CN104007390A - Battery state of charge tracking, equivalent circuit selection and benchmarking - Google Patents

Abstract

A method includes calculating a first estimated state of charge (SOC) of a battery at a first time, receiving a voltage value representing a measured voltage across the battery at a second time, calculating a filter gain at the second time, and calculating a second estimated SOC of the battery at the second time based on the first estimated SOC, the voltage value, and the filter gain. Another method includes storing, in a memory, a library of equivalent circuit models representing a battery, determining an operational mode of a battery based on a load associated with the battery, selecting one of the equivalent circuit models based on the determined operational mode, and calculating a state of charge of charge (SOC) of the battery using the selected equivalent circuit model.

Description

Battery state of charge tracking, equivalent electrical circuit selection and reference test method and system

Technical field

Embodiment relates to the state of charge that calculates battery.

Background technology

Electrochemical energy storage device plays an important role in future source of energy strategy.In fact, battery is current with feasible in the near future energy storage technology.Diversified equipment such as portable electric appts, mobile household electrical appliance, aerospace equipment etc. are day by day battery-powered.Use known system and method may be difficult to the state of charge of for example battery accurately to be estimated.Therefore, need to be in order to solve the not enough of current technology and other system, method and apparatus novel and character of innovation be provided.

Summary of the invention

An embodiment comprises a kind of method.The method is included in first of very first time calculating battery and estimates state of charge (SOC), in the second time, receive the magnitude of voltage of the measuring voltage that represents battery two ends, at described the second Time Calculation filter gain, and in described the second time, based on the first estimation SOC, magnitude of voltage and filter gain, calculate second of battery and estimate SOC.

Another embodiment comprises a kind of system.This system comprises battery and battery electric quantity meter module, it is configured to use Reduced Order Filter to calculate the estimation state of charge (SOC) of described battery, described Reduced Order Filter is single state filter, and the SOC estimated value that described single state filter is configured to based on calculating before to estimate SOC described in recursive calculation.

Another embodiment comprises a kind of computer-readable medium, and it comprises code segment.Code segment makes described processor calculate the estimation state of charge (SOC) of battery when being carried out by processor, estimation SOC is stored in to impact damper, estimation SOC after the renewal of use Reduced Order Filter calculating battery, described Reduced Order Filter is single state filter, and described single state filter is configured to based on estimating that SOC carrys out the estimation SOC after recursive calculation is upgraded.

Another embodiment comprises a kind of method.The method is included in the storehouse of storing the equivalent-circuit model that represents battery in storer, based on the load relevant to described battery, determine the operational mode of battery, based on determined operational mode, select one of equivalent-circuit model, and the state of charge (SOC) that calculates battery with the equivalent-circuit model of selecting.

Another embodiment comprises a kind of system.This system comprises and is configured to the data-carrier store in storehouse that storage represents the equivalent-circuit model of battery, the operational mode being configured to based on battery is selected the Model Selection module of equivalent-circuit model, and is configured to the filter module that equivalent-circuit model based on selecting calculates the estimation state of charge (SOC) of battery.

Another embodiment comprises a kind of computer-readable medium, and it comprises code segment.Code segment makes the operational mode of described processor based on battery select equivalent-circuit model from represent the storehouse of equivalent-circuit model of battery when being carried out by processor; And the state of charge (SOC) that calculates described battery with the equivalent-circuit model of selecting.

Accompanying drawing explanation

According to following embodiment and the accompanying drawing providing of this paper, to understand more comprehensively exemplary embodiment, in accompanying drawing, similarly element is represented by similar reference number, and these reference numbers only provide to illustrate mode, therefore not the restriction to exemplary 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 block diagram for selecting the signal of battery equivalent model to flow according at least one exemplary embodiment.

Fig. 4 shows the block diagram flowing for calculating the signal of battery state of charge (SOC) according at least one exemplary embodiment.

Fig. 5 shows according to the block diagram of battery electric quantity meter (BFG) system of at least one exemplary embodiment.

Fig. 6 shows according to the block diagram of the signal stream of the parameter module for BFG system of at least one exemplary embodiment.

Fig. 7 shows according to the block diagram of the signal stream of the SOC module for BFG system of at least one exemplary embodiment.

Fig. 8 shows according to the block diagram of the SOC module of at least one exemplary embodiment.

Fig. 9 shows according to the block diagram of total least square (TLS) module of the SOC module of at least one exemplary embodiment.

Figure 10 shows according to the block diagram of recurrence least square (RLS) module of the SOC module of at least one exemplary embodiment.

Figure 11 and 12 shows according to the process flow diagram of the method for at least one exemplary embodiment.

Figure 13 A-13D shows according to the schematic diagram of the battery equivalent model of at least one exemplary embodiment.

Figure 14 is the characteristic schematic diagram of OCV-SOC that shows Portable lithium ion cell.

Figure 15 A and 15B are the figure that shows load curve.

Figure 16 A and 16B are the figure that shows fictitious load curve.

Figure 17 shows the schematic diagram that example system realizes.

Figure 18 shows to realize with system the schematic diagram of the user interface being combined with.

Figure 19 A and 19B comprise the figure that shows exemplary sparking voltage/current curve.

Figure 20 A and 20B are the figure that shows exemplary coulomb of count evaluation method.

Figure 21 A and 21B are for showing the figure of shut-in time (TTS) appraisal procedure.

Figure 22 A, 22B and 22C are for representing the table of voltameter reading.

Should be noted that, these figure are intended to illustrate the method used in some exemplary embodiment and/or the general features of structure, and the printed instructions providing is as follows provided.Yet these accompanying drawings may not be drawn in proportion and may accurately not reflect precise structural characteristics or the performance characteristic of any given embodiment, and should not be construed as and limit or value that restriction is contained by exemplary embodiment or the scope of character.For example, for clarity sake, may reduce or exaggerate relative thickness and the location of structural detail.

Embodiment

Although exemplary embodiment can comprise various modification and alternative form, embodiment illustrates by way of example in the accompanying drawings and will describe in detail in this article.Yet, should be appreciated that and be not intended to exemplary embodiment to be limited to particular form disclosed in this invention, but antithesis, exemplary embodiment will contain all modifications form, equivalents and the alternative form falling within the scope of claims.In to the whole description of accompanying drawing, similarly numeral refers to similar element.

Battery status for example the accurate estimation of state of charge (SOC), health status (SOH) and remaining life (RUL) for reliable, safety with to be widely used battery-powered device be vital.Estimate that these quantity are called battery electric quantity metering (BFG).Different from the HC fuel in many current automobiles, the memory capacity of battery is not constant.Conventionally, battery capacity changes with battery tenure of use, use pattern and temperature, thereby to BFG, cause challenging self-adaptation estimation problem, need to consider, on temperature variation, SOC variation and the basis of tenure of use, battery behavior is carried out to modeling and on-line parameter identification.

Fig. 1 and 2 shows according to the block diagram of the system 100 of at least one exemplary embodiment.As shown in Figure 1, system 100 comprises that battery 105, battery management system (BMS) 110, display 120, unrestricted power supply 125(are as wall outlet, vehicle charging station etc.) and switch 130.

BMS110 can be configured to manage utilization and/or the state of battery 105.For example, BMS110 can be configured to use switch 130 unrestricted power supply 125 is connected with battery 105 or disconnects that battery 105 is charged.For example, BMS110 can be configured to load (not shown) be connected or disconnect with battery 105.For example, BFG115 can be configured to calculate state of charge (SOC) and/or the health status (SOH) of battery 105.SOC and/or SOH can show that (for example,, with the form of number percent, with form of excess time etc.) is on display 120.

As shown in Figure 2, BMS110 at least comprises analog to digital converter (ADC) 205,220, wave filter 210,225, digital amplifier 215 and battery electric quantity meter (BFG) 115.BFG115 comprises storer 230, processor 235 and controller 240.ADC205,220, wave filter 210,225, at least one in digital amplifier 215 and BFG115 can be, for example special IC (ASIC), digital signal processor (DSP), field programmable gate array (FPGA) and/or processor, etc.Or, BMS110 can be comprise shown in ASIC, DSP, FPGA and/or the processor of functional block, etc.Or system 100 can be embodied as and is stored on storer and by software that for example processor is carried out.

BMS110 can be configured to use digital quantizer (ADC) 205,220, the combination of wave filter 210,225 and digital amplifier 215 by analog measurement (as, I _band V _b) be converted to digital value (for example, calculating SOC and/or SOH for BFG115).For example, digital amplifier 215 can be differential amplifier, and it is according to the voltage drop V at battery 105 two ends _b(for example, the magnitude of voltage between positive and negative terminal poor) generate (as, produce) simulating signal, then use ADC220 and wave filter 225 that this simulating signal is converted to the digital value through filtering.

System 100 can be the subsystem that utilizes battery powered any system or electronic equipment.In some concrete enforcements, electronic equipment can be and maybe can comprise that (for example) has the laptop devices of conventional laptop form factor.In some concrete enforcements, electronic equipment can be maybe (for example can comprise (for example) wireline equipment and/or wireless device, the equipment of support Wi-Fi), computational entity (for example, personal computing devices), server apparatus (for example, web server), toy, mobile phone, audio frequency apparatus, electric machinery control device, power supply are (for example, off-line power supply), PDA(Personal Digital Assistant), flat-panel devices, electronic reader, TV and/or automobile, etc.In some concrete enforcements, electronic equipment can be maybe can comprise (for example) display device (for example, liquid crystal display (LCD) watch-dog, for showing information to user), keyboard, pointing device (for example, mouse, Trackpad, by this equipment, user can provide input to computing machine).

Fig. 3 shows the block diagram 300 for selecting the signal of battery equivalent model to flow according at least one exemplary embodiment.As shown in Figure 3, Model Selection piece 310 receive input 320(as, from voltage and/or the current signal of battery and/or load) and use input 320(or its some modification) from equivalent model storehouse 305, select the equivalent model of representative (or corresponding to) battery.Then by this equivalent model of state of charge calculator block 315 use, carry out calculated charge state (SOC) 325.Equivalent model storehouse 305 can comprise the equivalent model that at least one represents battery.Each equivalent model can be based on battery (or battery eliminator) operational mode.Operational mode can be based on relevant to battery load.For example, the voltage drop that operational mode can be based on load two ends.For example, operational mode can the voltage drop based on load two ends be relatively high or lower, be relatively constant or dynamically and/or their combination.

Equivalent model (referring to following Figure 13 A-13D) can comprise resistor, voltage (as, voltage drop or voltage source), any combination of resistance-electric current (RC) circuit and/or impedance circuit etc.Therefore, can set up mathematics (as, the formula) equivalents of battery equivalent model.The mathematics equivalents relevant to battery operation pattern can be stored in equivalent model storehouse 305.This mathematics equivalents can be used for carrying out by state of charge calculator block 315 calculating of SOC.For example, mathematics equivalents can be used for determining variable, as for calculating the estimated value of SOC(or SOC) the input of formula.Therefore, BFG system can select equivalent model to improve counting yield and to reduce the processing time based on operational mode.For Fig. 5-12, provide more details below.

Fig. 4 shows the block diagram 400 flowing for calculating the signal of battery state of charge (SOC) according at least one exemplary embodiment.As shown in Figure 4, block diagram 400 comprises extended Kalman filter (EKF) piece 405, state of charge (SOC) piece 410,420, filter gain parameter block 41,425 and impact damper 430.EKF piece 505 can be configured to state of charge 410 and the filter gain parameter 415 based on before, calculated, calculate SOC420 and determine filter gain parameter 425(as, the SOC variance of reading and/or calculating, the voltage recording, the capacity calculating and/or the variable relevant to equivalent electrical circuit, etc.).Therefore, impact damper 430 can be configured to store in cycle for the treatment of for example before the SOC and the filter gain parameter that calculate.In other words, can calculate current (or next) SOC by the SOC based on calculating before at least one.In other words, the SOC calculating in the very first time can be used for the SOC calculating in the second (after a while) time.

In exemplary concrete enforcement, can use the set of at least two SOC410 and/or filter gain parameter 415.Therefore, the vector of at least two SOC, the array of at least two SOC, at least two SOC on average and the mean value of at least two SOC and corresponding filter gain parameter can be used for calculating next SOC420(or the SOC of the second time) and determine/calculate corresponding filter gain parameter 425.Therefore, impact damper 430 can be configured to store the SOC410 that calculate before a plurality of and calculate/definite filter gain parameter 415.Therefore the SOC that, BFG system calculates before can utilizing improves counting yield and reduces the processing time.For Fig. 5-12, provide more details below.

Fig. 5 shows according to the block diagram of battery electric quantity meter (BFG) 115 systems of at least one exemplary embodiment.As shown in Figure 5, BFG115 comprises estimation module 510, tracking module 520, prediction module 530, open-circuit voltage-state of charge (OCV-SOC) characterization module 540, offline parameter estimation module 545 and battery life characterization module 550.In addition, this system comprises off-line data collection module 555 and battery MBM 560.

Off-line data collection module 555 can be configured to measure battery behavior in relatively controlled test environment.For example, can in test laboratory environment, collect battery 105(or battery eliminator) open-circuit voltage (OCV) measured value and SOC measured value.For example, battery 105(or battery eliminator) can be initialized to charging completely (as, approach charging completely, charging completely substantially), standing (rested) state.Can carry out OCV and SOC measures.Then can make battery 105(or battery eliminator) slowly electric discharge, at regular intervals simultaneously (as, regularly, periodically, irregularly, the schedule time) carry out OCV and SOC measures, until battery 105(or battery eliminator) (or substantially) electric discharge completely.OCV and SOC measured value can be used for determining, calculate or estimate that battery parameter is (as, OCV parameter K hereinafter described _i∈ { K ₀; K ₁; K ₂; K ₃; K ₄; K ₅; K ₆; K ₇).

Data from off-line data collection module 555 can be used in battery MBM 560 to determine for example battery 105(or battery eliminator) equivalent model and/or the mathematics equivalents of equivalent model.Data from off-line data collection module 555 can be used in offline parameter estimation module 545 to determine and/or calculating and battery 105(or battery eliminator) relevant parameter (as, the value of the element relevant to above-mentioned equivalent model).From the data of off-line data collection module 555 can be used in OVC-SOC characterization module 540 to determine and/or calculate OCV and SOC battery parameter (as, OCV parameter K hereinafter described _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.For example, from the data of offline parameter estimation module 545, can be used for calculating initial health (SOH) characteristics (as, maximum SOC) by battery life characterization module 550.

