WO2007110970A1

WO2007110970A1 - Method for calculating interface resistance

Info

Publication number: WO2007110970A1
Application number: PCT/JP2006/307161
Authority: WO
Inventors: Hideo Michibata
Original assignee: The Tokyo Electric Power Company, Incorporated
Priority date: 2006-03-29
Filing date: 2006-03-29
Publication date: 2007-10-04
Also published as: JP5007963B2; JPWO2007110970A1

Abstract

A method for calculating interface resistance in which the complex impedance of a cell for a calculation object fuel cell is measured under measurement conditions where only the gas composition of fuel pole side gas is different and measurement conditions where only the gas composition of air pole side gas is different to obtain a graph of real part resistance difference, a decision is then made from which of the fuel pole side interface and the air pole side interface an arc in the call call plot of the cell for calculation object fuel cell is derived under work condition, fuel pole side interface resistance Ria and air pole side interface resistance Ric are determined from the call call plot or determined by performing fitting on the call call plot and an equivalent circuit. The interface resistance can be calculated even if the thickness of electrolyte in the cell for fuel cell is small or the area or profile at the joint is not identical on the fuel pole side and the air pole side.

Description

Specification

Interfacial resistance calculation method

'' The present invention is a method for measuring the interface resistance at the time of operation of a fuel cell, specifically, calculating the interface resistance at the interface between the fuel electrode and the electrolyte and the interface resistance at the interface between the air electrode and the electrolyte. Regarding the method. Background art

The fuel cell has a fuel cell unit configured such that an electrolyte is sandwiched between a fuel electrode and an air electrode. The fuel cell will be described with reference to FIG. Fig. 1'4 is a schematic diagram showing a fuel cell. In FIG. 14, the fuel cell 4 4 is formed so that the electrolyte 4 1 is sandwiched between the fuel electrode 4 2 and the air electrode 4 3.

Since the resistance value of the fuel cell 4 4 during operation is one of the important factors related to the performance of the fuel cell 4, the resistance value during operation of the fuel cell 4 4 is grasped. That is important. The resistance at the time of operation of the fuel cell 44 is mainly the ohmic resistance of the electrolyte 41 itself, the ohmic resistance of the fuel electrode 42 itself, the ohmic resistance of the air electrode 43 itself, The sum of the interface resistance at the interface between the fuel electrode 4 2 and the electrolyte 4 1 at the time and the interface resistance at the interface between the air electrode 4 3 and the electrolyte 4 1 during operation. Hereinafter, the total of the ohmic resistance of the electrolyte 41 itself, the ohmic resistance of the fuel electrode 42 itself, and the ohmic resistance of the air electrode 43 itself is also referred to as the ohmic resistance Rb of the cell. The interface resistance at the electrode-electrolyte interface is also described as the fuel electrode-side interface resistance Ria, and the interface resistance at the air electrode-electrolyte interface is also described as the air electrode-side interface resistance Ric. Of the above resistances, the ohmic resistance of the fuel electrode 42 itself is applied to the electrolyte 41. It is obtained by measuring the resistance of the fuel electrode 42 before being bonded, or by preparing the fuel electrode 42 not bonded to the electrolyte 41 and measuring its resistance. . The same applies to the ohmic resistance of the electrolyte 41 itself and the ohmic resistance of the air electrode 43 itself.

On the other hand, the fuel electrode side interface resistance R ia and the air electrode side interface resistance R ic are resistances at the interface between the fuel electrode 42 or the air electrode 43 and the electrolyte 41, so The resistance cannot be measured unless the electrode 4 2 or the air electrode 4 3 is joined to the electrolyte 4 1.

Therefore, a conventional method for measuring interface resistance will be described with reference to FIG. FIG. 15 is a schematic diagram showing a conventional method for measuring interface resistance, and is a schematic diagram of a cross section of a cell for a fuel cell at the time of measuring interface resistance. First, the respective ohmic resistances before joining the fuel electrode 4 1a and the air electrode 4 3a to the electrolyte 4 1a, that is, the ohmic resistance of the electrolyte 4 1a, the resistance of the fuel electrode 4 2a, Measure the ohmic resistance and the ohmic resistance of the air electrode 4 3 a. Next, as shown in FIG. 15, the fuel cell 4 4 a is formed by sandwiching the electrolyte 4 1 a between the fuel electrode 4 2 a and the air electrode 4 3 a, and The reference electrode 5 1 is provided at the intermediate potential point 5 5 a. Usually, the position where the reference electrode 51 is installed is the side surface of the electrolyte 41a, and the middle point in the thickness direction of the electrolyte 41a. Next, the resistance between the fuel electrode terminal 53 and the reference electrode 51 and the resistance between the reference electrode 51 and the air electrode terminal 54 under the same operating conditions as the fuel cell 44a. Measure the resistance of each. And the following formula (5): the fuel electrode side interface resistance R ia = resistance _{5 3} — _{5 1} — (R ba + O. 5 R bs) (5)

(Wherein, resistance _{5 3} _ _{5 1} represents the resistance between the fuel electrode terminal 5 3 and the reference electrode 51, R ba represents the ohmic resistance of the fuel electrode 4 2 a, and R bs Represents the ohmic resistance of the electrolyte 41a.) From the fuel electrode side interface resistance R ia, the following equation (6):

Air electrode side interface resistance R ic = Resistance ₅ i— _{5 4} — (R bc + 0.5 R bs) (6)

(Wherein, resistance _{5 1} — _{5 4} represents the resistance between the reference electrode 5 1 and the negative electrode terminal 5 4, and R bc represents the ohmic resistance of the air electrode 4 3 a, R bs represents the ohmic resistance of the electrolyte 4 1 a.)

Thus, the air electrode side interface resistance R ic is calculated. The intermediate potential point 55a refers to a point that bisects the ohmic resistance of the electrolyte 41a.

In the conventional method for calculating the interfacial resistance as described above, the reference electrode can be installed without any problem as long as the thickness of the electrolyte is sufficient. However, since the thickness of the electrolyte of the fuel cell currently in practical use is extremely thin, about 5 to 100 μm, the reference electrode is used as the electrolyte of the fuel cell currently in practical use. It was difficult to install. In other words, there is a problem that the interface resistance cannot be calculated in the case of fuel cell cells that are currently in practical use.

Further, in the case of the fuel cell 4 4 a shown in FIG. 15, the area and shape of the junction between the electrolyte 4 1 a and the fuel electrode 4 2 a are the same as those of the electrolyte 4 1 a and the air electrode. Since the area and shape of the junction with 4 3 a are the same, the potential change in the electrolyte 4 1 a is subject to up and down. That is, when the equipotential line 5 2 a in the electrolyte 4 1 a is shown, in the case of the fuel cell 4 4 a, the equipotential line 5 2 a is connected to the fuel electrode 4 2 a and the air electrode 4. 3 From a, spread in the shape of the top and bottom objects. Therefore, in the fuel cell 4 4 a, the intermediate potential point 55 a appears on the side surface of the electrolyte 41 a and is the intermediate point in the thickness direction of the electrolyte 41 a.

