JP2009064617A - Equivalent circuit model of fuel cell and characteristic evaluation method of fuel cell - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a characteristic evaluation method of a fuel cell using an equivalent circuit model, which expresses characteristics of the fuel cell as an electrical circuit easily available in simulation software. <P>SOLUTION: The characteristic evaluation method of a fuel cell evaluates electrical characteristics of the fuel cell by fitting the fuel cell to an equivalent circuit model. In the equivalent circuit model, a plurality of circuits each of which is formed by connecting a resistor and a capacitor in parallel are connected in series, and, the resistor is a nonlinear resistor whose resistance value varies as a function of an electric current flowing in the resistor. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a fuel cell, and more particularly to an equivalent circuit model of a fuel cell and a characteristic evaluation method for evaluating electrical characteristics of the fuel cell using the equivalent circuit model.

  In recent years, fuel cells have attracted attention as one of new energy sources. Fuel cells do not depend on the natural environment and have the advantage of being able to supply stable power, but on the other hand, there is a problem that the output voltage fluctuates due to load fluctuations and cannot be regarded as a constant voltage source. . Therefore, when designing a system using a fuel cell, the influence of load fluctuations must be taken into account. Although there is a method of trial and error using an actual fuel cell device as a system design method, since the actual fuel cell device is expensive, a method using simulation software is efficient. And when performing simulation, an equivalent circuit model of a fuel cell is required. In addition, the following patent document 1 is mentioned as a prior art document relevant to this invention.

JP 2007-66589 A

  At present, however, several equivalent circuit models of fuel cells have been proposed, but none have been established yet. Therefore, the problem to be solved by the present invention is to provide an equivalent circuit model capable of expressing the characteristics of a fuel cell as an electric circuit that is easy to use with simulation software, and a method for evaluating the characteristics of a fuel cell using the equivalent circuit model.

  In order to solve the above problems, the equivalent circuit model of the fuel cell according to the present invention includes a plurality of circuits in which a resistor and a capacitor are connected in parallel connected in series, and the resistor is a function of a current flowing through the resistor. As a gist, it is a non-linear resistance whose resistance value changes.

  In this case, the resistance value of the resistor may be changed as a quadratic function of the current flowing through the resistor. Further, it is preferable that five circuits in which the resistor and the capacitor are connected in parallel are connected in series.

  Further, the fuel cell characteristic evaluation method according to the present invention is a fuel cell characteristic evaluation method for evaluating electrical characteristics of a fuel cell by performing fitting to an equivalent circuit model, and the equivalent circuit model includes: A gist is that a plurality of circuits in which a resistor and a capacitor are connected in parallel are connected in series and incorporated, and the resistor is a non-linear resistor whose resistance value changes as a function of a current flowing through the resistor.

  In this case, the resistance value of the resistor may be changed as a quadratic function of the current flowing through the resistor. Further, it is preferable that five circuits in which the resistor and the capacitor are connected in parallel are connected in series.

  Further, a first step of connecting a load to the fuel cell, and changing the waveform of the current flowing through the load so as to be a sine wave around a predetermined current value, and changing the frequency of the sine wave to A second step of measuring the frequency characteristic of the impedance of the load; a third step of measuring the second step by changing the magnitude of the predetermined current value of the first step; A fourth step of fitting the parameters of the equivalent circuit model based on the load current and voltage may be provided.

  According to the present invention having the above configuration, as an equivalent circuit model, a circuit in which a plurality of resistors and capacitors are connected in parallel is used in series, and the resistance value changes as a function of the current flowing through the resistor. For example, a load is connected to the fuel cell, and the waveform of the current flowing through the load is changed so as to be a sine wave around a predetermined current value, and the frequency of the sine wave at that time The electrical characteristics of the fuel cell can be evaluated by performing fitting to an equivalent circuit model so that the frequency characteristics of the impedance of the load measured by changing can be expressed. In addition, the electrical characteristics of the fuel cell are evaluated by fitting to an equivalent circuit model so that the frequency characteristics of the impedance of the load measured when the predetermined current value at the center of the sine wave is changed can also be expressed. can do. This makes it possible to express the characteristics of the fuel cell as an electric circuit that is easy to use with simulation software.

  Embodiments of a fuel cell equivalent circuit model and a fuel cell characteristic evaluation method using the same according to the present invention will be described below in detail with reference to the drawings.

1. Measurement of Fuel Cell Characteristics FIG. 1A shows an experimental apparatus 2 that measures the steady characteristics of the fuel cell 1. As shown in FIG. 1A, the steady characteristics of the fuel cell 1 are measured by connecting a resistor R as a load 3 to the output terminal of the fuel cell 1 and measuring the output current I and voltage V of the fuel cell 1.