Display 120 be shown as have that SOC shows 565, SOH shows 570, the shut-in time (TTS) show 575 and remaining life (RUL) show 580.Each demonstration can be for example the instrument of show percent.Can calculate or determine by BFG115 the value of each demonstration.For example, TTS can be shown as time value as calculated by TTS module 532 (as, hour and/or minute).

Estimation module 510 comprises parameter module 512 and capacity module 510.Estimation module 510 can be configured to calculate and/or definite battery 105(or battery eliminator) be specifically worth (as, parameter and capability value).In stable environment (as, test laboratory), parameter and capability value may be fix (as, do not change).Yet in real world, parameter and capability value may be dynamic or change.For example, complete SOC follows the tracks of solution and is usually directed to (1) estimation to the OCV parameter of a part for formation state-space model by off-line OCV sign.It is stable about temperature variation and cell degradation that OCV-SOC characterizes.Once estimate these parameters, these parameters just form a part for the state-space model with known parameters.(2) estimation of dynamic equivalent circuit parameter.Observed these parameters with changing temperature, SOC and tenure of use of battery, therefore should in BFG operation, estimate adaptively.(3) estimation of battery capacity: although the nominal capacity of battery is specified by manufacturer, known available battery capacity can be because manufacturing process error, temperature variation, use pattern and aging and change.And (4) are followed the tracks of by the SOC of model parameter constraint.Once known models parameter, SOC follows the tracks of and has just become Nonlinear Filtering Problem.Yet, observed gained state-space model and comprised correlated process and measure noise process.Appropriate these correlativity effects of processing will draw better SOC tracking accuracy.Therefore,, in exemplary concrete enforcement, for calculating parameter and capacity, tracking module 520 can be by data feedback to estimation module 510.

In addition, typically estimate that the method for battery capacity has been ignored lag-effect, and suppose that standing cell voltage represents the true open-circuit voltage (OCV) of battery.Yet according to exemplary embodiment, estimation module 510 is modeled as hysteresis the error in the OCV of battery 105, and adopts the combination of real-time linear parameter estimation and SOC tracking technique to compensate the error in OCV.

Tracking module 520 comprises SOC module 522 and SOH module 524." electric weight " in SOC pilot cell 105.As mentioned above, SOC is active volume, its be expressed as certain benchmark (as, rated capacity or current capacity) number percent.According to exemplary embodiment, SOC module 522 is by being used the error (combining with parameter estimation) of below following the tracks of in greater detail in compensation OCV to calculate SOC.SOH indicates a battery and state new or that ideal battery is compared.SOH can be based on charge acceptance, internal resistance, voltage and/or self discharge, etc.

Prediction module 530 comprises TTS module 532 and RUL module 534.TTS module 532 and RUL module 534 can be configured to calculate TTS and RUL based on SOC.

Fig. 6 shows according to the block diagram of the signal stream of the parameter module 412 for BFG115 of at least one exemplary embodiment.BFG system can select equivalent model to improve counting yield and to reduce the processing time based on operational mode.As shown in Figure 6, parameter module 412 comprises operational mode module 605 and Model Selection module 610.Operational mode module 605 can be configured at least one input based on from battery 105 and/or determine (battery) operational mode from least one input of load 615.Described at least one input can based on at least one relevant electric current and at least one in voltage in battery 105 and load 615.For example, the voltage drop at load 615 two ends.For example, operational mode can the voltage drop based on load 615 two ends be relatively high or lower, be relatively constant or dynamically and/or their combination.Model Selection module 610 can the operational mode based on definite be selected equivalent model (or its mathematics equivalents).For example, Model Selection module 610 can generate for searching for the query term in equivalent model storehouse 305.

In some concrete enforcements, definable or characterize a plurality of operational modes.In exemplary concrete enforcement, four operational modes relevant to the system of battery and use battery have below been described.

In the first operational mode, battery 105 can be connected in load heavy and that change.In other words, load 615 can combine use high voltage relatively with dynamically or variable current consumption (or the high voltage load that consumes variable current).For example, in mobile phone, the first operational mode can comprise such environment for use, and wherein mobile phone uses and comprises long video playback, multimedia and game application etc.Equivalent electrical circuit shown in following Figure 13 A can represent to be connected to battery heavy and load that change.

In the second operational mode, battery 105 can be connected to dynamic load and/or variable voltage load.In other words, load 615 can be used dynamically or the voltage changing.For example, in mobile phone, the second operational mode can comprise such environment for use, and wherein mobile phone uses the routine that comprises call, web-browsing and/or displaying video montage to use.Equivalent electrical circuit shown in following Figure 13 B can represent to be connected to the battery of dynamic load.

In the 3rd operational mode, battery 105 can be connected to or consume steady current.In other words, just constant (or substantial constant) load of traction of load 615.Or battery 105 can just utilize steady current to be recharged.For example, at charge cycle, battery 105 can disconnect with load 615 (as, can use switch 130 that unrestricted power supply 125 is connected to battery 105 so that battery 105 is charged).Equivalent electrical circuit shown in following Figure 13 C can represent to be connected to the battery of steady current.

In the 4th operational mode, battery 105 can be connected to the load of relatively low voltage.Or battery 105 can be in periodicity static condition, wherein battery 105 stands underload, and charging, then standing, minimum or non-loaded subsequently.In other words, minimum voltage can be seldom used in load 615.For example, in mobile phone, the 4th operational mode can comprise such environment for use, and wherein mobile phone uses and is included in after (or substantially complete) charging completely, uses the call not taking place frequently to carry out routine contact to base station.Equivalent electrical circuit shown in following Figure 13 D can represent to be connected to the battery of dynamic load.

Fig. 7 shows according to the block diagram of the signal stream of the SOC module 422 for BFG115 system of at least one exemplary embodiment.As shown in Figure 7, SOC module 422 comprises that buffer block 705, model estimation piece 710, SOC follow the tracks of piece 715 and voltage drop prediction module or piece 720.

In the exemplary embodiment, hysteresis is modeled as to the error in the OCV of battery 105.Voltage drop v _d[k] can represent internal cell model element R ₀, R ₁, R ₂and x _hthe voltage at [k] two ends (referring to Figure 13 A).X _h[k] item can be used for illustrating the error in the SOC predicting.In other words, x _h[k] can be " instantaneous lagging ", and its SOC that can be calculated or be estimated by adjustment is modified to zero.If the SOC that calculates or estimate equals SOC, the x that calculates or estimate _h[k] should equal zero.In other words, the x that calculates or estimate _h[k] is not equal to zero, and the SOC that indication is calculated or estimated exists error.Voltage drop model parameter vector (b) comprises corresponding to the x that calculates or estimate _hthe element of [k].

Therefore,, in the flow process of Fig. 7, from SOC, follow the tracks of the current calculating of piece 715 or the SOC that estimates is used in voltage block prediction piece 720 and falls v with calculating voltage _d[k].The voltage drop v that at least one is passing _d[k] is stored in impact damper 705 and for the estimation of parameter vector b.The x that correspondence in parameter vector b is calculated or estimated _h[k] indicates and has instantaneous lagging for nonzero value.This means SOC evaluated error.The SOC track algorithm that SOC follows the tracks of piece 715 is configured at the x that calculates or estimate _h[k] is the whenever correction SOC of non-zero.Below (on mathematics) has described relevant voltage drop v _d[k], hysteresis, estimation x _hthe more details that [k], voltage drop model parameter vector (b) and SOC follow the tracks of.Therefore the SOC that, BFG system calculates before can utilizing and SOC error are accurately estimated SOC, are improved counting yield and reduce the processing time.

Fig. 8 shows according to the block diagram of the SOC module 422 of at least one exemplary embodiment.As shown in Figure 8, SOC module 422 comprises extended Kalman filter (EKF) piece 805.EKF piece can be configured to calculate SOC845 and SOC error 840.EKF piece 805 can be configured to use equation 1 to calculate SOC845 as estimating SOC, and uses equation 2 to calculate SOC error 840 as estimating SOC error (or variance).Under establish an equation each in, k refers to instantaneous iteration, k+1|k refers to one, previous or iteration before, and k+1|k+1 refers to current, renewal, the next one or successive iterations. $\hat{x}[k+1|k+1]=\hat{x}[k+1\left|k\right]+G[k+1]v_{k+1}---\left(1\right)$

Wherein:

current or the estimation SOC of renewal iteration;

be ^onone or prediction iteration estimation SOC;

G[k+1] be upper one or prediction iteration filter gain; And

V _k+1be upper one or prediction iteration load voltage.

Wherein:

P _s[k+1|k+1] is current or upgrades SOC evaluated error or the variance of iteration;

G[k+1] be upper one or prediction iteration filter gain;

H[k+1] be linearizing observed differential;

P _s[k+1|k] be upper one or prediction iteration SOC evaluated error or variance; And

it is the voltage drop noise when initialization with zero mean and correlativity.

SOC module 422 comprises OCV parameter block 810.OCV parameter block 810 can be configured to from 540 storages of OVC-SOC characterization module and/or receive OCV parameter { K _i.OCV parameter { K _ibe constant because they be off-line measurement and the variation in 105 serviceable lifes can ignore (or not existing) at battery.OCV parameter is for calculating OCV according to equation 3 with SOC.

$V_0\left(s\right[k\left]\right)=K_0+\frac{K_1}{s\left[k\right]}+\frac{K_2}{s^2\left[k\right]}\frac{K_3}{s^3\left[k\right]}+\frac{K_4}{s^4\left[k\right]}+K_{5}s\left[k\right]+K_6\ln \left(s\right[k\left]\right)+K_7\ln (1-s[k\left]\right)---\left(3\right)$

Wherein:

S[k] be SOC; And

V _o(s[k]) be open-circuit voltage (OCV);

SOC module 422 comprises voltage drop model block 825.Voltage drop piece 825 can be configured to use according to the voltage drop at voltage drop model (above discussing) the computational load two ends of equation 4 or 5.

Z _v[k]＝V _o(x _s[k])+a[k] ^Tb+n _D[k] (4)

$Z_v\left[k\right]=V_o\left(x_s\right[k\left]\right)+\hat{a}{\left[k\right]}^T\hat{b}+n_D\left[k\right]---\left(5\right)$

Wherein:

Z _v[k] is the voltage of measuring;

V _o(x _s[k])] be open-circuit voltage (OCV);

A[k] ^tit is voltage drop model;

B is voltage drop model parameter vector;

that model falls in estimated voltage;

that model parameter vector falls in estimated voltage; And

N _d[k] is voltage drop observation noise.

As mentioned above, voltage drop model can change based on selected equivalent-circuit model.Selected equivalent-circuit model and/or voltage drop model can read from data-carrier store 855.For example, data-carrier store 855 can comprise equivalent model storehouse 305.

EKF(module or) piece 805 can be configured to use equation 1 to calculate SOC845 as estimating SOC, and the SOC845 of gained is stored in impact damper 850.EKF piece 805 can be configured to use equation 2 to calculate SOC error 840 and calculate as estimating SOC error (or variance), and the SOC error 840 of gained is stored in impact damper 850.SOC and the SOC error of storage can be read as SOC815 and SOC error 820, i.e. SOC845 and the SOC error 840 of storage.Therefore, EKF piece can be recursively (as, in circulation) calculate SOC845 and SOC error 840, make follow-up (in time for upgrading, next and/or afterwards) SOC845 and SOC error 840 calculate can based on before at least one (in time for current, upper one or before) SOC815 and SOC error 820 calculate.

As shown in Figure 8, recurrence least square (RLS) piece 830 and total least square (TLS) piece 835 can be generated to the input of EKF piece 805.RLS piece can generate initial estimation voltage drop model parameter vector (it can comprise at least one voltage drop model parameter), and TLS piece 835 can generate initial estimation capacity.Can generate initial estimation voltage drop model parameter vector and initial estimation capacity for each circulation.In exemplary concrete enforcement, along with iterations (k) increases, the variation of initial estimation voltage drop model parameter vector and initial estimation capacity can become and ignore.

Fig. 9 shows according to the block diagram of total least square (TLS) piece 835 of the SOC module 422 of at least one exemplary embodiment.As shown in Figure 9, TLS piece 635 comprises impact damper 910 and TLS computing module 915.Impact damper 910 is configured to receive, stores and output SOC data, for example changing value of Δ SOC data 920(or SOC data 920), for TLS computing module 915, use.Impact damper 910 is also configured to receive, store and export the changing value of Δ coulomb data 925(or coulomb data 925), for TLS computing module 915, use.Impact damper 910 can receive the current data 905 of the electric current relevant to battery 105 based on recording as for example coulombmeter logarithmic data.

TLS computing module 915 can be configured to calculate based on Δ SOC920 and Δ coulomb 925 capacity 930 of battery 105.For example, TLS computing module 915 can be used equation 6 calculated capacities 930.The derivation of equation 6 is shown in further detail hereinafter.

Wherein:

it is estimated capacity;

it is the covariance of augmentation observing matrix; And

Δ ^k(2,2) are diagonal angle 2 * 2 matrixes of non-negative eigenwert;

Figure 10 shows according to the block diagram of recurrence least square (RLS) piece 830 of the SOC module 422 of at least one exemplary embodiment.As shown in figure 10, TLS piece 635 comprises impact damper 1005 and RLC computing module 1010.Impact damper 1005 is configured to receive and storage SOC815, SOC error 820 and as the voltage-drop data of the output from voltage drop model block 825 (as, Z _v[k] or OCV).Impact damper 1005 is configured to output voltage and falls 1015 and electric current and electric capacity (I & C) matrix 1020.

RLC computing module 1010 can be configured to calculate initiation parameter 1025 based on voltage drop 1015 and (I & C) matrix 1020.For example, RLC computing module 1010 can be used equation 7 to calculate initiation parameter 1025.The derivation of equation 7 is shown in further detail hereinafter.

