Method and system for identifying third-order model parameters of lithium battery based on likelihood function

Abstract

A method and a system for identifying third-order model parameters of a lithium battery based on a likelihood function are provided, which relates to a method for estimating battery model parameters of a lithium battery under different temperatures, different system-on-chips (SOCs), and charge-discharge currents. The method includes the following steps. A third-order battery model of the lithium battery is established. A battery model output voltage U.sub.d and a total battery current I under different temperatures, different SOCs, and charge-discharge currents are collected. The likelihood function is adopted to construct an identification model, and the collected data is substituted into the identification model to calculate the battery model parameters. Identified parameters are substituted into the third-order battery model to obtain a battery terminal voltage to be compared with a measured terminal voltage. The operation method of the disclosure is simple and effective, and can accurately estimate internal resistance parameters of the lithium battery.

Claims

1. A method for identifying third-order model parameters of a lithium battery based on a likelihood function, characterized by comprising the following steps executing by a processor: Step (1) of establishing a third-order battery circuit of the lithium battery; Step (2) of collecting an output voltage and a total battery current of the third-order battery circuit under different temperatures, different system-on-chips (SOCs), and charge-discharge currents; Step (3) of adopting the likelihood function to construct an identification model; and Step (4) of substituting the collected output voltage and total battery current of the third-order battery circuit into the identification model to calculate the third-order battery circuit parameters; wherein the third-order battery circuit comprises a battery (OCV), an ohmic resistor (R.sub.ac), a charge transfer resistor (R.sub.ct), a charge transfer capacitor (C.sub.ct), a first diffused resistor (R.sub.wb1), a first diffused capacitor (C.sub.wb1), a second diffused resistor (R.sub.wb2), and a second diffused capacitor (C.sub.wb2), wherein a first terminal of the battery (OCV) is connected to a first terminal of the ohmic resistor (R.sub.ac); a second terminal of the ohmic resistor (R.sub.ac)is connected to a first terminal of the charge transfer resistor (R.sub.ct) and a first terminal of the charge transfer capacitor (C.sub.ct); after being connected, a second terminal of the charge transfer resistor (R.sub.ct) and a second terminal of the charge transfer capacitor (C.sub.ct) are connected to a first terminal of the first diffused resistor (R.sub.wb1) and a first terminal of the first diffused capacitor (C.sub.wb1); after being connected, a second terminal of the first diffused resistor (R.sub.wb) and a second terminal of the first diffused capacitor (C.sub.wb1) are connected to a first terminal of the second diffused resistor (R.sub.wb2) and a first terminal of the second diffused capacitor (C.sub.wb2); and after being connected, a second terminal of the second diffused resistor (R.sub.wb2) and a second terminal of the second diffused capacitor (C.sub.wb2) are connected to a second terminal of the battery (OCV).

2. The method according to claim 1, characterized in that Step (1) comprises: a discretized battery state equation of the third-order battery circuit is: $\{\begin{array}{c}{U}_{ct}\left(k+1\right)=U_{ct}\left(k\right)*\exp \left(-T/{\tau }_{ct}\right)+I\left(k\right)R_{ct}*\left(1-\exp \left(-T/{\tau }_{ct}\right)\right)\\ U_{wb1}\left(k+1\right)=U_{wb1}\left(k\right)*\exp \left(-T/{\tau }_{wb1}\right)+I\left(k\right)R_{wb1}*\left(1-\exp \left(-T/{\tau }_{wb1}\right)\right)\\ U_{wb2}\left(k+1\right)=U_{wb2}\left(k\right)*\exp \left(-T/{\tau }_{wb2}\right)+I\left(k\right)R_{wb2}*\left(1-\exp \left(-T/{\tau }_{wb2}\right)\right)\\ SOC\left(k+1\right)=SOC\left(k\right)-\frac{T*I\left(k\right)}{C}\end{array}\hspace{1em}$ where T is a sampling interval, k is a sampling time, I represents a total battery current, U.sub.ct represents a voltage of R.sub.ctC.sub.ct network, τ.sub.ct represents a time constant of R.sub.ctC.sub.ct network, U.sub.wb1 represents a voltage of R.sub.wb1C.sub.wb1 network, τ.sub.wb1 represents a time constant of R.sub.wb1C.sub.wb1 network, U.sub.wb2 represents a voltage of R.sub.wb2C.sub.wb2 network, τ.sub.wb2 represents a time constant of R.sub.wb2C.sub.wb2 network, SOC represents a battery state of charge, C represents a battery capacity, and R.sub.wb1=3R.sub.wb2 and τ.sub.wb1=τ.sub.wb2; and a discretized predicted battery module terminal voltage of the third-order battery circuit is:
y.sub.k+1=U.sub.ocv−U.sub.ct(k)−U.sub.wb1(k)−U.sub.wb2(k)−R.sub.acI(k) where y.sub.k+1 represents the predicted battery module terminal voltage, U.sub.ocv , represents a battery open circuit voltage, and R.sub.ac represents an ohmic internal resistance.

