CN104007390B  Battery state of charge tracking, equivalent circuit selection and reference test method and system  Google Patents
Battery state of charge tracking, equivalent circuit selection and reference test method and system Download PDFInfo
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 CN104007390B CN104007390B CN201410062166.6A CN201410062166A CN104007390B CN 104007390 B CN104007390 B CN 104007390B CN 201410062166 A CN201410062166 A CN 201410062166A CN 104007390 B CN104007390 B CN 104007390B
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Abstract
The application is related to battery state of charge tracking, equivalent circuit selection and reference test method and system.This method is included in the first estimation state of charge for the very first time calculating battery（SOC）The magnitude of voltage for the measurement voltage for representing the battery both ends is received in the second time, filter gain is calculated in second time, and calculates the second of the battery based on the described first estimation SOC, the magnitude of voltage and the filter gain in second time and estimates SOC.Another method includes the storehouse that storage in memory represents the equivalentcircuit model of battery, the operational mode of battery is determined based on the load related to the battery, one of described equivalentcircuit model is selected based on identified operational mode, and the state of charge of the battery is calculated using selected equivalentcircuit model（SOC）.
Description
Technical field
Embodiment is related to the state of charge for calculating battery.
Background technology
Electrochemical energy storage device plays an important role in future source of energy strategy.In fact, battery be at present and soon
Energy storage technology feasible in the future.Diversified equipment such as portable electric appts, mobile household electrical appliance, aerospace equipment
Deng being increasingly battery powered.It is likely difficult to accurately estimate the state of charge of such as battery using known system and method.
Therefore, it is necessary to solve the deficiency of current technology and provide other novel and character of innovation system, methods and apparatus.
The content of the invention
One embodiment includes a kind of method.This method is included in the first estimation state of charge for the very first time calculating battery
(SOC) magnitude of voltage for the measurement voltage for representing battery both ends, is received in the second time, calculating wave filter in second time increases
Benefit, and calculate the second of battery based on the first estimation SOC, magnitude of voltage and filter gain in second time and estimate SOC.
Another embodiment includes a kind of system.The system includes battery and battery meter module, and it is configured as making
The estimation state of charge (SOC) of the battery is calculated with Reduced Order Filter, the Reduced Order Filter is single state filter, described
Single state filter is configured as estimating SOC described in recursive calculation based on the SOC estimation calculated before.
Another embodiment includes a kind of computerreadable medium, and it includes code segment.Code segment is by computing device
When the processor is calculated the estimation state of charge (SOC) of battery, estimation SOC is stored in buffer, filtered using depression of order
Device calculates the estimation SOC after the renewal of battery, and the Reduced Order Filter is single state filter, single state filter by with
The estimation SOC being set to after being updated based on estimation SOC come recursive calculation.
Further embodiment includes a kind of method.This method includes the equivalent circuit mould that storage in memory represents battery
The storehouse of type, the operational mode of battery is determined based on the load related to the battery, selected based on identified operational mode
One of equivalentcircuit model, and calculate the state of charge of battery (SOC) using the equivalentcircuit model of selection.
Another embodiment includes a kind of system.The system includes being configured as the equivalentcircuit model that storage represents battery
Storehouse data storage, be configured as selecting the Model selection module of equivalentcircuit model based on the operational mode of battery,
And it is configured as calculating the filter module of the estimation state of charge (SOC) of battery based on the equivalentcircuit model of selection.
Another embodiment includes a kind of computerreadable medium, and it includes code segment.Code segment is by computing device
When the processor is selected equivalent circuit mould from the storehouse of equivalentcircuit model for representing battery based on the operational mode of battery
Type；And the state of charge (SOC) of the battery is calculated using the equivalentcircuit model of selection.
Brief description of the drawings
According to this paper detailed description given below and accompanying drawing, exemplary embodiment will be more fully understood, in accompanying drawing
Similar element is denoted by like reference characters, and these reference numbers are only provided in a manner of illustration, therefore is not to showing
The limitation of example property embodiment, and wherein：
Fig. 1 and 2 shows the block diagram of the battery management system (BMS) according at least one exemplary embodiment.
Fig. 3 shows the frame for being used to select the signal stream of battery equivalent model according at least one exemplary embodiment
Figure.
Fig. 4 shows the signal stream for being used to calculate battery state of charge (SOC) according at least one exemplary embodiment
Block diagram.
Fig. 5 shows the block diagram of battery meter (BFG) system according at least one exemplary embodiment.
Fig. 6 shows the frame of the signal stream of the parameter module for BFG systems according at least one exemplary embodiment
Figure.
Fig. 7 shows the frame of the signal stream of the SOC module for BFG systems according at least one exemplary embodiment
Figure.
Fig. 8 shows the block diagram of the SOC module according at least one exemplary embodiment.
Fig. 9 shows the frame of total least square (TLS) module of the SOC module according at least one exemplary embodiment
Figure.
Figure 10 shows recurrence least square (RLS) module of the SOC module according at least one exemplary embodiment
Block diagram.
Figure 11 and 12 shows the flow chart of the method according at least one exemplary embodiment.
Figure 13 A13D show the schematic diagram of the battery equivalent model according at least one exemplary embodiment.
Figure 14 is the characteristic schematic diagrames of OCVSOC for showing Portable lithium ion cell.
Figure 15 A and 15B are the figure for showing load curve.
Figure 16 A and 16B are the figure for showing fictitious load curve.
Figure 17 is to show the schematic diagram that example system is realized.
Figure 18 is to show the schematic diagram that the user interface being used in combination can be realized with system.
Figure 19 A and 19B include the figure for showing exemplary discharge voltage/current curve.
Figure 20 A and 20B are the figure for showing exemplary coulomb count evaluation method.
Figure 21 A and 21B are the figure for showing shutin time (TTS) appraisal procedure.
Figure 22 A, 22B and 22C are the table for representing voltameter reading.
It should be noted that these figures are intended to show that method used in some exemplary embodiments and/or structure
General features, and supplement the printed instructions being provided below.However, these accompanying drawings are not necessarily drawn to scale and may be inaccurate
Reflect the precise structural characteristics or performance characteristic of any given embodiment, and should not be construed as defining or limiting by exemplary reality
Apply the scope of value that example covered or property.For example, for clarity, may reduce or exaggerate structural detail relative thickness and
Positioning.
Embodiment
Although exemplary embodiment may include various modifications and alternative form, embodiment is in the accompanying drawings with citing
Mode shows and will be described in detail herein.It will be appreciated, however, that it is not intended to exemplary embodiment being limited to the present invention
Particular forms disclosed, but antithesis, exemplary embodiment will cover all modifications fallen within the scope of the appended claims
Form, equivalents and alternative form.In the whole description to accompanying drawing, similar numeral refers to similar element.
The accurate estimation of battery status such as state of charge (SOC), health status (SOH) and remaining life (RUL)
For reliable, safety and to widely use the device being battery powered be vital.Estimate that these quantity are referred to as battery electric quantity
Measure (BFG).Different from the HC fuel in many current automobiles, the memory capacity of battery is not constant.Generally, battery capacity
Change with battery service life, use pattern and temperature, so as to cause challenging ART network problem to BFG,
Need in consideration temperature change, SOC to change and be modeled battery behavior on the basis of service life and online parameter identifies.
Fig. 1 and 2 shows the block diagram of the system 100 according at least one exemplary embodiment.As shown in figure 1, system 100
Including battery 105, battery management system (BMS) 110, display 120, unrestricted power supply 125 (such as wall outlet, automobile
Charging station etc.) and switch 130.
BMS110 can be configured as managing utilization and/or the state of battery 105.For example, BMS110 can be configured with
Unrestricted power supply 125 is connected or disconnected to be charged to battery 105 by switch 130 with battery 105.For example, BMS110 can quilt
It is configured to that load (not shown) is connected or disconnected with battery 105.For example, BFG115 can be configured as calculating the electricity of battery 105
Lotus state (SOC) and/or health status (SOH).SOC and/or SOH can be shown (for example, in the form of percentage, during with residue
Between form etc.) on display 120.
As shown in Fig. 2 BMS110 comprises at least analogdigital converter (ADC) 205,220, wave filter 210,225, numeral amplification
Device 215 and battery meter (BFG) 115.BFG115 includes memory 230, processor 235 and controller 240.ADC205、
220, wave filter 210,225, at least one of digital amplifier 215 and BFG115 can be, such as application specific integrated circuit
(ASIC), digital signal processor (DSP), field programmable gate array (FPGA) and/or processor, etc..Or BMS110
Can be to include ASIC, DSP, FPGA and/or processor of shown functional block, etc..Or system 100 can be realized to be stored in
On memory and by the software of such as computing device.
BMS110 can be configured with digital quantizer (ADC) 205,220, wave filter 210,225 and digital amplifier
215 combination is by analog measurement (e.g., I_{b}And V_{b}) be converted to digital value (for example, so that BFG115 calculates SOC and/or SOH).
For example, digital amplifier 215 can be difference amplifier, it is according to the voltage drop V at the both ends of battery 105_{b}(for example, positive and negative terminal
Between magnitude of voltage difference) generation (e.g., produce) analog signal, then using ADC220 and wave filter 225 by the analog signal
It is converted into the digital value of filtering.
System 100 can be the subsystem using battery powered any system or electronic equipment.In some specific implementations,
Electronic equipment can be or may include (such as) have conventional laptop desktop, laptop laptop devices.In some specific implementations
In, electronic equipment can be or may include (such as) wireline equipment and/or wireless device (for example, supporting WiFi equipment), calculate
Entity (for example, personal computing devices), server apparatus (for example, web server), toy, mobile phone, audio frequency apparatus, electricity
Machine control device, power supply (for example, offline power supply), personal digital assistant (PDA), tablet device, electronic reader, TV and/
Or automobile, etc..In some specific implementations, electronic equipment can be or may include (such as) display device is (for example, liquid crystal display
(LCD) monitor, for user's display information), keyboard, pointing device (for example, mouse, Trackpad, pass through the equipment, use
Family can provide input to computer).
Fig. 3 shows the block diagram for being used to select the signal stream of battery equivalent model according at least one exemplary embodiment
300.As shown in figure 3, model selection block 310 receives input 320 (voltage and/or electric current letter e.g., from battery and/or load
Number) and select using 320 (or its some modification) of input the equivalent mould of representative (or corresponding to) battery from equivalent model storehouse 305
Type.Then by state of charge calculator block 315 using the equivalent model come calculated charge state (SOC) 325.Equivalent model storehouse
305 may include at least one equivalent model for representing battery.Each equivalent model can be based on the operation of battery (or battery eliminator)
Pattern.Operational mode can be based on the load related to battery.For example, operational mode can the voltage drop based on load both ends.For example,
Operational mode can based on load both ends voltage drop be of a relatively high or relatively low, be relative constancy or dynamic and/or they
Combination.
Equivalent model may include (referring to figure 13 below A13D) resistor, voltage (e.g., voltage drop or voltage source), resistance
Any combinations of electric current (RC) circuit and/or impedance circuit etc..Therefore, the mathematics that can establish battery equivalent model is (e.g., public
Formula) equivalents.Equivalent model storehouse 305 can store the mathematical equivalent form related to battery operation pattern.The mathematical equivalent shape
Formula can be used for carrying out SOC calculating by state of charge calculator block 315.For example, mathematical equivalent form can be used for determining variable, make
For the input of the formula for calculating SOC (or SOC estimate).Therefore, BFG systems can be based on operational mode and select equivalent mould
Type with improve computational efficiency and reduce processing time.More details are provided below for Fig. 512.
Fig. 4 shows the signal stream for being used to calculate battery state of charge (SOC) according at least one exemplary embodiment
Block diagram 400.As shown in figure 4, block diagram 400 include extended Kalman filter (EKF) block 405, state of charge (SOC) block 410,
420th, filter gain parameter block 41,425 and buffer 430.EKF blocks 505 can be configured as based on the electric charge shape calculated before
State 410 and filter gain parameter 415, calculate SOC420 and determine filter gain parameter 425 (e.g., reading and/or calculating
SOC variances, the voltage measured, the capacity calculated and/or variable related to equivalent circuit, etc.).Therefore, buffer 430
The SOC calculated before and filter gain parameter in such as processing cycle can be configured as storing.In other words, can be based on
The SOC calculated before at least one calculates current (or next) SOC.In other words, the SOC calculated in the very first time can
For calculating the SOC in the second (later) time.
In exemplary specific implementation, the set of at least two SOC410 and/or filter gain parameter 415 can be used.
Therefore, at least two SOC vector, at least two SOC array, the average and at least two SOC of at least two SOC are put down
Average and corresponding filter gain parameter can be used for calculating next SOC420 (or SOC of the second time) and determining/calculating
Corresponding filter gain parameter 425.Therefore, buffer 430 can be configured as storing it is multiple before the SOC410 that calculate and
Calculate/determine filter gain parameter 415.Therefore, the SOC that BFG systems calculate before, which is improved, calculates effect
Rate and reduction processing time.More details are provided below for Fig. 512.
Fig. 5 shows the block diagram of the system of battery meter (BFG) 115 according at least one exemplary embodiment.Such as Fig. 5
Shown, BFG115 includes estimation module 510, tracking module 520, prediction module 530, opencircuit voltagestate of charge (OCVSOC)
Characterization module 540, offline parameter estimation module 545 and battery life characterization module 550.In addition, the system includes offline number
According to collection module 555 and fuel cell modelling module 560.
Offline data collection module 555 can be configured as measuring battery behavior in relatively controlled test environment.For example,
Opencircuit voltage (OCV) measured value and SOC measured values of battery 105 (or battery eliminator) can be collected in test laboratory environment.
For example, battery 105 (or battery eliminator) can be initialized to it is fully charged (e.g., close to it is fully charged, substantially completely charge),
(rested) state of standing.OCV and SOC measurements can be carried out.Then battery 105 (or battery eliminator) can be made slowly to discharge, simultaneously
At regular intervals (e.g., periodically, periodically, irregularly, the scheduled time) carry out OCV and SOC measurements, until battery 105 (or waits
Imitate battery) completely (or substantially) electric discharge.OCV and SOC measured values can be used for determining, calculate or estimate battery parameter (e.g., hereafter
Described OCV parameters K_{i}□{K_{0}；K_{1}；K_{2}；K_{3}；K_{4}；K_{5}；K_{6}；K_{7}})。
Data from offline data collection module 555 can be used in fuel cell modelling module 560 to determine such as battery 105
The equivalent model of (or battery eliminator) and/or the mathematical equivalent form of equivalent model.Number from offline data collection module 555
According to that can be used in offline parameter estimation module 545 to determine and/or calculate the parameter related to battery 105 (or battery eliminator)
(e.g., the value of the element related to abovementioned equivalent model).Data from offline data collection module 555 can be used in OVCSOC
To determine and/or calculate OCV and SOC battery parameters (e.g., OCV parameters K described below in characterization module 540_{i}□{K_{0}；K_{1}；
K_{2}；K_{3}；K_{4}；K_{5}；K_{6}；K_{7}}).Data from offline parameter estimation module 545 can be used in battery life characterization module 550.Example
Such as, the data from offline parameter estimation module 545 can be used for calculating initial health by battery life characterization module 550
(SOH) characteristic (e.g., maximum SOC).