Fig. 16 shows a fuel cell in which the area or shape of the junction between the electrolyte and the fuel electrode is not the same as the area or shape of the junction between the electrolyte and the air electrode It is typical sectional drawing. In FIG. 16, in the fuel cell 4 4 b, the area and shape of the junction between the electrolyte 4 1 b and the fuel electrode 4 2 b are the same as the junction between the electrolyte 4 1 b and the air electrode 4 3 b. It is not the same as the area and shape of the part. In this case, the equipotential line 5 2 b extends from the fuel electrode 4 2 b and the air electrode 4 3 b in a shape that is not vertically aligned. Therefore, in the fuel cell 44b, the intermediate potential point 55b does not appear on the side surface of the electrolyte 41b, but appears on the surface 56 where the fuel electrode 42b is joined, and The position where the intermediate potential point 5 5 b appears varies depending on the area or shape of the junction. Therefore, in the case of the fuel cell 4 4 b, the reference electrode cannot be installed at an accurate position. There was a problem that accurate interface resistance could not be measured.

Therefore, the problem of the present invention is that even if the thickness of the electrolyte of the fuel cell cell is small, or the area or shape of the junction between the electrolyte and the fuel electrode is the same as the area or shape of the junction between the electrolyte and the air electrode. An object of the present invention is to provide an interface resistance calculation method that can calculate the interface resistance even if they are not the same. Disclosure of the invention

The present invention (1) is an interface resistance calculation method for calculating a fuel electrode side interface resistance R ia and an air electrode side interface resistance R ic during operation of a calculation target fuel cell.

A first step of obtaining a Cole-Cole plot of the calculation target fuel cell by performing a complex impedance measurement of the calculation target fuel cell under an operating condition for calculating the interface resistance;

The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real number when the frequency in the first measurement condition is n Difference between the resistance value R 1 rn and the real resistance value R 2 rn when the frequency in the second measurement condition is n (1-2) rn in the following formula (1):

Δ R (1-2) rn = R lr nR 2 rn (1) to calculate (1— 2) rn for each frequency, then the horizontal axis is frequency and the vertical axis is AR (1— 2) rn Plot AR (1−2) rn for each frequency to obtain the first real part resistance value difference graph, and then from the peak top frequency in the first real part resistance value difference graph, the first step A second step of certifying an arc derived from the fuel electrode side interface among the arcs in the call-call-plot of the fuel cell to be calculated obtained in

The complex impedance measurement of the calculation target fuel cell is performed under the third measurement condition and the fourth measurement condition, which differ only in the gas composition of the air electrode side gas, and then the frequency in the third measurement condition is n The difference between the real part resistance value R 3 rn and the real part resistance value R 4 rn when the frequency in the fourth measurement condition is n 厶 R (3 -4) rn is expressed by the following equation (2):

Δ R (3 -4) rn = R 3 r n-R4 rn (2) to calculate AR (3 — 4) rn for each frequency, then frequency on the horizontal axis and AR (3- 4) Plot rn to obtain a real part resistance difference second graph, and then calculate the target fuel cell obtained in the first step from the peak top frequency in the real part resistance difference second graph. Cell call and call for the cell The third step of certifying the arc originating from the air electrode side interface among the arcs in the plot,

The maximum of the resistance value of the real part of the arc that is recognized as the arc derived from the fuel electrode side interface in the second step in the call / call / plot of the fuel cell to be calculated obtained in the first step The difference between the value R ra (max) and the minimum value R ra (min) of the real part resistance is expressed by the following equation (3):

R i a = R r a (max) -R r a (m i n) (3)

To calculate the fuel electrode side interface resistance R ia, and then the first step During the call 'call' plot of the fuel cell to be calculated obtained in step 3, the maximum resistance R rc (ma of the real part of the arc that was identified as the arc derived from the air electrode side interface in the third step x) and the difference between the real part resistance value R rc (min) and the following equation (4):

R i c = R r c (ma x) — R r c (m i n) (4)

And an interface resistance calculation step for obtaining an air electrode side interface resistance R ic, and a method for calculating the interface resistance, comprising: Further, the present invention (2) is a method for calculating the interface resistance for calculating the fuel electrode side interface resistance R ia and the air electrode side interface resistance R ic during operation of the calculation target fuel cell.

A first step of performing a complex impedance measurement of the calculation target fuel cell under an operating condition for calculating an interface resistance and obtaining a Cole-Cole plot of the calculation target fuel cell;

The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real number when the frequency in the first measurement condition is n The difference between the part resistance value R 1 rn and the real part resistance value R 2 rn when the frequency in the second measurement condition is n is R (1− 2) rn as the following formula (1):

厶 R (l— 2) r n = R l r n-R 2 r n (1)

Calculate AR (1-2) rn for each frequency, then plot the AR (1 — 2) rn for each frequency, with the horizontal axis representing frequency and the vertical axis representing (1-2) rn. The resistance value difference first graph is obtained, and then, from the peak top frequency in the real part resistance value difference first graph, the cell of the calculation target fuel cell obtained in the first step is called Of the arcs in the plot, the second step of certifying arcs originating from the fuel electrode side interface,

Third measurement condition and fourth measurement condition differing only in gas composition of the air electrode side gas Then, the complex impedance measurement of the calculation target fuel cell is performed, and then the real part resistance value R 3 rn when the frequency under the third measurement condition is n and the frequency under the fourth measurement condition is n Difference between real part resistance R 4 rn and R (3 -4) rn in the following formula (2):

Δ R (3-4) rn = R 3 r n-R4 rn (2) Calculate (3 -4) rn for each frequency, then frequency on the horizontal axis and (3 -4) on the vertical axis rn is plotted to obtain a second graph of the real part resistance difference, and then the calculation target fuel cell obtained in the first step is obtained from the peak top frequency in the real part resistance difference No. 7 The third step to certify the arc originating from the air electrode side interface among the arcs in the cell call, call, plot,

An equivalent circuit having (i) a first resistor connected in series; (ii) a second resistor and a first capacitor connected in parallel; and (iii) a third resistor and a second capacitor connected in parallel. The fitting step of fitting the fuel cell for the calculation target cell obtained in the first step with the Cole-Cole 'plot to obtain the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric When,

It is intended to provide a method for calculating an interface resistance characterized by comprising: According to the present invention, even if the thickness of the electrolyte of the fuel cell is small, or the area or shape of the junction between the electrolyte and the fuel electrode is the same as the area or shape of the junction between the electrolyte and the air electrode. Even if they are not the same, it is possible to provide a method for calculating the interface resistance that can calculate the interface resistance. Brief Description of Drawings

Fig. 1 is a schematic diagram of the call-call plot of the fuel cell for calculation consisting of two arcs. Fig. 2 shows the calculation consisting of three arcs. It is a schematic diagram of the Cole-Cole-plot of the target fuel cell.

