Impedance determination with phase determination

Abstract

The present invention relates to a method for correcting a synchronization error Δt when measuring the impedance of an electrical or electrochemical structural element, in particular a lithium-ion single cell. Generally, a synchronization error may occur between the excitation signal and the response signal during impedance measurement, and the synchronization error may cause phase distortion of the obtained impedance value. According to the present invention, the synchronization error can be determined by measuring the impedance at two different frequencies f1 and f2 and solving an optimization problem regarding the phase deviation with respect to an equivalent circuit diagram, which has at least a resistor R and an inductor L. Thereby, the phase of the obtained impedance value can be corrected.

Description

Field of the Invention

[0001] The present invention relates to a method for phase determination in impedance calculations, in particular in the measurement of the impedance of a lithium-ion single cell. Background Art

[0002] Electrochemical impedance spectroscopy (EIS) is an established method for characterizing electrochemical systems, in particular also for characterizing primary batteries, which generally involves measuring the impedance, i.e. the complex AC resistance, as a function of the frequency of an excitation signal.

[0003] It is known in the prior art to use impedance measurements or impedance spectroscopy to diagnose the state of a lithium-ion single cell and in particular also to determine the temperature of a lithium-ion single cell by means of impedance.

[0004] DE 10 2013 103 921 relates to single cell temperature measurement and degradation measurement in a lithium battery system of an electrically operated vehicle by determining the single cell impedance based on an AC voltage signal preset by an inverter. The method is based on the observation that the curve of the plot of impedance versus signal frequency is temperature-dependent.

[0005] EP 2 667 166 A2 relates to a method for determining the temperature and finding the frequency (at which the imaginary part has a zero crossing) by measuring the imaginary part of the impedance at multiple frequencies. The method is based on the observation that the frequency of the zero crossing essentially depends on the temperature for a given charge and aging state of the single cell.

[0006] US 2013 / 0264999 relates to a battery charging system that includes a temperature sensor that is alternately connected to each single cell to be charged in a time-division multiplexing method to measure the impedance of the single cell and determine the temperature from the phase of the impedance. Here, the rate of change of temperature over time is used as an indicator of whether the single cell is fully charged.

[0007] All these methods have in common that in order to determine the temperature, not only the modulus of the impedance but also the impedance as a complex parameter (i.e., modulus and phase or real and imaginary parts) must be determined.

[0008] Excitation is usually carried out with a constant current (i.e., as a current signal with a defined amplitude), the resulting voltage signal is measured and the impedance is calculated from the amplitudes and phases of the two signals. In principle, two methods are considered for excitation.

[0009] On the one hand, each individual cell can be individually excited by means of a balancing current. Here, the cell supervision unit (Cell Supervision Circuit, CSC) applies an excitation signal to the balancing current and simultaneously measures the high-frequency component of the falling voltage in order to calculate the impedance therefrom. The cell supervision unit also performs charge equalization (balancing) between the individual cells. This has the advantage that very precise phase information is obtained because the generation of the excitation signal, the recording of the measurement signal, and the impedance calculation are performed by the same control device. The disadvantages are high current consumption and high requirements for the accuracy of the voltage measurement.

[0010] Alternatively, the excitation can be applied externally, for example via an inverse rectifier or a DC-DC converter. This enables a higher excitation signal level, thereby improving the signal-to-noise ratio (S / N ratio) and reducing the requirements for the voltage measurement accuracy. In addition, the current consumption and the device cost are reduced because the individual cell supervision units no longer have to be provided with their own excitation circuits, and the impedance calculation from the measured voltage signal can also be performed externally in a separate control device.

[0011] Especially in the method using external excitation - where the signals of different control devices are processed - there is a risk that a synchronization error occurs between the excitation signal and the response signal, whereby the accuracy of the temperature determination deteriorates. Even an asynchronism of 10 μs already results in a phase error of 3.6°. If the temperature of a cell is to be determined, for example, from the phase of the impedance, then for a 60 Ah cell at 300 Hz, a phase accuracy of 3.6° results in a temperature inaccuracy of 7.2 K. Summary of the Invention

[0012] The task is posed:

[0013] In view of the above problems, a method for phase calibration of an excitation signal and a response signal is needed so that even in the presence of a synchronization error Δt in the signals, the impedance can be determined with high phase accuracy in order to enable an accurate temperature determination.

