CN104502858B - Electrokinetic cell SOC methods of estimation and system based on backward difference discrete model - Google Patents
Electrokinetic cell SOC methods of estimation and system based on backward difference discrete model Download PDFInfo
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Abstract
The present invention is electrokinetic cell SOC methods of estimation and system based on backward difference discrete model, and this method first step, the backward difference discrete model for setting up electrokinetic cell are recognized by the least square method containing forgetting factor to the parameter of backward difference discrete model.Second step, the backward difference discrete model based on the electrokinetic cell obtained by the first step, with reference to the non-linear relation of open-circuit voltage and SOC, using adaptive extended kalman filtering, complete electrokinetic cell SOC effective estimation.Voltage that the system electrokinetic cell is connect, current sensor connect embedded microcontroller through analog-to-digital conversion module.The discrete battery model on-line parameter identification module of microcontroller pretreatment module containing LPF, backward difference and AEKF algorithm SOC estimation modules.Gained SOC results send the CAN network of display apparatus.The present invention is simple in construction, improves parameter identification speed and precision, and reduce historical data influences on identification, and convenience of calculation, SOC estimated accuracies are high.
Description
Technical field
The present invention relates to the state of charge estimation technique field of automobile power cell, specially based on backward difference walk-off-mode
The electrokinetic cell SOC methods of estimation and system of type.
Background technology
In recent years, as electrokinetic cell, lithium battery is compared with traditional lead-acid battery, Ni-MH battery, with energy density
Height, memory-less effect, have extended cycle life, it is environment-friendly the features such as, so lithium battery has become electric automobile power battery
Main body.
In electric automobile, the state of charge SOC (state-of-charge) of accurate estimation battery, i.e. remaining battery electricity
Amount, is premise and key that cell management system of electric automobile BMS (battery management system) is well run.
Battery state of charge SOC accurate estimation mainly includes two parts：The estimation of parameter identification and state of charge SOC.
Conventional parameter identification method has genetic algorithm, least square method, double card Kalman Filtering etc.；Conventional state of charge SOC's estimates
Calculation method has open circuit voltage method, current integration method, Kalman filtering, EKF, Unscented kalman filtering, self adaptation
Kalman filtering etc..
The different combination in the two parts, constitutes different SOC methods of estimation, and obtaining SOC speed and precision has substantially poor
It is different.Had at present using more, more representational：1. the battery charge state estimation experimental study of Unscented kalman filtering,
The combination of least square method and Unscented kalman filtering；2. the combination of least square method and open circuit voltage method；3. self adaptation karr
Application of the graceful wave filter in vehicle lithium-ion power battery SOC estimations, the combination of genetic algorithm and adaptive Kalman filter；
4. the lithium battery SOC estimations based on RLS and EKF algorithms, the combination of least square method and EKF；5. double card is utilized
Kalman Filtering algorithm estimates the internal state of electronic vehicle lithium-ion power battery, is estimated simultaneously using double Kalman filtering algorithms
SOC and the inner parameter change of lithium ion power storage battery used for electric vehicle.
But these existing SOC methods of estimation are that precision is not high a bit, some are to calculate complicated speed slowly, fail to meet
The online accurate estimation of automobile power cell --- lithium battery state of charge.
The content of the invention
The purpose of the present invention is to disclose a kind of electrokinetic cell SOC methods of estimation based on backward difference discrete model, power
The charge and discharge process of battery is a more slow process, i.e., open-circuit voltage is stablized relatively in a short time, after this method is used
To difference, electrokinetic cell backward difference discrete model simple in construction is obtained；Using the least square method containing forgetting factor
(Forgetting Factor Recursive Least Squares algorithm, FFRLS) is to backward difference discrete model
Parameter identification is carried out, with reference to adaptive extended kalman filtering (AEKF) computational methods based on maximum likelihood criterion, completes dynamic
Power battery state of charge SOC effective estimation.
Another object of the present invention designs an electrokinetic cell SOC estimating system based on backward difference discrete model, its
It can be embedded in the equipment using electrokinetic cell, realize real-time SOC On-line Estimations and the display of electrokinetic cell.
