Battery Impedance Estimation Method

Abstract

A method (1000) for estimating the impedance of a battery (B), comprising: acquiring (S1100) data of the battery (B) during at least a predetermined time range, including at least a plurality of voltage measurements (V) and a plurality of current measurements (I); determining (S1200) a time window (W) within the predetermined time range, which starts after a relaxation voltage interval (RVI) and includes a dynamic load interval (DLI); determining (S1300) an initial voltage, which is the voltage measurement (V) at the start of the time window (W); determining (S1400, S4400) a plurality of dynamic voltages based on the voltage measurements (V) and the initial voltage within the time window (W); performing a subspace identification analysis (S1500, S5500) based on the plurality of current measurements (I) and the plurality of dynamic voltages; and calculating (1600) the impedance (S1500) from the output of the subspace identification analysis.

Description

Technical Field

[0001] The present invention relates to a method and apparatus for estimating battery impedance. Background Art

[0002] Batteries have found more and more applications in daily use. To ensure the proper use of batteries, battery analysis and management are becoming increasingly important, and the proper use of batteries is crucial for achieving maximum performance and extending their lifespan.

[0003] Various battery parameters are used for battery analysis and management. Among them, the impedance of the battery has a relevant role for the following reasons.

[0004] Impedance is used to determine the power capacity of the battery. In addition, batteries, especially lithium-ion batteries, may be sensitive to overvoltage / undervoltage. The impedance value can be used to determine the maximum allowable current, thus avoiding exceeding the voltage limit. In addition, batteries, especially lithium-ion batteries, typically age over time. The impedance value is also a key indicator of battery aging. In addition, the heat generation of the battery can be quantified using impedance. Thermal management control can thus use impedance knowledge to achieve more effective / efficient operation. In addition, in various advanced battery control systems, the impedance value is used for various model-based estimations such as state of charge and state of energy, and predictions such as EV driving range.

[0005] The impedance value of the battery is thus highly relevant for improving the use and / or management of the battery. Since this value changes over time, its measurement over time is also usually desired.

[0006] There are various ways known in the art for measuring and / or estimating battery impedance.

[0007] The impedance can be determined before the start of life. The simplest method is to have an impedance static lookup table. This lookup table can be created using characteristic tests at the start of battery life. Then the impedance of similar batteries can be estimated through the lookup table. As an extension, data collected in laboratory tests can be used to model the impedance change over battery life. In particular, sample batteries can be tested from the start of life to the end of life in the laboratory. Then, the lookup table can be extended to also consider aging issues.

[0008] Due to the large number of tests, this method is costly. In addition, it is complex to model the impedance throughout the entire battery life.

[0009] An alternative way to estimate impedance can be based on measurements made on the battery during operation. For example, during the service life of the battery, the operation of the battery can be periodically interrupted for diagnosis. During these interruptions, a given current and / or voltage pulse is input into the battery, and the corresponding voltage and / or current response is measured. In this way, the DC resistance can be calculated. Similarly, an AC current and / or voltage can be input into the battery, and its voltage and / or current response can be measured to obtain the AC impedance. The AC frequency can be kept constant by a 1 kHz resistance measuring device commonly used in the automotive industry, or varied by electrochemical impedance spectroscopy.

[0010] The disadvantages of this method are that the operation of the battery needs to be periodically interrupted, which is usually unacceptable to the user. In addition, it requires the measuring device to be connected to the battery at all times, which increases the cost. Furthermore, due to unreasonable optimization and noisy data from the sensors, the analysis of data from such measuring devices is usually inaccurate and requires a large amount of computational effort.

[0011] Therefore, there is a need for a method to estimate the impedance of a battery that can be implemented in a simple and / or cost-effective manner and provide reliable results. Summary of the Invention

[0012] The present invention is generally based on the concept that the impedance of a battery can be measured from voltage and / or current measurements when the battery is in use. In particular, embodiments of the present invention generally relate to how to select and manipulate data from these measurements to obtain an estimate of the impedance.

[0013] Therefore, the present invention allows the impedance to be estimated without the need for extensive battery characterization and without interrupting the operation of the battery. In addition, since only voltage and / or current data from the battery are required, the present invention can be implemented in most systems that include a battery, because most systems have sensors for measuring these values. Advantageously, the impedance can thus be estimated remotely without the need to physically access the battery.

[0014] One aspect of the present invention may particularly relate to a method for estimating the impedance of a battery, the method may include the following steps: obtaining data of the battery during at least a predetermined time range, the data including at least a plurality of voltage measurements and a plurality of current measurements; determining a time window within the predetermined time range, the time window starting after a relaxation voltage interval and including a dynamic load interval; determining an initial voltage, the initial voltage being the voltage measurement at the start of the time window; determining a plurality of dynamic voltages based on the voltage measurements and the initial voltage within the time window; performing subspace identification analysis based on the plurality of current measurements and the plurality of dynamic voltages; calculating the impedance from the output of the subspace identification analysis.

[0015] Due to this method, the dynamic component of the voltage measurement value can be advantageously decoupled from its static component. Due to this separation, the dynamic component can be input into the subspace identification analysis, enabling the calculation of the impedance of the battery.

[0016] In some cases, the time window may start immediately after the end of the relaxation voltage interval.

