CN107192959B - A state-of-charge estimation method for lithium batteries based on Takagi-Sugeno fuzzy model - Google Patents

A state-of-charge estimation method for lithium batteries based on Takagi-Sugeno fuzzy model Download PDF

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CN107192959B
CN107192959B CN201710458245.2A CN201710458245A CN107192959B CN 107192959 B CN107192959 B CN 107192959B CN 201710458245 A CN201710458245 A CN 201710458245A CN 107192959 B CN107192959 B CN 107192959B
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lithium battery
observer
soc
takagi
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CN107192959A (en
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黄炜
刘之涛
谢磊
苏宏业
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Zhejiang University ZJU
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables

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Abstract

The invention discloses a kind of lithium battery charge state estimation methods based on Takagi-Sugeno fuzzy model, second order equivalent-circuit model including establishing lithium battery, and second order equivalent-circuit model is linearized, obtain several sub-line modular models, and suitable subordinating degree function is selected for each sub- linear model, and after being normalized, design the observer of system, finally solve linear matrix inequality, the feedback oscillator of observer is obtained, to obtain obtaining the state-of-charge of lithium battery.The analysis theories of linearisation and method are introduced into the estimation of lithium battery SOC by the present invention, avoid directly carrying out analysis and Design of Observer to non-linear lithium battery model, and have higher precision compared to traditional lithium battery charge state estimation method.