The electrokinetic cell SOC methods of estimation based on backward difference discrete model that the present invention is designed, including two steps：
The first step, the backward difference discrete model for setting up electrokinetic cell, pass through the least square method containing forgetting factor
(FFRLS) parameter to backward difference discrete model is recognized.
Second step, the backward difference discrete model based on the electrokinetic cell obtained by the first step, with reference to open-circuit voltage and SOC
Non-linear relation, using adaptive extended kalman filtering (AEKF) computational methods, completes electrokinetic cell SOC effective estimation.
The first step, electrokinetic cell backward difference discrete model and parameter identification
1.1. electrokinetic cell model
For battery management system, conventional battery model has：Thermal model, electrochemical model and equivalent-circuit model etc..
Equivalent-circuit model can more intuitively show the relation between electric current and voltage, it is easy to mathematics compared with other battery models
The expression of analytic expression, is easy to analysis and the identification of Model Parameters of battery.
The present invention uses a kind of most widely used battery equivalent model, the Thevenin models of battery, description electricity
The static state and dynamic property in pond.The polarization resistance R of batterypWith the polarization capacity C of batterypParallel connection constitutes single order reinforced concrete structure, represents electricity
The polarization reaction in pond, RC both end voltages are Up(t)；Concatenate Ohmic resistance R0And the open-circuit voltage OCV that Uoc, Uoc are battery, sampling
Obtain battery terminal voltage U (t) and flow through ohmic internal resistance R0Electric current i (t).
Battery Thevenin models are expressed as follows：
U (t)=UOC(t)-R0i(t)-Up(t) (2)
1.2 model discretizations and parameter identification
1.2.1 model discretization
With backward-difference method to above-mentioned battery model discretization, difference equation is obtained, after arrangement
U(k)-UOC(k)=a [U (k-1)-UOC(k-1)]+bI(k)+cI(k-1) (3)
In formula, Uoc (k) represents the open-circuit voltage at k moment；U (k) is k moment battery terminal voltage sampled values；When I (k) is k
Carve loop current sampled value；A, b, c are model parameter.
The charge and discharge process of battery is a more slow process, and open-circuit voltage Uoc stablizes relatively in a short time, that is, has
△UOC(k)=UOC(k)-UOC(k-1)≈0 (5)
Then formula (3) is combined with formula (5), and the backward difference discrete model of battery is：
U (k)=aU (k-1)+bI (k)+cI (k-1)+(1-a) UOC(k)
After arrangement
U(k)-UOC(k)=a [U (k-1)-UOC(k-1)]+bI(k)+cI(k-1) (6)
A, b and c represent that battery backward difference discrete model parameter is as follows：
Wherein T is the sampling period.
Compared with conventional bilinear transformation discrete model, battery backward difference walk-off-mode pattern (6) of the invention, model ginseng
Number relation is simple, is easy to open-circuit voltage Uoc to estimate.
1.2.2 the parameter identification of battery difference discrete model
The present invention is using least-squares algorithm (FFRLS) the identification battery model parameter containing forgetting factor, and process is as follows：
Wherein
In formula：φ (k) is data vector, and θ (k) is estimation parameter vector.E (k) is U (k) prediction error.For θ
(k) estimate, initial valueWith P (0) rule of thumb assignment, K (k) is gain, and λ is forgetting factor, λ=0.95~1.
Variable is specially in corresponding least square (11) formula of backward difference discrete model (10) of battery：
φ (k)=[U (k-1), I (k), I (k-1), 1]T (11)
θ (k)=[a, b, c, (1-a) UOC(k)]T (12)
A, b, c value are tried to achieve by the least-squares algorithm (FFRLS algorithms) containing forgetting factor, formula (7) (8) (9) is substituted into,
Obtain battery model parameter R0, Rp,Cp,UOCValue.