Wherein:

α _jr ₁c ₁current attenuation coefficient in circuit;

β _ir ₂c ₂current attenuation coefficient in circuit;

r ₁estimation resistance value;

r ₂estimation resistance value;

it is the estimation lagging voltage of battery; And

X _h[k] is instantaneous lagging;

It should be noted that as above for described in Fig. 7, the estimation lagging voltage of battery should be zero.Therefore,, in exemplary concrete enforcement, owing to using SOC to follow the tracks of piece 715, by SOC, follow the tracks of and removed (or substantially having removed) error because lagging behind and producing, so the b in equation 7 (6) should be zero.Therefore, SOC estimated value is more accurate, because hysteresis can be taken into account.

In Fig. 8-10, impact damper 1005 length can be the L for parameter estimation _b, and impact damper 905 length can be the L for capacity estimation _c.EKF piece 805 carries out iteration for each k, and RLS830 for each as L _b, the k of integral multiple carries out iteration, and TLS835 for each as L _cthe k of integral multiple carries out iteration, and wherein k is time index.BFG estimates that SOC follows the tracks of required all required model parameter and battery capacity, but the voltage and current measuring error standard deviation sigma of removing OCV parameter (it is that off-line is estimated) and calibrating from measurement instrument circuit _v, σ _ioutside.RLS piece, without any need for outside starting condition, only need arrange λ=1, and it is initial value that firm LS estimated value just can be provided, with wherein with for Mission Number.The mathematical justification of EKF piece 805 is below being described.

Figure 11 and 12 shows according to the process flow diagram of the method for at least one exemplary embodiment.For the step described in Figure 11 and 12, can carry out due to the execution of software code, described software code be stored in equipment (as, BMS110 shown in Fig. 1 and 2) relevant storer (as, storer 230) in and by device-dependent at least one processor (as, processor 235), carry out.Yet, can imagine alternate embodiment, be for example embodied as the system of application specific processor.Although following step is described to be carried out by for example processor, these steps needn't be carried out by same processor.In other words, at least one processor can be carried out below for the step described in Figure 11 and 12.

Figure 11 has described and has selected the equivalent model that represents battery for calculating the process flow diagram of the method for estimating SOC.As shown in figure 11, in step S1105, represent that the library storage of equivalent-circuit model of battery is in storer.For example, use off-line data collection module 555, can collect and battery 105(or battery eliminator) relevant data.Use described data and universal circuit instrument, can generate at least one equivalent electrical circuit that represents battery.This equivalent electrical circuit can comprise any combination of at least one equivalent voltage, resistance, electric capacity and/or equiva lent impedance.Referring to for example following Figure 13 A-13D.Also can generate the mathematics equivalents of each equivalent electrical circuit.Equivalent electrical circuit and/or mathematics equivalents for example can be stored in equivalent model storehouse 305.

In step S1110, the operational mode of battery is determined in the load based on relevant to battery.For example, the operational mode that each equivalent model can be based on battery (or battery eliminator).Operational mode can be based on relevant to battery load.For example, the voltage drop that operational mode can be based on load two ends.For example, operational mode can the voltage drop based on load two ends be relatively high or lower, be relatively constant or dynamically and/or their combination.Therefore the electric current that, operational mode can be based on relevant to battery and/or voltage and/or with battery relevant load determine.

In step S1115, based on determined pattern, select one of equivalent-circuit model for determined pattern.For example, can search for equivalent model storehouse 305 based on determined operational mode.For example, represent the equivalent electrical circuit of battery and/or mathematics equivalents can adopt with operational mode identification (as, unique name or unique identiflication number) corresponding mode is stored in equivalent model storehouse 305.Therefore, determine that operational mode can comprise definite operational mode identification, this operational mode identification is subsequently for searching for equivalent model storehouse 305.Select equivalent electrical circuit can comprise equivalent electrical circuit or mathematics equivalents that selection is returned by search equivalent model storehouse 305.

In step S1120, with selected equivalent-circuit model, calculate the state of charge (SOC) of battery or estimate SOC.For example, as mentioned above, calculating SOC can be based on voltage drop model parameter vector (b).Voltage drop model parameter vector can have the parameter (referring to above-mentioned equation 7) of the equivalent electrical circuit based on battery.Therefore, definite voltage drop model parameter vector can have or high or low complexity based on equivalent electrical circuit.For example, as described below, equivalent electrical circuit can not comprise RC circuit component, because capacitor charging walk around resistance.Therefore, b (3) can be unique remaining voltage drop model parameter vector element.Thereby simplified the calculating of SOC or estimation SOC.In addition, the voltage v[k between battery 105 terminals] (can be used for calculating SOC or estimate SOC) can be based on equivalent-circuit model.V[k] relevant equation, SOC and equivalent-circuit model be described in more detail hereinafter.

Figure 12 shows the process flow diagram that uses regressive filter to calculate the method for estimating SOC.As shown in figure 12, in step S1205, from impact damper, read the estimation state of charge (SOC) of stored battery.For example, impact damper 850 can be stored at least one SOC error and the SOC calculating in the front iteration for the step described in this process flow diagram therein.Can read at least one storage SOC value from impact damper 850.

In step S1210, read the measuring voltage at battery two ends.For example, can use that for example digital amplifier 215 reads or definite voltage (as, the v[k shown in figure below 13A-13D]).In an exemplary concrete enforcement, store voltages is in impact damper.Therefore, different iteration can be used different voltage measuring values.In other words, previous (on the time) voltage measuring value can be used for current iteration or v[k+1] can be used for iteration k+2.

In step S1215, calculating filter gain.For example, as concise and to the point above, describe and be below described in more detail, the filter gain of calculating EKF piece 805 (as, G[k+1]).At least one capability value that filter gain can calculate based on use weighted least square algorithm.For example, at least one at least one capability value calculating that filter gain can be based on being used in weighting recurrence least square (RLS) algorithm and total least square (TLS) algorithm.The capability value that filter gain can calculate based on use weighting RLS algorithm, described weighting RLS algorithm is based on SOC tracking error covariance and current measurement errors standard deviation.Filter gain can be based on estimating SOC variance.The capability value that filter gain can calculate based on use TLS algorithm, the recurrence of described TLS algorithm based on covariance matrix upgraded.Filter gain can be based on using open-circuit voltage (OCV) to search the capability value calculating.Each in SOC tracking error covariance, current measurement errors standard deviation, SOC variance, covariance matrix and OCV is in below (as on mathematics) description more in detail.

In step S1220, the estimation SOC that the storage SOC based on battery, the voltage at battery two ends and filter gain calculate battery.For example, the SOC of estimation can equal filter gain and is multiplied by the estimation SOC that digital voltage value adds storage.In step S1225, the estimation SOC calculating is stored in impact damper (as, impact damper 850).If necessary and/or need further to calculate estimate SOC(S1230), process and be back to step S1205.For example, if battery 105 is in continue being used, if SOC error surpass desirable value and further iteration can reduce error, if and/or battery testing carry out, etc., may be necessary so and/or need further to calculate.

Figure 13 A-13D shows according to the schematic diagram of the battery equivalent model of at least one exemplary embodiment.Below will be optionally with reference to Figure 13 A-13D to describe one or more exemplary concrete enforcement.As shown in Figure 13 A-13D, represent that equivalent model 1300-1,1300-2,1300-3, the 1300-4 of battery can comprise resistor 1315,1325,1340, any combination of capacitor 1330,1345 and equivalent voltage source 1305,1310.The voltage drop at battery two ends when voltage 1355 represents to load.The electric current of the element of (or flowing to) equivalent model is flow through in electric current 1320,1335 and 1350 expressions.For example, electric current 1350 represents to flow to the electric current of load.

Resistor and capacitor definable one RC circuit.For example, resistor 1325 and 1330 definition one RC circuit.In some exemplary concrete enforcements, capacitor can, by charging short circuit completely, cause RC circuit in fact from equivalent model, to disappear.For example, in representing the equivalent model 1300-2 of battery, the RC circuit being defined by resistor 1340 and capacitor 1345, not in model, because capacitor 1345 is charged completely, has formed short circuit.In some exemplary embodiments, do not have hysteresis that (or few) is relevant to battery (as, battery is in the standing or few load of traction).Therefore, as represented, as shown in the equivalent model 1300-4 of battery, owing to not there is not hysteresis, equivalent voltage source 1310 is not in model.

Next the application has described the details of exemplary concrete enforcement.Described details can comprise at least one above-mentioned equation foundation (as, mathematical justification or simplification).For clarity sake, can repeat these equations, yet these equations will retain the equation numbering shown in square bracket ([]).From real-time model identification, it can be with reference to following annotation.

The element of SOC track algorithm can comprise:

A. the estimation of OCV parameter: when being normalized with the battery capacity that depends on tenure of use by tenure of use, it is stable that OCV-SOC sign varies with temperature with cell degradation.

B. the estimation of dynamic equivalent circuit parameter: observed these parameters with changing temperature, SOC and tenure of use of battery, therefore should estimate adaptively in BFG operation.

C. the estimation of battery capacity: although the nominal capacity of battery is specified by manufacturer, known available battery capacity can be because manufacturing process error, temperature variation, loading mode and aging and change.

Followed the tracks of by the SOC of model parameter constraint: once known models parameter, SOC follows the tracks of and just become Nonlinear Filtering Problem.

Exemplary embodiment allows the dynamic equivalent circuit parameter of battery to carry out real-time Linear Estimation.By solving following point, realized in this exemplary embodiment the method for improving the modeling of existing battery equivalent electrical circuit and parameter estimation:

A. some models are only considered resistance, are not suitable for dynamic load.

B. they adopt nonlinear method to carry out system identification.

C. need to estimate for the initial parameter of method of model identification.

D. suppose that single dynamic equivalent model represents all battery operation patterns.

In this exemplary concrete enforcement, solved above-mentioned four problems and be summarized as follows:

A. for the online linear method of model parameter estimation, without the parameter of estimating the accurate physical representation form of battery equivalent electrical circuit.SOC tracking mode spatial model has utilized the estimation of amended parameter that can Linear Estimation.

B. be applicable to various batteries, without any initial value or calibration: due to the adaptivity of exemplary status spatial model, the SOC tracking proposing does not need any off-line initialization of model parameter.Least square (LS) method provide needs whenever to the initialization of parameter (or reinitializing), piece recurrence least square (RLS) is used to continue trace model parameter.In addition, shown that amended open-circuit voltage (OCV) model is effective under different battery models, different temperatures and different loads condition.This just makes exemplary BFG can plug and play mode be applied to the battery of broad range, without relative any other other information.

C. different battery modes are carried out the possibility of seamless SOC tracking.Can identify four different battery equivalent models with the very light load of reflection or the heavy duty of static condition, steady current or low frequency load, dynamic load and variation.Also identify four (a little) different dynamic equivalent model with these patterns of optimum matching.These models can be used for seamless SOC to be followed the tracks of, no matter and the patterns of change of battery operation.

D. the modeling that lags behind, it has eliminated the needs of hysteresis modeling: the modeling that may (ideally) off-line lags behind is recognized hardly in exemplary concrete enforcement, because it is relevant with load current I ∈ R with SOC ∈ [01] to lag behind.Therefore, according to exemplary embodiment, in voltage drop model, hysteresis is modeled as to the error in OCV, and online filtering method continues to attempt by adjustment SOC(to modified value) carry out fill in a gap.

Real-time model identification comprises the real-time model parameter estimation of using equivalent electrical circuit to carry out.Figure 13 A is the exemplary battery equivalent electrical circuit of (as, battery 105).When battery is when standing, V ₀(s[k]) be the OCV of battery.The unique SOC that depends on battery of OCV, s[k] ∈ [0,1].When battery is during in active state, for example, when there is current active, the behavior of battery represents by dynamic equivalent circuit, and described dynamic equivalent circuit is by lag element h[k], resistance in series R ₀and two RC circuit (R in parallel that are connected in series ₁, C ₁) and (R ₂, C ₂) form.Discrete time is used [k] indication.

In Figure 13 A, the measurement electric current that flows through battery is write as:

z _i[k]=i[k]+n _i[k] （8）

I[k wherein] be the real current that flows through battery, and n _i[k] is current measurement noise, supposes that current measurement noise is zero mean and has standard deviation (s.d.) σ _i. the measuring voltage at battery two ends is:

z _v[k]=v[k]+n _v[k] （9）

V[k wherein] be the real voltage at battery two ends, and n _v[k] is voltage measurement noise, supposes that voltage measurement noise is the zero mean with s.d..σ _v。

According to following form, write inner member R ₀, R ₁, R ₂with h[k] battery voltage drop at two ends:

$v_D\left[k\right]\stackrel{\mathrm{\Δ}}{=}{z}_V\left[k\right]-V_0\left[s\right[k\left]\right]=i\left[k\right]R_0+x_{i_1}\left[k\right]R_1+x_{i_2}\left[k\right]R_2+x_h\left[k\right]+n_V\left[k\right]---\left(10\right)$

Wherein flow through resistor R ₁and R ₂electric current can write according to following form

$x_{i_1}[k+1]\stackrel{\mathrm{\Δ}}{=}{i}_1[k+1]={\mathrm{\α}}_1{i}_1\left[k\right]+(1-{\mathrm{\α}}_1)i\left[k\right].---\left(11\right)$

$x_{i_2}[k+1]\stackrel{\mathrm{\Δ}}{=}{i}_2[k+1]={\mathrm{\α}}_2{i}_2\left[k\right]+(1-{\mathrm{\α}}_2)i\left[k\right]---\left(12\right)$

Wherein,

${\mathrm{\α}}_1\stackrel{\mathrm{\Δ}}{=}{e}^{-}\frac{\mathrm{\Δ}}{R_1{C}_1};---\left(13\right)$

${\mathrm{\α}}_2\stackrel{\mathrm{\Δ}}{=}{e}^{-}\frac{\mathrm{\Δ}}{R_2{C}_2};$ And (14)

Δ is sample interval.

