CN106443471A - System on chip (SOC) estimation method for lithium ion battery and hardware implementation of estimation method - Google Patents
System on chip (SOC) estimation method for lithium ion battery and hardware implementation of estimation method Download PDFInfo
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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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- 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]
- G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
Abstract
The invention discloses a system on chip (SOC) estimation method for a lithium ion battery. The method comprises the following steps: 1, performing SOC real-time update; 2, introducing a dynamic variable; 3, identifying parameters in a battery circuit model; 4, realizing SOC estimation of the lithium ion battery by using an unscented Kalman filter algorithm according to the identified model parameters; 5, implementing the SOC estimation algorithm of the lithium ion battery based on the unscented Kalman filter. The method disclosed by the invention has the following advantages: (1), an improved second order RC equivalent circuit considers the rate capacity effect and recovery effect of the lithium ion battery compared with other circuit models, and compared with the traditional second order equivalent circuit, the dynamic and static characteristics of the battery are well simulated; (2), compared with the other algorithms, the unscented Kalman filter algorithm is low in initial value dependence, accurate in prediction and capable of well solving the nonlinear problem; (3), by utilizing the characteristics of flexibility and convenience of Xilinx FPGA development, the SOC estimation algorithm of the lithium ion battery is implemented on a hardware platform, so that the algorithm is not only theoretical, but also can be applied to portable equipment.
Description
Technical field
The present invention relates to a kind of lithium ion battery SOC (system level chip) method of estimation and its hardware are realized.Particularly to
A kind of foundation of improved Order RC equivalent-circuit model, the relevant parameter no mark card being picked out based on the circuit model set up
Kalman Filtering algorithm (UKF) carries out to the SOC of battery estimating and finally uses verilog in ISE Foundation development platform
Hardware description language realizes UKF algorithm, and is emulated with modelsim software.
Background technology
In terms of lithium ion battery modeling, document Battery Comparison Chart proposes as shown in Figure 1 within 2012
Order RC equivalent-circuit model, model can regard two parts as, and the left side comprises the current source of resistance, electric capacity and current control,
For predicting continued to run with time and the SOC of battery, wherein CcapacityRepresent the electricity of battery storage, electric current source-representation pair
CcapacityDischarge and recharge, RselfFor self discharge resistance.The right is the RC network of second order, for the transient response of simulated battery, electricity
Each element also variable in road, can be continually changing according to the change of the temperature, cell degradation and SOC of environment.
This model existing defects, it does not account for battery rate capability effect (Rate Capacity Effect) and extensive
Multiple effect (Recovery Effect).So-called battery rate capability effect refers to the extra electricity that battery loses in electric discharge, that is,
Can not power consumption, increase and can not power consumption can increase therewith with discharge time, the capacity losing when battery is unloaded will be extensive
Multiple, and electricity recovers to be exactly the recovery Effects of battery.Based on these considerations, propose a kind of on the basis of Order RC equivalent circuit
Improved Order RC equivalent circuit, in order to more accurately predict the real-time SOC of battery and the time of sustainable work in this model,
Introduce the concept of dynamic electricity, can simulated battery well static and dynamic performance.
In terms of estimation battery SOC algorithm, it can be found that the estimation SOC of early stage mainly has following several method：Ampere-hour method,
Road voltage method, internal resistance method, zero load voltage method, electrochemical principle analytic approach etc..But all there is the accumulation of error, standard in these algorithms
Exactness is low, protected from environmental big, the problems such as gain of parameter is complicated.In view of these problems, Unscented kalman is adopted to filter here
Ripple (UKF) algorithm is estimated to lithium ion battery SOC.With respect to other prediction algorithms, Kalman filtering method has and shows as follows
The advantage writing：First, in the case of original state is uncertain, algorithm can rapidly converge to actual value；2nd, algorithm not only may be used
The bouds on error of output variable to estimate the value of SOC, can also be evaluated, can more intuitively know the accurate of prediction
Degree, for preventing from battery from overcharging and cross being placed with more preferable effect；3rd, algorithm is no matter under constant current charge-discharge environment, or
Under the working environment of electric current acute variation, accurately predicted value can be obtained.Simultaneously for solution nonlinear problem aspect,
Unscented kalman filtering (UKF) does not need linearization approximate, but is solved by Unscented transform (UnscentedTransform, UT)
Certainly nonlinear problem.
Content of the invention
Purpose：The purpose of the present invention is to propose to a kind of method of estimation of lithium ion battery SOC and its hardware are realized.There is spy
Levy that distinctness, construction be directly perceived, explicit physical meaning, each parameter convenient identify and consider battery rate capability effect and recovery Effects this
One important factor in order, it is easy to the advantages of realize in engineering.
