Identifying impedance by identifying phase

Abstract

The present invention relates to a method for correcting a synchronization error Δt when measuring the impedance of an electrical or electrochemical component, particularly a lithium-ion battery. Generally, during impedance measurement, a synchronization error may occur between an excitation signal and a response signal, which may distort the phase 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 difference with an equivalent circuit having at least one resistance R and inductance L. This allows the phase of the obtained impedance value to be corrected.

Description

[Technical field]

[0001] The present invention particularly relates to a method for identifying a phase when calculating impedance when measuring the impedance of a lithium ion battery. [Background technology]

[0002] Electrochemical impedance spectroscopy (EIS) is an established method for characterizing electrochemical systems, in particular galvanic cells, and generally involves measuring the impedance depending on the frequency of an excitation signal, i.e. the complex AC resistance.

[0003] It is known in the prior art to use impedance measurements or impedance spectroscopy to diagnose the condition of lithium ion batteries, and in particular to determine the temperature of lithium ion batteries by impedance.

[0004] Patent document 1 relates to cell temperature and degradation measurement in a lithium-ion battery system of an electric vehicle by determining the cell impedance based on an AC voltage signal set by an inverter. The method is based on the observation that the progression of a plot of impedance against signal frequency depends on temperature.

[0005] US Patent No. 5,399,633 describes a method for determining temperature by measuring the imaginary part of the impedance at several frequencies and determining the frequency at which the imaginary part crosses zero. This method is based on the observation that for a given state of charge and ageing of a cell, the frequency of the zero crossing is largely temperature dependent.

[0006] No. 5,399,633 relates to a battery charging system having temperature sensors alternately connected in a time division multiplexed manner to each cell being charged in order to measure the impedance of the cell and determine the temperature from the phase of the impedance. The rate of change of temperature over time then serves as an indication of whether the cell is fully charged.

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

[0008] Typically, excitation is performed in a constant current fashion (i.e. as a current signal with a constant amplitude), the resulting voltage signal is measured, and the impedance is calculated from the amplitude and phase of the two signals. There are two basic ways to perform the excitation:

[0009] On the one hand, each cell can be excited individually with a balancing current. In this case, a cell supervision unit (Cell Supervision Circuit, CSC (Battery Monitoring Board)), which also performs charge equalization (balancing) between the cells, applies an excitation signal to the balancing current and at the same time measures the high-frequency components of the falling voltage and calculates the impedance from it. This has the advantage that very accurate phase information is obtained, since the generation of the excitation signal, the acquisition of the measurement signal and the calculation of the impedance are performed by the same control device. The disadvantages are high power consumption and strict requirements on the accuracy of the voltage measurement.

[0010] Alternatively, excitation can be applied externally, for example via an inverter or DC-DC converter. This allows higher excitation signal levels, improving the signal-to-noise ratio and relaxing the requirements for voltage measurement accuracy. Moreover, no excitation circuitry is required in the individual cell monitoring units, and impedance calculations from the measured voltage signals can be performed externally by a separate control device, reducing power consumption and equipment costs.

[0011] Methods with external excitation, where the signals are processed by different control devices, entail, inter alia, the risk of synchronization errors between the excitation signal and the response signal, which in turn reduces the accuracy of the temperature determination. As a result, an asynchrony of 10 μs leads to a phase error of 3.6°. If, for example, the temperature of a cell has to be determined from the phase of the impedance, then, for example, for a 60 Ah cell, at 300 Hz, a phase accuracy of 3.6° leads to a temperature accuracy of 7.2 K. [Prior art documents] [Patent documents]

[0012] [Patent Document 1] DE 102013103921 A1 [Patent Document 2] European Patent Application Publication No. 2667166 [Patent Document 3] US Patent Application Publication No. 2013 / 0264999 Summary of the Invention [Problem to be solved by the invention]

[0013] In view of the above problems, a method is needed to calibrate the phase of the excitation signal and the response signal to allow impedance determination with high phase accuracy, in order to enable accurate temperature determination even when the signals have a synchronization error Δt. [Means for solving the problem]