3. The method according to claim 2, characterized in that Step (3) comprises: Step (3.1) of performing an inverse Z-transformation after performing a Z-transformation on the battery state equation and the predicted battery module terminal voltage, so as to obtain:
U.sub.d(k+3)=θ.sub.1U.sub.d(k+2)+θ.sub.2U.sub.d(k+1)+θ.sub.3U.sub.d(k)+θ.sub.4I(k+3)+θ.sub.5I(k+2)+θ.sub.6I(k+1)+θ.sub.7I(k) and U.sub.d(k)=(y.sub.k−U.sub.OCV); and Step (3.2) of obtaining the identification model from y.sub.k=θ.sup.Tφ(k), where y.sub.k is the predicted battery module terminal voltage, where: θ=[θ.sub.1 θ.sub.2 θ.sub.3 θ.sub.4 θ.sub.5 θ.sub.6 θ.sub.7], φ(k)=U.sub.d(k)=[U.sub.d(k−1) U.sub.d(k−2) U.sub.d(k−3) I(k) I(k−1) I(k−2) I(k−3)], θ.sub.1=b.sub.1+b.sub.3+b.sub.5, θ.sub.2=−(b.sub.1b.sub.3+b.sub.1b.sub.5+b.sub.3b.sub.5), θ.sub.3=b.sub.1b.sub.3b.sub.5, θ.sub.4=−R.sub.ac, θ.sub.5=R.sub.ac(b.sub.1+b.sub.3+b.sub.5)−(b.sub.2+b.sub.4+b.sub.6), θ.sub.6=(b.sub.3+b.sub.5)b.sub.2+(b.sub.1+b.sub.5)b.sub.4+(b.sub.1+b.sub.3)b.sub.6−R.sub.ac(b.sub.1b.sub.3+b.sub.1b.sub.5+b.sub.3b.sub.5), θ.sub.7=b.sub.1b.sub.3b.sub.5R.sub.ac−b.sub.3b.sub.5b.sub.2−b.sub.1b.sub.4b.sub.5−b.sub.1b.sub.3b.sub.6, b.sub.1=exp(−T/τ.sub.ct), b.sub.2=R.sub.ct*(1−exp(−T/τ.sub.ct)), b.sub.3=exp(−T/τ.sub.wb1), b.sub.4=R.sub.wb1*(1−exp(−T/τ.sub.wb1)), and b.sub.5=exp(−T/τ.sub.wb2).

4. The method according to claim 3, characterized in that Step (4) comprises: Step (4.1) of taking a logarithm of a distribution function of the battery module terminal voltage to obtain: $\ln L\left(\theta \right)=\frac{-1}{2{\sigma }^2}\underset{k=1}{\overset{n}{.Math.}}{\left(y\left(k\right)-{\theta }^T\phi \left(k\right)\right)}^2-n\ln \sigma \sqrt{2\pi },$ where n represents a total sample number of the collected output voltage and total battery current of the battery model, σ represents a variance, where y(.sup.k) is an actual measured battery module terminal voltage, and φ(k)=U.sub.d(k)=(y.sub.k−U.sub.OCV); Step (4.2) of setting a gradient operator as ${\nabla }_{\theta }=\left[\begin{array}{ccccccc}\frac{\partial }{\partial {\theta }_1}& \frac{\partial }{\partial {\theta }_2}& \frac{\partial }{\partial {\theta }_3}& \frac{\partial }{\partial {\theta }_4}& \frac{\partial }{\partial {\theta }_5}& \frac{\partial }{\partial {\theta }_6}& \frac{\partial }{\partial {\theta }_7}\end{array}\right],$ substituting the collected output voltage and total battery current of the third-order battery circuit into an equation in Step (4.1), and ${\nabla }_{\theta }\ln L\left(\theta \right)=\frac{-1}{{\sigma }^2}\underset{k=1}{\overset{n}{.Math.}}{\left(y\left(k\right)-{\theta }^T\phi \left(k\right)\right)}^2\left(-\phi \left(k\right)\right)=0$ to calculate each element value of a matrix θ=[θ.sub.1 θ.sub.2 θ.sub.3 θ.sub.4 θ.sub.5 θ.sub.6 θ.sub.7]; and Step (4.3) of inferring a magnitude of a third-order battery circuit parameter value according to a relationship between the third-order battery circuit parameter value and θ.