Technical scheme：
It is as shown in Figure 2 that the present invention proposes a kind of improved Order RC equivalent-circuit model.It is made up of two parts, and the right is
Conventional Order RC circuit model, for the current-voltage characteristic of simulated battery, wherein VocFor the electromotive force of battery, in same temperature
The lower SOC with battery of degree has certain functional relation, R0It is the ohmic internal resistance of battery, RsAnd RLFor the polarization cell of battery, CSWith
CLFor the polarization capacity of battery, RsAnd CSThe parallel circuit time constant of composition is less, electric in current break for simulated battery
Press fast-changing process, RLAnd CLTime constant larger, for the process that analog voltage is slowly stable.The module on the left side is
Renewal for battery SOC and the prediction of run time, because the exportable capacity of the reality of battery is relevant with Multiple factors, simultaneously
There are recovery Effects in view of battery, thus be necessary the input according to Multiple factors, calculate the SOC of battery in real time.SOCinit
Represent battery initial SOC, IbatFor real-time load current, T is environment temperature, and N uses cycle-index for battery.
A kind of present invention lithium ion battery SOC (system level chip) method of estimation, specifically includes following steps：
Step one：SOC real-time update, concrete grammar is as follows：
The present invention passes through fitting formula f (x)=ae-bx+c1x3+c2x2+c3x+c4To enter with the function relation figure of OCV and SOC
Row data matching, tries to achieve the functional relation of SOC and OCV.
Step 2：Introduce dynamic variable
In order to preferably describe battery rate capability effect and recovery Effects, introduce C hereindynamic, for representing because again
The overhead provision loss that rate capacity effect causes.C can be obtained by derivingdynamicClose during discharging and during standing respectively
Expression formula in time t.Then by multiple constant-current discharge experiment is carried out to battery, determine the parameter beta in expression formula.β determines
Afterwards, can be according to CdynamicElectric discharge and standing expression formula draw the electric discharge of dynamic electricity and stand curve.Corresponding to curve negotiating
Fitting formula carries out data matching, can try to achieve the dynamic voltameter after abbreviation and reach formula.Finally according to the matching knot in the case of constant current
The dynamic voltameter of battery that fruit is tried to achieve under time-dependent current reaches formula.
Step 3：Parameter identification in battery circuit model
Order RC equivalent-circuit model according to Fig. 1, in its right half part circuit, current-voltage correlation is
Vbat=Voc(SOC)-i(t)R0-Vs-Vl(1)
Battery during discharging, polarization capacity CSAnd CLIt is in charged state, the voltage of RC parallel circuit exponentially rises,
Battery from discharge condition enter standing after, electric capacity CSAnd CLRespectively to respective conductive discharge in parallel, voltage exponentially declines.Formula
Middle τs=RSCS, τs=RLCL, it is the time constant of two RC parallel circuits.Resistance in model and electric capacity are not constants, it
All relevant with the SOC of battery, need in different SOC pass through test, the voltage response curves of acquirement, then utilize minimum
Square law carries out curve fitting, and obtains the occurrence of each element in circuit.Using the method for data matching, tried to achieve according to experiment
Data, can get following fitting result (unit of resistance is m Ω, and unit of capacity is F)：
R0(SOC)=154.7e-33.8SOC+29.1 (4)
Rs(SOC)=6037000e-74.99SOC+809.1 (5)
RL(SOC)=388900e-35.02SOC+771.9 (6)
CS(SOC)=- 135200e93.83SOC+36.29 (7)
CL(SOC)=- 2214e-13.24SOC+693.6 (8)
Step 4：According to the model parameter picking out, realize lithium ion battery SOC estimation with Unscented kalman filtering algorithm
Step 5：Lithium ion battery SOC estimating algorithm based on Unscented kalman filtering is realized on hardware.
Advantage and effect：The present invention compared with prior art, has following obvious advantage and high-lighting effect：
1. fuel cell modelling aspect, improved Order RC equivalent circuit considers lithium ion battery compared to other circuit models
Rate capability effect and recovery Effects.Compared with traditional second order equivalent circuit, the sound state being capable of preferably simulated battery is special
Property.
2. estimate lithium ion battery SOC algorithm aspect, Unscented kalman filtering algorithm is compared and other algorithms, to initial
Value dependency degree is low, and prediction is more accurate, and can solve nonlinear problem.
3. utilize the flexible feature of Xilinx FPGA exploitation, lithium ion battery SOC algorithm will be estimated in hardware platform
Upper realization, so that this algorithm is merely not only theoretical, applies also for portable set.
Brief description
Fig. 1 is second order equivalent-circuit model.
Fig. 2 is improved second order equivalent-circuit model.
Fig. 3 is SOC and OCV matched curve.
Fig. 4 is with dynamic electricity C during 1A electric current constant-current dischargedynamicThe time graph of (t).
Fig. 5 is dynamic electricity C during standingdynamicThe time graph of (t).
Fig. 6 is to carry out periodic discharging experiment to lithium ion battery, and top half is discharge current, and the latter half is battery
Output voltage curve.