Display 120 is shown as showing that 565, SOH shows 570, shutin time (TTS) display 575 and residue with SOC
Service life (RUL) display 580.Each display may be, for example, the instrument of show percent.It can be calculated or determined by BFG115 often
The value of individual display.For example, TTS can be shown as the time value (e.g., hour and/or minute) such as calculated by TTS module 532.
Estimation module 510 includes parameter module 512 and capacity module 510.Estimation module 510 can be configured as calculate and/
Or determine that battery 105 (or battery eliminator) is specifically worth (e.g., parameter and capability value).In stable environment (e.g., test experiments
Room) in, parameter and capability value are probably fixed (e.g., not changing).However, in real world environments, parameter and capability value
Be probably it is dynamic or change.For example, complete SOC tracking solution is usually directed to (1) and characterized by offline OCV to shape
Into the estimation of the OCV parameters of a part for statespace model.It is stable that OCVSOC, which is characterized on temperature change and cell degradation,
's.Once estimating these parameters, these parameters just form a part for the statespace model with known parameters.(2) move
The estimation of state equivalent circuit parameter.It has been observed that these parameters change with the temperature of battery, SOC and service life, therefore should
When adaptively being estimated while BFG is run.(3) estimation of battery capacity：Although the nominal capacity of battery is by manufacturing
Specified by business, but known available battery capacity can change because of manufacturing process error, temperature change, use pattern and aging.
And the SOC that (4) are constrained by model parameter is tracked.Once known models parameter, SOC tracking has reformed into nonlinear filtering and asked
Topic.But, it has been observed that gained statespace model includes correlated process and measurement noise process.Appropriately handle these correlations
Effect will draw more preferable SOC tracking accuracies.Therefore, in exemplary specific implementation, for calculating parameter and capacity, mould is tracked
Block 520 can be by data feedback to estimation module 510.
In addition, typically the method for estimation battery capacity ignores hysteresis effect, and assume the cell voltage generation stood
The true opencircuit voltage (OCV) of table battery.However, according to exemplary embodiment, estimation module 510 will be late by being modeled as battery
Error in 105 OCV, and the error in OCV is compensated using the combination of real time linear parameter Estimation and SOC tracking techniques.
Tracking module 520 includes SOC module 522 and SOH modules 524." electricity " in SOC instruction batteries 105.As above institute
State, SOC is active volume, and it is expressed as the percentage of some benchmark (e.g., rated capacity or current capacity).According to exemplary reality
Example is applied, SOC module 522 is by using the error (being combined with parameter Estimation) in the tracing compensation OCV being described in more below
To calculate SOC.SOH indicates state of the battery compared with new or ideal battery.SOH can be based on charge acceptance, internal resistance, electricity
Pressure and/or self discharge, etc..
Prediction module 530 includes TTS module 532 and RUL modules 534.TTS module 532 and RUL modules 534 can be configured
To calculate TTS and RUL based on SOC.
Fig. 6 shows the signal stream of the parameter module 412 for BFG115 according at least one exemplary embodiment
Block diagram.BFG systems can be based on operational mode selection equivalent model to improve computational efficiency and reduce processing time.As shown in fig. 6,
Parameter module 412 includes operational mode module 605 and Model selection module 610.Operational mode module 605 can be configured as being based on
At least one input and/or next selfsupported 615 at least one input from battery 105 determine (battery) operational mode.
At least one input can based on in battery 105 and load 615 at least one related electric current and voltage at least one
It is individual.For example, the voltage drop at 615 both ends of load.For example, operational mode can be of a relatively high based on the voltage drop at 615 both ends of load
Or it is relatively low, be relative constancy or dynamic and/or combinations thereof.Model selection module 610 can the operation mould based on determination
Formula selection equivalent model (or its mathematical equivalent form).For example, Model selection module 610 can be generated for searching for equivalent model storehouse
305 query term.
In some specific implementations, definable or the multiple operational modes of sign.In exemplary specific implementation, it is described below
To battery and use related four operational modes of the system of battery.
In the first operational mode, battery 105 may connect to weight and the load changed.In other words, load 615 can combine
Consumed (or the high voltage of consumption variable current loads) using of a relatively high voltage and dynamic or variable current.For example, in movement
In phone, the first operational mode may include such use environment, wherein mobile phone using include prolonged video playback,
Multimedia and game application etc..Equivalent circuit shown in figure 13 below A can represent the load for being connected to weight and change
Battery.
In the second operational mode, battery 105 loads connectable to dynamic load and/or variable voltage.In other words, bear
Carry 615 voltages that dynamic or change can be used.For example, in the mobile phone, the second operational mode may include such to use ring
Border, wherein mobile phone, which use, includes call, webbrowsing and/or the conventional use for playing video clipping.Figure 13 below B
Shown in equivalent circuit can represent to be connected to the battery of dynamic load.
In the 3rd operational mode, battery 105 may be connected to or consume constant current.In other words, load 615 can towing ahead
With constant (or substantial constant) load.Or battery 105 just can be electrically charged using constant current.For example, in charging week
Phase, battery 105 can disconnect with load 615 (e.g., can be used switch 130 that unrestricted power supply 125 is connected into battery 105 with to electricity
Charged in pond 105).Equivalent circuit shown in figure 13 below C can represent to be connected to the battery of constant current.
In the 4th operational mode, battery 105 may be connected to the load of relatively low voltage.Or battery 105 can be at
Periodicity static condition, wherein battery 105 are subjected to gently loading, then charging, then stand, be minimum or nonloaded.In other words,
Minimum voltage can be rarely employed in load 615.For example, in the mobile phone, the 4th operational mode may include such use environment,
After wherein mobile phone use is included in (or substantially completely) charging completely, base station is carried out using the call not taken place frequently
Conventional contact.Equivalent circuit shown in figure 13 below D can represent to be connected to the battery of dynamic load.
Fig. 7 shows the signal stream of the SOC module 422 for BFG115 systems according at least one exemplary embodiment
Block diagram.As shown in fig. 7, SOC module 422 includes buffer block 705, model estimation block 710, SOC tracking blocks 715 and voltage drop
Prediction module or block 720.
In the exemplary embodiment, it will be late by the error being modeled as in the OCV of battery 105.Voltage drop v_{D}In [k] can be represented
Portion battery model element R_{0}、R_{1}、R_{2}And x_{h}The voltage (referring to Figure 13 A) at [k] both ends.x_{h}[k] item can be used in the SOC of explanation prediction
Error.In other words, x_{h}[k] can be " instantaneous lagging ", and it can be modified to zero by Adjustable calculation or the SOC estimated.
If the SOC for calculating or estimating is equal to SOC, the x for calculating or estimating_{h}[k] should be equal to zero.In other words, calculate or estimate
The x gone out_{h}[k] is not equal to zero, it indicates that the SOC for calculating or estimating has error.Voltage drop model parameter vector (b) include pair
Should be in the x for calculating or estimating_{h}The element of [k].
Therefore, in Fig. 7 flow, the SOC for tracking the current calculating of block 715 from SOC or estimating is used in voltage block
To calculate voltage drop v in prediction block 720_{D}[k].At least one passing voltage drop v_{D}[k] is stored in buffer 705 and is used for
Parameter vector b estimation.The x that correspondence in parameter vector b is calculated or estimated_{h}[k] is that nonzero value instruction has instantaneous lagging.
This means SOC evaluated errors.The SOC track algorithms of SOC tracking blocks 715 are configured as in the x for calculating or estimating_{h}[k] is
Nonzero whenever amendment SOC.Hereafter (mathematically) describe relevant voltage drop v_{D}[k], hysteresis, estimation x_{h}[k], voltage
The more details of model parameter vector (b) and SOC tracking drop.Therefore, the SOC and SOC that BFG systems calculate before are missed
Poor accurate estimation SOC, improve computational efficiency and reduce processing time.
Fig. 8 shows the block diagram of the SOC module 422 according at least one exemplary embodiment.As shown in figure 8, SOC module
422 include extended Kalman filter (EKF) block 805.EKF blocks can be configured as calculating SOC845 and SOC errors 840.EKF blocks
805, which can be configured with equation 1, calculates SOC845 as estimation SOC, and uses equation 2 to calculate SOC errors 840 as estimation
SOC errors (or variance).In each of following equations, k refers to instantaneous iteration, k+1  k refer to one, it is previous or it
Preceding iteration, and k+1  k+1 refers to current, renewal, next or successive iterations.
Wherein：
It is estimation SOC that is current or updating iteration；
It is the estimation SOC of upper one or prediction iteration；
G [k+1] is the filter gain of upper one or prediction iteration；And
v_{k+1}It is the load voltage of upper one or prediction iteration.
Wherein：
P_{s}[k+1  k+1] it is SOC evaluated errors or variance that be current or updating iteration；
G [k+1] is the filter gain of upper one or prediction iteration；
H [k+1] is the observed differential of linearisation；
P_{s}[k+1  k] is upper one or predicts the SOC evaluated errors or variance of iteration；And
It is the voltage noise reducing in initialization with zero mean and correlation.
SOC module 422 includes OCV parameter blocks 810.OCV parameter blocks 810 can be configured as from OVCSOC characterization modules 540
Storage and/or reception OCV parameters { K_{i}}.OCV parameters { K_{i}It is constant, because they are offline measurement and made in battery 105
It is negligible (or in the absence of) with the change in the lifespan.OCV parameters are used to calculate OCV according to equation 3 with SOC.
Wherein：
S [k] is SOC；And
V_{o}(s [k]) is opencircuit voltage (OCV)；
SOC module 422 includes voltage drop model block 825.Voltage drop block 825 can be configured with according to equation 4 or 5
The voltage drop at voltage drop model (as discussed above) computational load both ends.
Z_{v}[k]=V_{0}(x_{s}[k])+a[k]^{T}b+n_{D}[k] (4)
Wherein：
Z_{v}[k] is the voltage of measurement；
V_{0}(x_{s}[k]) it is opencircuit voltage (OCV)；
a[k]^{T}It is voltage drop model；
B is voltage drop model parameter vector；
It is estimated voltage drop model；
It is estimated voltage drop model parameter vector；And
n_{D}[k] is voltage drop observation noise.
As described above, voltage drop model can be based on selected equivalentcircuit model and change.Selected equivalentcircuit model and/or
Voltage drop model can be read from data storage 855.For example, data storage 855 may include equivalent model storehouse 305.
EKF (module or) block 805 can be configured with equation 1 and calculate SOC845 as estimation SOC, and by gained
SOC845 is stored in buffer 850.EKF blocks 805 can be configured with equation 2 and calculate the calculating of SOC errors 840 as estimation
SOC errors (or variance), and the SOC errors 840 of gained are stored in buffer 850.SOC the and SOC errors of storage are readable
SOC815 and SOC errors 820 are taken as, that is, SOC845 the and SOC errors 840 stored.Therefore, EKF blocks recursively (can e.g., follow
In ring) calculate SOC845 and SOC errors 840 so that followup (be renewal in time, next and/or afterwards) SOC845
With SOC errors 840 calculate can based on (in time for current, upper one or before) SOC815 before at least one and
SOC errors 820 calculate.
As shown in figure 8, recurrence least square (RLS) block 830 and total least square (TLS) block 835 can be generated to EKF blocks
805 input.RLS blocks can generate initial estimation voltage drop model parameter vector, and (it may include at least one voltage drop model ginseng
Number), and TLS blocks 835 can generate initial estimation capacity.Each circulation can be directed to and generate initial estimation voltage drop model parameter
Vector sum initial estimation capacity.In exemplary specific implementation, with iterations (k) increase, initial estimation voltage drop model
The change of parameter vector and initial estimation capacity can become to ignore.
Fig. 9 shows total least square (TLS) block 835 according to the SOC module 422 of at least one exemplary embodiment
Block diagram.As shown in figure 9, TLS blocks 635 include buffer 910 and TLS computing modules 915.Buffer 910 be configured as receive,
Storage and output SOC data, such as Δ SOC data 920 (or changing value of SOC data 920), so that TLS computing modules 915 make
With.Buffer 910 is additionally configured to receive, store and export Δ coulomb data 925 (or changing value of coulomb data 925), with
Used for TLS computing modules 915.Buffer 910 can receive the current data based on the electric current related to battery 105 measured
905 are used as such as coulomb enumeration data.
TLS computing modules 915 can be configured as calculating the capacity of battery 105 based on Δ SOC920 and Δ coulomb 925
930.For example, equation 6 can be used to calculate capacity 930 for TLS computing modules 915.The derivation of equation 6 is shown in further detail below.
Wherein：
It is estimated capacity；
It is the covariance of augmentation observing matrix；And
Δ^{K}(2,2) be nonnegative feature value diagonal 2 × 2 matrix；
Figure 10 shows recurrence least square (RLS) block according to the SOC module 422 of at least one exemplary embodiment
830 block diagram.As shown in Figure 10, TLS blocks 635 include buffer 1005 and RLC computing modules 1010.Buffer 1005 is configured
For receive and store SOC815, SOC error 820 and as the output from voltage drop model block 825 voltagedrop data (e.g.,
Z_{V}[k] or OCV).Buffer 1005 is configured as output voltage drop 1015 and electric current and electric capacity (I＆C) matrix 1020.
RLC computing modules 1010 can be configured as calculating initialization ginseng based on voltage drop 1015 and (I＆C) matrix 1020
Number 1025.For example, equation 7 can be used to calculate initiation parameter 1025 for RLC computing modules 1010.The derivation of equation 7 is hereinafter
It is shown in further detail.
Wherein：
α_{i}It is R_{1}C_{1}Current attenuation coefficient in circuit；
β_{i}It is R_{2}C_{2}Current attenuation coefficient in circuit；
It is R_{1}Estimation resistance value；
It is R_{2}Estimation resistance value；
It is the estimation lagging voltage of battery；And
x_{h}[k] is instantaneous lagging；
It is worth noting that, as described above for described in Fig. 7, the estimation lagging voltage of battery should be zero.Therefore, in exemplary tool
During body is implemented, (or substantially removing) is eliminated because being missed caused by hysteresis by SOC tracking due to tracking block 715 using SOC
Difference, therefore the b (6) in equation 7 should be zero.Therefore, SOC estimation is more accurate, because can will be late by taking into account.