By use, measure electric current z _i[k] replaces i[k], (11) can be write into following form again with the electric current in (12):

$x_{i_1}[k+1]={\mathrm{\α}}_1{x}_{i_1}\left[k\right]+(1-{\mathrm{\α}}_1)z_i\left[k\right]-(1-{\mathrm{\α}}_1)n_i\left[k\right]---\left(15\right)$

$x_{i_2}[k+1]={\mathrm{\α}}_2{x}_{i_2}\left[k\right]+(1-{\mathrm{\α}}_2)z_i\left[k\right]-(1-{\mathrm{\α}}_2)n_i\left[k\right]---\left(16\right)$

Use now (8), (10) can in z territory, again write into following form:

$V_D\left[z\right]=Z_i\left[z\right]R_0+X_{i_1}\left[z\right]R_1+X_{i_1}\left[z\right]R_2+x_h\left[z\right]+N_v\left[z\right]-R_0{N}_i\left[z\right]---\left(17\right)$

Next, in z territory, again write (15):

$z{X}_{i_1}\left[z\right]={\mathrm{\α}}_1{X}_{i_1}\left[z\right]+(1-{\mathrm{\α}}_1)Z_i\left[z\right]-(1-{\mathrm{\α}}_1)N_i\left[z\right]---\left(18\right)$

Draw

$X_{i_1}\left[z\right]=\frac{1-{\mathrm{\α}}_1}{z-{\mathrm{\α}}_1}\left(Z_i\right[z]-N_i[z\left]\right)---\left(19\right)$

And for (16) similarly,

$X_{i_2}\left[z\right]=\frac{1-{\mathrm{\α}}_2}{z-{\mathrm{\α}}_2}\left(Z_i\right[z]-N_i[z\left]\right)---\left(20\right)$

By by (19) and (20) substitutions (17):

$\begin{array}{c}{V}_D\left[z\right]=Z_i\left[z\right]R_0+\frac{1-{\mathrm{\α}}_1}{z-{\mathrm{\α}}_1}{Z}_i\left[z\right]R_1+\frac{1-{\mathrm{\α}}_2}{z-{\mathrm{\α}}_2}{Z}_i\left[z\right]R_2+X_h\left[z\right]+N_v\left[z\right]\\ -(R_0+\frac{1-{\mathrm{\α}}_1}{z-{\mathrm{\α}}_1}{R}_1+\frac{1-{\mathrm{\α}}_2}{z-{\mathrm{\α}}_2}{R}_2)N_i\left[z\right]\end{array}---\left(21\right)$

Rearrange (21) and convert it back to time domain:

Wherein,

α=α ₁+α ₂,（23）

β=α ₁α ₂,（24）

$\stackrel{\‾}{h}\left[k\right]=x_h\left[k\right]-\mathrm{\α}{x}_h[k-1]+\mathrm{\β}{x}_h[k-2],---\left(27\right)$

${\stackrel{\‾}{n}}_v\left[k\right]=n_v\left[k\right]-\mathrm{\α}{n}_v[k-1]+\mathrm{\β}{n}_v[k-2],$ And (28)

Now (22) are write into following form again:

v _D[k]=[k] ^T+n _D[k] （30）

Observation model a[k wherein] ^tprovide as follows with model parameter vector b:

$a{\left[k\right]}^T{=}_4{\left[k\right]}^T\stackrel{\mathrm{\Δ}}{=}[\left[\begin{array}{cccccc}{v}_D[k-1]& -v_D[k-2]& z_i\left[k\right]& z_i[k-1]& -z_i[k-2]& 1\end{array}\right].---\left(31\right)$

Wherein subscript 4 is indicated the above-mentioned model corresponding with the model 4 of four models shown in Figure 13 A-13B.

(30) noise of the voltage drop observation in is write into:

$n_D\left[k\right]\stackrel{\mathrm{\Δ}}{=}{\stackrel{\‾}{n}}_i\left[k\right]+{\stackrel{\‾}{n}}_v\left[k\right]---\left(33\right)$

It has the autocorrelation providing as follows:

And supposition is in length L _bthe time interval batch during lagging component be constant, for example,

$\stackrel{\‾}{h}\left[l\right]=x_h\left[l\right]-({\mathrm{\α}}_1+{\mathrm{\α}}_2)x_h[l-1]+{\mathrm{\α}}_1{\mathrm{\α}}_2{x}_h[l-2]\≈H,l=k-L_b+1,...,k---\left(35\right)$

Now, four the different battery operations " pattern " that can describe and the suitable battery equivalent model that mates these patterns.

A. pattern 1 – underload or static condition: when battery is only subject to underload, be then recharged, when then standing, lagging component will be so small as to and can ignore.The example of this pattern will be cell phone, and it expends nearly all time contact base station until the event of charging next time, except possible minority call after charging completely.Very adaptive this pattern of single resistor (referring to Figure 13 D).

B. pattern 2 – steady current operations: when flowing through the current constant of battery, the capacitor in RC circuit becomes charging completely.Therefore,, from parameter estimation viewpoint, the circuit of gained can be regarded as single resistor and hysteresis/biasing element (referring to Figure 13 C).The constant current charge of battery is the good example of this pattern.

C. pattern 3 – dynamic loads: when battery is during in this pattern, have a large amount of loads of different sizes.Example: termly for the smart phone of call, web-browsing, video clipping etc.Very adaptive this scene of battery eliminator shown in Figure 13 B.

D. the heavy and use that changes of pattern 4 –: for mobile phone, use heavy and that change comprises video playback, multimedia and game application when long etc.Figure 13 A mates this scene very much.

Note, the different model complicacy of dynamic equivalent circuit can be by only changing [k] ^trepresent.Below show [k] for each model ^tdefinition.For each in above-mentioned model complicacy, noise item n _d[k] according to following form with with represent:

Wherein,

α=α ₁+α ₂ （38）

β=α ₁α ₂ （39）

${\tilde{R}}_1={\mathrm{\α}}_1{R}_0-(1-{\mathrm{\α}}_1)R_1---\left(40\right)$

The least-squares estimation of constant dynamic model parameter while relating to is below discussed.The true SOC at time k place is expressed as:

$x_s\left[k\right]\stackrel{\mathrm{\Δ}}{=}s\left[k\right]---\left(41\right)$

The SOC track algorithm of setting up can be used for obtaining be x _sthe renewal of [k] is estimated.Now, the voltage drop v in (10) _d[k] can write into:

$v_D\left[k\right]=z_v\left[k\right]-V_0\left({\hat{x}}_s\right[k\left|k\right])---\left(42\right)$

Wherein the estimation open-circuit voltage (OCV) that represents battery, it can be described to estimate the function of SOC.Can adopt following OCV-SOC relation:

$\begin{array}{c}\end{array}\begin{array}{c}{V}_0\left({\hat{x}}_s\right[k\left|k\right])=K_0+\frac{K_1}{{\hat{x}}_s\left[k\right|k]}+\frac{K_2}{{\hat{x}}_s{\left[k\right|k]}^2}+\frac{K_3}{{\hat{x}}_s{\left[k\right|k]}^3}+\frac{K_4}{{\hat{x}}_s{\left[k\right|k]}^4}\\ +K_5{\hat{x}}_s\left[k\right|k]+K_6\ln \left({\hat{x}}_s\right[k\left|k\right])+K_7\ln (1-{\hat{x}}_s[k\left|k\right])\end{array}---\left(43\right)$

Can be by step as described below to OCV parameter K _i∈ { K ₀, K ₁, K ₂, K ₃, K ₄, K ₅, K ₆, K ₇carry out off-line estimation.By considering L _bobservation batch, (30) can be write into following form again:

$v_D^{\mathrm{\κ}}=A^{\mathrm{\κ}}+n_D^{\mathrm{\κ}}---\left(44\right)$

Wherein κ is Mission Number,

$v_D^{\mathrm{\κ}}=\left[v_D\right[\mathrm{\κ}{L}_b-L_b+1\left]v_D\right[\mathrm{\κ}{L}_b-L_b+2]...v_D{\left[\mathrm{\κ}{L}_b\right]]}^T---\left(45\right)$

A ^κ=[[κL _b-L _b+1][κL _b-L _b+2]…[κL _b]] ^T （46）

And noise there is following covariance

${\mathrm{\Σ}}_D^{\mathrm{\κ}}=E\left\{n_D^{\mathrm{\κ}}{n_D^{\mathrm{\κ}}}^T\right\}---\left(47\right)$

Wherein be five diagonal angle toeplitz matrixs, wherein diagonal entry, the first and second off diagonal elements pass through respectively with provide (seeing (32)).Now, dynamic model parameter vector can be estimated as follows by (42) by least square (LS) optimization:

${\hat{b}}_{\mathrm{LS}}\left[\mathrm{\κ}\right]={\left({\left(A^{\mathrm{\κ}}\right)}^T{\left({\mathrm{\Σ}}_D^{\mathrm{\κ}}\right)}^{-1}{A}^{\mathrm{\κ}}\right)}^{-1}{A^{\mathrm{\κ}}}^T{\left({\mathrm{\Σ}}_D^{\mathrm{\κ}}\right)}^{-1}{v}_D^{\mathrm{\κ}}---\left(48\right)$

The covariance matrix of LS estimator provides as follows:

$P_b\left[\mathrm{\κ}\right]={\left({\left(A^{\mathrm{\κ}}\right)}^T\left({\mathrm{\Σ}}_D^{\mathrm{\κ}}\right){A^{-1}}^{\mathrm{\κ}}\right)}^{-1}---\left(49\right)$

When obtaining the measured value of new lot, can be by repeating (50) – (51) recurrence renewal LS estimated values

$P_b^{-1}[\mathrm{\κ}+1]=\mathrm{\λ}{P}_b^{-1}\left[\mathrm{\κ}\right]+{\left(A^{\mathrm{\κ}+1}\right)}^T{\left({\mathrm{\Σ}}_D^{\mathrm{\κ}}\right)}^{-1}{A}^{\mathrm{\κ}+1}---\left(50\right)$

${\hat{b}}_{\mathrm{RLS}}[\mathrm{\κ}+1]=P_b[\mathrm{\κ}+1]\left(\mathrm{\λ}{P}_b^{-1}\right[\mathrm{\κ}\left]{\hat{b}}_{\mathrm{RLS}}\right[\mathrm{\κ}]+{\left(A^{\mathrm{\κ}+1}\right)}^T{\left({\mathrm{\Σ}}_D^{\mathrm{\κ}}\right)}^{-1}{v}_D^{\mathrm{\κ}+1})---\left(51\right)$

Wherein λ is for forgeing (Attenuation Memory Recursive) factor, () ^trepresent transposition, () ^-1expression is inverted, and be called as information matrix, this information matrix can be multiplied by suitable constant and carry out initialization by the unit matrix of suitable size.Can notice, when λ=0, become can exist and make approximate several different methods.Can select following two kinds of method of approximation for comparing:

A. can carry out following method of approximation:

${\mathrm{\Σ}}_D^{\mathrm{\κ}}\≈I_{l_b}---\left(52\right)$

B _.estimated value before using to build electric current covariance matrix, for example, is used:

in ${\hat{b}}_{\mathrm{RLS}}[\mathrm{\κ}-1]---\left(53\right)$

The least mean-square error (MMSE) of the dynamic model parameter becoming while relating to is below discussed to be estimated.Suppose that dynamic model parameter is for the stochastic variable of following slow variation Wiener-Hopf equation occurs:

x _b[k+1]=x _b[k]+w _b[k] （54）

W wherein _b[k] is for having covariance ∑ _bzero mean white Gaussian noise.Now, use (30) as measurement model and (53) as process model, the MMSE that Kalman filter provides b estimates.SOC can be used for determining v _d[k] (seeing (42)), SOC follows the tracks of/and the parameter estimation based on Kalman filtering that level and smooth iterative algorithm and the observation window by sufficient length carry out can be used for improving that SOC follows the tracks of and the precision of parameter estimation.

Below discuss and relate to open-circuit voltage (OCV) parameter estimation.SOC estimates can utilize open-circuit voltage (OCV) and the uniqueness between SOC and the stable relations of battery and allow to calculate SOC for the OCV recording.Yet, only when battery is when standing, just can directly measure OCV.When battery is in use time, the dynamic relationship between cell voltage and electric current must describe by parameter and method for estimating state.State of charge method of estimation based on OCV-SOC comprises and following relevant error: the modeling of dynamic equivalent electric model of (1) battery and the uncertainty of parameter estimation; And the error of the voltage and current of (2) measurement.(43) parameter that in, OCV-SOC characterizes can be estimated by gather OCV characterization data on sample battery as follows:

A. from charging completely, complete standing battery

B. record its open-circuit voltage V _batt=V _full

C. set k=1

D. record v[k]=V _batt; Record SOC[k]=1

E. set k=k+1

F. use (C/30 or C/40, the wherein battery capacity of C for representing with Ah conventionally) steady current i[k of minute quantity] make battery continuous discharge, until battery discharges completely.Once electric discharge completely, just make battery keep standing, and after this charging is until battery is full of electricity.Then

1. measure battery terminal voltage, the V of every Δ second _batt

2. record v[k]=V _batt

G. record SOC[k]=SOC[k-1]+c _hi[k] Δ

Now, OCV model (43) is for all measured value v[k] as follows vector format represent:

v=A _ocvk （55）

Wherein

v=[v[1],v[2]…,v[Nv]] ^T （56）

A _ocv=[a _ocv(1),a _ocv(2),…,a _ocv(Nv)] ^T （57）

k=[K ₀ K ₁ K ₂ K ₃ K ₄ K ₅ K ₆ K ₇ R ₀] ^T （58）

Then by assignment s[k]=SOC[k]

$a_{\mathrm{ocv}}\left[k\right]=\left[\begin{array}{ccccccccc}1& \frac{1}{s\left[k\right]}& \frac{1}{s^2\left[k\right]}& \frac{1}{s^3\left[k\right]}& \frac{1}{s^4\left[k\right]}& s\left[k\right]& \ln \left(s\right[k\left]\right)& \ln (1-s[k\left]\right)& i\left[k\right]\end{array}\right]T^{}---\left(59\right)$

Now, the least-squares estimation value of OCV parameter and internal resistance of cell R ₀provide as follows:

$\hat{k}={\left(A_{\mathrm{ocv}}^T{A}_{\mathrm{ocv}}\right)}^{-1}{A}_{\mathrm{ocv}}^{T}v---\left(60\right)$

Below discuss and relate to four exemplary equivalent-circuit models.