Fig. 3 is a schematic diagram of the call-call plot of the fuel cell for calculation when complex impedance is measured under the first measurement condition and the second measurement condition, and Fig. 4 is a real number. Part resistance difference first graph 14 and real part resistance difference second graph 1 4 1 is a schematic diagram, FIG. 5 is a complex impedance measurement under the third measurement condition and the fourth measurement condition FIG. 6 is a diagram showing an equivalent circuit 21 and FIG. 7 is a diagram showing an equivalent circuit 30. FIG. Fig. 8 shows the call 1 plot for measurement 1, Fig. 9 shows the call call for measurement 2. Fig. 10 shows the plot for call 2. Fig. 10 shows the call for measurement 3. Figure 1 shows the Cole 'plot, Figure 1 shows the Cole Cole plot for measurement 4. A drawing, Fuitsutin _{first 2} figure is a graph showing a first Darafu and real part resistance difference second graph real resistance value difference, the first 3 figures obtained in Fuitsutingu step in Example 1 Fig. 14 is a schematic diagram showing a fuel cell, and Fig. 15 is a schematic diagram showing a conventional interface resistance measurement method. Yes, Fig. 16 is a schematic diagram showing a fuel cell, where the area or shape of the junction between the electrolyte and the fuel electrode is not the same as the area or shape of the junction between the electrolyte and the air electrode. FIG. BEST MODE FOR CARRYING OUT THE INVENTION

The method for measuring the interface resistance according to the first aspect of the present invention is a method for calculating the interface resistance by calculating the fuel electrode side interface resistance R ia and the air electrode side interface resistance R ic when the fuel cell for calculation is operated. Because

Under the operating conditions for calculating the interface resistance, the complex impedance measurement of the calculation target fuel cell is performed, and the call of the calculation target fuel cell is called 'call. A first step of obtaining a plot;

The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real part when the frequency in the first measurement condition is n The difference between the resistance value R 1 rn and the real part resistance value R 2 rn when the frequency in the second measurement condition is n (R (1−2) rn is expressed by the following equation (1):

△ R (l− 2) rn = R lr nR 2 rn Calculate (1-2) rn for each frequency, then set the horizontal axis to frequency and the vertical axis to (1-2) rn Plot AR (1−2) rn for each frequency to obtain a real part resistance difference first graph, and then from the peak top frequency in the real part resistance difference first graph, The obtained call of the fuel cell to be calculated is derived from the fuel electrode side interface among the arcs in the call plot, and the second step of certifying the arc,

The complex impedance measurement of the calculation target fuel cell is performed under the third measurement condition and the fourth measurement condition that are different only in the gas composition of the air electrode side gas, and then the frequency in the third measurement condition is n. The difference between the real part resistance R 3 rn at the time and the real part resistance R 4 rn when the frequency in the fourth measurement condition is n 厶 R (3-4) rn is expressed by the following equation (2):

厶 R (3 -4) rn = R 3 r n-R4 rn Calculate (3 -4) rn for each frequency, then frequency on the horizontal axis and (3 -4) on the vertical axis rn is plotted to obtain a second real part resistance value difference graph, and then from the peak top frequency in the second real part resistance value difference graph, the fuel cell for calculation cell obtained in the first step A third process for certifying arcs originating from the air electrode side interface among the arcs in the call, call, and plot

The call of the cell for the fuel cell to be calculated obtained in the first step In the lot, the maximum value R ra (max) of the real part resistance value of the arc and the minimum value R ra (min) of the real part resistance value of the arc that was recognized as the arc derived from the fuel electrode side interface in the second process The difference between the following formula (3):

R ia = R ra max) — R ra (min) (3) is calculated to obtain the fuel electrode side interface resistance R ia, and then the calculation target fuel cell cell obtained in the first step is calculated. During the Cole Cole plot, the maximum value R rc (max) of the real part resistance value and the minimum value R rc of the real part resistance value of the arc identified as the arc originating from the air electrode side interface in the third step The difference from (min) is the following formula (4):

R i c = R r c (max) −R r c (m i n) (4) to obtain the air electrode side interface resistance R i c, and a method for calculating the interface resistance.

The calculation target fuel cell for the interface resistance calculation method according to the first aspect of the present invention is a fuel cell for which the interface resistance is calculated. In the first step, first, the complex impedance of the calculated fuel cell is measured under the operating condition for calculating the interface resistance.

The operating condition for calculating the interface resistance is a specific operating condition for which the interface resistance is desired to be calculated. That is, in the first step, first, the complex impedance measurement of the calculation target fuel cell is performed under a specific operating condition for which calculation of the interface resistance is desired.

The operating conditions for calculating the interface resistance are the fuel concentration of the fuel electrode side gas, the oxygen concentration of the air electrode side gas, the operating temperature of the cell, the water vapor concentration of the fuel electrode side gas, the water vapor concentration of the air electrode side gas, etc. Consists of various elements. The operating conditions for calculating the interface resistance always include three elements: the gas composition of the fuel electrode side gas, the gas composition of the air electrode side gas, and the operating temperature of the cell.

The calculation target fuel cell includes an electrolyte sandwiched between a fuel electrode and an air electrode. For example, a solid oxide fuel cell, a phosphoric acid fuel cell, a molten carbonate fuel cell, solid A polymer fuel cell is exemplified.

The complex impedance measurement means that when a voltage is applied by applying a slight voltage AC component of 100 mV or less between the fuel electrode and the air electrode of the calculation target fuel cell, the AC component It is to measure the current and its phase difference when the frequency is changed from about 100 kHz to about 1 MHz. The method for performing the complex impedance measurement is not particularly limited as long as it is a complex impedance measurement method that is usually used for grasping the characteristics of the fuel cell. The complex impedance measurement is also called AC impedance measurement. Further, the complex impedance measurement according to the second step and the complex impedance measurement according to the third step described later are the same as the complex impedance measurement according to the first step.

Then, based on the current obtained by performing the complex impedance measurement and its phase difference, the real part resistance value Ζ ′ (Ω) and the imaginary part resistance value Z ″ (Ω) for each frequency when the frequency is changed, The horizontal axis is plotted with the real part resistance value Z ′, and the vertical axis is plotted with the imaginary part resistance value Z ″ to obtain a call call plot of the calculation target fuel cell. The method of obtaining the call call plot of the calculation target fuel cell is also called the complex plane display method. The call-call plot of the calculation target fuel cell obtained in the first step will be described with reference to FIG. 1 and FIG. Fig. 1 is a schematic diagram of the call cell plot of the calculation target fuel cell consisting of two arcs. Fig. 2 is a call of the cell for calculation target fuel cell consisting of three arcs. · Schematic diagram of call 'plot. The call cell plot for the calculation target fuel cell obtained in the first step is the simplest of the two plots, as shown in Fig. 1. Cole · call 'plot 1 a consisting of 2 a and second arc 3 a. In addition, as a call call plot of the calculation target fuel cell obtained in the first step, there are three arcs, that is, the first arc 2 as shown in FIG. b, a call consisting of the second arc 3 b and the third arc 4. Coll. Plot lb or more than four arcs, ie, other than the first and second arcs and the first and second arcs Call consisting of two or more arcs. Cole plot. Many of the Cole-Cole-Plots of the calculation target fuel cell obtained in the first step are composed of two or three arcs.

In the present invention, the first arc is counted from the side where the real part resistance value is small in the arc of the Cole-Cole 'plot of the calculation target fuel cell obtained in the first step, This refers to the first arc, and the second arc is counted from the side with the smaller real part resistance value in the arc of the Cole Cole plot of the fuel cell to be calculated obtained in the first step. , Refers to the second arc. One of the first arc and the second arc is an arc derived from the fuel electrode side interface, and the other is an arc derived from the air electrode side interface.

Note that the Cole-Cole-Plot curve of the calculation target fuel cell obtained by actually performing the complex impedance measurement rarely has the same shape as a perfect circular arc. However, in the present invention, the wording of arc is used.

