CN106405433A - Extended Kalman particle filtering based SOC (State Of Charge) estimation method and system - Google Patents
Extended Kalman particle filtering based SOC (State Of Charge) estimation method and system Download PDFInfo
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Abstract
The invention relates to an extended Kalman particle filtering based SOC (State Of Charge) estimation method and system. The method comprises the steps of performing a discharging-standing test on a battery through a single battery test system so as to acquire an SOC-OCV (Open Circuit Voltage) function relational expression; building an equivalent circuit model of the battery; generating a particle set according to initial probability distribution; performing online parameter identification on the model according to the current data; and performing extended Kalman particle filtering on the particles by using the updated model; and updating a particle weight, and judging whether resampling is required or not according to the number of effective particles. In allusion to problems of low estimation accuracy, existence of an accumulative error, high requirements for model precision and the like of an existing SOC estimation method, the invention adopts the method for online model parameter identification to improve the model precision and adopts the method of combining Kalman filtering and particle filtering to improve the SOC estimation accuracy. The method provided by the invention can effectively estimate the SOC and suppress noises, has the advantage of high precision, and can be applied to the field of a battery management system.
Description
Technical field
The present invention relates to electric automobile power battery management system field, especially one kind are based on the filter of spreading kalman particle
The SOC method of estimation of ripple and system.
Background technology
After oil crisis outburst, energy problem and environmental problem are progressively taken seriously, the urgent need of people
New-energy automobile is wanted therefore to obtain concern solving these problems, electric automobile.Electrokinetic cell is as the power of electric automobile
Source, undertakes all or part of power output of electric automobile.Batteries of electric automobile group is in the course of the work often because of the discharge and recharge time
Long and produce overcharge, overdischarge phenomenon, not only have impact on the serviceability of battery, and shorten the use longevity of battery
Life, reduces car load cost performance.State-of-charge SOC (State Of Charge) the i.e. electrokinetic cell dump energy of electrokinetic cell,
It is one of important parameter of description battery status.The SOC of battery directly cannot be recorded using sensor, and it must be by some
The measurement of other physical quantitys simultaneously to be estimated to obtain using certain mathematical model and algorithm.Battery SOC is subject to ambient temperature, work electricity
The impact of the many factors such as stream and cycle-index, has very strong nonlinear characteristic so that accurately estimating that SOC difficulty is very big,
The estimation of SOC also becomes the focus of Chinese scholars research.
SOC method of estimation main both at home and abroad at present is divided into offline estimation and On-line Estimation two big class.The offline estimation of SOC
Have that estimated accuracy is high a little, be usually used in determining the initial value of SOC, mainly have open circuit voltage method and internal resistance method etc..In reality
In engineer applied, SOC On-line Estimation method is more practical, mainly includes ampere-hour integration method, neural network and Kalman at present
Filter method etc..Ampere-hour integration law theory is simple and amount of calculation is little, but does not have the effect of feedback modifiers, has cumulative error and produces
Raw；Neural network is applied to the system to nonlinearity and is simulated, however it is necessary that setting up accurate neural network model
And need mass data to train；Kalman filtering method can reduce the storage of data volume, but the requirement to model accuracy is very
High.
Above removing ampere-hour integration method, additive method is required for according to model feedback, SOC value being modified, for mould
The having high demands of type precision, and electrokinetic cell generally has the characteristics that nonlinearity, the model of preset parameter obviously can not meet
The requirement of high precision.
Content of the invention
It is an object of the invention to：A kind of SOC method of estimation based on spreading kalman particle filter and system are provided, with
Improve the precision that the precision of battery model and SOC estimate.
The present invention solves its technical problem and is adopted the technical scheme that：A kind of based on spreading kalman particle filter
SOC method of estimation, including step：
Step 1, tests to battery, battery is carried out discharging-standing experiment by cell test system, obtains
State-of-charge and the corresponding data of open-circuit voltage (Open circuit voltage, OCV), simulate the relation letter of SOC-OCV
Number expression formula；
Step 2, sets up the equivalent-circuit model of electrokinetic cell, and obtains separate manufacturing firms model；
Step 3, according to initial probability distribution, produces initial SOC particle collection and arranges weights；
Step 4, according to current data, carries out on-line identification, more new model to model parameter；
Step 5, using spreading kalman particle filter, obtains the predictive value of particle；
Step 6, more new particle weights are simultaneously normalized, and calculate number of effective particles.If number of effective particles is less than
Given threshold value, exports SOC estimation after carrying out resampling；If greater than given threshold value, then directly export SOC estimation；
Step 7, repeat step 4 arrives step 6.
