Method, apparatus and computer program for determining an impedance of an electrically conducting device

Abstract

A method for determining an impedance of an electrically conducting device, such as a battery or a welded metal joint, includes applying a time-varying electric current to the electrically conducting device. The current varies at least between a first level and a second level. The current changes between the first level and second level within a time interval that is so short that a voltage response of the electrically conducting device exhibits a first local voltage extremum followed by a decay. An ohmic resistance voltage is adopted by the voltage response, when the first local voltage extremum has decayed. The method further includes acquiring the voltage response at least partially and determining an impedance of the electrically conducting device from the acquired voltage response.

Claims

1. A method for determining an impedance of an electrically conducting device comprising: applying a time-varying electric current to the electrically conducting device, wherein: the current varies at least between a first level and a second level, the current changes between the first level and second level within a time interval, said time interval is so short that a voltage response of the electrically conducting device exhibits a first local voltage extremum followed by a decay, and an ohmic resistance voltage is adopted by the voltage response, when the first local voltage extremum has decayed, acquiring the voltage response at least partially, such that the acquired voltage response comprises and resolves the first volt local voltage extremum and the ohmic resistance voltage, wherein the sampling rate of the acquisition is selected such that at least two measurement points for the local voltage extremum are acquired, and determining an impedance of the electrically conducting device from the acquired voltage response, particularly from the ohmic resistance voltage, and the applied current.

2. The method according to claim 1, wherein: the first local voltage extremum is followed by a second opposite local voltage extremum or a voltage plateau, and the ohmic resistance voltage is the voltage at the second opposite local voltage extremum, particularly wherein the second opposite local voltage extremum is spaced apart closer than 0.5 milliseconds, particularly closer than 100 microseconds, more particularly closer than 10 microseconds, particularly closer than 5 microseconds from the first local extremum.

3. The method according to claim 1, wherein the time interval is less than 0.5 milliseconds, particularly less than 0.1 milliseconds, more particularly less than 50 microseconds, even more particularly less than 10 microseconds, particularly 5 microseconds.

4. The method according to claim 1, wherein the electrically conducting device is: a battery, a battery pack, a battery bank, or a system of batteries.

5. The method according to claim 1, wherein the electrically conducting device's voltage response is modelled as an equivalent electric circuit comprising at least one inductive element, at least one ohmic resistance element, an RC-element and particularly an RL element, wherein the elements are particularly connected in series.

6. The method according to claim 1, wherein: an ohmic resistance R.sub.Ω of the impedance of the electrically conducting device is determined, wherein the ohmic resistance is particularly determined from R.sub.Ω=|(U.sub.sum,min−U.sub.sum,0)/(I.sub.2−I.sub.0)|, and I.sub.0 is the first level, I.sub.2 is the second level, U.sub.sum,min is the ohmic resistance voltage, of the voltage response and U.sub.sum,0 is the voltage of the voltage response, when the current is at the first level.

7. The method according to claim 1, wherein: the voltage response comprises an inductive voltage response U.sub.sum,1, the inductive voltage response U.sub.sum,1 is determined from the voltage response that is acquired at the instant the applied current starts changing from the first level to the second level, and the inductive voltage response U.sub.sum,1 is particularly an initial voltage step exhibited by the voltage response at said instant.

8. The method according to claim 1, wherein the applied current changes from the first level with a constant rate di/dt, wherein the rate is particularly higher than 1 kA/s.

9. The method according to claim 7, wherein an external inductance of the electrically conducting device is determined from L.sub.e=|(U.sub.sum,1−U.sub.sum,0).Math.dt/di|, wherein U.sub.sum,1 is the inductive voltage response, and Leis the external inductance of the electrically conducting device.

10. The method according to claim 1, wherein the applied current is changing from a constant first level to a constant second level.

11. The method according to claim 1, wherein the first level or the second level is 0 Ampere and particularly wherein the modulus of the other level, the second or the first level, is greater than 0.01 Ampere.

12. The method according to claim 1, wherein the applied current alternates repeatedly between the first level and the second level and particularly wherein the applied current changes between the first level and the second level within different time intervals and/or at variable rates 321), wherein particularly the second level is different particularly with each repetition.