[0017] Due to this method, it can be advantageously ensured that the open state of the charge calculated at the end of the relaxation voltage interval can correspond to the charge state at the start of the time window.

[0018] In some cases, the time window may start within a predetermined time after the end of the relaxation voltage interval RVI.

[0019] Due to this method, it can be advantageously ensured that the open state of the charge calculated at the end of the relaxation voltage interval substantially corresponds to the charge state at the start of the time window.

[0020] In some cases, the dynamic load interval may be a time interval during which the following conditions apply: the integral value of the absolute value of the current measurement is within a predetermined range, preferably higher than 1% of the battery capacity, and / or preferably lower than 5% of the battery capacity, and / or even more preferably lower than 2.5% of the battery capacity.

[0021] In some cases, the dynamic load interval may be a time interval during which the following conditions apply: the difference between the maximum value of the integral of the current measurement during the time interval and the minimum value of the integral of the current measurement during the time interval is within a predetermined range, preferably higher than 2.5% of the battery cell capacity and / or preferably lower than 5% of the battery cell capacity.

[0022] Due to these methods, the amount of battery charge / discharge during the dynamic load interval can be advantageously included in the values leading to a reliable estimate of the battery impedance, while also ensuring sufficient dynamic behavior of the battery, which helps in the correct estimation of the impedance.

[0023] In some cases, the dynamic load interval may be a time interval during which the following conditions apply: the value of the statistical measure of the dispersion of the current measurement, preferably the standard deviation of the current measurement, is higher than a predetermined value, preferably higher than 10% of the battery charge and discharge rate (C-rate), and even more preferably higher than 25% of the battery C-rate.

[0024] In some cases, the dynamic load interval can be a time interval during which the following condition applies: the absolute value of the derivative of the current measurement reaches a predetermined threshold, preferably higher than 1 C-rate / s.

[0025] In some cases, the dynamic load interval can be a time interval during which the following condition applies: the absolute value of the derivative of the moving average of the current measurement reaches a predetermined threshold, preferably higher than 1 C-rate / s.

[0026] In some cases, the dynamic load interval can be a time interval during which the following condition applies: the Fourier transform of the current measurement results in one or more frequency peaks at non-0 Hz.

[0027] Due to these methods, it can be advantageously ensured that the sufficient dynamic behavior of the battery is part of the dynamic load interval.

[0028] In some cases, the dynamic load interval can have a duration of and / or at least 1 minute, preferably and / or at least 5 minutes.

[0029] In some cases, the battery can be modeled as having one or more RC elements, and the dynamic load interval can have a duration of the largest of the one or more RC elements and / or at least 1 times, preferably and / or at least 5 times the largest duration.

[0030] Due to these methods, it can be advantageously ensured that the length of the dynamic load interval contains sufficient data for reliably observing the battery dynamics and thus for reliably calculating the impedance.

[0031] In some cases, the step of determining the dynamic voltage can include the following steps: determining an estimated initial state of charge based on the initial voltage, where the estimated initial state of charge is the estimated state of charge at the start of the time window; determining a plurality of estimated states of charge for the entire time window based on the estimated initial state of charge; determining a plurality of estimated open-circuit voltages over the entire time window based on the plurality of estimated states of charge; and determining a plurality of dynamic voltages at any given time over the entire time window as the difference between the voltage measurement at the given time and the corresponding estimated open-circuit voltage.

[0032] Due to this method, it can be advantageously ensured that the static component of the voltage measurement is tracked over the entire time window, thereby removing the static component from the voltage measurement and leaving the dynamic component for subsequent analysis.

[0033] In some cases, the subspace identification analysis can be performed with the plurality of current measurements as input and the plurality of dynamic voltages as output.

[0034] Due to this method, a state - space representation of the battery can be advantageously created, and subspace identification analysis allows the extraction of impedance therefrom.

[0035] In some cases, subspace identification analysis can be based on the following type of state - space representation

[0036] x k+1 = Ax k + Bu k

[0037] y k+1 = Cx k + Du k

[0038] where

[0039] - k represents the moment of the time window,

[0040] - k + 1 represents the moment after k,

[0041] - x k represents the state vector at time k,

[0042] - u k represents the current measurement value at time k,

[0043] - y k represents the values of multiple dynamic voltages at time k,

[0044] - A represents the state - transition matrix,

[0045] - B represents the control - input matrix,

[0046] - C represents the output matrix,

[0047] - D represents the feed - through matrix.

[0048] Due to this method, a state - space representation of the battery can be advantageously created easily and reliably.

[0049] In some cases, the steps of performing subspace identification analysis can include any of the following steps: orthogonal projection of the block Hankel matrix of current measurement values, orthogonal projection of the block Hankel matrix of dynamic voltages, oblique projection of the orthogonal projection of the block Hankel matrix of current measurement values, and oblique projection of the orthogonal projection of the block Hankel matrix of dynamic voltages.

[0050] Due to this method, noise can be advantageously projected out of the state by orthogonal projection, and a filtered observability matrix can be obtained by oblique projection.

[0051] In some cases, the step of performing subspace identification analysis may further include the step of performing singular value decomposition to obtain the system matrix A.

[0052] Due to this method, the resistance and time constant can be advantageously extracted from the system matrix A, thus allowing the calculation of impedance.