Wherein, in step 4, model parameter is recognized, concrete grammar is as follows：
For model For data vector, θ is parameter vector to be estimated, and y (k) is output
Vector, ε (k) is system noise, can carry out parameter identification using forgetting factor least squares algorithm to θ, its formula is：
Method of least square gain calculates：
Method of least square covariance matrix calculates：
Method of least square optimal estimation of parameters：
WhereinEstimated value for k moment parameter to be estimated；K (k) is the gain matrix in k moment；P (k) is the association in k moment
Variance matrix, generally its initial value P (0) take sufficiently large unit matrix, and value is 10 here5× I, wherein I are unit matrix；
λ is weighter factor (0 ＜ λ≤1), and between 0.9～1.0, value is 0.98 to general value here.
Wherein, in step 5, using spreading kalman particle filter, obtain the predictive value of particle, concrete grammar is as follows：
It is x for system state equationk+1=Akxk+Bkuk+wk, systematic observation equation is yk=Ckxk+Dkuk+vkSystem,
Each particle can be predicted revise using EKF method, recurrence formula is as follows：
State variable priori estimates calculate：
The covariance matrix of forecast error calculates：
Kalman gain matrix calculates：
State variable optimal estimation value calculates：
Update error co-variance matrix：
Wherein, '-' represent priori value, '+' represent posterior value, ' ' represents estimated value.
Wherein xkFor state vector；ukFor input stimulus；ykFor observation vector；AkFor state-transition matrix；BkSwash for input
Encourage matrix；CkFor state vector observing matrix；DkFor input stimulus observing matrix；wkFor process noise；vkFor observation noise；I is
Unit matrix；Q is process noise covariance matrix；R is observation noise covariance matrix；KgkFor kalman gain matrix；PkFor
The covariance matrix of forecast error.
Wherein, specifically adopt formula in described step 6Carry out more new particle weights, adopt
Use formulaCalculate number of effective particles, contrast number of effective particles and particle threshold set in advance,
Judge whether to need to carry out resampling according to result.
Wherein parWageiWeights for i-th particle；ykObservation vector for particle；Prediction for i-th particle
Value；R is observation noise covariance matrix；NeffFor effective particle number.
A kind of system based on spreading kalman particle filter, including electrokinetic cell, cell test system, computer
Deng three parts.
Wherein, cell test system, is made up of four parts, is that current control module, calorstat, data are adopted respectively
Collection equipment and D.C. regulated power supply.Current control module is connected with the input of the cell in calorstat, current control mould
Tuber realizes the control to cell charging and discharging currents size according to extraneous instruction, can simulate different battery testing operating modes,
Calorstat controls the operating ambient temperature of cell according to extraneous instruction.Cell in calorstat and data acquisition equipment
Input be connected, data acquisition equipment is acquired to the voltage and current data of cell according to extraneous instruction, and
Simple analog-to-digital conversion process and then output data are carried out to the data collecting.D.C. regulated power supply respectively with current control mould
Block, calorstat data collecting device are connected, and provide the energy for whole test system.
Current control module is by photoelectrical coupler, digital to analog converter, integrated operational amplifier, MOSFET field effect transistor and health
Copper wire resistance is constituted.
Data acquisition equipment includes current acquisition module and voltage acquisition module and analog-to-digital conversion module.
A kind of SOC method of estimation based on spreading kalman particle filter of the present invention and system, have the advantages that：
Using forgetting factor least squares algorithm computation model parameter, and real-time update battery model data, obtain high-precision electricity
Pool model, meets the requirement to model accuracy for traditional SOC method of estimation.EKF is tied with particle filter
Close, improve the estimated accuracy to state-of-charge (SOC), using the method for resampling, solve the particle of particle filter presence
Degenerate problem.More than summary, the present invention improves the precision that the precision of battery model and SOC estimate.
Brief description
Fig. 1 be the present invention a kind of based on the SOC method of estimation of spreading kalman particle filter and the overall flow figure of system.
Fig. 2 is the structured flowchart of the system based on spreading kalman particle filter for the present invention.