Fig. 7 is the voltage change when current vanishes after during periodic discharging.It is due to battery that V0 to V1 voltage rapidly rises
The pressure drop disappearance that ohmic internal resistance produces causes, and the voltage change in V1 to V2 stage is to be disappeared by the polarization of battery to cause.
Fig. 8 removes the part of V0 to V1 for Fig. 7.
Fig. 9 is ohmic internal resistance R0Measured value and SOC graph of a relation.
Figure 10 is polarization resistance RSMeasured value with SOC graph of a relation.
Figure 11 is polarization resistance RLMeasured value with SOC graph of a relation.
Figure 12 is polarization capacity CSMeasured value and SOC graph of a relation.
Figure 13 is polarization capacity CLMeasured value and SOC graph of a relation.
Figure 14 is the contrast that improved Order RC equivalent-circuit model surveys voltage under 1A electric current constant-current discharge with battery
Figure.
Figure 15 is the contrast that improved Order RC equivalent-circuit model surveys voltage under the electric discharge of cycle time-dependent current with battery
Figure.
Figure 16 is that improved Order RC equivalent-circuit model surveys the right of voltage with battery under quick variable-current is discharged
Than figure.
Figure 17 is the SOC estimated value being obtained with UKF, EKF algorithm under 1A constant-current discharge and the contrast of battery actual soc-value
Figure.
Figure 18 is the SOC estimated value and battery actual soc-value pair being obtained with UKF, EKF algorithm under the electric discharge of cycle time-dependent current
Than figure.
Figure 19 is the SOC estimated value and battery actual soc-value pair being obtained with UKF, EKF algorithm under the electric discharge of quick time-dependent current
Than figure.
Figure 20 is exponential function exp (x) discretization.
Figure 21 is hardware identification code flow chart.
Figure 22 is to carry out emulating the simulation result figure obtaining under cycle time-dependent current discharge scenario with modelsim software.
Figure 23 is the comparison diagram of the SOC estimated value of FPGA output and battery actual soc-value under the electric discharge of cycle time-dependent current.
Figure 24 is the flow chart of the inventive method.
Specific embodiment
Below in conjunction with the accompanying drawings, technical scheme is described further.
A kind of method of estimation of present invention lithium ion battery SOC and its hardware are realized, and as shown in figure 24, specifically include as follows
Step：
Step one：SOC real-time update, concrete grammar is as follows：
The relation curve of OCV (Open Circuit Voltage, open-circuit voltage) and SOC, is that in model, two parts connect
Bridge together, and it is necessary to the function using battery OCV and SOC closes in the prediction of the parameter identification in model and SOC
System.Adopt fitting formula f (x)=ae herein-bx+c1x3+c2x2+c3x+c4Carry out the functional relation of matching OCV and SOC.Fig. 3 is to survey
The curve that the magnitude of voltage measuring and matching obtain.Table 1 is the fitting parameter tried to achieve.
| a | b | c1 | c2 | c3 | c4 |
| -0.031611 | 1.81 | 0.2656 | 0.0931 | 0.1686 | 3.82 |
The parameter value that table 1 matching obtains
Then the SOC and OCV functional relation of battery is：
Voc(SOC)=- 0.3161e-1.81soc+0.2656SOC3+0.0931SOC2+0.1686SOC+3.82 (9)
Step 2：Introduce dynamic variable
(1) in order to preferably describe battery rate capability effect and recovery Effects, introduce C hereindynamic, for representing
Because the overhead provision that rate capability effect causes loses.Consider the temperature of environment, after these factors of cell degradation, obtain battery
The computing formula of SOC be:
Wherein CcapThe maximum electricity that battery can store under a certain fixed temperature, i.e. the actual capacity of battery, i (t)
It is the real-time current of battery, CdynamicT () is the extra electricity that battery loses in electric discharge.
(2) analytic modell analytical model based on diffusion theory being proposed according to Rakhmatov et al., sets up improved second order equivalent
Circuit model, according to Faraday's law and Fick's law, calculates the concentration of active material on battery two electrode, thus predicting battery
Life-span, by being derived by
β represents the speed being compensated in electrode surface activity carrier, and for weighing battery discharge ability, β is bigger, battery
The electricity released under high current is more.t0To tdPeriod is discharged with electric current I, C in discharge processdynamicT () is gradually increased,
I.e. the part electricity in battery be converted into unavailable, then in tdTo trPeriod, battery stops electric discharge, CdynamicT () gradually subtracts
Few, battery can not be converted into available by power consumption, the available power of battery increases.
(3) if wanting to draw dynamic electric quantity curve when discharging and standing, identified parameters β are needed.