[0014] To solve the above task, the present invention provides a phase calibration method and an impedance measurement method using the phase calibration method.

[0015] The method according to the invention can advantageously be used in combination with external excitation. By means of the method according to the invention, the energy requirement during impedance measurement can be reduced and the impedance measurement quality can be improved. At the same time, the method allows a decentralized architecture in which the generation of the excitation signal, the voltage measurement, and the impedance calculation can exist separately from each other without high requirements for the synchronization of the two systems.

[0016] Summary of the Invention:

[0017] The present invention relates to a method for correcting a synchronization error Δt when measuring the impedance of an electrical or electro-chemical structural element, in particular a lithium-ion single cell, the method comprising:

[0018] - selecting an impedance model for the structural element, the impedance model having at least one resistance R and an inductance L;

[0019] - applying one or more excitation signals I(t) or U(t) at at least two frequencies f1 or f2;

[0020] - measuring a response signal U(t+Δt) or I(t+Δt), which can have a synchronization error Δt relative to the excitation signal;

[0021] - determining impedances Z1 and Z2 from the excitation signal and the response signal in the case of f1 or f2;

[0022] - determining Δt as the value for which the deviation between the difference Z diff =Z2-Z1 of the measured values and the corresponding value calculated for the equivalent circuit diagram for Z diff is below a predetermined threshold with respect to at least one impedance component;

[0023] - correcting the impedance value using the determined synchronization error Δt.

[0024] In the method according to the invention, a plurality of excitation signals having different frequencies can be applied alternately, or a superimposed excitation signal comprising a plurality of frequencies can be used.

[0025] The at least two frequencies f1 and f2 for determining the synchronization error Δt are preferably 1 kHz or greater, such that the capacitive contribution to the impedance is negligible and the impedance model only includes resistance and inductance.

[0026] The synchronization error Δt determined by the method according to the invention can preferably also be used to correct impedance measurements at one or more frequencies f0 below f1 or f2. Description of the Drawings

[0027] Figure 1 Shows the general flow of the method according to the invention for the case of measuring the impedance at three frequencies f0, f1 and f2 and using the measured values for determining Δt in the case of f1 and f2 assuming an LR model.

[0028] Figure 2 Shows a flow chart of an embodiment of the method according to the invention, wherein Δt is determined by an iterative adjustment algorithm.

[0029] Figure 3 Shows Figure 2Convergence behavior of the algorithms outlined in

[0030] Figure 4 A battery system is shown which is set up to carry out the method according to the invention. Detailed Description

[0031] Basis:

[0032] For the introduction of terms, the basis of impedance measurement will be briefly summarized below. The embodiments relate to the constant current case which is usually relevant in practice, in which an alternating current signal I(t) with a known amplitude I0 and a known frequency f is fed and the voltage drop U(t) is measured. However, they are also applicable in a corresponding manner to the opposite case, that is to say, feeding a predefined voltage signal and measuring the current, which is equally possible.

[0033] The signals I(t) and U(t) can be represented in the complex plane as

[0034] I(t) = I0 * e iω

[0035] U(t) = U0 * e i(ωt+φ)

[0036] Below, the frequency f and the angular frequency ω = 2πf can jointly be referred to as "frequency", provided that it can be seen from the context or the symbols ω / f used which frequency is meant.

[0037] The signals I(t) and U(t) are usually phase-shifted from each other by a phase angle Φ which is defined as the zero angle of the voltage and the current. The impedance Z is calculated as U(t) / I(t) and is complex if Φ is non-zero:

[0038] Z = U(t) / I(t) = (U0 / I0) * e iφ = Z0 * (cos φ + i * sin φ) = R + iX

[0039] The real part Re(Z) = R corresponds to the ohmic resistance and is also called the active impedance. The imaginary part Im(Z) = X is caused by the phase shift and is also called the reactive impedance.

