JP5585248B2 - Gas concentration measuring device - Google Patents

Description

  The present invention relates to a gas concentration measuring apparatus for measuring the gas concentration of a reaction gas supplied to an electrochemical cell in which an electrolyte is held between a pair of electrodes.

Conventionally, a solid electrode reaction in an electrochemical cell that is applied to a polymer electrolyte membrane fuel cell or the like, a capacitor component Cd by electric double layer, the virtual device called Faraday impedance Z _f connected in parallel with the capacitor component Cd, It is possible to simplify the circuit to an equivalent circuit composed of a resistor Ro connected in series with these. Of this equivalent circuit, Faraday impedance Z _f are known to vary depending on the gas concentration Cs of the reaction gas (the active substance) to be supplied to the electrochemical cell (e.g., see Non-Patent Document 1). This Non-Patent Document 1 suggests that the gas concentration Cs of the reaction gas supplied to the battery chemical cell can be measured based on the internal impedance Z of the battery chemical cell.

Itagaki Masayuki, “The Principle, Measurement and Analysis of Electrochemical Impedance Method”, 1st Edition, Maruzen Co., Ltd., August 2008, p.124-127

  However, since the resistance component of the internal impedance Z of the electrochemical cell changes according to the dry state inside the electrochemical cell, even if the gas concentration Cs of the reaction gas is simply measured from the internal impedance Z of the electrochemical cell. The actual gas concentration and the measured value may deviate due to the influence of drying in the battery chemical cell. That is, when measuring the gas concentration of the reaction gas supplied to the battery chemical cell from the internal impedance of the conventional battery chemical cell, there is a problem that the measurement accuracy is low.

  In view of the above points, an object of the present invention is to improve the measurement accuracy of a gas concentration in a gas concentration measurement device that measures the gas concentration of a reaction gas in an electrochemical cell in which an electrolyte is held between a pair of electrodes. .

In order to achieve the above object, according to the first aspect of the present invention, the gas concentration of the reaction gas supplied into the electrochemical cell (10) in which the electrolyte (101) is held between the pair of electrodes (102, 103). A gas concentration measuring device for measuring (Cs), current detection means (41) for detecting the output current of the electrochemical cell (10), and voltage detection means for detecting the output voltage of the electrochemical cell (10) ( 42), an AC signal generating means (43) for generating an AC signal of an arbitrary frequency as an output signal of the electrochemical cell (10), and an output current and an output voltage when the AC signal is generated as an output signal. The impedance calculating means (44) for calculating the alternating current impedance (Z) of the electrochemical cell (10) and the AC impedance (Z) calculated by the impedance calculating means (44) are corrected. And a gas concentration calculating means (45b) for calculating the gas concentration (Cs) of the reaction gas based on the corrected impedance (Z ′) corrected by the impedance correcting means (45a). The impedance correction means (45a) is a circular arc formed by the real part and the imaginary part of the AC impedance (Z) on the high frequency side when the frequency of the AC signal generated in the output signal is changed from a high frequency to a low frequency. The frequency when reaching the top of the trajectory is defined as the reference frequency (fo), and the total value (Zro + Zio) obtained by adding the real part (Zro) and the imaginary part (Zio) of the AC impedance (Zo) at the reference frequency (fo). calculated as the change amount of the resistance component due to the drying of the electrochemical cell (10) ([Delta] Z), the sum (Zro + Zio) a reference frequency ( and correcting the AC impedance in a low frequency band by subtracting the real part of the AC impedance (Zr) in a low frequency band lower than o).

  According to this, the gas of the reaction gas of the electrochemical cell (10) using the corrected impedance (Z ′) corrected based on the change amount (ΔZ) of the resistance component due to the drying inside the electrochemical cell (10). Since the concentration (Cs) is measured, the measurement accuracy of the gas concentration (Cs) of the reaction gas can be improved.

  In addition, the code | symbol in the bracket | parenthesis of each means described in this column and the claim shows the correspondence with the specific means as described in embodiment mentioned later.