Second step, the battery state of charge SOC estimations based on adaptive extended kalman filtering AEKF
Choose SOC and electric capacity CpTerminal voltage be state variable, correspondence k moment state variables, i.e. Xk=[SOCk Up,k]T,
System state equation and measurement equation are as follows：
Wherein, Uoc(SOCk) represent battery open circuit voltage UocK moment non-linear relations between SOC are as follows：
Uoc(SOCk)=k1SOCk 8+k2SOCk 7+k3SOCk 6+k4SOCk 5+
(14)
k5SOCk 4+k6SOCk 3+k7SOCk 2+k8SOCk+k9
With least square method, some the model electrokinetic cell open-circuit voltage U obtained by on-line identificationocObtained with experiment
The model electrokinetic cell SOC, try to achieve the model electrokinetic cell coefficient k1~k9。
AEKF algorithms estimation SOC detailed processes are as follows：
2.1 state estimations：
Xk=[SOCk Up,k]TEstimate of the state at current time (k moment) be
Wherein Kk、Expression formula is
Wherein k represents current time, and k-1 represents previous moment,Represent based on obtained by current time (k moment) state
Xk=[SOCk Up,k]TK moment estimates,Represent based on k moment X obtained by previous moment ((k-1) moment) statek's
Estimate,Represent based on (k-1) moment X obtained by previous moment ((k-1) moment) statekThe estimate of state.Ym|kIt is
The measured value of k moment battery terminal voltages,It is the terminal voltage predicted value after updating at the k moment.It is to be based on previous moment
The discreet value at k moment SOC, Q obtained by statekIt is k moment systematic procedure noises wkCovariance.RkIt is k moment system measurements noises
vkCovariance.
The renewal of parameter and state during 2.2 recurrence calculations：
2.2.1 parameter Qk、RkUpdate
Wherein, μkIt is k moment terminal voltage actual values and the difference of the terminal voltage predicted value after renewal, FkIt is every L moment pair
The average value of difference is answered, L is self-adapting window.
2.2.2 stateUpdate：
Wherein, QNFor the rated capacity of electrokinetic cell, η represents efficiency for charge-discharge, and T represents the sampling period.
Electrokinetic cell SOC estimating systems of the invention based on backward difference discrete model, including microcontroller and its connection
Display, the microcontroller is embedded microcontroller, and electrokinetic cell output is terminated with voltage sensor and current sense
Device.Voltage sensor and current sensor connect embedded microcontroller through analog-to-digital conversion module, and embedded microcontroller contains low pass
The on-line parameter identification module and AEKF algorithm SOC state estimation moulds of the discrete battery model of filter preprocessing module, backward difference
Block.Embedded microcontroller connection display, is further connected with CAN (controller local area network Controller Area Network) total
Line interface and/or RS232 interfaces.The system is embedded in the equipment using electrokinetic cell, adopted at one together with electrokinetic cell
Voltage, the collection of electric current, battery model parameter identification and modification and SOC On-line Estimations are completed in the sample cycle, gained SOC results exist
The controller local area network of the equipment is shown or is transferred directly on display.
Compared with prior art, the method for electrokinetic cell SOC estimation of the present invention based on backward difference discrete model is with being
The advantage of system is：1st, using in the discrete battery model of backward difference, the history value with battery model inner parameter is unrelated, structure letter
It is single, be conducive to improving the identification speed and precision of parameter；2nd, with the least square method of recursion containing forgetting factor to backward difference from
The parameter for dissipating model is recognized, and is focused on renewal of the new data to weights, is reduced historical data parameter identification influence degree, effectively
Ground avoid conventional least square method of recursion with slowly varying battery parameter data continuous iteration, update and will appear from
" data saturation " problem；3rd, in view of SOC and open-circuit voltage Uoc non-linear relation, using the self adaptation of maximum likelihood criterion
EKF (AEKF) algorithm carries out On-line Estimation to SOC, and features simple structure, convenience of calculation, SOC estimated accuracies are high.
Brief description of the drawings
Fig. 1 is battery in the originally embodiment of the method for the electrokinetic cell SOC estimations based on backward difference discrete model
Thevenin model circuit diagrams.
Fig. 2 for this based on backward difference discrete model electrokinetic cell SOC estimation embodiment of the method SOC estimation with
SOC tests the comparative graph of acquired value.
Fig. 3 is the system embodiment structural representation of this electrokinetic cell SOC estimation based on backward difference discrete model.