FIG. 1B shows an experimental apparatus 4 that measures the frequency characteristics of the fuel cell 1. The frequency characteristic of the fuel cell 1 is measured by connecting a FET 5 as shown in FIG. 1B and a load 5 having a resistor R, and using the fuel cell 1 as a current source to generate a current i _D flowing through the resistor R. Control and measure. In actual measurement, the command value v ₁ in FIG. 1B gives a sine wave with an offset. Note that oxygen / hydrogen supplied to the fuel cell 1 and water to be generated are omitted.

  The output current I and voltage V of the fuel cell 1 in a steady state are measured using the experimental apparatus 2 in FIG. The measurement uses the resistance R as the load 3 in FIG. 1A and measures the output current I and voltage V of the fuel cell 1 at various resistance values. The measurement results are shown in FIG.

  As shown in FIG. 2, the output voltage V gradually decreased as the output current I was increased. Further, as the output current I is increased, the current value becomes constant, and the output voltage V decreases rapidly. It has been experimentally found that this is because sufficient power cannot be generated due to a shortage of oxygen and hydrogen supplied to the fuel cell 1. Therefore, in the experiment, measurement was performed in a region where oxygen and hydrogen were not insufficient.

  As shown in FIG. 2, in the region where the output current I of the fuel cell 1 is about 0.4 to 1.0 A, the output current I and the output voltage V can be regarded as having an approximately linear relationship. it can. Therefore, in the embodiment of the fuel cell characteristic evaluation method according to the present invention, the region where the current flowing through the resistor R is 0.4 to 1.0 A is targeted.

Next, the frequency characteristic of the fuel cell 1 is measured using the experimental apparatus 4 in FIG. In this case, the frequency characteristic is an impedance characteristic when the current and voltage on the load 5 side are changed in a sine wave shape and the frequency of the sine wave is changed variously. The experimental apparatus 4 in FIG. 1B controls the impedance of the load 5 by inputting the command voltage v ₁ between the gate and source of the FET and controlling the current flowing through R. As a result, a continuous impedance change is possible.

Variables of the current i _D to be controlled include I _pp corresponding to the peak-to-peak of the sine wave shown in FIG. 3 and I _ofs corresponding to the offset, and the characteristics are examined by changing them. The impedance Z _sin is calculated from the ratio of the fundamental wave component (v _sin , i _{D sin} ) of the sine wave fluctuation of the output voltage v of the fuel cell 1 and the current i _D as shown in the equation (1).

_First, the constant _{I ofs,} in order to examine the frequency characteristics when changing the _{I p-p,} the _{I ofs} and 0.60A _constant, 0.20A and _{I p-p,} 0.40A, 0.60A Four characteristics were measured at 0.80A. The measurement results are shown in FIG. From the results of FIG. 4, it can be seen that there is no significant change in the frequency characteristics even when I _p-p is changed.

_Next, in the constant _{I p-p,} to examine the frequency characteristics in the case of changing the _{I ofs,} and 0.20A constant _{I p-p,} 0.40A and _{I ofs,} 0.60A, 0 Four characteristics were measured as .80A and 1.00A. The measurement results are shown in FIG. From the results of FIG. 5, it can be seen that the characteristics are almost the same even if I _ofs is changed in a band of 10 Hz or more. On the other hand, it can be seen that in the low frequency region of 10 Hz or less, the impedance Z _sin increases as I _ofs decreases.

2. Construction of an Equivalent Circuit Model for a Fuel Cell First, FIG. 6 shows a conventional equivalent circuit model 6 for a fuel cell. Then, showing the frequency characteristics when using an appropriate value for the parameter of the equivalent circuit model 6 experiments _{(I p-p = 0.20A,} I ofs = 0.60A) with Figure 7. FIG. 7 shows that the conventional equivalent circuit model 6 cannot be expressed in the high frequency region. Therefore, it is necessary to construct a new equivalent circuit model.

Frequency characteristic of FIG. 4 and FIG than 5 experimental results, the fuel cell 1 in any condition, the impedance Z _sin is constant in the following approximate 1Hz low frequency region, decreases as the frequency increases, and 0Ω at approximately 100kHz It has become a characteristic. From this result, it can be seen that the equivalent circuit model of the fuel cell is constituted by only RC parallel when expressed by an electric circuit.