1 is an overall configuration diagram of a fuel cell system according to an embodiment. It is a schematic diagram of the gas concentration measuring apparatus and electrochemical cell which concern on embodiment. It is explanatory drawing explaining the change of the alternating current impedance accompanying the change of the hydrogen concentration in an electrochemical cell. It is explanatory drawing explaining the change of alternating current impedance by the influence of the drying in an electrochemical cell. It is explanatory drawing explaining the equivalent circuit of the electrode reaction of an electrochemical cell. FIG. 5 is a schematic diagram of the Cole-Cole plot of FIG. 4. It is explanatory drawing explaining the variation | change_quantity of the resistance component by the influence of the drying in an electrochemical cell. It is a flowchart which shows the control processing which the arithmetic unit which concerns on embodiment performs. It is explanatory drawing explaining the Cole-Cole plot of correction | amendment impedance. It is explanatory drawing explaining the execution timing of the process which calculates the variation | change_quantity of a resistance component, and the process which calculates correction | amendment impedance.

  Hereinafter, an embodiment of the present invention will be described with reference to FIGS. FIG. 1 is an overall configuration diagram of a fuel cell system to which a gas concentration measuring device 40 of the present embodiment is applied, and FIG. 2 is a schematic diagram of an electrochemical cell 10 and a gas concentration measuring device 40 of the fuel cell 1. This fuel cell system is applied to a so-called fuel cell vehicle, which is a kind of electric vehicle, and supplies electric power to various electric loads 2 such as an electric motor for vehicle travel.

  As shown in FIG. 1, the fuel cell system includes a fuel cell 1 that generates electric power using an electrochemical reaction of hydrogen (fuel gas) and oxygen (oxidant gas that oxidizes the fuel gas). The fuel cell 1 supplies electric power to various electric loads 2, and in this embodiment, a solid polymer electrolyte fuel cell is adopted. The fuel cell 1 is not limited to the solid polymer electrolyte membrane type, and may be applied to other types of fuel cells.

  Specifically, the fuel cell 1 is configured by electrically connecting a plurality of electrochemical cells 10 (hereinafter abbreviated as “cells 10”) as basic units in series.

  As shown in FIG. 2, each cell 10 includes a membrane electrode assembly (MEA) 10a in which a pair of electrodes 102 and 103 are arranged on both sides of an electrolyte membrane 101 made of a solid polymer, and the membrane electrode. It consists of a pair of separators 104 and 105 holding the joined body 10a. In addition, on the surface facing the hydrogen electrode (anode electrode) 102 in the pair of separators 104 and 105, a hydrogen flow path through which hydrogen flows is formed, while on the surface facing the air electrode (cathode electrode) 103, An air channel through which air containing oxygen flows is formed.

  In each cell 10, as shown below, hydrogen and oxygen are electrochemically reacted to output electric energy.

(Hydrogen electrode side) H ₂ → 2H ⁺ + 2e ⁻
(Air electrode side) 2H ⁺ + 1 / 2O ₂ + 2e ⁻ → H ₂ O
The cell 10 is connected to a gas concentration measuring device 40 that measures the gas concentration of the reaction gas in the cell 10. The gas concentration measuring device 40 of the present embodiment measures the hydrogen gas concentration Cs in the cell 10. Details of the gas concentration measuring device 40 will be described later.

  Returning to FIG. 1, on the air electrode 103 side of the fuel cell 1, the air supply pipe 20 for supplying air (oxygen) to each cell 10 of the fuel cell 1 and the electrochemical reaction in the fuel cell 1 are finished. An air discharge pipe 21 for discharging the excess air and the generated water generated by the air electrode 103 from the fuel cell 1 to the outside is connected.

  An air pump 22 for pumping air sucked from the atmosphere to the fuel cell 1 is provided at the most upstream portion of the air supply pipe 20, and an air pressure in the fuel cell 1 is adjusted in the air discharge pipe 21. An air pressure regulating valve 23 is provided. In the present embodiment, the air pump 22 and the air pressure regulating valve 23 constitute oxidant gas supply means for supplying air of a predetermined flow rate and pressure to the fuel cell 1.

  On the hydrogen electrode 102 side of the fuel cell 1, a hydrogen supply pipe 30 for supplying hydrogen to the fuel cell 1, and the generated water accumulated on the hydrogen electrode 102 side is discharged from the fuel cell 1 together with a small amount of hydrogen. For this purpose, a hydrogen discharge pipe 31 is connected.

  A high-pressure hydrogen tank 32 filled with high-pressure hydrogen is provided at the uppermost stream portion of the hydrogen supply pipe 30, and is supplied to the fuel cell 1 between the high-pressure hydrogen tank 32 and the fuel cell 1 in the hydrogen supply pipe 30. A hydrogen pressure regulating valve 33 for adjusting the hydrogen pressure is provided. In the present embodiment, the hydrogen pressure regulating valve 33 constitutes a fuel gas supply means for supplying hydrogen at a predetermined pressure to the fuel cell 1.