Embodiment
The embodiment of the method for electrokinetic cell SOC estimations based on backward difference discrete model
The embodiment of the method for this electrokinetic cell SOC estimation based on backward difference discrete model, is comprised the following steps that：
The first step, electrokinetic cell backward difference discrete model and parameter identification
1.1. electrokinetic cell model
Using the Thevenin models of battery, as shown in figure 1, the polarization resistance R of batterypWith the polarization capacity C of batterypAnd
Connection constitutes single order reinforced concrete structure, represents the polarization reaction of battery, and RC both end voltages are Up(t)；Concatenate Ohmic resistance R0And Uoc, Uoc
For the open-circuit voltage OCV of battery, sampling obtains battery terminal voltage U (t) and flows through ohmic internal resistance R0Electric current i (t).
Battery Thevenin models are expressed as follows：
U (t)=UOC(t)-R0i(t)-Up(t) (2)
1.2 model discretizations and parameter identification
1.2.1 model discretization
With backward-difference method to above-mentioned battery model discretization, difference equation is obtained, after arrangement
U(k)-UOC(k)=a [U (k-1)-UOC(k-1)]+bI(k)+cI(k-1) (6)
In formula, Uoc (k) represents the open-circuit voltage at k moment；U (k) is the battery terminal voltage sampled value at current k moment；I(k)
For the loop current sampled value at current k moment；A, b, c are model parameter.
The relation of a, b and c and battery backward difference discrete model parameter is as follows：
Wherein T is the sampling period.
1.2.2 the parameter identification of battery difference discrete model
The estimate of least-squares algorithm (FFRLS) identification model parameter θ (k) containing forgetting factorProcess such as
Under：
Wherein：
In formula：φ (k) is data vector, and θ (k) is estimation parameter vector.E (k) is U (k) prediction error.Initial value
With P (0) rule of thumb assignment.For θ (k) estimate.λ is forgetting factor, and this example takes λ=0.99.
A, b, c value are tried to achieve by FFRLS algorithms, so as to obtain model parameter R0, Rp,Cp,UOCValue.
Second step, the battery state of charge SOC estimations based on adaptive extended kalman filtering AEKF
Choose SOC and electric capacity CpTerminal voltage be that the state representation at state variable X, k moment is Xk=[SOCk Up,k]T, it is
System state equation and measurement equation are as follows：
Wherein, νkIt is to measure noise, Uoc(SOCk) represent battery open circuit voltage UocNon-linear relation between SOC, such as
Under：
Uoc(SOCk)=k1SOCk 8+k2SOCk 7+k3SOCk 6+k4SOCk 5+
k5SOCk 4+k6SOCk 3+k7SOCk 2+k8SOCk+k9 (14)
The open-circuit voltage U of some model electrokinetic cell is obtained by on-line identificationoc, and by being somebody's turn to do that traditional means of experiment is obtained
Model electrokinetic cell SOC, the model electrokinetic cell coefficient k is tried to achieve with least square method1~k9。
AEKF algorithms estimation SOC processes are as follows：
2.1 state estimations：
Xk=[SOCk Up,k]TThe k estimates at current time of state
Wherein Kk、Expression formula is
WhereinState X is represented respectivelyk=[SOCk Up,k]TK estimation at the time of state is seen based on current time
Value,The moment k estimate under based on previous moment state,The moment k-1 under based on previous moment state
Estimate, k is current time, and k-1 is previous moment.Ym|kIt is the measured value of k moment battery terminal voltages,It is to update at the k moment
Terminal voltage predicted value afterwards,
It is the discreet value based on k moment SOC under previous moment state, QkIt is systematic procedure noise wkAssociation side
Difference.RkIt is system measurements noise vkCovariance.
The renewal of parameter and state during 2.2 recurrence calculations：
2.2.1 parameter Qk、RkUpdate
Wherein, μkIt is k moment terminal voltage actual values and the difference of the terminal voltage predicted value after renewal, FkIt is every L moment pair
The average value of difference is answered, L is self-adapting window.