Indeed experiments the frequency characteristic of RC parallel first stage in FIG. _{8 (I p-p = 0.20A} , I ofs = 0.60A) together with. However, appropriate values were used for the parameters. FIG. 8 shows that the reduction rate of the impedance Z _{sin in} a band of about 10 Hz or more cannot be expressed sufficiently in one RC parallel stage. In this case, even if the parameter value is changed, the cut-off frequency only changes and the reduction rate of the impedance Z _sin does not change, and the characteristic cannot be expressed. For this reason, the RC parallel is changed from one stage to a plurality of stages, the reduction interval of the impedance Z _sin is considered as a distribution constant, and the characteristic is expressed by setting the cutoff frequencies of the RC parallel to different values.

The decrease rate of the impedance Z _sin is about −0.067Ω / decade on average as shown in FIG. 9 from the experimental results. It can be seen that the RC parallel cut-off frequency needs to be about every 5.6 times in order to realize this reduction rate. Further, the interval between the maximum cutoff frequency (f _{c max} ) and the minimum cutoff frequency (f _{c min} ) is about 2 decades. Therefore, at least five cut-off frequencies are required. From these, as an equivalent model of the fuel cell, an RC parallel 5-stage equivalent circuit model 7 as shown in FIG. 10 is proposed.

Appropriate parameters in the equivalent circuit model 7 shown in FIG. 10 are calculated. There are three types of parameters: capacitors C _{a to} C _e , resistors R _{a to} R _e , and electromotive force E. First, the combined impedance of the equivalent circuit model 7 of FIG. 10 is calculated, parameters are obtained by trial and error so as to match the experimental results, and regularity is derived from the results.

First, capacitors C _{a to} C _e are calculated. It was found that the values of the capacitors C _{a to} C _e did not change substantially under any condition. Therefore, the value of the capacitor C _a -C _e was using the average value of C _a -C _e values each trial and error determined in various conditions. Specifically, C _a = 0.375F, C _b = 0.1275F, C _c = 0.03F, C _d = 0.003625F, and C _e = 0.0005F.

Next, the resistances R _{a to} R _e are calculated. The values of the resistors R _{a to} R _e are all set to the same value for simplification of calculation. Resistance _R a to R _e has been found that the resistance _R a value by the current _{i D} flowing through to R _e is changed. It has also been found that the resistances R _{a to} R _e and the current i _D are approximately quadratic functions. Therefore, the resistance R _a to R _e is assumed to change the resistance value as a function of the current i _D, is determined as equation (2). Therefore, in the simulation, the resistances R _{a to} R _e are used as nonlinear resistances, and the equation is determined as an expression that is differentiated by the current i _D flowing through the resistances R _{a to} R _e as shown in Equation 2. The resistors R _{a to} R _e are each expressed as R (i _D ) as shown in Equation 3. R (i _D ) is a quadratic function of the current i _D.

Finally, the electromotive force E is calculated. First, the integral of equation Equation 2 at a current i _D in equation (4). Since the value of the integral constant can be set to an arbitrary value in consideration of the calculation method of the electromotive force E, it is set to 0 this time for simplification of calculation. The Formula 4, it is found possible to determine uniquely the value of the voltage drop across each of the resistors _R a to R _e is the value of the resistor _R a to R current flowing through the _{e i D.}

In calculating the electromotive force E, it is necessary to express the steady characteristics of the fuel cell shown in FIG. Therefore, an equivalent circuit model 8 of the fuel cell 1 in a steady state is shown in FIG. As can be seen from FIG. 11, when the flowing current I is determined, the voltage drop across the resistor R is uniquely determined from Equation 4, and the output voltage of the fuel cell 1 is uniquely determined from FIG. Therefore, the electromotive force E is uniquely determined as E = V−5v _R by the flowing current. As a result, as a result of investigating the relationship between the current i _D and the electromotive force E, it was found that the equation can be approximately obtained as in Expression 5.

FIGS. 12 and 13 show the simulation results of the steady state characteristic and the frequency characteristic of the equivalent circuit model 7 using the parameters obtained as described above. As shown in FIG. 12, in the steady characteristics, the simulation result can be expressed so as to match the measurement result of FIG. Further, as shown in FIG. 13, the simulation result can be expressed like the measurement result of FIG. In particular, using a resistance R _a to R _e in the equivalent circuit model 7 shown in FIG. 10 as a nonlinear resistance, by determining the expression of differentiation by the current i _D flowing through the resistor R _a to R _e as equation 2 the _{I p-p} in Fig. 5 and 0.20A _constant, 0.40A and _{I ofs,} 0.60A, 0.80A, the measurement results of the four types that the 1.00A, the simulation results of FIG. 13 can be expressed ing.

