JP2014044106A - Equivalent circuit analysis device, and equivalent circuit analysis method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To calculate respective parameter values of an equivalent circuit including an inductor.SOLUTION: An equivalent circuit analysis method includes: actual value measurement processing for measuring respective component measured values of real numbers and imaginary numbers of impedance of a measurement object at respective frequencies; first impedance calculation processing for calculating an inductance value of an inductor from an imaginary-number component measured value at a specific frequency; correction processing for calculating reactances at respective frequencies from the inductance value and correcting imaginary-number component measured values at the respective frequencies; fitting processing for calculating a half circle corresponding to an arcuate region of a Nyquist plot curve comprising real-number component measured values and corrected imaginary-number measured values; parameter value calculation processing for calculating respective parameter values of the equivalent circuit from the half circle; and second inductance calculation processing for calculating a new inductance value from an imaginary-number component logical value and an imaginary-number component measured value at the specific frequency with respect to a partial equivalent circuit of each parameter value. The new inductance value is used to perform the processing from the correction processing to the parameter value calculation processing again.

Description

  The present invention relates to an equivalent circuit analysis apparatus and an equivalent circuit analysis method for analyzing and calculating each parameter of an equivalent circuit such as a battery.

  As an equivalent circuit analysis method of this type, Patent Document 1 below measures the frequency characteristics of the internal impedance of the battery by the AC impedance method, and then, based on the measured frequency characteristics, the equivalent circuit of the battery (capacitor and Measure each parameter of a circuit model in which multiple unit circuits composed of parameters such as resistance are connected in series), and then calculate the frequency characteristics of impedance using an equivalent circuit to which each measured parameter is applied. In addition, the optimum value for each parameter of the equivalent circuit is determined by repeating a series of processes of adjusting each parameter of the equivalent circuit so that the frequency characteristic of the impedance for the calculated equivalent circuit approaches the measured frequency characteristic. An equivalent circuit analysis method (battery measurement method) is disclosed.

  Also, in this Patent Document 1, when an inductance component appears in the frequency characteristic for the measured internal impedance, that is, a Cole-Cole plot diagram showing the frequency characteristic for the internal impedance in a complex plane shows a positive reactance. If there is a region (region where the imaginary component value is a positive value), even if this inductance component is ignored and analysis is performed using only the capacitance component, a correct result cannot be obtained. The technical matter of analyzing by adding an inductor is disclosed.

JP2009-97878A (page 5-8)

  However, the above-described equivalent circuit analysis method has the following problems to be solved. In other words, this equivalent circuit analysis method discloses the technical matter of performing analysis by adding an inductor to an equivalent circuit model when an inductance component appears in the frequency characteristic of the measured internal impedance. However, there is a problem to be solved that it is difficult to calculate the value of each parameter including an inductance component because there is no disclosure of a specific adjustment method for adjusting each parameter in an equivalent circuit model to which ing.

  The present invention has been made to improve such a problem, and it is a main object of the present invention to provide an equivalent circuit analysis device and an equivalent circuit analysis method capable of reliably calculating each parameter value of an equivalent circuit including an inductor. .

  In order to achieve the above object, the equivalent circuit analysis apparatus according to claim 1 is an actual measurement of the impedance of a measurement object represented by an equivalent circuit in which a solution resistance and an inductor are connected in series to a parallel circuit of a capacitance and a charge transfer resistance. Based on the frequency characteristics, an actual value measurement process for measuring the actual component actual value and the imaginary component actual value of the impedance at each frequency, and an imaginary component actual value at a specific frequency on the high frequency side of the imaginary component actual value A first inductance calculation process for calculating an inductance value of the inductor based on the calculation value, a reactance at each frequency is calculated using the calculated inductance value, and the imaginary component actual measurement value at the corresponding frequency is calculated. Correction process that corrects the imaginary component actual measurement value at each frequency by applying the reactance and the real component Dots plotted in the orthogonal plane with the horizontal axis and the imaginary number component as the vertical axis, with the actual component measured value as the coordinate of the horizontal axis and the corrected imaginary component measured value as the coordinate of the vertical axis A semicircle corresponding to the arcuate region is calculated by a curve fitting method based on the measured actual number component value and the corrected imaginary component actual value of the dot included in the arcuate region in the Nyquist plot curve composed of The frequency at the actual measurement value of the imaginary component of the minimum of the actual measurement value of each real component at the two intersections of the fitting process and the horizontal axis of the calculated semicircle, and the corrected imaginary component measurement value A parameter value calculation process for calculating each parameter value of the capacitance, the charge transfer resistance and the solution resistance constituting the equivalent circuit based on the equivalent circuit; Calculating the imaginary component theoretical value of the impedance at the specific frequency of the partial equivalent circuit composed of the capacitance, the charge transfer resistance and the solution resistance of each calculated parameter value of the path, and the imaginary component theory And a second inductance calculation process for calculating a new inductance value of the inductor based on the measured value and the imaginary component actual measurement value at the specific frequency. The unit calculates the parameter value calculation process by executing the correction process, the fitting process, and the parameter value calculation process again by using the new inductance value calculated by the second inductance calculation process. Each parameter value of the capacitance, charge transfer resistance and solution resistance to be converged .