2.2.2 stateUpdate：
Wherein, QNFor the rated capacity of electrokinetic cell, η represents efficiency for charge-discharge, and T represents the sampling period.Based on backward poor
Divide the electrokinetic cell SOC estimating system embodiments of discrete model
This electrokinetic cell SOC estimating systems embodiment based on backward difference discrete model is as shown in Fig. 2 the microcontroller
Device is embedded microcontroller, and electrokinetic cell output is terminated with voltage sensor and current sensor.This example, which is used, has isolation
The voltage sensor and Hall current sensor of function.Voltage sensor and current sensor are connected through analog-to-digital conversion module to be embedded in
Microcontroller, the parameter that embedded microcontroller contains the discrete battery model of LPF pretreatment module, backward difference is distinguished online
Know module and AEKF algorithm SOC state estimation modules.Embedded microcontroller connection display, be further connected with CAN interface and
RS232 interfaces.The system is embedded in the equipment using electrokinetic cell together with electrokinetic cell, complete within a sampling period
Into voltage, the collection of electric current, battery model parameter identification and modification and SOC On-line Estimations, gained SOC results show over the display
Show or be transferred directly to the controller local area network of the equipment.
With the system embodiment of the above-mentioned electrokinetic cell SOC estimation based on backward difference discrete model, by this method pair
The state of charge SOC of certain model electrokinetic cell gamut change, take respectively SOC initial values for SOC (0)=1, SOC (0)=
0.8, SOC (0)=0.6, SOC (0)=0.4, carries out SOC estimations, gained SOC estimated result is as shown in figure 3, wherein, indulging and sitting
SOC value is designated as, abscissa is the time, and great Tu chronomeres are the second (s), and the little Tu chronomeres of upper right are 10-4Second.SOC (0)=
1 curve is solid line, and SOC (0)=0.8 curve is dash dotted line, and SOC (0)=0.6 curve is short stroke of dotted line, SOC (0)
=0.4 curve is chain-dotted line, and the curve of the SOC value of the model electrokinetic cell obtained by traditional experiment is pecked line.Can by big figure
To see, SOC estimation obtained by this law is consistent with the SOC curves obtained by experiment substantially.Small in upper right can be seen in the figure, no
With initial value start the difference for having maximum 0.6 in very short time with SOC experiment values in estimation, can after 0.004 second it is different just
The SOC estimated results of initial value just reach unanimity with SOC traditional experiment values.It can be seen that this method initial value influences on SOC estimated accuracies
It is weaker, and this SOC methods of estimation have higher estimated accuracy, there is practicality.
Gamut change to the state of charge SOC of certain model electrokinetic cell is estimated with the system by this method, passes through
The experiment for going through 10 hours obtains SOC estimation data, model obtained by SOC estimation and traditional experiment that this method is obtained
The SOC of electrokinetic cell is compared, corresponding error statistics data result is shown in Table 1, and the inventive method SOC estimated accuracies reach
0.45%.
The SOC error statistics results of table 1
Above-described embodiment, is only to the specific of the purpose of the present invention, technical scheme and beneficial effect further description
Individual example, the present invention is not limited to this.All any modifications made within the scope of disclosure of the invention, equivalent, change
Enter, be all contained within protection scope of the present invention.
Claims (5)
1. the method for the electrokinetic cell SOC estimations based on backward difference discrete model, is comprised the following steps that：
The first step, electrokinetic cell backward difference discrete model and parameter identification
1.1. electrokinetic cell model
Using the Thevenin models of battery, the polarization resistance R of batterypWith the polarization capacity C of batterypParallel connection constitutes single order RC knots
Structure, represents the polarization reaction of battery, and RC both end voltages are Up(t)；Concatenate Ohmic resistance R0And Uoc, Uoc are the open circuit electricity of battery
It is the open-circuit voltage of t battery to press OCV, Uoc (t), and sampling obtains battery terminal voltage U (t) and flows through ohmic internal resistance R0Electricity
Flow i (t)；
Battery Thevenin models are expressed as follows：
U (t)=UOC(t)-R0i(t)-Up(t)；
1.2 model discretizations and parameter identification
1.2.1 model discretization
With backward-difference method to above-mentioned battery model discretization, difference equation is obtained, after arrangement
