CN108196200A - A kind of combined simulation appraisal procedure of lithium battery health and state-of-charge - Google Patents
A kind of combined simulation appraisal procedure of lithium battery health and state-of-charge Download PDFInfo
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- CN108196200A CN108196200A CN201810080690.4A CN201810080690A CN108196200A CN 108196200 A CN108196200 A CN 108196200A CN 201810080690 A CN201810080690 A CN 201810080690A CN 108196200 A CN108196200 A CN 108196200A
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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]
- G01R31/392—Determining battery ageing or deterioration, e.g. state of health
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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
Abstract
The invention belongs to lithium battery health control technical field, the combined simulation appraisal procedure of specially a kind of lithium battery health and state-of-charge.The present invention provides description means using lithium battery equivalent circuit description battery behavior for hysteretic phenomenon existing for open-circuit voltage and state-of-charge relationship；It is used as state variable by introducing the internal resistance of cell, and it is associated with the cell health state defined from battery capacity and internal resistance angle, so as to by updating the current capacities of internal resistance real-time update battery, thus can adaptive battery aging and be always maintained at high description precision.Compared with the conventional method, the present invention can realize the real-time online capacity estimation that conventional method is difficult to realize, and ensure the real-time order of accuarcy of circuit equivalent model, and provide reference for cell health state and state-of-charge.
Description
Technical field
The invention belongs to lithium battery health control technical fields, and in particular to the connection of a kind of lithium battery health and state-of-charge
Close simulation evaluation method.
Background technology
Lithium ion battery is due to having many advantages, such as high-energy density, low self-discharge rate and long-life so that it is in movement
The fields such as electronic equipment and power vehicle have been more and more widely used.But these advantages are only in the operating environment of safety
It is middle to be just guaranteed.Therefore in order to ensure that lithium battery can be operated in such operating environment, it is necessary to carry out pipe to battery
Reason.And the On-line Estimation of lithium battery interior state is then the precondition of battery management.The internal state of lithium battery is primarily referred to as
Its state-of-charge (State of Charge, SOC) and health status (State of Health, SOH).The former is used for showing to work as
Preceding battery dump energy is how many, and the latter then can release the attenuation degree of electricity for describing battery maximum.
The definition of SOC is the ratio of battery dump energy and battery Full Charge Capacity.In battery management module, to prevent battery
It overcharges and overdischarge, charging and discharging currents is required for being controlled using SOC information, so accurate SOC estimations are that have
Critically important practical significance.But SOC can not be obtained by measuring directly, it can only be carried out by some way
Estimation[1].At present, the main methods of estimation of SOC have following four：1) current integration method, it passes through inflow/outflow battery current
Integration estimate SOC, since any open-loop prediction method is all inevitably present error, its estimated result can be with
The increase of the time of integration and continuous cumulative errors.In addition, need in advance could be into there are one accurate SOC initial values for its estimation
Row, this just brings difficulty to its practical application[2]；2) open circuit voltage method, it utilizes open-circuit voltage (Open Circuit
Voltage, OCV) obtain SOC estimation with the correspondence of SOC, but such correspondence, it needs to carry out battery
After standing for a long time, can just it measure, therefore be not used to real-time estimation[3]；3) internal resistance method, this method need high-precision measurement
Instrument can just carry out, therefore be not suitable for the scene of real-time working[4]；4) equivalent-circuit model method, it is according to battery both ends electric current electricity
Pressure relationship constructs an equivalent-circuit model to describe battery, i.e., gives expression to battery charging/discharging characteristic with circuit equation
Come[5~6]。
At present, most common battery method of estimation is all based on the method for estimation of battery equivalent circuit model[1].Document