Table 1

Pattern number	Equivalent electrical circuit
		Model 1	Figure 13 D
Model 2	Figure 13 C
		Model 3	Figure 13 B
Model 4	Figure 13 A

In four equivalent-circuit models shown in table 1 voltage drop at the circuit component two ends of each as follows form write:

v _D[k]=[k] ^T[k]+n _D[k] （61）

Wherein,

For model 3:

${\tilde{R}}_1={\mathrm{\α}}_1{R}_0-(1-{\mathrm{\α}}_1)R_1---\left(64\right)$

$\tilde{H}=h\left[k\right]-{\mathrm{\α}}_{1}h[k-1]---\left(65\right)$

And, for model 4:

α ⁼α ₁+α ₂ （66）

β=α ₁α ₂ （67）

Below relate to the derivation of Noise Correlation.In this part, for | l|=0,1,2 and for | the autocorrelation of l|>2 (27) can be derived as follows by (33):

l=0：

l=1：

l=2：

Now, above-mentioned can be as follows for each model representation:

Real time capacity estimation is proceeded in this discussion, and it can be with reference to following annotation.

The state of charge of battery (SOC), is defined as:

Formula 78 provides the information of relevant battery status.The understanding of SOC and battery capacity is for estimating shut-in time (TTS) or the complete duration of charging (TTF) of battery.Battery capacity varies with temperature conventionally and its root Ju is used pattern and passes in time tenure of use and weaken.Battery capacity tracking is accurately the key element of battery electric quantity metering.

In this exemplary concrete enforcement, online capacity estimation can be based on:

The weighting recurrence least square (RLS) a. with the capacity of accurate weight derivation is estimated.For the weighting RLS method of online capacity estimation, comprise variance and covariance in the whole time that the SOC based on after renewal follows the tracks of and the expression formula of current measurement errors standard deviation derivation weight.

B. for the TLS method of real-time follow-up battery capacity.TLS method provides the closed expression formula for capacity estimation.The method can be used for the variation of Continuous Tracking battery capacity.

C. the adaptive capacity that the OCV based on resting batteries searches is estimated.TLS method for on-line tracing battery capacity is estimated by the SOC that utilizes battery standing point to carry out searching based on OCV.

The fusion of the capacity estimation d. obtaining by distinct methods.

Below discuss and relate to battery capacity estimation and fusion.The instantaneous state of charge (SOC) of battery can be written as following process model, and it represents to measure electric current according to following form also referred to as coulomb Counting Formula:

$x_s[k+1]=x_s\left[k\right]+\frac{\mathrm{\η\Δ}}{3600C_{\mathrm{batt}}}{z}_i\left[k\right]+w_s\left[k\right]---\left(79\right)$

X wherein _s[k] ∈ [0,1] represents the SOC of battery, C _battfor the battery capacity representing with ampere hour (Ah), and z _i[k] is for measuring electric current

z _i[k]=i[k]+n _i[k] （80）

It is had standard deviation (s.d.) σ _i. zero mean white noise n _i[k] damages.(79) process noise in is relevant to the measurement noise in (80), as

w _s[k]=-c _hΔn _i[k] （81）

And for having zero mean, and s.d. is:

σ _s=c _hΔσ _i （82）

Wherein coulombmeter number system number is

$c_h\≅\frac{\mathrm{\η}}{3600C_{\mathrm{batt}}}---\left(83\right)$

Here, η depends on that battery is charging or the constant discharging, for example,

$\mathrm{\&eta;}=\left\{\begin{array}{cc}{\mathrm{\&eta;}}_c& i\left[k\right]>0\\ {\mathrm{\&eta;}}_d& i\left[k\right]<0\end{array}\right.---\left(84\right)$

And Δ is (constant) sample interval.

Below discuss and relate to the online battery capacity estimation of using recurrence least square (RLS).Estimate that SOC can be based on voltage and current measured value.Two continuous SOC value x _s[k] and x _s[k+1] is written as with its estimated value:

$x_s\left[k\right]={\hat{x}}_s\left[k\right|k]+{\tilde{x}}_s[k\left|k\right]---\left(84\right)$

$x_s]k+1]={\hat{x}}_s[k+1|k+1]+{\tilde{x}}_s[k+1|k+1]---\left(85\right)$

Evaluated error wherein with there is respectively zero mean and variance P _s[k|k] and P _s[k+1|k+1].Covariance between two continuous evaluated errors is:

$E\left\{{\tilde{x}}_s\right[k\left|k{]\tilde{x}}_s\right[k+1|k+1]\}=(1-G[k+1\left]H\right[k+1\left]\right)P_s[k\left|k\right]---\left(86\right)$

G[k+1 wherein] be scalar kalman gain, and H[k+1] be the scalar linearization observation model at time k+1 place.Now, with following form, again write (80):

$x_s[k+1]-x_s\left[k\right]=\frac{\mathrm{\&eta;\&Delta;}}{3600C_{\mathrm{batt}}}{z}_i\left[k\right]+w_s\left[k\right]---\left(87\right)$

(84) and (85) substitutions (87) are obtained:

$\mathrm{\&Delta;}{x}_s[k+1,k]\&cong;{\hat{x}}_s[k+1|k+1]-{\hat{x}}_s[k\left|k\right]=\frac{{\mathrm{\&eta;}}_h\mathrm{\&Delta;}}{C_{\mathrm{batt}}}{z}_i\left[k\right]+{\tilde{w}}_s\left[k\right]---\left(88\right)$

Wherein,

${\mathrm{\&eta;}}_h=\frac{\mathrm{\&eta;}}{3600}---\left(89\right)$

And differential error provides as follows:

${\tilde{w}}_s\left[k\right]={\hat{x}}_s\left[k\right|k]+{\tilde{x}}_s[k+1|k+1]+-w_s\left[k\right]--\left(90\right)$

For having zero mean, and variance is as follows:

$E\left\{{\tilde{w}}_s{\left[k\right]}^2\right\}\&cong;R_{{\tilde{w}}_S\left[k\right]}=G{[k+1]}^{2}S[k+1]---\left(91\right)$

S[k+1 wherein] be new breath (innovation) covariance of Kalman filter.By considering L _csample batch, (88) can vector form write into following form:

$d_s^{\mathrm{\&kappa;}}=C_{\mathrm{batt}}^{-1}{d}_c^{\mathrm{\&kappa;}}+{\tilde{w}}_s^{\mathrm{\&kappa;}}---\left(92\right)$

Wherein,

κ is Mission Number,

L _cfor a batch length,

$\begin{array}{c}{d}_s^{\mathrm{\&kappa;}}=\left[\mathrm{\&Delta;}{x}_s\right[\mathrm{\&kappa;}{L}_c-L_c+1,\mathrm{\&kappa;}{L}_c-L_c\left]\mathrm{\&Delta;}{x}_s\right[\mathrm{\&kappa;}{L}_c-L_c+2,\mathrm{\&kappa;}{L}_c-L_c+1]...\\ \mathrm{\&Delta;}{x}_s{[\mathrm{\&kappa;}{L}_c,\mathrm{\&kappa;}{L}_c-1]]}^T\end{array}---\left(93\right)$

$\begin{array}{c}{d}_c^{\mathrm{\&kappa;}}=\left[{\mathrm{\&eta;}}_h{\mathrm{\&Delta;}}_{\mathrm{\&kappa;}{L}_c-L_c+1}{z}_i\right[\mathrm{\&kappa;}{L}_c-L_c+1\left]{\mathrm{\&eta;}}_h{\mathrm{\&Delta;}}_{\mathrm{\&kappa;}{L}_c-L_c+1}{z}_i\right[\mathrm{\&kappa;}{L}_c-L_c+2]...\\ {\mathrm{\&eta;}}_h{\mathrm{\&Delta;}}_{\mathrm{\&kappa;}{L}_c}{z}_i{\left[\mathrm{\&kappa;}{L}_c\right]]}^T\end{array}---\left(94\right)$

${\tilde{w}}_s^{\mathrm{\&kappa;}}=\left[\tilde{w}\right[\mathrm{\&kappa;}{L}_c-L_c+1]\tilde{w}[\mathrm{\&kappa;}{L}_c-L_c+2]...\tilde{w}{\left[\mathrm{\&kappa;}{L}_c\right]]}^T---\left(95\right)$

And for thering is the white Gaussian noise vector of following covariance:

${\mathrm{\&Sigma;}}_{{\tilde{w}}_s}^{\mathrm{\&kappa;}}=E\left\{\begin{array}{c}\mathrm{\&kappa;}\\ s\end{array}{\left(\begin{array}{c}\mathrm{\&kappa;}\\ s\end{array}\right)}^T\right\}---\left(96\right)$

It is L _c* L _cdiagonal matrix, its n diagonal element provides as follows:

${\left({\mathrm{\&Sigma;}}_{{\tilde{w}}_s}^{\mathrm{\&kappa;}}\right)}_{\mathrm{nn}}=G{[\mathrm{\&kappa;}{L}_c-L_c+n]}^{2}S[\mathrm{\&kappa;}{L}_c-L_c+n]---\left(97\right)$

Now, the LS of battery capacity inverse estimates to provide as follows:

${\hat{C}}_{\mathrm{LS}}^{-1}={\left({\left(d_c^{\mathrm{\&kappa;}}\right)}^T{\left({\mathrm{\&Sigma;}}_{{\tilde{w}}_s}^{\mathrm{\&kappa;}}\right)}^{-1}{d}_c^{\mathrm{\&kappa;}}\right)}^{-1}{\left(d_c^{\mathrm{\&kappa;}}\right)}^T{\left({\mathrm{\&Sigma;}}_{{\tilde{w}}_s}^{\mathrm{\&kappa;}}\right)}^{-1}{d}_s^{\mathrm{\&kappa;}}---\left(98\right)$

And the LS capacity variance of estimating reciprocal is:

${\hat{R}}_{\mathrm{RLS}}\left[\mathrm{\&kappa;}\right]={\left({\left(d_c^{\mathrm{\&kappa;}}\right)}^T{\left({\mathrm{\&Sigma;}}_{{\tilde{w}}_s}^{\mathrm{\&kappa;}}\right)}^{-1}{d}_c^{\mathrm{\&kappa;}}\right)}^{-1}---\left(99\right)$

New a collection of when obtaining to time, LS estimates recurrence to upgrade as follows:

${\hat{R}}_{\mathrm{RLS}}^{-1}[\mathrm{\&kappa;}+1]=\mathrm{\&lambda;}{\hat{R}}_{\mathrm{RLS}}^{-1}\left[\mathrm{\&kappa;}\right]+{\left(d_c^{\mathrm{\&kappa;}+1}\right)}^T{\left({\mathrm{\&Sigma;}}_{{\tilde{w}}_s}^{\mathrm{\&kappa;}+1}\right)}^{-1}{d}_c^{\mathrm{\&kappa;}+1}---\left(100\right)$

${\hat{C}}_{\mathrm{RLS}}^{-1}[\mathrm{\&kappa;}+1]={\hat{R}}_{\mathrm{RLS}}[\mathrm{\&kappa;}+1]\left(\mathrm{\&lambda;}{\hat{R}}_{\mathrm{RLS}}^{-1}\right[\mathrm{\&kappa;}\left]{\hat{C}}_{\mathrm{RLS}}^{-1}\right[\mathrm{\&kappa;}]+{\left(d_c^{\mathrm{\&kappa;}+1}\right)}^T{\left({\mathrm{\&Sigma;}}_{{\tilde{w}}_s}^{\mathrm{\&kappa;}+1}\right)}^{-1}{d}_b^{\mathrm{\&kappa;}+1})---\left(101\right)$

Wherein for the L for capacity estimation _c* L _cinformation matrix, and λ is Attenuation Memory Recursive constant.Should be noted that, in (92) by known noisy measurement current value, built, and above-mentioned LS and RLS method of estimation hypothesis completely known.For actual solution, should consider in uncertainty.Next, described the method for optimizing based on total least square (TLS), it has solved in error.

Below discuss and relate to the online battery capacity estimation of using self-adaptation total least square (TLS).In this part, based on TLS, set up online capacity estimation method, it is supposed in (92) with in all exist uncertain.Build following augmentation observing matrix:

$H^{\mathrm{\&kappa;}}=\left[\begin{array}{cc}{d}_s^{\mathrm{\&kappa;}}& d_c^{\mathrm{\&kappa;}}\end{array}\right]---\left(102\right)$

The information matrix relevant to augmentation observing matrix is:

$S_H^k={\left(H^{\mathrm{\&kappa;}}\right)}^T{H}^{\mathrm{\&kappa;}}---\left(103\right)$

With following form, write feature decomposition:

$S_H^k=V^{\mathrm{\&kappa;}}{\mathrm{\&Lambda;}}^{\mathrm{\&kappa;}}{V}^{\mathrm{\&kappa;T}}---\left(104\right)$

Wherein,

Λ ^κfor by from being up to diagonal angle 2 * 2 matrixes of minimum non-negative eigenwert of arranging, i.e. Λ ^κ(1,1) represents eigenvalue of maximum, and Λ ^κ(2,2) represent minimal eigenvalue.

2 * 2 matrixes every row there is character pair vector, i.e. first row for the proper vector corresponding to eigenvalue of maximum, and secondary series for the proper vector corresponding to minimal eigenvalue.

Then the TLS of battery capacity inverse estimates to pass through the ratio of component provides,

${\hat{C}}_{\mathrm{TLS}}^{-1}\left[\mathrm{\&kappa;}\right]=-\frac{v_2^{\mathrm{\&kappa;}}\left(1\right)}{v_2^{\mathrm{\&kappa;}}\left(2\right)}=\frac{S_H^k\left(\mathrm{1,2}\right)}{S_H^k\left(\mathrm{1,1}\right)-{\mathrm{\&Lambda;}}^{\mathrm{\&kappa;}}\left(\mathrm{2,2}\right)}---\left(105\right)\left[6\right]$

Wherein for i element, and for (i, j) element.(105) derivation illustrates as follows.