  The hydrogen discharge pipe 31 is provided with an electromagnetic valve 34 that opens and closes at predetermined time intervals in order to discharge the produced water together with a small amount of hydrogen to the outside air. In the above-described electrochemical reaction, although generated water is not generated on the hydrogen electrode side, generated water that has permeated the electrolyte membrane 101 of each cell 10 from the oxygen electrode side may accumulate on the hydrogen electrode side. For this reason, in this embodiment, the hydrogen discharge piping 31 and the solenoid valve 34 are provided.

  The fuel cell system is provided with a control device (ECU) 50 as power generation control means for performing various controls. The control device 50 controls the operation of various electric actuators constituting the fuel cell system based on the input signal, and is composed of a well-known microcomputer comprising a CPU, ROM, RAM, etc. and its peripheral circuits. ing.

  A detection signal of the gas concentration measuring device 40 is input to the input side of the control device 50, and various electric devices such as an air pump 22, an air pressure adjustment valve 23, a hydrogen pressure adjustment valve 33, and an electromagnetic valve 34 are input to the output side. Type actuators are connected.

  Next, the gas concentration measuring device 40 of this embodiment will be described. As shown in FIG. 2, the gas concentration measuring device 40 mainly includes a current sensor 41, a voltage sensor 42, an oscillation circuit 43, a signal processing circuit 44, and an arithmetic device 45.

  The current sensor 41 is current detection means for detecting an output current output from the cell 10 (measuring cell) for measuring the gas concentration, and the voltage sensor 42 is an output voltage (a pair of electrodes 102) output from the cell 10. , 103 is a voltage detection means for detecting a potential difference between the two. Each of the current sensor 41 and the voltage sensor 42 is connected to a signal processing circuit 44, and each detection signal of each sensor 41, 42 is configured to be output to the signal processing circuit 44.

  The oscillation circuit 43 constitutes AC signal generating means for generating an AC signal such as a sine wave at an arbitrary frequency in the output signal of the cell 10. Specifically, the oscillation circuit 43 can be configured by a load variable device capable of extracting an AC signal having an arbitrary frequency from the cell 10 by a variable resistor or the like. Of course, the oscillation circuit 43 may be configured by an AC applying device that generates an AC signal having an arbitrary frequency by applying an AC signal such as a sine wave to the output signal of the cell 10. The frequency of the alternating current generated by the oscillation circuit 43 can be adjusted by the signal processing circuit 44.

  The signal processing circuit 44 generates an AC impedance Z (internal impedance) of the cell 10 based on the detection signals output from the current sensor 41 and the voltage sensor 42 when the oscillation circuit 43 generates an AC signal having an arbitrary frequency. ) Is calculated. The signal processing circuit 44 is connected to the arithmetic device 45, and is configured to output the calculation result of the AC impedance Z calculated by the signal processing circuit 44 to the arithmetic device 45.

  The arithmetic unit 45 is composed of a well-known microcomputer comprising a CPU, ROM, RAM, etc. and its peripheral circuits. The arithmetic unit 45 of the present embodiment corrects the alternating current impedance Z calculated by the signal processing circuit 44 and, based on the corrected alternating current impedance Z ′ (corrected impedance), the hydrogen gas concentration Cs inside the cell 10. Is calculated. Specifically, the arithmetic unit 45 performs correction to remove the resistance component variation ΔZ caused by drying in the cell 10 from the AC impedance Z calculated by the signal processing circuit 44.

  In the present embodiment, the configuration (hardware and software) for correcting the AC impedance Z in the arithmetic unit 45 is the impedance correction means 45a, and the configuration for calculating the gas concentration Cs (hardware and software) is the gas concentration calculation means. 45b.

  Here, it is known that the AC impedance Z of the cell 10 has a correlation with the gas concentration Cs in the cell 10. This point will be described with reference to FIG.

  FIG. 3 is an explanatory diagram illustrating an example of a change in AC impedance Z due to a change in gas concentration Cs. Here, FIG. 3A shows a case where the frequency generated in the output signal of the cell 10 is changed from a high frequency to a low frequency under the condition that the inside of the cell 10 becomes high humidity (for example, dew point = 45 ° C.). The change of the real part Zr (resistance component) and the imaginary part Zi (reactance component) of the alternating current impedance Z is shown. FIG. 3B is a complex plane showing the real part Zr and the imaginary part Zi of FIG. 3A (Cole-Cole plot).