[0040] The modulus of the impedance |Z| is the ratio of the effective current amplitude and the voltage amplitude and is also called the apparent impedance. The apparent impedance contains both the active impedance and the reactive impedance and is typically frequency-dependent. However, power is dissipated only due to the active impedance.

[0041] For an ideal ohmic resistor, the phase shift is zero and the impedance corresponds to the active impedance R. For an ideal capacitor (capacitive resistor), the phase shift is -90° and the impedance is purely imaginary and decreases with increasing frequency (Z = -i*(1 / ωC); C: capacitance). For an ideal inductive component (inductive resistor), the phase shift is +90°. The impedance is also purely imaginary and Z = +iωL (L: inductance), i.e., the reactive impedance increases with increasing frequency.

[0042] According to the invention, impedance measurement is used in particular for detecting the state (temperature, state of charge, etc.) of a lithium-ion single cell. Most processes in the single cell based on charge transport, including ion conduction in the electrolyte and insertion and extraction kinetics at the electrodes, can be described here using the ohmic resistance. The capacitive resistance occurs, for example, at the electrical double layer on the electrodes. Thus, the single cell can be approximately modeled using an equivalent circuit diagram having at least one RC section for representing the electrode process and a series resistor R0 (the "R0-RC model") connected in series with the RC section for representing the electrolyte resistance.

[0043] The inductance is not very important for the electrochemical process itself and is essentially realized by the magnetic field in the participating electrical conductors (current collectors, leads, wiring). Overall, the inductance of this arrangement can definitely provide a significant share of the phase shift at higher frequencies. However, since this arrangement is fixed and not affected by the electrochemical process in the single cell, this share can be regarded as a (frequency-dependent) device constant and thus eliminated from the calculation of the state of the single cell to be diagnosed. However, at high frequencies, the contribution of L dominates the impedance. Therefore, especially at high frequencies, the equivalent circuit diagram for representing the impedance is supplemented with a series inductance L (the "L-R0-RC model").

[0044] Synchronization method:

[0045] The signals I(t) and U(t) usually can have a synchronization error, that is, the recording of the signals I(t) and U(t) is not synchronized, but the time zeros are offset from each other by an uncertain time difference Δt, for example, several μs. Therefore, for impedance calculation, I(t) and U(t) are not actually used, but I(t) and U(t + Δt). Thus, the phase angle Φ mess is distorted by a phase error ΔΦ with respect to the correct phase shift Φ:

[0046] φ mess = φ + Δφ

[0047] Δφ = ω*Δt = 2πf*Δt

[0048] Therefore, the actually measured impedance value (i.e., calculated from the signals I(t) and U(t) with synchronization error) is:

[0049] Z mess =(U0 / I0)*e iφmess =(U0 / I0)*e i(φ+Δφ) .=Z0*(cos(φ + Δφ)+i*sin(φ + Δφ))

[0050] Simplifying, the method according to the invention essentially utilizes the frequency dependence of the inductance of the arrangement structure and the resulting inductive resistance in order to synchronize the signals U(t) and I(t). Here, the frequency is preferably chosen to be large enough such that the capacitive contribution becomes negligible and the impedance is determined by the inductive contribution and the ohmic contribution.

[0051] Accordingly, the method according to the invention is first explained for the case of a pure LR model, which represents an approximation of the behavior of a single cell in the case of high frequencies.

[0052] As mentioned above, a single cell can generally be approximated by an L - R0 - RC model. The impedance of the RC section Z rc (ω) is frequency - dependent and is:

[0053] Z RC (ω)=R / (1 + iωRC)=R / (1+(ωRC) 2 ) - iωR 2 C / (1+(ωRC) 2 )

[0054] Therefore, Z rc (ω) vanishes in the case of high frequencies, and the series resistance R0 and the inductance L remain, such that the behavior of the single cell corresponds to an LR model.