5. A system for identifying third-order model parameters of a lithium battery based on a likelihood function, characterized by comprising: a battery model construction module, configured to establish a third-order battery circuit of a lithium battery; a data collection module, configured to collect an output voltage and a total battery current of the third-order battery circuit under different temperatures, different SOCs, and charge-discharge currents; an identification model construction module, configured to adopt the likelihood function to construct an identification model; and a parameter determination module, configured to substitute the collected output voltage and total battery current of the third-order battery circuit into the identification model to calculate the third-order battery circuit parameters; wherein the third-order battery circuit comprises a battery (OCV), an ohmic resistor (R.sub.ac), a charge transfer resistor (R.sub.ct), a charge transfer capacitor (C.sub.ct), a first diffused resistor (R.sub.wb1), a first diffused capacitor (C.sub.wb1), a second diffused resistor (R.sub.wb2), and a second diffused capacitor (C.sub.wb2), wherein a first terminal of the battery (OCV) is connected to a first terminal of the ohmic resistor (R.sub.ac) a second terminal of the ohmic resistor (R.sub.ac)is connected to a first terminal of the charge transfer resistor (R.sub.ct) and a first terminal of the charge transfer capacitor (C.sub.ct); after being connected, a second terminal of the charge transfer resistor (R.sub.ct) and a second terminal of the charge transfer capacitor (C.sub.ct) are connected to a first terminal of the first diffused resistor (R.sub.wb1) and a first terminal of the first diffused capacitor (C.sub.wb1); after being connected, a second terminal of the first diffused resistor (R.sub.wb1) and a second terminal of the first diffused capacitor (C.sub.wb1)are connected to a first terminal of the second diffused resistor (R.sub.wb2) and a first terminal of the second diffused capacitor (C.sub.wb2); and after being connected, a second terminal of the second diffused resistor (R.sub.wb2) and a second terminal of the second diffused capacitor (C.sub.wb2) are connected to a second terminal of the battery (OCV).

6. The system according to claim 5, characterized in that the battery model construction module comprises: a battery state equation establishment module, configured to establish a discretized battery state equation of the third-order battery circuit: $\{\begin{array}{c}{U}_{ct}\left(k+1\right)=U_{ct}\left(k\right)*\exp \left(-T/{\tau }_{ct}\right)+I\left(k\right)R_{ct}*\left(1-\exp \left(-T/{\tau }_{ct}\right)\right)\\ U_{wb1}\left(k+1\right)=U_{wb1}\left(k\right)*\exp \left(-T/{\tau }_{wb1}\right)+I\left(k\right)R_{wb1}*\left(1-\exp \left(-T/{\tau }_{wb1}\right)\right)\\ U_{wb2}\left(k+1\right)=U_{wb2}\left(k\right)*\exp \left(-T/{\tau }_{wb2}\right)+I\left(k\right)R_{wb2}*\left(1-\exp \left(-T/{\tau }_{wb2}\right)\right)\\ SOC\left(k+1\right)=SOC\left(k\right)-\frac{T*I\left(k\right)}{C}\end{array}\hspace{1em}$ where T is a sampling interval, k is a sampling time, I represents a total battery current, U.sub.ct represents a voltage of R.sub.ctC.sub.ct network, τ.sub.ct represents a time constant of R.sub.ctC.sub.ct network, U.sub.wb1 represents a voltage of R.sub.wb1C.sub.wb1 network, τ.sub.wb1 represents a time constant of R.sub.wb1C.sub.wb1 network, U.sub.wb2 represents a voltage of R.sub.wb2C.sub.wb2 network, τ.sub.wb2 represents a time constant of R.sub.wb2C.sub.wb2 network, SOC represents a battery state of charge, C represents a battery capacity, and R.sub.wb1=3R.sub.wb2 and τ.sub.wb1=3τ.sub.wb2; and a battery module terminal voltage acquisition module, configured to acquire a discretized predicted battery model terminal voltage of the third-order battery circuit:
y.sub.k+1=U.sub.ocv−U.sub.ct(k)−U.sub.wb1(k)−U.sub.wb2(k)−R.sub.acI(k) where y.sub.k+1, represents the predicted battery module terminal voltage, U.sub.ocv, represents a battery open circuit voltage, and R.sub.ac represents an ohmic internal resistance.