U(k)-UOC(k)=a [U (k-1)-UOC(k-1)]+bI(k)+cI(k-1)
In formula, Uoc (k) represents the open-circuit voltage at k moment；U (k) is the battery terminal voltage at current k moment；When I (k) is current k
The loop current at quarter；A, b, c are model parameter；
The relation of a, b and c and battery backward difference discrete model parameter is as follows：
Wherein T is the sampling period；
1.2.2 the parameter identification of battery difference discrete model
The estimate of least-squares algorithm identification model parameter θ (k) containing forgetting factorProcess it is as follows：
Wherein：
In formula：φ (k) is data vector, and θ (k) is estimation parameter vector, and e (k) is U (k) prediction error, initial valueAnd P
(0) rule of thumb assignment,For θ (k) estimate, λ is forgetting factor, λ=0.95~1；K (k), P (k) are middle anaplasia
Amount, it is as defined above shown in formula；
A, b, c value are tried to achieve by FFRLS algorithms, so as to obtain model parameter R0, Rp,Cp,UOCValue；
Second step, the battery state of charge SOC estimations based on adaptive extended kalman filtering AEKF
Choose SOC and electric capacity CpTerminal voltage be state variable X, i.e. k moment state X, be expressed as Xk=[SOCk Up,k]T, it is
System state equation and measurement equation are as follows：
Wherein, νkIt is to measure noise, Uoc(SOCk) represent battery open circuit voltage UocNon-linear relation between SOC is as follows：
Uoc(SOCk)=k1SOCk 8+k2SOCk 7+k3SOCk 6+k4SOCk 5+
k5SOCk 4+k6SOCk 3+k7SOCk 2+k8SOCk+k9
Some the model electrokinetic cell open-circuit voltage U obtained by on-line identificationocWith testing the obtained model electrokinetic cell
SOC, the model electrokinetic cell coefficient k is tried to achieve with least square method1~k9；
AEKF algorithms estimation SOC processes are as follows：
2.1 state estimations：
Xk=[SOCk Up,k]TThe k estimates at current time of state
Wherein Kk、Expression formula is
WhereinState X is represented respectivelyk=[SOCk Up,k]TK estimate at the time of state is seen based on current time,The moment k estimate under based on previous moment state,Moment k-1's estimates under based on previous moment state
Evaluation, k is current time, and k-1 is previous moment；Ym|kIt is the measured value of k moment battery terminal voltages,It is after updating at the k moment
Terminal voltage predicted value,It is the discreet value based on k moment SOC under previous moment state, QkIt is systematic procedure noise wk's
Covariance, RkIt is system measurements noise vkCovariance；Hk、Pk,k-1、Up,k、Ak,k-1、Bk-1It is intermediate variable, Hk、Pk,k-1With
Up,kIt is as defined above, Ak,k-1And Bk-1Definition see next section；
The renewal of parameter and state during 2.2 recurrence calculations：
2.2.1 parameter Qk、RkUpdate
Wherein, μkIt is the terminal voltage predicted value after updating at the k moment and the difference of terminal voltage actual value, FkIt is that every L moment correspondence is poor
The average value of value, L is self-adapting window；
2.2.2 stateUpdate：
Wherein, QNFor the rated capacity of electrokinetic cell, η represents efficiency for charge-discharge.
2. the base of the method design of the electrokinetic cell SOC estimations according to claim 1 based on backward difference discrete model
In the electrokinetic cell SOC estimating systems of backward difference discrete model, including microcontroller and its display of connection, electrokinetic cell
Output is terminated with voltage sensor and current sensor, and voltage sensor and current sensor are connected through analog-to-digital conversion module to be embedded in
Microcontroller, it is characterised in that：
The microcontroller is embedded microcontroller, and embedded microcontroller contains LPF pretreatment module, backward difference
The on-line parameter identification module and AEKF algorithm SOC state estimation modules of discrete battery model, the system together with electrokinetic cell,
It is embedded in the equipment using electrokinetic cell, gained battery state of charge estimate result shows or directly transmitted over the display
To the controller local area network of the equipment.
3. the electrokinetic cell SOC estimating systems according to claim 2 based on backward difference discrete model, its feature exists
In：
The system is embedded in the equipment using electrokinetic cell together with electrokinetic cell.
4. the electrokinetic cell SOC estimating systems according to claim 2 based on backward difference discrete model, its feature exists
In：
The microcontroller is connected to CAN interface and/or RS232 interfaces.
5. the electrokinetic cell SOC estimating systems according to claim 2 based on backward difference discrete model, its feature exists
In：
The voltage sensor is the voltage sensor with isolation features；The current sensor is Hall current sensor.
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