  In FIG. 3A, the change in the real part Zr is indicated by a white circle and the change in the imaginary part Zi is indicated by a black circle under the condition that the hydrogen gas concentration Cs is high (for example, hydrogen concentration = 30%). The change of the real part Zr is indicated by a white square and the change of the imaginary part Zi is indicated by a black square under the condition that the gas concentration Cs is low (for example, hydrogen concentration = 6.5%). In FIG. 3B, a plot under a condition where the hydrogen gas concentration Cs is high is indicated by a white circle, and a plot under a condition where the hydrogen gas concentration Cs is low is indicated by a white square.

  As shown in FIG. 3A, the real part Zr (white square) of the alternating current impedance Z under the condition that the inside of the cell 10 has high humidity and low concentration (high humidity and low concentration condition) is the inside of the cell 10. Compared with the real part Zr (white circle) of the AC impedance Z under conditions of high humidity and high concentration (high humidity and high concentration conditions), it is greatly reduced in the low frequency band (for example, frequency = 0.3 to 10 Hz). There is a tendency to increase. In addition, the imaginary part Zi (black square) of the AC impedance Z under high humidity and low concentration conditions tends to decrease significantly in the low frequency band as compared to the imaginary part Zi (black circle) of the AC impedance Z under high humidity and high concentration conditions. There is.

  And, as shown in FIG. 3 (b), the Cole-Cole plot (white circle) in the high humidity and high concentration condition becomes a semicircular locus, while the Cole-Cole plot (white square) in the high humidity and low concentration condition is The locus looks like a combination of two arcs. In the Cole-Cole plot (white square) under high humidity and low concentration conditions, the arc-shaped locus on the high frequency side (left side in the figure) is roughly the same as the locus of the Cole-Cole plot (white circle) under high humidity and high concentration conditions. Match.

  Thus, the AC impedance Z of the cell 10 and the gas concentration Cs in the cell 10 have a correlation that the AC impedance Z in the low frequency band increases as the hydrogen gas concentration Cs in the cell 10 decreases. I understand that there is.

  Further, it is known that the AC impedance Z of the cell 10 has a correlation with the degree of drying in the cell 10 other than the gas concentration Cs in the cell 10. This point will be described with reference to FIG.

  FIG. 4 is an explanatory diagram for explaining an example of a change in the AC impedance Z due to a change in the degree of drying in the cell 10. Here, FIG. 4A shows a case where the frequency generated in the output signal of the cell 10 is changed from a high frequency to a low frequency under the condition that the inside of the cell 10 has a low concentration (hydrogen concentration = 6.5%). The change of the real part Zr and the imaginary part Zi of the alternating current impedance Z is shown. FIG. 4B is a Cole-Cole plot of FIG.

  4A, the change in the real part Zr is indicated by a white square and the change in the imaginary part Zi is indicated by a black square in a condition where the inside of the cell 10 is at high humidity (for example, dew point = 45 °). The change of the real part Zr under the condition of low humidity (for example, dew point = 35 °) is indicated by a white triangle and the change of the imaginary part Zi is indicated by a black triangle. Further, in FIG. 4B, a plot in a condition where the inside of the cell 10 is at high humidity is indicated by a white square, and a plot in a condition where the inside of the cell 10 is at low humidity is indicated by a white triangle.

  As shown in FIG. 4 (a), the real part (white triangle) of the AC impedance Z under the condition that the inside of the cell 10 has low humidity and low concentration (low humidity and low concentration condition) is the high humidity and low concentration condition. Compared to the real part (white square) of the AC impedance Z in FIG. Further, the imaginary part (black triangle) of the alternating current impedance Z under the high humidity and low concentration condition tends to slightly increase compared to the imaginary part (black square) of the alternating current impedance Z under the high humidity and low concentration condition.

  And, as shown in FIG. 4 (b), the Cole-Cole plot (white triangle) in the low humidity and low concentration condition is different from the Cole-Cole plot (white square) in the high humidity and low concentration condition (in the figure). The left side) is an arc-shaped locus including a straight line portion. And the Cole-Cole plot (white square) in the low humidity and low concentration condition shows that the low frequency side (right side in the figure) after the straight line part is the Cole-Cole plot (white triangle) in the high humidity and low concentration condition. The real part Zr is approximated to a shape translated from the high resistance side (right side in the figure).