The identification process of β is：
The first step：Battery is carried out with multiple constant-current discharge, remembers that the electric current of each constant-current discharge is { I1,I2,…,In, with
When record each time { L used that discharges1, L2,…,Ln}.According to battery exportable maximum electricity C and electric current Ik, the time
LkRelational expression (33)
I.e. the dynamic electricity in the discharge off moment for the battery is
Second step：Cause battery life when discharge current is not very big especially in short-term, β2LkMore than 1, before can only taking
Approximate calculation is carried out in 5, face, and therefore formula (34) can be reduced to
3rd step：According to the experimental data of n time, using least square method, the then occurrence tried to achieve, i.e. β=0.075.Table 2
List the dynamic electricity that battery is tried to achieve after different discharge current electric discharges.
Dynamic electricity under each discharge-rate of table 2
(4) after β determines, during electric discharge, ifC then can be obtaineddynamic(t)=2Ifd(t).Using
Fitting formula fd(t)=a (1-e-bt)+c(1-e-dt) and bent with corona discharge dynamic during 1A electric current constant-current discharge according to Fig. 4
Line, matching can try to achieve battery dynamic electricity in electric discharge and changes over relation and be
Cdynamic(t)=2Ifd(t)=2I [199.8 (1-e-0.006215t)+91.43(1-e-0.08932t)] (15)
In the same manner, take fitting formula f during standingr(t)=a (e-bt)+c(e-dt), and dynamic electricity according to Fig. 5
Standing curve, can matching obtain battery standing when dynamic electricity change over relation
Cdynamic(t)=Cdynamic(td)fr(t)=Cdynamic(td)(0.2825e-0.05649t+0.66e-0.005896t) (16)
Dynamic electricity after therefore can be simplified, that is,
(5) according to the fitting result in the case of constant current, trying to achieve the dynamic electricity of battery under time-dependent current is
Cdynamic(tk+1)=Cdynamic(tk)fr(tk+1-tk)+2Ikfd(tk+1-tk) (18)
Step 3：Parameter identification in battery circuit model, detailed process is as follows：
(1) we carry out discharge test as shown in Figure 6 to battery, battery first with constant current discharge, battery
When SOC often reduces 10%, the discharge loop of cut-out battery, allow battery standing for a period of time, after the voltage stabilization of battery
Continue electric discharge.General trend is continuous decline to the voltage of battery in the process, but after discharge current is removed, voltage can be gradually
Rise and be finally stable at a certain magnitude of voltage.
(2) Fig. 7 is the voltage change curve that upper figure battery SOC is after removing electric current when 0.875, from the figure, it can be seen that
It it was zero moment in current break, cell voltage rises rapidly, this is to cause because the pressure drop that the ohmic internal resistance of battery produces disappears
, thus can obtain
(3) Fig. 8 be Fig. 7 remove V0 to V1 partly after curve, this portion voltage change be by battery polarization disappearance draw
Rise, in the process, the voltage output equation of battery is
(4) equation is entered row coefficient to replace
Vbat=f-ae-ct-be-dt(21)
Relatively two formulas obtain
Voc=f (22)
RS=a/I (23)
RL=b/I (24)
Cs=1/ (RSc) (25)
CL=1/ (RLc) (26)
Carry out multiple periodic discharging under different discharge-rates, SOC often declines 10%, carry out a secondary data matching,
Although the result of identification is variant under different experiments, occurrence is more or less the same, and tests the results change obtaining every time and become
Gesture is identical.Table 3 is the result picking out in 1A discharge current discharge test, chooses identification result now to set up electricity in literary composition
The model in pond.
(5) in order to can more intuitively between comparative cell SOC and each parameter of circuit relation, Fig. 9 to Figure 13 depicts
Graph of a relation between them.
| SOC | R0(mΩ) | Rs(mΩ) | Cs(F) | Rl(mΩ) | Cl(F) |
| 0.857 | 29.6 | 633.9 | 14.785 | 404.4 | 462.292 |
| 0.807 | 32.3 | 444.8 | 119.904 | 712.4 | 1387.016 |
| 0.758 | 33.6 | 568.7 | 47.18 | 692.88 | 582.426 |
| 0.708 | 32.0 | 501.2 | 54.44 | 1041.6 | 378.126 |
| 0.659 | 30.8 | 454.1 | 39.8 | 1144.2 | 481.263 |
| 0.611 | 27.0 | 580.4 | 12.369 | 718.1 | 59.233 |
| 0.563 | 29.8 | 461.1 | 100.965 | 1715.3 | 2510.717 |
| 0.516 | 30.8 | 1581.7 | 1.0763 | 488.99 | 384.044 |
| 0.468 | 27.7 | 472.7 | 13.836 | 522.0 | 445.617 |
| 0.421 | 29.5 | 2460 | 0.62 | 710.3 | 450.802 |
| 0.374 | 28.2 | 1900 | 0.837 | 839.0 | 608.155 |
| 0.327 | 28.2 | 677.5 | 8.729 | 650.7 | 382.754 |
| 0.280 | 28.2 | 548.4 | 10.21 | 628.0 | 567.281 |
| 0.233 | 30.8 | 567.9 | 21.385 | 971.9 | 620.995 |
| 0.185 | 30.8 | 595.9 | 67.913 | 921.3 | 809.413 |
| 0.138 | 31.1 | 683.2 | 66.866 | 4034 | 194.578 |
| 0.090 | 37.3 | 7898 | 6.681 | 17385.1 | 27.8 |
The fitting result of each parameter of battery under table 3 1A discharge test
(6) method passing through data matching, each parameter tried to achieve according to experiment and the relation curve of SOC and fitting formula
F (SOC)=a*e-b*SOC+c (27)
Can get the fitting result of formula (4) to (8).Figure 14 to Figure 16 is for improved Order RC equivalent-circuit model in perseverance
The comparison diagram of output voltage and virtual voltage in the case of stream, cycle time-dependent current and quick time-dependent current.