The structured flowchart of the cell test system that Fig. 3 adopts for the present invention.
The principle assumption diagram of current acquisition module in the cell test system that Fig. 4 adopts for the present invention.
The principle assumption diagram of voltage acquisition module in the cell test system that Fig. 5 adopts for the present invention.
Fig. 6 passes through, for the present invention, SOC-OCV curve chart and the curve-fitting results that electric discharge-standing experiment obtains.
The electrokinetic cell Order RC equivalent-circuit model schematic diagram that Fig. 7 adopts for the present invention.
Fig. 8 is used for verifying the measurement condition current curve of SOC estimated accuracy for the present invention.
Fig. 9 is used for verifying measurement condition voltage curve and the battery model matched curve of SOC estimated accuracy for the present invention.
Figure 10 is the comparison diagram with additive method estimated result for the SOC estimated result of the present invention.
Figure 11 is the comparison diagram with additive method estimation difference for the SOC estimation difference of the present invention.
Specific embodiment
Below in conjunction with the accompanying drawings technical scheme is described in detail：
According to Fig. 1, a kind of comprised the following steps based on the SOC method of estimation of spreading kalman particle filter：
Step 1, tests to battery, battery is carried out discharging-standing experiment by cell test system, obtains
State-of-charge and the corresponding data of open-circuit voltage, simulate the relation function expression formula of SOC-OCV；
It is illustrated in figure 2 the entire block diagram of the system based on spreading kalman particle filter, including electrokinetic cell, monomer electricity
The three parts such as pond test system, computer.Need in step 1 using cell test system therein, carry out to lithium from
The electric discharge of son-standing experiment, and then obtain SOC-OCV relation function.
Cell test system, it is possible to achieve to lithium ion battery charge-discharge test, and the voltage data collecting,
Current data, temperature data and other data upload to computer, provide data source for subsequently various algorithms.It is illustrated in figure 3
The detailed structure view of cell test system, whole system is made up of four parts, is current control module, constant temperature respectively
Case, data acquisition equipment and D.C. regulated power supply.Current control module is realized cell is filled according to the extraneous instruction sending
The control of discharge current size, can simulate different battery testing operating modes.Calorstat is used for controlling the building ring of cell
Border temperature.Data acquisition equipment is acquired to the voltage and current data of cell according to the extraneous instruction sending, and
Simple analog-to-digital conversion process and then output data are carried out to the data collecting.D.C. regulated power supply carries for whole test system
For the energy.
The operating mode of current test unit battery, as shown in figure 3, computer sends instructions to current control module, is set,
The electric current charge or discharge that cell sets according to current control module, the end electricity of data collecting module collected battery simultaneously
Pressure and the electric current flowing through battery, the analogue signal collecting, through analog-digital converter, are converted into digital signal and are sent to
Computer, data is stored by computer again with binary form, calculates for SOC filtering afterwards.
The theory diagram of wherein current control module is as shown in figure 4, current control module is by photoelectrical coupler, digital-to-analogue conversion
Device, integrated operational amplifier, MOSFET field effect transistor and constantan wire resistance are constituted.Photoelectrical coupler HCPL0631, for digital-to-analogue
Conversion numeral isolation, it is to avoid the interference between signal.Digital to analog converter MAX531, digital quantity input range [0,4096], change
Become voltage to be [0,2.048V], be transformed into [0A, 20A] electric current through voltage current transformating circuit.MOSFET field effect transistor
IRF540N, cut-in voltage 2.0～4.0V, hourglass source electrode conducting resistance 44m Ω, peak power 50W.Constantan wire resistance is 0.1
Ω, is used for converting voltages into electric current.
Data acquisition equipment includes current acquisition module and voltage acquisition module and analog-to-digital conversion module.Current acquisition mould
The theory diagram of block has, as shown in figure 5, being employed herein, the current mode Hall element CSM015NPT that closed loop compensation acts on,
At room temperature (25 degree), sensor accuracy is ± 0.5%.The primary coil resistance of CSM015NPT is 0.18m Ω, if
When flowing through 10A electric current in signal path, pressure drop is 1.8mv, meets test request.When CSM015NPT primary coil by with ginseng
When examining direction same direction current 15A, its secondary coil output voltage 3.125v；Primary coil flows through 15A electricity reverse with reference direction
During stream, its secondary coil output voltage 1.875v；When primary coil no current flows through, its secondary coil output voltage 2.5v.For
The dynamic range of coupling analog-digital converter, therefore add signal conditioning circuit behind, makes voltage amplitude decay half.This
In the case of, as collected current range [- 15A, 15A], through signal conditioning circuit output voltage be [0.9375v,
1.5625v].