7. The system according to claim 6, characterized in that the identification model construction module comprises: a transformation module, configured to perform an inverse Z-transformation after performing a Z-transformation on the battery state equation and the predicted battery module terminal voltage, so as to obtain:
U.sub.d(k+3)=θ.sub.1U.sub.d(k+2)+θ.sub.2U.sub.d(k+1)+θ.sub.3U.sub.d(k)+θ.sub.4I(k+3)+θ.sub.5I(k+2)+θ.sub.6I(k+1)+θ.sub.7I(k) and U.sub.d(k)=(y.sub.k−U.sub.OCV); and an identification model construction submodule, configured to obtain the identification model from y.sub.k=θ.sup.Tφ(k), where y.sub.k is the predicted battery module terminal voltage, where θ=[θ.sub.1 θ.sub.2 θ.sub.3 θ.sub.4 θ.sub.5 θ.sub.6 θ.sub.7], φ(k)=U.sub.d(k)=[U.sub.d(k−1) U.sub.d(k−2) U.sub.d(k−3) I(k) I(k−1) I(k−2) I(k−3)], θ.sub.1=b.sub.1+b.sub.3+b.sub.5, θ.sub.2=−(b.sub.1b.sub.3+b.sub.1b.sub.5+b.sub.3b.sub.5), θ.sub.3=b.sub.1b.sub.3b.sub.5, θ.sub.4=−R.sub.ac, θ.sub.5=R.sub.ac(b.sub.1+b.sub.3+b.sub.5)−(b.sub.2+b.sub.4+b.sub.6), θ.sub.6=(b.sub.3+b.sub.5)b.sub.2+(b.sub.1+b.sub.5)b.sub.4+(b.sub.1+b.sub.3)b.sub.6−R.sub.ac(b.sub.1b.sub.3+b.sub.1b.sub.5+b.sub.3b.sub.5), θ.sub.7=b.sub.1b.sub.3b.sub.5R.sub.ac−b.sub.3b.sub.5b.sub.2−b.sub.1b.sub.4b.sub.5−b.sub.1b.sub.3b.sub.6, b.sub.1=exp(−T/τ.sub.ct), b.sub.2=R.sub.ct*(1−exp(−T/τ.sub.ct)), b.sub.3=exp(−T/τ.sub.wb1), b.sub.4=R.sub.wb1*(1−exp(−T/τ.sub.wb1)), and b.sub.5=exp(−T/τ.sub.wb2).

8. The system according to claim 7, characterized in that the parameter determination module comprises: a first calculation module, configured to take a logarithm of a distribution function of the battery module terminal voltage, so as to obtain: $\ln L\left(\theta \right)=\frac{-1}{2{\sigma }^2}\underset{k=1}{\overset{n}{.Math.}}{\left(y\left(k\right)-{\theta }^T\phi \left(k\right)\right)}^2-n\ln \sigma \sqrt{2\pi },$ where n represents a total sample number of the collected output voltage and total battery current of the battery model, σ represents a variance, where y(.sup.k) is an actual measured battery module terminal voltage, and φ(k)=U.sub.d(k)=(y.sub.k−U.sub.OCV); a second calculation module, configured to set a gradient operator as ${\nabla }_{\theta }=\left[\begin{array}{ccccccc}\frac{\partial }{\partial {\theta }_1}& \frac{\partial }{\partial {\theta }_2}& \frac{\partial }{\partial {\theta }_3}& \frac{\partial }{\partial {\theta }_4}& \frac{\partial }{\partial {\theta }_5}& \frac{\partial }{\partial {\theta }_6}& \frac{\partial }{\partial {\theta }_7}\end{array}\right],$ substitute the collected output voltage and total battery current of the third-order battery circuit into an equation of the first calculation module, and ${\nabla }_{\theta }\ln L\left(\theta \right)=\frac{-1}{{\sigma }^2}\underset{k=1}{\overset{n}{.Math.}}{\left(y\left(k\right)-{\theta }^T\phi \left(k\right)\right)}^2\left(-\phi \left(k\right)\right)=0$ to calculate each element value of a matrix θ=[θ.sub.1 θ.sub.2 θ.sub.3 θ.sub.4 θ.sub.5 θ.sub.6 θ.sub.7]; and a parameter determination submodule, configured to infer a magnitude of a third-order battery circuit parameter value according to a relationship between the third-order battery circuit parameter value and θ.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic flowchart of a method for identifying third-order model parameters of a lithium battery based on a likelihood function according to an embodiment of the disclosure.

(2) FIG. 2A to FIG. 2B is experimental data collected at 0° according to an embodiment of the disclosure, where FIG. 2A is a charge-discharge current and FIG. 2B is an output terminal voltage.

(3) FIG. 3A to FIG. 3E is a parameterized result at 20A of charge-discharge current according to an embodiment of the disclosure, where FIG. 3A is the parameterized result of R.sub.ac, FIG. 3B is the parameterized result of R.sub.ct, FIG. 3C is the parameterized result of R.sub.wb1, FIG. 3D is the parameterized result C.sub.wb1, and FIG. 3E is the parameterized result of C.sub.ct.

(4) FIG. 4A to FIG. 4D is a parameter value of R.sub.ac under different charge-discharge currents under different temperatures according to an embodiment of the disclosure, where FIG. 4A is the parameter value at 35°, FIG. 4B is the parameter value at 20°, FIG. 4C is the parameter value at 0°, and FIG. 4D is the parameter value at −20°.

