CN108828449A - Lithium ion battery method for estimating remaining capacity based on proportional integration H ∞ observer - Google Patents
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Abstract
The invention discloses a kind of lithium ion battery method for estimating remaining capacity based on proportional integration H ∞ observer, collected voltage and current data are transferred data to remaining capacity estimation module by capture card, then low-pass filtered device by current detector and digital analog converter；Establish Order RC model；The nonlinear function of model parameter and open-circuit voltage about remaining capacity is picked out using the Current Voltage response of battery pack；Unilateral Lipschitz condition is proposed to nonlinear function part, to guarantee that nonlinear function plays positive effect on Design of Observer；Using the design proportion integral observer of the H ∞ design criteria based on linear matrix inequality.The present invention can reduce the traditional accumulated error of integral algorithm and requirement to initial value accuracy on time, the model established can effectively describe the physical characteristic of power battery charge and discharge, it being capable of real-time estimation remaining capacity, convergence is good, and estimated accuracy height is suitable for the remaining capacity estimation of electric automobile power battery.
Description
Technical field
The present invention relates to new energy car battery administrative skill fields, specially the lithium based on proportional integration H ∞ observer
Ion battery remaining capacity (state of charge, SOC) estimation method.
Background technique
In order to which response environment deterioration and energy crisis, ev industry rapidly develop in recent years.Power battery conduct
The main energy sources of electric car, performance and working condition play a crucial role vehicle.Charged state (SOC) is electricity
Pond one of most important parameter in use, it refers to its residual capacity after battery is shelved whithin a period of time or in a long time
With the ratio of total capacity, usually indicated in the form of percentage.One accurate SOC can not only can intuitively and quickly grasp and work as
Preceding battery status, and can also effectively prevent the overcharge and overdischarge of battery.Therefore, accurately the SOC of estimation battery is electricity
One of key technology of pond management system (BMS) and the key points and difficulties of battery management system research.However, SOC cannot be straight
It connects measurement to obtain, can only be estimated by a variety of different algorithms.Therefore, SOC estimation in the theoretical of electric car and is answered
All there is considerable meaning in.
In previous research, it is widely used the method for estimating remaining capacity based on model, it is big can be substantially divided into two
Class.One is the method based on filter, another kind is the method based on observer.Most widely used filtering technique is various
Kalman filter (KF), kalman filter method are using the general name of a kind of estimation method of Kalman filter theory, the party
The core concept of method is battery to be regarded as a dynamical system, and carry out optimal minimum estimation to the state of dynamical system.Specifically
Method includes extended Kalman filter (EKF), Unscented kalman filtering (UKF), adaptive Kalman filter (AKF), double expansions
It opens up Kalman filter (DEKF) etc., different kalman filter methods is selected according to the model of battery.In addition, based on seeing
The thought for surveying the method for device is analogous to kalman filter method, the state-space model of battery is established, using SOC as battery
Then the quantity of state of system designs a convergence state observer using control theory knowledge to estimate SOC.Specific method includes
Luenberger observer, H ∞ observer, nonlinear observer and sliding mode observer.Observer is in actual control system
Error is inevitable, because state is not easy to observe, result has serious noise jamming sometimes.
Summary of the invention
In view of the above-mentioned problems, the purpose of the present invention is to provide a kind of purpose of the present invention in Proportional integral observer
On the basis of a kind of effective non-gaussian interference for inhibiting model is provided, and there is good applicability to battery nonlinear system
Power battery method for estimating remaining capacity.Technical solution is as follows：
A kind of lithium ion battery method for estimating remaining capacity based on proportional integration H ∞ observer, includes the next steps：
S1：Establish the state space equation of Order RC model；
S11：Establish the equivalent-circuit model of controlled device：By resistance R0、R1、R2It is sequentially connected in series in battery pack UOCOutput
End, and by capacitor C1With resistance R1Parallel connection, capacitor C2With resistance R2It is in parallel；
S12：The differential equation group of system is established according to above-mentioned equivalent model；
State equation：
Output equation：
UT=UOC(SOC)-R0IT-U1-U2 (2)
Wherein, U1And U2Respectively indicate capacitor C1And C2Both end voltage, ITTo flow through resistance R0Electric current, SOC indicates remaining
Electricity, UOC(SOC) function of the open-circuit voltage about remaining capacity SOC, U are indicatedTIndicate end voltage, QnIndicate rated capacity；