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

[0015] The method according to the invention can be advantageously used in conjunction with external excitation. It allows the energy required during impedance measurement to be reduced and the quality of the impedance measurement to be improved. At the same time, it allows a distributed architecture in which the generation of the excitation signal and the voltage measurement can exist separately from each other due to the impedance calculation, without imposing high requirements on the synchronicity of both 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 electrochemical component, in particular a lithium-ion battery, comprising the steps of: - selecting an impedance model of said component comprising at least one resistance R and one inductance L, - applying one or more excitation signals I(t) or U(t) having at least two frequencies f1 or f2; - measuring the response signal U(t+Δt) or I(t+Δt) possibly with a synchronization error Δt with respect to the excitation signal; - determining impedances Z1 and Z2 at f1 or f2 from the excitation signal and the response signal; - Difference in measurements Z diff = Z2-Z1 and Z calculated for the equivalent circuit diff identifying, for at least one impedance component, a value of Δt that is below a predetermined threshold value; - Correcting the impedance value using the determined synchronization error Δt The present invention relates to a method comprising the steps of:

[0018] In the method according to the invention, excitation signals of different frequencies can be applied alternately or an excitation signal comprising a superposition of multiple frequencies can be used.

[0019] The at least two frequencies f1 or f2 used to determine the synchronization error Δt are preferably 1 kHz or higher, so that the capacitive contribution to the impedance can be neglected and the impedance model only comprises resistance and inductance.

[0020] 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 lower than f1 or f2. [Brief description of the drawings]

[0021] [Figure 1] FIG. 1 shows the general flow of the method according to the invention where impedance is measured at three frequencies f0, f1 and f2 and the measurements at f1 and f2 are used to determine Δt assuming an LR model. [Diagram 2] FIG. 2 shows a flow chart of an embodiment of a method according to the present invention in which Δt is determined by an iterative control algorithm. [Diagram 3] 3 shows the convergence behavior of the algorithm shown diagrammatically in FIG. 2. In the top left, the real and imaginary parts of the impedance at five different frequencies are plotted against the gradually converging Δt (counterclockwise) in a Nyquist diagram, in the top right, the evolution of the phase difference is plotted against the number of iterations, and in the bottom two diagrams, the differential change in Δt (left) as well as the accumulated value of Δt (right) are plotted against the number of iterations. [Figure 4] FIG. 1 shows a battery system provided for implementing the method according to the invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] [Basics]

[0023] To introduce the terminology, the fundamentals of impedance measurement are briefly summarized below. These explanations are for the constant current case, which is common in practice, where an alternating current signal I(t) with known amplitude I0 and known frequency f is applied and the voltage drop U(t) is measured. However, they are also valid in an equivalent manner for the reverse case, i.e. the equally possible case of applying a set voltage signal and measuring the current.

[0024] The signals I(t) and U(t) are expressed in the complex plane as follows:

number

[0025] In what follows, both the frequency f and the angular frequency ω=2πf may be referred to collectively as “frequency” only when it is clear from the context or from the symbol ω / f used which frequency is meant.

[0026] The signals I(t) and U(t) are generally out of phase with each other by a phase angle φ, defined as the zero angle between the voltage and current. The impedance Z is calculated as U(t) / I(t), and is a complex number unless φ is equal to zero:

number

[0027] The real part Re(Z)=R corresponds to the ohmic resistance and is also called the effective resistance. The imaginary part Im(Z)=X appears due to the phase shift and is also called the reactance.

[0028] The magnitude of impedance, |Z|, is the ratio of the effective current to the effective voltage, and is called impedance. It includes both effective resistance and reactance, and is usually frequency dependent. However, power is dissipated only due to the effective resistance.

[0029] For an ideal ohmic resistor, the phase shift is zero and the impedance corresponds to the effective resistance 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, Z=+iωL (L: inductance), i.e. the reactance increases with increasing frequency.

[0030] According to the invention, impedance measurements are used in particular to detect the state of a lithium-ion battery (temperature, state of charge, etc.). Most processes in the cell based on charge transport can then be described by an ohmic resistance, including the kinetics of ionic conduction in the electrolyte and intercalation and deintercalation at the electrodes. Capacitive resistances appear, for example, in the electric double layers at the electrodes. The cell can therefore be approximately modeled by an equivalent circuit with at least one RC component representing the electrode processes and a series resistance R0 representing the electrolyte resistance connected in series with it (the "R0-RC model").