In figs. 810, the length of buffer 1005 can be the L for parameter Estimation_{b}, and the length of buffer 905 can be to use
In the L of capacity estimation_{c}.EKF blocks 805 are iterated for each k, and RLS830 is for being each used as L_{b}, the k progress of integral multiple
Iteration, and TLS835 is for being each used as L_{c}The k of integral multiple is iterated, and wherein k is time index.BFG estimation SOC tracking
Required all required model parameters and battery capacity, but except OCV parameters (it estimates offline) and from measuring instrumentss
The voltage and current measurement error standard deviation sigma of circuit calibration_{v},σ_{i}Outside.RLS blocks do not need any outside primary condition, need to only set
λ=1 is put, it is initial value to provide for firm LS estimates, i.e.,WithWhereinWith
For Mission Number.The mathematical proof of EKF blocks 805 is described below.
Figure 11 and 12 shows the flow chart of the method according at least one exemplary embodiment.For described in Figure 11 and 12
The step of can be carried out due to the execution of software code, the software code is stored in and equipment (e.g., shown in Fig. 1 and 2
BMS110) in related memory (e.g., memory 230) and by devicedependent at least one processor (e.g., processor
235) perform.It is contemplated, however, that alternate embodiment, such as the system for being embodied as application specific processor.Although following step quilt
It is described as by such as computing device, but these steps need not be by same computing device.In other words, at least one processing
The executable step described in below for Figure 11 and 12 of device.
Figure 11 describes selection and represents the equivalent model of battery for the flow chart of calculating estimation SOC method.Such as figure
Shown in 11, in step S1105, the library storage of equivalentcircuit model of battery is represented in memory.For example, use offline number
According to collection module 555, the data related to battery 105 (or battery eliminator) are collected.Use the data and universal circuit work
Tool, can generate at least one equivalent circuit for representing battery.The equivalent circuit may include at least one equivalent voltage, resistance, electricity
Any combinations of appearance and/or equiva lent impedance.See, for example, following Figure 13 A13D.The mathematics of each equivalent circuit can also be generated
Equivalents.Equivalent circuit and/or mathematical equivalent form are storable in such as equivalent model storehouse 305.
In step S1110, the operational mode of battery is determined based on the load related to battery.It is for example, each equivalent
Model can be based on the operational mode of battery (or battery eliminator).Operational mode can be based on the load related to battery.For example, operation
Pattern can the voltage drop based on load both ends.For example, operational mode can based on load both ends voltage drop be it is of a relatively high or
It is relatively low, be relative constancy or dynamic and/or combinations thereof.Therefore, operational mode can based on the electric current related to battery and/
Or voltage and/or the load related to battery determine.
In step S1115, based on identified pattern come select for identified pattern equivalentcircuit model it
One.For example, equivalent model storehouse 305 can be searched for based on identified operational mode.For example, represent battery equivalent circuit and/
Or mathematical equivalent form can use the mode corresponding with operational mode identification (e.g., unique name or unique identification number) to store
In equivalent model storehouse 305.Accordingly, it is determined that operational mode may include to determine operational mode identification, operational mode identification is then
For searching for equivalent model storehouse 305.Selection equivalent circuit may include selection by search for equivalent model storehouse 305 returned it is equivalent
Circuit or mathematical equivalent form.
In step S1120, the state of charge of battery (SOC) or estimation are calculated using selected equivalentcircuit model
SOC.For example, as described above, voltage drop model parameter vector (b) can be based on by calculating SOC.Voltage drop model parameter vector can have
The parameter of equivalent circuit based on battery (referring to abovementioned equation 7).Accordingly, it is determined that voltage drop model parameter vector can be based on etc.
Effect circuit has high or low complexity.For example, as described below, equivalent circuit may not include RC circuit elements, because electric capacity
Charge and bypass resistance.Therefore, b (3) can be unique remaining voltage drop model parameter vector element.So as to simplify SOC or
Estimate SOC calculating.In addition, between the terminal of battery 105 voltage v [k] (can be used for calculate SOC or estimation SOC) can be based on it is equivalent
Circuit model.Equation, SOC and equivalentcircuit model related v [k] is more particularly described hereinafter.
Figure 12 shows the flow chart for the method that estimation SOC is calculated using recursion filter.As shown in figure 12, in step
In S1205, the estimation state of charge (SOC) of stored battery is read from buffer.For example, buffer 850 can be deposited wherein
Store up at least one SOC errors calculated in the preceding an iteration for the step described in the flow chart and SOC.It can postpone
Rush at least one in the reading storage SOC value of device 850.
In step S1210, the measurement voltage at battery both ends is read.For example, such as digital amplifier 215 can be used to read
Or determine voltage (e.g., the v shown in figure below 13A13D [k]).In an exemplary specific implementation, voltage is stored in buffering
In device.Therefore, different voltage measuring values can be used in different iteration.In other words, previous (on the time) voltage measuring value can use
It can be used for iteration k+2 in current iteration or v [k+1].
In step S1215, filter gain is calculated.For example, it is as briefly described above and be described in more below, calculate
The filter gain (e.g., G [k+1]) of EKF blocks 805.Filter gain can be based on being calculated using weighted least square algorithm
At least one capability value.For example, filter gain can be based on using weighting recurrence least square (RLS) algorithm and an overall most young waiter in a wineshop or an inn
Multiply at least one capability value that at least one of (TLS) algorithm calculates.Filter gain can be based on using weighting RLS algorithm
The capability value calculated, the weighting RLS algorithm are based on SOC tracking errors covariance and current measurement errors standard deviation.Filtering
Device gain can be based on estimation SOC variances.Filter gain can be based on the capability value calculated using TLS algorithms, the TLS algorithms
Recurrence renewal based on covariance matrix.Filter gain can be based on searching the capability value calculated using opencircuit voltage (OCV).
In SOC tracking errors covariance, current measurement errors standard deviation, SOC variances, covariance matrix and OCV each below
The description (as mathematically) in more detail.
In step S1220, storage SOC, the voltage at battery both ends and filter gain based on battery calculate battery
Estimation SOC.For example, the SOC of estimation, which can be equal to filter gain, is multiplied by estimation SOC of the digital voltage value plus storage.In step
In rapid S1225, the estimation SOC calculated is stored in buffer (e.g., buffer 850).If necessary and/or need into
One step calculates estimation SOC (S1230), then processing is back to step S1205.For example, if battery 105 is continuing in use, such as
Fruit SOC errors, which exceed desirable value and further iteration, can reduce error, and/or if battery testing is carried out, etc., then
It may be necessary to and/or need further to calculate.
Figure 13 A13D show the schematic diagram of the battery equivalent model according at least one exemplary embodiment.Below will
Optionally reference picture 13A13D is to describe one or more exemplary specific implementations.As shown in Figure 13 A13D, battery is represented
Equivalent model 13001,13002,13003,13004 may include resistor 1315,1325,1340, capacitor 1330,
1345 and any combinations of equivalent voltage source 1305,1310.Voltage 1355 represents the voltage drop at battery both ends during loading.Electric current
1320th, 1335 and 1350 represent to flow through the electric current of the element of (or flowing to) equivalent model.For example, electric current 1350 represents to flow to load
Electric current.
Resistor and the RC circuits of capacitor definable one.For example, resistor 1325 and 1330 defines a RC circuits.At some
In exemplary specific implementation, capacitor can be completely charged and short circuit, causes RC circuits actually to be disappeared from equivalent model.Example
Such as, in the equivalent model 13002 of battery is represented, the RC circuits defined by resistor 1340 and capacitor 1345 are not in model
In, because capacitor 1345 is completely charged, form short circuit.In some exemplary embodiments, there is no (or few) and electricity
The related hysteresis in pond (e.g., battery is in standing or traction seldom loads).Therefore, in the equivalent model 13004 for such as representing battery
Shown, due in the absence of hysteresis, equivalent voltage source 1310 is not in a model.
Next the application describes the details of exemplary specific implementation.The details may include at least one abovementioned equation
Foundation (e.g., mathematical proof or simplification).For clarity, these equations are repeated, however, these equations will retain square brackets
Equation numbering shown in ([]).Since identifying realtime model, it refers to following annotation.
a[k]^{T}Observation model
A^{κ}A [k] in batch κ^{T}Continuous Observation, stack in a matrix
B [k] observation model parameter
The LS estimations of model parameter
The RLS estimations of model parameter
I [k] flows through the electric current of battery
K_{i}OCV parameters：K_{0},K_{1},K_{2},K_{3},K_{4},K_{5},K_{6} K_{7}
L_{b}Batch length for parameter Estimation
n_{i}[k] current measurement errors
n_{v}[k] voltage measurement error
P_{b}The covariance matrix of [κ] LS estimators
R_{0}Inside battery series resistance
R_{1} R_{1}C_{1}The internal resistance of cell in circuit
R_{2} R_{2}C_{2}The internal resistance of cell in circuit
The voltage at v [k] batteries both ends
v_{D}[k] voltage drop
The Continuous Observation voltage drop of the vector form of kth batch
V_{D}The ztransform form of [z] voltage drop
Flow through R_{1}Electric current
Flow through R_{2}Electric current
x_{s}[k] state of charge (SOC) s [k]
x_{s}The estimation of [k]
z_{i}[k] flows through the measurement electric current of battery
z_{v}The measurement voltage at [k] battery both ends
Δ sample time
LS errors of fitting
C_{i}Percentage evaluated error
R_{i}Percentage evaluated error
Voltage drop observation noise covariance
The element of SOC track algorithms may include：
A. the estimation of OCV parameters：It is normalized when by using the time limit and dependent on the battery capacity of service life
When, it is stable that OCVSOC, which is characterized and varied with temperature with cell degradation,.
B. the estimation of dynamic equivalent circuit parameter：It has been observed that these parameters are with the temperature of battery, SOC and service life
And change, therefore should adaptively estimate while BFG is run.
C. the estimation of battery capacity：Although the nominal capacity of battery is as specified by manufacturer, known available battery capacity
It can change because of manufacturing process error, temperature change, loading mode and aging.
D. the SOC by model parameter constraint is tracked：Once known models parameter, SOC tracking has reformed into nonlinear filtering
Problem.
Exemplary embodiment allows to carry out real time linear estimation to the dynamic equivalent circuit parameter of battery.It is following by solving
Problem, the method for improving existing battery equivalent circuit modeling and parameter Estimation is realized in this exemplary embodiment：
A. some models only consider resistance, are not suitable for dynamic load.
B. they carry out system identification using nonlinear method.
C. the initial parameter estimation for method of model identification is needed.
D. assume that single dynamic equivalent model represents all battery operation patterns.
In the exemplary specific implementation, solve the problems, such as aforementioned four and be summarized as follows：
A. it is used for the online linear method of model parameter estimation, without estimating that the exact physical of battery equivalent circuit represents shape
The parameter of formula.SOC tracking mode spatial models make use of it is amended can Linear Estimation parameter estimation.
B. it is applied to various batteries, without any initial value or calibration：Due to exemplary status spatial model
Adaptivity, the SOC trackings proposed do not need any offline initialization of model parameter.Least square (LS) method carries
Supplied needs whenever the initialization (or reinitializing) to parameter, block recurrence least square (RLS) is used to hold
Continuous trace model parameter.Additionally, it has been suggested that amended opencircuit voltage (OCV) model different battery models, different temperatures and
It is effective under the conditions of different loads.This just makes the battery that exemplary BFG can be in a manner of plug and play applied to broad range, nothing
Need any other relative other information.
C. different battery modes are carried out with the possibility of seamless SOC tracking.Can recognize that four different battery equivalent models with
Reflection very light load or static condition, constant current or lowfrequency load, dynamic load and the heavy duty of change.Also identify
Four (somewhat) different dynamic equivalent models are with these patterns of best match.These models track available for seamless SOC, without
By the patterns of change of battery operation.
D. hysteresis modeling, it eliminates the needs of hysteresis modeling：Exemplary specific implementation is recognized hardly possible (complete
Hysteresis modeling beauteously) is carried out offline, because hysteresis is relevant with SOC ∈ [0 1] and load current I ∈ R.Therefore, according to exemplary
Embodiment, in voltage drop model, it will be late by being modeled as the error in OCV, and online filtering method constantly tries to pass through tune
Whole SOC carrys out fill in a gap (to correction value).
The realtime model parameter Estimation that realtime model identification is carried out including the use of equivalent circuit.Figure 13 A are exemplary battery
The equivalent circuit of (e.g., battery 105).When battery, which is in, to be stood, V_{0}(s [k]) is the OCV of battery.OCV uniquely depends on battery
SOC, s [k] ∈ [0,1].When battery is in active state, such as when current active be present, the behavior of battery, which passes through, to be moved
State equivalent circuit represents that the dynamic equivalent circuit is by lag element h [k], series resistance R_{0}And two be connected in series are simultaneously
Join RC circuits (R_{1},C_{1}) and (R_{2},C_{2}) composition.Discrete time uses [k] instruction.
In figure 13a, the measurement electric current for flowing through battery is write as：
z_{i}[k]=i [k]+n_{i}[k] (8)
Wherein i [k] is the real current for flowing through battery, and n_{i}[k] is current measurement noise, it is assumed that current measurement noise
For zero mean and there is standard deviation (s.d.) σ_{i}The measurement voltage at battery both ends is：
z_{v}[k]=v [k]+n_{v}[k] (9)
Wherein v [k] is the real voltage at battery both ends, and n_{v}[k] is voltage measurement noise, it is assumed that voltage measurement noise
For the zero mean with s.d..σ_{v}。
According to following form writing inner member R_{0},R_{1},R_{2}Dropped with the cell voltage at h [k] both ends：
Wherein flow through resistor R_{1}And R_{2}Electric current can be write according to following form
Wherein,
And (14)
Δ is sampling interval.
By using measurement electric current z_{i}[k] replaces i [k], the electric current in (11) and (12) again book can be written as into form：
(8) are used now, (10) can book be written as form again in z domains：
Next, write (15) again in z domains：
Draw
And for (16) similarly,
By the way that (19) and (20) are substituted into (17)：
Rearrange (21) and convert it back to time domain：
Wherein,
α=α_{1}+α_{2} (23)
β=α_{1}α_{2} (24)
^{}h[k]=X_{h}[k]αX_{h}[l of k mono]+β X_{h}[k2], (27)
And (28)
(29)
(22) are write into following form again now：
v_{D}[k]=[k]^{T}+n_{D}[k] (30)
Wherein observation model a [k]^{T}Provided with model parameter vector b as follows：
Wherein subscript 4 indicates abovementioned model corresponding with the model 4 of four models shown in Figure 13 A13B.
(30) in voltage drop observation noise writing into：
It has the autocorrelation being given below：
And assume in length L_{b}Time interval batch during lagging component be constant, for example,
Now, four different battery operations " pattern " can describing and match these patterns appropriate battery it is equivalent
Model.