[7] common equivalent-circuit model is described, due to the model with corresponding circuit element come simulated battery charge-discharge characteristic, because
This component parameters can be determined according to the voltage and current of battery charging and discharging.In this way based on the equivalent electricity that these are constructed
Road model, it is possible to build corresponding state equation, based on these state equations, people are just using Kalman filter[5]
Or sliding mode observer[6]The methods of to carry out real-time estimation to the battery parameters of needs.Although this class model can preferable simulation electricity
Pond charge-discharge characteristic, but there is also some problems.On the one hand, in this class model, usually all assume that OCV is corresponding with SOC and close
Be when tying up to charge and discharge it is changeless, and document [8] [9] research shows that：OCV is corresponding with SOC in battery charge and discharge process
There are hysteretic phenomenons for relationship, are embodied in：Under identical SOC states, OCV can be because of the different charge and discharge of battery previous moment
Electricity condition and generate deviation.This illustrates this kind of equivalent-circuit model, and there are model errors.On the other hand, with battery discharge to one
During the SOC states of a very little, lithium battery internal resistance can exponentially rise.In addition, with the attenuation aging of battery, internal resistance can therewith
Increase, capacity then reduce therewith.This variation can not in equivalent-circuit model with a normal resistance and a normal capacitance come
It represents, it means that under minimum SOC states or after cell decay aging, the model error of estimation can become very
Greatly, it is reduced so as to cause estimated accuracy.
Battery capacity refers to the electricity that battery maximum can release under current state, its attenuation can use battery SOH
To represent.It is less with the relevant research reports of SOH relative to the research of SOC.Document [10] proposes lithium ion battery
Cycle life empirical model, but the model considers many physical factors of battery, therefore can not be adapted well to not
Same battery；Similarly, document [11] also gives the mathematical model of a capacity of lithium ion battery attenuation, but the model is one
Kind empirical model, for different batteries, model has uncertainty, is not suitable for practical application scene.
For the estimation of above-mentioned battery charge state and these existing problems of health status estimation, the present invention is by by document
[7] the battery equivalent model proposed introduces the internal resistance of time-varying, also, for open-circuit voltage with opening a way in state-of-charge relation curve
Hysteretic phenomenon existing for voltage, it is uncertain existing for its curve to describe, it is characterized by introducing white Gaussian noise.It will
Internal resistance as state variable is associated with cell health state, and then provides a kind of new way for estimating battery capacity.In this way
We just establish a new model for battery charge state estimation and health status estimation.Analysis shows：Our model can
To describe the variation that may be present of battery SOC-OCV correspondences, particularly it can be directed to the change of the internal resistance of cell under different conditions
Change, can in real time be adjusted by internal resistance that model is estimated, precision is described in real time, and can also describe electricity which improves model
The ageing state in pond simultaneously estimates its parameter.The result verification of experiment proposes the feasibility of model.
Invention content
The purpose of the present invention is to provide a kind of lithium battery health and the combined simulation appraisal procedure of state-of-charge, can not only
Enough correct offer cell health states, and energy adaptive battery ageing state, keep higher simulation Evaluation accuracy.
The combined simulation appraisal procedure of lithium battery health proposed by the present invention and state-of-charge, using battery equivalent circuit mould
Type introduces white Gaussian noise in the relationship of state-of-charge and open-circuit voltage, and using internal resistance as variable real-time estimation, simultaneously will
Internal resistance is connected by cell health state with capacity to update battery real time capacity, so as to ensure model energy adaptive battery
Ageing state improves state-of-charge estimated accuracy, the specific steps are：
(1) equivalent-circuit model is constructed：Lithium battery equivalent-circuit model (model provided in for document [7]) is used, it is right
Battery carries out pre-arcing test, and resistance in model, capacitance are calculated according to measurement result, utilizes experimental data verification model
Accuracy.