  The equivalent circuit analysis device according to claim 2 is the equivalent circuit analysis device according to claim 1, wherein the processing unit uses the new inductance value calculated in the second inductance calculation processing, and performs the correction processing, The fitting process, the parameter value calculation process, and the second inductance calculation process are repeated a predetermined number of times.

  The equivalent circuit analysis method according to claim 3 is based on an actually measured frequency characteristic of an impedance to be measured represented by an equivalent circuit in which a solution resistor and an inductor are connected in series to a parallel circuit of a capacitor and a charge transfer resistor. Based on the actual value measurement processing for measuring the real component actual value and the imaginary component actual value of the impedance at each frequency, and the imaginary component actual value at a specific frequency on the high frequency side of the imaginary component actual value, A first inductance calculation process for calculating an inductance value, and a reactance at each frequency is calculated using the calculated inductance value, and the calculated reactance is applied to the actual measurement value of the imaginary component at the corresponding frequency. Correction processing for correcting the imaginary component actual measurement value at each frequency and the horizontal component of the real component, and the imaginary number Nyquist plot composed of dots plotted in the orthogonal plane with the minute as the vertical axis, the actual component actual measurement value as the horizontal axis coordinate, and the corrected imaginary component actual measurement value as the vertical axis coordinate A fitting process for calculating a semicircle corresponding to the arcuate region by a curve fitting method based on the real component actual measurement value and the corrected imaginary component actual measurement value of the dot included in the arcuate region in a curve; and the calculation The equivalent circuit is configured based on each real component value at two intersections with the horizontal axis of the half circle and the frequency at the minimum measured imaginary component value of the corrected imaginary component measured value. A parameter value calculation process for calculating each parameter value of the capacitance, the charge transfer resistance, and the solution resistance; and the calculated parameters of the equivalent circuit. Calculates the imaginary component theoretical value of the impedance at the specific frequency of the partial equivalent circuit composed of the capacitance of the meter value, the charge transfer resistance and the solution resistance, and the imaginary component theoretical value of the partial frequency and the imaginary number at the specific frequency. An equivalent circuit analysis method for executing a second inductance calculation process for calculating a new inductance value of the inductor based on a component actual measurement value, wherein the new inductance value calculated in the second inductance calculation process is used. Then, by executing the correction process, the fitting process, and the parameter value calculation process again, the parameter values of the capacitance, the charge transfer resistance, and the solution resistance calculated in the parameter value calculation process are converged. .

  The equivalent circuit analysis method according to claim 4 is the equivalent circuit analysis method according to claim 3, wherein the correction process, the fitting process, and the like are performed using the new inductance value calculated in the second inductance calculation process. The parameter value calculation process and the second inductance calculation process are repeated a predetermined number of times.

  In the equivalent circuit analysis device according to claim 1 and the equivalent circuit analysis method according to claim 3, the second inductance calculation process is executed to calculate a new inductance value closer to the true inductance value. Using the new inductance value, the correction process, the fitting process, and the parameter value calculation process are executed again, and the solution resistance, charge transfer resistance, and capacitance parameter values that constitute the partial equivalent circuit are calculated again.

  Therefore, according to the equivalent circuit analysis device and the equivalent circuit analysis method, the parameter values of the solution resistance, charge transfer resistance, capacitance, and inductor constituting the equivalent circuit to be measured are converged to a value closer to the true value. Therefore, each parameter value can be measured with higher accuracy.

  According to the equivalent circuit analysis device according to claim 2 and the equivalent circuit analysis method according to claim 4, the correction process, the fitting process, and the parameter value calculation process are performed using the new inductance value calculated in the second inductance calculation process. , And the second inductance calculation process is performed a predetermined number of times (for example, a plurality of times of 3 times or more), so that the parameter values of the solution resistance, charge transfer resistance, capacitance, and inductor constituting the equivalent circuit to be measured can be obtained. Since it is possible to converge to a value closer to the true value, each parameter value can be measured with higher accuracy.