For level and smooth estimation, the information matrix in (103) can adopt Attenuation Memory Recursive to upgrade, as follows:

$S_H^k=\mathrm{\&lambda;}{S}_H^{k-1}+\frac{{\left(H^{\mathrm{\&kappa;}}\right)}^T{H}^{\mathrm{\&kappa;}}}{L_c-1}---\left(106\right)$

Now, based on [85], TLS evaluated error covariance (being similar to) is:

${\hat{R}}_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]={\left(\frac{1}{{\left(z^{\mathrm{\&kappa;}}\right)}^T{S}_H^k{z}^{\mathrm{\&kappa;}}}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{h}_i^{\mathrm{\&kappa;}}{\left(h_i^{\mathrm{\&kappa;}}\right)}^T\right)}^{-1}---\left(107\right)$

Wherein for H ^κi capable, M is H ^κin line number, and

$z^{\mathrm{\&kappa;}}={[-\frac{v_2^{\mathrm{\&kappa;}}\left(1\right)}{v_2^{\mathrm{\&kappa;}}\left(2\right)}-1]}^T---\left(108\right)$

Below discuss and relate to the battery capacity estimation based on open-circuit voltage (OCV).For given standing voltage z _v[k], corresponding SOC estimates can be by (33) being got to reciprocal acquisition.Due to the hysteresis in battery, this SOC estimates to be different from actual SOC x _s[k], obtains OCV seek error oCV seek error will be always negative and just be always between charge period at interdischarge interval.The open-circuit voltage of battery (OCV) can be written as the nonlinear function of SOC, as

$\begin{array}{c}\end{array}\begin{array}{c}{V}_0\left(x_s\right[k\left]\right)=K_0+\frac{K_1}{x_s\left[k\right]}+\frac{K_2}{x_s{\left[k\right]}^2}+\frac{K_3}{x_s{\left[k\right]}^3}+\frac{K_4}{x_s{\left[k\right]}^4}+\\ K_5{x}_s\left[k\right]+K_6\ln \left(x_s\right[k\left]\right)+K_7\ln (1-x_s[k\left]\right)\end{array}---\left(109\right)$

Wherein can to battery, carry out the slowly charging voltage and current measured value that then electric discharge obtains by gathering, come COEFFICIENT K ₀, K ₁, K ₂, K ₃, K ₄, K ₅, K ₆and K ₇carry out off-line estimation.Battery sufficient standing whether no matter, the OCV-SOC family curve of gained all can be used for obtaining the measured value of SOC.For given standing terminal voltage (it is also open-circuit voltage) z _vthe SOC of the battery of [k] is written as:

${\hat{x}}_{s,\mathrm{ocv}}\left[k\right]=f_{\mathrm{ocv}-\mathrm{soc}}^{-1}\left(z_v\right[k\left]\right)---\left(110\right)$

Can use OCV-SOC to characterize by calculating the inverse of (109) calculates.Have a plurality of for example, for calculating the method reciprocal of nonlinear function, Newton method and binary chop.This can be described as the SOC searching based on OCV and estimates.(110) SOC in estimates to be damaged as follows by lagging voltage:

$x_s\left[k\right]={\hat{x}}_{s,\mathrm{pcv}}\left[k\right]+{\tilde{x}}_{s,\mathrm{ocv}}\left[k\right]---\left(111\right)$

OCV seek error wherein lag-effect in OCV causes.Should be noted that, when battery after discharge process, in time k place, become standing, OCV seek error should be negative.Similarly, when battery after charging process, in time k place, become standing, OCV seek error to just be always.Yet mistake extent will change with hysteresis size, it is standing front size of current, SOC and the function of time.Now, with following form, again write (79):

x _s[k+1]=x _s[k]+c _hΔz _i[k]+w _s[k] （112）

x _s[k+2]=x _s[k+1]+c _hΔ _k+1z _i[k+1]+w _s[k+1] （113）

.

.

.

x _s[k+N]=x _s[k+N-1]+c _hΔ _k+N-1z _i[k+N-1]+w _s[k+N-1] （114）

By being added respectively (112) on both sides to (114), obtain following result:

Wherein,

for thering is standard deviation zero mean.

Suppose battery at time k and k+N in standing, (115) can be written as:

$d_{s,\mathrm{ocv}}^k=C_{\mathrm{batt}}^{-1}{d}_{c,\mathrm{ocv}}^k+{\tilde{w}}_{s,\mathrm{ocv}}^k---\left(116\right)$

Wherein,

$d_{c,\mathrm{ocv}}^k=\frac{\mathrm{\&eta;}\underset{j=k}{\overset{j=K+N-1}{\mathrm{\&Sigma;}}}\mathrm{\&Delta;}{z}_i\left[k\right]}{3600}---\left(117\right)$

$d_{s,\mathrm{ocv}}^k={\hat{x}}_{s,\mathrm{ocv}}[k+N]-{\hat{x}}_{s,\mathrm{ocv}}\left[k\right]---\left(118\right)$

Should be noted that, no matter OCV seek error this fact of sign deflection battery mode ∈ { charging, electric discharge }, " differential error " (definition in (119)) can be plus or minus.By considering a large amount of differential errors, suppose be approximately white.Suppose the differential of k batch respectively at first group of standing point $k=k_1,k_2,...,k_{L_c}$ With second group of standing point $k+N=k_1+N_1,k_2+N_2,...,k_{L_c}+N_{L_c},$ Between gather, and provide as follows:

$d_{s,\mathrm{ocv}}^{\mathrm{\&kappa;}}=C_{\mathrm{batt}}^{-1}{d}_{c,\mathrm{ocv}}^{\mathrm{\&kappa;}}+{\tilde{w}}_{s,\mathrm{ocv}}^{\mathrm{\&kappa;}}---\left(120\right)$

Wherein,

$d_{s,\mathrm{ocv}}^{\mathrm{\&kappa;}}={[d_{s,\mathrm{ocv}}^{k_1},d_{s,\mathrm{ocv}}^{k_2},...,d_{s,\mathrm{ocv}}^{k_{L_c}}]}^T---\left(121\right)$

$d_{c,\mathrm{ocv}}^{\mathrm{\&kappa;}}={[d_{c,\mathrm{ocv}}^{k_1},d_{c,\mathrm{ocv}}^{k_2},...,d_{c,\mathrm{ocv}}^{k_{L_c}}]}^T---\left(122\right)$

${\tilde{w}}_{s,\mathrm{ocv}}^{\mathrm{\&kappa;}}={[w_{s,\mathrm{ocv}}^{k_1},w_{s,\mathrm{ocv}}^{k_2},...,w_{s,\mathrm{ocv}}^{k_{L_c}}]}^T---\left(123\right)$

Now, can find out that (120) have the form identical with (92), wherein with replaced respectively with thereby the capacity estimation based on RLS and TLS can be derived for the observation based on OCV, as follows.The RLS of the capacity based on OCV and TLS estimate to be expressed as with should be noted that the given given N that is interspersed with electric discharge _rthe static condition of quantity, can carry out N _r(N _r-1)/2 differential observations.For example,, for N _r=4,, suppose that battery is at time point t ₁, t ₂, t ₃and t ₄. in static condition.

Below relate to the capacity estimation of being undertaken by fusion.In this part, described for merging the exemplary concrete enforcement of the TLS estimated value of capacity.In this part, for the capacity estimation value based on TLS, set up and derive.These are derived and also can be applicable to merge the capacity estimation value based on RLS.

Online capacity estimation value error in measured electric current causes the uncertainty of (referring to (92)) and the error in SOC track algorithm cause uncertainty damage.Similarly, the capacity estimation value based on OCV error in measured electric current causes the uncertainty of (referring to (120)) and OCV search that differential error causes uncertainty damage.Suppose online capacity estimation value e _tthe error of [κ] and the capacity estimation value e searching based on OCV _tothe error of [κ] is uncorrelated.Based on these hypothesis, capacity merges the fusion that has become two independent flight paths.

First, should be noted that the estimated value of capacity inverse, for example capacity estimation value with 1/C respectively does for oneself _battestimated value.Correspondingly, evaluated error covariance separately with also corresponding to capacity estimated value reciprocal.Based on Taylor series expansion, expectation value and the corresponding estimation error variance of the dynamic capacity estimated value based on TLS are approximately:

${\hat{C}}_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]=\frac{1}{{\hat{C}}_{\mathrm{TLS}}^{-1}\left[\mathrm{\&kappa;}\right]}+\frac{{\hat{R}}_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]}{{\left({\hat{C}}_{\mathrm{TLS}}^{-1}\right[\mathrm{\&kappa;}\left]\right)}^3}---\left(124\right)$

$R_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]=\frac{{\hat{R}}_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]}{{\left({\hat{C}}_{\mathrm{TLS}}^{-1}\right[\mathrm{\&kappa;}\left]\right)}^4}---\left(125\right)$

Wherein for the C based on dynamic data _battestimated value, and R _tLS[κ] is estimation error variance.By following identical program, can obtain the capacity estimation value C based on OCV _tO[κ] and corresponding evaluated error covariance R _tO[κ].Now, suppose that battery capacity is stochastic variable, the following Wiener-Hopf equation slowly changing of its experience:

x _c[κ+1]=x _c[κ]+w _c[κ] （126）

W wherein _c[κ] is assumed to has variance Q _cthe zero mean white Gaussian noise of [κ].Capacity estimation value with adaptive following observation model:

z _c[κ]=x _c[κ]+n _c[κ] （127）

Wherein,

$z_c\left[\mathrm{\&kappa;}\right]\&Element;\left\{{\hat{C}}_{\mathrm{TLS}}\right[{\mathrm{\&kappa;}}^{\&prime;}],{\hat{C}}_{\mathrm{TO}}[{\mathrm{\&kappa;}}^{\&prime;\&prime;}\left]\right\}---\left(128\right)$

κ ' and κ " be according to the time index of the latest estimated value of corresponding algorithm (being respectively TLS and TO), and n _c[κ] is assumed to the zero mean white noise with following variance:

$R_c\left[\mathrm{\&kappa;}\right]=\left\{\begin{array}{cc}{R}_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]& \mathrm{if}{z}_c\left[\mathrm{\&kappa;}\right]={\hat{C}}_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]\\ R_{\mathrm{TO}}\left[\mathrm{\&kappa;}\right]& \mathrm{if}{z}_c\left[\mathrm{\&kappa;}\right]={\hat{C}}_{\mathrm{TO}}\left[\mathrm{\&kappa;}\right]\end{array}\right.---\left(129\right)$

Now, no matter when receive new measured value wherein κ '=κ or κ ' '=κ, the capacity estimation value of fusion obtains as follows:

$\begin{array}{c}{\hat{x}}_c\left[\mathrm{\&kappa;}\right|\mathrm{\&kappa;}]={\hat{x}}_c[\mathrm{\&kappa;}-1|\mathrm{\&kappa;}-1]+\\ \frac{P_c[k-1|k-1]+Q_c[\mathrm{\&kappa;}-1]}{P_c[\mathrm{\&kappa;}-1|\mathrm{\&kappa;}-1]+Q_c[\mathrm{\&kappa;}-1]+R_c[\mathrm{\&kappa;}]}\left(z_c\right[\mathrm{\&kappa;}]-{\hat{x}}_c(k-1|k-1))\end{array}---\left(130\right)$

Wherein for the previous renewal of capacity estimation value, and P _c[κ-1| κ-1] is previous estimation error variance, and it is updated to:

$P_c\left[\mathrm{\&kappa;}\right|\mathrm{\&kappa;}]=\frac{R_c\left[\mathrm{\&kappa;}\right]\left(P_c\right[\mathrm{\&kappa;}-1|\mathrm{\&kappa;}-1+Q_c[\mathrm{\&kappa;}-1])}{P_c[\mathrm{\&kappa;}-1|\mathrm{\&kappa;}-1]+Q_c[\mathrm{\&kappa;}-1]+R_c[\mathrm{\&kappa;}]}---\left(131\right)$

Above-mentioned fusion method can be similarly for merging the capacity estimation value based on RLS.

Below relate to the derivation of capacity estimation error covariance.In this part, derive the covariance of the differential error in (90).For convenience's sake, differential error (90) is rewritten as following form

${\tilde{w}}_s\left[k\right]={\tilde{x}}_s\left[k\right|k]-{\tilde{x}}_s[k+1|k+1]+w_s\left[k\right]---\left(90\right)$

Object is to calculate variance:

$E\left\{{\tilde{w}}_s\right[k\left]{\tilde{w}}_s{\left[k\right]}^T\right\}\&cong;R_{{\tilde{w}}_s\left[k\right]}---\left(132\right)$

According to following form writing process equation (79):

x _s[k+1]=x _s[k]+c _hΔz _i[k]+w _s[k] （134）

${\hat{x}}_s[k+1|k+1]={\hat{x}}_s[k\left|k\right]+c_h\mathrm{\&Delta;}{z}_i\left[k\right]+G[k+1]v[k+1]---\left(135\right)$

Wherein for x _sthe Kalman filter estimated value of [k+1], ν [k+1] newly ceases for wave filter, and G[k+1] be kalman gain.(134) difference and between (135) is:

${\tilde{x}}_s[k+1]={\tilde{x}}_s\left[k\right]+w_s\left[k\right]-G[k+1]v[k+1]---\left(136\right)$

It can be rearranged as following form:

${\tilde{x}}_s\left[k\right]-{\tilde{x}}_s[k+1]+w_s\left[k\right]={\tilde{w}}_s\left[k\right]=G[k+1]v[k+1]---\left(137\right)$

Thereby,

$R_{{\tilde{w}}_S\left[k\right]}=G{[k+1]}^{2}S[k+1]---\left(138\right)$

Wherein,

S[k+1] be new breath covariance.