Details are as follows for idiographic flow：
The lithium battery equivalent-circuit model provided in document [7], as shown in Figure 1.In (a) part, the capacity electricity consumption of battery
Hold CnIt characterizes, the electric current of battery inflow/outflow is then represented with controlled current source, such CnThe lifting of both end voltage just reflects
The increase and decrease of battery capacity, we represent C with 1VSOCnThe voltage at both ends；In (b) part, controlled voltage source OCV (SOC)
For representing battery SOC to the Nonlinear Mapping of open-circuit voltage, R0Represent the equivalent ohmic internal resistance of battery, R1And C1And R2And C2
Two RC networks formed are respectively intended to the dynamic characteristic of reflection short time for having simultaneously of battery and long-time constant.
First, SOC-OCV relationships are established, the charging modes for taking constant current-constant pressure are fully charged by battery, stand to battery
After reaching stable state, using suitable fixed discharge-rate electric current (such as：0.5C~1C) it discharges battery, it discharges one section
It is stood after time to obtain the open-circuit voltage under current state, battery discharge will be taken properly with the time stood in each period
Ratio (it is recommended that time of repose in discharge time 5 times or more), the sampling interval of battery current and voltage is 1s, is constantly recycled to
Battery discharge blanking voltage；Then it is charged using identical current versus cell, endless form is identical with discharge mode, until battery
Charge to charge cutoff voltage.It is averaging according to the charge and discharge data measured, state-of-charge and battery open circuit voltage can be obtained
Correspondence, as shown in Figure 2.
Furthermore, it is contemplated that hysteretic characteristic existing for battery, can add in white Gaussian noise in the relation curve and be subject to table
Sign.
Secondly, hybrid power pulse characteristic test is carried out to battery, can calculates that represent battery long according to discharge curve
With the resistance and capacitance in the RC network of short-time constant.
(2) state equation is built according to equivalent-circuit model：Suitable variable is as system state variables in Selection Model,
Equation is established according to model circuit.
Details are as follows for idiographic flow：
By the equivalent circuit of Fig. 1, battery model output voltage V, which can be written, is：
V (t+1)=OCV (t)+I (t) R0(t)+VRC1(t)+VRC2(t) (1)
Wherein, t represents the time, and I (t) is that t moment flows through the electric current of battery, and in charging for just, when electric discharge is negative, and
VRC1And VRC2Dynamic characteristic can then be expressed from the next：
The result of study of document [12] shows：The equivalent internal resistance R of battery0It can become with the SOC and its health status of battery
Change and changes, therefore different from reported in the literature such, if document [7] regards it as constant, it will be regarded as battery herein
One state variable, and characterize it with following walk random model：
R0(t+1)=R0(t)+r(t) (4)
In formula, r (t) represents random white noise.
Controlled voltage source OCV (SOC) in Fig. 1 reflects mapping of the battery SOC to its open-circuit voltage, typical charge and discharge
Procedure relation is as shown in Figure 2.From Fig. 2 (a) as can be seen that SOC and OCV relationships during charge and discharge are variations, i.e.,
Under identical SOC states, the OCV and OCV in discharge process is not same value in charging process, and document [8] claims the phenomenon
Hysteretic phenomenon for open-circuit voltage.In the research of document report, usually by taking the average value of OCV in charge and discharge process come table
Levy the relationship of SOC and OCV[9].Fig. 2 (b) gives represents OCV by average valueAV(SOC) example, average value are：
Wherein, OCVup(SOC) and OCVdown(SOC) the OCV values that the charging and discharging in Fig. 2 (a) obtain are represented respectively.
It, herein will be on the basis of average OCV voltages in order to describe influence of the charge and discharge OCV hysteretic phenomenons to battery behavior
On, which is described to uncertainty existing for charge and discharge OCV by introducing, is characterized with white Gaussian noise, this is made an uproar
The variance of sound can be determined, to cover possible deviation range, here according to the value of deviation maximum in the range of entire SOC
We use VHIt represents, i.e.,：
OCV (t)=OCVav(t)+VH(t) (6)
By Fig. 1 (a) it is found that capacitance CnThe voltage at both ends is 1VSOC, then the expression formula of SOC can be write as：
In formula (1) to (7), writ state variable is x=[SOC, VRC1,VRC2,R0], then lithium battery is described in time-varying
The state equation of the new model of resistance and hysteresis can be written as：
V (t+1)=OCVav(t)+VH(t)+I(t)R0(t)+VRC1(t)+VRC2(t)+v(t) (9)
Wherein, w (t) and v (t) represent state and observation noise respectively.