13. The method according to claim 1, wherein: the impedance of the electrically conducting device is determined by a model-function that is fitted to the acquired voltage response, the model-function comprises a term that accounts for a voltage response caused by at least one inductive element and a term accounting for a voltage response caused by at least one ohmic resistance element, particularly wherein the model-function is configured to model the equivalent electric circuit, wherein particularly the model function comprises fit parameters, and from the fitted model function, the fit parameters are determined and from the fit parameters at least the ohmic resistance, particularly the impedance of the electrically conducting device is determined.

14. A computer program for determining an impedance of an electrically conducting device comprising computer program code, wherein, when the computer program is executed on a computer, the method according to claim 1 is executed.

15. An apparatus for executing the method according to claim 1, wherein the apparatus comprises a current supply and wherein the apparatus is configured to acquire the voltage response with a temporal resolution that is sufficiently high to determine the first local voltage extremum and particularly the second local opposite voltage extremum of the voltage response, wherein the apparatus particularly has a temporal resolution for recording the voltage response of at least 10 microseconds.

16. The method according to claim 2, wherein the electrically conducting device is: a battery, a battery pack, a battery bank, or a system of batteries.

17. The method according to claim 2, wherein the electrically conducting device's voltage response is modelled as an equivalent electric circuit comprising at least one inductive element, at least one ohmic resistance element, an RC-element and particularly an RL element, wherein the elements are particularly connected in series.

18. The method according to claim 2, wherein the time interval is less than 0.5 milliseconds, particularly less than 0.1 milliseconds, more particularly less than 50 microseconds, even more particularly less than 10 microseconds, particularly 5 microseconds.

19. The method according to claim 18, wherein the electrically conducting device is: a battery, a battery pack, a battery bank, or a system of batteries.

20. The method according to claim 18, wherein the electrically conducting device's voltage response is modelled as an equivalent electric circuit comprising at least one inductive element, at least one ohmic resistance element, an RC-element and particularly an RL element, wherein the elements are particularly connected in series.

21. The method according to claim 1, wherein a temporal resolution of the acquired voltage response is better than 10 microseconds.

Description

(1) It is shown in

(2) FIG. 1 an equivalent electric circuit (EEC) model that represents the electric behavior of a battery;

(3) FIG. 2 a measured terminal voltage response u.sub.sum(t) of a lithium-ion battery over time;

(4) FIG. 3 voltages of the single components of the EEC model;

(5) FIG. 4 a schematic drawing of an apparatus for executing the method according to the invention; and

(6) FIG. 5 an applied current profile and the corresponding terminal voltage u.sub.sum(t) of a battery that is analyzed with an apparatus from the state of the art.

(7) Analyzing impedances of an electrically conducting device with methods that are state of the art is either fast, precise or easily operable. None of the existing methods are able to meet these three attributes at the same time. Above all, the fast-dynamic impedances of a device under test 11 (e.g. c.f. FIG. 4), which represent the ohmic and inductive behavior, cannot be determined exactly with known methods and measurement devices.

(8) FIG. 5 illustrates the current pulse method. In FIG. 5, the functional principle of the current pulse method is exemplified by results of a test performed with a lithium-ion battery cell. The current pulse i(t) 5 changes its value from an initial current I.sub.0=0.00 A 51 to a constant current I.sub.2=1.60 A 53. An apparatus that is able to apply such a current pulse i(t) 5 usually has a sample rate not better (slower) than 0.5 milliseconds. The single measurement points that were recorded in the example are marked by plus signs depicted in the profile of the terminal voltage response u.sub.sum(t) 6. Using conventional methods, the current change itself 52 is not exactly defined but usually shows a step with some transient oscillation caused by the current controller. These fast-dynamic control behavior and its effects on the voltage response u.sub.sum(t) are usually not detected since the first measurement point 62 is obtained 0.5 milliseconds after the start of the current pulse. Therefore, with conventional methods known from the state of the art, it is not possible to evaluate the fast-dynamic impedances of a device under test or to determine its ohmic and inductive impedances.

