CN114285117B - Lithium precipitation judgment and battery management method and system in battery charging process - Google Patents

Lithium precipitation judgment and battery management method and system in battery charging process Download PDF

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CN114285117B
CN114285117B CN202111563092.0A CN202111563092A CN114285117B CN 114285117 B CN114285117 B CN 114285117B CN 202111563092 A CN202111563092 A CN 202111563092A CN 114285117 B CN114285117 B CN 114285117B
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CN114285117A (en
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曹辉
聂荣荣
侯敏
刘婵
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Shanghai Ruipu Energy Co Ltd
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Abstract

The invention provides a lithium precipitation judgment and battery management method and system in a battery charging process, comprising the following steps: step 1: collecting voltage, current and time signals in constant voltage charging processes of the battery to be tested under different SOC states and different multiplying powers; step 2: under the corresponding stable voltage, obtaining a constant voltage charging curve of the battery to be tested, wherein the charging curve represents the change relation of current along with time; step 3: according to the charging curve, acquiring a current fluctuation curve of the battery to be tested, and representing a short-time Fourier transform curve by the curve; step 4: and detecting whether lithium is separated from the battery to be detected according to the peak value displayed by the Fourier transform curve. According to the invention, the irregular change is converted into the frequency change through the Fourier transform, the whole period process is decomposed into a plurality of small processes with equal length by using a windowing mode through the short-time Fourier transform, each small process is close to be in a steady state, and the accuracy for identifying the tiny mutation is higher.

Description

Lithium precipitation judgment and battery management method and system in battery charging process
Technical Field
The invention relates to the technical field of batteries, in particular to a lithium precipitation judgment and battery management method and system in a battery charging process.
Background
At present, the lithium ion battery still has the defects of difficult identification, unsuitable method and the like in the lithium ion battery lithium precipitation behavior in the charging process. In the rapid charging process of the battery under different charge states (SOC states), whether lithium is separated or not is generally observed by disassembling the battery.
Therefore, a method capable of effectively identifying lithium precipitation is important for judging lithium precipitation behavior through nondestructive detection.
Patent document CN105866695B (application number: CN 201610255360.5) discloses a method for detecting lithium precipitation of a rechargeable battery, a battery management system, and a battery system. On one hand, in the embodiment of the invention, in the process of pulse charging of the rechargeable battery, the charging voltage and the state of charge of the rechargeable battery are detected, and the charging voltage of the rechargeable battery is used as the first voltage, so that the voltage value corresponding to the state of charge is obtained from the corresponding relation between the preset open-circuit voltage and the state of charge and is used as the second voltage, and further, whether lithium precipitation occurs in the rechargeable battery in the pulse charging process is judged according to the first voltage and the second voltage. However, the patent judges whether lithium is separated or not through voltage, and the detection of the charging process of the battery in different SOC states under different multiplying powers cannot be realized unlike the technical means adopted by the invention.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a lithium precipitation judgment and battery management method and system in the battery charging process.
The lithium precipitation judgment and battery management method in the battery charging process provided by the invention comprises the following steps:
step 1: collecting voltage, current and time signals in constant voltage charging processes of the battery to be tested under different SOC states and different multiplying powers;
step 2: under the corresponding stable voltage, obtaining a constant voltage charging curve of the battery to be tested, wherein the charging curve represents the change relation of current along with time;
step 3: according to the charging curve, acquiring a current fluctuation curve of the battery to be tested, and representing a short-time Fourier transform curve by the curve;
step 4: and detecting whether lithium is separated from the battery to be detected according to the peak value displayed by the Fourier transform curve.
Preferably, the 1C discharge capacity of the battery at 25 ℃ is taken as a denominator, and the battery is charged to the capacity of a preset SOC point through capacity cut-off during charging;
or testing the charging dynamic SOC-OCV voltage curve of the battery under different multiplying powers, and charging the battery to the voltage under the corresponding multiplying power during charging;
the acquisition signals are acquired by using a terminal connected with a battery test system, the acquisition frequency is 100ms, and the real-time voltage value, the real-time current value, the capacity value and the energy value of each time point are acquired.