Step 4：Realize lithium ion battery SOC estimation with Unscented kalman filtering algorithm, the method step is as follows：
(1) obtain improving the state equation (28) of Order RC equivalent circuit by Fig. 2 and measure equation (29).
The measurement equation of system
Vbat(k)=Voc(SOC)-ikR0(k)-Vs(k)-VL(k) (29)
Wherein TsRepresent the interval of sampling, Vs(k) and VLK () is the voltage on two RC networks at sampling instant k,
CdynamicK () is the dynamic capacity in the k moment.State vector x of wherein systemk, system input stimulus matrix be ukFor
Because state equation and measurement equation are not and xk、ukLinear, in order to utilize extended Kalman filter
Recurrence formula, need first to try to achieve State-Vector Equation and measurement equation to xkLocal derviation Jacobian matrix, by formula (28) and
Formula (29) can be tried to achieve
(2) UT conversion
By state vector xkVariable is tieed up by 2n+1 n of acquisition that formula (33) uses symmetric sampling method：
WhereinRepresent the i-th row of matrix inside bracket；
The weight of each variable corresponding is：
Wherein, λ=α2(n+k)-n (35)
What wm represented is the average weight of sampled point, and what wc represented is the covariance weight using point；α determines sampled point
Degree of closeness and average between, generally take between 0-1 on the occasion of；K is scale factor, generally takes 0, if shape in UT conversion
When state is distributed as Gaussian Profile, k=n-3 can be taken；β generally takes 2 in the case of normal distribution.
(3) it is divided into forecast period and more new stage
1. forecast period：
The predicted value of k+1 moment system state variables is
A in formulak、BkIt is respectively the state-transition matrix of system in k moment tried to achieve in formula (31) and the control of system
Input matrix processed；ukIt is input stimulus；xi(i=1,2 ... 2n) is state vector x of systemk2n+1 n after UT conversion
Dimensional vector；So Ak×xi+Bk×ukPredicted value x for each sampling point k+1 momenti(k+1).
K+1 moment varivance matrix is
2. the more new stage：
Predicted value x according to each sampling point k+1 momenti(k+1) it is brought in the observational equation of system and obtain each
The predicted value of sampling point k moment output variable：
yi(k) '=Ck×xi(k+1) (38)
C thereinkFor the observing matrix mentioned in 5.1.1, it is calculated by formula (32).Thus can get the k+1 moment
The predicted value of output variable
Calculate the variance matrix of k+1 moment input variable value：
Calculate the state variable in k+1 moment and the covariance of output variable:
Calculate Kalman filtering gain:
Kk=Pxy/Pyy(42)
Update state variable value：
X (k+1)=x (k+1) '+Kk×(y(k)-y(k)′) (43)
Varivance matrix updates：
Pk+1=p 'k+1-KkPyyKk T(44)
A so known xkAnd PkInitial value it is possible to realize On-line Estimation to state variable and error matrix.Figure
The lithium ion battery that 17 to Figure 19 obtains in the case of constant current, cycle time-dependent current and quick time-dependent current for EKF algorithm and UKF algorithm
SOC estimated value and the comparison diagram of SOC measured value.
Step 5：A kind of hardware of present invention lithium ion battery SOC (system level chip) method of estimation is realized, and specifically exists
By the lithium ion battery SOC estimating algorithm Verilog based on Unscented kalman filtering in ISE Foundation development platform
Hardware description language is realized, and is then emulated with modelsim software.Its main design thought is divided into three below module：
The calling module of data, exp index computing module, UKF formula computing module in Excel.
(1) in Excel data calling module
Because the battery current required for estimation battery SOC and actual measurement voltage need to read the data in Excel, so
Need in FPGA to preserve these data by ROM, need ROM is designed.
1. generate a ROM under ISE engineering, generated by way of IP kernel.Need to arrange bit wide and the depth of ROM,
Due to the emulation of matlab here is 10001 length data, so depth is set to 10001, then if bit wide, more big more
Accurately, 24 are selected to be to arrange by the precision of decimal in the actual matlab of contrast here.