(5) FIG. 5A to FIG. 5D is a parameterized verification result of a battery model according to an embodiment of the disclosure, where FIG. 5A is a load cycle condition input current, FIG. 5B is a comparison between a measured voltage and a simulated voltage, FIG. 5C is the comparison between the measured voltage and the simulated voltage in a certain region after amplification, and FIG. 5D is an absolute error of the simulated voltage.

(6) FIG. 6 is a third-order equivalent circuit model according to an embodiment of the disclosure.

(7) FIG. 7 is a block diagram of a system according to an embodiment of the disclosure.

DETAILED DESCRIPTION OF DISCLOSED EMBODIMENTS

(8) In order for the objectives, technical solutions, and advantages of the disclosure to be clearer, the disclosure is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein only serve to explain the disclosure, but not to limit the disclosure. In addition, the technical features involved in the various embodiments of the disclosure described below may be combined with each other as long as there is no conflict therebetween.

(9) In the example of the disclosure, terms such as “first” and “second” are used to distinguish different objects, and are not necessarily used to describe a specific order or sequence.

(10) The disclosure provides a method and a system for identifying third-order model parameters of a lithium battery based on a likelihood function, which can accurately identify the parameters of the lithium battery under different temperatures, different SOCs, and charge-discharge currents.

(11) FIG. 1 is a schematic flowchart of a method for identifying third-order model parameters of a lithium battery based on a likelihood function according to an embodiment of the disclosure. Through establishing a third-order battery model of the lithium battery, a battery model output voltage U.sub.d and a total battery current I under different temperatures, different system-on-chips (SOCs), and charge-discharge currents are collected. Then, the likelihood function is adopted to construct an identification model. The collected data is substituted into the identification model to calculate the battery model parameters. The method includes the following steps.

(12) Step S1: A third-order battery model of a lithium battery is established.

(13) Step S2: A battery model output voltage U.sub.d and a total battery current I under different temperatures, different SOCs, and charge-discharge currents are collected.

(14) Step S3: A likelihood function is adopted to construct an identification model.

(15) Step S4: The collected data is substituted into the identification model to calculate battery model parameters.

(16) In the embodiment of the disclosure, Step S1 includes the following step.

(17) The third-order battery model of the lithium battery is established as shown in FIG. 6, specifically as follows.

(18) The third-order battery model of the lithium battery includes a battery OCV, an ohmic resistor R.sub.ac, a charge transfer resistor R.sub.ct, a charge transfer capacitor C.sub.ct, a first diffused resistor R.sub.wb1, a first diffused capacitor C.sub.wb1, a second diffused resistor R.sub.wb2, and a second diffused capacitor C.sub.wb2.

(19) A first terminal of the battery OCV is connected to a first terminal of the ohmic resistor R.sub.ac. A second terminal of the ohmic resistor R.sub.ac is connected to a first terminal of the charge transfer resistor R.sub.ct and a first terminal of the charge transfer capacitor C.sub.ct. After being connected, a second terminal of the charge transfer resistor R.sub.ct and a second terminal of the charge transfer capacitor C.sub.ct are connected to a first terminal of the first diffused resistor R.sub.wb1 and a first terminal of the first diffused capacitor C.sub.wb1. After being connected, a second terminal of the first diffused resistor R.sub.wb1 and a second terminal of the first diffused capacitor C.sub.wb1 are connected to a first terminal of the second diffused resistor R.sub.wb2 and a first terminal of the second diffused capacitor C.sub.wb2. After being connected, a second terminal of the second diffused resistor R.sub.wb2 and a second terminal of the second diffused capacitor C.sub.wb2 are connected to a second terminal of the battery OCV.

(20) A discretized battery state equation is:

(21) $\{\begin{array}{c}{U}_{ct}\left(k+1\right)=U_{ct}\left(k\right)*\exp \left(-T/{\tau }_{ct}\right)+I\left(k\right)R_{ct}*\left(1-\exp \left(-T/{\tau }_{ct}\right)\right)\\ U_{wb1}\left(k+1\right)=U_{wb1}\left(k\right)*\exp \left(-T/{\tau }_{wb1}\right)+I\left(k\right)R_{wb1}*\left(1-\exp \left(-T/{\tau }_{wb1}\right)\right)\\ U_{wb2}\left(k+1\right)=U_{wb2}\left(k\right)*\exp \left(-T/{\tau }_{wb2}\right)+I\left(k\right)R_{wb2}*\left(1-\exp \left(-T/{\tau }_{wb2}\right)\right)\\ SOC\left(k+1\right)=SOC\left(k\right)-\frac{T*I\left(k\right)}{C}\end{array}\hspace{1em}$

(22) where T is the sampling interval, k is the sampling time, I represents the total battery current, U.sub.ct represents the voltage of R.sub.ctC.sub.ct, network, τ.sub.ct represents the time constant of R.sub.ctC.sub.ct network, U.sub.wb1 represents the voltage of R.sub.wb1C.sub.wb1 network, τ.sub.wb1 represents the time constant of R.sub.wb1C.sub.wb1 network, U.sub.wb2 represents the voltage of R.sub.wb2C.sub.wb2 network, τ.sub.wb2 represents the time constant of R.sub.wb2C.sub.wb2 network, SOC represents the battery state of charge, C represents the battery capacity, and R.sub.wb1=3R.sub.wb2 and τ.sub.wb1=3τ.sub.wb2.