Preferably, the initial charging process is a constant current charging process, the current value is a constant value at this stage, the voltage is continuously increased along with time, when the voltage or the capacity reaches the voltage or the capacity of the set SOC point, the test system automatically changes into a constant voltage charging mode, the voltage value is a constant value at this stage, the current is continuously reduced along with time until the current is lower than the set current value;
in the charging process, the time is taken as the x axis, the current and the voltage are taken as the y axis, and the charging curve of the battery is obtained.
Preferably, in the charging process, the real-time characteristic curve signals of the battery are identified through the battery control system and the identification system, and when the signal identification system identifies that the battery is close to an early warning threshold value set by lithium precipitation in the charging process, the signals are fed back to the battery control system to charge and reduce the current of the battery;
and monitoring the full life cycle charging working state of the battery, and after detecting that the battery has a lithium precipitation risk, feeding back the battery state to the central control system, and determining whether the safety state of the battery is continued to work or is subjected to functional limitation or after-sales maintenance by the central control system.
Preferably, according to the short-time fourier transform principle, a time-domain base signal is converted into a frequency characteristic signal to achieve correlation, where the formula is:
wherein: STFT z (t, f) represents a short-time fourier function; z (u) represents a source signal function; g * (u-t) represents a small window signal function; e, e -i2πfu Representing a one-dimensional fourier transform under a natural constant; i represents an imaginary unit; u represents an integral unknown variable; t represents the time t; f represents frequency.
The lithium precipitation judgment and battery management system in the battery charging process provided by the invention comprises the following components:
module M1: collecting voltage, current and time signals in constant voltage charging processes of the battery to be tested under different SOC states and different multiplying powers;
module M2: under the corresponding stable voltage, obtaining a constant voltage charging curve of the battery to be tested, wherein the charging curve represents the change relation of current along with time;
module M3: according to the charging curve, acquiring a current fluctuation curve of the battery to be tested, and representing a short-time Fourier transform curve by the curve;
module M4: and detecting whether lithium is separated from the battery to be detected according to the peak value displayed by the Fourier transform curve.
Preferably, the 1C discharge capacity of the battery at 25 ℃ is taken as a denominator, and the battery is charged to the capacity of a preset SOC point through capacity cut-off during charging;
or testing the charging dynamic SOC-OCV voltage curve of the battery under different multiplying powers, and charging the battery to the voltage under the corresponding multiplying power during charging;
the acquisition signals are acquired by using a terminal connected with a battery test system, the acquisition frequency is 100ms, and the real-time voltage value, the real-time current value, the capacity value and the energy value of each time point are acquired.
Preferably, the initial charging process is a constant current charging process, the current value is a constant value at this stage, the voltage is continuously increased along with time, when the voltage or the capacity reaches the voltage or the capacity of the set SOC point, the test system automatically changes into a constant voltage charging mode, the voltage value is a constant value at this stage, the current is continuously reduced along with time until the current is lower than the set current value;
in the charging process, the time is taken as the x axis, the current and the voltage are taken as the y axis, and the charging curve of the battery is obtained.
Preferably, in the charging process, the real-time characteristic curve signals of the battery are identified through the battery control system and the identification system, and when the signal identification system identifies that the battery is close to an early warning threshold value set by lithium precipitation in the charging process, the signals are fed back to the battery control system to charge and reduce the current of the battery;
and monitoring the full life cycle charging working state of the battery, and after detecting that the battery has a lithium precipitation risk, feeding back the battery state to the central control system, and determining whether the safety state of the battery is continued to work or is subjected to functional limitation or after-sales maintenance by the central control system.
Preferably, according to the short-time fourier transform principle, a time-domain base signal is converted into a frequency characteristic signal to achieve correlation, where the formula is:
wherein: STFT z (t, f) represents a short-time fourier function; z (u) represents a source signal function; g * (u-t) represents a small window signal function; e, e -i2πfu Representing a one-dimensional fourier transform under a natural constant; i represents an imaginary unit; u represents an integral unknown variable; t represents the time t; f represents frequency.