In Fig. 1, in the call 'call' plot 1a, the smaller the real part resistance value, the higher the frequency, that is, the higher the frequency in the direction of arrow 5, while the real part resistance. The higher the value, the lower the frequency, that is, the lower the frequency in the direction of arrow 6. In the case of the call / call 'plot of the target fuel cell consisting of three or more arcs Similarly, the lower the real part resistance, the higher the frequency, while the higher the real part resistance, the lower the frequency.

In the second step, first, the complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas.

The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas. It means that the complex impedance measurement of the cell for the fuel cell to be calculated is performed under two measurement conditions in which only the gas composition of the fuel electrode side gas is fixed and only the gas composition of the fuel electrode side gas is changed. Specifically, for example, the hydrogen concentration of the fuel electrode side gas in the first measurement condition is set to 100 volume%, and the hydrogen concentration of the fuel electrode side gas in the second measurement condition is set to 10 volumes. / _0, and for the elements constituting the other measurement conditions, none of the first measurement condition and said second measurement conditions were the same, the complex Inpi of the calculated output target fuel cell - performing dance measurement. The measurement conditions related to the first measurement condition and the second measurement condition are as follows: fuel concentration in the fuel electrode side gas, oxygen concentration in the air electrode side gas, cell operating temperature, water vapor concentration in the fuel electrode side gas, air electrode It consists of various factors such as the water vapor concentration of the side gas. The measurement conditions always include three elements: the gas composition of the fuel electrode side gas, the gas composition of the air electrode side gas, and the operating temperature of the cell.

FIG. 3 shows a schematic diagram of a call / call plot of the cell for the calculation target fuel cell under the first measurement condition or the second measurement condition. FIG. 3 shows the calculation target fuel cell in which the number of arcs of the call / call plot of the calculation target fuel cell obtained by performing the first step is two. In the second measurement condition, when the complex impedance is measured, the cell of the cell to be calculated is called a Cole plot, and the first measurement condition The call / call 'plot 1 1 of the calculation target fuel cell at 1 consists of a first arc 2c and a second arc 3c, and the calculation target fuel cell for the second measurement condition Cole · Cole 'Plot 1 2 consists of a first arc 2d and a second arc 3d.

Next, a difference AR (1 − between the real part resistance value R 1 rn when the frequency under the first measurement condition is n and the real part resistance value R 2 rn when the frequency under the second measurement condition is n 2) rn with the following formula (1):

Δ R (1-2) r n = R l r n-R 2 r n (1)

Calculate AR (1-2) rn for each frequency.

Specifically, for example, a point where the frequency in the Cole Cole 'plot 1 1 is 1 000 Hz is pointed E 1 and a point where the frequency in the Cole Cole' plot 1 2 is 100 OH z Assuming E 2, the Cole-Cole 'plot 1 1 force and the real part resistance value R 1 r of the point E 1. . . From the Cole-Cole plot 1 2, the real part resistance R 2 r _{10 of the} point E 2. . Ask for. Next, the real part resistance R 1 r of the point E 1. . . And the real part resistance R 2 _{Γ ι of} the point E 2. . . The difference (R l .. 1 1 ^ 21 ^ ..) is calculated and Δ R (1 -2) r when the frequency is 1 00 0 H z. . . Ask for. The calculation of Δ R (1 — 2) rn is performed over the entire area of the Cole-Cole 'plot 1 1 and the Cole-Cole' plot 1 2, and Δ R (1-2 for each frequency is calculated. ) Find rn. The calculation of (1−2) rn is based on the change in Δ R (1-2) rn with respect to the change in frequency. It is sufficient that the frequency interval is such that it can be observed over a range of frequencies, and AR (1 1 2) rn corresponding to each frequency at a constant interval may be obtained, or the frequency interval may not be constant. .

Then, the horizontal axis is frequency and the vertical axis is (1-2) rn. Plot AR (1-2) rn and obtain the first real resistance difference graph. FIG. 4 shows a schematic diagram of the first real part resistance difference graph. In FIG. 4, the graph indicated by the symbol 14 is the real part resistance difference first graph 14, and the real part resistance difference first graph 14 is always compared to the other frequency ranges. (1− .2) · There is a frequency range where the amount of change of rn increases. That is, the real part resistance difference first graph 14 always has a peak 15. Then, the frequency of the peak top 16 of the peak 15 is read from the real part resistance difference first draft 14, and the frequency obtained in the first step is obtained from the frequency value of the peak top 16. Call the cell for the fuel cell to be calculated 'Cole. Of the plot, certify the arc originating from the fuel electrode side interface. For example, if the peak top frequency in the first real part resistance difference graph is X, the frequency of the call / call 'plot of the calculation target fuel cell obtained in the first step is The arc including the point X is identified as the arc originating from the fuel electrode side interface.

In the second step, only the gas composition of the fuel electrode side gas is changed. Therefore, in the first graph of the real part resistance difference, the fact that the peak top exists at the frequency X means that the influence of the change on the fuel electrode side has an effect. Is the portion corresponding to the frequency region in the vicinity of frequency X in the Cole-Cole-Plot of the calculation target fuel cell, so that the calculation target fuel obtained in the first step is Call of battery cell. In the call plot, an arc including a point with a frequency X can be recognized as an arc originating from the fuel electrode side interface. The fuel contained in the fuel electrode side gas is not particularly limited, and examples thereof include hydrogen and methane.

In the third step, first, the complex impedance measurement of the calculation target fuel cell is performed under the third measurement condition and the fourth measurement condition that differ only in the gas composition of the air electrode side gas. The complex impedance measurement of the calculation target fuel cell is performed under the third measurement condition and the fourth measurement condition, which are different only in the gas composition of the air electrode side gas, among the elements constituting the measurement condition, It means that the complex impedance measurement of the calculation target fuel cell is performed under two measurement conditions in which only the gas composition of the air electrode side gas is fixed and only the gas composition of the air electrode side gas is changed. Specifically, for example, the oxygen concentration of the air electrode side gas under the third measurement condition is 100% by volume, the oxygen concentration of the air electrode side gas under the fourth measurement condition is 10% by volume, etc. With respect to the elements constituting the measurement condition, the complex impedance measurement of the calculation target fuel cell is performed with the third measurement condition and the fourth measurement condition being the same. The measurement conditions related to the third measurement condition and the fourth measurement condition are as follows: fuel concentration in the fuel electrode side gas, oxygen concentration in the air electrode side gas, cell operating temperature, water vapor concentration in the fuel electrode side gas, air electrode side It consists of various elements such as the water vapor concentration of the gas. The measurement conditions always include three elements: the gas composition of the fuel electrode side gas, the gas composition of the air electrode side gas, and the operating temperature of the cell.

FIG. 5 shows a schematic diagram of the call-call-plot of the cell for calculation target fuel cell under the third measurement condition or the fourth measurement condition. FIG. 5 shows the calculation target fuel cell in which the number of arcs of the call / call plot of the calculation target fuel cell obtained by performing the first step is 2 and the third measurement condition and This is a call / call 'plot of the fuel cell to be calculated when complex impedance is measured under the fourth measurement condition, and a call / call of the cell for the fuel cell to be calculated under the third measurement condition. Plot 17 consists of a first arc 2 e and a second arc 3 e, and the call cell call of the calculation target fuel cell under the fourth measurement condition 'plot 1 8 shows the first arc 2 f and second arc 3 f.