1 is a configuration diagram showing a configuration of an equivalent circuit analysis device 1. FIG. 3 is an equivalent circuit (circuit model) of the battery 11. The Nyquist plot showing the relationship between the real component (actual component measured value: R), the imaginary component (imaginary component measured value: X), and the frequency f of the impedance Z obtained from the measured impedance Z of the battery 11 of the equivalent circuit of FIG. A curve CU1 (curve indicated by a broken line), another Nyquist plot curve CU2 (curve indicated by a solid line) indicating the relationship between the actual value of the imaginary component measured by correcting the actual value of the imaginary component, the actual value of the actual component, and the frequency f It is a figure which shows the circle | round | yen A (circle shown with a dashed-dotted line) containing the semicircle corresponding to the circular arc-shaped area | region W in the Nyquist plot curve CU2 calculated by the fitting method. 5 is a flowchart of an equivalent circuit analysis process 50. The Nyquist plot curve CU1 (curve indicated by a broken line) created based on the real component (R) and imaginary component (X) of the impedance Z for the equivalent circuit shown in FIG. 2 measured in the actual value measurement process of the flowchart of FIG. And the Nyquist plot curve CU3 (curve shown by a solid line) of impedance Z calculated based on other parameter values of the equivalent circuit calculated using the inductance value L1 calculated in the first inductance calculation process of the flowchart of FIG. FIG. The Nyquist plot curve CU1 (curve indicated by a broken line) created based on the real component (R) and imaginary component (X) of the impedance Z for the equivalent circuit shown in FIG. 2 measured in the actual value measurement process of the flowchart of FIG. 4 and the Nyquist plot curve CU4 (curve shown by a solid line) of impedance Z calculated based on each parameter value of the calculated equivalent circuit by executing the correction process to the second inductance calculation process of the flowchart of FIG. 4 twice. FIG.

  Hereinafter, embodiments of an equivalent circuit analysis device 1 and an equivalent circuit analysis method will be described with reference to the accompanying drawings.

  First, the configuration of the equivalent circuit analysis apparatus 1 will be described with reference to the drawings. As an example, an equivalent circuit analysis apparatus 1 that calculates and analyzes each parameter of the equivalent circuit using a battery as a measurement target will be described as an example.

  As shown in FIG. 1, the equivalent circuit analysis apparatus 1 includes an alternating current supply unit 2, a current detection unit 3, a voltage detection unit 4, a processing unit 5, a storage unit 6, a display unit 7, and an operation unit 8. Each parameter of an equivalent circuit for a secondary battery (secondary battery such as a lithium ion battery or a lead storage battery) 11 is calculated and analyzed. In addition, since the equivalent circuit of a battery changes according to the kind etc. of a battery, the equivalent circuit about the battery 11 to be measured is selected in advance. In this example, as an example, as an equivalent circuit of the battery 11 to be measured, an equivalent circuit shown in FIG. 2, that is, a resistance component 21 (resistance value Rs) as a solution resistance and a resistance component 22 (resistance value) as a charge transfer resistance. R1) and a capacitance component 23 as a capacitor (in this example, it is a CPE (Constant Phase Element) as an example, but it may be a capacitor) and an inductor 24 (inductance value L1) are connected in series. An equivalent circuit is selected.

  As an example, the alternating current supply unit 2 includes an alternating current source. In the AC current supply unit 2, the AC constant current source generates an AC current (AC constant current) I 1 having a constant amplitude at a frequency f designated by the processing unit 5 and supplies the generated current to the battery 11. The AC current supply unit 2 adopts a configuration that generates an AC current I1 having an amplitude specified by the processing unit 5 and a configuration that generates an AC current I1 by superimposing a DC component specified by the processing unit 5. You can also The current detection unit 3 includes an A / D conversion circuit (not shown), detects the AC current I1 supplied from the AC current supply unit 2 to the battery 11, and detects the AC current I1 detected in the A / D conversion circuit. Is converted into current waveform data Di and output to the processing unit 5 by sampling at a predetermined sampling cycle.

  The voltage detection unit 4 detects the AC voltage V1 generated between both ends of the battery 11 due to the supply of the AC current I1, and the waveform thereof is set to a predetermined sampling period (same as the sampling period of the current detection unit 3). And in a synchronized cycle), the voltage waveform data Dv is converted and output to the processing unit 5.

  The processing unit 5 includes a CPU, and as an example, an equivalent circuit analysis process including a measured value measurement process, a first inductance calculation process, a correction process, a fitting process, a parameter value calculation process, and a second inductance calculation process. (Refer to FIG. 4) is executed to calculate parameter values (resistance value Rs, resistance value R1, parameter values p and T described later of CPE, and inductance value L1) for each component of the equivalent circuit. In addition, the processing unit 5 executes display processing for displaying the calculated parameter values on the display unit 7.

  As an example, the storage unit 6 includes a semiconductor memory such as a RAM and a ROM, and an HDD (Hard Disk Drive), and stores an operation program for the processing unit 5 in advance. The storage unit 6 also functions as a work memory for the processing unit 5.

  The display unit 7 is configured by a display device such as a liquid crystal display as an example, and displays numerical values and graphs calculated by the processing unit 5 on the screen.