Here, as shown in FIG. 5A, an equivalent circuit of the cell 10 when the inside of the cell 10 is at high humidity is a capacitor component Cd by an electric double layer and a Faraday connected in parallel to the capacitor component Cd. It can be shown by a general equivalent circuit composed of the impedance Z _f and the membrane resistance Ro of the electrolyte membrane 101 connected in series therewith.

On the other hand, the equivalent circuit of the cell 10 when the inside of the cell 10 has low humidity can be represented by a distributed constant circuit, not a general equivalent circuit, as shown in FIG. Note that R _pore in the equivalent circuit shown in FIG. 5B indicates resistance due to fine particles contained in the electrolyte membrane 101 and the electrodes 102 and 103 of the cell 10.

When the inside of the cell 10 is dried and becomes low humidity, the resistance value of the resistance R _pore in the equivalent circuit increases, and the increase in the resistance value of the resistance R _pore is a Cole-Cole under the condition of low concentration. It appears as a straight line part of the plot, and the real part Zr on the low frequency side after the straight line part is translated to the high resistance side. Note that when the inside of the cell 10 has high humidity, the resistance value of the resistor R _pore in the equivalent circuit shown in FIG. 5B is very small and can be ignored. it can.

  Thus, the AC impedance Z of the cell 10 and the degree of dryness in the cell 10 have a correlation that the real part Zr of the AC impedance Z generally increases in the low frequency band when the inside of the cell 10 becomes low humidity. is there.

  Next, in the present embodiment, a method for correcting the AC impedance Z performed by the impedance correcting means will be described with reference to FIGS.

  FIG. 6 is a schematic diagram of the Cole-Cole plot shown in FIG. In FIG. 6, the locus of the Cole-Cole plot under the low humidity and low concentration condition is indicated by a solid line, and the locus of the Cole-Cole plot under the high humidity and low concentration condition is indicated by a broken line. For convenience of explanation, FIG. 6 shows a change in AC impedance from which the membrane resistance Ro of the electrolyte membrane 101 is removed under high humidity and low concentration conditions.

  As shown in FIG. 6, in the low humidity and low concentration condition, for example, the top of the arc-shaped locus shown on the high frequency side (left side in the figure) of the high humidity and low concentration condition due to the influence of drying (low humidity) in the cell 10 X1 moves parallel to the high resistance side to the top X2 of the arc-shaped locus shown on the high frequency side. Note that the top of the arc-shaped locus means the peak value in the imaginary part.

  The movement amount of the real part that has been translated can be considered as a change ΔZ of the resistance component caused by the inside of the cell 10 being dried, and the real part and the imaginary number in the coordinates (Zr2, Zi2) of the top X1. It is possible to estimate a total value (Zr2 + Zi2: Zr2 ≧ 0, Zi2 ≦ 0).

  This point will be described with reference to FIG. First, the straight line portion of the arc-shaped locus shown on the high frequency side in the low humidity and low concentration condition is replaced with an arc (virtual line L) with the absolute value | Zi2 | of the imaginary part Zi2 at the top X2 as a radius. Then, as shown in FIG. 7, the locus of the Cole-Cole plot under the low humidity and low concentration condition including the virtual line L is higher than the locus of the Cole-Cole plot under the high humidity and low concentration condition by the change amount ΔZ of the resistance component. It approximates the shape translated to the resistance side.

  Here, the intersection X3 (coordinates (Zr2- | Zi2 |, 0)) between the virtual line L and the real part axis is the arc-shaped locus shown on the high frequency side in the high humidity and low concentration condition and the real part axis. It can be considered that the intersection point X4 (coordinates (0, 0)) has moved parallel to the high resistance side.

  Therefore, the resistance component variation ΔZ that changes due to the drying of the inside of the cell 10 can be approximated by Zr2− | Zi2 | that is a real part at the intersection X3. Since the value of the imaginary part is 0 or less, the change amount ΔZ of the resistance component can also be expressed as Zr2 + Zi2.

  Accordingly, by subtracting the resistance component change ΔZ from the real part of the AC impedance calculated when the inside of the cell 10 is in a low humidity, the AC impedance in which the resistance component generated by drying the inside of the cell 10 is removed. Zc (correction impedance) can be calculated.

  Next, a method for calculating the gas concentration will be described. In the present embodiment, calculation is performed using a function Cs = f (Z) that defines the relationship between the gas concentration Cs and the AC impedance Z. As an example of this function, the theoretical formula shown by the following formula 1 can be used.