S13：State space equation is converted by formula (1) and formula (2)：
Wherein：X=[U1,U2,SOC]T, y=UT, u=IT, h (x)=UOC(SOC), x0It is original state, and
Wherein, τ1=R1C1, τ2=R2C2For the time constant of two RC rings；
S13：Distracter is added, obtains：
Wherein, ωxAnd ωyRespectively the state distracter of system and output distracter；
S2：Pick out model parameter R0、R1、R2、C1、C2And nonlinear function U of the open-circuit voltage about remaining capacityOC
(SOC)；
S3：Calculate bound of the open-circuit voltage about the nonlinear function derivative of remaining capacity：Due to UOCIt (SOC) is dullness
Function, then its derivative：
S4：Design proportion integral observer；
S41：Calculate the difference of nonlinear function h (x)：
S42：According to Order Derivatives in Differential Mid-Value Theorem, have
Wherein, ζSOCU respectively in x=ζ1,U2,SOC；
S43：Calculate the derivative of nonlinear function h (x) about quantity of state：
S44：Using unilateral Lipschitz condition, that is, there is matrix M and make：
Wherein,
S45：Design proportion integral observer is as follows：
Wherein, KpIt is PI observer proportional gain, KiIt is PI observer integral gain, z is the integral of output error；
State estimation error is as follows：
Wherein,Indicate state estimation error,F=[0,1,0],Expression state
The cumulative interference of interference and output interference；
S5：Reduce remaining capacity estimation error using H ∞ method；For given scalar γ, it is assumed that there are matrix P=
PT>0, Q=QT>0, N=PKiMeet following linear matrix inequality group with vector S：
Wherein：Π11=PA+ATP+T1SC+CTSTT1 T+ I-2M,Kp=P-1；N=
PKi, α expression attenuation coefficient；I0Indicate the unit matrix of 3x3；
Then H ∞ performance is as follows：
The index of J (t) expression H ∞ performance；
S6：Current and voltage data is acquired, remaining capacity estimation is carried out using above-mentioned observer.
Further, the nonlinear function of model parameter and open-circuit voltage about remaining capacity is picked out in the S2
Method is：
S21：During battery runs down is stood, battery discharge pine of the battery voltage measurement data about time of repose is obtained
Relaxation voltage response curves, and be fitted using the function containing undetermined parameter as follows：
Thus two above-mentioned RC ring time constants are obtained：τ1=R1C1, τ2=R2C2, initial voltage U1(0), U2(0), t table
Show current time；
S22：By accordingly obtaining for firstorder circuit：
S23：By τ1=R1C1, τ2=R2C2And formula (6)：
S24：It is dropped to obtain R by discharge voltage0Internal resistance：
Wherein,ΔU is discharge voltage drop；
S25：Under the operating condition of laboratory, in remaining capacity SOC ∈ [0,1] range, n SOC sampled point is looked for, for each
Sampled point such as stands at the durations, obtains the open-circuit voltage under corresponding SOC, using least-square fitting approach obtain remaining capacity about
The U of open-circuit voltageOC(SOC) function.
The beneficial effects of the invention are as follows：The present invention is seen using the proportional integration of the H ∞ method based on linear matrix inequality
Device design criteria is surveyed, can accurately estimate end voltage in real time, and system mode interference and output interference can be effectively reduced,
Constraint modeling error is influenced caused by state estimation, so as to remaining capacity estimation close to true value；Reduce tradition by
When integral algorithm accumulated error and requirement to initial value accuracy, the model established can effectively describe power battery and fill
The physical characteristic of discharge process；The algorithm for estimating is closed loop algorithm, and the nonlinear transformations of model are utilized, can be surplus with real-time estimation
Remaining electricity, convergence is good, and estimated accuracy is high, the remaining capacity estimation suitable for electric automobile power battery；It considers vehicle-mounted
Under practical situations, to the lower requirement of calculation amount, have a good application prospect.
Detailed description of the invention
Fig. 1 is method for estimating remaining capacity system block diagram provided by the invention.
Fig. 2 is method for estimating remaining capacity flow chart provided by the invention.
Fig. 3 is the controlled device equivalent model schematic diagram of method for estimating remaining capacity provided by the invention.
Fig. 4 is the flow chart step by step of step S4 in method for estimating remaining capacity provided by the invention.
Specific embodiment
The present invention is described in further details in the following with reference to the drawings and specific embodiments.When system has interference and noise
When, since the stable state accuracy of system can be improved in integral part link and inhibits to interfere, state estimation is not only realized, but also
Improve the estimation effect to unknown input disturbances.Therefore it is directed to the discrete sampling system of unknown disturbance, devises proportional integration
Observer.H ∞ method is to limit LDPC code error and measure the powerful that noise influences state estimation, this is meaned
, the PI observer based on H ∞ can be minimized influence of the external disturbance to state estimation result.Therefore, this method is to system
Model error and external disturbance have stronger robustness.