  The operation unit 8 includes, for example, a numeric key and a plurality of command keys (none of which are shown), and commands that indicate instruction contents assigned in advance to each command key when the command key is operated. Data Dcm is output to the processing unit 5. In addition, when the numerical key is operated, the operation unit 8 outputs the numerical data Dnu specified by the operation of the numerical key to the processing unit 5. In this example, as the numerical data Dnu, the lower limit value fmin and the upper limit value fmax of the frequency f to be swept in the measured value measurement process, and the number of repetitions of repeating the correction process, the fitting process, the parameter value calculation process, and the second inductance calculation process A numerical value indicating n (an integer of 2 or more) is output.

  Next, the analysis operation and equivalent circuit analysis method of the equivalent circuit analysis apparatus 1 will be described with reference to the drawings.

  In the equivalent circuit analysis apparatus 1, the processing unit 5 first repeatedly detects whether or not the command data Dcm is output from the operation unit 8, and the instruction content indicated by the detected command data Dcm is the lower limit value fmin, When an instruction to fetch the upper limit value fmax and the number of repetitions n is given, numerical data Dnu (numerical data indicating the lower limit value fmin, the upper limit value fmax and the number of repetitions n) output from the operation unit 8 is input and the numerical data Dnu is stored in the storage unit 6.

  Further, when the instruction content indicated by the detected instruction data Dcm is an instruction to start analysis, the processing unit 5 executes an equivalent circuit analysis process 50 shown in FIG. In the equivalent circuit analysis process 50, the processing unit 5 first executes an actual value measurement process (step 51). In this actual value measurement process, the processing unit 5 reads the lower limit value fmin and the upper limit value fmax of the frequency f from the storage unit 6 and designates the frequency f (fmin ≦ f ≦ fmax) for the alternating current supply unit 2. Thus, the alternating current I1 having the designated frequency f is supplied to the battery 11 to be measured. In a state where the alternating current I1 is supplied to the battery 11, the current detection unit 3 outputs current waveform data Di indicating the waveform of the alternating current I1 to the processing unit 5, and the voltage detection unit 4 detects the alternating current I1. The AC voltage V1 generated between both ends of the battery 11 due to the supply is detected, converted into voltage waveform data Dv, and output to the processing unit 5.

  The processing unit 5 acquires the current waveform data Di and the voltage waveform data Dv, for example, for one period, and stores them in the storage unit 6. Subsequently, based on the current waveform data Di and the voltage waveform data Dv stored in the storage unit 6, the processing unit 5 determines the impedance Z (the real component (R) of the impedance Z) for the battery 11 at the specified frequency f. And the imaginary component (X)) are calculated and stored in the storage unit 6 as the real component actual measurement value and the imaginary component (X) as the imaginary component actual measurement value corresponding to the designated frequency f. Let

  The processing unit 5 sequentially changes (for example, increments by unit frequency) from the lower limit value fmin to the upper limit value fmax (for example, from 0.1 Hz to 10 kHz) while sequentially changing the frequency f specified for the alternating current supply unit 2. The real number component (R) and the imaginary number component (X) of the impedance Z at the designated frequency f are calculated, and the measured real number component and the imaginary number component are stored in the storage unit 6 in correspondence with the frequency f. It memorizes as an actual measurement value. Thereby, the actual measurement process is completed.

  Next, the processing unit 5 executes a first inductance calculation process (step 52). In the first inductance calculation process, the processing unit 5 uses a specific frequency on the high frequency side of the imaginary component measurement values at each frequency f stored in the storage unit 6 (in this example, the upper limit value fmax as an example). The inductance value L1 of the inductor 24 is calculated based on the actual imaginary component measured value and stored in the storage unit 6.

In general, as in the equivalent circuit of the battery 11 shown in FIG. 2, the impedance Z _CPE of the CPE in the equivalent circuit including the CPE as the capacitance component 23 in the state of being connected in parallel with the resistance component 22 is represented by the following formula ( 1).
Z _CPE = 1 / [(jω) ^p × T]
Here, p = 1− (2 / π) × cos ⁻¹ (Cx / r), T = 1 / (ω ^p × R1), ω = 2π × fp (1)
Cx is a central coordinate on an orthogonal coordinate plane (complex plane) in which a horizontal axis is a real component (R) of a circle (a circle A described later) calculated in the fitting process and an ordinate is an imaginary component (X). This is the real component value of (Cx, Cy), and r represents the radius of this circle. Further, the frequency fp is a frequency at a minimum point in the Nyquist plot curve to which the fitting process is applied (dot P3 at which an imaginary number component actual measurement value in the Nyquist plot curve CU2 in FIG. 3 to be described later is minimum).