A. pattern 1light load or static condition：When battery is only gently loaded, then it is electrically charged, it is stagnant when then standing
Component will be so small as to negligible afterwards.The example of the pattern will be cell phone, and it is after fully charged, when expending nearly all
Between contact base station until charge event next time, in addition to possible a small number of calls.Single resistor is non(referring to Figure 13 D)
Often it is adapted to the pattern.
B. 2constant current of pattern is run：When the electric current for flowing through battery is constant, the capacitor in RC circuits is changed into complete
Charging.Therefore, in terms of parameter Estimation viewpoint, the circuit of gained can be considered as single resistor and hysteresis/biasing element (referring to figure
13C).The constant current charge of battery is the good example of the pattern.
C. 3dynamic load of pattern：When battery is in the pattern, different size of a large amount of loads be present.Example：Periodically
Ground is used for the smart phone of call, webbrowsing, video clipping etc..Battery eliminator shown in Figure 13 B is adapted to this very much
Scene.
D. pattern 4heavy and change use：For mobile phone, video when heavy and change use includes long
Broadcasting, multimedia and game application etc..Figure 13 A match the scene very much.
Pay attention to, the different model complexities of dynamic equivalent circuit can be by only changing [k]^{T}To represent.It shown below pin
To [k] of each model^{T}Definition.For each in abovementioned model complexity, noise item n_{D}[k] according to following form withWithRepresent：
Wherein,
α=α_{1}+α_{2} (38)
β=α_{1}α_{2} (39)
The leastsquares estimation of constant dynamic model parameters when following discussion is related to.True SOC at time k is represented
For：
The SOC track algorithms of foundation can be used for obtaining, i.e. x_{s}The more new estimation of [k].Now, the voltage in (10)
V drops_{D}[k] can write into：
Wherein v_{0}(x_{s}[k  k]) the estimation opencircuit voltage (OCV) of battery is represented, it can be described as the function for estimating SOC.
Following OCVSOC relations can be used：
Can be by step as described below to OCV parameters K_{i}∈{K_{0},K_{1},K_{2},K_{3},K_{4},K_{5},K_{6},K_{7}Estimated offline
Meter.By considering L_{b}Batch is observed, can book be written as form again by (30)：
Wherein κ is Mission Number,
And noiseWith following covariance
WhereinFor five diagonal toeplitz matrixs, wherein diagonal entry, the first and second off diagonal elements point
Do not pass throughWithProvide (see (32)).Now, dynamic model parameters vector can pass through a most young waiter in a wineshop or an inn
Multiply (LS) optimization to be estimated as follows by (42)：
The covariance matrix of LS estimators provides as follows：
When obtaining the measured value of new lot, LS estimates can be updated by repeating (50)(51) recurrence
Wherein λ is to forget (Attenuation Memory Recursive) factor, ()^{T}Represent transposition, ()^{1}Expression is inverted, and P_{b} ^{1}[κ] is claimed
For information matrix, the information matrix can be multiplied by suitable constant to initialize by appropriately sized unit matrix.It can pay attention to
Arrive, as λ=0,It is changed into.May be present makesApproximate a variety of methods.May be selected following two approximation methods be used for than
Compared with：
A. following approximation method can be carried out：
B. the estimate before use to be to build electric current covariance matrix, such as using：
In
Following discussion is related to least meansquare error (MMSE) estimation of the dynamic model parameters of timevarying.Assuming that dynamic model is joined
Number is the stochastic variable that following slowly varying WienerHopf equation occurs：
x_{b}[k+1]=x_{b}[k]+w_{b}[k] (54)
Wherein w_{b}[k] is with covariance ∑_{b}Zero mean white Gaussian noise.Now, (30) are used to be used as measurement model
And (53) are used as process model, Kalman filter provides b MMSE estimations.SOC can be used for determining v_{D}[k] (see (42)),
SOC tracking/smooth iterative algorithm and pass through the parameter Estimation based on Kalman filtering that the observation window of sufficient length is carried out can
For improving the precision of SOC tracking and parameter Estimation.
Following discussion is related to opencircuit voltage (OCV) parameter Estimation.SOC estimation can utilize battery opencircuit voltage (OCV) with
Uniqueness and stable relations between SOC simultaneously allow to calculate SOC for the OCV measured.However, only when battery, which is in, to be stood,
Just can direct measurement OCV.When battery is in use, the dynamic relationship between cell voltage and electric current must pass through parameter and shape
State method of estimation illustrates.State of charge method of estimation based on OCVSOC includes and following related error：(1) battery
The modeling of dynamic equivalent electric model and the uncertainty of parameter Estimation；And the error of the voltage and current of (2) measurement.(43)
The parameter that middle OCVSOC is characterized can be estimated by gathering OCV characterize datas on Sample Cell as follows：
A. since battery that is fully charged, standing completely
B. its opencircuit voltage V is recorded_{batt}=V_{full}
C. k=1 is set
D. v [k]=V is recorded_{batt}；Record SOC [k]=1
E. k=k+1 is set
F. using minimal amount of (usual C/30 or C/40, wherein C are the battery capacity represented with Ah) constant current i [k]
Make battery continuous discharge, until battery discharges completely.Once electric discharge completely, battery is just set to keep standing, and hereafter charging is straight
It is fully charged to battery.Then
1. battery terminal voltage is measured, the V per the Δ second_{batt}
2. record v [k]=V_{batt}
G. SOC [k]=SOC [k1]+c is recorded_{h}i[k]Δ
Now, OCV models (43) vector format can represent as follows for all measured value v [k]：
V=A_{ocv}k (55)
Wherein
V=[v [1], v [2] ..., v [N_{v}]]^{T} (56)
A_{ocv}=[a_{ocv}(1),a_{ocv}(2),…,a_{ocv}(N_{v})]^{T} (57)
K=[K_{0} K_{1} K_{2} K_{3} K_{4} K_{5} K_{6} K_{7} R_{0}]^{T} (58)
Then assignment s [k]=SOC [k] is passed through
Now, the leastsquares estimation value and internal resistance of cell R of OCV parameters_{0}Provide as follows：
Following discussion is related to four exemplary equivalent circuit models.
Table 1
Pattern number  Equivalent circuit 
Model 1  Figure 13 D 
Model 2  Figure 13 C 
Model 3  Figure 13 B 
Model 4  Figure 13 A 
The voltage drop at the circuit element both ends of each can following form in four equivalentcircuit models shown in table 1
Writing：
v_{D}[k]=[k]^{T}[k]+n_{D}[k] (61)
Wherein,
For model 3：
And for model 4：
α=α_{1}+α_{2} (66)
β=α_{1}α_{2} (67)
It is related to the derivation of Noise Correlation below.In this part, for  l =0,1,2 and be directed to  l >2 autocorrelation
Property (27) can by (33) derive it is as follows：
L=0：
L=1：
L=2：
Now, it is abovementioned to represent as follows for each model：
The discussion continues real time capacity estimation, and it refers to following annotation.
C_{batt}Battery capacity
c_{h}Coulomb meter number system number
The LS estimates of battery capacity
The RLS estimates of battery capacity
The TLS estimates of battery capacity
The vector of SOC differences
The vector of SOC differences between two standings
Coulomb vector
Coulomb vector between two standings
H^{κ}Augmentation observing matrix
I [k] flows through the electric current of battery
K_{i}OCV parameters：K_{0},K_{1},K_{2},K_{3},K_{4},K_{5},K_{6} K_{7}
n_{i}Noise in [k] measurement electric current
P_{s}[k  k] SOC estimation error variances
Q_{c}[κ] capacitance variability variance
R_{c}[κ] uses the capacity estimation error of TLS, RLS or OCV method
RLS capacity estimation error variances
R_{TLS}[κ] TLS capacity estimation error variances
w_{s}[k] process noise
Differential SOC errors
The process noise accumulation between standing and followup standing at k
The differential SOC errors searched based on OCV
The vector of differential SOC errors
The vector of differential SOC errors based on OCV
x_{c}The battery capacity of [κ] fusion
SOC estimates
Error in SOC estimations
x_{s}[k+1] SOC
The SOC estimations searched based on OCV
Error in the SOC estimations searched based on OCV
z_{c}The capacity estimation that [κ] is carried out by TLS, RLS or OCV method
z_{i}[k] measures electric current
Capacity estimation error
η_{c}Charge efficiency (η=η_{c})
η_{d}Discharging efficiency (η=η_{d})
The covariance of augmentation observing matrix
The covariance of differential SOC errors
The state of charge (SOC) of battery, is defined as：
Formula 78 provides the information about battery status.When the understanding of SOC and battery capacity is used to estimate the closing of battery
Between (TTS) or fully charged time (TTF).Battery capacity generally varies with temperature and its root Ju use pattern and service life
Weaken over time.Accurate battery capacity tracking is the key element of battery electric quantity metering.
In the exemplary specific implementation, online capacity estimation can be based on：
A. there is weighting recurrence least square (RLS) estimation of the capacity of accurate weight derivation.For online capacity estimation
Weighting RLS methods include based in the updated SOC tracking the whole time in variance and covariance and current measurement
Error to standard deviation derives the expression formula of weight.
B. it is used for the TLS methods of realtime tracking battery capacity.TLS methods provide to be reached for the closed meter of capacity estimation
Formula.This method can be used for the change of continuous tracking battery capacity.
C. the adaptive capacity estimation that the OCV based on resting batteries is searched.For tracking the TLS side of battery capacity online
The SOC that method by using battery standing point search based on OCV estimates.
D. the fusion of the capacity estimation obtained by distinct methods.
Following discussion is related to battery capacity estimation and fusion.The instantaneous charge state (SOC) of battery can be written as following mistake
Journey model, it is also referred to as coulomb Counting Formula, is represented according to following form with measuring electric current：
Wherein x_{s}[k] ∈ [0,1] represents the SOC, C of battery_{batt}For the battery capacity represented with amperehour (Ah), and
z_{i}[k] is measurement electric current
z_{i}[k]=i [k]+n_{i}[k] (80)
It is by with standard deviation (s.d.) σ_{i}Zero mean white noise n_{i}[k] is damaged.(79) process noise in
(80) measurement noise in is related, such as
w_{s}[k]= c_{h}Δn_{i}[k] (81)
And for zero mean, and s.d. is：
σ_{s}=c_{h}Δσ_{i} (82)
Wherein Coulomb meter number system number is
Here, η be depending on battery charging or discharge constant, for example,
And Δ is (constant) sampling interval.
Following discussion is directed to use with the online battery capacity estimation of recurrence least square (RLS).Estimation SOC can be based on voltage
And current measurement value.Two continuous SOC value x_{s}[k] and x_{s}[k+1] is written as with its estimate：
Wherein evaluated errorWithThere is zero mean and variance P respectively_{s}[k  k] and P_{s}[k+1
k+1].Covariance between two continuous evaluated errors is：
Wherein G [k+1] is scalar Kalman gain, and H [k+1] is the scalar linearisation observation model at time k+1.
Now, write again in the form of following (80)：
(84) and (85) substitution (87) is obtained：
Wherein,
And differential error provide it is as follows：
For with zero mean, and variance is as follows：
Wherein S [k+1] is the new breath of Kalman filterCovariance.By considering L_{c}Sample batch,
(88) following form can be write into the form of vectors：
Wherein,
κ is Mission Number,
L_{c}For batch length,
AndFor the white Gaussian noise vector with following covariance：
It is L_{c}×L_{c}Diagonal matrix, its nth diagonal element provide as follows：
Now, battery capacity LS estimations reciprocal provide as follows：
And the variance of LS capacity estimation reciprocal is：
It is new a collection of when obtainingPair when, LS estimation can recurrence renewal it is as follows：
WhereinFor the L for capacity estimation_{c}×L_{c}Information matrix, and λ are Attenuation Memory Recursive constant.It should be noted that
, in (92)By known noisy measurement current value structure, and abovementioned LS and RLS methods of estimation are assumedIt has been
It is complete known.For actual solution, it is considered asIn uncertainty.Next, describe based on overall minimum
Two multiply the method for (TLS) optimization, which solveIn error.
Following discussion is directed to use with the online battery capacity estimation of adaptive total least square (TLS).In this part,
Online capacity estimation method is established based on TLS, it is assumed in (92)WithIn exist uncertainty.Structure is following
Augmentation observing matrix：
The information matrix related to augmentation observing matrix be：
Write in the form of followingFeature decomposition：
Wherein,
Λ^{κ}For by diagonal 2 × 2 matrix from the nonnegative characteristic value for being up to minimum arrangement, i.e. Λ^{κ}(1,1) represent maximum special
Value indicative, and Λ^{κ}(2,2) minimal eigenvalue is represented.
2 × 2 matrixesEach column have that character pair is vectorial, i.e. first rowFor corresponding to maximum feature
The characteristic vector of value, and secondary seriesFor the characteristic vector corresponding to minimal eigenvalue.
Then battery capacity TLS estimations reciprocal pass throughThe ratio of component provides, i.e.,
WhereinForThe ith element, andFor(i, j) element.(105) derivation show as
Under.
For smooth estimation, the information matrix in (103) can use Attenuation Memory Recursive to update, as follows：
Now, it is based on [85], TLS evaluated errors covariance (approximation)：
WhereinFor H^{κ}The ith row, M H^{κ}In line number, and
Following discussion is related to the battery capacity estimation based on opencircuit voltage (OCV).For given standing voltage z_{v}[k],
Corresponding SOC estimationsCan be by (33) inverted acquisition.Due to the hysteresis in battery, SOC estimationsWill
Different from actual SOC x_{s}[k], obtain OCV and search errorOCV search error will be always during electric discharge it is negative and
It is always just during charging.The opencircuit voltage (OCV) of battery can be written as SOC nonlinear function, such as
Wherein can be by gathering the voltage and current measured value for battery slowly charge and then discharging and obtaining, come to being
Number K_{0},K_{1},K_{2},K_{3},K_{4},K_{5},K_{6}And K_{7}Estimated offline.No matter battery whether sufficient standing, the OCVSOC characteristics of gained are bent
Line can be used in obtaining SOC measured value.For given standing terminal voltage (it is also opencircuit voltage) z_{v}The battery of [k]
SOC is written as：
It OCVSOC can be used to characterize to be calculated by calculating the inverse of (109).Have multiple for calculating nonlinear function
Method reciprocal, such as Newton method and binary chop.This can be described as the SOC estimations searched based on OCV.(110) SOC in estimates
Meter is damaged as follows by lagging voltage：
Wherein OCV searches errorCaused by the hysteresis effect in OCV.It should be noted that when battery is discharging
Process is changed into standing at time k, and OCV searches errorIt should be negative.Similarly, when battery charging process after when
Between be changed into standing at k, OCV searches errorTo be always just.However, the size of error will change with hysteresis size
Become, it is size of current, SOC and the function of time before standing.Now, write again in the form of following (79)：
x_{s}[k+1]=x_{s}[k]+c_{h}Δz_{i}[k]+w_{s}[k] (112)
x_{s}[k+2]=x_{s}[k+1]+c_{h}Δ_{k+1}z_{i}[k+1]+w_{s}[k+1] (113)
·
·
·
x_{s}[k+N]=x_{s}[k+N1]+c_{h}Δ_{k+N1}z_{i}[k+N1]+w_{s}[k+N1] (114)
By being separately summed (112) to (114) on both sides, following result is obtained：
Wherein,
For with standard deviationZero mean.