As shown in Figure 1, the estimating system of power battery remaining capacity includes the electric current for acquiring battery pack current data
Detector, and the digital analog converter for acquiring battery pack voltage data, current detector and digital analog converter pass data
Defeated to arrive capture card, by pci interface, low-pass filtered device transfers data to remaining capacity estimation module to capture card again.
Using current monitor INA170EA, current data is acquired, digital analog converter AD7091R, collection voltages number are used
According to being transferred on data collecting card NI-6229, by pci interface to low-pass filter, and estimated on computers using remaining capacity
The remaining capacity estimation of meter method progress battery pack.
Specific steps are as shown in Fig. 2 block diagram：
S1：Establish the state space equation of Order RC model.
S11：Establish the equivalent-circuit model of controlled device.I.e. by resistance R0、R1、R2It is sequentially connected in series in battery pack UOCIt is defeated
Outlet, and by capacitor C1With resistance R1Parallel connection, capacitor C2With resistance R2It is in parallel.
S12：The differential equation group of system is established according to above-mentioned equivalent model.
State equation：
Output equation：
UT=UOC(SOC)-R0IT-U1-U2 (2)
Wherein, U1And U2Respectively indicate capacitor C1And C2Both end voltage, ITTo flow through resistance R0Electric current, SOC indicates remaining
Electricity, UOC(SOC) function of the open-circuit voltage about remaining capacity SOC, U are indicatedTIndicate end voltage, QnIndicate rated capacity.
S13：State space equation is converted by formula (1) and formula (2)：
Wherein：X=[U1,U2,SOC]T, y=UT, u=IT, h (x)=UOC(SOC), x0It is original state, and
Wherein, τ1=R1C1, τ2=R2C2For the time constant of two RC rings.
S13：Distracter is added, obtains：
Wherein, ωxAnd ωyRespectively the state distracter of system and output distracter.
S2：Pick out model parameter R0、R1、R2、C1、C2And nonlinear function U of the open-circuit voltage about remaining capacityOC
(SOC)。
S21：During battery runs down is stood, battery discharge pine of the battery voltage measurement data about time of repose is obtained
Relaxation voltage response curves, and be fitted using the function containing undetermined parameter as follows：
Thus two above-mentioned RC ring time constants are obtained：τ1=R1C1, τ2=R2C2, initial voltage U1(0), U2(0)；
S22：By accordingly obtaining for firstorder circuit：
S23：By τ1=R1C1, τ2=R2C2And formula (6)：
S24：It is dropped to obtain R by discharge voltage0Internal resistance：
Wherein,ΔU is discharge voltage drop；
S25：Under the operating condition of laboratory, in remaining capacity SOC ∈ [0,1] range, n SOC sampled point is looked for, for each
Sampled point stands t duration, obtains the open-circuit voltage under corresponding SOC, using least-square fitting approach obtain remaining capacity about
The U of open-circuit voltageOC(SOC) function.
S3：Calculate bound of the open-circuit voltage about the nonlinear function derivative of remaining capacity.Due to UOCIt (SOC) is dullness
Function, then its derivative：
S4：Design proportion integral observer, specific steps are as shown in Fig. 4 block diagram：
S41：Calculate the difference of nonlinear function h (x)：
S42：According to Order Derivatives in Differential Mid-Value Theorem, have
Wherein, ζSOCU respectively in x=ζ1,U2,SOC。
S43：Calculate the derivative of nonlinear function h (x) about quantity of state：
S44：Using unilateral Lipschitz condition, that is, there is matrix M and make：
Wherein,
S45：Design proportion integral observer is as follows：
Wherein, KpIt is PI observer proportional gain, KiIt is PI observer integral gain, z is the integral of output error；
State estimation error is as follows：
Wherein,Indicate state estimation error,F=[0,1,0],Expression state
The cumulative interference of interference and output interference；
S5：Reduce remaining capacity estimation error using H ∞ method；For given scalar γ, it is assumed that there are matrix P=
PT>0,
Q=QT>0, N=PKiMeet following linear matrix inequality group with vector S：
Wherein：Π11=PA+ATP+T1SC+CTSTT1 T+ I-2M,Kp=P-1；N=
PKi, α expression attenuation coefficient；I0Indicate the unit matrix of 3x3；
Then H ∞ performance is as follows：
The index of J (t) expression H ∞ performance；
S6：Current and voltage data is acquired, remaining capacity estimation is carried out using above-mentioned observer.