Below described and confirmed substituting or the second method of above-mentioned derivation.Launch (132):

Wherein,

E ₁=P _s[k|k] （139）

E ₂=P _s[k+1|k+1] （140）

$E_3={\mathrm{\&sigma;}}_s^2---\left(141\right)$

E ₅=0 （143）

$\begin{array}{c}{E}_6=E\left\{{\tilde{x}}_s\right[k+1\left]w_s\right[k\left]\right\}\\ =E\left\{{\tilde{x}}_s\right[k\left|k\right]w_s\left[k\right]\}+E\\ ={\mathrm{\&sigma;}}_s^2\end{array},\left\{w_s\right[k\left]w_s\right[k\left]\right\}-G[k+1]H[k+1]E\left\{{\tilde{x}}_s\right[k\left|k\right]w_s\left[k\right]\}---\left(144\right)$

$\begin{array}{c}E\left\{{\tilde{w}}_s\right[k\left]{\tilde{w}}_s\right[k\left]\right\}=E1+E2+E3-2E4+2E5-2E6\\ =P_s\left[k\right|k]+P_s[[k+1|k+1]+{\mathrm{\&sigma;}}_s^2-2(1-G[k+1\left]H\right[k+1\left]\right)P_s[k\left|k\right]-2{\mathrm{\&sigma;}}_s^2\\ =P_s\left[k\right|k]+{(1-G[k+1\left]G\right[k+1\left]H\right[k+1\left]\right)}^2{P}_s[k\left|k\right]+{\mathrm{\&sigma;}}_s^2+G[k+1]R_D\left[0\right]G[k+1]\\ +{\mathrm{\&sigma;}}_s^2-2\left(\right[1-G[k+1]H[k+1])P_s\left]k\right|k]-2{\mathrm{\&sigma;}}_s^2\\ =G{[k+1]}^{2}H{[k+1]}^2{P}_s\left[k\right|k]+G[k+1\left]R_D\left(0\right)G\right[k+1]\\ G{[k+1]}^2\left(H{[k+1]}^2{P}_s\right[k\left|k\right]+R_D\left(0\right))\\ =G{[k+1]}^{2}S[k+1]\end{array}---\left(145\right)$

The enclosed that below relates to total least square (TLS) capacity estimation value is derived.By 2 * 2 matrixes $A\stackrel{\mathrm{\&Delta;}}{=}{S}_H^k$ Write into:

$A=\left[\begin{array}{cc}{\mathrm{\&sigma;}}_{11}& {\mathrm{\&sigma;}}_{12}\\ {\mathrm{\&sigma;}}_{12}& {\mathrm{\&sigma;}}_{22}\end{array}\right]---\left(146\right)$

The eigenwert of A meets

|A-λI|=0 （147）

$|\begin{array}{cc}{\mathrm{\&sigma;}}_{11}-\mathrm{\&lambda;}& {\mathrm{\&sigma;}}_{12}\\ {\mathrm{\&sigma;}}_{12}& {\mathrm{\&sigma;}}_{22}-\mathrm{\&lambda;}\end{array}|=0---\left(148\right)$

It is reduced to

${\mathrm{\&lambda;}}_1=\frac{{\mathrm{\&sigma;}}_{11}+{\mathrm{\&sigma;}}_{22}+\sqrt{{({\mathrm{\&sigma;}}_{11}-{\mathrm{\&sigma;}}_{22})}^2+4{\left({\mathrm{\&sigma;}}_{12}\right)}^2}}{2}---\left(149\right)$

${\mathrm{\&lambda;}}_2=\frac{{\mathrm{\&sigma;}}_{11}+{\mathrm{\&sigma;}}_{22}-\sqrt{{({\mathrm{\&sigma;}}_{11}-{\mathrm{\&sigma;}}_{22})}^2+4{\left({\mathrm{\&sigma;}}_{12}\right)}^2}}{2}---\left(150\right)$

λ wherein ₁for eigenvalue of maximum and λ ₂for minimal eigenvalue.Corresponding to λ ₂eigenwert meet

$A{v}_2^{\mathrm{\&kappa;}}={\mathrm{\&lambda;}}_2{v}_2^{\mathrm{\&kappa;}}---\left(151\right)$

Wherein

$v_2^{\mathrm{\&kappa;}}=\left[\begin{array}{c}\frac{-{\mathrm{\&sigma;}}_{12}}{\sqrt{{\mathrm{\&sigma;}}_{12}^2+{({\mathrm{\&sigma;}}_{11}-{\mathrm{\&lambda;}}_2)}^2}}\\ \frac{{\mathrm{\&sigma;}}_{11}-{\mathrm{\&lambda;}}_2}{\sqrt{{\mathrm{\&sigma;}}_{12}^2+{({\mathrm{\&sigma;}}_{11}-{\mathrm{\&lambda;}}_2)}^2}}\end{array}\right]---\left(152\right)$

For example,

$v_2^{\mathrm{\&kappa;}}\left(1\right)=\frac{-{\mathrm{\&sigma;}}_{12}}{\sqrt{{\mathrm{\&sigma;}}_{12}^2+{({\mathrm{\&sigma;}}_{11}-{\mathrm{\&lambda;}}_2)}^2}}---\left(153\right)$

$v_2^{\mathrm{\&kappa;}}\left(2\right)=\frac{{\mathrm{\&sigma;}}_{11}-{\mathrm{\&lambda;}}_2}{\sqrt{{\mathrm{\&sigma;}}_{12}^2+{({\mathrm{\&sigma;}}_{11}-{\mathrm{\&lambda;}}_2)}^2}}---\left(154\right)$

And

${\hat{C}}_{\mathrm{TLS}}^{-1}\left[\mathrm{\&kappa;}\right]=-\frac{v_2^{\mathrm{\&kappa;}}\left(1\right)}{v_2^{\mathrm{\&kappa;}}\left(2\right)}$

$=\frac{S_H^{\mathrm{\&kappa;}}\left(\mathrm{1,2}\right)}{S_H^{\mathrm{\&kappa;}}\left(\mathrm{1,1}\right)-{\mathrm{\&Lambda;}}^{\mathrm{\&kappa;}}\left(\mathrm{2,2}\right)}---\left(155\right)\left[6\right]$

Below relate to the capacity conversion of estimating reciprocal.Exemplary concrete enforcement comprises the method that draws capacity estimation value and estimation error variance based on estimated value reciprocal and estimation error variance reciprocal.For capacity estimation value reciprocal and error variance assignment simple variable, for example,

$x\&cong;C_{\mathrm{TLS}}^{-1}\left[\mathrm{\&kappa;}\right]---\left(156\right)$

$x_0\&cong;E\left\{x\right\}=C_{\mathrm{TLS}}^{-1}\left[\mathrm{\&kappa;}\right]---\left(157\right)$

$R_x\&cong;E\left\{{(x-x_0)}^2\right\}={\hat{R}}_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]---\left(158\right)$

Definition:

$y\&cong;f\left(x\right)=\frac{1}{x}---\left(159\right)$

Our object is to find E{y} and E{ (y-E{y}) ²approximate value.

Below relate to the expectation value of determining y.Second order Taylor series approximation value is by given below:

$y=f\left(x\right)=f\left(x_0\right)+f^{\&prime;}\left(x_0\right)(x-x_0)+\frac{1}{2}{f}^{\&prime;\&prime;}\left(x_0\right){(x-x_0)}^2---\left(160\right)$

The second order approximate value of E{y} is by given below:

The variance that below relates to the expectation value of determining y.At actual value x ₀. f (x) is expanded into single order Taylor series around

y=f(x)=f(x ₀)+f'(x ₀)(x-x ₀) （162）

The variance of y is by given below:

$\begin{array}{c}E\left\{{(y-E\{y\left\}\right)}^2\right\}=E\left\{{\left(f^{\&prime;}\left(x_0\right)(x-x_0)\right)}^2\right\}\\ =\frac{R_x}{x_0^4}\end{array}---\left(163\right)$

Now, the expectation value of capacity estimation value and estimation error variance thereof are by given below:

$C_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]=\frac{1}{{\hat{C}}_{\mathrm{TLS}}^{-1}\left[\mathrm{\&kappa;}\right]}+\frac{{\hat{R}}_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]}{{\left({\hat{C}}_{\mathrm{TLS}}^{-1}\right[\mathrm{\&kappa;}\left]\right)}^3}---\left(164\right)$

$R_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]=\frac{{\hat{R}}_{\mathrm{TLS}}\left[\mathrm{\&kappa;}\right]}{{\left({\hat{C}}_{\mathrm{TLS}}^{-1}\right[\mathrm{\&kappa;}\left]\right)}^4}---\left(165\right)$

Next present disclosure is that state of charge (SOC) is followed the tracks of, and it can be with reference to following symbol.

In this exemplary concrete enforcement, based on instantaneous terminal voltage, load current and measured temperature, follow the tracks of the state of charge (SOC) of electrochemical energy storage device (battery).SOC track algorithm is used the understanding of above-mentioned model parameter estimation and battery capacity estimation.Exemplary SOC follows the tracks of and hysteresis is modeled as to the error in open-circuit voltage (OCV) and adopts parameter estimation and the combination of SOC tracking technique compensates it.This has eliminated hysteresis off-line modeling is the needs of the function of SOC and load current.The depression of order that this exemplary model causes following the tracks of for SOC (as, single status) filtering, no matter wherein the complexity level of battery equivalent model how, all without following the tracks of supplementary variable.The existence of identification correlated noise is also used it for and is improved SOC tracking.Different from conventional " model adaptation is all " strategy, identified four different equivalent models of battery, these models represent that four unique patterns of representative cells operation the model based on suitable set up the framework of following the tracks of for seamless SOC.

Comprise that SOC relates to matrix operation expensive on calculating and reduced the precision that SOC estimates with the typical depression of order state filtering method of combining (recurrence) estimation of other redundancies (unnecessary) amount.In this exemplary concrete enforcement, used the depression of order filtering that does not increase state space dimension, thereby obtained the computational complexity of better SOC precision and reduction.By hysteresis being modeled as to the error in OCV, eliminated the needs of hysteresis modeling, and online filtering method continues to attempt by adjustment SOC(to modified value) carry out fill in a gap.Thereby, lag behind and become and setover while being modeled as.Using noise albefaction program, and derive amended state-space model, to guarantee that SOC track algorithm draws result as well as possible in least mean-square error meaning.Use the difference " pattern " of battery to follow the tracks of SOC.At least four different battery equivalent models load (as, charging), dynamic load and heavy duty for reflecting very light load or static condition, steady current operation or low frequency.Also identify four (a little) different dynamic equivalent model with these patterns of optimum matching.The depression of order filtering method providing has guaranteed that seamless SOC follows the tracks of, no matter and the patterns of change of battery operation.

Below discuss and relate to example system model.The battery equivalent-circuit model of considering is herein shown in Figure 13 A.When battery is when standing, V ₀(s[k]) be the OCV of battery.The unique SOC that depends on battery of OCV, s[k].When battery is during in active state, for example, when there is current active, the behavior of battery represents by dynamic equivalent circuit, and described dynamic equivalent circuit is by lag element h[k], resistance in series R ₀and two the RC the circuit in parallel, (R that are connected in series ₁, C ₁) and (R ₂, C ₂) form.Discrete time is used [k] indication.

The battery equivalent-circuit model that this part is considered is shown in Figure 13 A.Terminal voltage v[k with regard to the element in battery equivalent electrical circuit] 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）

V wherein ₀(s[k]) represents the open-circuit voltage (with voltmeter) of time k place battery, and it is write as the function of the SOC at time k place, s[k herein] ∈ [0,1]; H[k] hysteresis in cell voltage is described; i ₁[k] and i ₂[k] is respectively and flows through R ₁and R ₂electric current.

Have some non-linear expression forms, it makes OCV be similar to the function of SOC.In this exemplary concrete enforcement, for represent the polynomial expression log-linear model reciprocal of OCV with SOC:

$\begin{array}{c}\end{array}\begin{array}{c}{V}_0\left(s\right[k\left]\right)=K_0+\frac{K_1}{s\left[k\right]}+\frac{K_2}{s^2\left[k\right]}+\frac{K_3}{s^3\left[k\right]}+\frac{K_4}{s^4\left[k\right]}+\\ K_{5}s\left[k\right]+K_6\ln \left(s\right[k\left]\right)+K_7\ln (1-s[k\left]\right)\end{array}---\left(167\right)\left[3\right]$

K wherein ₀, K ₁, K ₂, K ₃, K ₄, K ₅, K ₆and K ₇can characterize off-line by OCV-SOC estimates.The transient change of SOC can be write into following form (introduce x under be marked with indicating status component):

$x_s[k+1]\&cong;s[k+1]=s\left[k\right]+c_h\mathrm{\&Delta;i}\left[k\right]---\left(168\right)$

I[k wherein] in amperage;

c _h=η/3600C _batt （169）

For with ampere ^-1second ^-1the coulombmeter number system number of meter, C _battfor the battery capacity in ampere hour (Ah), Δ is in the sample interval of second, and η is constant, and it depends on that battery is charging or electric discharge, for example,

$\mathrm{\&eta;}=\left\{\begin{array}{cc}{\mathrm{\&eta;}}_c& i\left[k\right]>0\\ {\mathrm{\&eta;}}_d& i\left[k\right]<0\end{array}\right.---\left(170\right)$

Should be noted that, (168) draw the instantaneous SOC of battery.This technology of calculating SOC is called as coulomb counting and/or " SOC for prediction ".Coulomb counting is supposed and is understood initial charge state and understand battery capacity completely and calculate residual charge state to shift certainly/shift after the coulomb amount of battery in consideration.Coulomb counting error packet is drawn together (1) uncertainty to the understanding of initial SOC; (2) uncertainty to the understanding of battery capacity; And (3) because measure electric current error and because of timing oscillator inaccurate/error of the measurement coulomb that the error of time difference due to drift causes.