(23) A discretized predicted module model terminal voltage is:
y.sub.k+1=U.sub.ocv−U.sub.ct(k)−U.sub.wb1(k)−U.sub.wb2(k)−R.sub.acI(k)

(24) where y.sub.k+1 represents the predicted battery module terminal voltage, U.sub.ocv represents the battery open circuit voltage, and R.sub.ac represents the ohmic internal resistance.

(25) In the embodiment of the disclosure, Step S2 includes the following step.

(26) The battery model output voltage U.sub.d and the total battery current I under different temperatures, different SOCs, and charge-discharge currents are collected. For example, the specific values that may be collected are temperature T=[−2002035], SOC=[10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%], and charge-discharge current I=[−140, −40, 0, 20, 65] A.

(27) In the embodiment of the disclosure, Step S3 includes the following steps.

(28) The likelihood function is adopted to construct the identification model, specifically as follows.

(29) Step S3.1: After performing a Z-transformation on the battery state equation and the predicted battery module terminal voltage obtained in Step S1, an inverse Z-transformation is performed to obtain:
U.sub.d(k+3)=θ.sub.1U.sub.d(k+2)+θ.sub.2U.sub.d(k+1)+θ.sub.3U.sub.d(k)+θ.sub.4I(k+3)+θ.sub.5I(k+2)+θ.sub.6I(k+1)+θ.sub.7I(k), and U.sub.d(k)=(y.sub.k−U.sub.OCV).

(30) Step S3.2: The predicted battery module terminal voltage is obtained: y.sub.k=θ.sup.Tφ(k), where: θ=[θ.sub.1 θ.sub.2 θ.sub.3 θ.sub.4 θ.sub.5 θ.sub.6 θ.sub.7], φ(k)=U.sub.d(k)=[U.sub.d(k−1) U.sub.d(k−2) U.sub.d(k−3) I(k) I(k−1) I(k−2) I(k−3)], and the corresponding relationship between the parameters is as follows: θ.sub.1=b.sub.1+b.sub.3+b.sub.5, θ.sub.2=−(b.sub.1b.sub.3+b.sub.1b.sub.5+b.sub.3b.sub.5), θ.sub.3=b.sub.1b.sub.3b.sub.5, θ.sub.4=−R.sub.ac, θ.sub.5=R.sub.ac(b.sub.1+b.sub.3+b.sub.5)−(b.sub.2+b.sub.4+b.sub.6), θ.sub.6=b.sub.3+b.sub.5)b.sub.2+(b.sub.1+b.sub.5)b.sub.4+(b.sub.1+b.sub.3)b.sub.6−R.sub.ac(b.sub.1b.sub.3+b.sub.1b.sub.5+b.sub.3b.sub.5), θ.sub.7=b.sub.1b.sub.3b.sub.5R.sub.ac−b.sub.3b.sub.5b.sub.2−b.sub.1b.sub.4b.sub.5−b.sub.1b.sub.3b.sub.6, b.sub.1=exp(−T/τ.sub.ct), b.sub.2=R.sub.ct*(1−exp(−T/τ.sub.ct)), b.sub.3=exp(−T/τ.sub.wb1), b.sub.4=R.sub.wb1*(1−exp(−T/τ.sub.wb1)), and b.sub.5=exp(−T/τ.sub.wb2).

(31) In the embodiment of the disclosure, in Step S4, the collected data are the battery model output voltage U.sub.d and the total battery current I under different times. The battery model parameters that need to be calculated are: R.sub.ac, R.sub.ct, R.sub.wb1, C.sub.wb1, and C.sub.ct. The specific calculation method is as follows.