Next, the real part resistance value R when the frequency in the third measurement condition is n The difference AR (3-4) rn between 3 rn and the real part resistance R4 rn when the frequency in the fourth measurement condition is n is expressed by the following equation (2):

Δ R (3 -4) r n = R 3 r n-R4 r n (2)

Calculate AR (3-4) rn for each frequency.

Specifically, for example, the point where the frequency in the Cole Cole 'plot 1 7 is 1 000 Hz is pointed G 1, and the point in the Cole Cole' plot 1 8 is the point where the frequency is 1000 Hz. Assuming G 2, the real part resistance value R 3 r of the point G 1 from the Cole-Cole plot 17. . . From the Cole-Cole plot 18, the real part resistance value R 4 r ₁₀₀₀ of the point G 2 is obtained. Next, the real part resistance value R 3 r of the point G 1. . . And the real part resistance R 4 _{ri of the} point G 2. . . The difference (R 3 _ri .. One R4 r _100. ) Is calculated and Δ R (3-4) r ₁ when the frequency is 1 00 0 Hz. . . Ask for. This calculation of Δ R (3 — 4) rn is performed over the entire area of the Cole-Cole plot 17 and the Cole-Cole plot 1 8 to obtain (3 -4) rn for each frequency. Ask for. The calculation of AR (3-4) rn is based on the change in AR (3-4) rn with respect to the frequency change, and the entire area of Cole Cole Plot 1 7 and Cole Cole Cole 'Plot 1 8 It is sufficient that the frequency interval is such that it can be observed over a range of intervals, and Δ R (3 −4) rn corresponding to each frequency at a constant interval may be obtained, or the frequency interval may not be constant. Good.

Next, plot the 厶 R (3_4) rn for each frequency, with the horizontal axis representing frequency and the vertical axis representing AR (3-4) rn, to obtain the second real part resistance difference graph. FIG. 4 shows a schematic diagram of the second resistance difference second graph. In FIG. 4, the graph denoted by reference numeral 141 is the real part resistance difference second graph 141, and the real part resistance difference second graph 141 is always compared to other frequency ranges.

(3-4) There is a frequency range where the amount of change in rn increases. That is, The real part resistance difference second graph 1 4 1 always has a peak 1 5 1. Then, the frequency of the peak top 16 1 of the peak 1 51 is read from the second resistance difference second graph 141, and the frequency value of the peak top 1 61 1 is obtained in the first step. In addition, the arc derived from the air electrode side interface is identified in the call / call plot of the fuel cell to be calculated. For example, if the frequency of the peak top of the second resistance difference second graph is y, the frequency of the Cole-Cole 'plot of the calculation target fuel cell obtained in the first step is: An arc including a point where y is y is recognized as an arc derived from the air electrode side interface.

In the third step, only the gas composition of the air electrode side gas is changed. Therefore, in the real part resistance difference second graph, the fact that the frequency top has the peak top means that the air electrode side changes. Is the portion corresponding to the frequency region in the vicinity of the frequency y in the Cole-Cole-Plot of the calculation target fuel cell, so that the calculation target fuel obtained in the first step is In the Cole-Cole 'plot of the battery cell, the arc including the point where the frequency is y can be recognized as the arc originating from the air electrode side interface. In the interfacial resistance calculation step, the arc determined as the arc originating in the fuel electrode side interface in the second step in the Cole-Cole plot of the calculation target fuel cell obtained in the first step The difference between the maximum real part resistance value R ra (max) and the minimum real part resistance value R ra (min) is given by the following equation (3): R ia = R ra (max) — R ra (min) (3)

To calculate the fuel electrode side interface resistance R ia, and the arc derived from the air electrode side interface in the third step during the Cole-Cole plot of the calculation target fuel cell obtained in the first step The difference between the maximum real part resistance value R rc (ma) and the minimum real part resistance value R rc (min) of the arc certified as R ic = R rc (max) — R rc (min) (4)

To calculate the air electrode side interface resistance R ic.

The interface resistance calculation step will be described with reference to FIG. As a result of performing the second step and the third step, the first arc 2a of the Cole Cole plot 1a is an arc originating from the fuel electrode side interface, It is assumed that the circular arc 3a is recognized as an arc originating from the air electrode side interface. In the Cole Cole 'plot 1a, the intersection of the first arc 2a and the horizontal axis, that is, the point where the resistance value of the imaginary part of the first arc 2a is "0" is point A 1 The intersection of the first arc 2a and the second arc 3a is the point B1, the intersection of the second arc 3a and the horizontal axis, that is, the imaginary part resistance of the second arc 3a. Assuming that the point where the value is “0” is the point C 1, in this case, the R ra (min) is the real part resistance value of the point A 1, and the R ra (max) is the point B 1 R c (min) is the real part resistance value of the point B 1, and R rc (max) is the real part resistance value of the point C 1. Then, the fuel electrode side interface resistance R i a is obtained from the above equation (3), and the air electrode side interface resistance R i c is obtained from the above equation (4).

The case where the call / call plot of the calculation target fuel cell obtained by performing the first step is composed of three arcs will be described with reference to FIG. As a result of performing the second step and the third step, the first arc 2b of the Cole-Cole 'plot 1b is an arc originating from the fuel electrode side interface, and the second arc 3 It is assumed that b is an arc derived from the air electrode side interface. In the Cole-Cole plot lb, the intersection of the first arc 2b and the horizontal axis, that is, the point where the imaginary part resistance value of the first arc 2b is “0” is the point A2, the second If the intersection of one arc 2b and the second arc 3b is point B2, and the intersection of the second arc 3b and the third arc 4 is point C2, then in this case R ra (min ) Is the real part resistance at point A 2. R ra (max) is the real part resistance value of the point B 2, the R c (min) is the real part resistance value of the point B 2, and the R rc (max) is This is the real part resistance at point C2. Then, the fuel electrode side interface resistance R ia is obtained from the above equation (3), and the air electrode side interface resistance R ic is obtained from the above equation (4).

In addition, when the call call plot of the calculation target fuel cell obtained by performing the first step is composed of four arcs, the arc is on the side where the real part resistance value is larger than the third arc. Since the relationship between the first arc, the second arc, and the third arc does not change only by increasing, the call plot of the calculation target fuel cell obtained by performing the first step is The same as the case of three circles.

