aged. In an exemplary embodiment of the present disclosure, the initial state in which the fuel cell 100 is not aged may be a state in which the number of electricity generation times of the fuel cell 100 does not exceed a minimum number of times after the fuel cell 100 is first mounted in a fuel cell system. Furthermore, in an exemplary embodiment of the present disclosure, the minimum number of electricity generation times of the fuel cell 100 may be set to 5 times, and the controller 600 may determine a reference reduction amount of the gas discharge amount in a state in which the number of electricity generation times of the fuel cell 100 does not exceed the minimum number of times. Furthermore, the controller 600 may store the determined reference reduction amount in a separate non-volatile memory to use the stored reference reduction amount upon determining a reduction variation amount.

Furthermore, the reference reduction variation amount represents a minimum value of a reduction variation amount of the gas discharge amount when degradation occurs in the fuel cell 100. When degradation of the fuel cell 100 occurs, a reduction amount of a gas discharge amount may be varied due to an increase in a crossover amount in the interior of the fuel cell 100. To the present end, it is necessary for the controller 600 to set a minimum value of the reduction variation amount of the gas discharge amount as a reference reduction variation amount, and to determine that degradation has occurred in the fuel cell 100, when the determined reduction variation amount of the gas discharge amount is greater than the reference reduction variation amount.

Thereafter, the controller 600 derives a degradation rate of the fuel cell 100 based on the reduction variation amount determined when degradation has occurred in the fuel cell 100, checking a degradation level of the fuel cell 100. The controller 600 is required to reflect occurrence of degradation in the fuel cell 100, upon estimating a hydrogen concentration in the interior of the fuel cell 100. When degradation occurs in the fuel cell 100, crossover may be generated in the interior of the fuel cell 100, and the hydrogen concentration in the interior of the fuel cell 100 may be increased or decreased due to the crossover. Therefore, the controller 600 is required to check a degradation level according to occurrence of degradation in the fuel cell 100, to enhance accuracy of hydrogen concentration estimation in a state in which degradation of the fuel cell 100 has occurred. To the present end, the controller 600 checks a degradation level of the fuel cell 100 based on a previously-determined reduction variation amount of a gas discharge amount.

To derive a degradation rate of the fuel cell 100 based on a reduction variation amount of a gas discharge amount, the controller 600 is provided with a data map using, as an input thereof, a reduction variation amount of a gas discharge amount, and as an output thereof, a degradation rate of the fuel cell 100 according to the reduction variation amount of the gas discharge amount. The data map includes data obtained through experiments. A situation in which degradation has occurred in the fuel cell 100 is established, and a reduction variation amount of a gas discharge amount in the fuel cell 100 according to a degradation rate of the fuel cell 100 is then measured after cut-off of the discharge valve 310. Thereafter, the measured degradation rate of the fuel cell 100 according to the reduction variation amount of the gas discharge amount is previously stored in the controller 600 in a form of a data map. Thus, the controller 600 may derive a degradation rate of the fuel cell 100 according to a reduction variation amount of a gas discharge amount, through the data map.

Furthermore, the controller 600 checks a degradation level of the fuel cell 100 based on the derived degradation rate of the fuel cell 100. FIG. 2 shows a degradation rate variation graph of the fuel cell 100 according to a reduction variation amount of a gas discharge amount in the hydrogen concentration estimation system for the fuel cell 100 according to the exemplary embodiment of the present disclosure. In FIG. 2, “V” represents a reduction variation amount of a gas discharge amount, and “R” represents a degradation rate of the fuel cell 100. “V_Min” represents a reference reduction variation amount of a gas discharge amount when degradation of the fuel cell 100 occurs, and “V_Max” represents a maximum reduction variation amount of a gas discharge amount when the fuel cell 100 has been degraded to R_Max. Referring to FIG. 2, it may be seen that, as the reduction variation amount of the gas discharge amount increases, the degradation rate of the fuel cell 100 is also increased. An increase in degradation rate of the fuel cell 100 means an increase in degradation level of the fuel cell 100. Furthermore, in accordance in accordance with an increase in degradation rate of the fuel cell 100, the amount of gas crossing over in the interior of the fuel cell 100 is increased, and accordingly, a reduction variation amount of a gas discharge amount is also increased.

Thereafter, the controller 600 corrects a crossover coefficient value of the fuel cell 100 based on the derived degradation rate of the fuel cell 100, and then estimates a hydrogen concentration of the fuel cell hydrogen electrode in the interior of the fuel cell 100 based on the corrected crossover coefficient value. The controller 600 corrects the crossover coefficient value of the fuel cell 100 based on the degradation rate of the fuel cell 100 derived using the following Expression 3:

$\begin{matrix} K^{'} = k (1 + R) & [Expression 3] \end{matrix}$

In Expression 3, “k” represents an existing crossover coefficient value of the fuel cell 100, and “R” represents a degradation rate of the fuel cell 100. Furthermore, “K” represents a corrected crossover coefficient value of the fuel cell 100. The controller 600 corrects the crossover coefficient value of the fuel cell 100 through Expression 3, and estimates the hydrogen concentration of the fuel cell hydrogen electrode in the interior of the fuel cell 100 based on the corrected crossover coefficient value.