Compared with the prior art, the invention has the following beneficial effects:
1. the Fourier transform can convert irregular change into frequency change, the short-time Fourier transform uses a windowing mode to decompose the whole period process into a plurality of small processes with equal length, each small process is close to be in a steady state, and the accuracy for identifying tiny mutation is higher;
2. the fourier transform results are more frequency representative and are also more easily identified by software and systems;
3. by using the method for detecting the lithium precipitation, the charging process of the battery in different SOC states under different multiplying powers can be effectively detected, and the detection precision is greatly improved;
4. the method is used for judging the corresponding battery management system for lithium precipitation in the charging process of the battery with different multiplying power under different SOC states, and the method can be used for detecting, identifying and effectively managing the lithium precipitation behavior of the battery.
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Other features, objects and advantages of the present invention will become more apparent upon reading of the detailed description of non-limiting embodiments, given with reference to the accompanying drawings in which:
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of a lithium-ion-free transition;
fig. 3 is a fourier transform diagram of a lithium-ion battery.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present invention.
Examples:
in the embodiment of the invention, the change signals of voltage and current along with time are collected in the constant voltage charging process of the battery to be tested under different SOC states and different multiplying powers. According to different product requirements, the SOC state and the multiplying power also change along with the product requirements. The SOC state of the battery generally takes the SOC point in the range of 20-100% and can be spanned every 5-10% SOC. The preferred SOC range here is the 40-90% SOC range, tested at every 10% SOC as span.
The multiplying power is selected according to the product requirement and the temperature, the temperature range can be-40 ℃ to +60 ℃, the multiplying power range can be 0.05 to 6 ℃, and the span takes every 0.1 to 1.5 ℃ as the span. The preferred temperature range is 0 to +45 ℃, the rate of use is 0.5 to 4.5C, and the span is 0.5 to 1C. Further preferably, the temperature is 20 to 25 ℃, the magnification is in the magnification range of 1 to 4C, and the span is 1C as the span (for example, the magnifications of 1C, 2C, 3C, 4C are measured at 25 ℃).
There are 2 methods for determining the SOC point, 1 is a capacity for charging a battery to a certain SOC point by capacity cut-off at the time of charging using 1C discharge capacity of the battery at normal temperature 25 ℃ as a denominator. And 2, firstly testing a charging dynamic SOC-OCV voltage curve of the battery under different multiplying powers, and charging the battery to a voltage under a corresponding multiplying power during charging, so that the set SOC point is considered to be reached.
The acquisition signals are acquired by using a terminal connected with the battery test system, the acquisition frequency is 100ms, and data such as a real-time voltage value, a real-time current value, a capacity value, an energy value and the like at each time point are acquired.
And under the corresponding stable voltage, obtaining a constant voltage charging curve of the battery to be tested, wherein the charging curve represents the change relation of current along with time. When the test starts, a terminal connected with the battery test system starts to collect battery state signals, the collection frequency is 100ms, and the collection content comprises data such as a real-time voltage value, a real-time current value, a real-time capacity value, a real-time energy value and the like. The initial charging process is a constant current charging process, the current value is constant at this stage, and the voltage is continuously increased along with time. When the voltage or capacity reaches the voltage or capacity of the set SOC point, the test system automatically changes to a constant voltage charging mode. At this stage, the voltage value is constant and the current is reduced over time until the current is below the set current value, which may range from 0.001 to 0.2C, preferably from 0.005 to 0.05C, where 0.01C is used. Then during the charging process, the charging curve of the battery can be obtained with time as X-axis and current and voltage as y-axis. In order to obtain the constant voltage charging curve, only the current (y axis) in the constant voltage stage is needed to be used for carrying out data graph on time (x axis).
Then, a Short-time Fourier transform (Short-time Fourier Transform, STFT) curve is characterized by using a charging curve, and finally, whether lithium precipitation occurs in the battery to be tested is detected according to the peak value shown by the Fourier transform curve, as shown in fig. 2 and 3. The physical meaning of the fourier transform is to convert a time domain signal into a frequency domain signal, so as to obtain higher resolution and analysis. However, the conventional fourier transform (FFT) has defects in processing non-stationary signals, and cannot effectively distinguish the time when different components appear, while stationary signals are mostly manufactured by man, and a large number of signals in nature are almost non-stationary. Therefore, a short-time fourier transform needs to be used here. I.e., windowing, breaks the entire time domain process into numerous equally long small processes, each of which is approximately stationary, and then fourier transforms to determine events that occur at different time frequencies.