(3) state equation (8) is estimated, and the internal resistance according to estimation and capacity using Unscented kalman filtering algorithm
It connects, real-time update equivalent model, to ensure the real-time accuracy of model.
Details are as follows for idiographic flow：
Battery current capacities CnIt can reflect the health status SOH of battery, with the recycling of battery, battery capacity declines
Subtract the continuous reduction that degree also illustrates the health status SOH of battery.The SOH defined from battery capacity angle is as follows[1]：
Wherein, CnowAfter representing cell degradation, in the case of fully charged, maximum electricity that present battery can release；
CnewNew battery is represented in the case of fully charged, the maximum electricity that can be released.According to IEEE1188-1996 standards, work as battery
When fully charged, when capacity is less than the 80% of battery rated capacity, then it is assumed that battery end of life, it should be replaced.At this point,
The SOH that formula (10) representsCVariation range to represent the battery for 1~0.8,1 be new battery, 0.8 to represent the battery weathered
The final state in its service life is arrived.
Formula (10) shows：In the case that known to SOH, present battery capacity can be obtained by formula (10).In addition, SOH may be used also
To be defined as follows from internal resistance angle[13]：
From the report result of document [13] it is found that under conditions of mutually synthermal and identical SOC, the internal resistance of cell can be with electricity
Pond aging is deepened and is constantly increased.Resistance all should be the value measured under mutually synthermal and SOC in this pattern (11), wherein
R0,EOLInternal resistance when representing cell degradation to end-of-life status, according to IEEE1188-1996 standards, it is believed that the internal resistance is electricity
Pond maximum can release electricity and decay to internal resistance when new battery maximum can release the 80% of electricity, R0,newThen represent the interior of new battery
Resistance, R0,nowRepresent the internal resistance of present battery.By formula (11) as can be seen that SOHRVariation range represent the electricity for 1~0, i.e., 1
Pond is new battery, and 0 represents that the battery is weathered to have arrived its end-of-life status.
As the above analysis, with cell degradation, battery capacity CnWith internal resistance R0It will change.And in formula (8)
In state equation, R0Variation characterized with walk random equation, but capacity CnVariation do not retouched but
It states.For real-time update capacity Cn, so that description battery model it is more accurate, below we will provide update capacity CnSide
Method.
Document [14] the result shows that：Battery capacity decays between the internal resistance of cell, and there are following linear relationships：
Cfnow(%)=kR0,now+b (12)
Wherein, Cfnow(%) represents that present battery maximum can release the percentage of electricity attenuation, i.e.,：
The formula (12) is substituted into formula (11) to obtain：
Wherein, C is allowednew-Cnew(kR0,EOL+ b)=CEOLMaximum can release electricity, table when reaching end-of-life status for battery
Show have：
And capacity and internal resistance are all given values when battery initial capacity and internal resistance and end-of-life, then it can by formula (15)
Newer capacity is obtained：
Enable R in formula (8)0(t)=R0,now, then have：
In formulaRepresent definition, it is meant that new model formula (8) in the present invention, (9) and (17) just can be according to the use of battery
(health or aging) state carrys out simulated battery.