In electric discharge-standing experiment, discharge current is set to by 0.2C by current control module, battery is discharged,
SOC at interval of 5% stops electric discharge and battery is stood, and standing collected battery by voltage acquisition module after 10 minutes
Open-circuit voltage values OCV.By above method, it is possible to obtain the relation database table of open-circuit voltage and SOC, using curve matching
Method, is fitted to the data obtaining, thus obtaining SOC-OCV functional relationship expression formula, the present invention adopts 9 rank multinomials pair
Curve is fitted, and obtained SOC-OCV relation curve and matched curve are as shown in fig. 6, the functional relation obtaining is as follows：
OCV=4.6985e3*SOC9-2.2229e4*SOC8+4.4403e4*SOC7-4.8684e4*SOC6+
3.1913e4*SOC5
-1.2773e4*SOC4+3.061e3*SOC3-413.4218*SOC2+28.2351*SOC-2.9493；
Step 2, sets up the equivalent-circuit model of electrokinetic cell, and obtains separate manufacturing firms model；
The present invention is modeled to electrokinetic cell using equivalent-circuit model, and wherein second order equivalent-circuit model is compared to one
Rank equivalent-circuit model, can more preferable simulated battery non-linear partial, therefore present invention employs second order equivalent circuit mould
Type is modeled to battery, and Fig. 7 is second order equivalent-circuit model schematic diagram, can obtain model terminal voltage output equation by figure
For：
Wherein V represents the terminal voltage of battery, VOCRepresent the open-circuit voltage of battery, the electric current that I representative is flow through from battery, Re
For the ohmic internal resistance of battery, RsAnd RlIt is respectively the polarization resistance of battery, CsAnd ClIt is respectively the polarization capacity of battery, τs=
RsCs, τl=RlClIt is respectively the time constant in two RC loops.
Row write the separate manufacturing firms model of battery model, writ state vector x=[SOC；Vs；Vl], wherein VsAnd VlFor two
Voltage on individual RC parallel network；Electric current I is made to be input stimulus；Terminal voltage V is output, can obtain model
State equation is：
Output equation is：
V (k)=VOC(SOC,k)-Vs(k)-Vl(k)-ReI(k) (3)
Wherein η is coulomb coefficient, and value is 1 here；C is the nominal capacity of battery；T is sampling time interval.
Step 3, according to initial probability distribution, produces initial SOC particle collection and arranges weights；
If particle number is N, the OCV-SOC tables of data being obtained according to electrokinetic cell off-line test, by open circuit voltage method
Table look-up and obtain the initial value SOCInit of SOC, calculate maximum error SOCError of look-up table, according to " 3 σ rule ", make SOC's
N～(SOCInit, (SOCError/3) obeyed by primary collection2) normal distribution, according to this normal distribution produce particle, and
The initial weight making each particle is 1/N；
Step 4, according to current data, carries out on-line identification, more new model to model parameter；
The present invention is identified it is therefore desirable to try to achieve the difference of model using the parameter that forgetting factor least squares algorithm carries out model
Equation.Laplace conversion is carried out to formula (1), obtains：
Arrange formula (4) to obtain：
τsτlVOCs2+(τs+τl)VOCs+VOC=
τsτlReIs2+[(τs+τl)Re+Rsτl+Rlτs]Is+I(Re+Rs+Rl)+τsτlVs2+
(τs+τl)Vs+V (5)
Order：
A=τsτl
B=τs+τl
C=Re+Rs+Rl
D=(τs+τl)Re+Rsτl+Rlτs
Arrange formula (5) to obtain：
aVOCs2+bVOCs+VOC=aReIs2+dIs+cI+aVs2+bVs+V (6)
Make s=[x (k)-x (k-1)]/T, s2=[x2(k)+x2(k-1)-2x(k)x(k-1)]/T
Arrange formula (6), can obtain：
Then have：
Parameter matrix to be estimated
Data vector
Output vector y (k)=VOC(k)-V(k).