ここで、「Ａ」は定数、「Ｉ」は電流（発電電流）、「Ｒｏ」は膜抵抗、「ω」は交流の角周波数、「Ｃｄ」はコンデンサ成分、「Ｄ」は拡散係数、「δ」は電極における拡散層の厚さ、「ｎ」は電極反応に寄与した電子数、「Ｆ」はファラデー定数、「ｂ」はターフェル係数を示している。

Here, “A” is a constant, “I” is a current (generated current), “Ro” is a membrane resistance, “ω” is an AC angular frequency, “Cd” is a capacitor component, “D” is a diffusion coefficient, “ “δ” is the thickness of the diffusion layer in the electrode, “n” is the number of electrons contributing to the electrode reaction, “F” is the Faraday constant, and “b” is the Tafel coefficient.

  The theoretical formula shown by the formula 1 can be derived from the formulas shown in the following formulas 2 to 7 (see Non-Patent Document 1).

ここで、数２に示す数式に示す「ｋ」は、電極における反応速度定数である。なお、数２に示す数式は、電極反応速度を示す電流（発電電流）を導出する式である。

Here, “k” shown in the mathematical formula 2 is a reaction rate constant in the electrode. In addition, the numerical formula shown in Formula 2 is an expression for deriving a current (generated current) indicating the electrode reaction rate.

数３に示す数式は、図５（ａ）に示す一般的な等価回路におけるファラデーインピーダンスＺ_ｆを示す式である。

Formula shown in Formula 3 is a formula showing the Faraday impedance Z _f in the general equivalent circuit shown in Figure 5 (a).

ここで、数４に示す数式に示す「Ｊ」は、電極における拡散のフラックスを示している。なお、数４に示す数式は、電流変化量および電圧変化量からファラデーインピーダンスＺ_ｆを導出する示す式である。

Here, “J” shown in the mathematical formula 4 represents the diffusion flux in the electrode. Incidentally, the formula shown in Formula 4 is a formula showing deriving a Faraday impedance Z _f from the current change amount and the voltage change amount.

数５に示す数式は、電位Ｅの変化量ΔＥに対するガス濃度Ｃｓの変化量ΔＣｓを示す式である。

The numerical formula shown in Equation 5 is an expression showing the change amount ΔCs of the gas concentration Cs with respect to the change amount ΔE of the potential E.

数６に示す数式は、フラックスの変化ΔＪとガス濃度の変化ΔＣｓとの関係を示す式である。

The mathematical formula shown in Equation 6 is a formula showing the relationship between the flux change ΔJ and the gas concentration change ΔCs.

数７に示す数式は、数２で示す数式から導出される反応速度定数ｋとガス濃度Ｃｓとの関係を示す式である。

The equation shown in Equation 7 is an equation showing the relationship between the reaction rate constant k derived from the equation shown in Equation 2 and the gas concentration Cs.

Here, the process of deriving the theoretical formula shown in the formula 1 from the formulas shown in the formulas 3 to 7 will be briefly described. First, the formula shown in the formula 4 is changed to “ΔCs / ΔE” of the formula shown in the formula 5. Substituting “ΔJ / ΔCs” in the equation shown in Equation 6 and “k” in the equation shown in Equation 7. Then, by substituting “1 / Z _f ” shown in Equation 3 into the equation shown in Equation 4 and rearranging the equation, the theoretical equation shown in Equation 1 can be derived.

  As described above, the gas concentration can be calculated from the AC impedance Z of the cell 10 by using the theoretical formula expressed by Equation (1). For parameters (A, I, Ro, ω, Cd, D, δ, n, F, b) other than the AC impedance Z of the theoretical formula shown in Equation 1, the frequency generated in the output signal of the cell 10 is a high frequency. In order to minimize the error between the calculation result of the gas concentration Cs calculated by the theoretical formula shown in Equation 1 and the actual measurement value of the gas concentration Cs when the frequency is changed from low to low frequency, a calculation such as the least square method is performed in advance. What is necessary is just to calculate by a method.

  Next, a control process performed by the arithmetic device 45 of the gas concentration measuring device 40 of the present embodiment will be described with reference to FIG. FIG. 8 is a flowchart showing a control process performed by the arithmetic unit 45 of the gas concentration measuring apparatus. The control routine of FIG. 8 is executed as a subroutine of a main control routine executed by the arithmetic unit 45.