Then the data that setting ROM calls, is to be preserved with COE document form, design COE file is described below to preserve
Excel data.
2. write .coe file, as the initialization files of ROM.
In ISE, the initialization files of ROM are .coe files, so needing to write the .coe literary composition of battery current and actual measurement voltage
Part.
MEMORY_INITIALIZATION_RADIX=10 in coe file；The data form of expression ROM content is ten
System.Separated with comma or space or newline after each data in file, bonus point after last data
Number.By form above, store data in excel.
3. ROM core is called by verilog sentence.Input signal has clock signal, a reset signal, 14 input address,
Output signal is 24 actual voltage values.
4. a .mif file can be generated after the example completing ROM with Core Generator, this is that Modelsim is carried out
The initialization files needing during ROM emulation, by under .mif file copy to Modelsim engineering, imitate for Modelsim afterwards
Very.
By above-mentioned steps it is possible to complete the design of ROM, by way of address is read and write, read the data in ROM,
Thus realizing calling the function of excel data in matlab.
(2) exp index computing module
State-transition matrix A due to computing system in the matlab program of estimation battery SOCk, system control defeated
Enter matrix Bk, dynamic electricity CdynamicT () has used more exp function, FPGA directly cannot calculate exp, so needing to carry out
Design, mentality of designing needs to refer to the use of ROM here.
If exponential function is exp (x) it is assumed that the span of x is-N arrives positive N, then the result of calculation scope of exp (x)
As follows：Exp (- N) arrives exp (N).In the case of ensureing precision, x is divided into M part by equal intervals, and every part is 2N/M,
That is, the span of x is carried out sliding-model control, obtain several x values as follows.I.e.-M/ (2N), -2M/ (2N), -3M/ (2N), -
Each value of 4M/ (2N), -5M/ (2N) ... corresponds to an address, then after one x of input, carried out by ROM
Address searching, obtains corresponding exp (x), as shown in figure 20.Each is worth corresponding exp result.So pass through look-up table permissible
Quickly calculate corresponding exp value.
(3) UKF formula computing module.
UKF formula computing module is main modular, and that uses in the matlab program relating generally to estimation battery SOC is all
Formula, is translated into Verilog hardware description language.Its code flow diagram is as shown in figure 21.
(4) emulated using modelsim software.
After emulating by modelsim, a txt file data_out.txt can be produced, above-noted emulation knot
Really, system emulation result is as shown in figure 22.Then pass through matlab simulation comparison, obtain comparing result as shown in figure 23, at this
In we only done battery cycle time-dependent current electric discharge emulation.
Claims (5)
1. a kind of lithium ion battery SOC method of estimation, is characterised by：The method specifically includes following steps：
Step one：SOC real-time update
By fitting formula f (x)=ae-bx+c1x3+c2x2+c3x+c4To carry out data plan with the function relation figure of OCV and SOC
Close, try to achieve the functional relation of SOC and OCV；
Step 2：Introduce dynamic variable
In order to preferably describe battery rate capability effect and recovery Effects, introduce Cdynamic, for representing because of rate capability effect
The overhead provision loss causing；C can be obtained by derivingdynamicRespectively with regard to time t's during discharging and during standing
Expression formula；Then by multiple constant-current discharge experiment is carried out to battery, determine the parameter beta in expression formula；After β determines, can basis
CdynamicElectric discharge and standing expression formula draw the electric discharge of dynamic electricity and stand curve；To curve negotiating, corresponding fitting formula enters
Row data matching, can try to achieve the dynamic voltameter after abbreviation and reach formula；Try to achieve power transformation finally according to the fitting result in the case of constant current
The dynamic voltameter of battery flowing down reaches formula；
Step 3：Parameter identification in battery circuit model
According to Order RC equivalent-circuit model, in its right half part circuit, current-voltage correlation is
Vbat=Voc(SOC)-i(t)R0-Vs-Vl(1)
Battery during discharging, polarization capacity CSAnd CLIt is in charged state, the voltage of RC parallel circuit exponentially rises, battery
After discharge condition enters standing, electric capacity CSAnd CLRespectively to respective conductive discharge in parallel, voltage exponentially declines；τ in formulas
=RSCS, τs=RLCL, it is the time constant of two RC parallel circuits；Resistance in model and electric capacity are not constants, and they are all
Relevant with the SOC of battery, need to pass through test, the voltage response curves of acquirement in different SOC, then utilize least square
Method carries out curve fitting, and obtains the occurrence of each element in circuit；Using the method for data matching, the number tried to achieve according to experiment
According to can get following fitting result (unit of resistance is m Ω, and unit of capacity is F)：
R0(SOC)=154.7e-33.8SOC+29.1 (4)
Rs(SOC)=6037000e-74.99SOC+809.1 (5)
RL(SOC)=388900e-35.02SOC+771.9 (6)
CS(SOC)=- 135200e93.83SOC+36.29 (7)
CL(SOC)=- 2214e-13.24SOC+693.6 (8)
Step 4：According to the model parameter picking out, realize lithium ion battery SOC estimation with Unscented kalman filtering algorithm；
Step 5：Lithium ion battery SOC estimating algorithm based on Unscented kalman filtering is realized on hardware.