The simulation evaluation method (new model) of joint lithium battery health proposed by the present invention and state-of-charge, overall flow is such as
Shown in Fig. 3.Time-varying internal resistance and hysteretic characteristic are introduced in original circuit equivalent model, internal resistance is characterized with walk random model,
The uncertainty of SOC-OCV curves is characterized with white Gaussian noise.The internal resistance value that walk random model estimates and battery are good for
Health state relation gets up, and then can be using updated internal resistance value come for model modification battery capacity parameters.Finally, Wo Menwei
Battery charge state is estimated and health status estimation establishes a new model.Held by the internal resistance value and battery of model modification
Amount, can not only improve the real-time description precision of model, and can provide the health parameter of battery, and ensureing that battery can meet is
System work requirements.The experimental results showed that：State-of-charge estimated result based on the new model can reach very high precision, big portion
Point result can be maintained in 3% error range；In addition, in the state of cell degradation, capacity update energy degree of precision
Close to actual value, cell health state is provided to the user, and in the state of cell degradation, state-of-charge estimation still has
Degree of precision.
Description of the drawings
Fig. 1 is the circuit equivalent illustraton of model used.
Fig. 2 is SOC-OCV relational graphs.Wherein, two curves are respectively SOC-OCV relationships song when being charged and discharged in (a)
Line, (b) obtain final SOC-OCV curves to be averaged according to charge and discharge relation curve.
Fig. 3 is the flow chart of entire model state estimation.
Fig. 4 is model verification result, it is shown that cell voltage estimated value and measured value.
Fig. 5 is model verification result, the absolute error figure for cell voltage estimation.
Fig. 6 is model verification result, it is shown that battery SOC estimated value and actual value.
Fig. 7 is model verification result, it is shown that the absolute error of battery SOC estimation.
Fig. 8 is model verification result, is the percentage error of battery capacity estimation.
Fig. 9 be cell degradation to SOH=91% when verification result.Wherein, battery SOC estimated value is shown in (a)
With the comparison result of actual value, the percentage error of battery capacity estimation is shown in (b).
Specific embodiment
1st, equivalent-circuit model is constructed
Used in test experiments is a kind of lithium ion polymer battery core LGABF1L18650 batteries, and rated capacity is
3350mAh, rated voltage 3.7V.Model parameter needs to recognize by some charge-discharge tests.All experiments are taken the photograph 25
It is carried out under family name's degree.
It first has to establish SOC-OCV relationships, the charging modes for taking constant current-constant pressure are fully charged by battery, after standing 1h, make
The current versus cell for being 0.6C with discharge-rate discharges, then battery discharge 120s in each period stands 720s, battery
The sampling interval of electric current and voltage is 1s, is constantly recycled to battery discharge blanking voltage；Then identical current versus cell is used
Charging, endless form is identical with discharge mode, until battery charges to charge cutoff voltage.Charge and discharge data according to measuring are asked
It is average, the correspondence of state-of-charge and battery open circuit voltage can be obtained, as shown in Figure 2.The curve of Fig. 2 uses piecewise linearity
The mode of fitting constructs the relationship of SOC and OCV, and specific fitting parameter is as shown in table 1.It is furthermore, it is contemplated that stagnant existing for battery
Return characteristic can add in the white Gaussian noise that standard deviation is 0.02 in the relation curve and be characterized.
Secondly, hybrid power pulse characteristic test is carried out to battery, bibliography [6] [9] can be counted according to discharge curve
Calculate the resistance and capacitance in the RC network for representing battery length and short-time constant：R1=0.001 Ω, C1=618F, R2=
0.0257 Ω, C2=707.7F.
2nd, state equation is built
Writ state variable is x=[SOC, VRC1,VRC2,R0], the resistance capacitance measured in 1 is substituted into formula (8) (9), structure
Build state equation.
3rd, state estimation and real-time update equivalent model
For the state equation built in 2, the present invention estimates it using Unscented kalman filtering algorithm, estimates every time
The internal resistance counted out is connected by health status and battery capacity, and capacity is estimated by formula (17).Each estimation
As a result battery health information can not only be provided, moreover it is possible to which real-time update battery model ensures the precision of model under various regimes.