Stood assuming that battery is in time k and k+N, then (115) can be written as：
Wherein,
It should be noted that no matter OCV searches errorSign deviation battery mode ∈ (charging, electric discharge } this
One is true, " differential error "(defined in (119)) can be positive or negative.By considering a large amount of differential errors, it is assumed that
It is approximately white.Assuming that the differential of kth batchRespectively in first group of standing pointIt is quiet with second group
Put a littleBetween gather, and provide as follows：
Wherein,
Now, it can be seen that (120) have with (92) identical form, whereinWithReplace respectively
WithSo as to which the capacity estimation based on RLS and TLS can be derived for the observation based on OCV, following institute
Show.RLS and the TLS estimation of capacity based on OCV are expressed asWithIt should be noted that given be interspersed with
The given N of electric discharge_{r}The static condition of quantity, N can be carried out_{r}(N_{r} 1)/2 differential is observed.For example, for N_{r}=4, it is assumed that battery exists
Time point t_{1},t_{2},t_{3}And t_{4}It is in static condition.
It is related to below by merging the capacity estimation carried out.In this part, describe the TLS for merging capacity and estimate
The exemplary specific implementation of value.In this part, for the capacity estimation value based on TLS, establish and derive.These derivations can also answer
For merging the capacity estimation value based on RLS.
Online capacity estimation valueIt is measured caused by the error in electric currentThe uncertainty of (referring to (92))
Caused by the error in SOC track algorithmsUncertain damage.Similarly, the capacity estimation value based on OCVIt is measured caused by the error in electric currentThe uncertainty and OCV of (referring to (120)) search differential error institute
Caused byUncertain damage.It is assumed that online capacity estimation value e_{t}The error of [κ] and the capacity estimation value searched based on OCV
e_{to}The error of [κ] is uncorrelated.Based on these it is assumed that capacity fusion becomes the fusion of two independent flight paths.
First, it should be noted that capacity estimate reciprocal, such as capacity estimation valueWithRespectively
1/C_{batt}Estimate.Correspondingly, respective evaluated error covarianceWithAlso correspond to capacity estimation reciprocal
Value.Based on Taylor series expansion, the desired value of the dynamic capacity estimate based on TLS and corresponding estimation error variance are approximately：
WhereinFor the C based on dynamic data_{batt}Estimate, and R_{TLS}[κ] is estimation error variance.By following
Identical program, the capacity estimation value C based on OCV can be obtained_{TO}[κ] and corresponding evaluated error covariance R_{TO}[κ].Now, it is false
It is stochastic variable to determine battery capacity, and it undergoes following slowly varying WienerHopf equation：
x_{c}[κ+1]=x_{c}[κ]+w_{c}[κ] (126)
Wherein w_{c}[κ] is assumed to have variance Q_{c}The zero mean white Gaussian noise of [κ].Capacity estimation valueWithIt is adapted to following observation model：
z_{c}[κ]=x_{c}[κ]+n_{c}[κ] (127)
Wherein,
κ ' and κ " is according to the time index of the latest estimated value of corresponding algorithm (being respectively TLS and TO), and n_{c}[κ] is false
It is set to the zero mean white noise with following variance：
Now, new measured value no matter when is receivedWherein κ '=κ or κ ' '=κ, melts
The capacity estimation value of conjunction obtains as follows：
WhereinFor the previous renewal of capacity estimation value, and P_{c}[κ 1  κ 1] it is previous estimation
Error variance, it is updated to：
Abovementioned fusion method can be similarly used for merging the capacity estimation value based on RLS.
It is related to the derivation of capacity estimation error covariance below.In this part, differential error in (90) is derived
Covariance.For convenience's sake, differential error (90) is rewritten as following form
Purpose is to calculate variance：
According to following form writing process equation (79)：
x_{s}[k+1]=x_{s}[k]+c_{h}Δz_{i}[k]+w_{s}[k](134)
WhereinFor x_{s}The Kalman filter estimate of [k+1], ν [k+1] is that wave filter newly ceases, and G
[k+1] is kalman gain.(134) difference between (135) is：
It can be rearranged as following form：
So as to,
Wherein,
S [k+1] is new breath covariance.
The following describe the replacement or second method for confirming abovementioned derivation.Deploy (132)：
Wherein,
E_{1}=P_{s}[kk] (139)
E_{2}=P_{s}[k+1k+1] (140)
E_{5}=0 (143)
The enclosed for being related to total least square (TLS) capacity estimation value below derives.By 2 × 2 matrixesWrite into：
A characteristic value meets
 A λ I =0 (147)
It is reduced to
Wherein λ_{1}For eigenvalue of maximum and λ_{2}For minimal eigenvalue.Corresponding to λ_{2}Characteristic value meet
Wherein
For example,
And
It is related to the conversion of capacity estimation reciprocal below.Exemplary specific implementation includes estimating based on estimate reciprocal and inverse
The method that error variance draws capacity estimation value and estimation error variance.It is simple for capacity estimation value reciprocal and error variance assignment
Variable, for example,
Definition：
Our purpose be find E { y } andApproximation.
It is related to the desired value for determining y below.Second order Taylor series approximation value is by given below：
E { y } Twoorder approximation value is by given below：
It is related to the variance for the desired value for determining y below.In actual value x_{0}F (x) is expanded into first order Taylor series around
Y=f (x)=f (x_{0})+f'(x_{0})(xx_{0}) (162)
Y variance is by given below：
Now, the desired value of capacity estimation value and its estimation error variance are by given below：
Present disclosure tracks followed by state of charge (SOC), and it refers to following symbol.
a[k]^{T}Voltage drop model
Amended voltage drop model for SOC tracking
BFG battery meters
B voltage drop model parameters
Amended voltage drop model parameter for SOC tracking
C_{batt}Battery capacity
c_{h}Coulomb meter number system number
G [k+1] SOC tracking filter gains
The lagging voltage of h [k] battery
I [k] flows through the electric current of battery
i_{1}[k] flows through R_{1}Electric current
i_{2}[k] flows through R_{2}Electric current
K_{i}OCV parameters：K_{0},K_{1},K_{2},K_{3},K_{4},K_{5},K_{6} K_{7}
n_{D}[k] voltage drop observation noise
n_{i}Noise in [k] measurement electric current
n_{v}Noise in [k] measurement voltage
Noise in measurement model
OCV opencircuit voltages
P_{s}[k+1  k] SOC estimation error variances
P_{s}[k+1  k+1] SOC estimation error variances
R_{0}The internal resistance of cell of series connection
R_{1} R_{1}C_{1}The internal resistance of cell in circuit
R_{2} R_{2}C_{2}The internal resistance of cell in circuit
The autocorrelation of voltage drop observation noise
SOC state of charge
S [k] state of charge (SOC)
Cross correlations of the U [k] between measurement noise and process noise
The voltage at v [k] battery terminals both ends
V_{0}(s [k]) opencircuit voltage (OCV)
x_{h}[k] corresponds to h [k] state component
Corresponding to i_{1}The state component of [k]
Corresponding to i_{2}The state component of [k]
x_{s}[k] corresponds to s [k] state component
The SOC estimation of prediction
Update SOC estimation
The state of x [k] vector form
z_{i}[k] measures electric current
z_{v}[k] measures voltage
α_{i}(k) the current attenuation coefficient in RC circuits,
Time difference between Δ neighboring samples
SOC tracking errors
η_{c}Charge efficiency
η_{d}Discharging efficiency
In the exemplary specific implementation, electrochemistry is tracked based on instantaneous terminal voltage, load current and measured temperature
The state of charge (SOC) of energy storage device (battery).SOC track algorithms use abovementioned model parameter estimation and battery capacity estimation
Understand.Exemplary SOC tracking will be late by the error being modeled as in opencircuit voltage (OCV) and using parameter Estimation and SOC tracking skills
The combination of art compensates to it.This, which is eliminated, will be late by offline modeling as SOC and the needs of the function of load current.The example
Property model cause for SOC tracking depression of order (e.g., single status) filtering, no matter wherein the complexity level of battery equivalent model
How, it need not track supplementary variable.Identify the presence of correlated noise and use it for improving SOC tracking.With routine " one
Model adaptation owns " unlike strategy, four different equivalent models of battery are identified, these models represent representative cells fortune
Capable four unique patterns simultaneously establish the framework for seamless SOC tracking based on appropriate model.
It is related to including SOC with the typical reduced order state filtering method for combining (recurrence) estimation of (unnecessary) amount of other redundancies
Expensive matrix operation and the precision of SOC estimations is reduced in calculating.In the exemplary specific implementation, having used does not increase
The depression of order filtering of state space dimension, so as to the computational complexity for obtaining more preferable SOC precision and reducing.By will be late by modeling
For the error in OCV, the needs that hysteresis models are eliminated, and online filtering method is constantly tried to by adjusting SOC (to amendment
Value) carry out fill in a gap.So as to which hysteresis is modeled as timevarying biasing.Using noise whitening program, and derive amended state
Spatial model, to ensure that SOC track algorithms draw result as well as possible in least meansquare error meaning.Using battery not
With " pattern " tracking SOC.At least four different battery equivalent models are used to reflect very light load or static condition, constant electricity
Stream operation or low frequency loading (e.g., charging), dynamic load and heavy duty.Also identify four (somewhat) different dynamic equivalent moulds
Type is with these patterns of best match.The depression of order filtering method provided ensure that seamless SOC tracking, regardless of whether the mould of battery operation
Formula changes.
Following discussion is related to exemplary system models.Battery equivalent circuit model considered here is shown in figure 13a.
When battery, which is in, to be stood, V_{0}(s [k]) is the OCV of battery.OCV uniquely depends on the SOC, s [k] of battery.Lived when battery is in
During jump state, such as when current active be present, the behavior of battery is represented by dynamic equivalent circuit, the dynamic equivalent circuit
By lag element h [k], series resistance R_{0}And two parallel RC circuits, (R being connected in series_{1},C_{1}) and (R_{2},C_{2}) composition.It is discrete
Time uses [k] instruction.
The battery equivalent circuit model that this part is considered is shown in figure 13a.With regard to the element in battery equivalent circuit
The terminal voltage v [k] of speech is by given below：
V [k]=V_{0}(s[k])+i[k]R_{0}+i_{1}[k]R_{1}+i_{2}[k]R_{2}+h[k] (166)
Wherein V_{0}(s [k]) represents the opencircuit voltage (with voltmeter) of battery at time k, and it is write as at time k here
SOC function, s [k] ∈ [0,1]；H [k] illustrates the hysteresis in cell voltage；i_{1}[k] and i_{2}[k] is respectively to flow through R_{1}And R_{2}'s
Electric current.
Some nonlinear representations be present, it makes the function that OCV is similar to SOC.In the exemplary specific implementation, use
In the multinomial loglinear model reciprocal that OCV is represented with SOC：
Wherein K_{0},K_{1},K_{2},K_{3},K_{4},K_{5},K_{6}And K_{7}Offline estimation can be characterized by OCVSOC.SOC transient change can book
Write as following form (introduce under x and be marked with instruction state component)：
Wherein i [k] is in terms of amperage；
c_{h}=η/3600C_{batt} (169)
For with ampere^{1}Second^{1}The Coulomb meter number system number of meter, C_{batt}For the battery capacity in terms of amperehour (Ah), Δ be with
The sampling interval of second meter, and η be constant, and it is charging or electric discharge depending on battery, for example,
It should be noted that (168) draw the instantaneous SOC of battery.Calculate SOC the technology be referred to as coulomb count and/
Or " the SOC " of prediction.Coulomb count assume solution initial charge state and completely understand battery capacity so as to consider transfer certainly/
The coulomb amount for being transferred into battery calculates residual charge state afterwards.Coulomb counting error includes the understanding of (1) to initial SOC not
Certainty；(2) uncertainty of the understanding to battery capacity；And (3) because measurement electric current error and because of timing oscillator
The error of coulomb is measured caused by the error of the time difference caused by inaccuracy/drift.
Electric current i [k] is measured and error easily occurs in current measurement value.Will measurement electric current z_{i}[k] is write as：
z_{i}[k]=i [k]+n_{i}[k] (171)
Wherein n_{i}[k] is current measurement noise, and it is considered to have white zero mean and with known standard deviation
(s.d.)σ_{i}..Can be by using z as follows_{i}[k] replaces i [k] and carrys out rewrites status equation (168)：
x_{s}[k+1]=x_{s}[k]+c_{h}Δz_{i}[k]c_{h}Δn_{i}[k] (172)
It can as follows write and flow through resistor R_{1}And R_{2}Electric current：
Wherein
By using measurement electric current z_{i}[k] replaces i [k], can rewrite the electric current in (172) and (173) as follows：
Lagging voltage h [k] is the load current of battery and SOC nonlinear function.Delay Process can be write as：
Wherein n_{h}[k] is the process noise of lag model, it is assumed that it is zero mean white Gaussian noise and has s.d. σ_{h}。
(166) voltage in for measurement amount and measures voltage z_{v}Easily there is error in [k].Measurement voltage is write as：
z_{v}[k]=v [k]+n_{v}[k]=V_{0}(s[k])+i[k]R_{0}+i_{1}[k]R_{1}+i_{2}[k]R_{2}+h[k]+n_{v}[k] (179)
Wherein n_{v}[k] is assumed to have zero mean and s.d. σ_{v}White Gaussian noise.Now, by by (171),
(172), (173) and (178) are substituted into (179), derive following measurement model：
Wherein,
Now, instantaneous voltage and current measurement value z are provided_{v}[k] and z_{i}[k], BFG purpose is the instantaneous of tracking battery
SOCx_{s}[k].." unnecessary " variable in observation model (180)And x_{h}There are problems that of [k] causes Combined estimator,
That is SOC and these variables must Combined estimators.This can be by forming the multidimensional mistake of vector form as shown in (183)(189)
Journey and measurement model and/or by application Bayes's nonlinear filtering technique recursively to estimate to realize：
All measured values until time k are provided, { [0], [1], [2] ..., [k] }, wherein by (171) and (180) group
Into.This can pass through nonlinear filtering technique known to application (such as extended Kalman filter (EKF), Unscented kalman filtering
Device (UKF) or particle filter) effectively carry out.Can be in the form of vectors by process equation (172), (176), (177) and (178)
Write into：
Or, it is abbreviated as：
X [k+1]=F_{k}x[k]+u[k]+Γ_{L}w[k] (184)
Wherein,
For with the white noise of zero mean and following covariance vector：
Correspondingly, measuring equation (180) can write into：
Wherein,
And the n with zero mean and following s.d._{z}[k] noise vector.