Moreover, said Formula (1) is also represented like the following formula (2) by dividing into a real number component and an imaginary number component.
Z _CPE = 1 / (ω ^p × T) × cos (π × p / 2)
−j × 1 / (ω ^p × T) × sin (π × p / 2) (2)

Therefore, the impedance Z _TOTAL of the entire equivalent circuit of FIG.
Z _TOTAL = jωL1 + Rs + 1 / (1 / R1 + 1 / Z _CPE )
= Z ' _TOTAL -jZ " _TOTAL (3)
Here, Z ′ _TOTAL = Rs + {R1 × [1 / ω ^2p + 1 / ω ^p × T × R1 × cos (π × p / 2)]} / [1 / ω ^2p + 2 / ω ^p × T × R1 × cos (π × p / 2) + (T × R1) ² ] (4)
Z " _TOTAL = R1 * [1 / [omega] ^p * T * R1 * sin ([pi] * p / 2)] / [1 / [omega] ^2p + 2 / [omega] ^p * T * R1 * cos ([pi] * p / 2) + ( T × R1) ² ] −ωL1 (5)

For this reason, when the frequency f is sufficiently high, ω (= 2πf) also has a sufficiently large value, so that the numerator of the second term in the above equation (4) can be regarded as almost zero. (4) can be approximated by the following equation (6). Similarly, the numerator of the first term in the above formula (5) can be regarded as almost zero, and this formula (5) can be approximated as the following formula (7).
Z ' _TOTAL ≒ Rs (6)
Z " _TOTAL ≒ -ωL1 (7)

Therefore, in the first inductance calculation process, the processing unit 5 sets the upper limit value fmax of the frequency f as the most preferable specific frequency on the high frequency side as described above, and the imaginary component measurement value (Z " _TOTAL at the upper limit value fmax). ) And ω (= 2π × fmax), the inductance value L1 (= _−Z ″ _TOTAL / ω) of the inductor 24 is calculated from the above equation (7). Note that the configuration using the upper limit value fmax of the frequency f is adopted as the most preferable specific frequency on the high frequency side. However, if ω (= 2πf) is a sufficiently large value, the high frequency other than the upper limit value fmax is used. A configuration in which the frequency on the side is used as the specific frequency can also be employed.

  Subsequently, the processing unit 5 executes a correction process (step 53). In this correction process, the processing unit 5 calculates the reactance (ωL1) at each frequency stored in the storage unit 6 by using the inductance value L1 calculated in the first inductance calculation process, and the corresponding frequency. By applying this reactance to the actual imaginary component measured value (specifically, adding), the actual imaginary component measured value at each frequency is corrected, and the actual measured imaginary component value at each frequency is stored in the storage unit 6. Remember. For example, when correcting the actual value of the imaginary component at the frequencies f1 and f2, the processing unit 5 calculates the reactance (2π × f1 × L1) at the frequency f1 when correcting the actual value of the imaginary component at the frequency f1. Then, correction is performed by applying (adding) to the actual value of the imaginary component, and when correcting the actual value of the imaginary component at the frequency f2, the reactance (2π × f2 × L1) at the frequency f2 is calculated. Then, correction is performed by applying (adding) to the actually measured value of the imaginary component.

In the equivalent circuit of the battery 11 shown in FIG. 2, the influence (ωL1) of the inductor 24 does not appear in the real component Z ′ _TOTAL of the impedance Z _TOTAL of the entire equivalent circuit as shown in the above equation (4). As shown in the equation (5), it appears as a negative term only in the imaginary component Z ″ _TOTAL . For this reason, in this correction process, the processing unit 5 calculates reactance (ωL1) at each frequency, and at the corresponding frequency. By adding this reactance (ωL1) to the actual value of the imaginary number component, it is possible to cancel the influence of the inductor 24 on the imaginary number component Z ″ _TOTAL . However, since L1 in the reactance (ωL1) used for the correction is calculated from the approximate expression represented by the above formula (7), the reactance is calculated from the imaginary component Z ″ _TOTAL represented by the formula (5). Although (ωL1) is not completely canceled, the influence of the inductor 24 on the imaginary component Z ″ _TOTAL is greatly reduced. For this reason, the actual component measured value at each frequency stored in the storage unit 6 and the corrected imaginary component measured value are equivalent circuits (hereinafter referred to as an equivalent circuit) in which the inductor 24 is omitted from the equivalent circuit of the battery 11 shown in FIG. It is considered that the actual component actual measurement value and the imaginary component actual measurement value at each frequency of the impedance for the “sub-equivalent partial circuit” are substantially represented.

  Subsequently, the processing unit 5 executes a fitting process (step 54). In this fitting process, as shown in FIG. 3, the processing unit 5 displays the actual measurement value of the real component in an orthogonal plane with the real component (R) on the horizontal axis and the imaginary component (X) on the vertical axis. The real number of dots included in the arcuate region W in the Nyquist plot curve CU2 (curve indicated by the solid line) composed of dots plotted with the imaginary component actual value corrected with the coordinate of the axis and the coordinate of the vertical axis Based on the component actual measurement value and the corrected imaginary component actual measurement value, a semicircle corresponding to the arcuate region W (in this example, a circle A including the arcuate region W) is converted into a curve fitting method (for example, the least square method). Curve fitting method using In this case, the calculated coordinates of the center O of the circle A are (Cx, Cy) and the radius is r. Note that a curve CU1 indicated by a broken line in FIG. 3 is a Nyquist plot curve composed of plots in which the actual component actual measurement value is the horizontal axis coordinate and the uncorrected imaginary component actual measurement value is the vertical axis coordinate. Represents.