[0053] Another aspect of the present invention may relate to a device for estimating battery impedance, the device including a memory and a processor, wherein the memory includes instructions that are configured to cause the processor to perform any of the steps described above when executed.

[0054] Due to this method, the present invention can be advantageously implemented in the form of hardware.

[0055] In some cases, the device may further include a communication device for obtaining the plurality of voltage measurements and the plurality of current measurements.

[0056] Due to this method, the impedance of the battery can be advantageously determined remotely based on simple current and voltage measurements.

[0057] Another aspect of the present invention may relate to a software that, when executed on a processor, causes the processor to perform any of the steps described above.

[0058] Due to this method, the present invention can be advantageously provided in the form of software, which can be independently executed at the location of the battery. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Hereinafter, various aspects of the present invention will be described with reference to the drawings, in which like reference numerals denote like elements, and wherein:

[0060] Figure 1 Schematically illustrates a method 1000 for estimating battery impedance;

[0061] Figure 2 Schematically illustrates a device 2000 for estimating battery impedance;

[0062] Figure 3A Schematically illustrates exemplary voltage measurements over time;

[0063] Figure 3B Schematically illustrates exemplary current measurements over time;

[0064] Figure 4 Schematically illustrates a possible implementation of the dynamic voltage determination step S4400;

[0065] Figure 5 Schematically illustrates a possible implementation of the subspace identification analysis execution step S5500;

[0066] Figure 6A Schematically illustrates an exemplary charge state over time;

[0067] Figure 6B Schematically illustrates an exemplary open - circuit voltage over time;

[0068] Figure 7A Schematically illustrates an exemplary voltage measurement over time;

[0069] Figure 7B Schematically illustrates an exemplary dynamic voltage over time. Detailed implementation

[0070] Some examples of the present application generally provide multiple circuits or other electrical devices. All references to circuits and other electrical devices and the functions provided by each circuit and other electrical device are not intended to be limited to only what is illustrated and described herein. Although specific labels may be assigned to the various circuits or other electrical devices disclosed, such labels are not intended to limit the scope of operation of these circuits and other electrical devices. Such circuits and other electrical devices can be combined and / or separated in any manner based on the desired specific type of electrical implementation. It should be recognized that any circuit or other electrical device disclosed herein can include any number of microcontrollers, graphics processing units (GPUs), integrated circuits, storage devices (e.g., flash memory, random access memory (RAM), read - only memory (ROM), electrically programmable read - only memory (EPROM), electrically erasable programmable read - only memory (EEPROM) or other suitable variants thereof) and software, which cooperate with each other to perform the operations disclosed herein. In addition, any one or more electrical devices can be configured to execute program code embodied in a non - transitory computer - readable medium programmed to perform any number of the functions disclosed.

[0071] Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be understood that the following description of the embodiments is not restrictive in nature. The scope of the present invention is not intended to be limited by the embodiments or the drawings described below, and the embodiments or the drawings are only considered illustrative.

[0072] The accompanying drawings should be regarded as schematic diagrams, and the elements illustrated in the drawings are not necessarily shown to scale. Instead, the representations of the various elements are made to make their functions and general uses apparent to those skilled in the art. Any connection or coupling between the functional blocks, devices, components or other physical or functional units shown in the drawings or described herein can also be achieved through indirect connection or coupling. The coupling between components can also be established through wireless connection. The functional blocks can be implemented in hardware, firmware, software or a combination thereof.

[0073] Figure 1 Method 1000 for estimating the impedance of battery B is schematically illustrated. The method includes step S1100 of acquiring data of battery B during at least a predetermined time period, the data including at least a plurality of voltage measurement values and a plurality of current measurement values. Example voltage measurement values are visible in Figure 3A while example current measurement values are visible in Figure 3B . In some embodiments, the measurement values are preferably sampled at at least the Nyquist frequency of the corresponding signal.

[0074] Method 1000 further includes step S1200 of determining a time window W within a predetermined time range, the time window W starting after the relaxation voltage interval RVI of the battery and including the dynamic load interval DLI of the battery. In some preferred embodiments, the time window W starts immediately after the end of the relaxation voltage interval RVI. In other words, the end time of the relaxation voltage interval RVI can correspond to the start time of the time window W. In some preferred embodiments, the time window W starts within a predetermined time after the end of the relaxation voltage interval RVI. The predetermined time is preferably less than 1 minute. Alternatively or additionally, a predetermined time can be determined such that the state of charge of the battery does not change significantly during the predetermined time.

[0075] Generally speaking, it is obvious that usually the dynamic load interval DLI can start at any point after the relaxation voltage interval RVI. The relaxation voltage interval RVI can be used to reliably measure the open-circuit voltage and thus reliably derive the state of charge of the battery. Then the state of charge of the battery can be tracked over any amount of time, especially at least until the start of the relaxation voltage interval RVI, thereby providing the initial state of charge of the relaxation voltage interval RVI and thus the initial open-circuit voltage. Selecting the dynamic load interval DLI close to or immediately following the relaxation voltage interval RVI provides the advantage that the tracking of the state of charge can be at least reduced or completely avoided.