It is additionally noted that statespace representation form (183)(189) involve a need to pass through system identification technique
Come the following model parameter estimated, including battery capacity：C_{batt}, opencircuit voltage model parameter：K_{0},K_{1},K_{2},K_{3},K_{4},K_{5},K_{6},K_{7},
Dynamic equivalent circuit model parameter：R_{0},R_{1},C_{1},R_{2},C_{2}, it is charged and discharged efficiency：η_{c},η_{d}, processnoise variance：And
Measurement noise variance
Requirement to all model parameter estimations makes SOC tracking problems have more challenge.In addition, the chemical property meeting of battery
Change because of temperature change, aging and use pattern, therefore these model parameters can time to time change.So as to be pushed away with the time
Move, it is necessary to reevaluate model parameter.
In exemplary specific implementation, it is assumed that the OCV parameters K of battery_{0},K_{1},…,K_{7}Estimate offline.Described above is
Estimate the program of these parameters.It is assumed that voltage and current error to standard deviation, i.e., respectively σ_{v}And σ_{i}, can be designed to from measuring circuit
Arrive.It is assumed that it is charged and discharged efficiency, i.e., respectively η_{c}And η_{d}, known by calibration.So as to, it is therefore an objective to by assuming electrolytic cell
Capacity C_{batt}With the electrical equivalent model parameter R of battery_{0},R_{1},R_{2},C_{1}And C_{2}To establish online SOC track algorithms.
Discussion below is related to SOC tracking.The purpose of depression of order filtering is tracking x_{s}[k], while redundant variables need not be trackedAnd x_{h}[k].First, rewritten (172) according to following form：
x_{s}[k+1]=x_{s}[k]+c_{h}Δz_{i}[k]+w_{s}[k] (190)
Wherein,
W_{s}[k]= c_{h}Δn_{i}[k] (191)
For process noise, it is the white noise with following s.d.：
σ_{s}=c_{h}Δσ_{i} (192)
Now, voltage measuring value (180) is rewritten as：
z_{v}[k]=V_{0}(x_{s}[k])+a[k]^{T}b+n_{D}[k] (193) [4]
Wherein,
a[k]^{T}B=[v_{D}[kl]v_{D}[k2]z_{i}[k]z_{i}[k1]z_{i}[k2]1] (194)
And voltage drop is by being given below：
v_{D}[k]=z_{v}[k]V_{0}(x_{s}[k]) (195)
Wherein b is parameter vector to be estimated, and n_{D}[k] is measurement noise.It should be noted that [k] in (194)
With voltage drop v_{D}[k1] and v_{D}[k2] is defined.Described above is the estimation parameter b based on voltage drop observation model.By estimation
Parameter is derived as according to the parameter of the battery equivalent model in Figure 13 A：
B (3)=R_{o} (198)
Measurement noise n_{D}[k] is zero mean and has the autocorrelation by being given below
Next, voltage drop is described in the meaning for estimating the parameter b in (193).Use (193), voltage drop (195) can
Write as：
v_{D}[k]=a [k]^{T}b+n_{D}[k] (203)
Given voltage drop observation, abovementioned model (203) can be used for Linear Estimation b.However, in order to obtain the electricity as observation
Pressure drop, the predicted value that SOC can be used areOr the SOC estimation after renewal isSOCx_{s}The understanding of [k],
For example,
Describe below and how to be predictedAfter renewal(respectively referring to
(209) and (215)).BFG existing method uses voltage and current observation z_{v}[k] and z_{i}[k] carries out Model Identification and SOC
Tracking.Consider conventional voltage observation model (180).x_{h}Item in [k] represents lagging voltage, and it is electricity as shown in (178)
Flow i [k], SOCx_{s}[k] and time k. function.For example, when battery experience 1A load (this is heavy duty in Mobile solution)
During the several seconds, compared with when load continuous 30 minutes for 1A situation, caused by the amplitude that lags it is smaller.In addition, the amplitude of hysteresis
Also it is SOC function in the time.
Due to observing (180) using for the voltage between the battery terminal of Model Identification, it is also necessary to lagging x_{h}[k] is modeled
And model parameter must be estimated.The model of the hysteresis represented using SOC, electric current and time is complete to be nonlinear, and not yet
Understand.Attempt to model hysteresis and another shortcoming of estimation is that it make it that ontime model identification is hardly possible.Due to stagnant
It is SOC function afterwards, Model Identification needs the data across whole SOC scopes.This there may come a time when it is impossible, because some
Using may be never by battery from completely using sky.Because hysteresis or electric current function, Model Identification need across should
Use data for the possibility load current of various duration.So as to which complete hysteresis modeling and Model Identification become not
Reality.
It is also important that, it is noted that model parameter is estimated offline using Sample Cell, then these parameters are used for electricity
Metering may be unsatisfactory；Some battery parameters have been notified based on use pattern and changed.Exemplary embodiment passes through introducing
Abovementioned voltage drop model avoids hysteresis modeling.Voltage drop v_{D}[k] represents internal cell model element R_{0},R_{1},R_{2}And x_{h}[k] two
The voltage at end.Item x_{h}[k] is deliberately introduced to consider to be used for derive voltage drop " measured value "PredictionIn error.x_{h}[k] is referred to alternatively as " instantaneous lagging ", and it should pass through adjustment according to exemplary embodiment
SOC estimationTo correct to zero.As described above for described in Fig. 7, the use of voltage drop model can be used for eliminating hysteresis effect
Should.Existing SOC is understood for calculating voltage drop.Estimating in a buffer and for parameter b is collected in a collection of passing voltage drop
Meter.(determined by such as in model estimation module or block 710)Nonzero value instruction instantaneous lagging presence, this
Mean SOC evaluated errors be present.SOC track algorithms are designed in estimationFor nonzero whenever, (SOC with
In track block 715) amendment SOC.
OCVSOC models (167) represent OCVSOC relations.It is assumed that in voltage drop (195)(201)
InEstimate will beHowever,Mean to be used to calculate voltage drop observation v_{D}The SOC of [k] estimates
Error be present in evaluation.So as to which SOC track algorithms need corresponding adjustmentThis is by using following amended observation mould
Type substitutes (193) to realize.
Wherein,
By removing a [k] respectively^{T}Obtained with last element in b.In other words, hysteresis item is removed.Retouch below
The meaning of amended observation model is stated.In addition, the process noise w in (190)_{s}Measurement noise n in [k] and (205)_{D}[k]
Between following covariance be present.
The estimate of given state of chargeWith related variance P_{s}[k  k], following EKF recurrence (referring to Fig. 8) uses
Voltage and current measured value z_{v}[k+1],z_{i}[k],z_{i}[k+1] is drawnRenewal after SOC estimation and its
Related variance P_{s}[k+1k+1]..These steps also ensure SOC estimation by optimum apjustment to consider the covariance of (208).
Filtering recurrence is made up of following：
Wherein c_{h}[k] andIt is the latest estimated value of Coulomb meter number system number and model parameter vector respectively.It should describe to make
With in statespace model (190)(205)WithCarry out the importance of SOC tracking.Hysteresis can be considered as OCV
Error in SOC indicatrixes.It is likely difficult to modeling and accurate estimation lags, because it can becomes with previous electric current and SOC
Change (referring to (178)).However, true OCVSOC relations can be estimated.In fact, the V in (205)_{0}(x_{s}[k]) it is based on true OCV
SOC models.For example it is assumed that the hysteresis of estimation isThis means wave filter, " OCV " of perception is true with battery
OCV differs 10mV.For BFG algorithms, the OCV of perception, V_{0}(x_{s}[k]), with SOC estimationDirectly (and monotonously) phase
Close.In other words, if the OCV of wave filter is different from actual OCV, then wave filter estimateAlso different from battery
True SOC.So as to when wave filter finds that it predicts terminal voltage in (212)Decline 10mV, it can be adjusted in (215)
Its whole SOC estimationSo that " the OCV errors of perception " (or hysteresis H of estimation) (little by little) is adjusted to zero.From
And the good instruction of the normal operation of the method proposed is estimationAll the time close to zero.
In the absence of the reliable apparatus and method for verifying electric quantity metering algorithm in desired manner.Voltameter is assessed using simulation
It is infeasible, in default of can for example allow simulated battery dynamically reliable mathematical modeling.For example, the selfcorrecting positive model of enhancing
The influence of cell degradation can not be considered.Because the uncertainty in state of charge, battery capacity and the true value of internal resistance (all may be used
For the amount constantly drifted about), may be difficult to verify voltameter using single measurement or verification method.Need to calculate multiple checking degree
Measure to understand the overall picture of voltameter precision.
Present disclosure is followed by benchmark test, and it is since measurement.In the exemplary specific implementation, use is described
In multiple reference test methods of the electric quantity metering algorithm of checking electrochemical energy storage device (battery).Relatively accurate electric quantity metering
(FG) cycle life of battery can be extended.The embodiment also describes accurate and objective voltameter evaluation scheme.This
Measurement described in text can be used for measuring FG precision in many aspects and returning may indicate that at least one of voltameter overall performance
Numeral.Benchmark test as described herein can be applied to a variety of electric quantity metering algorithms.E.g., including in this specific embodiment
Details can be with entitled " Methods and Apparatus Related to Tracking Battery State of
Charge:The A Reduced Order Filtering Approach (method and apparatus related to tracking battery state of charge：
Depression of order filtering method) " description described in any concept combine.
Benchmark test described in the embodiment can for example, by be calculated as follows in three kinds of measurements of definition one
Person or more persons are carried out：
First Exemplary metrology is coulomb counting error.With reference to the battery capacity to experiment and the state of charge of starting
(SOC) understanding of point, coulomb counting methods and/or equipment can provide the accurate estimation to battery state of charge.Based on Coulomb meter
Several SOC estimations and voltameter can be used as benchmark survey through the error (such as root mean square (RMS)) between SOC after a while estimates
First measurement of examination.Error between SOC based on FG and the SOC based on coulomb counting might mean that the FG phases with being verified
One or more problems of pass：
 the model characterized for opencircuit voltage state of charge (OCVSOC) may be not accurate enough (assuming that FG uses OCV
SOC is characterized)
 the battery capacity estimation carried out by FG may be inaccurate
 dynamic equivalent circuit model may have problem in terms of for the selection of FG model and parameter Estimation scheme.
Second Exemplary metrology is OCVSOC errors.(can be used what one or more methods and/or equipment were carried out) battery
OCVSOC characterize can provide for search SOC search program.So as to by making battery be in (or at least part) completely
Static condition and the voltage by measuring battery, can by voltameter preset time SOC estimation can be characterized with OCVSOC into
Row compares to obtain error.OCVSOC errors may indicate that one or more problems with of voltameter：
 the dynamic model for battery equivalent model may be invalid
 minimum OCVSOC errors may indicate that the actual dynamic property of dynamic model and battery used is well matched with.
3rd Exemplary metrology reaches voltage time (TTV) error for prediction.Provide constant load/charging current, voltameter
(can using one or more methods and/or equipment), prediction reaches a certain voltage spent time (TTV).Shutin time (TTS) and
Fully charged time (TTF) can be the special circumstances of TTV estimations.Error in TTV estimations can reach the actual electricity that is considered
Calculated after pressure.The TTV errors may indicate that it is related to the voltameter being evaluated it is following one or more：
The impedance estimation precision ofbattery,
The battery capacity estimation precision ofvoltameter,
Understanding (such as information) ofvoltameter to battery SOC,
The precision thatOCVSOC is characterized.
Battery can show different qualities in response to temperature change.For example, the impedance of battery can it is higher at low temperature (and
So as to which available horsepower may be relatively low).In response to the load under relatively low SOC, compared with the identical load of higher SOC level,
OCV rates of change may be larger and nonlinearity.Highquality voltameter can have in the range of wide in range temperature and SOC level
The ability of operational excellence.Benchmark test as described herein can be configured to ensure that during Performance Evaluation by these key elements extremely
Some are included in test less.
Following discussion is related to the measurement characterized based on OCVSOC.The state of charge of battery can uniquely with its opencircuit voltage
(OCV) it is relevant.Figure 14 illustrates for curve map for one example of such relation.
A variety of methods can be used for obtaining OCV characterize datas.A kind of illustrative methods are summarized as follows：
1) since battery that is fully charged, standing completely
2) its opencircuit voltage V is recorded_{BAT}=V_{full}
3) i=1 is set
4) OCV (i)=V is recorded_{BAT}
Record SOC (i)=1
5) i=i+1 is set
6) battery discharge is made up to Δ T duration using constant current I
7) make battery sufficient standing (such as at least 2 hours)
8) battery terminal voltage, V are measured_{BAT}
9) OCV (i)=V is recorded_{BAT}
Calculate SOC (i)=SOC (i1)+c_{h}I (i) Δ T, wherein c_{h}=η/(3600C_{batt}), η is instruction charge/discharge effect
The constant of rate, C_{batt}Battery capacity and I (i) to be represented with amperehour (Ah) are to flow into the electric current of battery.
10) repeat step 5 to 9 closes voltage VSD until OCV (i) reaches battery.
Now, { OCV (i) is used；SOC (i) } it is right, SOC ∈ [0 can be directed to；1] OCV is obtained to characterize.
Note：
1) OCVSOC, which is characterized, to change because temperature is different.(if drying method can be used to calculate in certain use range
OCV at any temperature is characterized).
2) in some specific implementations, battery capacity C_{batt}Being available from manufacturer's tables of data or its can estimate.
3) OCVSOC signs can be with unchanged, regardless of whether the service life of battery.
4) characterized using abovementioned OCVSOC, the OCV of given SOC s battery can be calculated, write as υ=OCV (s).
5) characterized, can be calculated for given standing terminal voltage υ using abovementioned OCVSOC_{r}Battery SOC, write as s=
OCV^{1}(υ_{r}).If the SOC estimation of certain electric quantity metering algorithm at time k is reported asThen corresponding error can
It is calculated as
Wherein υ_{r}[k] is the terminal voltage (after battery standing) at time k.
The checking characterized based on OCVSOC can be used to calculate the OCV errors (217) of whole temperature and/or SOC region.
Checking in of a relatively high SOC region can be by being carried out as follows：First since full rechargeable battery and apply timevarying
Load up to one time for being enough to consume 1/2 capacity that (about) is less than tested battery.Similarly, testing in low SOC region
Card can be by being carried out as follows：First since the battery after full rechargeable battery or high SOC checkings, and apply and be enough battery band
To the dynamic load of relatively low SOC region.