Wherein VOCK () can be tried to achieve according to the OCV-SOC functional relation tried to achieve in step 1.
Tried to achieve after estimating parameter vector θ by forgetting factor least squares algorithm, can try to achieve：
Re=k5/k2
Rl=(c τl-Reτl-d-bRe)/(τl-τs)
Rs=c-Re-Rl
Step 5, using EKF, obtains the predictive value of particle；
Kalman filtering to be extended, needs to obtain the separate manufacturing firms equation of system.Two have been tried to achieve in step 2
The state-space model of rank RC equivalent-circuit model, such as shown in formula (2), (3).By this nonlinear model in (xk,ik) nearby enter
Row first order Taylor launches, and obtains
According to the R obtaining in step 4e、Rs、Rl、Cs、ClValue, you can try to achieve A furtherk、Bk、CkOccurrence, extension
Kalman filtering is divided into prediction and revises two processes：
EKF predicts process：
State variable priori estimates calculate：
The covariance matrix of forecast error calculates：
EKF makeover process：
Kalman gain matrix calculates：
State variable optimal estimation value calculates：
Update error co-variance matrix：
Can be in the hope of the optimal estimation value of SOC particle according to formula.
Step 6, more new particle weights are simultaneously normalized, and calculate number of effective particles.If number of effective particles is less than
Given threshold value, exports SOC estimation after carrying out resampling；If greater than given threshold value, then directly export SOC estimation；
First according to formulaCalculate particle weights, wherein R is the covariance of observation noise
Matrix, ykFor observation,Predictive value for particle；After obtaining particle weights, according to formula
Calculate the number of effective particle.Preset effective particle threshold Nthreshold, work as Neff≥NthresholdWhen, sample degeneracy is described
Phenomenon is inconspicuous, directly can carry out next step operation, work as Neff＜ NthresholdWhen, illustrate that number of effective particles is less, need into
Row resampling, after resampling, the weights of each particle are set to 1/N.
After above step terminates, the estimated value of output SOC
Step 7, repeat step 4 arrives step 6.
Make k=k+1, carry out the cycle calculations of subsequent time.
In order to verify the accuracy of Order RC model and the precision of spreading kalman particle filter, to the lithium of 5000mAh from
Sub- battery is charged testing.Electricity in battery is discharged, at ambient temperature, at interval of 15 minutes electric currents with 1A to electricity
Pond is charged, and charging current waveform is as shown in Figure 8.A length of 2.7609 × 10 during whole test process4S, the sampling interval is
7.92s.
In this experiment, set particle number N=50, effective particle threshold Nthreshold=30.As shown in figure 9, being terminal voltage
The identification of measured value and on-line parameter estimate the model voltage value comparison diagram that obtains, it can be found that the electricity that on-line parameter identification obtains
Pool model has very high precision, can be very good to follow the tracks of terminal voltage value, is that the accurate estimation of SOC establishes basis.This experiment
Employ EKF and EKPF method SOC to be predicted contrasting respectively, as shown in Figure 10, be estimation result and the reality of two methods
The comparison diagram of border SOC.Wherein actual SOC is in the case that the sampling interval is for 1s, is calculated according to the definition of SOC, because
Interval time is short, is therefore closer to true SOC value.By Figure 10 it is found that the EKPF value that obtains of prediction closer to
Actual value, especially phase after charging, are compared to EKF and can preferably follow actual value.Figure 11 is two methods of EKF and EKPF
Predict the error amount comparison diagram of SOC obtaining it is found that the SOC value fluctuating error that obtains of EKPF is less, and global error is little
In EKF method.By calculating root-mean-square error and the maximum error that can obtain EKF and EKPF, as shown in table 1：
| Algorithm | Root-mean-square error | Maximum error |
| EKF | 0.0054 | 0.0304 |
| EKPF | 0.0028 | 0.0183 |
Table 1
By comparison diagram and the error analyses of two kinds of algorithms, it is seen that, EKPF algorithm is more preferable to the inhibition of noise,
And higher to the estimated accuracy of SOC, illustrate that EKPF algorithm is better than EKF in SOC estimation.