[0055] Z R-L (ω)=R0 + iωL

[0056] According to the invention, the impedance is measured at at least two frequencies f1 and f2 (or ω1 and ω2), and the difference Z diff =Z2 - Z1 is formed. Subsequently, Δt is determined as the value for which the difference Z diff =Z2 - Z1 between the measured values and the corresponding value of Z diff calculated for the equivalent circuit diagram has a deviation with respect to at least one impedance component below a predetermined threshold;

[0057] Since R0 is frequency - independent, the real part vanishes in the pure LR model when forming the difference, and the pure imaginary component remains.

[0058] Z diff= Z2 - Z1 = iL(ω2 - ω1)

[0059] In the diagram of Z, the real part corresponds to the cosine term, i.e., the synchronization error can be determined as the point at which the difference of the cosine terms vanishes:

[0060] Re(Z diff ) = Z 0，diff (COS(φ2 + Δφ2) - COS(φ1 + Δφ1)) = 0

[0061] Thus, in this case, the asynchrony Δt can be calculated as the value at which the difference of the real parts vanishes, which can be done analytically or numerically. This has the advantage that the model parameters R and L do not have to be known, since the above considerations apply to every choice of L and R in the pure LR model.

[0062] By rotating the phases of Z1 and Z2 by ΔΦ1 = 2πf1*Δt or ΔΦ2 = 2πf2*Δt, the corrected impedance values can then be calculated.

[0063] In this consideration, based on the pure LR model, this can be reasonable for cases where the two frequencies f1 and f2 are large enough so that the capacitive contribution becomes negligible (e.g., about 1 kHz or greater).

[0064] For diagnosing the single - cell state, especially the electrode process, it may be necessary to perform impedance measurements at one or more lower frequencies f0, such as in the range of 10 Hz to 300 Hz, preferably about 30 Hz to 200 Hz, where the capacitive contribution is not negligible. In this case, the method according to the invention can still be performed at frequencies f1 and f2 above 1 kHz, to which the LR model can be applied, and then the value obtained for Δt can be used for the correction of the impedance at f0. Figure 1 Such a method is schematically shown, where three frequencies f0, f1, and f2 are used, but only f1 and f2 are considered for determining Δt.

[0065] Furthermore, more complex impedance models may be required if necessary, e.g., extended by using additional resistors (R - LR model). Finally, it may also be necessary to explicitly consider the capacitive contribution, e.g., if there is an upper limit on the available frequencies regarding equipment costs.

[0066] In these cases, a more complex impedance model is set up, which can include other elements such as ohmic resistance R, capacitance C or an LR section, or, if necessary, also a Warburg element. In order to determine Δt by minimizing the deviation from the equivalent circuit diagram, the values of the model parameters (R, L, etc.) must generally be known. For this purpose, the model parameters can, for example, be determined and stored with high precision in a separate measurement, and the method according to the invention is carried out using such predetermined model parameters.

[0067] Alternatively, within the scope of the method according to the invention, some or all of the model parameters can also be determined simultaneously with Δt. This is a numerical optimization problem, where the system has the synchronization error Δt and the model parameters to be determined as degrees of freedom. Therefore, in this case, the number of frequency points f1, f2, etc. and / or the number of measured impedance values Z1, Z2 should preferably be equal to or greater than the number of degrees of freedom for which the system is determined or overdetermined. The solution of the optimization problem is based on the system of equations obtained for the impedance at different frequencies and is carried out according to methods known per se.

[0068] In one possible embodiment, an iterative adjustment algorithm is used here to optimize based on the difference Z between the measured impedances Z1 and Z2, diff where the phase of Z diff specifies the step size of the iteration weighted by a scaling factor a, as shown in Figure 2 . Here, in each iteration, the difference Z diff = Z2 - Z1 is calculated, the differential Δt diff is calculated and accumulated from the phase of Z korr , and the phases of Z2 and Z1 are corrected again using the accumulated value.

[0069] The individual steps are as follows:

[0070] 1. Initialize with Δt = 0; in each run, the differential Δt korr is calculated and added to finally obtain an estimated value for Δt.