Hereinafter, estimation of a hydrogen concentration of the fuel cell hydrogen electrode in the interior of the fuel cell 100 will be briefly mentioned with reference to the related art. Generally, a diffusion coefficient according to crossover generated in the fuel cell 100 is determined upon estimation of a hydrogen concentration of the fuel cell hydrogen electrode in the interior of the fuel cell 100. Thereafter, the number of moles of a gas crossing over in the fuel cell 100 is determined using the determined diffusion coefficient, and the number of moles of hydrogen at the fuel cell hydrogen electrode is then determined based on the determined number of moles of the gas, estimating a hydrogen concentration. In in accordance with the exemplary embodiment of the present disclosure, however, a degradation level of the fuel cell 100 is reflected in a hydrogen concentration estimation procedure for the fuel cell hydrogen electrode in the interior of the fuel cell 100 in the related art, and accordingly, variation is applied to determination of a diffusion coefficient according to crossover generated in the fuel cell 100.

Referring to the related art, diffusion coefficients according to crossover of hydrogen and nitrogen produced in the interior of the fuel cell 100 may be determined through the following Expression 4:

$\begin{matrix} \begin{matrix} D_{H_{2}} = K_{H_{2}} e \frac{E_{H_{2}}}{R} (\frac{1}{333.15} - \frac{1}{T}) \\ D_{H_{2}} = K_{N_{2}} e \frac{E_{N_{2}}}{R} (\frac{1}{333.15} - \frac{1}{T}) \end{matrix} & [Expression 4] \end{matrix}$

In Expression 4, “D_H2” and “D_N2” represent diffusion coefficients of hydrogen and nitrogen according to crossover, respectively, “E_H2” represents activation energy of hydrogen, and “E_N2” represents activation energy of nitrogen. Furthermore, “K_H2” and “K_N2” represent crossover coefficient values of hydrogen and nitrogen in the fuel cell 100, which are coefficient values corrected in accordance with a degradation level of the fuel cell 100, respectively. It may be possible to enhance accuracy in determination of a diffusion coefficient according to crossover generated in the fuel cell 100 by use of a crossover coefficient value corrected in accordance with a degradation level of the fuel cell 100 when degradation has occurred in the fuel cell 100.

After completion of determination of the diffusion coefficient according to the crossover, the controller 600 determines numbers of moles of nitrogen and vapor crossing over per hour in the fuel cell 100, through the following Expression 5:

$\begin{matrix} \begin{matrix} {\dot{n}}_{N_{2_} X O} = \frac{D_{N_{2}}}{R T} \frac{P_{Ca, N_{2}} - P_{An, N_{2}}}{δ} A \\ {\dot{n}}_{V_X O} = \frac{D_{V}}{R T} \frac{P_{Ca, V} - P_{An, V}}{δ} A \end{matrix} & [Expression 5] \end{matrix}$

In Expression 5, the subscript “V” represents vapor, and the subscript “XO” represents crossover. “A” represents a specific catalyst area of an electrolyte membrane in the interior of the fuel cell 100, and “δ” represents a diffusion distance of each gas. After determination of the numbers of moles of nitrogen and vapor crossing over per hour in the fuel cell 100, the controller 600 determines the number of moles of the entire gas purged due to a pressure difference between the pressure of the fuel cell hydrogen electrode of the fuel cell 100 and the pressure at an outlet side of the air electrode of the fuel cell 100. Thereafter, the controller 600 determines numbers of nitrogen and vapor discharged due to the purge, through the following Expression 6:

$\begin{matrix} \begin{matrix} {\dot{n}}_{purge} = C (P_{An} - P_{stk_out}) \\ {\dot{n}}_{N_{2_} purge} = y_{N_{2}} {\dot{n}}_{purge}, y_{N_{2}} = \frac{n_{N_{2}}}{n_{An}} \\ {\dot{n}}_{V_purge} = y_{V} {\dot{n}}_{purge}, y_{V} = \frac{n_{V}}{n_{An}} \\ n_{An} = \frac{P_{An} V_{An}}{R T} \end{matrix} & [Expression 6] \end{matrix}$

In Expression 6, “C” represents a purge constant. After determination of the numbers of moles of nitrogen and vapor purged at the fuel cell hydrogen electrode of the fuel cell 100 through Expression 6 as described above, the controller 600 determines numbers of moles of nitrogen and vapor remaining at the fuel cell hydrogen electrode. The controller 600 may determine the numbers of moles of nitrogen and vapor remaining at the fuel cell hydrogen electrode of the fuel cell 100 by adding the number of moles according to the crossover to the number of moles, which was present at the fuel cell hydrogen electrode in an initial stage, and then deducting the number of purged moles from the resultant value, through Expression 7:

n

N
2

=

n

N

2
⁢
_

⁢
init

+

∫

(

n
.

N

2
⁢
_

⁢
X
⁢
O

-

n
.

N

2
⁢
_

⁢
purge

)

⁢
dt

n
V

=

n

V
⁢
_
⁢
init

+

∫

(

n
.

V
⁢
_
⁢
X

⁢

O