(9) From an engineering perspective, the electric behavior of battery cells and systems, in particular, those based on the lithium-ion technology, can be modeled by an equivalent electric circuit (EEC) model 2, as shown in FIG. 1. Therein, the external inductance L.sub.e 21 is caused by electro-magnetic fields surrounding the current conductors and paths that run through a battery. So, the external inductance L.sub.e 21 provides information on the general integrity of a battery and on possible geometrical deformations, as caused by a mechanical impact. The RL element R.sub.skin∥L.sub.i represents the internal inductance L.sub.i 23, which is caused by electromagnetic fields inside the current collectors, and the skin effect of the current collectors, which leads to an increased resistance R.sub.skin 24 when the current changes quickly. The ohmic resistance R.sub.Ω 22 is one of the most important parameters to characterize a battery or technical component. In the exemplary case of lithium-ion batteries, it represents the limited electrical conductivity of the electrolyte, the electrode materials, the separator, the conductors, the welded joints, etc. Above all, a precise method and apparatus for analyzing impedances has to be able to precisely and analytically determine at least the ohmic resistance R.sub.Ω 22 and preferably the external inductance L.sub.e 21 of a device under test 11 as well. None of the state-of-the-art methods and apparatus is able to determine these two highly important parameters.

(10) The EEC model of a battery cell 2 comprises one or more RC elements, for example, to represent a double layer capacity C.sub.RC 25 in parallel to a charge transfer resistance R.sub.RC 26. Additionally, a complex impedance Z 27 and a voltage source u.sub.eq(C.sub.batt) 28 are comprised by the EEC model to represent mass transport phenomena and the equilibrium voltage depending on the residual capacity of a battery C.sub.batt.

(11) No matter what kind of device under test shall be analyzed, a connection between the testing apparatus and the device under test has to be established somehow. For this exemplary embodiment of the apparatus, of which the schematic layout is shown in FIG. 4, and for the present example of analyzing a lithium-ion battery the plus pole 12 and the minus pole 13 are used to induce the current pulse i(t) and measure the response of the terminal voltage u.sub.sum(t). Four-terminal sensing, also called Kelvin connection, is preferably used to connect the two terminals of the battery.

(12) The objective of the present invention is to provide a tool for analyzing the impedances of batteries and other technical components that meets all three attributes: fast, precise and simple.

(13) In FIG. 2, FIG. 3, and FIG. 4, an embodiment of the invention is presented for a lithium-ion battery cell. The example illustrates the operating principle of the method according to the invention and the general functionality of an apparatus based on this method.

(14) An overview on the functional principle of the disclosed invention is given by FIG. 2. The shown current pulse i(t) 30 is generated and measured by an apparatus (4), which is configured to execute the method according to the invention. This current pulse i(t) 30 is applied to the terminals of a lithium-ion battery cell 12, 13. The measured terminal voltage of the battery cell 39 as well as the simulated voltage response u.sub.sum(t) 34, which is obtained from the EEC model 2 shown in FIG. 1, is depicted over the time t. The two voltage profiles, the measured one 39 and the simulated one 34, are almost equal and therefore validate the chosen EEC model 2.

(15) In the present example, the current i(t) 30 changes from a constant current I.sub.0=0 A 31 to a constant current I.sub.2=1.60 A 33. The current change 32 itself is realized with a ramp that lasts for 5 μs and has a constant change rate di/dt=320 kA/s. As one of the basic characteristics of the disclosed invention, the current change 32 is quick enough to cause a defined inductive overshoot 36 in the voltage response u.sub.sum(t) 34, 39 that decays before possible other impedances with slower time constants significantly contribute to the total terminal voltage u.sub.sum(t) 34, 39. A local minimum U.sub.sum,min 37 occurs in the measured response of the terminal voltage u.sub.sum(t) 34, 39 after the inductive voltage overshoot 36 decayed and before impedances with slower time constants significantly contribute to the total terminal voltage u.sub.sum(t) 34, 39.

(16) The characteristic voltage response u.sub.sum(t) 39 is measured with a sample rate that is high enough to detect at least the local minimum U.sub.sum,min 37. Then, the desired impedances can be determined by analyzing the relation between the applied current profile 30 and the measured terminal voltage response 39. A detailed view of the pulse is done by a zooming into the boxed area 38, 381 that is described in detail in FIG. 3.

(17) FIG. 3 shows the functional principle of the method whereby a current pulse i(t) 301 is applied to the EEC model of a lithium-ion battery cell 2. The current profile i(t) 301 does not show any noise or oscillation in this example and is defined by an initial current I.sub.0=0.00 A 311 that changes within 5 μs to a constant current I.sub.2=1.60 A 331. The current change itself is done with a linear ramp 321 with a constant change rate di/dt=320 kA/s. The current pulse is similar to the measured current pulse shown in FIG. 2.