(32) Step S4.1: The identification model is y.sub.k=θ.sup.Tφ(k), where φ(k)=U.sub.d(k)=(y.sub.k−U.sub.OCV) U.sub.OCV is the open circuit voltage obtained from the experiment, and y.sub.k is the predicted battery module terminal voltage. Since the measurement error is normally distributed, the distribution function of y.sub.k satisfies the following equations:

(33) 0$f\left(x\right)=\frac{1}{\sqrt{2\pi \sigma }}{e}^{-\frac{{\left(x-\mu \right)}^2}{2{\sigma }^2}}\mathrm{and}L\left(\theta \right)=\underset{k=1}{\overset{n}{.Math.}}f\left(x\right)=\underset{k=1}{\overset{n}{.Math.}}\frac{1}{\sqrt{2\pi \sigma }}{e}^{-\frac{{\left(x-\mu \right)}^2}{2{\sigma }^2}}.$

(34) A logarithm of L(θ) is taken to obtain:

(35) $\begin{array}{cc}\ln L\left(\theta \right)=\frac{-1}{2{\sigma }^2}\underset{k=1}{\overset{n}{.Math.}}{\left(y\left(k\right)-{\theta }^T\phi \left(k\right)\right)}^2-n\ln \sigma \sqrt{2\pi }& \left(1\right)\end{array}$

(36) where n represents the total sample number of the collected battery model output voltage U.sub.d and the total battery current I, σ represents the variance, and y(k) is the actual measured battery module terminal voltage.

(37) Step 4.2: A gradient operator is set as

(38) ${\nabla }_{\theta }=\left[\begin{array}{ccccccc}\frac{\partial }{\partial {\theta }_1}& \frac{\partial }{\partial {\theta }_2}& \frac{\partial }{\partial {\theta }_3}& \frac{\partial }{\partial {\theta }_4}& \frac{\partial }{\partial {\theta }_5}& \frac{\partial }{\partial {\theta }_6}& \frac{\partial }{\partial {\theta }_7}\end{array}\right].$
The collected data is substituted into Equation (1), and

(39) ${\nabla }_{\theta }\ln L\left(\theta \right)=\frac{-1}{{\sigma }^2}\underset{k=1}{\overset{n}{.Math.}}{\left(y\left(k\right)-{\theta }^T\phi \left(k\right)\right)}^2\left(-\phi \left(k\right)\right)=0$
to calculate each element value of a matrix θ=[θ.sub.1 θ.sub.2 θ.sub.3 θ.sub.4 θ.sub.5 θ.sub.6 θ.sub.7].

(40) Step 4.3: A magnitude of a third-order battery model parameter value is inferred according to a relationship between the third-order battery model parameter value and θ.

(41) The likelihood function is a statistical method that considers the estimation problem from the perspective of a large sample. Let a population X be a discrete random variable, θ=(θ.sub.1, θ.sub.2, . . . , θ.sub.k) be a multi-dimensional parameter vector, X.sub.1, X.sub.2, . . . X.sub.n be the sample from X, x.sub.1, x.sub.2, . . . , x.sub.n be the sample value, and the probability calculation equation be P{X.sub.i=x.sub.i}=p(x.sub.i;θ.sub.1, . . . , θ.sub.k). Then, the likelihood function is as follows:

(42) $L\left(\theta \right)=L\left(x_1,x_2,\mathrm{.Math.},x_n;{\theta }_1,{\theta }_2,\mathrm{.Math.},{\theta }_7\right)=\underset{i=1}{\overset{n}{.Math.}}p\left(x_i;{\theta }_1,{\theta }_2,\mathrm{.Math.},{\theta }_7\right).$

(43) In the case where the test results (that is, the samples) are known, L(θ) is used to estimate the parameters that satisfy the distribution of the samples, and the most likely parameters are used as the true parameter estimation.

(44) As shown in FIG. 7, in another embodiment of the disclosure, a system for identifying third-order model parameters of a lithium battery based on a likelihood function is also provided, which includes the following.

(45) A battery model construction module 201 is configured to establish a third-order battery model of a lithium battery.

(46) A data collection module 202 is configured to collect an output voltage and a total battery current of the third-order battery model under different temperatures, different SOCs, and charge-discharge currents.

(47) An identification model construction module 203 is configured to adopt a likelihood function to construct an identification model.

(48) A parameter determination module 204 is configured to substitute the collected output voltage and total battery current of the third-order battery model into the identification model to calculate third-order battery model parameters.

(49) For the specific implementation of each module, reference may be made to the descriptions of the foregoing embodiment of the method, which will not be reiterated.

(50) In order to demonstrate the identification of the third-order model parameters of the lithium battery based on the likelihood function provided by the disclosure, an example is described here. A LR1865SV lithium battery provided by a certain company is used as an experimental object. Experimental data, battery charge-discharge system Arbin BT2000-5V500A, high and low temperature experimental box HL T402P, LR1865SV lithium battery nominal voltage 4.1 V, and nominal capacity 7.65 Ah, are collected through a battery test platform. Battery experimental data is collected. The temperature includes 4 temperature points of −20, 0, 20, and 35, which cover the temperature points traversed by the battery operation. The SOC value is 10%-90% and is collected every 10%. For the parameters of R.sub.ac that change with current, the charge-discharge current and the output terminal voltage under input currents of −140, −40, 0, 20, 65 are collected.