  Next, the processing unit 5 executes a parameter value calculation process (step 55). In this parameter value calculation process, the processing unit 5 calculates the real component values at the two intersections P1 and P2 with the calculated horizontal axis of the circle A (the line segment where the imaginary component (X) in FIG. 3 is zero), and Based on the frequency fp of the minimum imaginary component actual measurement value (imaginary component actual measurement value at the dot P3) among the corrected imaginary component actual measurement values, the resistance component 21, the resistance component 22 and the capacitance component constituting the partial equivalent circuit 23, each parameter value (resistance value Rs, resistance value R1, p, T) is calculated.

Specifically, the processing unit 5 calculates the real component value at the intersection P1 as the resistance value Rs, and calculates a value obtained by subtracting the real component value at the intersection P1 from the real component value at the intersection P2 as the resistance value R1. Further, the processing unit 5 substitutes the real component value Cx of the center O of the circle A, the radius r of the circle A, the resistance value R1 of the resistance component 22, and the frequency fp into the above equation (1), and sets each parameter value. In addition to calculating p and T, Z _CPE is calculated.

  Subsequently, the processing unit 5 executes a second inductance calculation process (step 56). In the second inductance calculation process, the processing unit 5 uses the above formula (5) to calculate the theoretical value of the imaginary component of the impedance at the specific frequency of the partial equivalent circuit (in this example, the upper limit value fmax as described above). And a new inductance value L1 of the inductor 24 is calculated based on the calculated theoretical value of the imaginary number component and the actually measured value of the imaginary number component at the specific frequency, and is updated and stored in the storage unit 6.

In this case, the first term in the above equation (5) represents the imaginary component value of the impedance for the partial equivalent circuit. Therefore, the processing unit 5 first applies each parameter value (resistance value R1, frequency fmax, parameter value p, T) calculated in the parameter value calculation process to the first term in the equation (5), An imaginary component value of impedance (hereinafter, also referred to as “imaginary component theoretical value”) for the partial equivalent circuit is calculated. Next, the processing unit 5 subtracts the calculated imaginary component theoretical value from the imaginary component actual measurement value Z ″ _TOTAL at a specific frequency, and divides the value obtained by this subtraction by (−ω) to thereby generate the inductor 24. A new inductance value L1 (= − (Z ″ _TOTAL −imaginary component theoretical value) / ω) is calculated.

In the second inductance calculation process, the inductance value L1 of the inductor 24 is calculated from the imaginary component actual measurement value Z ″ _{TOTAL in} consideration of the value of the first term in the equation (5) as described above. Therefore, the inductance value L1 closer to the true inductance value L1 is calculated than when the inductance value L1 is calculated using the above equation (7) in which the value of the first term in the equation (5) is regarded as zero. It is possible.

  Next, the processing unit 5 determines whether or not the number of execution times of the second inductance calculation process has reached the number of repetitions (a predetermined number) n stored in the storage unit 6 (step 57). If not, the process returns to the correction process in step 53, and the correction process, the fitting process, the parameter value calculation process, and the second inductance calculation process are executed again using the new inductance value L1 calculated in the second inductance calculation process. As described above, the processing unit 5 performs the correction process, the fitting process, the parameter value calculation process, and the second inductance calculation process again by using the inductance value L1 that is closer to the true inductance value L1, and thereby the inductor 24 The inductance value L1 is converged to a value closer to the true inductance value L1, and the parameter values (Rs, R1, p, T) of the resistance component 21, the resistance component 22, and the capacitance component 23 constituting the partial equivalent circuit. Also, by calculating again using an inductance value L1 closer to the true inductance value L1, it is converged to a value closer to the true value (calculated with higher accuracy).

On the other hand, when it is determined in step 57 that the number of executions of the second inductance calculation process has reached the number of repetitions n, the processing unit 5 executes a display process (step 58). In this display process, the processing unit 5 calculates the calculated parameter values (resistance value Rs, resistance value R1, parameter values p, T, Z _{CPE for CPE} , and inductance value L1 (calculated in the last second inductance calculation process). The latest inductance value L1)) is displayed on the display unit 7. Thereby, the equivalent circuit analysis processing 50 is completed.

  As described above, in the equivalent circuit analysis device 1 and the equivalent circuit analysis method, the second inductance calculation process (step 56) is executed to calculate a new inductance value L1 closer to the true inductance value L1. Further, using this new inductance value L1, the correction process (step 53), the fitting process (step 54), and the parameter value calculation process (step 55) are executed again, and the resistance constituting the partial equivalent circuit The parameter values (Rs, R1, p, T) of the component 21, the resistance component 22, and the capacitance component 23 are calculated again.