[0031] The inductance is not so much related to the electrochemical process itself, but arises primarily from the magnetic fields in the conductors involved (current collectors, supply lines, wiring). Overall, the inductance of the device configuration can introduce a significant portion of the phase shift in terms of magnitude at relatively high frequencies. However, this portion can be treated as a (frequency-dependent) device constant, since the device configuration is fixed and is not influenced by the electrochemical processes in the cell, and can therefore be omitted from the calculation of the cell state being diagnosed. Nevertheless, at high frequencies, the contribution of L becomes dominant in the impedance. Therefore, especially at high frequencies, the equivalent circuit representing the impedance must further include a series inductance L (the “L-R0-RC model”).

[0032] [Synchronization method]

[0033] The signals I(t) and U(t) may generally have a synchronization error. That is, the signals I(t) and U(t) are not recorded synchronously, and the time zero points are shifted from each other by an unspecified time difference Δt, for example, a few μs. Therefore, in practice, I(t) and U(t) are not used for impedance calculation, but I(t) and U(t+Δt). Therefore, the phase angle φ measured in this way mess is disguised by a phase error Δφ relative to the correct phase shift φ:

number

[0034] The impedance value actually measured (i.e. calculated from the signals I(t) and U(t) with synchronization error) is then:

number

[0035] The method according to the invention, in brief, essentially exploits the frequency dependence of the inductance of the arrangement and the resulting inductive resistance in order to synchronize the signals U(t) and I(t), the frequency being preferably chosen high enough so that the capacitive contribution is negligible and the impedance is determined by the inductive and ohmic contributions.

[0036] Therefore, the method according to the present invention will be concretely demonstrated for the case of a pure LR model which approximately represents the behavior of the cell at high frequencies.

[0037] As explained above, a cell can generally be approximately represented as an L-R0-RC model. The impedance Z of the RC component is RC (ω) depends on frequency:

number

[0038] Therefore, at high frequencies, Z RC Since (ω) disappears and only the series resistance R0 and inductance L remain, the behavior of the cell follows the LR model.

number

[0039] According to the present 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. Next, the difference between the measurements, Z diff = Z2-Z1 and Z calculated for the equivalent circuit diff Δt is identified as a value for which the difference between the corresponding value of Δt and the corresponding value of Δt is below a preset threshold for at least one impedance component.

[0040] R0 is frequency independent, so when we take the difference (form the difference) in a pure LR model the real part disappears and we are left with a purely imaginary component.

number

[0041] In the representation of Z, the real part corresponds to the sine term, i.e. the synchronization error can be identified as the point where the difference in the sine terms vanishes:

number

[0042] So in this case the asynchrony Δt is calculated as the value where the real difference vanishes, which can be done analytically or numerically. This has the advantage that the model parameters R and L do not need to be known, since the above ideas for the pure LR model hold for any choice of L and R.

[0043] By rotating the phase of Z1 and Z2 by Δφ1=2πf1*Δt or Δφ2=2πf2*Δt, a corrected impedance value can be calculated.

[0044] This approach was based on a pure LR model, which may be valid when both frequencies f1 and f2 are high enough that the capacitive contribution becomes negligible, for example above about 1 kHz.

[0045] To diagnose the cell condition, in particular the electrode processes, it is necessary to carry out impedance measurements at one or more relatively low frequencies f0, for example in the region of 10-300 Hz, preferably about 30-200 Hz, where the capacitive contribution is not negligible. In this case, the method according to the invention can still be carried out at frequencies f1 and f2 above 1 kHz, where the LR model is applicable, and the value of Δt thus obtained is then used to correct the impedance at f0. Figure 1 shows diagrammatically such a method, where three frequencies f0, f1 and f2 are used, but only f1 and f2 are used to determine Δt.

[0046] Furthermore, more complex impedance models may be required in some cases, e.g. by extending them with additional resistors (R-LR model). Finally, it may be necessary to explicitly take capacitive contributions into account, e.g. when there is an upper limit on the usable frequencies due to the cost of the equipment.

[0047] In these cases, more complex impedance models must be prepared, which may include ohmic resistance R, capacitance C or LR components or possibly even other elements such as Warburg elements. In order to determine Δt with minimal deviation from the equivalent circuit, it is usually necessary to know the values ​​of the model parameters (R, L, etc.). For this purpose, the model parameters can be determined and stored with high accuracy, for example in separate measurements, and the method according to the invention is carried out using the model parameters thus pre-specified.