The method for measuring the interface resistance according to the second aspect of the present invention is to calculate the interface resistance by calculating the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric when the fuel cell for calculation is operated. A method,

Under the first measurement condition and the second measurement condition where only the gas composition of the fuel electrode side gas is different, the complex impedance measurement of the cell for the fuel cell to be calculated is performed, and then when the frequency in the first measurement condition is n The difference AR (1-2) rn between the real part resistance value R 1 rn and the real part resistance value R 2 rn when the frequency in the second measurement condition is n is expressed by the following equation (1):

厶 R (l— 2) r n = R l r n-R 2 r n (1)

Calculate AR (1-2) rn for each frequency, then plot AR (1-2) rn for each frequency, with the horizontal axis representing frequency and the vertical axis representing AR (1-2) rn. Real part resistance value difference first graph is obtained, then the real part Difference in resistance value From the peak top frequency in the first graph, among the arcs in the Cole-Cole 'plot of the calculation target fuel cell obtained in the first step, the arc derived from the fuel electrode side interface A second process to certify,

The complex impedance measurement of the calculation target fuel cell is performed under the third measurement condition and the fourth measurement condition that are different only in the gas composition of the air electrode side gas, and then the frequency in the third measurement condition is n. The difference Δ R (3-4) rn between the real part resistance value R 3 rn and the real part resistance value R 4 rn when the frequency in the fourth measurement condition is n is expressed by the following equation (2):

厶 R (3— 4) r n = R 3 r n-R 4 r n (2)

'' To find AR (3 -4) rn for each frequency, then plot the frequency on the horizontal axis and AR (3 -4) r η on the vertical axis to obtain the second real part resistance difference graph Then, from the frequency of the peak top in the second resistance value difference second graph, the call of the calculation target fuel cell obtained in the first step. Of the arcs in the call plot, the air electrode A third step to certify the arc originating from the side interface;

An equivalent circuit having (i) a first resistor connected in series; (ii) a second resistor and a first capacitor connected in parallel; and (iii) a third resistor and a second capacitor connected in parallel. A fitting step of fitting the cell for the calculation target fuel cell obtained in the first step with the Cole-Cole 'plot to obtain the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric; ,

It is the calculation method of the interface resistance which has this.

The first step, the second step and the third step according to the method for measuring the interfacial resistance according to the second aspect of the present invention are the first step and the second step according to the method for measuring the interfacial resistance according to the first aspect of the present invention. And it is the same as that of a 3rd process.

In the fitting step, first, the equivalent circuit is constructed. The first When the call “call” plot of the cell for the fuel cell to be calculated obtained in the step is the call “call” plot 1 a shown in FIG. 1, that is, the calculation obtained in the first step. When the Cole-Cole-Plot of the target fuel cell consists of two arcs, the equivalent circuit to be constructed is the equivalent circuit 21 shown in Fig. 6. In FIG. 6, the equivalent circuit 21 includes (i) a first resistor 22a, (ii) a second resistor 24a and a first capacitor 23a connected in parallel, and (iii) connected in parallel. The third resistor 2 6 a and the second capacitor 2 5 a are connected in series.

Next, fitting is performed between the equivalent circuit 21 and the cornole-conore plot 1 a of the senore for the calculation target fuel cell obtained in the first step. For the fitting, input the circuit diagram of the equivalent circuit, the resistance value of the resistor in the equivalent circuit, the capacitance value of the capacitor in the equivalent circuit, and the reactance, and calculate the Cole Cole plot and output the shape Use existing software that can. The existing software used for the fitting is not particularly limited, and examples thereof include Z V i e w2 -E qu i v a l nt-C i rc u i ts.

The fitting is performed by first softening the circuit diagram of the equivalent circuit 21, the initial value of the first resistor 2 2 a, the initial value of the second resistor 24 a, and the initial value of the first capacitor 23 a Value, the initial value of the third resistor 26a, the initial value of the second capacitor 25a, and the input value necessary for the calculation of reactance, etc., and then changing the input value little by little The calculation by the software is repeated, and the shape of the call / call plot obtained by the calculation by the software is changed to the call / call plot of the calculation target fuel cell obtained in the first step. This is done by approximating the shape of the G. The shape of the call · call · plot obtained by the calculation in the software is the same as that of the cell for the fuel cell to be calculated obtained in the first step. The input value when it matches or substantially matches the shape of the mouthpiece is obtained as the input value at the time of fitting.

The relationship between the equivalent circuit 21 and the Cole-Cole 'plot 丄_a of the calculation target fuel cell obtained in the first step will be described by the second step and the third step. ) When the first arc 2a of the Cole Cole 'plot 1a is an arc derived from the fuel electrode side interface, and the second arc 3a is an arc derived from the air electrode side interface The second resistance 24 a is a fuel electrode side interface resistance Ria, the first capacitor 23 a is a capacitor component at the fuel electrode side interface, and the third resistance 26 a is an air electrode side interface resistance. The second capacitor 25 a corresponds to the capacitor component at the air electrode side interface, respectively. Further, by the second step and the third step, (2) the first arc _2a of the Cole-Cole plot 1a is an arc derived from the air electrode side interface, and the second arc 3a Is identified as a circular arc originating from the fuel electrode side interface, the second resistance 24 a is the air electrode side interface resistance R ic, and the first capacitor 23 a is the capacitor component of the air electrode side interface. The third resistor 26 a corresponds to the fuel electrode side interface resistance R ia, and the second capacitor 25 a corresponds to the capacitor component on the fuel electrode side interface.

Therefore, (1) If it is determined that the first arc 2a is an arc derived from the fuel electrode side interface and the second arc 3a is an arc derived from the air electrode side interface, Among the input values, the input value of the second resistance 24 a is the fuel electrode side interface resistance Ria, and the input value of the third resistance 26 a is the air electrode side interface resistance R ic. (2) If it is determined that the first arc 2a is an arc derived from the air electrode side interface and the second arc 3a is an arc derived from the fuel electrode side interface, the fitting The input value of the second resistance 24 a is the air electrode side interface resistance R ic, and the input value of the third resistance 26 a is the fuel electrode side interface resistance R ia . In addition, when the call / call plot of the calculation target fuel cell obtained in the first step is the call / call plot 1b shown in FIG. 2, that is, the first call When the Cole-Cole-plot of the calculation target fuel cell obtained in the process consists of three arcs, the equivalent circuit to be constructed is the equivalent circuit 30 shown in FIG. In FIG. 7, the equivalent circuit 30 includes (i) a first resistor 2 2 b, (ii) a second resistor 2 4 b connected in parallel and a first capacitor 2 3 b, (iii) connected in parallel. The third resistor 26b and the second capacitor 25b, and (iv) the fourth resistor 28b and the third capacitor 27b connected in parallel are connected in series. The fitting is performed by first applying the soft circuit diagram of the equivalent circuit 30, the initial value of the first resistor 2 2 b, the initial value of the second resistor 24 b, and the first capacitor 23 b Initial value, initial value of the third resistor 26b, initial value of the second capacitor 25b, initial value of the fourth resistor 28b, initial value of the third capacitor 27b, reactance In the same manner as described above, the Cole-Cole plot of the calculation target fuel cell obtained in the first step is composed of two arcs, except that the input values necessary for the calculation are input. The input value at the time of fitting and fitting is obtained.

The relationship between the equivalent circuit 30 and the call cell call 'plot 1 _b of the fuel cell to be calculated obtained in the first step will be described by the second step and the third step. ) When it is determined that the first arc 2b of the call 'call' plot 1b is an arc derived from the fuel electrode side interface and the second arc 3b is an arc derived from the air electrode side interface The second resistance 24 b is the fuel electrode side interface resistance Ria, the first capacitor 23 b is the capacitor component of the fuel electrode side interface, and the third resistance 26 b is the air electrode side interface resistance. The second capacitor 25 b corresponds to the capacitor component at the air electrode side interface. In addition, by the second process and the third process, (4) the call · When it is determined that the first arc 2b of Cole 'plot 1b is an arc derived from the air electrode side interface and the second arc 3b is an arc derived from the fuel electrode side interface, the second arc 3b The resistance 24 b is the air electrode side interface resistance R ic, the first capacitor 23 b is the capacitor component of the air electrode side interface, the third resistance 26 b is the fuel electrode side interface resistance R ia, The second capacitor 25 b corresponds to the capacitor component on the fuel electrode side interface.