[0076] The relaxation voltage interval RVI is generally such a time interval during which the battery is not in an obvious charging and / or discharging state, as is known to those skilled in the art, preferably not in charging and / or discharging, and even more preferably for a time sufficient to stabilize the open-circuit voltage. In some embodiments, the relaxation voltage interval RVI can thus be determined as a time interval during which the voltage stabilizes within a predetermined range for at least a predetermined duration. Alternatively or additionally, in some embodiments, the relaxation voltage interval RVI can be determined as a time interval during which the absolute value of the current is below a predetermined threshold for at least a predetermined duration. In preferred embodiments, the time interval can be at least 1 minute, preferably at least 5 minutes.

[0077] The dynamic load interval DLI is typically an interval that includes battery charging and / or discharging, preferably both charging and discharging. In some embodiments, the dynamic load interval DLI can thus be determined as the interval during which the voltage varies outside a predetermined range for at least a predetermined duration. Alternatively or additionally, in some embodiments, the dynamic load interval DLI can be determined as the interval during which the absolute value of the current is higher than a predetermined threshold for at least a predetermined duration. It will be understood that the values of these ranges, thresholds, and durations depend on the characteristics of the battery, such as technology, capacity, voltage, and maximum rated output current, and those skilled in the art will know how to identify the relaxation voltage interval RLG and the dynamic load interval DLI for a given specific battery.

[0078] In some embodiments, the dynamic load interval DLI can be defined as the interval during which one or more of the following conditions apply.

[0079] One condition for identifying the dynamic load interval DLI can be whether the integral of the absolute value of the current measurement I is within a predetermined range. That is, the absolute value of the current measurement I can be integrated over the interval, and if the result is within the predetermined range, that interval can be considered the dynamic load interval DLI. In some embodiments, the predetermined range can be higher than 1% of the capacity of battery B, and / or preferably lower than 5% of the capacity of battery B, and / or even more preferably lower than 2.5% of the capacity of battery B.

[0080] Due to the upper limit of the integral of the absolute value of the current measurement I, it can be advantageously ensured that the change in the open-circuit voltage is included over the entire dynamic load interval DLI.

[0081] Another condition for identifying the dynamic load interval DLI can be whether the difference between the maximum value of the integral of the current measurement I during the interval and the minimum value of the integral of the current measurement I during the interval is within a predetermined range. That is, the current measurement I can be integrated over the entire interval, and the integral will take different values over the entire interval, with a minimum and a maximum value. In some embodiments, the predetermined range is preferably higher than 2.5% of the capacity of the battery cell and / or preferably lower than 5% of the capacity of the battery cell.

[0082] Another condition for identifying the dynamic load interval DLI is whether a statistical measure of the dispersion of the current measurement I, preferably the standard deviation of the current measurement I, is higher than a predetermined value. In some embodiments, the predetermined value is preferably higher than 10% of the battery C-rate, even more preferably higher than 25% of the battery C-rate.

[0083] Another condition for identifying the dynamic load interval DLI can be whether the absolute value of the derivative of the current measurement I reaches a predetermined threshold. In some embodiments, the predetermined threshold is preferably higher than 1 C-rate / s.

[0084] Another condition for identifying the dynamic load interval DLI can be whether the absolute value of the derivative of the moving average of the current measurement I reaches a predetermined threshold. In some embodiments, the predetermined threshold is preferably higher than 1 C-rate / s.

[0085] Another condition for identifying the dynamic load interval DLI can be whether the Fourier transform of the current measurement I results in one or more non-0 Hz frequency peaks.

[0086] Alternatively or additionally, in some embodiments, the dynamic load interval DLI can be defined as a time interval having a duration that can be and / or at least 1 minute, preferably and / or at least 5 minutes. That is, in some embodiments, this can be considered the complete duration of the dynamic load interval DLI, while in some other embodiments, this can be considered the minimum duration of the dynamic load interval DLI.

[0087] Still alternatively or additionally, in some embodiments, the dynamic load interval DLI can be defined as a time interval having a minimum duration that depends on the RC value associated with the battery impedance. In particular, the battery B can be modeled as having one or more RC elements, which will be described in more detail below, and the dynamic load interval DLI can have a duration that is 1 times, preferably 5 times, the largest of the one or more RC elements. That is, in some embodiments, this can be considered the complete duration of the dynamic load interval DLI, while in some other embodiments, this can be considered the minimum duration for the dynamic load interval DLI. For example, in Figure 3A and 3B an exemplary time window W from time T1 to time T2 is illustrated.

[0088] From Figure 3A it can be seen that for the battery under consideration, the relaxation voltage interval RVI can be visible by the voltage signal V remaining substantially stable within the time interval before T1 (approximately from 8.6×10 4 seconds to 8.62×10 4 seconds, which is sufficient to determine the relaxation voltage state). Alternatively or additionally, as Figure 3B shown, for the battery under consideration, the relaxation voltage interval RVI can be by the current signal I within the time interval before T1 (approximately from 8.6×10 4 seconds to 8.62×10 4seconds, which is sufficient to identify that it remains substantially 0 within the relaxation voltage state).

[0089] Similarly, as Figure 3A shown, the dynamic load interval DLI can be seen by the voltage signal V changing outside a predetermined range after T1, approximately starting from 8.62×10 4 seconds. Alternatively or additionally, as Figure 3B shown, the dynamic load interval DLI can be identified by the current signal I conforming to one or more of the previously indicated criteria.