To sum up, the Proportional integral observer based on H ∞ performance, which designs, completes, and is a kind of on-line Algorithm, can be accurate in real time
Estimate end voltage.Real-time estimation remaining capacity, and system mode interference and output interference, constraint modeling can be effectively reduced
Error is influenced caused by state estimation, so as to remaining capacity estimation close to true value.The remaining capacity estimation proposed
Method, it is contemplated that under vehicle-mounted practical situations, to the lower requirement of calculation amount, have a good application prospect.
Claims (2)
1. a kind of lithium ion battery method for estimating remaining capacity based on proportional integration H ∞ observer, which is characterized in that including one
Lower step：
S1：Establish the state space equation of Order RC model；
S11：Establish the equivalent-circuit model of controlled device：By resistance R0、R1、R2It is sequentially connected in series in battery pack UOCOutput end, and
By capacitor C1With resistance R1Parallel connection, capacitor C2With resistance R2It is in parallel；
S12：The differential equation group of system is established according to above-mentioned equivalent model；
State equation：
Output equation：
UT=UOC(SOC)-R0IT-U1-U2 (2)
Wherein, U1And U2Respectively indicate capacitor C1And C2Both end voltage, ITTo flow through resistance R0Electric current, SOC indicate remaining capacity,
UOC(SOC) function of the open-circuit voltage about remaining capacity SOC, U are indicatedTIndicate end voltage, QnIndicate rated capacity；
S13：State space equation is converted by formula (1) and formula (2)：
Wherein：X=[U1,U2,SOC]T, y=UT, u=IT, h (x)=UOC(SOC), x0It is original state, and
Wherein, τ1=R1C1, τ2=R2C2For the time constant of two RC rings；
S13：Distracter is added, obtains：
Wherein, ωxAnd ωyRespectively the state distracter of system and output distracter；
S2：Pick out model parameter R0、R1、R2、C1、C2And nonlinear function U of the open-circuit voltage about remaining capacityOC(SOC)；
S3：Calculate bound of the open-circuit voltage about the nonlinear function derivative of remaining capacity：Due to UOCIt (SOC) is dull letter
It counts, then its derivative：
S4：Design proportion integral observer；
S41：Calculate the difference of nonlinear function h (x)：
S42：According to Order Derivatives in Differential Mid-Value Theorem, have
Wherein, ζSOCU respectively in x=ζ1,U2,SOC；
S43：Calculate the derivative of nonlinear function h (x) about quantity of state：
S44：Using unilateral Lipschitz condition, that is, there is matrix M and make：
Wherein,
S45：Design proportion integral observer is as follows：
Wherein, KpIt is PI observer proportional gain, KiIt is PI observer integral gain, z is the integral of output error；
State estimation error is as follows：
Wherein,Indicate state estimation error,F=[0,1,0],The interference of expression state
With the cumulative interference of output interference；
S5：Reduce remaining capacity estimation error using H ∞ method；For given scalar γ, it is assumed that there are matrix P=PT>0,
Q=QT>0, N=PKiMeet following linear matrix inequality group with vector S：
Wherein：Π11=PA+ATP+T1SC+CTSTT1 T+ I-2M,Kp=P-1；
N=PKi, α expression attenuation coefficient；I0Indicate the unit matrix of 3x3；
Then H ∞ performance is as follows：
The index of J (t) expression H ∞ performance；
S6：Current and voltage data is acquired, remaining capacity estimation is carried out using above-mentioned observer.
2. the lithium ion battery method for estimating remaining capacity according to claim 1 based on proportional integration H ∞ observer, institute
It states and picks out model parameter and open-circuit voltage in S2 about the method for the nonlinear function of remaining capacity and be：
S21：During battery runs down is stood, battery discharge relaxation electricity of the battery voltage measurement data about time of repose is obtained
Response curve is pressed, and is fitted using the function containing undetermined parameter as follows：
Thus two above-mentioned RC ring time constants are obtained：τ1=R1C1, τ2=R2C2, initial voltage U1(0), U2(0)；
T indicates current time；
S22：By accordingly obtaining for firstorder circuit：
S23：By τ1=R1C1, τ2=R2C2And formula (6)：
S24：It is dropped to obtain R by discharge voltage0Internal resistance：
Wherein, Δ U is discharge voltage drop；
S25：Under the operating condition of laboratory, in remaining capacity SOC ∈ [0,1] range, n SOC sampled point is looked for, for each sampling
The durations such as point standing obtain the open-circuit voltage under corresponding SOC, obtain remaining capacity about open circuit using least-square fitting approach
The U of voltageOC(SOC) function.
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