Therefore, (3) when it is determined that the first arc 2 b is an arc derived from the fuel electrode side interface and the second arc 3 b is an arc derived from the air electrode side interface, Among these input values, the input value of the second resistance 24 b is the fuel electrode side interface resistance R ia, and the input value of the third resistance 26 b is the air electrode side interface resistance R ic. (4) If it is determined that the first arc 2b is an arc derived from the air electrode side interface and the second arc 3b is an arc derived from the fuel electrode side interface, the fitting Of the input values at the time, the input value of the second resistance 24 b is the air electrode side interface resistance R ic, and the input value of the third resistance 26 b is the fuel electrode side interface resistance R ia .

In addition, when the call / call plot of the calculation target fuel cell obtained in the first step is composed of four or more arcs, the equivalent shown in FIG. 7 regardless of the number of arcs. Fitting with circuit 30 can be performed. In the calculation method of the interfacial resistance according to the first aspect of the present invention and the interfacial resistance calculation method according to the second aspect of the present invention, the call of the cell for calculation target fuel cell obtained in the first step. Cole plot (1) In the second step, it is easy to determine whether the first arc and the second arc are from the fuel electrode side interface or the air electrode side interface. The first measurement condition and the second measurement condition are measurement conditions that differ only in the fuel concentration in the fuel electrode side gas, and the third measurement condition and the fourth measurement condition in the third step are Preferably, the measurement conditions are different only in the oxygen concentration in the air electrode side gas. (2) The first measurement condition and the second measurement condition in the second step are measurement conditions that differ only in the hydrogen concentration in the fuel electrode side gas, and the third measurement condition and in the third step It is particularly preferable that the fourth measurement condition is a measurement condition in which only the oxygen concentration in the air electrode side gas is different. (3) The first measurement condition and the second measurement condition in the second step Are the measurement conditions that differ only in the water vapor concentration in the fuel electrode side gas, and the third measurement condition and the fourth measurement condition in the third step are the oxygen conditions in the air electrode side gas. More preferably, the measurement conditions differ only in concentration.

Further, in the calculation method of the interfacial resistance of the first aspect of the present invention and the calculation method of the interfacial resistance of the second aspect of the present invention, the complex impedance measurement of the cell for the fuel cell to be calculated and the The temperature at which the complex impedance measurement of the calculation target fuel battery cell in the third step is not particularly limited and is appropriately selected depending on the type of cell and the operating conditions, and is usually from 1 to 120 ° C. Yes, for example, in the case of a solid oxide fuel cell, the temperature is from 600 to 120 ° C.

Conventionally, it has been known to obtain a Cole-Cole plot by measuring the complex impedance of a fuel cell cell under the operating conditions during operation. However, it was not possible to determine whether the obtained arc in the Cole-Cole plot originated from the fuel electrode side interface or the air electrode side interface. Therefore, the fuel electrode side interface resistance and the air electrode side interface resistance during operation could not be calculated.

On the other hand, in the calculation method of the interfacial resistance according to the first aspect of the present invention and the interfacial resistance calculation method according to the second aspect of the present invention, the first step and the third step are carried out to perform the first step. It is possible to reliably identify the interface from which the first arc and the second arc in the call plot of the calculation target fuel cell obtained in the process are derived. Therefore, the interface of the first aspect of the present invention According to the calculation method of the resistance and the calculation method of the interface resistance according to the second aspect of the present invention, the fuel electrode side interface resistance and the resistance when the calculation target fuel cell is operated under a specific operating condition desired to be calculated. The air electrode side interface resistance can be calculated.

EXAMPLES Next, the present invention will be described more specifically with reference to examples. However, this is merely an example and does not limit the present invention.

(Example)

(Example 1)

(Manufacture of cells)

A slurry for forming a fuel electrode containing a mixed powder of nickel oxide (N i O) and scandiaceria stabilized zirconia (10 S c 1 C e SZ) having a mixing ratio of 50:50 was prepared, Using the slurry for forming the fuel electrode, a slurry layer for forming the fuel electrode with a film thickness of 100 μm was formed by screen printing. After drying, the slurry was fired at 1400 ° C for 5 hours to produce a fuel electrode. · Nickel oxide; average particle size 0.8 μπι

• Scandiaceria stabilized zirconia; content of scandia in zirconia 1 Omo 1%, ceria content 1 mo 1%, average particle size 0.6 / ^ m A slurry for forming an electrolyte containing scandiaceria-stabilized zirconia (l OS cl C e SZ) was prepared, and the electrolyte-forming slurry was formed on the surface of the fuel electrode layer by a screen printing method. The coating was applied to a thickness of 0.3 mm, dried, and then fired at 1400 ° C. for 5 hours to obtain a fuel electrode on which an electrolyte was formed. Then, lanthanum strontium manganate _{_{(L n 0. 8 S r}} 0. 2 M !! .O 3) to prepare a cathode-forming slurry containing, then the surface of the electrolyte, for the air Kikyoku formed The slurry was applied by screen printing to a film thickness of 100 m, dried, and then 1 200 ° C for 3 hours Firing was carried out to produce a fuel cell A.

(Complex impedance measurement)

The complex impedance of the fuel cell A is determined under the conditions that the operating temperature of the cell is 100 ° C. and the gas composition is the hydrogen concentration of the fuel electrode side gas and the oxygen concentration of the air electrode side gas shown in Table 1. Measurement mode: potentiostat, set voltage: 0.0 V, current range: 10 A, delay time: 0.1 sec, number of sweep measurement data: 50 times, integration number: 10 times maximum frequency: 1 0 0 k H _Z, minimum frequency:. 0 1 H z, sinusoidal voltage:. 0 0 3 V rms, EM measurement time: 5 seconds, the polarization retention time:. 0 were measured at 2 seconds. The results are shown in Tables 2-5. Also, Cole-Cole 'plots for measurements 1 to 4 are shown in Figs.

Then, the operating condition for calculating the interfacial resistance in the first process is set as measurement 1, the first measurement condition in the second process is measured 4, the second measurement condition is measured 2, and the third measurement condition in the third process is measured 1 Using the fourth measurement condition as measurement 2, the real part resistance difference No. 2 -Draft and real part resistance difference second graph was obtained. The results are shown in Tables 6 and 12. . ez

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(Certified arc)

In Fig. 12, since the peak top of the first resistance difference graph in the real part is near the frequency of 100 Hz, it can be seen that the influence of the change on the fuel electrode side is strongly around the frequency of 100 Hz. It was. From Table 2, the first arc 31 that is the arc including the point with the frequency of 100 Hz out of the arcs in the measurement 1 call and call 'plot of Fig. 8 is derived from the fuel electrode side. Can be recognized as an arc. Similarly, since the peak top of the second resistance value difference graph in the real part is near the frequency of 10 Hz, it was found that the influence of the change on the air electrode side is strongly around the frequency of 10 Hz. . Then, from Table 2, the second arc 32, which is the arc including the point of frequency 1 OH z, is the arc originating from the air electrode side among the arcs in the call, call, and plot of measurement 1 in Fig. 8. It can be recognized that there is.