[0090] As can be seen from the following description, the identification of the time window W starting after the relaxation voltage interval RVI of the battery B and including the appropriate dynamic load interval DLI of the battery B allows the separation of the signals from the future dynamic load interval DLI, in particular the dynamic components of the voltage V, from their static components.

[0091] Specifically, the battery voltage V includes a dynamic component, also known as overpotential or dynamic voltage, and a static component, also known as open-circuit voltage or static voltage. For reasons that will become clearer below, it is advantageous to remove the static component to allow the method 1000 to estimate the dynamic component. By selecting the time window W starting after the relaxation voltage interval RVI, it is possible to estimate and / or measure the static component, i.e., the open-circuit voltage, at the start of the window W and easily remove the static component from the voltage measurement V, which will be described in more detail in the following description.

[0092] Furthermore, for the execution of the method 1000, it is advantageous to have an initial estimate of the dynamic component, i.e., an initial estimate of the overpotential. By selecting the window W starting at the end of the relaxation voltage interval RVI, these estimates can be approximated to zero, which simplifies the estimation procedure.

[0093] Therefore, it is obvious that the time window W selected based on one or more of the aforementioned criteria can allow data to be extracted in a particularly advantageous manner and then allow these data to be used for subspace identification analysis to determine the battery impedance.

[0094] The method 1000 further includes a step S1300 of determining an initial voltage, which is the voltage measurement V at the start of the time window W. In some embodiments, especially when the time window W is close to the end of the relaxation voltage interval RVI, the initial voltage can also correspond to the voltage measurement V at the end of the relaxation voltage interval RVI, or to the average value of the voltage measurements V during the relaxation voltage interval RVI, or more generally to the open-circuit voltage based on the voltage measurements V during the relaxation voltage interval RVI.

[0095] Method 1000 further includes step S1400 of determining a plurality of dynamic voltages based on the voltage measurements V and the initial voltage within the time window W. Generally speaking, as described below, knowledge of the initial voltage allows determination of the dynamic component of the voltage over the entire time window W.

[0096] In particular, in the preferred embodiment as Figure 4 shown, step S4400 can implement step S1400 of determining the dynamic voltage and can include step S4410 of determining an estimated initial state of charge based on the initial voltage, where the estimated initial state of charge is the estimated state of charge at the start of the time window W. Those skilled in the art will be aware that there are various ways known for determining the estimated state of charge based on voltage values. For example, a look-up table can be used to relate the open-circuit voltage and the estimated state of charge.

[0097] For example, for the exemplary battery under consideration, performing the method on the exemplary current measurements I and voltage measurements V of Figure 3A and 3B can result in an initial voltage of approximately 4.072 V, corresponding to an estimated initial state of charge of approximately 86.4%.

[0098] Step S4400 can further include step S4420 of determining a plurality of estimated states of charge over the entire time window W based on the estimated initial state of charge. Again in this case, those skilled in the art will be aware that there are various methods known for estimating the evolution of the state of charge of a battery based on a known initial state of charge. For example, the estimated charge at any given time over the entire time window can be obtained by adding the integrated value of the current measurement I to the initial state of charge.

[0099] Returning to the exemplary execution pointed out above, Figure 6A shows an exemplary evolution of the estimated state of charge over the entire time window W. In this example, the estimated state of charge decreases significantly over the entire time window W.

[0100] Step S4400 can further include step S4430 of determining a plurality of estimated open-circuit voltages over the entire time window W based on the plurality of estimated states of charge. As previously mentioned, various means such as a look-up table can be employed to effect the conversion.

[0101] Returning to the exemplary execution mentioned above, Figure 6B shows an exemplary evolution of the estimated open-circuit voltage over the entire time window W.

[0102] Then, step S4400 may further include step S4440 of determining a plurality of dynamic voltages at any given time within the entire time window W, the plurality of dynamic voltages being determined as the difference between the voltage measurement V and the corresponding estimated open-circuit voltage at the given time. In this way, at any given time, the static component of the voltage measurement V is removed from the voltage measurement V, leaving only the dynamic component.

[0103] Returning to the exemplary implementation pointed out above, Figure 7A shows an enlarged portion of the voltage measurements for the time window W (approximately from 8.615×10 4 seconds to 8.645×10 4 seconds).

[0104] Similarly, Figure 7B shows the dynamic voltage during the time window obtained from the difference between the voltage measurement V and the static component, i.e., the estimated open-circuit voltage.

[0105] By this method, therefore, the dynamic component can be extracted from the corresponding voltage measurement V at any time point within the time window W in a simple and reliable manner. However, it is obvious that alternative ways for extracting the dynamic component from the corresponding voltage measurement V can be implemented, and the present invention is not limited to Figure 4 the specific implementation shown. Generally speaking, the purpose of step S1400 is to obtain a plurality of dynamic voltages, i.e., the dynamic component of the voltage measurement V, over the entire time window W based on the knowledge of the initial voltage.

[0106] Alternatively, in some embodiments, the open-circuit voltage of the entire dynamic load interval DLI may be considered to be substantially constant, especially if the dynamic load interval DLI is selected such that the integral of the absolute value of the current measurement during the dynamic load interval DLI is below a predetermined threshold. The advantage of this method is that it is not necessary to determine a plurality of open-circuit voltages throughout the dynamic load interval DLI, but instead a single value can be used, thus simplifying the method.