The peak value means occurrence of lithium precipitation, and in a state close to the occurrence of the peak value, it means that lithium precipitation is close to the occurrence of the peak value, and there may be a safety risk. In the charging process, the real-time characteristic curve signals of the battery are identified through the battery control system and the identification system. 1. When the signal recognition system recognizes that the battery is close to an early warning threshold value set by lithium precipitation in the charging process, a signal is fed back to the battery control system, and the control system can charge and reduce the current of the battery so as to reduce the possibility of lithium precipitation in the charging process. 2. The full life cycle charging working state of the battery is monitored, after the lithium precipitation risk of the battery is detected, the battery state is fed back to the central control system, and the central control system confirms whether the safety state of the battery can continue to work or needs to be subjected to functional limitation or after-sales maintenance.
Therefore, the technical scheme provided by the embodiment of the invention can solve the defects of high manpower and material consumption and low detection efficiency in the method for detecting the lithium precipitation of the battery in the prior art. In addition, the Fourier transform signal is very easy to be identified by the management system, so that the identification efficiency and accuracy of the management system can be effectively improved.
According to the short-time Fourier transform formula:
the short-time fourier transform is a time-frequency analysis transform, and a signal characteristic at a certain moment is represented by a signal segment within a time window of each small window. The principle of the formula is that a source function and a small window function are multiplied firstly, then one-dimensional Fourier transform is carried out, fourier transform is displayed through sliding, and finally an integral expansion is carried out to obtain a two-dimensional result.
Wherein: STFT z (t, f) represents a short-time fourier function; z (u) represents a source signal function; g * (u-t) represents a small window signal function; e, e -i2πfu Representing a one-dimensional fourier transform under a natural constant; i represents an imaginary unit; u represents an integral unknown variable; t represents the time t; f represents frequency.
Thus, according to the short-time fourier transform principle, a time-domain base signal can be converted into a frequency-characteristic signal to achieve correlation. And for irregular non-stationary signals, a spectrum signal in a regular small window can be effectively obtained.
For the computer processing mode of the control system, for convenience, discretization processing of signals is generally adopted. The computer processing formula from the short-time fourier transform principle formula change is as follows:
wherein, STFT z (m, n) represents a conversion matrix of a short-time Fourier series in the computer processing result, m×n matrix; z (k) represents a source function; g * (kT-mT) represents a window function; e, e -i2π(nF)k Representing a one-dimensional fourier transform under a natural constant; t represents a time point of spectrogram calculation; f represents a frequency vector; k represents the kth time domain point; n represents the number of sampling points.
And the battery is charged at constant voltage under different SOC states and different multiplying powers, a change curve of current along with time is obtained, and a Short-time Fourier transform (Short-time FourierTransform, STFT) curve is represented by using the charging curve. From the peak map of the fourier transform, it can be determined whether or not lithium precipitation has occurred in the battery.
And the corresponding battery management system for judging the occurrence of lithium precipitation in the charging process of the battery with different multiplying powers under different SOC states by using the method is used for detecting, identifying and effectively managing the lithium precipitation behavior of the battery.
As shown in fig. 1, the method of the present invention includes: step 1: collecting voltage, current and time signals in constant voltage charging processes of the battery to be tested under different SOC states and different multiplying powers; step 2: under the corresponding stable voltage, obtaining a constant voltage charging curve of the battery to be tested, wherein the charging curve represents the change relation of current along with time; step 3: according to the charging curve, acquiring a current fluctuation curve of the battery to be tested, and representing a short-time Fourier transform curve by the curve; step 4: and detecting whether lithium is separated from the battery to be detected according to the peak value displayed by the Fourier transform curve.
The lithium precipitation judgment and battery management system in the battery charging process provided by the invention comprises the following components: module M1: collecting voltage, current and time signals in constant voltage charging processes of the battery to be tested under different SOC states and different multiplying powers; module M2: under the corresponding stable voltage, obtaining a constant voltage charging curve of the battery to be tested, wherein the charging curve represents the change relation of current along with time; module M3: according to the charging curve, acquiring a current fluctuation curve of the battery to be tested, and representing a short-time Fourier transform curve by the curve; module M4: and detecting whether lithium is separated from the battery to be detected according to the peak value displayed by the Fourier transform curve.