Claims (5)
1. a kind of SOC method of estimation based on spreading kalman particle filter, is characterised by：The method comprising the steps of：
Step 1, tests to battery, battery is carried out discharging-standing experiment by cell test system, obtains charged
State and the corresponding data of open-circuit voltage, simulate the relation function expression formula of SOC-OCV；
Step 2, sets up the equivalent-circuit model of electrokinetic cell, and obtains separate manufacturing firms model；
Step 3, according to initial probability distribution, produces initial SOC particle collection and arranges weights；
Step 4, according to current data, carries out on-line identification, more new model to model parameter；
Step 5, using spreading kalman particle filter, obtains the predictive value of particle；
Step 6, more new particle weights are simultaneously normalized, and calculate number of effective particles；If number of effective particles is less than given
Threshold value, exports SOC estimation after carrying out resampling；If greater than given threshold value, then directly export SOC estimation；
Step 7, repeat step 4 arrives step 6.
2. a kind of SOC method of estimation based on spreading kalman particle filter according to claim 1, is characterised by：Institute
State in step 4 and model parameter is recognized, concrete grammar is as follows：
For model For data vector, θ is parameter vector to be estimated, y (k) be output to
Amount, ε (k) is system noise, can carry out parameter identification using forgetting factor least squares algorithm to θ, its formula is：
Method of least square gain calculates：
Method of least square covariance matrix calculates：
Method of least square optimal estimation of parameters：
WhereinEstimated value for k moment parameter to be estimated；K (k) is the gain matrix in k moment；P (k) is the covariance in k moment
Matrix, generally its initial value P (0) take sufficiently large unit matrix, and value is 10 here5× I, wherein I are unit matrix；λ is
Weighter factor (0 ＜ λ≤1), between 0.9～1.0, value is 0.98 to general value here.
3. a kind of SOC method of estimation based on spreading kalman particle filter according to claim 1, is characterised by：Institute
State in step 5, using spreading kalman particle filter, obtain the predictive value of particle, concrete grammar is as follows：
It is x for system state equationk+1=Akxk+Bkuk+wk, systematic observation equation is yk=Ckxk+Dkuk+vkSystem, can adopt
Each particle is predicted revise with EKF method, recurrence formula is as follows：
State variable priori estimates calculate：
The covariance matrix of forecast error calculates：
Kalman gain matrix calculates：
State variable optimal estimation value calculates：
Update error co-variance matrix：
Wherein, '-' represent priori value, '+' represent posterior value, ' ' represents estimated value；
Wherein xkFor state vector；ukFor input stimulus；ykFor observation vector；AkFor state-transition matrix；BkFor input stimulus square
Battle array；CkFor state vector observing matrix；DkFor input stimulus observing matrix；wkFor process noise；vkFor observation noise；I is unit
Matrix；Q is process noise covariance matrix；R is observation noise covariance matrix；KgkFor kalman gain matrix；PkFor prediction
The covariance matrix of error.
4. a kind of SOC method of estimation based on spreading kalman particle filter according to claim 1, is characterised by：Institute
State and in step 6, specifically adopt formulaCarry out more new particle weights, using formulaCalculate number of effective particles, contrast number of effective particles and particle threshold set in advance, according to knot
Fruit judges whether to need to carry out resampling；
Wherein parWageiWeights for i-th particle；ykObservation vector for particle；Predictive value for i-th particle；R is
Observation noise covariance matrix；NeffFor effective particle number.
5. a kind of system based on spreading kalman particle filter it is characterised in that：This system includes electrokinetic cell, cell
Test system, computer three parts；
Wherein, cell test system, is made up of four parts, is that current control module, calorstat, data acquisition set respectively
Standby and D.C. regulated power supply；Current control module is connected with the input of the cell in calorstat, current control module root
Realize the control to cell charging and discharging currents size according to extraneous instruction, different battery testing operating modes, constant temperature can be simulated
Case controls the operating ambient temperature of cell according to extraneous instruction；Cell in calorstat is defeated with data acquisition equipment
Enter end to be connected, data acquisition equipment is acquired to the voltage and current data of cell according to extraneous instruction, and to adopting
The data collecting carries out simple analog-to-digital conversion process and then output data；D.C. regulated power supply respectively with current control module,
Calorstat data collecting device is connected, and provides the energy for whole test system；
Current control module is by photoelectrical coupler, digital to analog converter, integrated operational amplifier, MOSFET field effect transistor and constantan wire
Resistance is constituted；
Data acquisition equipment includes current acquisition module and voltage acquisition module and analog-to-digital conversion module.
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