[0071] 2. Calculate ΔΦ1 or ΔΦ2 as ΔΦ 1,2 = 2πf 1,2 * Δt

[0072] from the current value of Δt respectively. mess 3. Rotate the original (i.e., with the synchronization error Δt) measured values Z mess (f1) and Z mess,korr (f2) by ΔΦ1 or ΔΦ2 in order to obtain the phase-corrected measured values Z mess,korr (f1) or Z

[0073] 4. Form the difference Z diff = Z mess,korr (f2) - Z mess,korr (f2)

[0074] 5. Determine the phase ΔΦ of Z diff ; diff ;

[0075] 6. Determine the correction term Δt korr = ΔΦ diff / 2πf1

[0076] 7. Increment the value of Δt by Δt weighted with the factor a korr ;

[0077] 8. Repeat steps 2 to 7 with the incremented value of Δt until ΔΦ diff is below a determined threshold;

[0078] 9. Obtain the corrected impedance value from the calculated Δt.

[0079] The weighting factor a adjusts the step size of the iteration and can be appropriately selected, for example, in the range of 0.1 to 1.0, so that on the one hand, fast convergence can be achieved and on the other hand, the cumulative value of Δt is prevented from oscillating around the actual value. It is also possible to adapt a to the corresponding differential value Δt korr in each iteration.

[0080] The frequencies f1 and f2 are preferably large enough (e.g., 1 kHz or greater) such that the capacitance term becomes negligible and the LR model can be employed. However, the Δt calculated from f1 and f2 can be used for synchronous correction for a lower frequency f0 for which pure LR behavior is no longer applicable.

[0081] Figure 3 Shows the convergence behavior of the algorithm. In the upper left, the real and imaginary parts of the impedance at five different frequencies are plotted in the Nyquist diagram for the (counterclockwise) convergent increase of Δt. In the upper right, the curve of the phase difference versus the number of iterations is plotted. In the two lower graphs, the differential change of Δt (left) and the cumulative value of Δt (right) are plotted versus the number of iterations.

[0082] Implementation:

[0083] The method according to the invention can in particular be used to improve the accuracy of impedance measurement in the context of the monitoring and state diagnosis of single cells, in particular lithium-ion single cells, in a battery system.

[0084] In particular, this can relate to a battery system for an electric vehicle or a hybrid electric vehicle. Such a battery system includes a plurality of lithium-ion single cells that are controlled by a battery management system (BMS).

[0085] Typically, these single cells are connected in series and / or in parallel in groups to form a battery pack and are respectively connected to a single cell monitoring unit (CSC), which monitors at least the single cell voltage and also controls the charging balance (equalization). Here, each individual single cell can be provided with a single cell monitoring unit, or multiple single cells can be connected to one single cell monitoring unit. The single cell monitoring unit can have multiple input channels for voltage measurement in order to be able to monitor the single cells connected to the single cell monitoring unit simultaneously, or can be monitored by a multiplexing method. The entirety of the single cells and the single cell monitoring unit is in turn monitored by a battery management unit (BCU).

[0086] Preferably, the excitation signal for impedance measurement is applied as an alternating current signal, which can be done cell by cell, for example by means of an equalization current, or globally from the outside, for example by means of an inverter. The recording of the response signal can be carried out by the voltage monitoring function of the CSC. As described above, there is a risk of synchronization errors especially in the case of global external excitation, so the method according to the invention is preferably applicable to this application case.

[0087] Figure 4 An example of a battery system for an electrically operated vehicle is schematically shown, in which the method according to the invention can be used. Here, multiple single cells are respectively connected into modules, and each module is provided with a CSC that monitors the voltage of the single cells in the module. The modules are in turn connected in series. The excitation signal is applied globally to the current by means of an inverter, and the recording of the response signal is carried out by the CSC.

[0088] The calculation of the impedance and the execution of the method according to the invention can equally be carried out by the CSC, especially Δt can be different for each single cell or for each module. Alternatively, the recorded response signal can be transmitted to the BCU, which then takes over the execution of the method according to the invention and the calculation of the impedance. In order to avoid overloading of the communication channel, it is preferred to calculate the impedance in the CSC.