Average OCVSOC errors (in terms of %) can be calculated as
Wherein ∈_{OCV}(s_{L}, T_{i}) represent at low SOC region and in temperature T_{i}Under the error that calculates.It is specific real at some
Shi Zhong,Lower, FG algorithms are better.
Following discussion is related to the measurement based on relative coulomb counting error.Battery SOC can pass through coulomb as follows
(CC) is counted to calculate：
It is assumed that battery capacity C_{batt}With sufficiently exact startingIt is known.So as to Coulomb meter
The related FG errors of number may be defined as (in terms of %)：
Wherein T is the duration (in seconds) for performing validation test.
1) in some specific implementations, some in battery measuring equipment and/or method may include that coulomb counting is used as it
Part.However, abovementioned measurement still can be considered verification tool, this is due to it has been assumed that understanding of battery capacity and checking
BeginAnd FG methods may not assume that the understanding.
2) can be used for by the way that battery is discharged into empty (or basic overhead) completely from full (or substantially full) to preestimate
CheckingBattery capacity.Or validation test can be carried out from full (or substantially full) to sky (or basic overhead), and
And it can be updated with the battery capacity Cbatt of latest estimated, can be in this mode in some specific implementations
Hysteresis and relaxation factor are considered in battery capacity estimation.In some specific implementations, FG algorithms can be forbidden so to do.
3) in some specific implementations, the temperature for the battery just assessed is in whole (e.g., substantially entirely) verification process
It can keep constant.
Following discussion is related to based on the measurement up to voltage time (TTV).If the SOC of the electricity calculating method at time k estimates
Evaluation is s_{FG}[k], then its reach the time of voltage υ needs can book be written as form：
Wherein electric current I (I in charging process>0 and discharge process in I<0) keep constant (or substantial constant) until up to
To voltage υ.
Once reach terminal voltage υ in the process of running, you can record reaches the real time during voltage.When specific
Between when reaching voltage υ, following TTV checkings measurement can be calculated
Wherein T_{v}[i]=Ti are the real times for reaching voltage υ needs from time i.∈_{TTV}Value can be in minutes.One
In a little specific implementations, metric can be calculated (in terms of %)：
The measurement of combination may be defined as：
WhereinIn terms of %.In some specific implementations, the value is lower, and voltameter is better.
In some specific implementations, benchmark may include to use (e.g., allusion quotation for evaluated battery loading reflection battery
Type use) one or more different current loadings, and record voltameter report SOC and TTV readings.This method may include
These steps are repeated under different temperatures, until for example Table I, II and III are filled.
In some specific implementations, simulation and actual loading curve can be used in verification process.Fictitious load curve
The advantages of be the amount (e.g., correct amount) that can calculate the coulomb obtained from battery, so as to avoid by sampling and current sense institute
One or more errors of cause.This can be based on such hypothesis：Load simulating device may not introduce one or more notable
Error.Various actual loading curves and fictitious load curve can be created.
Actual loading curve：Can be used for example smart phone as load, come create actual loading curve (such as Figure 15 A and
Shown in 15B).When load is connected to the battery being verified, following activity can perform：Call (15 minutes), web punchings
Wave, email is read, game etc. (20 minutes) is played, sends short messages (10 message), music is listened using loudspeaker or sees (30 points of video
Clock video), it is standbyto enable cellular radio electrical communication base station (1 hour).
Load curve shown in Figure 15 A and 15B shows such scene, wherein three kinds can be calculated in single test
(the input of each during e.g., 1515) OCV measurements 1505, TTV measure 1510 and CC measurements of type measurement.The experiment is from complete
Rechargeable battery starts, and dynamic applies about 3 hours 15 minutes again using load.Battery is in leisure state 2 hours afterwards.5
Hoursymbols, which provide, calculates OCVSOC error metrics ∈_{OCV}(s_{H}, T_{i}) chance.Constant current when experiment closes to an end
Load allows to calculate ∈_{TTV}(s_{L}, T_{i}) coulomb count metric ∈ can be calculated according to whole data_{CC}(T_{i})。
The load curve shown in Figure 15 A and 15B can be used to calculate temperature T_{i}Under metric：
OCVOSC error metrics ∈ at high SOC region_{OCV}(s_{H}, T_{i})
TTC measurements ∈ at low SOC region_{TTV}(s_{L}, T_{i})
Coulomb count metric ∈_{CC}(T_{i})
Fictitious load curve：Short duration Δ can be used_{s}The piecewise constant current loading I of interior different amplitudes_{m}To create
Fictitious load curve.These segment loads can be mixed and be connected together, so as to obtain the fictitious load shown in Figure 16 A and 16B
Curve.It note that fictitious load can occur between about 3.5 hours to 6.5 hours of test.Example can be used in the load curve
Such as Δ_{s}=2 seconds and I_{m}={ 40,120,130,160,300,400,440,520,600,640,800,880 } (unit：MA)
Kikusui programmable loads devices is simulated.
Fictitious load curve shown in Figure 16 A and 16B shows such scene, wherein can be calculated in single test
(the input of each during e.g., 1615) OCV measurements 1605, TTV measure 1610 and CC measurements of three types measurement.The experiment
Since full rechargeable battery, and apply constant 500mA and load about 1.5 hours.Battery is in leisure state 2 hours afterwards, so
Afterapplied dynamic load curve 3 hours.Mark within 15 minutes to provide again within 3 hours and calculate OCVSOC error metrics ∈_{OCV}(s_{H}, T_{i})
Chance.Constant current load when experiment closes to an end allows to calculate ∈_{TTV}(s_{L},T_{i}).Storehouse can be calculated according to whole data
Logical sequence count metric ∈_{CC}(T_{i})。
In some specific implementations, the fictitious load curve shown in Figure 16 A and 16B can be used to calculate temperature T_{j}Under under
Row measurement：
OCVOSC error metrics ∈ at high SOC region_{ocv}(s_{H}, T_{i})
TTC measurements ∈ at low SOC region_{TTV}(s_{L}, T_{i})
Coulomb count metric ∈_{CC}(T_{i})
Abovementioned example specific implementation describe SOC suitable for battery powdered device (e.g., portable mobile device) with
Track.The exemplary embodiment realizes linear method, and computationally inexpensive and effectiveness of performance is better than now the linear method
Some is used for ontime model and knows method for distinguishing.Describe the weighted leastsquares method for parameter Estimation.Parameter is described to estimate
It is attested in weight (being based on variance) and parameter Estimation in the LS methods of meter to significantly improve.For the different operation moulds of battery
The applicability of formula includes four different equivalent models that identification represents the battery of representative cells operational mode, and establishes seamless SOC
The framework of tracking.Methods described will be late by the error being modeled as in opencircuit voltage (OCV), will be late by being modeled as so as to eliminate
The needs of the function of SOC and load current.This method additionally aids from the SOC of mistake and initializes fast quickrecovery.
Abovementioned example specific implementation is described for battery capacity estimation to promote the feature of battery electric quantity metering progress.
Weighting recurrence least square (RLS) estimation of the capacity derived with accurate weight.The formula of weight can be based on SOC tracking errors
Covariance and current measurement errors standard deviation calculate.Describe the TLS methods for battery capacity realtime tracking.TLS estimates
Value with it is closed derive and available for by using Attenuation Memory Recursive renewal covariance matrix carry out ART network.It is electric based on standing
The technology for the adaptive capacity estimation that the OCV in pond is searched.The OCV in deriving is considered to search the source of error (hysteresis) and describe
The method that the adaptive capacity searched by OCV is estimated.Described based on capacity estimation value and evaluated error covariance by not
The method of the optimum fusion of the capacity estimation value obtained with method, the method proposed is carried out adaptive using Kalman filter
Answer optimum fusion.
Abovementioned example specific implementation describe SOC suitable for battery powdered device (e.g., portable mobile device) with
Track.For by the way that other nuisance parameter is stacked in state vector to estimate other nuisance parameter together with SOC
Routine techniques is computationally high and effectiveness of performance is low.In order to avoid these problems, exemplary embodiment describes depression of order filter
Wave pattern, for carrying out SOC tracking by new statespace model.Describe the state space with decorrelation noise model
Model.SOC tracking problems are related to two measurement amounts, i.e. voltage and current, and this allows for the state of SOC tracking problems and measurement is made an uproar
There is correlation between acoustic model.Describe and showed with the amended state space of uncorrelated state and measurement noise process
Form.Exemplary embodiment describes the different operational modes of battery, and identifies the battery for representing representative cells operational mode
At least four different equivalent models, and establish the framework of seamless SOC tracking.Exemplary embodiment describes a kind of method, the party
Method will be late by the error being modeled as in opencircuit voltage (OCV), so as to eliminate the function that will be late by being modeled as SOC and load current
Needs.This method additionally aids from the SOC of mistake and initializes fast quickrecovery.
Abovementioned example specific implementation describes the SOC realized by some strategies and tracked.First, built by minimum battery
Mould.The method proposed uniquely needs to carry out offline modeling to opencircuit voltage (OCV) characteristic of battery.Parameter needed for every other
Estimated by firm means.Due to the single set equipped with OCV parameters, the method proposed can perform at any temperature
SOC is tracked, without any other parameter.Second, voltage drop observation model.The voltage drop model of observation allow online SOC with
Track, without worrying that the lag element to battery models.This allows for proposed method and can obtain more preferable precision and sane
Property.3rd, estimated by stability parameter.Identify the effect of the correlated noise structure in the least square model for parameter Estimation
Should.For parameter estimation algorithm, this has just obtained obvious preferably precision and has enhanced robustness.4th, pass through battery capacity
Estimation.Total least square (TLS) method for capacity estimation proposed ensure that the excellent precision of capacity estimation.And
Finally, by using filtering, depression of order EKF methods consider noise process in statespace model correlation (be derived with
Tracked for SOC) and correlation filter is gone so that the error in SOC tracking minimizes using appropriate.
In a specific embodiment, the benchmark based at least three battery meter quantity algorithms for assessing measurement is described to survey
Method for testing.First assesses opencircuit voltage (OCV) sign that measurement can be based on battery.Second assesses measurement can the phase based on voltameter
To coulomb counting error, and the 3rd benchmark can reach the calculating of the time needed for specific voltage based on battery.Each checking degree
Amount may include to calculate some measurements at various SOC levels, different temperatures and/or voltage regime, such place.
Some SOC trackings include at least following weak point：(1) some models only consider resistance, are not suitable for dynamic
Load；(2) they carry out system identification using nonlinear method；(3) need to estimate for the initial parameter of method of model identification
Meter；(4) assume that single dynamic equivalent model represents all battery operation patterns；(5) importance of online capacity estimation is not solved；
(6) existing online battery capacity estimation technology is influenceed by SOC and parameter estimating error, i.e., they are built on the sand；(7) remove
Outside SOC, also using the online tracking of many amount of redundancys, (this causes to increase computational complexity and reduces SOC tracking essences for they
Degree)；(8) they need individually to model battery hysteresis, and it is that the function of SOC and load current (therefore is nothing that battery, which lags,
Limit model), it is only possible to carry out approximate modeling to hysteresis；(9) it is any in existing method not recognize the process and measurement
Correlation be present in noise process；And any one is not recognized due to temperature, aging, SOC and born in (10) existing method
The fact that change and single equivalent model in battery behavior caused by carrying change may not be adapted to all these conditions.
Therefore, specific implementation as described herein can have short design time (in a couple of days), can have comparatively faster algorithm
Convergence, and may have about in " real world " use condition 1% SOC and the precision of battery capacity report precision.
In some specific implementations, can not (or seldom) need to customize battery model or data, and may include to have relatively fast SOC with
The convergent adaptive learning algorithm of track.Some specific implementations may include automatic temperatureadjusting, service life and load compensation.
Some specific implementations can be based on such as decoupling of reducedorder EKF device, correlated measurement noise, online electric mould
Shape parameter estimates and real time capacity estimation.
Depression of order Kalman filter may include the accurate SOC estimations (tracking) for being related to common four different parameters of estimation：
SOC, the electric current for flowing through two different resistors in dynamic equivalent model and hysteresis, it is all these battery be in load/
It can change during charging.This is related to the complex matrix operation of commonly referred to as recursive filtering.The depression of order filtering method enters in this way
Simplification is gone：SOC is only estimated by recursive filtering program.Three other specifications are by mathematical operation by marginalisation.The one of gained
Individual or multiple SOC track algorithms are computationally feasible in voltameter SOC now.
Correlated measurement noise decoupling may include Kalman filter, its Kernelbased methods noise and the incoherent vacation of measurement noise
And if run.In voltameter application, intrinsic measurement noise can be coupled to SOC and voltage in depression of order EKF in current measurement
Both the measurement noise of variable and process noise.A kind of unique method is employed, this method is by electric current induced noise and karr
The process noise decoupling of graceful wave filter.
Online electrical model parameters estimation may include the dynamic estimation of model parameter (coefficient).The dynamic of model parameter (coefficient)
Estimation may include when it changes with SOC, changing currents with time load curve, temperature, chargedischarge cycles and/or the like
Estimation.EKF wave filters are applicable, and precondition is that the model parameter of the dynamic equivalent circuit of battery is known, however, waiting
Effect circuit represents the inner member of battery；These model parameters, which can also be used, is available from the measured value of battery to estimate：Voltage and
Electric current.Solution as described herein estimates model parameter in real time fashion, so as to use kalman filter method.
Realtime or online capacity estimation may include to update (e.g., based on actual service conditions, load, temperature, service life
Continuous updating) active volume one or more algorithms.Some specific implementations may include coulomb counting methods, and this method reports FG
The SOC of announcement based on coulomb compared with counting the SOC that (bookkeeping method) calculates.Some specific implementations may include that TTE (use by electric power
Time to the greatest extent) method, FG can be used to predict TTE and compared with actual conditions in this method.Some specific implementations may include
SOC/OCV profile lookup methods, the SOC that this method can report FG is compared with SOC/OCV curves.
In some specific implementations, various batteries can be supported, it has a variety of particular battery models and every kind of electricity
Chemical composition, battery manufacturers and/or the aging data in pond, it is such.In some specific implementations, voltameter appraisal procedure
Alterable.For example, state of charge precision assessment method and test program, dynamic load and/or detailed test request, all such
Class alterable.In some specific implementations, to requiring specification (such as key system perameter and required precision and/or the system integration
It is required that such) feedback alterable.In some specific implementations, operating system driving requires alterable.
Figure 17 is to show the schematic diagram that example system is realized.System 1700 includes voltameter evaluation module 1705, electricity
Pond 1710, battery meter 1715 and computing device 1715.Voltameter evaluation module 1705 can be realized as the software in BMS110
Module or ASIC.In other words, voltameter evaluation module 1705 can be code, the code be stored in memory 230 and by
Processor 235 and/or another module related to BMS110 perform.Computing device 1715 can be from voltameter evaluation module 1705
Receive information and by the presentation of information on a graphical user interface (as shown in figure 18).