  First, as pre-processing before starting the control routine shown in FIG. 8, when the frequency generated in the output signal of the cell 10 is changed from a high frequency to a low frequency, the top of the high frequency side arc in the Cole-Cole plot is displayed. The frequency (for example, 20 Hz) when reaching is calculated. And the said frequency is memorize | stored in the memory | storage part of the arithmetic unit 45 as the reference frequency fo. The reference frequency fo is a frequency corresponding to the resonance frequency in the equivalent circuit of the electrode reaction of the cell 10.

  Further, the membrane resistance Ro of the electrolyte membrane 101 in the cell 10 under the condition that the inside of the cell 10 is at high humidity is calculated, and the membrane resistance Ro is stored in the storage unit of the arithmetic device 45. Note that the membrane resistance Ro of the electrolyte membrane 101 is a convergent value that converges when the frequency generated in the output signal of the cell 10 is increased under high humidity conditions, that is, a high-frequency side arc shape indicated by a Cole-Cole plot. Corresponds to the real part Zr of the AC impedance Z when the trajectory and the axis of the real part Zr intersect.

  When the control routine shown in FIG. 8 is executed after performing the above-described preprocessing, an AC signal having a reference frequency fo stored in the storage unit of the arithmetic unit 45 is generated in the output signal of the cell 10, and the current sensor 41 And the detection signal of the voltage sensor 42 is read (S10). Based on the detection signals of the sensors 41 and 42, the AC impedance Zo of the cell 10 at the reference frequency fo is calculated (S20).

  Next, based on the real part Zro and the imaginary part Zio of the AC impedance Zo calculated in S20, a resistance component variation ΔZ caused by drying is calculated (S30). Specifically, the total value (Zro + Zio) of the real part Zro (≧ 0) and the imaginary part Zio (≦ 0) of the AC impedance Zo at the reference frequency fo is calculated as the resistance component change amount ΔZ.

  When the membrane resistance Ro of the electrolyte membrane 101 cannot be ignored with respect to the change amount ΔZ of the resistance component, the membrane resistance Ro calculated in the preprocessing from the total value of the real part Zro and the imaginary part Zio of the AC impedance Zo. A value obtained by subtracting may be used as the resistance component change amount ΔZ.

  Next, an AC signal of the measurement frequency f in the low frequency band lower than the reference frequency is generated in the output signal of the cell 10, and the AC impedance Z of the cell 10 at the measurement frequency f is calculated (S40). The measurement frequency f can be set to an arbitrary frequency within a low frequency band lower than the reference frequency fo. The measurement frequency f is preferably set to a frequency at which the change in the hydrogen concentration Cs is large.

  Next, the correction impedance Z ′ is calculated by subtracting the resistance component variation ΔZ calculated in S30 from the real part Zr of the AC impedance Z calculated in S40 (S50).

  As a result, as shown in FIG. 9, the locus (solid line) of the Cole-Cole plot of the corrected impedance Z ′ is the amount of change in the resistance component with respect to the locus (dashed line) of the Cole-Cole plot of the AC impedance before correction. This translates to the low resistance side by ΔZ. In the correction impedance Z ′, the real part Zr ′ is Zr− (Zro + Zio), and the imaginary part Zi ′ is Zi.

  Next, after calculating the corrected impedance Z ′ calculated in S50, the hydrogen gas concentration Cs (hydrogen concentration) is calculated (S60). The gas concentration Cs of hydrogen can be calculated by substituting the corrected impedance Z ′ calculated in S50 for the AC impedance Z expressed by Equation 1 described above.

  Next, it is determined whether to change the measurement frequency f to calculate the hydrogen concentration (S70). If it is determined in this determination that the measurement frequency f is changed to calculate the hydrogen concentration (S70: YES), the process proceeds to S80, where the measurement frequency f is changed, and the process returns to S40. On the other hand, when it is determined not to calculate the hydrogen concentration by changing the measurement frequency f (S70: NO), the process returns to the main control routine.

  In the main control routine, when the control routine of FIG. 8 is called at predetermined intervals, the execution timing of the processing of S30 (calculation processing of AC impedance Zo at the reference frequency) and the processing of S60 (calculation processing of gas concentration Cs) is shown in FIG. As shown in FIG. 10, after the process of S30 is completed, the process of S60 is executed a plurality of times.