[0107] Method 1000 further includes step S1500 of performing subspace identification analysis based on the plurality of current measurements I and the plurality of dynamic voltages.

[0108] Subspace identification analysis is a known method for determining the variable state of a system that cannot be directly measured given various measurements of the system at different times. In the case of method 1000, generally speaking, subspace identification analysis can be used to determine the impedance value of the battery B based on the plurality of current measurements I and the plurality of dynamic voltages. Specifically, in a preferred embodiment, subspace identification analysis can be performed with the plurality of current measurements I as inputs and the plurality of dynamic voltages as outputs.

[0109] Various techniques for performing subspace identification analysis are known. For purposes of explanation, one possible implementation will be described below. However, it is obvious that the present invention is not limited thereto.

[0110] In some preferred embodiments, the subspace identification analysis can be based on the following type of state - space representation:

[0111] x k+1 = Ax k + Bu k

[0112] y k+1 = Cx k + Du k

[0113] where

[0114] - k represents the moment of the time window W,

[0115] - k + 1 represents the moment after k. In some embodiments, the time distance between k and k + 1 can correspond to the time distance between the sampling points of the current measurement value I and / or the voltage measurement value V.

[0116] - x k represents the state vector at time k,

[0117] - u k represents the current measurement value I at time k,

[0118] - y k represents the values of multiple dynamic voltages at time k,

[0119] - A represents the state - transition matrix, also known as the system matrix,

[0120] - B represents the control - input matrix, which can include multiple current measurements (I),

[0121] - C represents the output matrix, which can include multiple dynamic voltages,

[0122] - D represents the feed - through matrix

[0123] An example of using this implementation will be discussed below, where N represents the total number of data points in the time window W.

[0124] The state vector x can be represented as a matrix with one column and several rows, which depends on the number P of RC elements or poles of the battery B. That is, the impedance of the battery B can be described by a function with the number of poles P, or an equivalent RC circuit with P RC elements. In some embodiments, the number of poles P is at least 1, preferably 2, and even more preferably 3. For a general number of poles P, the state vector x can be described as:

[0125]

[0126] Each row in the state vector x can include the dynamic potential of a given RC element. For example, in the case where the battery B is modeled by a function having two poles, the state vector can be expressed as

[0127]

[0128] where V RC1 corresponds to the dynamic potential of the first RC element, and V RC2 corresponds to the dynamic potential of the second RC element.

[0129] The state transition matrix A can be a diagonal matrix whose number of rows is equal to the number of poles P. The diagonal elements represent the time constants of the corresponding RC elements.

[0130]

[0131] where corresponds to the time constant of the first RC element, corresponds to the time constant of the Pth RC element, and t represents time, preferably the amount of time between two consecutive sampling points in the time window W.

[0132] For example, for a two-pole system, A can be expressed as:.

[0133]

[0134] Then, the control input matrix B can be expressed as a matrix having one column and P rows:

[0135]

[0136] where R1 - RP represent the resistances of the corresponding RC elements. For example, for a two-pole system, B can be expressed as:

[0137]

[0138] The output matrix C can be expressed as a matrix having one row and P columns, where each element of the matrix is substantially equal to 1. For example, for a two-pole system, C can be expressed as:

[0139] C = [1 1]

[0140] and the feedthrough matrix D can be expressed as

[0141] D = R0

[0142] where R0 can be referred to as the ohmic resistance. Due to this configuration, it is possible to extract the impedance value of the battery B.

[0143] More specifically, for a general data point k, the general state space equation can be repeated for each subsequent sample, and the resulting output equation takes the form:

[0144]

[0145] where O i is called the observability matrix.

[0146] In addition, for a general data point k, the general state equation can be rewritten as:

[0147]

[0148] where is called the reverse controllability matrix.

[0149] Relating to the observability matrix O i and the reverse controllability matrix The above two equations constitute the basis of the subspace identification method.

[0150] Generally speaking, the subspace identification method uses the above equations and performs geometric transformation operations on the Hankel matrix to obtain the battery impedance value. More specifically, various subspace identification methods are known to those skilled in the art and can be implemented to obtain the impedance value.

[0151] Preferably, a subspace identification method defined for a combination of stochastic and deterministic systems is used. An example embodiment can be found, for example, in Chapter 6.1 on page 169 of "Subspace Identification for Linear Systems Theory - Implementation - Applications" by Peter Van Overschee / Bart De Moor, published in 1996.

[0152] Then, method 1000 may further include step S1600 of calculating the impedance from the output of the subspace identification analysis.

[0153] More specifically, step S1600 can calculate the eigenvectors of the state transition matrix A and thus obtain the time constants of the RC elements of battery B Then the remaining unknowns found in the B matrix (i.e., R1 - RP) can be calculated by solving the state equation using linear algebra.

[0154] In addition, in some preferred embodiments, the subspace identification analysis may include steps S5510 and S5520 to perform orthogonal projections on the current measurement value I obtained in step S1100 and the block Hankel matrix of the dynamic voltage obtained from steps S1400 and S4400, respectively. The orthogonal projection advantageously allows noise to be projected out of the state.