Description

Lithium battery state-of-charge estimation method based on Takagi-Sugeno fuzzy model
Technical Field
The invention relates to a method for estimating the state of charge (SOC) of a lithium battery, in particular to a method for designing a state estimator by using a Takagi-Sugeno fuzzy model (T-S model).
Background
The method for estimating the SOC of the lithium battery accurately is an important function of a battery management system of the electric automobile and an important premise for reasonably using the lithium battery. The use and control of the lithium battery depend on the state of charge (SOC) of the lithium battery, the SOC represents the percentage of the residual electric quantity of the lithium battery in the total capacity of the battery, and the SOC is an important basis for controlling the safe charging and discharging of the battery by a lithium battery management system of the electric automobile and is also an important parameter for estimating the residual cruising ability of the electric automobile. Currently, the commonly used methods for estimating the state of charge of the lithium battery include: (1) current integration method: under the condition that the initial state of charge of the battery is known, the residual capacity and the current state of charge of the lithium battery can be calculated through current integration of the lithium battery, but if the state of charge cannot be corrected regularly, small errors of the current integration can be gradually accumulated, so that larger and larger errors are generated in estimation of the state of charge of the battery; (2) current integration method based on open circuit voltage: the open-circuit voltage of the lithium battery which is kept for a long enough time has a unique corresponding relation with the state of charge of the lithium battery, and the state of charge estimation error is increased due to the accumulation of the integration error by a simple current integration method, so the state of charge estimation value obtained by the current integration method is corrected by the open-circuit voltage of the lithium battery which is kept for a long enough time by combining the two methods. However, the lithium battery needs to be kept still for a long time for correction by using an open-circuit voltage method, the time is not easy to guarantee, and the estimated charge state may jump after correction, so that the customer experience is influenced; (3) kalman filtering algorithm: the Kalman filtering algorithm adopts an optimal estimation idea, can better estimate the state of charge of the lithium battery, and is an effective algorithm, but the method has higher requirement on the model precision of the lithium battery, and the lithium battery model has high nonlinearity, so the precision of the Kalman filtering algorithm is limited by the lithium battery model precision.
The invention provides a method for designing a state observer based on a lithium battery T-S fuzzy model to estimate the SOC value of a lithium battery. Because the lithium battery is interfered by external factors such as temperature, charging and discharging current and the like in the operation process, the lithium battery model has strong nonlinear property, the capacitance resistance and the state of charge SOC in the model established by adopting the equivalent circuit have strong nonlinear characteristic, and the state of charge SOC cannot be measured in the operation process of the battery, so that the estimation of the state of charge SOC has great challenge. In the patent, a method based on a T-S fuzzy model is adopted, a lithium battery T-S fuzzy model based on unknown precursor variables (Premisvariable) is established, and an observer of the model is designed, so that the SOC value of the battery can be effectively estimated.
Disclosure of Invention
The invention mainly provides a method for establishing a lithium battery model by using a T-S fuzzy model and obtaining an estimated value of the lithium battery SOC by designing a state estimator through the model.
A SOC estimation method based on a lithium battery T-S fuzzy model comprises the following steps:
the method comprises the following steps: establishing a second-order equivalent circuit model of the lithium battery, and expressing the second-order equivalent circuit model by using the following nonlinear space model:
where t is time, x represents a system state variable, and x is [ SOC u ]TS uTL]T, wherein uTSAnd uTLRespectively represent capacitances CTransient_S、CTransient_LThe value of the voltage across the two terminals,refers to the first derivative of the state variable x; u is system input quantity, and battery charging and discharging current is obtained; f (x, u) and g (x, u) represent non-linear functions with respect to the state variable x and the input quantity u, respectively; y represents the model output, here the lithium battery terminal voltage.
Step two: based on the characteristics of the lithium battery in the discharging process, taking a certain number of stable points, and linearizing a second-order equivalent circuit model established in each stable point pair (1) to obtain the following sub-module models:
where i is 1,2 … n,where x isiRepresenting the steady-state point taken by the ith submodule model;
step three: selecting SOC as a front part variable z of the model by using a T-S fuzzy model method, and selecting a proper membership function zeta of each linear modeli(z) expressing the non-linear model of the lithium battery in (1) as
Wherein,and satisfy
Step four: based on the lithium battery T-S fuzzy model in the step (3), an observer of the system is designed as follows:
wherein L isiIn order to feed back the gain to the observer,respectively representing observed values of a state variable x, an output variable y and a front piece variable z in the observer;
step five: to obtain LiThe value of (1) is determined by the Design method of the fourth chapter T-S fuzzy model Observer in the book of Stablity Analysis and relating Observer Design Using Takagi-Sugeno fuzzy models by Zs Lo xi fia Lendek
In the formula,μ is a constant greater than zero. If P is presentT> 0 and Q ═ QTIf > 0, then LiThe following linear matrix inequalities are satisfied:
in the formula, I is a unit array with the same order as P,
step six: to obtain LiThereafter, the SOC of the lithium battery can be monitored by an observer (4) in step four) And (6) observing and obtaining.
The invention has the beneficial effects that:
the lithium battery has the characteristic of great nonlinearity due to the internal complex chemical change, the lithium battery needs to be linearized when the SOC value of the lithium battery is acquired by a method for designing an observer, the T-S fuzzy model provides a method for linearizing the lithium battery nonlinear model into a plurality of sub-models, a sub-linear system is integrated into a system through a fuzzy membership function, and the method can use a method of linear matrix inequality to design a state observer for the lithium battery, so that the estimated value of the SOC of the lithium battery can be obtained. Tests show that the method can well estimate the SOC value of the lithium battery under the condition that the initial SOC value is unknown. The method introduces a linear analysis theory and method into the estimation of the SOC of the lithium battery, avoids directly analyzing a nonlinear lithium battery model and designing an observer, and has higher precision compared with the traditional estimation method of the state of charge of the lithium battery.
Drawings
FIG. 1 is a second-order circuit equivalent model of a lithium battery;
FIG. 2 is a graph showing a piecewise-approximately linear SOC-OCV curve for a battery;
FIG. 3 is a schematic diagram of a T-S fuzzy model of a lithium battery;
FIG. 4 is a comparison of the output of the T-S fuzzy model with the output of the equivalent circuit model;
FIG. 5 is a schematic diagram of a design of a lithium battery T-S fuzzy model estimator;
FIG. 6 is a comparison of the output of the designed estimator with the actual output;
fig. 7 shows the comparison of the estimated SOC of the estimator with the actual SOC and the error thereof.
Detailed Description
The lithium battery state of charge estimation method based on the T-S fuzzy model is further explained by combining a specific test verification process.
A lithium battery state of charge estimation method based on a T-S fuzzy model comprises the following steps:
the method comprises the following steps: establishing a second-order equivalent circuit model of the lithium battery, as shown in FIG. 1, wherein C iscapcityRepresenting a capacitance equal to the battery capacity in units of F; vSOCVoltage equal to the SOC in V; controlled current source IbattControlled by the battery discharge current, the controlled voltage source voltage is a nonlinear function of the SOC; rseries、Rtransient_s、Rtransient_LIs resistance, in ohms, Ctransient_s、Ctransient_LIs a capacitor with the unit of F; i isbattFor the input current of the battery, the unit is A, VbattIs the battery terminal voltage in V.
The second order equivalent model can be represented by the following nonlinear spatial model:
where t is time, x represents a system state variable, and x is [ SOC u ]TS uTL]T, wherein uTSAnd uTLRespectively represent capacitances CTransient_S、CTransient_LThe value of the voltage across the two terminals,is the first derivative of the state variable x; u is system input quantity, and battery charging and discharging current is obtained; f (x, u) and g (x, u) represent non-linear functions with respect to the state variable x and the input quantity u, respectively; y table
Model output is shown, here the lithium battery terminal voltage.
Derived from the second order equivalent model:
g(x(t),u(t))＝Vsoc(SOC)-uTS-uTL-RSeries*i
and identifying the value of each element through experiments to obtain the following parameters:
step two: based on the characteristics of the lithium battery in the discharging process, a certain number of stable points are taken, and each stable point pair is
(1) The second-order equivalent circuit model built in the step (2) is linearized to obtain the following sub-module models:
where i is 1,2 … n,where x isiRepresenting the steady-state point taken by the ith submodule model;
selecting the number n of subsystems: the more the number of the subsystems n is, the more the system can approach the original nonlinear system. Because the nonlinear relation between the open-circuit voltage and the SOC of the lithium battery presents the characteristic of three-stage type, as shown in the attached figure 2, when the SOC is between 0-0.2, 0.2-0.8 and 0.8-1.0 respectively, the open-circuit voltage and the SOC of the lithium battery present approximate linearity, so that one point is selected at 0-0.2 and 0.8-1.0 respectively, and considering that the span of 0.2-0.8 is large, two points are taken at 0.2-0.8, and 4 steady-state points are taken in total, specifically as follows:
at x ═ 0.07500, there are:
C1＝[2.8173 -1 -1]D1＝0.049347
at x ═ 0.300 ] there are:
C2＝[0.23234 -1 -1]D2＝0.074356
at x ═ 0.700 ] there are:
C3＝[0.52123 -1 -1]D3＝0.074460
at x ═ 0.900 ] there are:
C4＝[0.78140 -1 -1]D4＝0.074460
step three: selecting SOC as a front part variable z of the model by using a T-S fuzzy model method, and selecting a proper membership function zeta of each linear modeli(z), as shown in FIG. 3, the normalized membership function is used to equate the original nonlinear system to the sum of n linear submodules, so that the nonlinear model of the lithium battery in (1) can be expressed as
Wherein,and satisfy
a) Around z ═ 0.075
b) Around z 0.3
c) Around z 0.7
d) Around z 0.9
To verify the correctness of the T-S model, the output of the T-S model and the original nonlinear model under the condition of the same input are compared by MATLAB, as shown in FIG. 4, it can be seen that the output of the T-S model is very close to the output of the original model except for the increase of the error in the last 10% SOC stage, which also proves that the T-S model has good accuracy.
Step four: based on the lithium battery T-S fuzzy model in the step (3), an observer of the system is designed as follows:
wherein L isiIn order to feed back the gain to the observer,respectively representing observed values of a state variable x, an output variable y and a front-piece variable z in the observer. As shown in FIG. 5, the input of the observer includes the input u and the error e between the original model and the output of the observer, and an appropriate L is selectediThe observer will be able to track the output of the original nonlinear system.
Step five: to obtain LiThe value of (1) is the value of (1), the Design method of the fourth chapter T-S fuzzy model Observer in the book of Stability Analysis and nonlinear Observer Design Using Takagi-Sugeno fuzzy models by Zs Lo, Huang fia Lendek is adopted in the present application, and the hypothesis is that
In the formulaμ is a constant greater than zero. If P is presentT> 0 and Q ═ QTIf > 0, then LiThe following linear matrix inequalities are satisfied:
in the formula, I is a unit array with the same order as P,
when mu is 1, the formula (5) is satisfied, and the matrix inequality (6) is solved by matlab calculation:
L1＝[-0.21583 -0.079398 -0.11180]T
L2＝[-0.20131 -0.073420 -0.10453]T
L3＝[-0.20104 -0.073451 -0.10438]T
L4＝[-0.20104 -0.073451 -0.10438]T
step six: to obtain LiAnd then, the SOC of the lithium battery can be obtained by observing through an observer (4) in the fourth step.
Comparing the output of the observer with the actual system output as shown in fig. 6, the output of the observer is very close to the output of the nonlinear model in (1); fig. 7 shows that the observer estimates the error of the SOC of the lithium battery, and it can be seen that even if the initial SOC value of the observer has a large error with the actual SOC, the observer can track the actual SOC value well.