(18) The terminal voltage response u.sub.sum(t) 341 of the EEC model is the sum of the voltage responses of the single EEC elements. The single voltage responses are shown separately in FIG. 3, wherein the voltage u.sub.Ω(t) 342 is the contribution of the ohmic resistance R.sub.Ω 22, the voltage u.sub.Le(t) 343 is caused by the external inductance L.sub.e 21, the voltage u.sub.RL(t) 344 is caused by the internal inductance L.sub.i 23 in parallel to the resistance for the skin effect R.sub.skin 24, and the voltage u.sub.RC(t) 345 is the contribution of the RC element 25, 26.

(19) The voltage drop u.sub.Ω(t) 342 over the ohmic resistance R.sub.Ω 22 is directly proportional and instantaneous to the current profile. The voltage u.sub.Le(t) 343 at the external inductance L.sub.e 21 is 0 V for constant current phases 311, 331 and changes its value for time-variant currents. For the current ramp 321 the gradient di/dt is constant and thus the voltage at the external inductance u.sub.Le(t) 343 has a constant level U.sub.Le 363 during the rise time 321. The voltage contribution u.sub.RL(t) 344 caused by the RL element 23, 24 is zero when the current starts to change, reaches a maximum during the rise of the current, and vanishes in the subsequent constant current phase 331. Most other processes, as represented by the voltage u.sub.RC(t) 345 at the RC element 25, 26, usually have far slower time constants and do not significantly contribute to the total terminal voltage u.sub.sum(t) 341 at the beginning of the current profile i(t) 301.

(20) Based on these findings and this knowledge, a method to analytically and uniquely determine the values of the ohmic resistance R.sub.Ω 22 and the external inductance L.sub.e 21 is derived. This method can be implemented in an apparatus that applies the described current pulse i(t) 301 and measures the response in the overall terminal voltage u.sub.sum(t) 341.

(21) The ohmic resistance R.sub.Ω 22 is determined at the instant of time t.sub.3 that is given by the local minimum, i.e. the second local opposite voltage extremum, U.sub.sum,min 371 in the terminal voltage response u.sub.sum(t) 341 after the current i(t) 301 reached its target value I.sub.2 (i.e. the second level) 331 and the inductive overshoot (361) decayed. At this instant of time t.sub.3, the overpotentials u.sub.Le(t) (343) of the external inductance L.sub.e (21) and u.sub.RL(t) (344) of the RL element (23, 24) vanished and voltages of slower dynamic processes, such as u.sub.RC(t) (345), do not yet significantly contribute to the terminal voltage u.sub.sum(t) (341). With the initial voltage U.sub.sum,0 351, the ohmic resistance R.sub.Ω (22) can be calculated from the voltage difference U.sub.sum,min−U.sub.sum,0 and the current change I.sub.2−I.sub.0 to with:
R.sub.Ω=|(U.sub.sum,min−U.sub.sum,0)/(I.sub.2−I.sub.0)|.

(22) At the beginning of the current ramp at the instant of time t.sub.1, the terminal voltage u.sub.sum(t) steps from U.sub.sum,0 351 to U.sub.sum,1 362. This step can be assigned to the external inductance L.sub.e 21, because the voltage contribution u.sub.Ω(t) 342 of the ohmic resistance R.sub.Ω 22, the voltage u.sub.RL(t) 344 of the RL element 23, 24, and the voltage u.sub.RC(t) 345 at the RC element 25, 26 do not significantly contribute to the terminal voltage u.sub.sum(t) 341 at the very beginning of the current ramp. With this step 362 in the terminal voltage response u.sub.sum(t) 341 and the linear current ramp 321 with a constant change rate di/dt, the external inductance L.sub.e 21 can be calculated:
L.sub.e=|(U.sub.sum,1−U.sub.sum,0).Math.dt/di|.

(23) When the initial terminal voltage U.sub.sum,0 351 and the voltage contributions u.sub.Ω(t) 342 of the ohmic resistance R.sub.Ω 22 and u.sub.Le(t) 343 at the external inductance L.sub.e 21 are subtracted from the terminal voltage response u.sub.sum(t) 341, only the voltage u.sub.RL(t) 344 of the RL element 23, 24 remains and the values of the internal inductance L.sub.i 23 and its parallel resistance R.sub.skin 24 can be determined.