Taking the 1C discharge capacity of the battery at 25 ℃ as a denominator, and charging the battery to the capacity of a preset SOC point through capacity cut-off during charging; or testing the charging dynamic SOC-OCV voltage curve of the battery under different multiplying powers, and charging the battery to the voltage under the corresponding multiplying power during charging; the acquisition signals are acquired by using a terminal connected with a battery test system, the acquisition frequency is 100ms, and the real-time voltage value, the real-time current value, the capacity value and the energy value of each time point are acquired. The initial charging process is a constant-current charging process, the current value is a constant value at the stage, the voltage is continuously increased along with time, when the voltage or the capacity reaches the voltage or the capacity of a set SOC point, the test system automatically changes into a constant-voltage charging mode, the voltage value is a constant value at the stage, and the current is continuously reduced along with time until the current is lower than the set current value; in the charging process, the time is taken as the x axis, the current and the voltage are taken as the y axis, and the charging curve of the battery is obtained. In the charging process, the real-time characteristic curve signals of the battery are identified through the battery control system and the identification system, and when the signal identification system identifies that the battery is close to an early warning threshold value set by lithium precipitation in the charging process, the signals are fed back to the battery control system to charge and reduce the current of the battery; and monitoring the full life cycle charging working state of the battery, and after detecting that the battery has a lithium precipitation risk, feeding back the battery state to the central control system, and determining whether the safety state of the battery is continued to work or is subjected to functional limitation or after-sales maintenance by the central control system.
According to the short-time Fourier transformation principle, a time domain base signal is converted into a frequency characteristic signal to realize correlation, and the correlation is commonThe formula is:wherein: STFT z (t, f) represents a short-time fourier function; z (u) represents a source signal function; g * (u-t) represents a small window signal function; e, e -i2πfu Representing a one-dimensional fourier transform under a natural constant; i represents an imaginary unit; u represents an integral unknown variable; t represents the time t; f represents frequency.
Those skilled in the art will appreciate that the systems, apparatus, and their respective modules provided herein may be implemented entirely by logic programming of method steps such that the systems, apparatus, and their respective modules are implemented as logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, etc., in addition to the systems, apparatus, and their respective modules being implemented as pure computer readable program code. Therefore, the system, the apparatus, and the respective modules thereof provided by the present invention may be regarded as one hardware component, and the modules included therein for implementing various programs may also be regarded as structures within the hardware component; modules for implementing various functions may also be regarded as being either software programs for implementing the methods or structures within hardware components.
The foregoing describes specific embodiments of the present invention. It is to be understood that the invention is not limited to the particular embodiments described above, and that various changes or modifications may be made by those skilled in the art within the scope of the appended claims without affecting the spirit of the invention. The embodiments of the present application and features in the embodiments may be combined with each other arbitrarily without conflict.

Claims (10)

1. A lithium analysis judgment and battery management method in a battery charging process is characterized by comprising the following steps:
step 1: collecting voltage, current and time signals in constant voltage charging processes of the battery to be tested under different SOC states and different multiplying powers;
step 2: under the corresponding stable voltage, obtaining a constant voltage charging curve of the battery to be tested, wherein the charging curve represents the change relation of current along with time;
step 3: according to the charging curve, acquiring a current fluctuation curve of the battery to be tested, and representing a short-time Fourier transform curve by the curve;
step 4: and detecting whether lithium is separated from the battery to be detected according to the peak value displayed by the Fourier transform curve.
2. The method for determining and managing lithium separation in a battery charging process according to claim 1, wherein the battery is charged to a capacity of a preset SOC point by capacity cut-off when charged, with 1C discharge capacity of the battery at 25 ℃ as a denominator;
or testing the charging dynamic SOC-OCV voltage curve of the battery under different multiplying powers, and charging the battery to the voltage under the corresponding multiplying power during charging;
the acquisition signals are acquired by using a terminal connected with a battery test system, the acquisition frequency is 100ms, and the real-time voltage value, the real-time current value, the capacity value and the energy value of each time point are acquired.