Therefore, according to the equivalent circuit analysis device 1 and the equivalent circuit analysis method, the resistance value Rs of the resistance component 21, the resistance value R1 of the resistance component 22, and the parameter values p of the capacitance component 23 that constitute the equivalent circuit of the battery 11, Since T (and Z _CPE ) and the inductance value L1 of the inductor 24 can be converged to a value closer to the true value, each parameter value can be measured (calculated) with higher accuracy.

Further, according to the equivalent circuit analysis device 1 and the equivalent circuit analysis method, the correction process, the fitting process, the parameter value calculation process, and the second inductance are performed using the new inductance value L1 calculated in the second inductance calculation process. By executing the calculation process a predetermined number of times (in this example, n times: for example, 3 times or more), the resistance value Rs of the resistance component 21 and the resistance value R1 of the resistance component 22 constituting the equivalent circuit of the battery 11, Since each parameter value p, T (and Z _CPE ) of the capacitance component 23 and the inductance value L1 of the inductor 24 can be converged to a value closer to the true value, each parameter value is measured with higher accuracy. (Calculation).

Specifically, description will be made with reference to FIGS. A curve indicated by a solid line in FIG. 5 indicates the resistance of the resistance component 21 obtained by executing the correction process, the fitting process, and the parameter value calculation process once using the inductance value L1 calculated in the first inductance calculation process. The Nyquist plot curve CU3 (theoretical curve) for the equivalent circuit of the battery 11 shown in FIG. 2 calculated based on the value Rs, the resistance value R1 of the resistance component 22, and the parameter values p, T (and Z _CPE ) of the capacity component 23. ). In addition, a curve indicated by a broken line in FIG. 5 is a Nyquist plot curve CU1 (plotted by plotting the actual component actual value and the imaginary component actual value at each frequency f measured in the actual measurement process (step 51)). Measured curve). According to the figure, since the theoretical curve is greatly deviated from the actual measurement curve, the resistance value Rs of the resistance component 21, the resistance value R1 of the resistance component 22, and the parameter values p, T (and Z _CPE ) and the inductance value L1 of the inductor 24 can be confirmed to be calculated as values greatly deviating from the true value.

On the other hand, the curve indicated by the solid line in FIG. 6 indicates the resistance component 21 obtained by executing the correction process, the fitting process, the parameter value calculation process, and the second inductance calculation process twice using the new inductance value L1. 2 is calculated based on the resistance value Rs, the resistance value R1 of the resistance component 22, the parameter values p and T (and Z _CPE ) of the capacitance component 23, and the inductance value L1 of the inductor 24. Is a Nyquist plot curve CU4 (theoretical curve). In addition, a curve indicated by a broken line in FIG. 6 is a Nyquist plot curve CU1 (plotted by plotting the actual component measured value and the imaginary component measured value at each frequency f measured in the measured value measurement process (step 51)). Measured curve). According to the figure, since the theoretical curve is very close to the actual measurement curve, from this, the resistance value Rs of the resistance component 21, the resistance value R1 of the resistance component 22, and the parameter values p, T (and Z _{CPE of the} capacitance component 23). ) And that the inductance value L1 of the inductor 24 is calculated as a value close to the true value. That is, according to the equivalent circuit analysis device 1 and the equivalent circuit analysis method, the resistance value Rs of the resistance component 21, the resistance value R1 of the resistance component 22, and the parameter values p of the capacitance component 23 constituting the equivalent circuit of the battery 11 T (and Z _CPE ) and the inductance value L1 of the inductor 24 can be measured (calculated) with higher accuracy.

In the equivalent circuit analysis device 1 and the equivalent circuit analysis method, as described above, the resistance value Rs of the resistance component 21 and the resistance value of the resistance component 22 constituting the equivalent circuit of the battery 11 are increased as the number of repetitions n is increased. R1, the parameter values p and T (and Z _CPE ) of the capacitance component 23, and the inductance value L1 of the inductor 24 can be converged to values closer to the true value, but the number of repetitions n increases. The time required for analysis becomes longer. For this reason, in this equivalent circuit analysis device 1, the number n of repetitions can be set in the processing unit 5 by the operator via the operation unit 8, and the resistance value Rs of the resistance component 21 that constitutes the equivalent circuit of the battery 11 is set. It is possible to balance accuracy and time required for analysis.

  Further, in the equivalent circuit of the battery 11 shown in FIG. 2, there is only one set of parallel circuit of the resistance component 22 and the capacity component 23, but although not shown, it is configured by an equivalent circuit having two or more of this kind of parallel circuit. There is also a battery to be used, and the equivalent circuit analysis processing 50 described above can be applied when calculating each parameter value of such an equivalent circuit.

  In addition, the battery has been described as an example of the measurement target. However, as long as the equivalent circuit is a circuit as illustrated in FIG. 2, each parameter value of the equivalent circuit is calculated as the measurement target for elements other than the battery. be able to.