Claims (1)

1. A lithium battery state of charge estimation method based on a Takagi-Sugeno fuzzy model is characterized by comprising the following steps:
the method comprises the following steps: establishing a second-order equivalent circuit model of the lithium battery, and expressing the second-order equivalent circuit model by using the following nonlinear space model:
where t is time, x represents a system state variable, and x is [ SOC u ]TSuTL]TWherein u isTSAnd uTLRespectively represent capacitances CTransient_S、CTransient_LThe value of the voltage across the two terminals,refers to the first derivative of the state variable x; u is system input quantity, and battery charging and discharging current is obtained; f (x, u) and g (x, u) represent non-linear functions with respect to the state variable x and the input quantity u, respectively; y represents the model output, here the lithium battery terminal voltage;
step two: based on the characteristics of the lithium battery in the discharging process, taking a certain number of stable points, and linearizing a second-order equivalent circuit model established in each stable point pair (1) to obtain the following sub-module models:
where i is 1,2 … n,where x isiRepresenting the steady-state point taken by the ith submodule model;
step three: selecting SOC as a front piece variable z of the model by using a Takagi-Sugeno fuzzy model method, and selecting a proper membership function zeta of each linear modeli(z) expressing the non-linear model of the lithium battery in (1) as
Wherein,and satisfy
Step four: based on the Takagi-Sugeno fuzzy model of the lithium battery in the step (3), an observer of the system is designed as follows:
wherein L isiIn order to feed back the gain to the observer,respectively representing observed values of a state variable x, an output variable y and a front piece variable z in the observer;
step five: to obtain LiThe value of (1) is determined by the Design method of Takagi-Sugeno fuzzy model observer in the fourth chapter of Stablity Analysis and nonlinear observer Design Using Takagi-Sugeno fuzzy models, Zs Lolo fia Lendek
In the formula,μ is a constant greater than zero. If P is presentT> 0 and Q ═ QTIf > 0, then LiThe following linear matrix inequalities are satisfied:
in the formula, I is a unit array with the same order as P,
step six: to obtain LiAnd then, the SOC of the lithium battery can be obtained by observing through an observer (4) in the fourth step.
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