3. The method for determining and managing lithium precipitation in a battery charging process according to claim 1, wherein the initial charging process is a constant current charging process, the current value is constant at this stage, the voltage is continuously increased with time, and when the voltage or capacity reaches the voltage or capacity of the set SOC point, the test system automatically changes to a constant voltage charging mode, the voltage value is constant at this stage, the current is continuously decreased with time until the current is lower than the set current value;
in the charging process, the time is taken as the x axis, the current and the voltage are taken as the y axis, and the charging curve of the battery is obtained.
4. The method for judging and managing lithium precipitation in the battery charging process according to claim 1, wherein the real-time characteristic curve signals of the battery are identified through the battery control system and the identification system in the charging process, and when the signal identification system identifies that the battery is close to an early warning threshold value set by lithium precipitation in the charging process, the signals are fed back to the battery control system to charge and reduce the current of the battery;
and monitoring the full life cycle charging working state of the battery, and after detecting that the battery has a lithium precipitation risk, feeding back the battery state to the central control system, and determining whether the safety state of the battery is continued to work or is subjected to functional limitation or after-sales maintenance by the central control system.
5. The method for determining and managing lithium ion battery in battery charging according to claim 1, wherein a time domain base signal is converted into a frequency characteristic signal according to a short time fourier transform principle to achieve correlation, wherein the formula is:
wherein: STFT z (t, f) represents a short-time fourier function; z (u) represents a source signal function; g * (u-t) represents a small window signal function; e, e -i2πfu Representing a one-dimensional fourier transform under a natural constant; i represents an imaginary unit; u represents an integral unknown variable; t represents the time t; f represents frequency.
6. A lithium analysis judging and battery management system in the battery charging process is characterized by comprising the following components:
module M1: collecting voltage, current and time signals in constant voltage charging processes of the battery to be tested under different SOC states and different multiplying powers;
module M2: under the corresponding stable voltage, obtaining a constant voltage charging curve of the battery to be tested, wherein the charging curve represents the change relation of current along with time;
module M3: according to the charging curve, acquiring a current fluctuation curve of the battery to be tested, and representing a short-time Fourier transform curve by the curve;
module M4: and detecting whether lithium is separated from the battery to be detected according to the peak value displayed by the Fourier transform curve.
7. The system for determining and managing lithium separation during battery charging according to claim 6, wherein the battery is charged to a capacity of a preset SOC point by capacity cut-off when charging, using the 1C discharge capacity of the battery at 25 ℃ as a denominator;
or testing the charging dynamic SOC-OCV voltage curve of the battery under different multiplying powers, and charging the battery to the voltage under the corresponding multiplying power during charging;
the acquisition signals are acquired by using a terminal connected with a battery test system, the acquisition frequency is 100ms, and the real-time voltage value, the real-time current value, the capacity value and the energy value of each time point are acquired.
8. The system according to claim 6, wherein the initial charging process is a constant current charging process, the current value is constant at this stage, the voltage is continuously increased with time, and when the voltage or capacity reaches the voltage or capacity of the set SOC point, the test system automatically changes to the constant voltage charging mode, the voltage value is constant at this stage, the current is continuously decreased with time until the current is lower than the set current value;
in the charging process, the time is taken as the x axis, the current and the voltage are taken as the y axis, and the charging curve of the battery is obtained.
9. The system for judging and managing lithium precipitation in the battery charging process according to claim 6, wherein the real-time characteristic curve signals of the battery are identified through the battery control system and the identification system in the charging process, and when the signal identification system identifies that the battery is close to an early warning threshold value set by lithium precipitation in the charging process, the signals are fed back to the battery control system to charge and reduce the current of the battery;
and monitoring the full life cycle charging working state of the battery, and after detecting that the battery has a lithium precipitation risk, feeding back the battery state to the central control system, and determining whether the safety state of the battery is continued to work or is subjected to functional limitation or after-sales maintenance by the central control system.
10. The system for determining and managing lithium ion battery charging according to claim 6, wherein a time domain base signal is converted into a frequency characteristic signal according to a short time fourier transform principle to achieve correlation, wherein the formula is:
wherein: STFT z (t, f) represents a short-time fourier function; z (u) represents a source signal function; g * (u-t) represents a small window signal function; e, e -i2πfu Representing a one-dimensional fourier transform under a natural constant; i represents an imaginary unit; u represents an integral unknown variable; t represents the time t; f represents frequency.
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