1 Equivalent circuit analyzer
5 treatment part 11 battery
R Real component
X Imaginary component
Z impedance

Claims (4)

Based on the measured frequency characteristics of the impedance to be measured represented by an equivalent circuit in which a solution resistor and an inductor are connected in series to a parallel circuit of a capacitance and a charge transfer resistance, the actual component actual measurement value of the impedance at each frequency And an actual value measurement process for measuring the actual value of the imaginary component,
A first inductance calculation process for calculating an inductance value of the inductor based on an imaginary component measurement value at a specific frequency on a high frequency side of the imaginary component measurement value;
The reactance at each frequency is calculated using the calculated inductance value and the calculated reactance is applied to the actual value of the imaginary component at the corresponding frequency to correct the actual value of the imaginary component at each frequency. Correction processing,
Plotting the real component actual measurement value as the horizontal axis coordinate and the corrected imaginary component actual measurement value as the vertical axis coordinate in an orthogonal plane with the real component as the horizontal axis and the imaginary component as the vertical axis Curve fitting method for semicircle corresponding to the arc-shaped region based on the measured actual value of the dot and the corrected actual measured value of the imaginary component of the dot included in the arc-shaped region in the Nyquist plot curve composed of the formed dots Fitting process calculated by
The equivalent value based on the frequency at the actual measurement value of each of the real component at two intersections with the horizontal axis of the calculated semicircle and the actual measurement value of the minimum imaginary component of the corrected actual value of the imaginary component A parameter value calculation process for calculating each parameter value of the capacitor, the charge transfer resistance and the solution resistance constituting the circuit;
While calculating the imaginary component theoretical value of the impedance at the specific frequency of the partial equivalent circuit composed of the capacitance, the charge transfer resistance, and the solution resistance of the calculated parameter values of the equivalent circuit, and the imaginary number An equivalent circuit analysis device including a processing unit that executes a second inductance calculation process for calculating a new inductance value of the inductor based on a component theoretical value and an imaginary component actual measurement value at the specific frequency,
The processing unit uses the new inductance value calculated in the second inductance calculation process to execute the correction process, the fitting process, and the parameter value calculation process again, thereby performing the parameter value calculation process. An equivalent circuit analysis device that converges the parameter values of the capacitance, the charge transfer resistance, and the solution resistance calculated in step (1).   The processing unit uses the new inductance value calculated in the second inductance calculation process, and performs the correction process, the fitting process, the parameter value calculation process, and the second inductance calculation process in a predetermined number of times. The equivalent circuit analysis apparatus according to claim 1, wherein the equivalent circuit analysis apparatus repeats only. Based on the measured frequency characteristics of the impedance to be measured represented by an equivalent circuit in which a solution resistor and an inductor are connected in series to a parallel circuit of a capacitance and a charge transfer resistance, the actual component actual measurement value of the impedance at each frequency And an actual value measurement process for measuring the actual value of the imaginary component,
A first inductance calculation process for calculating an inductance value of the inductor based on an imaginary component measurement value at a specific frequency on a high frequency side of the imaginary component measurement value;
The reactance at each frequency is calculated using the calculated inductance value and the calculated reactance is applied to the actual value of the imaginary component at the corresponding frequency to correct the actual value of the imaginary component at each frequency. Correction processing,
Plotting the real component actual measurement value as the horizontal axis coordinate and the corrected imaginary component actual measurement value as the vertical axis coordinate in an orthogonal plane with the real component as the horizontal axis and the imaginary component as the vertical axis Curve fitting method for semicircle corresponding to the arc-shaped region based on the measured actual value of the dot and the corrected actual measured value of the imaginary component of the dot included in the arc-shaped region in the Nyquist plot curve composed of the formed dots Fitting process calculated by
Based on each frequency component value at two intersections with the horizontal axis of the calculated semicircle and the frequency at the minimum imaginary component actual measurement value of the corrected imaginary component actual measurement value, the equivalent circuit is A parameter value calculation process for calculating each parameter value of the capacitor, the charge transfer resistance and the solution resistance;
Calculates an imaginary component theoretical value of the impedance at the specific frequency of the partial equivalent circuit composed of the capacitance, the charge transfer resistance, and the solution resistance of the calculated parameter values of the equivalent circuit, and the imaginary component An equivalent circuit analysis method for executing a second inductance calculation process for calculating a new inductance value of the inductor based on a theoretical value and an imaginary component actual measurement value at the specific frequency,
Using the new inductance value calculated in the second inductance calculation process, the correction process, the fitting process, and the parameter value calculation process are executed again, thereby calculating the parameter value calculation process. An equivalent circuit analysis method for converging each parameter value of capacitance, charge transfer resistance, and solution resistance.   4. The correction process, the fitting process, the parameter value calculation process, and the second inductance calculation process are repeated a predetermined number of times while using the new inductance value calculated in the second inductance calculation process. The equivalent circuit analysis method described.

Images