[0155] In particular, the input Hankel matrix of the current measurement value I can be defined as:

[0156]

[0157] where;

[0158] -i is a value greater than P, preferably i = 2*P, or greater, where P is the number of electrode plates of the battery B described above,

[0159] -N is the total number of data points in the window

[0160] -M = N + 1 - (2*i)

[0161] Similarly, the output Hankel matrix of the dynamic voltage V can be defined as:

[0162]

[0163]

[0164] It should be noted here that the formal difference between the past components (i.e., U p and Y p ) and the future components (i.e., U f and Y f ) is arbitrary because all the data in the matrix have been measured and are available.

[0165] In addition, in some preferred embodiments, the subspace identification analysis may include steps S5530 and S5540 to perform oblique projections on the calculated orthogonal projections of the current measurement value I and the block Hankel matrix of the dynamic voltage, respectively. The oblique projection advantageously allows the filtered observability matrix to be obtained.

[0166] In addition, in some preferred embodiments, the subspace identification analysis may further include the step S5550 of singular value decomposition to obtain the system matrix A. In particular, using the outputs of steps S5330 and S5340 as the inputs of step S5550, the observability matrix O i value can be calculated using linear algebra, and the observability matrix O iIncludes system matrix A. It is possible to obtain the impedance value of the system matrix from system matrix A. Alternatively or additionally, in some embodiments, step S5550 can be changed to use the outputs of steps S5510 and S5520 as inputs. Alternatively or additionally, step S5550 can use the outputs of steps S1400 and S4400 as inputs.

[0167] That is to say, in summary, the outputs of steps S1500 and S5500 can provide the eigenvectors of system matrix A. Calculating the eigenvalues of the subspace output can calculate, for example, the exponential term values of system matrix A for a two-pole piece system and . These exponential terms can be calculated using the sampling time and the natural logarithm. Once the exponential terms are known, the unknown resistances, namely R0, R1 - RP, will appear linearly in the system matrix equation. Therefore, the values of R0, R1 - RP can be calculated by solving for the window dynamic voltage with respect to the current measurement using, for example, the linear least squares method. This provides the values of R0, R1 - RP, which are the parameters defining the dynamic impedance of the battery system. For example, for a two-pole piece system, the values of R0, R1, R2 and can be obtained, from which the impedance of battery B can be calculated.

[0168] The above description is provided for a method. However, the present invention is not limited to being implemented as a method. In particular, as Figure 2 shown, the present invention can also be implemented by a device 2000 for estimating the impedance of battery B. In particular, the device can include a memory 2200 and a processor 2300, where the memory 2200 includes instructions configured to cause the processor 2300 to execute any of the steps described above when executed.

[0169] Preferably, device 2000 can further include a communication device 2100 for obtaining a plurality of voltage measurements V and a plurality of current measurements I. In the Figure 2 illustrated embodiment, the plurality of voltage measurements V and the plurality of current measurements I can be obtained by a voltmeter VM and an ammeter IM respectively. The communication device 2100 can communicate directly with one or more of the voltmeter VM and the ammeter IM. Alternatively or additionally, one or more of the voltmeter VM and the ammeter IM can communicate with another entity (such as the controller of battery B), and the other entity can then transmit the measurement values to the communication device 2100.

[0170] This advantageously allows the device 2000t to perform the method on the remote battery B simply by using a voltmeter VM and an ammeter IM connected to the battery B and / or the load L. It is obvious that the acquisition step S1100 can similarly be performed by the communication device 2100, such that the method can similarly be performed on the remote battery B.

[0171] Similarly, the present invention can be implemented as any one of software, a computer program, a computer program product, a computer-readable storage medium including program code, which when executed on a processor 2300 causes the processor 2300 to perform any of the steps described above.

[0172] It should be understood that the above features can be used not only in the corresponding combinations indicated, but also in other combinations or alone, without departing from the scope of the present invention.

[0173] Thus, it has been described how the present invention allows for an accurate estimation of the impedance of a battery based only on voltage and current measurements, and the method used has a low computational workload and can therefore be performed quickly and efficiently to correctly calculate the impedance value at any particular time, without the drawbacks of the prior art.