(51) The disclosure will be further described below in conjunction with the drawings and implementation methods.

(52) As shown in FIG. 2A to FIG. 2B, the method to measure and obtain the battery model output voltage U.sub.d and the total battery current I under different temperatures, different SOCs, and charge-discharge currents of the lithium battery is a composite pulse test, which include the following main test steps.

(53) (1) Before the test, a standard constant current-constant voltage (CC-CV) charging method is used to fully charge a battery to 100%, and let the battery stand for about three hours to tend to a balanced state.

(54) (2) A constant current (usually ⅓ C, where C is the battery nominal capacity value, and ⅓ C is 12 A of current) discharge is implemented on a power battery, so that the SOC thereof moves down to 90%. Let the power battery stand for about 1 hour. Then, a composite pulse excitation sequence (which is a customized sequence, as shown in FIG. 2A) is loaded. Here, the charge-discharge current is 1 C-3 C.

(55) (3) The previous step is repeated to continuously move the SOC to 80%, 70%, until the SOC is 20%.

(56) FIG. 2A to FIG. 2B shows part of the data collected at 0° and 70% SOC. In FIG. 2A is the charge-discharge current and FIG. 2B is the output terminal voltage.

(57) The parameters collected at a certain SOC point at a certain temperature are substituted into the model established by the likelihood function provided by the disclosure for calculation. The battery parameter value ((1) R.sub.ac (2) R.sub.ct (3) R.sub.wb1 (4) C.sub.wb1 (5) C.sub.ct) at the SOC value at the temperature may be obtained. Battery parameter values at all SOC values at all temperatures are calculated and obtained, which are shown in a drawing according to the corresponding parameter values to obtain the parameterized results under different temperatures in FIG. 3A to FIG. 3E. In FIG. 3A is the parameterized result of R.sub.ac, FIG. 3B is the parameterized result of R.sub.ct, FIG. 3C is the parameterized result of R.sub.wb1, FIG. 3D is the parameterized result C.sub.wb1, and FIG. 3E is the parameterized result of C.sub.ct. In the same way, the parameter values under different charge-discharge currents under different temperatures may be obtained in FIG. 4A to FIG. 4D. In FIG. 4A is the parameter value at 35°, FIG. 4B is the parameter value at 20°, FIG. 4C is the parameter value at 0°, and FIG. 4D is the parameter value at −20°.

(58) The above model parameter values are made into a table. A battery simulation model is established in MATLAB. Response values are assigned to the battery parameters by adopting a lookup table method. At room temperature T=20°, a load cycle condition of a hybrid electric vehicle is adopted for algorithm simulation and experimental verification. The load cycle condition refers to a typical condition of a heavy hybrid electric vehicle, which is similar to test conditions such as urban dynamometer driving schedule (UDDS) and new European driving cycle (NEDC). Through the statistics of actual conditions of a test vehicle in multiple typical suburban areas, common condition data, including urban, suburban, high-speed, cross-country, and other conditions, and covering the switching of internal combustion driving mode, pure electric driving mode, hybrid electric mode, idling power generation mode, and other working modes are extracted. The vehicle simulation software Cruse is used to simulate such driving cycle to obtain the load cycle condition battery. The current is as shown in FIG. 5A. In the case of full load of T=20° and SOC=70%, the verification result is as shown in FIG. 5B to FIG. 5D. The simulated voltage is the battery model output voltage obtained by the simulation under the load cycle condition current. In FIG. 5B is a comparison between a measured voltage and a simulated voltage, FIG. 5C is the comparison between the measured voltage and the simulated output voltage in a certain region after amplification, and FIG. 5D is an absolute error of the simulated voltage. It can be seen from FIG. 5A to FIG. 5D that although the conditions are complex, the battery is constantly charged and discharged and the charge-discharge rate is constantly changing, the simulated value of the battery terminal voltage may follow the experimental measured value well, which indicates the parameter value obtained by adopting the likelihood function for parameter estimation follows the actual parameter value. The absolute maximum error is less than 0.036 V, the mean absolute error (MAE) is 0.0084 V, and the root mean square error is 0.0149 V, so the precision is relatively high.

(59) The identification of the third-order battery model parameters based on the likelihood function according to the disclosure can implement the estimation of the battery model parameters, is simple and effective, and has high precision.

(60) It should be pointed out that according to the implementation requirements, each step/component described in the present application may be split into more steps/components, or two or more steps/components or partial operations of a step/component may be combined into a new step/component to implement the objectives of the disclosure.

(61) Persons skilled in the art may easily understand that the above descriptions are only preferred embodiments of the disclosure and are not intended to limit the disclosure. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the disclosure should be included in the protection scope of the disclosure.