(24) A schematic overview of an embodiment of the apparatus according to the invention is shown in FIG. 4. The apparatus 4 comprises a user interface 42, which provides the measurement results and evaluated data 41 to the user. In one embodiment of the invention, the user is able to make individual settings via the user interface 42, as for example set the target value of the current I.sub.2. The device under test 11 is placed on the right side of the apparatus 4 that is schematically shown in FIG. 4. The terminals 12, 13 of the device under test 11 are electrically connected to the apparatus 4 by a Kelvin connection. The first pair of lines connected to the terminals 12, 13 of the device under test 11 is used to induce the current pulse i(t) that is generated by the pulse generator 44 (i.e. current supply) of the apparatus 4. A current sensor 46 is integrated into the current path to allow a separate current measurement 45. The second pair of lines allows a precise measurement of the response of the terminal voltage u.sub.sum(t) by the voltage measurement unit 47 of the apparatus 4. The measured current i(t) and terminal voltage response u.sub.sum(t) is brought together and evaluated by the evaluation unit 43. This unit also implies the analytical determination of the ohmic resistance R.sub.Ω 22 and the external inductance L.sub.e 21.

(25) It is a major advantage of the invention to allow the unique and comprehensible determination of the ohmic resistance R.sub.Ω 22 and the external inductance L.sub.e 21 by simple analytic equations. To determine these two impedances with conventional methods and apparatus is either not possible or requires elaborate fitting algorithms.

REFERENCE NUMERALS

(26) 11 device under test also referred to as electrically conducting device 12 first terminal of the device under test 13 second terminal of the device under test 2 EEC model of a battery 21 external inductance L.sub.e 22 ohmic resistance R.sub.Ω 23 internal inductance L.sub.i 24 skin effect resistance R.sub.skin 25 capacitor of RC element R.sub.RC 26 resistance of RC element C.sub.RC 27 complex impedance Z 28 equilibrium voltage U.sub.eq(C.sub.batt) 30 measured current of a functional model of the apparatus 301 current profile 302 time interval 31, 311 constant initial current I.sub.0, also referred to as first level 32, 321 current ramp from time instant t.sub.1 to t.sub.2 323 linear increase of u.sub.Ω(t) 33, 331 constant current I.sub.2, also referred to as second level 332 voltage u.sub.Ω(t) 342 of ohmic resistance R.sub.Ω (22) for I.sub.2 331 34 simulated terminal voltage response u.sub.sum(t) for measured current pulse i(t) 30 341 simulated terminal voltage response u.sub.sum(t) for the current profile i(t) 301 342 voltage u.sub.Ω(t) at ohmic resistance R.sub.Ω 22 343 voltage u.sub.Le(t) at external inductance L.sub.e 21 344 voltage u.sub.RL(t) at RL element R.sub.skin∥L.sub.i 23, 24 345 voltage drop u.sub.RC(t) of RC element R.sub.RC∥C.sub.RC 25, 26 35, 351 initial terminal voltage U.sub.sum,0 for I.sub.0 31, 311 352 initial voltage level of u.sub.Ω(t) 342 for I.sub.0 311 36, 361 overshoot of terminal voltage U.sub.sum,2 at time instant t.sub.2 362 initial step in terminal voltage from U.sub.sum,0 351 to U.sub.sum,1 at instant of time t.sub.1 363 constant voltage U.sub.Le over external inductance L.sub.e 21 during current ramp 321 364 decay 37, 371 ohmic resistance voltage, second local extremum U.sub.sum,min of terminal voltage u.sub.sum(t) 341 38, 381 zoom for current ramp 32, 321 39 measured terminal voltage response u.sub.sum(t) for measured current pulse 30 4 schematic of one embodiment of the apparatus 41 flow of information to user 42 user interface 43 evaluation unit 44 pulse generator 45 current measurement 46 current sensor 47 voltage measurement 5 state-of-the-art current pulse i(t) 51 initial constant current value I.sub.0 52 unknown change of current from I.sub.0 51 to I.sub.2 53 53 constant current value I.sub.2 6 response of terminal voltage u.sub.sum(t) measured with state-of-the-art equipment 61 initial terminal voltage U.sub.sum,0 for I.sub.0 51 62 first measurement point of terminal voltage response u.sub.sum(t) 6