Figure 18 is to show the schematic diagram that the user interface being used in combination can be realized with system.Figure 19 A and 19B include showing
Exemplary discharge voltage/current curve is to illustrate the figure that SOC lookup verifies 1905 and TTS tests 1910.Figure 20 A and
20B is to show exemplary CC appraisal procedures to illustrate electricity calculating method 2005 and the figure of the proximity of coulomb counting 2010.
Figure 21 A and 21B are the schematic diagram for showing TTS appraisal procedures, and it illustrates voltameter 2105 and actual SOC2110 obvious weight
Folded and TTS errors 2115.
Some in abovementioned example embodiment are described as the process or method illustrated with flow.Although flow chart will
Operation is described as sequential process, but many operations parallel, can be performed concurrently or simultaneously.In addition, order of operation can be rearranged.This
A little processes can terminate when completing its operation, but can also have the other step not included in figure.These process sides of may correspond to
Method, function, program, subroutine, subprogram etc..
The above method (some of them are illustrated by flow) can be retouched by hardware, software, firmware, middleware, microcode, hardware
Predicate is sayed or any combination of them is realized.When being realized with software, firmware, middleware or microcode, necessary task is performed
Program code or code segment are storable in machine or computerreadable medium such as storage medium.It can be handled by one or more
Device performs necessary task.
Concrete structure and function detail disclosed herein are only representational, to describe exemplary embodiment.However,
Exemplary embodiment is embodied as many alternative forms and should not be construed as limited to embodiments set forth herein.
It should be appreciated that although term first, second etc. can be used to describe various elements herein, these elements are not
Should be limited by these terms.These terms are only used for making an element distinguish with another element.For example, the first element can
To be referred to as the second element, and similarly, the second element is properly termed as the first element, without departing from the model of exemplary embodiment
Enclose.As used herein, term "and/or" includes any and all combination of one or more of the continuous item listed.
It should be appreciated that when element be referred to as " connecting " or " coupling " to another element when, it can be directly connected to or be coupled to
Intermediary element may be present in another element.On the contrary, when element is referred to as " being directly connected to " or " directcoupling " to another element
When, in the absence of intermediary element.Other words for describing the relation between element should explain in a similar manner (e.g., " between ...
Between " and " directly between ... between ", " adjacent " and " direct neighbor " etc.).
It should also be noted that in some replacement specific implementations, it is indicated that function/action can not press it is pointed in figure
Order occurs.For example, two figures shown in a continuous manner actually can concurrently be performed or can performed sometimes with inverted order, specifically take
Certainly in involved function/action.
The specific implementation of various techniques described herein can be in Fundamental Digital Circuit or in computer hardware, firmware, soft
Realized in part or in combinations thereof.Specific implementation can be achieved as computer program product, i.e., tangible embodiment is in information carrier
In, such as machinereadable storage device, (computerreadable medium, nontransitorycomputer readable storage medium, tangible computer can
Read storage medium) in or the signal propagated in computer program, for passing through data processing equipment (such as programmable processing
Device, computer or multiple stage computers) processing, or the operation of the control data processing equipment.Computer program for example abovementioned one
Individual or multiple computer programs (including compiling or interpretative code) can be write in the form of any programming language, and can be with any shape
Formula is disposed, including standalone program or the module suitable for computing environment, component, subroutine or other units.
Each several part in abovementioned example embodiment and corresponding embodiment is according to in computer storage
The software or algorithm and symbol of operation in data bit are represented to propose.Algorithm is (when the term is here using and when it with one
As mode when using) be envisioned for result needed for drawing be in harmony sequence of steps certainly.These steps are that requirement carries out thing to physical quantity
The step of reason manipulates.Generally, although it is not necessary, this tittle uses can store, shift, combining, comparing and with its other party
The form of optical signal, electric signal or magnetic signal that formula manipulates.Have proven to be more conveniently sometimes, particularly for general original
Cause, these signals are referred to as bit, value, element, symbol, character, item, numeral etc..
In exemplary embodiment above, what is referred to can be achieved the operation for program module or function course (e.g., with flow
The form of figure) action and symbol represent to include execution specific tasks or realize the routine of specific abstract data type, be program, right
As, component, data structure etc., and the existing hardware at existing structure element can be used to describe and/or realize.Some are existing
There is hardware to may include one or more CPU (CPU), digital signal processor (DSP), application specific integrated circuit, scene
Programmable gate array (FPGA) computer etc..
However, it should be remembered that all these and similar terms are related to appropriate physical quantity, and be only to be applied to these
The facilitate label of amount.Unless otherwise specified, otherwise such as from discussion it will be evident that term for example " handles " or " calculating "
(computing) or " calculating " (calculating) or " it is determined that " or " display " etc. refer to computer system or similar electronics
The action of computing device and process, the data represented with the physics in computer system register and memory, amount of electrons are grasped
Make and be transformed into similarly with computer system memory or register or the storage of other this type of informations, transmission or display device
Physical quantity represent other data.
It shall yet further be noted that the aspect realized by software of exemplary embodiment is generally encoded in some form of nontransitory journey
Realize in sequence storage medium or over some type of transmission medium.Program recorded medium can be (e.g., floppy disk or the hard disk of magnetic
Driver) or it is optical (e.g., compact disc readonly memory, or " CDROM "), and be readonly or randomaccess.Similarly,
Transmission medium can be twistedpair feeder, coaxial cable, optical fiber or some other suitable transmission mediums.Exemplary embodiment is not by any
Limitation in terms of these of specified specific implementation.
Although some features of the specific implementation have been shown as described herein, those skilled in the art is existing will
It is contemplated that many modifications, replacement, change and equivalents.It will thus be appreciated that appended claims are intended to fall into
All such modifications and modification in the range of specific implementation.It should be appreciated that the embodiment is only with the side of citing
Formula rather than present in a restricted way, and various changes can be carried out in terms of form and details.Device as described herein and/
Or any portion of method can be combined with any combinations, but except mutually exclusive combination.It is as described herein specific real
Apply the function of may include the different specific implementations, part and/or the various combinations of feature and/or subportfolio.
Claims (32)
1. a kind of method for the state of charge SOC for calculating battery, this method include：
The first estimation SOC of the battery is calculated in the very first time；
Voltage drop is calculated based on the described first estimation SOC；
The magnitude of voltage for the measurement voltage for representing the battery both ends is received in the second time；
Filter gain is calculated in second time；And
SOC, the magnitude of voltage and the filter gain are estimated to calculate the electricity based on described first in second time
The second estimation SOC in pond,
Wherein, this method further comprises：
At least one voltage drop model parameter is calculated based on the equivalent model for representing the battery, the equivalent model represents institute
The operation of battery is stated, at least one voltage drop model parameter includes indicating the instantaneous of the error in the second estimation SOC
Hysteresis；And
By making at least one voltage drop model parameter change reduce the second estimation SOC to remove instantaneous lagging
In error, according to described second estimation SOC calculate SOC.
2. the method according to claim 11, in addition to：
By the described second estimation SOC storages in a buffer；And
Before the second estimation SOC of the battery is calculated, the first estimation SOC is read from the buffer.
3. the method according to claim 11, in addition to：
By the described first estimation SOC storages in a buffer, before the second estimation SOC of the battery is calculated, from institute
State buffer and read the first estimation SOC as one of following：
At least two SOC vector,
At least two SOC array,
At least two SOC average and
At least two SOC average.
4. the method according to claim 11, in addition to：Estimation SOC variances are read from buffer, wherein the wave filter increases
Benefit is based on the estimation SOC variances.
5. according to the method for claim 1, wherein, calculating filter gain includes：Use weighting recurrence least square RLS
At least one in algorithm and total least square TLS algorithms calculates at least one capability value.
6. according to the method for claim 1, wherein, calculating filter gain includes：Using based on SOC tracking errors association side
The weighting RLS algorithm of difference and current measurement errors standard deviation calculates capability value.
7. according to the method for claim 1, wherein, calculating filter gain includes：Use passing based on covariance matrix
Return the TLS algorithms of renewal to calculate capability value.
8. according to the method for claim 1, wherein, calculating filter gain includes：Searched using opencircuit voltage OCV to count
Calculate capability value.
9. the method according to claim 11, wherein
The second estimation SOC is multiplied by the magnitude of voltage plus the described first estimation SOC equal to the filter gain.
10. the method according to claim 11, in addition to：
Reaching in voltage time TTV error metrics at least for error metrics, OCVSOC error metrics and prediction is counted based on coulomb
One, benchmark test is carried out to the described second estimation SOC.
11. a kind of system for being configured as calculating the state of charge SOC of battery, the system include：
Battery；And
Battery meter module, it is configured with the estimation SOC that Reduced Order Filter calculates the battery, the depression of order filtering
Device is single state filter, and single state filter is configured as based on the SOC estimation calculated before come recursive calculation
The estimation SOC,
Wherein, the battery meter module includes：
Voltage drop prediction module, it is configured as calculating voltage drop based on the estimation SOC；
Model estimation module, it is configured as calculating at least one voltage drop model based on the equivalent model for representing the battery
Parameter, the equivalent model represent the operation of the battery, and at least one voltage drop model parameter includes estimating described in instruction
Count the instantaneous lagging of the error in SOC；And
Tracking module, its be configured as by make at least one voltage drop model parameter change with remove instantaneous lagging so as to
The error in the estimation SOC is reduced, SOC is calculated according to the estimation SOC.
12. system according to claim 11, wherein, the battery meter includes capacity module, the capacity module
The total least square TLS algorithms for being configured with the renewal of the recurrence based on covariance matrix calculate the capacity of the battery
Value.
13. system according to claim 11, wherein, the battery meter includes capacity module, the capacity module
Opencircuit voltage OCV is configured with to search to calculate the capability value of the battery.
14. system according to claim 11, wherein
The battery meter includes buffer, and the buffer is configured to store at few estimation SOC value, and
The SOC estimation calculated before described is read from the buffer.
15. system according to claim 11, in addition to data storage, the data storage is configured as storing
OCV parameters, voltage measurement error standard deviation and current measurement errors standard deviation, wherein it is related to the Reduced Order Filter at least
One voltage drop model parameter is by the OCV parameters, the voltage measurement error standard deviation and the current measurement errors standard
One of difference defines.
16. system according to claim 11, in addition to：Display, the display are configured as showing the estimation
SOC。
17. a kind of method for the state of charge SOC for calculating battery, this method include：
Storage represents the storehouse of the equivalentcircuit model of battery in memory；
The operational mode of battery is determined based on the load related to the battery；
One of described equivalentcircuit model is selected based on identified operational mode；And
The SOC of the battery is calculated using selected equivalentcircuit model,
Wherein, this method further comprises：
At least one voltage drop model parameter is calculated based on the equivalentcircuit model selected in the storehouse from equivalentcircuit model,
The equivalentcircuit model represents the operation of the battery, and at least one voltage drop model parameter includes instruction estimation SOC
In error instantaneous lagging；And
By making at least one voltage drop model parameter change be reduced to remove instantaneous lagging in calculated SOC
Error, SOC is calculated according to the estimation SOC.
18. the method according to claim 11, wherein
High voltage load of the operational mode based on consumption variable current,
The operational mode includes corresponding equivalentcircuit model, and the equivalentcircuit model includes first resistorelectric current RC electricity
Road and the 2nd RC circuits.
19. the method according to claim 11, wherein
The operational mode is loaded based on variable voltage,
The operational mode includes corresponding equivalentcircuit model, and the equivalentcircuit model includes resistanceelectric current RC circuits.
20. the method according to claim 11, wherein
The operational mode is loaded based on variable voltage,
The operational mode includes corresponding equivalentcircuit model, and the equivalentcircuit model includes resistor and biasing element.
21. the method according to claim 11, wherein
The operational mode is loaded based on lowvoltage,
The operational mode includes corresponding equivalentcircuit model, and the equivalentcircuit model includes resistor.
22. the method according to claim 11, wherein
It is at least one including lag element in the equivalentcircuit model, and
The lag element is modeled as opencircuit voltage OCV calculation errors.
23. the method according to claim 11, in addition to：
During battery eliminator discharges, the terminal voltage of the battery eliminator is measured；
Linear equation is determined based on measured terminal voltage；And
At least one parameter is calculated using weighted least square algorithm based on the linear equation, to described in the battery
SOC calculating is based at least one parameter.
24. the method according to claim 11, in addition to：
Reaching in voltage time TTV error metrics at least for error metrics, OCVSOC error metrics and prediction is counted based on coulomb
One, benchmark test is carried out to the SOC.
25. a kind of system for being configured as calculating the state of charge SOC of battery, the system include：
Data storage, it is configured as the storehouse that storage represents the equivalentcircuit model of battery；
Model selection module, it is configured as selecting equivalentcircuit model based on the operational mode of the battery；And
Filter module, it is configured as the estimation SOC that the battery is calculated based on selected equivalentcircuit model；
Wherein, the system further comprises：
Model estimation module, it is configured as selecting from the storehouse of equivalentcircuit model based on the Model selection module equivalent
Circuit model calculates at least one voltage drop model parameter, and the equivalentcircuit model represents the operation of the battery, described
At least one voltage drop model parameter includes indicating the instantaneous lagging of the error in the estimation SOC；And
Tracking module, its be configured as by make at least one voltage drop model parameter change with remove instantaneous lagging so as to
The error of the estimation SOC is reduced, SOC is calculated according to the estimation SOC.
26. system according to claim 25, in addition to：
Operational mode module, it is configured as in the voltage related based on the electric current related to the battery and with the battery
It is at least one to determine the operational mode of the battery.
27. system according to claim 25, wherein
High voltage load of the operational mode based on consumption variable current,
The operational mode includes corresponding equivalentcircuit model, and the equivalentcircuit model includes first resistorelectric current RC electricity
Road and the 2nd RC circuits.
28. system according to claim 25, wherein
The operational mode is loaded based on variable voltage,
The operational mode includes corresponding equivalentcircuit model, and the equivalentcircuit model includes resistanceelectric current RC circuits.
29. system according to claim 25, wherein
The operational mode is loaded based on variable voltage,
The operational mode includes corresponding equivalentcircuit model, and the equivalentcircuit model includes resistor and biasing element.
30. system according to claim 25, wherein
The operational mode is loaded based on lowvoltage,
The operational mode includes corresponding equivalentcircuit model, and the equivalentcircuit model includes resistor.
31. system according to claim 25, wherein
It is at least one including lag element in the equivalentcircuit model, and
The lag element is modeled as opencircuit voltage OCV calculation errors.
32. system according to claim 25, in addition to display, the display is configured as showing the estimation SOC.
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