  In the present embodiment described above, the AC impedance Z is corrected based on the resistance component change amount ΔZ caused by drying in the cells 10 of the fuel cell 1. Then, the hydrogen gas concentration Cs of the cell 10 is calculated using the corrected AC impedance Z ′ (corrected impedance).

  As described above, by correcting the AC impedance that changes due to drying in the cell 10 of the fuel cell 1, it is possible to suppress the deviation between the measured value and the measured value of the hydrogen gas concentration Cs in the cell 10, It becomes possible to improve the measurement accuracy of the hydrogen gas concentration Cs.

(Other embodiments)
As mentioned above, although embodiment of this invention was described, this invention is not limited to this, Unless it deviates from the range described in each claim, it is not limited to the wording of each claim, and those skilled in the art Improvements based on the knowledge that a person skilled in the art normally has can be added as appropriate to the extent that they can be easily replaced. For example, various modifications are possible as follows.

  (1) In the above-described embodiment, the arithmetic device 45 of the gas concentration measuring device 40 and the control device 50 of the fuel cell system are configured separately, but the arithmetic device 45 and the control device 50 are used as a common control means. It may be integrated.

  (2) In the above-described embodiment, the correction impedance Z ′ is configured to calculate the hydrogen concentration in the cell 10 using the theoretical formula shown in Equation 1, but is not limited thereto. For example, a control map that associates the corrected impedance with the hydrogen concentration in the cell 10 may be prepared in advance, and the hydrogen concentration Cs in the cell 10 may be calculated with reference to the control map.

  (3) In the arithmetic unit 45 of the above-described embodiment, the calculation process of the gas concentration Cs is executed a plurality of times after the calculation process of the AC impedance Zo at the reference frequency fo is completed. The calculation process of the gas concentration Cs may be executed once after the calculation process of the AC impedance Zo at the frequency fo is completed.

  (4) In the above-described embodiment, the gas concentration measuring device 40 is configured to measure the hydrogen concentration Cs in the cell 10 of the fuel cell 1, but the oxygen concentration in the cell 10 of the fuel cell 1 is measured. Also good.

  (5) In the above-described embodiment, the gas concentration measuring device 40 is applied to the fuel cell system. However, the gas concentration measuring device 40 is not limited to the fuel cell system, and the electrolyte is sandwiched between a pair of electrodes. It can be applied to various electrochemical devices including electrochemical cells in which the resistance component of the internal impedance Z changes by drying.

10 Electrochemical cell 101 Electrolyte membrane (electrolyte)
102 Hydrogen electrode (anode electrode)
103 Air electrode (cathode electrode)
41 Current sensor (current detection means)
42 Voltage sensor (voltage detection means)
43 Oscillation circuit (AC signal generating means)
44 Signal processing circuit (impedance calculation means)
45 arithmetic unit 45a impedance correction means 45b gas concentration calculation means

Claims (1)

A gas concentration measuring device for measuring a gas concentration (Cs) of a reaction gas supplied into an electrochemical cell (10) in which an electrolyte (101) is held between a pair of electrodes (102, 103),
Current detection means (41) for detecting the output current of the electrochemical cell (10);
Voltage detection means (42) for detecting the output voltage of the electrochemical cell (10);
AC signal generating means (43) for generating an AC signal having an arbitrary frequency as an output signal of the electrochemical cell (10);
Impedance calculating means (44) for calculating an alternating current impedance (Z) of the electrochemical cell (10) based on the output current and the output voltage when the alternating signal is generated in the output signal;
Impedance correction means (45a) for correcting the AC impedance (Z) calculated by the impedance calculation means (44);
Gas concentration calculation means (45b) for calculating the gas concentration of the reaction gas based on the corrected impedance (Z ′) corrected by the impedance correction means (Z),
The impedance correction means (45a)
When the frequency of the AC signal generated in the output signal is changed from a high frequency to a low frequency, the peak of the arc-shaped locus formed by the real part and the imaginary part of the AC impedance (Z) on the high frequency side is reached. The frequency obtained by setting the reference frequency (fo) as the reference frequency (fo), and adding the real part (Zro) and imaginary part (Zio) of the AC impedance (Zo) at the reference frequency (fo) to the sum (Zro + Zio) Calculated as a change amount (ΔZ) of the resistance component due to drying inside the cell (10), and the total value (Zro + Zio) is a real part of the AC impedance in a low frequency band lower than the reference frequency (fo) ( A gas concentration measuring device for correcting the AC impedance in the low frequency band by subtracting from Zr) .

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