(Fitting process)

The equivalent circuit shown in Fig. 7 was constructed. From the result of the above-mentioned arc recognition, in FIG. 7, the second resistance 24 b corresponds to the fuel electrode side interface resistance R i a, and the third resistance 26 b corresponds to the air electrode side interface resistance R i c. Next, using the existing software ZV ie w2—Equivalent—Circuits, fitting was performed with the call-call-plot of measurement 1 shown in Fig. 8, and the call 'call' plot shown in Fig. 13 was obtained. . The input value of the second resistor 24b in the case of the Cole-Cole-plot shown in Figure 1 is 0.99697.

The input value of the third resistor 26 b was 0.555527 Ω. Accordingly, the fuel cell A has a gas composition with a hydrogen concentration of 10 0 on the fuel electrode side.

When operated under the operating conditions of 0%, gas composition on the air electrode side with oxygen concentration of 10%, and cell operating temperature of 100 ° C, the fuel electrode side interface resistance of the fuel cell A Is 0.969 76 Ω, interface resistance on the air electrode side R ic is 0.5 552

7 Ω. (Explanation of symbols)

a, 1 b, 1 1, 1 2, 1 7, 1 8 n Cole plot a, 2 b, 2 c, 2 d, 2 e, 2 f, 3 1 1st arc

a, 3 b, 3 c, 3 d, 3 e, 3 f, 3 2 second arc

3rd arc

4 Real part resistance difference 1-graph

4 1 Real part resistance difference 2: Graph

5, 1 5 1 peak

6, 1 6 1 Peak top

Equivalent circuit

b First resistance

b 1st condenser

b Second resistance

b Second capacitor

b Third resistor

Third capacitor

Fourth resistance

4 1b electrolyte

4 2 b Fuel electrode

, 3 b

4 4 b Fuel cell

Reference pole

b Equipotential lines

Fuel electrode terminal

Air electrode terminal 5 5 a, 5 5 b Intermediate potential point

5 6 Surface where fuel electrode 4 2 b is joined Industrial applicability

According to the present invention, the interfacial resistance of the fuel cell can be ascertained under operating conditions, so that it is easy to construct a power generation system having the fuel cell.

Claims

The scope of the claims

1. A method for calculating an interface resistance for calculating a fuel electrode side interface resistance R ia and an air electrode side interface resistance R ic at the time of operation of a calculation target fuel cell, under an operating condition for calculating the interface resistance, A first step of performing a complex impedance measurement of the calculation target fuel cell and obtaining a call-call plot of the calculation target fuel cell;

The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real number when the frequency in the first measurement condition is n The difference between the part resistance value R 1 rn and the real part resistance value R 2 rn when the frequency in the second measurement condition is n is R (1-2) rn as the following formula (1):

厶 R (l _ 2) r n = R l r n-R 2 r n (1)

Calculate ΔΙ (1− 2) rn for each frequency, then plot the AR (1− 2) rn for each frequency, with the horizontal axis representing frequency and the vertical axis representing (1-2) rn. The resistance value difference first graph is obtained, and then the call of the calculation target fuel cell obtained in the first step is obtained from the peak top frequency in the real part resistance value difference first graph. Of the arcs in the plot, the second step of certifying arcs originating from the fuel electrode side interface,

AR (3— 4) r n = R 3 r n—R4 r n (2)

Calculate (3 -4) rn for each frequency, and then on the horizontal axis Plot AR (3 -4) rn on the vertical axis and obtain the second graph of the real part resistance difference. Next, from the peak top frequency in the second real part resistance value difference graph, the first step A third step of certifying an arc derived from the air electrode side interface among the arcs in the call-call-plot of the calculation target fuel cell obtained in

R i a = R r a (max)-R r a (m i n) (3)

Then, the fuel electrode side interface resistance Ria is obtained, and then, in the call “call” plot of the calculation target fuel cell obtained in the first step, the air electrode side interface is obtained in the third step. The difference between the real part resistance maximum value R rc (max) and the real part resistance minimum value R rc (min) of the arc that is recognized as the arc derived from the following equation (4):

R i c = R r c (ma x) — R r c, m i n), 4)

An interface resistance calculation step of calculating an air electrode side interface resistance R ic by calculating the interface resistance, and calculating the interface resistance.

2. A calculation method of interface resistance to calculate the fuel electrode side interface resistance R ia and the air electrode side interface resistance R ic at the time of operation of the target fuel cell, and under the operating conditions for calculating the interface resistance, A first step of performing a complex impedance measurement of the calculation target fuel cell and obtaining a call-call plot of the calculation target fuel cell;

The complex impedance measurement of the calculation target fuel cell is performed under the first measurement condition and the second measurement condition that are different only in the gas composition of the fuel electrode side gas, and then the real number when the frequency in the first measurement condition is n Resistance value R 1 rn The difference AR (1-2) rn from the real part resistance value R 2 rn when the frequency is n under the two measurement conditions is expressed by the following formula (1):

厶 R (l— 2) rn = R lr nR 2 rn (1) to calculate AR (1-2) rn for each frequency, then the horizontal axis is frequency and the vertical axis is (1-2) rn Plot AR (1−2) rn for each frequency to obtain a real part resistance value difference first graph, and then from the peak top frequency in the real part resistance value difference first graph, the first step The second step of certifying an arc derived from the fuel electrode side interface among the arcs in the call / call 'plot of the fuel cell to be calculated obtained in

The complex impedance measurement of the calculation target fuel cell is performed under the third measurement condition and the fourth measurement condition that are different only in the gas composition of the air electrode side gas, and then the frequency in the third measurement condition is n. The difference between the real part resistance value R 3 rn at the time and the real part resistance value R 4 rn when the frequency in the fourth measurement condition is n ^ R (3 -4) rn is expressed by the following equation (2):

厶 R (3— 4) r n = R 3 r n— R 4 r n (2)

Calculate (3-4) rn for each frequency, then plot the frequency on the horizontal axis and AR (3 -4) rn on the vertical axis to obtain the real part resistance difference second graph, From the peak-top frequency in the real part resistance difference second graph, on the air electrode side interface among the arcs in the call-coal-plot of the calculation target fuel cell obtained in the first step A third step of certifying the arc

An equivalent circuit having (i) a first resistor connected in series; (ii) a second resistor and a first capacitor connected in parallel; and (iii) a third resistor and a second capacitor connected in parallel. Fitting with the Cole-Cole plot of the calculation target fuel cell obtained in the first step to obtain the fuel electrode side interface resistance Ria and the air electrode side interface resistance Ric The fitting process,

A method for calculating the interfacial resistance, comprising:

3. The first measurement condition and the second measurement condition in the second step are measurement conditions that differ only in the fuel concentration in the fuel electrode side gas, and the third measurement condition and the above in the third step The interface resistance calculation method according to claim 1 or 2, wherein the fourth measurement condition is a measurement condition in which only the oxygen concentration in the air electrode side gas is different.

4. The interface resistance calculation according to claim 3, wherein the first measurement condition and the second measurement condition in the second step are measurement conditions that differ only in the hydrogen concentration in the fuel electrode side gas. Method.

5. The first measurement condition and the second measurement condition in the second step are measurement conditions that differ only in the water vapor concentration in the fuel electrode side gas, and the third measurement condition in the third step and The interface resistance calculation method according to claim 1, wherein the fourth measurement condition is a measurement condition in which only the oxygen concentration in the air electrode side gas is different.