[0089] The frequencies f1 and f2 and, if necessary, additional frequencies f3, f4,... for determining Δt, which depend on the complexity of the model and the desired accuracy, are preferably large enough such that the capacitive contribution becomes negligible. For example, frequencies in the range from 1 kHz to 20 kHz can be used. These frequencies have a predetermined distance from each other, which can be, for example, from 100 Hz to 5 kHz, preferably from 500 Hz to 2 kHz or from 1 kHz to 2 kHz. In addition to determining Δt, the impedance values in the case of the frequencies f1, f2, etc. can also be taken into account for determining the electrolyte resistance.

[0090] In contrast, in order to characterize the electrode process (the contribution of which to the impedance can be described by an RC element), it is preferable to have one or more lower frequencies f0 at which the capacitive contribution is no longer negligible and which are, for example, within the range of the inverse time constant of the RC element involved. These frequencies f0 can be, for example, from 10 Hz to 300 Hz, preferably from 20 Hz to 200 Hz. For the sake of simplicity of the impedance model, it is preferable that the frequencies f0 are not considered for determining Δt by the method according to the invention. Instead, the calculated values of Δt can be used for the correction of the impedance at f0.

[0091] An excitation signal having only a single frequency that varies can be employed. However, preferably, a superposition of a plurality or all of the required frequencies f1 and f2 and, if necessary, f0 or f3, f4, etc. is used.

Claims

1. A method for determining the impedance of an electrical or electro-chemical structural element by means of correction of a synchronization error Δt, the method comprising: - selecting an impedance model for the structural element, the impedance model having at least one resistance R and an inductance L; - applying one or more excitation signals I(t) or U(t) at at least two frequencies f1 and f2 respectively; - measuring a response signal U(t+Δt) or I(t+Δt), the response signal being able to have a synchronization error Δt relative to the excitation signal; - determining impedances Z1 and Z2 from the excitation signal and the response signal in each case at f1 and f2; - Determine Δt as the value for which the difference Z diff = Z2 - Z1 between the measured values and the corresponding value diff calculated for the equivalent circuit diagram deviates by less than a predetermined threshold with respect to at least one impedance component; - correcting the impedance values using the determined synchronization error Δt.

2. The method according to claim 1, wherein The electrical or electro-chemical structural element is a lithium-ion single cell.

3. The method according to claim 1, wherein, The determination of Δt is performed iteratively, where the difference Z is calculated in each iteration diff = Z2 - Z1, and Δt of the phase calculation and the cumulative differential is calculated from Z diff , and the phases of Z2 and Z1 are corrected by the accumulated value korr .

4. The method according to any one of claims 1 to 3, wherein, f1 and f2 are from 1 kHz to 20 kHz.

5. The method according to any one of claims 1 to 3, wherein The method further comprises determining the impedance at one or more further frequencies f0 below f1 and f2.

6. The method according to claim 5, wherein f0 is from 10 Hz to 300 Hz.

7. The method according to any one of claims 1 to 3, wherein The excitation signal comprises a superposition of the frequencies f1, f2.

8. The method according to claim 5, wherein The excitation signal comprises a superposition of the frequencies f1, f2 and f0 and further frequencies.

9. A battery system, the battery system being set up to carry out the method according to any one of claims 1 to 8, the battery system comprising: - a plurality of lithium-ion single cells, where individual cells or blocks formed by a plurality of cells connected in parallel are connected in series; - one or more signal generators for applying the excitation signal; - one or more single cell monitoring units (CSC) for monitoring the single cell voltage of the lithium-ion single cells, the single cell monitoring units being set up to record the response signal; and - one or more computing units, the computing units being set up to carry out the method according to any one of claims 1 to 8.

10. The battery system according to claim 9, the battery system comprising a single signal generator which globally applies the excitation signal to the total current.

11. The battery system according to claim 9 or 10, wherein, The computing unit is integrated into the single cell monitoring unit.

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