[0174] List of reference numerals

[0175] 1000: Method for estimating battery impedance

[0176] S1100: Acquisition of voltage and current data

[0177] S1200: Identification of time window

[0178] S1300: Determination of open-circuit voltage

[0179] S1400: Determination of dynamic voltage

[0180] S1500: Execution of subspace identification analysis

[0181] S1600: Impedance calculation

[0182] 2000: Device for estimating battery impedance

[0183] 2100: Communication device

[0184] 2200: Memory

[0185] 2300: Processor

[0186] B: Battery

[0187] IM: Ammeter

[0188] VM: Voltmeter

[0189] L: Load

[0190] T1, T2: Time

[0191] I: Measured current value

[0192] V: Measured voltage value

[0193] RVI: Relaxation voltage interval

[0194] DLI: Dynamic load interval

[0195] S4400: Dynamic voltage determination

[0196] S4410: Estimated initial charge state determination

[0197] S4420: Multiple estimated charge state determination

[0198] S4430: Multiple estimated open circuit voltage determination

[0199] S4440: Multiple dynamic voltage determination

[0200] S5500: Subspace identification analysis execution

[0201] S5510: Orthogonal projection of block Hankel matrix

[0202] S5520: Orthogonal projection of block Hankel matrix

[0203] S5530: Oblique projection of orthogonal projection of block Hankel matrix

[0204] S5540: Oblique projection of orthogonal projection of block Hankel matrix

[0205] S5550: Linear fitting and singular value decomposition

Claims

1. A method (1000) for estimating the impedance of a battery (B), the method comprising the following steps: Acquire (S1100) data of the battery (B) during at least a predetermined time range, the data including at least a plurality of voltage measurements (V) and a plurality of current measurements (I); Determine (S1200) a time window (W) within the predetermined time range, the time window (W) starting after a relaxation voltage interval (RVI) and including a dynamic load interval (DLI); Determine (S1300) an initial voltage, which is the voltage measurement (V) at the start of the time window (W); Based on the voltage measurements (V) and the initial voltage within the time window (W), determine (S1400, S4400) a plurality of dynamic voltages; Perform subspace identification analysis (S1500, S5500) based on the plurality of current measurements (I) and the plurality of dynamic voltages; Calculate (1600) the impedance (S1500) from the output of the subspace identification analysis; Wherein, the step of determining (S4400) the dynamic voltages includes the following steps: Determine (S4410) an estimated initial state of charge based on the initial voltage, the estimated initial state of charge being the estimated state of charge at the start of the time window (W); Based on the estimated initial state of charge, determine (S4420) a plurality of estimated states of charge over the entire time window (W); Based on the plurality of estimated states of charge, determine (S4430) a plurality of estimated open circuit voltages over the entire time window (W); Determine (S4440) the plurality of dynamic voltages as the difference between the voltage measurement (V) and the corresponding estimated open circuit voltage at a given time over the entire time window (W).

2. The method according to claim 1, wherein, The time window (W) starts immediately after the relaxation voltage interval (RVI) ends.

3. The method according to claim 1, wherein, The time window (W) starts within a predetermined time after the relaxation voltage interval (RVI) ends.

4. The method according to any one of the preceding claims, wherein, The dynamic load interval (DLI) is a time interval during which one or more of the following conditions apply: - The integral value of the absolute value of the current measurement (I) is within a predetermined range, higher than 1% of the battery capacity and / or lower than 5% of the battery capacity; - The difference between the maximum value of the integral of the current measurement (I) and the minimum value of the integral of the current measurement (I) during the time interval is within a predetermined range, higher than 2.5% of the battery cell capacity and / or lower than 5% of the battery cell capacity; - A statistical measure for the dispersion of the current measurement (I) is higher than a predetermined value; - The absolute value of the derivative of the current measurement (I) reaches a predetermined threshold, higher than 1C-rate / s; - The absolute value of the derivative of the moving average of the current measurement (I) reaches a predetermined threshold, higher than 1C-rate / s; - The Fourier transform of the current measurement (I) results in one or more frequency peaks at non-0 Hz.

5. The method according to claim 4, wherein, The statistical measure for the dispersion of the current measurement (I) is the standard deviation of the current measurement.

6. The method according to claim 4, wherein, The statistical measure of the dispersion of the current measurement value (I) is higher than 10% of the C-rate of the battery.

7. The method according to claim 1, wherein, The dynamic load interval (DLI) has a duration of and / or at least 1 minute.

8. The method according to claim 1, wherein, The battery (B) can be simulated as having one or more RC elements, and wherein the dynamic load interval (DLI) has the maximum duration among the one or more RC elements and / or at least 1 times the maximum duration.

9. The method according to claim 1, wherein, The subspace identification analysis is performed using the plurality of current measurements (I) as inputs and the plurality of dynamic voltages as outputs.

10. The method according to claim 1, wherein, The subspace identification analysis is based on the following type of state space representation x k+1 = Ax k + Bu k y k+1 = Cx k + Du k where -k represents the moment of the time window, -k + 1 represents the moment after k, -x k represents the state vector at time k -u k represents the current measurement value (I) of k at time -y k represents the values of multiple dynamic voltages at time k -A represents the state transition matrix, -B represents the control input matrix, -C represents the output matrix, -D represents the feedthrough matrix.

11. The method according to claim 1, wherein the step (S5500) of performing subspace identification analysis comprises any of the following steps: Orthogonal projection (S5510) of the block Hankel matrix of the current measurement value (I); Orthogonal projection (S5520) of the block Hankel matrix of the dynamic voltage; Orthogonal projection (S5530) of the block Hankel matrix of the current measurement value (I); Oblique projection (S5530) of the orthogonal projection of the block Hankel matrix of the dynamic voltage.

12. The method according to claim 11, wherein The step (S5500) of performing the subspace identification analysis further includes the following steps: Singular value decomposition (S5550) to obtain the system matrix A.

13. An apparatus (2000) for estimating the impedance of a battery (B), the apparatus comprising a memory (2200) and a processor (2300), wherein, The memory (2200) includes instructions that are configured to cause the processor (2300) to perform the steps described in any one of the preceding claims when executed.

14. The apparatus (2000) according to claim 13 further comprises: A communication device (2100) for obtaining the plurality of voltage measurements (V) and the plurality of current measurements (I).

15. A software which, when executed on a processor (2300), causes the processor (2300) to perform the steps of any one of claims 1-12.

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