2. a kind of lithium ion battery SOC method of estimation according to claim 1 it is characterised in that：Described step 2 is concrete
Process is as follows：
(1) introduce Cdynamic, for representing the overhead provision loss causing because of rate capability effect；Consider environment temperature,
After these factors of cell degradation, the computing formula obtaining the SOC of battery is:
Wherein CcapThe maximum electricity that battery can store under a certain fixed temperature, i.e. the actual capacity of battery, i (t) is electricity
The real-time current in pond, CdynamicT () is the extra electricity that battery loses in electric discharge；
(2) set up improved second order equivalent-circuit model, according to Faraday's law and Fick's law, calculate on battery two electrode
The concentration of active material, thus predict the life-span of battery, by being derived by
β represents the speed being compensated in electrode surface activity carrier, and for weighing battery discharge ability, β is bigger, and battery is big
The electricity released under electric current is more；t0To tdPeriod is discharged with electric current I, C in discharge processdynamicT () is gradually increased, i.e. electricity
Part electricity in pond is converted into unavailable, then in tdTo trPeriod, battery stops electric discharge, CdynamicT () gradually decreases, electricity
Pond can not be converted into available by power consumption, the available power of battery increases；
(3) if wanting to draw dynamic electric quantity curve when discharging and standing, identified parameters β are needed；
(4) after β determines, during electric discharge, ifC then can be obtaineddynamic(t)=2Ifd(t)；Using matching
Formula fd(t)=a (1-e-bt)+c(1-e-dt) and according to dynamic electricity discharge curve during 1A electric current constant-current discharge, can matching ask
Battery dynamic electricity in electric discharge changes over relation and is
Cdynamic(t)=2Ifd(t)=2I [199.8 (1-e-0.006215t)+91.43(1-e-0.08932t)] (15)
In the same manner, take fitting formula f during standingr(t)=a (e-bt)+c(e-dt), and curve is stood according to dynamic electricity, can
Matching obtains battery dynamic electricity in standing and changes over relation
Cdynamic(t)=Cdynamic(td)fr(t)=Cdynamic(td)(0.2825e-0.05649t+0.66e-0.005896t) (16)
Dynamic electricity after therefore can be simplified, that is,
(5) according to the fitting result in the case of constant current, trying to achieve the dynamic electricity of battery under time-dependent current is
Cdynamic(tk+1)=Cdynamic(tk)fr(tk+1-tk)+2Ikfd(tk+1-tk) (18) .
3. according to claim 2 a kind of lithium ion battery SOC method of estimation it is characterised in that：The mistake of wherein identified parameters β
Cheng Wei：
The first step：Battery is carried out with multiple constant-current discharge, remembers that the electric current of each constant-current discharge is { I1,I2,…,In, remember simultaneously
Lower time { the L used that discharges every time of record1, L2,…,Ln}；According to battery exportable maximum electricity C and electric current Ik, time Lk's
Relational expression (33)
I.e. the dynamic electricity in the discharge off moment for the battery is
Second step：Cause battery life when discharge current is not very big especially in short-term, β2LkMore than 1, can only take above 5
Item carrys out approximate calculation, and therefore formula (34) can be reduced to
3rd step：According to the experimental data of n time, using least square method, the then occurrence tried to achieve, i.e. β=0.075.