[0048] Alternatively, some or all of the model parameters may be identified simultaneously with Δt as part of the method according to the invention. This is a numerical optimization problem in which the system has as degrees of freedom the synchronization error Δt as well as the model parameters to be identified. Therefore, in this case, the number of frequency points f1, f2 etc. or the number of measured impedance values ​​Z1, Z2 must preferably be equal to or greater than the number of degrees of freedom so that the system is specified or over-specified. The optimization problem is solved on the basis of a system of simultaneous equations obtained for the impedance at various frequencies, solved according to methods well known per se.

[0049] In one possible embodiment, the optimization is performed by subtracting the difference Z between the measured impedances Z1 and Z2. diff This is done by a repetitive control algorithm based on diff The phase of (weighted by a proportionality factor a) gives the iteration step size, as shown in Figure 2. Then, at each iteration, the difference Z diff =Z2-Z1 is calculated, and Z diff The difference between the phase of Δt korr is calculated and accumulated, and the accumulated value also corrects the phase of Z2 and Z1.

[0050] The individual steps are as follows: 1. Initialize with Δt=0; to get a final estimate of Δt, we first iterate over the difference Δt korr are calculated and added. 2.From the current value of Δt to Δφ 1,2 =2πf 1,2 *Calculate Δφ1 or Δφ2 as Δt; 3. Phase-corrected measurement value Z mess,korr (f1) or Z mess,korr To obtain (f2), we use the raw (i.e., with synchronization error Δt) measurement Z mess (f1) and Z mess Rotate (f2) by Δφ1 or Δφ2; 4. Difference Zdiff =Z mess,korr (f2)-Z mess,korr Formation of (f2); 5.Z diff Phase Δφ diff Identification of; 6. Correction term Δt korr = Δφ diff Identifying / 2πf1; 7. Δt weighted by coefficient a korr Increment the value of Δt in; 8.Δφ diff Repeat steps 2 to 7 by incrementing the value of Δt until it falls below a predefined threshold; 9. Obtain the corrected impedance value from the calculated Δt.

[0051] The weighting coefficient a controls the step size of the iterations and can be appropriately selected, for example in the interval 0.1 to 1.0, to enable fast convergence on the one hand and to avoid oscillations of the cumulative value of Δt around the actual value on the other hand. a is the time constant for each difference value Δt korr The frequencies f1 and f2 are preferably high enough that the capacitive terms are negligible and the LR model applies, for example 1 kHz or higher. The Δt calculated from f1 and f2 can still be used to correct the synchronization at lower frequencies f0, where the pure LR characteristic no longer holds.

[0052] 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 a Nyquist diagram for a gradually converging (counterclockwise) Δt. In the upper right, the evolution of the phase difference is plotted against the number of iterations. In the two bottom diagrams, the differential change in Δt (left) and the accumulated value of Δt (right) are plotted against the number of iterations.

[0053] [implementation]

[0054] The method according to the invention can be used in particular to improve the accuracy of impedance measurements as part of the monitoring and condition diagnostics of cells in a battery system, in particular lithium ion batteries.

[0055] This may in particular be a battery system for an electric or hybrid electric vehicle.A battery system of this kind comprises a number of lithium-ion batteries controlled by a battery management system (BMS).

[0056] Typically, several cells are connected together in series and / or parallel to form a battery pack, each connected to a cell monitoring unit (CSC) that monitors at least the cell voltage and also controls the charge equalization. Either one cell monitoring unit may be provided for each individual cell or several cells may be connected to one cell monitoring unit. This unit may have several input channels for voltage measurement so that several connected cells of the unit can be monitored simultaneously or in a division multiplexed manner. The whole set of cells and cell monitoring units is also monitored by a battery management unit (BCU, Battery Control Unit).

[0057] The excitation signal for the impedance measurement is preferably applied as an alternating signal, which can be done cell by cell, for example via a balancing current, or globally from the outside, for example via an inverter. The recording of the response signal can be done by the voltage monitoring function of the CSC. As explained above, a risk of synchronization errors is present especially in the case of global external excitation, so that the method according to the invention is preferably suitable for this application.