Fig. 4 and Fig. 5 is the measured value of battery terminal voltage and model estimate value comparison result, is as can be seen from Figure 4 estimated
Voltage curve has been bonded actual measurement profile well, and test absolute error is shown in Figure 5, it is seen from it that the two
Between error be always held in minimum range, it can be seen that estimated voltage have higher precision；Fig. 6 and Fig. 7 is electricity
The actual value of pond SOC and model estimate value comparison result, the actual value of wherein battery SOC is by improved current integration method meter
It acquires[6], the estimation curve in Fig. 6 has been bonded actual value curve well, and test absolute error is shown in the figure 7, from it
As can be seen that difference therebetween is maintained in smaller range, evaluated error is largely maintained within 3%, can be seen
Going out SOC estimations has very high precision.Fig. 8 give using estimation internal resistance more new size percentage error figure as a result, by
Exponentially trend rises for internal resistance when as SOC ＜ 0.2, so the internal resistance estimated when only using SOC ＞ 0.2 when updating Cn
Value.The capacity of experiment battery is 3350mAh, and the percentage error of estimated result is within 5%.
Fig. 9 be cell degradation to SOH=91% when test result.Fig. 9 (a) is that the actual value of battery SOC is estimated with model
Evaluation comparison result；Fig. 9 (b) gives the percentage error figure result of the internal resistance more new size using estimation.It can from result
To find out, under ageing state, model remains to keep good performance.
Table 1：SOC-OCV curve segmentation fitting coefficients
Bibliography
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Claims (4)
1. the combined simulation appraisal procedure of a kind of lithium battery health and state-of-charge, which is characterized in that using battery equivalent circuit
Model, introduces white Gaussian noise in the relationship of state-of-charge and open-circuit voltage, and using internal resistance as variable real-time estimation, simultaneously
Internal resistance and capacity are connected by cell health state to update battery real time capacity, so as to ensure that model can adaptive electricity
Pond ageing state improves state-of-charge estimated accuracy；The specific steps are：
(1) equivalent-circuit model is constructed：Using lithium battery equivalent-circuit model, pre-arcing test is carried out to battery, according to measurement
As a result resistance in model, capacitance are calculated, utilizes the accuracy of experimental data verification model；
(2) state equation is built according to equivalent-circuit model：Variable is returned as system state variables according to model in Selection Model
Equation is established on road；
(3) state equation is estimated using Unscented kalman filtering algorithm, and has been contacted according to the internal resistance and capacity of estimation
Come, real-time update equivalent model, to ensure the real-time accuracy of model.
2. the combined simulation appraisal procedure of lithium battery health according to claim 1 and state-of-charge, which is characterized in that step
Suddenly the flow of (1) is：
In lithium battery equivalent-circuit model shown in Fig. 1, the capacity capacitance C of batterynIt characterizes, the electricity of battery inflow/outflow
It flows and is then represented with controlled current source, such CnThe lifting of both end voltage just reflects the increase and decrease of battery capacity, with 1VSOC come
Represent CnThe voltage at both ends, the expression battery charge state of SOC are defined as the ratio of battery dump energy and battery Full Charge Capacity；
Controlled voltage source OCV (SOC) is for representing battery SOC to the Nonlinear Mapping of open-circuit voltage OCV, R0Represent the equivalent Europe of battery
Nurse internal resistance, R1And C1And R2And C2Two RC networks formed are respectively intended to short time and length that reflection battery has simultaneously
The dynamic characteristic of time constant；
First, SOC-OCV relationships are established, the charging modes for taking constant current-constant pressure are fully charged by battery, stand to battery and reach
After stable state, discharged using suitable fixed discharge-rate current versus cell, stand to obtain after a period of time of discharging
Open-circuit voltage under current state, battery discharge will take proper ratio with the time stood in each period, battery current and
The sampling interval of voltage is 1s, is constantly recycled to battery discharge blanking voltage；It is averaging, obtained according to the charge and discharge data measured
The correspondence of state-of-charge and battery open circuit voltage；White Gaussian noise is added in the relation curve to be characterized；
Then, hybrid power pulse characteristic test is carried out to battery, is calculated according to discharge curve and represent battery length and short time
Resistance and capacitance in the RC network of constant.