4. a kind of lithium ion battery SOC method of estimation according to claim 1 it is characterised in that：Described step 4 is concrete
As follows：
(1) obtain state equation (28) and measurement equation (29) improving Order RC equivalent circuit：
The measurement equation of system
Vbat(k)=Voc(SOC)-ikR0(k)-Vs(k)-VL(k) (29)
Wherein TsRepresent the interval of sampling, Vs(k) and VLK () is the voltage on two RC networks at sampling instant k, Cdynamic
K () is the dynamic capacity in the k moment；State vector x of wherein systemk, system input stimulus matrix be ukFor
Because state equation and measurement equation are not and xk、ukLinear, for passing using extended Kalman filter
Apply-official formula, needs first to try to achieve State-Vector Equation and measurement equation to xkLocal derviation Jacobian matrix, by formula (28) and formula
(29) can try to achieve
(2) UT conversion
By state vector xkVariable is tieed up by 2n+1 n of acquisition that formula (33) uses symmetric sampling method：
WhereinRepresent the i-th row of matrix inside bracket；
The weight of each variable corresponding is：
Wherein, λ=α2(n+k)-n (35)
What wm represented is the average weight of sampled point, and what wc represented is the covariance weight using point；α determine sampled point with all
Degree of closeness between value, generally take between 0-1 on the occasion of；K is scale factor, generally takes 0, if state is divided in UT conversion
When cloth is Gaussian Profile, k=n-3 can be taken；β generally takes 2 in the case of normal distribution；
(3) it is divided into forecast period and more new stage
1. forecast period：
The predicted value of k+1 moment system state variables is
A in formulak、BkIt is respectively the state-transition matrix of the system in k moment tried to achieve in formula (31) and the control of system is defeated
Enter matrix；ukIt is input stimulus；xi(i=1,2 ... 2n) is state vector x of systemkThrough UT conversion after 2n+1 n tie up to
Amount；So Ak×xi+Bk×ukPredicted value x for each sampling point k+1 momenti(k+1)；
K+1 moment varivance matrix is
2. the more new stage：
Predicted value x according to each sampling point k+1 momenti(k+1) it is brought in the observational equation of system and obtain each sampling point k
The predicted value of moment output variable：
yi(k) '=Ck×xi(k+1) (38)
C thereinkFor the observing matrix mentioned in 5.1.1, it is calculated by formula (32)；Thus can get the k+1 moment exports change
The predicted value of amount
Calculate the variance matrix of k+1 moment input variable value：
Calculate the state variable in k+1 moment and the covariance of output variable:
Calculate Kalman filtering gain:
Kk=Pxy/Pyy(42)
Update state variable value：
X (k+1)=x (k+1) '+Kk×(y(k)-y(k)′) (43)
Varivance matrix updates：
Pk+1=p 'k+1-KkPyyKk T(44)
A so known xkAnd PkInitial value it is possible to realize On-line Estimation to state variable and error matrix.
5. a kind of hardware of lithium ion battery SOC method of estimation according to claim 1 is realized, specifically in ISE
By the lithium ion battery SOC estimating algorithm Verilog hardware based on Unscented kalman filtering in Foundation development platform
Description language is realized, and is then emulated with modelsim software；Its main design thought is divided into three below module：Excel
The calling module of middle data, exp index computing module, UKF formula computing module；
(1) in Excel data calling module
Because the battery current required for estimation battery SOC and actual measurement voltage need to read the data in Excel, so in FPGA
In need to preserve these data by ROM, need ROM is designed：
1. generate a ROM under ISE engineering, generated by way of IP kernel；Need to arrange bit wide and the depth of ROM, depth
It is set to 10001；Bit wide is more big more accurate, selects 24 to be to arrange by the precision of decimal in the actual matlab of contrast here
's；
Then the data that setting ROM calls, is to be preserved with COE document form；
2. write .coe file, as the initialization files of ROM；
In ISE, the initialization files of ROM are .coe files, so needing to write the .coe file of battery current and actual measurement voltage；
MEMORY_INITIALIZATION_RADIX=10 in coe file；The data form of expression ROM content is the decimal system
's；Separated with comma or space or newline after each data in file, last data is followed by branch；Logical
Cross form above, store data in excel；
3. ROM core is called by verilog sentence；Input signal has clock signal, reset signal, 14 input address, output
Signal is 24 actual voltage values；
4. a .mif file can be generated after the example completing ROM with Core Generator, this be Modelsim carry out ROM imitate
The initialization files that true time needs, by under .mif file copy to Modelsim engineering, emulate for Modelsim afterwards；
By above-mentioned steps it is possible to complete the design of ROM, by way of address is read and write, read the data in ROM, thus
Realize in matlab, calling the function of excel data；
(2) exp index computing module
State-transition matrix A due to computing system in the matlab program of estimation battery SOCk, the control input matrix of system
Bk, dynamic electricity CdynamicT () has used more exp function, FPGA directly cannot calculate exp, so needing to be designed,
Here mentality of designing needs to refer to the use of ROM；
If exponential function is exp (x) it is assumed that the span of x is-N arrives positive N, then the result of calculation scope of exp (x) is as follows
Shown：Exp (- N) arrives exp (N)；In the case of ensureing precision, x is divided at equal intervals M part, every part is 2N/M, i.e. by x's
Span carries out sliding-model control, obtains several x values as follows；I.e.-M/ (2N), -2M/ (2N), -3M/ (2N), -4M/ (2N), -
Each value of 5M/ (2N) ... corresponds to an address, then after one x of input, carry out address searching by ROM,
Obtain corresponding exp (x)；Each is worth corresponding exp result；So corresponding exp value can quickly be calculated by look-up table；
(3) UKF formula computing module
UKF formula computing module relates generally to estimate all formula used in the matlab program of battery SOC, is translated into
Verilog hardware description language；
(4) emulated using modelsim software
After emulating by modelsim, a txt file data_out.txt can be produced, above-noted simulation result,
Then pass through matlab simulation comparison, obtain comparing result.
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