[0058] Figure 4 shows a schematic diagram of an example of an electric vehicle battery system in which the method according to the invention can be used. In this system, a number of cells are connected to form modules, each of which is provided with a CSC that monitors the voltages of the cells in the module. These modules are further connected in series. An excitation signal is added to the overall current through an inverter, and a response signal is recorded by the CSC.

[0059] Since Δt may vary from cell to cell or from module to module, the impedance calculation and the execution of the method according to the invention may be performed by the CSC as well. Alternatively, the recorded response signal may be sent to the BCU, which then takes over the execution of the method according to the invention and the impedance calculation. To avoid overloading the communication channel, the impedance calculation in the CSC is preferred.

[0060] The frequencies f1 and f2 used to determine Δt, and further frequencies f3, f4, ... if necessary depending on the complexity of the model and the desired accuracy, are preferably high enough so that the capacitive contribution can be neglected. For example, frequencies between 1 kHz and 20 kHz can be used. These frequencies have a set interval from each other, and the magnitude can be, for example, 100 Hz to 5 kHz, preferably 500 Hz to 2 kHz or 1 kHz to 2 kHz. Besides determining Δt, the impedance values ​​at frequencies f1, f2, etc. can also be used to determine the electrolyte resistance.

[0061] In contrast, for the characterization of electrode processes whose contribution to the impedance can be described by RC components, one or more relatively low frequencies f0 are preferred, where the capacitive contribution is not negligible (e.g. in the range of the inverse of the time constant of the RC component involved). These frequencies f0 are, for example, between 10 and 300 Hz, preferably between 20 and 200 Hz. In view of the simplicity of the impedance model, it is preferred that the frequency f0 is not used for the determination of Δt by the method according to the invention. Conversely, the calculated value of Δt can be used to correct the impedance at f0.

[0062] It is possible to use an excitation signal which has only one single frequency at a time and which is then varied, however it is preferred that a superposition of multiple or all the required frequencies f1 and f2 and, if necessary, f0 or f3, f4 etc. is used.

Claims

1. 1. A method for determining the impedance of an electrical or electrochemical component, in particular the impedance of a lithium-ion battery, with correction for a synchronization error Δt, comprising: - selecting an impedance model of said component, comprising at least one resistance R and one inductance L; At least two frequencies f １ Or f ２ applying one or more excitation signals I(t) or U(t) having - measuring a response signal U(t+Δt) or I(t+Δt) possibly with a synchronization error Δt with respect to the excitation signal; -f １ Or f ２ Impedance Z at １ and Z ２ from the excitation signal and the response signal; - Difference in measurement value Z ｄｉｆｆ =Z ２ -Z １ and Z calculated for the equivalent circuit ｄｉｆｆ identifying, for at least one impedance component, a value of Δt that is below a predetermined threshold; - Correcting the impedance value using the determined synchronization error Δt The method includes:

2. The determination of Δt is repeated, and the difference Z ｄｉｆｆ =Z ２ -Z １ is calculated, and Z ｄｉｆｆ The difference between the phase of Δt ｋｏｒｒ is calculated and accumulated, and Z is calculated from the accumulated value. ２ and Z １ The method of claim 1 , wherein the phase of

3. f １ and f ２ The method according to claim 1 or 2, wherein the frequency is between 1 kHz and 20 kHz.

4. 4. The method according to claim 1, further comprising the steps of: １ and f ２ One or more further frequencies f lower than ０ The method further comprising determining an impedance in the

5. f ０ The method of claim 4, wherein the frequency is between 10 and 300 Hz.

6. The excitation signal has a frequency f １ , f ２ and optionally f ０ 6. The method according to claim 1, further comprising superposition with other frequencies.

7. A battery system configured to carry out a method according to any one of claims 1 to 6, comprising: - several blocks of cells connected in parallel or several lithium ion batteries each of which is connected in series; - one or more signal generators for applying excitation signals; - one or more cell monitoring units (CSC) for monitoring the cell voltages of the lithium-ion battery, configured to record the response signals; - one or more computing units configured to carry out the method according to at least one of claims 1 to 6; A battery system having

8. 8. The battery system of claim 7 including a single signal generator that applies the excitation signal generally to all of the currents.

9. 9. The battery system according to claim 7 or 8, wherein the calculation unit is incorporated in the cell monitoring unit.

Images