3. the combined simulation appraisal procedure of lithium battery health according to claim 2 and state-of-charge, which is characterized in that step
Suddenly the idiographic flow of (2) is：
According to lithium battery equivalent-circuit model, output voltage V is：
V (t+1)=OCV (t)+I (t) R0(t)+VRC1(t)+VRC2(t) (1)
Wherein, t represents the time, and I (t) is that t moment flows through the electric current of battery, and in charging for just, when electric discharge is negative, and VRC1
And VRC2Dynamic characteristic be expressed from the next：
R0For the equivalent internal resistance of battery, it can change with the SOC and its health status of battery and change, it is regarded as the one of battery
A state variable, and characterize it with following walk random model：
R0(t+1)=R0(t)+r(t) (4)
In formula, r (t) represents random white noise；
In lithium battery equivalent-circuit model, controlled voltage source OCV (SOC) reflects mapping of the battery SOC to its open-circuit voltage, right
In the hysteretic phenomenon of wherein open-circuit voltage, the relationship of SOC and OCV are characterized by taking the average value of OCV in charge and discharge process,
Average value is：
Wherein, OCVup(SOC) and OCVdown(SOC) the OCV values that charging and discharging obtain are represented respectively；
On the basis of average OCV voltages, to the average value to uncertain existing for charge and discharge OCV, with white Gaussian noise come
It is characterized, the variance of the noise, is determined according to the value of deviation maximum in the range of entire SOC, it is possible inclined to cover
Poor range, uses V hereHIt represents, i.e.,：
OCV (t)=OCVav(t)+VH(t) (6)
Capacitance CnThe voltage at both ends is 1VSOC, then the expression formula of SOC is just write as：
In formula (1) to (7), writ state variable is x=[SOC, VRC1,VRC2,R0], then describe lithium battery with time-varying internal resistance and
The state equation of the new model of hysteresis is：
V (t+1)=OCVav(t)+VH(t)+I(t)R0(t)+VRC1(t)+VRC2(t)+v(t) (9)
Wherein, w (t) and v (t) represent state and observation noise respectively.
4. the combined simulation appraisal procedure of lithium battery health according to claim 3 and state-of-charge, which is characterized in that step
Suddenly the idiographic flow of (3) is：
Battery current capacities CnReflect the health status SOH of battery, the SOH defined from battery capacity angle is as follows：
Wherein, CnowAfter representing cell degradation, in the case of fully charged, maximum electricity that present battery can release；CnewTable
Show new battery in the case of fully charged, the maximum electricity that can be released；
SOH is defined as follows from internal resistance angle：
Wherein, R0,EOLInternal resistance when representing cell degradation to end-of-life status；
With cell degradation, battery capacity CnWith internal resistance R0It will change；In the state equation of formula (8), R0Variation
Through being characterized with walk random equation, update capacity C is given belownMethod；
Battery capacity decays between the internal resistance of cell, and there are following linear relationships：
Cfnow(%)=kR0,now+b (12)
Wherein, Cfnow(%) represents that present battery maximum can release the percentage of electricity attenuation, i.e.,：
Formula (12) is substituted into formula (11) to obtain：
Wherein, C is allowednew-Cnew(kR0,EOL+ b)=CEOLMaximum can release electricity when reaching end-of-life status for battery, represent then
Have：
And capacity and internal resistance are all given values when battery initial capacity and internal resistance and end-of-life, then are acquired more by formula (15)
New capacity：
Enable R in formula (8)0(t)=R0,now, then have：
In formulaRepresent definition, by modular form (8), (9) and (17) just can be according to the use state of battery come simulated battery.
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