3. Usefulness of Equivalent Circuit Model Simulate that the proposed equivalent circuit model 7 and the calculated parameters are useful. The simulation is performed for a step change including steady characteristics and various frequency components. The experiment measured the voltage response when the load resistance value was stepped from 0.6Ω to 1.5Ω. The simulation was performed under the same conditions as in the experiment. The experimental results are shown in FIG. 14 and the simulation results are shown in FIG.

  14 and 15, the steady state is within the error of the measurement result, so that the characteristics of the fuel cell can be expressed. Further, since the time constant is substantially the same in the transient state, the characteristics of the fuel cell can be expressed.

  The embodiments of the equivalent circuit model of the fuel cell and the method of evaluating the characteristics of the fuel cell using the fuel cell according to the present invention have been described above. However, the present invention is not limited to these embodiments, and Needless to say, various embodiments can be implemented without departing from the scope of the invention.

(A) is the experimental apparatus which measures the steady state characteristic of the fuel cell which concerns on this invention, (b) is the figure which showed the experimental apparatus which measures the frequency characteristic of the fuel cell which concerns on this invention. It is the figure which showed the measurement result of the experimental apparatus of Fig.1 (a). Is a diagram showing the output current i _D of the fuel cell which is controlled sinusoidally by the load of the experimental apparatus of FIG. 1 (b). Is a view showing a measurement result of I _ofs fixed · I _p-p changes upon the frequency characteristic of the output current i _D of the fuel cell in the test device of FIG. 1 (b). Is a view showing a measurement result of I _p-p fixed · I _ofs change when the frequency characteristic of the output current i _D of the fuel cell in the test device of FIG. 1 (b). It is the figure which showed the equivalent circuit model of the fuel cell conventionally used. FIG. 7 is a diagram illustrating the experimental result of FIG. 4 together with the simulation result of the equivalent circuit model of FIG. 6. FIG. 8 is a diagram illustrating the experimental result of FIG. 4 together with the simulation result when the RC circuit of the equivalent circuit model of FIG. It is a figure used for the setting of the stage number of RC circuit of the equivalent circuit model of this invention. It is the figure which showed the equivalent circuit model of the fuel cell which concerns on this invention. It is the figure which showed the equivalent circuit model of the fuel cell in a stationary characteristic. It is the figure which showed the experimental result of FIG. 2 with the simulation result of the equivalent circuit model of FIG. It is the figure which showed the experimental result of FIG. 5 with the simulation result of the equivalent circuit model of FIG. It is the figure which showed the measurement result which measured the voltage response at the time of changing the value of the load resistance connected to the fuel cell in steps. It is the figure which showed the simulation result which simulated the voltage response at the time of changing the value of the load resistance connected to the equivalent circuit model of FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Fuel cell 2 Stationary characteristic measurement experimental apparatus 3 Stationary characteristic measurement load 4 Frequency characteristic measurement experimental apparatus 5 Frequency characteristic measurement load 6 Conventional circuit equivalent circuit model 7 Fuel cell equivalent circuit model 8 of the present invention Equivalent circuit model in steady state of fuel cell

Claims (7)

  An electric equivalent circuit model of a fuel cell, wherein a plurality of circuits in which a resistor and a capacitor are connected in parallel are incorporated in the equivalent circuit model, and the resistor is a function of a current flowing through the resistor. An equivalent circuit model of a fuel cell, which is a non-linear resistance whose resistance value changes as follows.   2. The fuel cell equivalent circuit model according to claim 1, wherein a resistance value of the resistor changes as a quadratic function of a current flowing through the resistor. 3.   The equivalent circuit model of the fuel cell according to claim 1 or 2, wherein five circuits in which the resistor and the capacitor are connected in parallel are connected in series.   A fuel cell characteristic evaluation method for evaluating electrical characteristics of a fuel cell by performing fitting to an equivalent circuit model, wherein a plurality of circuits in which a resistor and a capacitor are connected in parallel are connected in series in the equivalent circuit model And the resistance is a non-linear resistance whose resistance value changes as a function of the current flowing through the resistance.   5. The fuel cell characteristic evaluation method according to claim 4, wherein a resistance value of the resistor changes as a quadratic function of a current flowing through the resistor.   6. The fuel cell characteristic evaluation method according to claim 4, wherein five circuits in which the resistor and the capacitor are connected in parallel are connected in series.   A first step of connecting a load to the fuel cell, and changing a waveform of a current flowing through the load so as to be a sine wave around a predetermined current value; and changing a frequency of the sine wave to A second step of measuring the frequency characteristic of the impedance; a third step of measuring the second step by changing the magnitude of the predetermined current value of the first step; and a measured load 7. The method for evaluating characteristics of a fuel cell according to claim 4, further comprising a fourth step of fitting a parameter of the equivalent circuit model based on a current and a voltage.

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