Easily there is error in the measured and current measurement value of current i [k].To measure electric current z _i[k] write as:

z _i[k]=i[k]+n _i[k] （171）

N wherein _i[k] is current measurement noise, and it is considered to have white zero mean and has known standard deviation (s.d.) σ _i..Can be by using in the following manner z _i[k] replaces i[k] rewrite state equation (168):

x _s[k+1]=x _s[k]+c _hΔz _i[k]-c _hΔn _i[k] （172）

Can write in the following manner and flow through resistor R ₁and R ₂electric current:

$x_{i_1}[k+1]\&cong;i_1[k+1]={\mathrm{\&alpha;}}_1{i}_1\left[k\right]+(1-{\mathrm{\&alpha;}}_1)i\left[k\right]---\left(172\right)$

$x_{i_2}[k+1]\&cong;i_2[k+1]={\mathrm{\&alpha;}}_2{i}_2\left[k\right]+(1-{\mathrm{\&alpha;}}_2)i\left[k\right]---\left(173\right)$

Wherein

${\mathrm{\&alpha;}}_1=e^{-\frac{\mathrm{\&Delta;}}{R_1{C}_1}}---\left(174\right)$

${\mathrm{\&alpha;}}_2=e^{-\frac{\mathrm{\&Delta;}}{R_2{C}_2}}---\left(175\right)$

By use, measure electric current z _i[k] replaces i[k], can rewrite in the following manner the electric current in (172) and (173):

$x_{i_1}[k+1]={\mathrm{\&alpha;}}_1{x}_{i_1}\left[k\right]+(1-{\mathrm{\&alpha;}}_1)z_i\left[k\right]-(1-{\mathrm{\&alpha;}}_1)n_i\left[k\right]---\left(176\right)$

$x_{i_2}[k+1]={\mathrm{\&alpha;}}_2{x}_{i_2}\left[k\right]+(1-{\mathrm{\&alpha;}}_2)z_i\left[k\right]-(1-{\mathrm{\&alpha;}}_2)n_i\left[k\right]---\left(177\right)$

Lagging voltage h[k] be the load current of battery and the nonlinear function of SOC.Delay Process can be write as:

$x_h\left[k\right]\&cong;h\left[k\right]=f_h\left(x_s\right[k],i[k\left]\right)x_h\left[k\right]+n_h\left[k\right]---\left(178\right)$

N wherein _h[k] is the process noise of lag model, supposes that it is zero mean white Gaussian noise and has s.d. σ _h.(166) voltage in is measuring amount and measuring voltage z _veasily there is error in [k].Measuring 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）

N wherein _v[k] is assumed to has zero mean and s.d. σ _vwhite Gaussian noise.Now, by by (171), (172), (173) and (178) substitutions (179), derive following measurement model:

$z_v\left[k\right]=V_0\left(x_s\right[k\left]\right)+z_i\left[k\right]R_0+x_{i_1}\left[k\right]R_1+x_{i_2}\left[k\right]R_2+x_h\left[k\right]+n_{z_v}\left[k\right]---\left(180\right)$

Wherein,

$n_{z_v}\left[k\right]=n_v\left[k\right]-R_0{n}_i\left[k\right]---\left(181\right)$

Now, provide instantaneous voltage and current measurement value z _v[k] and z _i[k], the object of BFG is to follow the tracks of the instantaneous SOC x of battery _s[k].." unnecessary " variable in observation model (180) with existence cause associating estimation problem, SOC and these variablees must be combined estimation.This can by form as (the multidimensional process of the vector form as shown in 183) – (189) and measurement model and/or realize recursively estimating by applying Bayes's nonlinear filtering technique:

$\left[k\right]\&cong;\left[\begin{array}{c}{x}_s\left[k\right]\\ x_h\left[k\right]\\ x_{i_1}\left[k\right]\\ x_{i_2}\left[k\right]\end{array}\right]---\left(182\right)$

Provide until all measured values of time k, [0], [1], [2] ..., [k] }, wherein by (171) and (180), formed.This nonlinear filtering technique that can know by application (for example extended Kalman filter (EKF), Unscented kalman filtering device (UKF) or particle filter) effectively carries out.Can vector form be write into (178) by process equation (172), (176), (177):

$\begin{array}{c}\left[\begin{array}{c}{x}_s[k+1]\\ x_h[k+1]\\ x_{i_1}[k+1]\\ x_{i_2}[k+1]\end{array}\right]=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& f_h\left(s\right[k],i[k\left]\right)& 0& 0\\ 0& 0& {\mathrm{\&alpha;}}_1& 0\\ 0& 0& 0& {\mathrm{\&alpha;}}_2\end{array}\right]\left[\begin{array}{c}{x}_s\left[k\right]\\ x_h\left[k\right]\\ x_{i_1}\left[k\right]\\ x_{i_2}\left[k\right]\end{array}\right]+\left[\begin{array}{c}{c}_h\mathrm{\&Delta;}\\ 0\\ 1-{\mathrm{\&alpha;}}_1\\ 1-{\mathrm{\&alpha;}}_2\end{array}\right]z_i\left[k\right]\\ +\left[\begin{array}{cc}-c_h\mathrm{\&Delta;}& 0\\ 0& 1\\ {\mathrm{\&alpha;}}_1-1& 0\\ {\mathrm{\&alpha;}}_2-1& 0\end{array}\right]\left[\begin{array}{c}{n}_i\left[k\right]\\ n_h\left[k\right]\end{array}\right]\end{array}---\left(183\right)$

Or, be abbreviated as:

x[k+1]=F _kx[k]+u[k]+Γ _kw[k] （184）

Wherein,

$w\left[k\right]=\left[\begin{array}{c}{n}_i\left[k\right]\\ n_h\left[k\right]\end{array}\right]---\left(185\right)$

For thering is the white noise vector of zero mean and following covariance:

${\mathrm{\&Sigma;}}_w=\left[\begin{array}{cc}{\mathrm{\&sigma;}}_i^2& 0\\ 0& {\mathrm{\&sigma;}}_h^2\end{array}\right]---\left(186\right)$

Correspondingly, measuring equation (180) can write into:

$z_v\left[k\right]=g\left(\right[k\left]\right)+z_i\left[k\right]R_0+n_{z_v}\left[k\right]---\left(187\right)$

Wherein,

$g\left(\right[k\left]\right)=V_0\left(x_s\right[k\left]\right)+x_h\left[k\right]+x_{i_1}\left[k\right]R_1+x_{i_2}\left[k\right]R_2---\left(188\right)$

And the n with zero mean and following s.d. _z[k] noise vector.

${\mathrm{\&sigma;}}_z=\sqrt{{\mathrm{\&sigma;}}_v^2+R_0^2{\mathrm{\&sigma;}}_i^2}---\left(189\right)$

In addition, should be noted that, (183) – (189) relate to the following model parameter that need to estimate by system identification technique to state-space representation form, comprise battery capacity: C _batt, open-circuit 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, charging and discharging efficiency: η _c, η _d, process noise variance: and measurement noise variance

To the requirement of all model parameter estimation, make SOC tracking problem have more challenge.In addition, the chemical property of battery can change because of temperature variation, aging and use pattern, so these model parameters can times to time change.Thereby, pass in time, must reappraise model parameter.

In exemplary concrete enforcement, suppose the OCV parameter K of battery ₀, K ₁..., K ₇that off-line is estimated.The program of estimating these parameters has above been described.Suppose voltage and current error to standard deviation, be respectively σ _vand σ _i, can obtain from metering circuit design.Suppose charging and discharging efficiency, be respectively η _cand η _d, by calibrating, know.Thereby object is to understand battery capacity C by supposition _battelectrical equivalent model parameter R with battery ₀, R ₁, R ₂, C ₁and C ₂set up online SOC track algorithm.

Following discussion relates to SOC and follows the tracks of.The object of depression of order filtering is to follow the tracks of x _s[k], needn't follow the tracks of redundant variables simultaneously and x _h[k].First, according to following form, rewrite (172):

x _s[k+1]=x _s[k]+c _hΔz _i[k]+w _s[k] （190）

Wherein,

w _s[k]=-c _hΔn _i[k] （191）

For process noise, it is the white noise with following s.d.:

σ _s=c _hΔσ _i （192）

Now, voltage measuring value (180) is rewritten as:

z _v[k]=V ₀(x _s[k])+a[k] ^Tb+n _D[k] （193）[4]

Wherein,

a[k] ^Tb=[v _D[k-1]v _D[k-2]z _i[k]z _i[k-1]-z _i[k-2]1] （194）

And voltage drop is by providing as follows:

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 for measuring noise.Should be noted that, [k] in (194) is with voltage drop v _d[k-1] and v _d[k-2]. definition.Estimated parameter b based on voltage drop observation model has above been described.The parameter of estimation is derived as according to the parameter of the battery equivalent model in Figure 13 A:

$b\left(1\right)\&cong;\mathrm{\&alpha;}\left(k\right)={\mathrm{\&alpha;}}_1+{\mathrm{\&alpha;}}_2---\left(196\right)$

$b\left(2\right)\&cong;\mathrm{\&beta;}\left(k\right)={\mathrm{\&alpha;}}_1{\mathrm{\&alpha;}}_2---\left(197\right)$

b(3)=R ₀ （198）

$b\left(6\right)\&cong;\hat{h}\left[k\right]=x_h\left[k\right]-\mathrm{\&alpha;}\left(k\right)x_h[k-1]+\mathrm{\&beta;}\left(k\right)x_h[k-2]---\left(201\right)$

Measure noise n _d[k] is zero mean and has by following given autocorrelation

Next, voltage drop has been described in the meaning of estimating the parameter b in (193).Use (193), voltage drop (195) can be write as:

v _D[k]=a[k] ^Tb+n _D[k] （203）

Given voltage drop observation, above-mentioned model (203) can be used for Linear Estimation b.Yet, in order to obtain the voltage drop as observation, can use the predicted value of SOC to be or the SOC estimated value after upgrading is sOCx _sthe understanding of [k], for example,

$v_D\left[k\right|k]=z_v[k]-V_0\left({\hat{x}}_s\right[k\left|k\right])---\left(204\right)$

Describe below and how to obtain prediction with upgrade after (respectively referring to (209) and (215)).The existing method of BFG is used voltage and current observed reading z _v[k] and z _i[k] carries out Model Identification and SOC follows the tracks of.Consider conventional voltage observation model (180).X _hitem in [k] represents lagging voltage, and it is current i [k], SOC x as shown in (178) _sthe function of [k] and time k..For example, when the load (this is heavy duty in mobile application) of battery experience 1A is during the several seconds, and continue for the situation of 1A, to compare for 30 minutes when load, the amplitude of the hysteresis causing is less.In addition, the amplitude of hysteresis is also the function of SOC in this time.

Owing to using for the voltage observation (180) between the battery terminal of Model Identification, also need hysteresis xh[k] modeling and necessary estimation model parameter.Take the model of hysteresis of SOC, electric current and time representation as nonlinear, and understand not yet completely.Trial is that it hardly may online Model Identification to another shortcoming of hysteresis modeling and estimation.Owing to lagging behind, be the function of SOC, Model Identification need to be across the data of whole SOC scope.This may be impossible sometimes, because some application may never can be by battery from completely using sky.Because lag behind or the function of electric current, so Model Identification need to be across the usage data that is applied to the possible load current of various duration.Thereby complete hysteresis modeling and Model Identification become unrealistic.

It is also important that, it should be noted that, use sample battery off-line estimation model parameter, then may be unsatisfactory for electric quantity metering by these parameters; Some battery parameter has been notified based on use pattern and has been changed.Exemplary embodiment has been avoided hysteresis modeling by introducing above-mentioned voltage drop model.Voltage drop v _d[k] represents internal cell model element R ₀, R ₁, R ₂and x _h[k]. the voltage at two ends.Item x _h[k] had a mind to introduce to consider to be used for deriving voltage drop " measured value " prediction SOC in error.X _h[k] can be called as " instantaneous lagging ", and it, should be by adjusting SOC estimated value according to exemplary embodiment revise to zero.As above, for as described in Fig. 7, the use of voltage drop model can be used for eliminating lag-effect.Existing SOC understanding is fallen for calculating voltage.A collection of passing voltage drop is collected in impact damper and for the estimation of parameter b.(as determined in model estimation module or piece 710) the existence of nonzero value indication instantaneous lagging, this means and have SOC evaluated error.SOC track algorithm is designed to estimating for non-zero whenever, (at SOC, following the tracks of in piece 715) revises SOC.

OCV-SOC model (167) represents in OCV-SOC relation supposition voltage drop (195) (201) estimated value will be yet, mean for calculating voltage and fall observed reading v _dthere is error in the SOC estimated value of [k].Thereby SOC track algorithm needs corresponding adjustment this realizes by adopting following amended observation model to replace (193).

$z_v\left[k\right]=V_0\left(x_s\right[k\left]\right)+\tilde{a}{\left[k\right]}^T\tilde{b}+n_D\left[k\right]---\left(205\right[5\left]\right)$

Wherein,

$\tilde{a}{\left[k\right]}^T=\left[v_D\right[k-1\left]v_D\right[k-2\left]z_i\right[k\left]z_i\right[k-1]-z_i[k-2\left]\right]---\left(206\right)$

By removing respectively a[k] last element in T and b obtains.In other words, remove the item that lags behind.The meaning of amended observation model is described below.In addition, the process noise w in (190) _smeasurement noise n in [k] and (205) _dbetween [k], there is following covariance.

$E\left\{w_s\right[k\left]n_D\right[k\left]\right\}\&cong;U\left[k\right]=R_0{c}_h\mathrm{\&Delta;}{\mathrm{\&sigma;}}_i^2---\left(208\right)$

The estimated value of given state of charge with relevant variance P _s[k|k], following EKF recurrence (referring to Fig. 8) is used voltage and current measured value z _v[k+1], z _i[k], z _i[k+1] draws renewal after SOC estimated value and relevant variance P thereof _s[k+1|k+1]..These steps have also guaranteed that SOC estimated value considered the covariance of (208) by the best adjustment.Filtering recurrence is comprised of following:

${\hat{x}}_s[k+1|k]={\hat{x}}_s[k\left|k\right]+c_h\left[k\right]\mathrm{\&Delta;}{z}_i\left[k\right]---\left(209\right)$

$P_s[k+1|k]=P_s[k\left|k\right]+{\mathrm{\&sigma;}}_s^2---\left(210\right)$

$H[k+1]=\frac{d{z}_v\left[k\right]}{d{x}_s\left[k\right]}{|}_{{\hat{x}}_S[k+1|k]}---\left(211\right)$

${\hat{z}}_v[k+1]=V_0\left({\hat{x}}_s\right[k+1\left|k\right])+{\left[k\right]}^T\left[k\right]---\left(212\right)$

$S[k+1]=H[k+1]P\left[k\right|k]H{[k+1]}^T+R_{n_D}\left(0\right)+2H[k+1U\left[k\right]---\left(213\right)$

$G[k+1]=\frac{P[k+1|k]H{[k+1]}^T+U[k]}{S[k+1]}---\left(214\right)$

${\hat{x}}_s[k+1|k+1]={\hat{x}}_s[k+1\left|k\right]+G[k+1](z_{v}k+1]-{\hat{z}}_v[k+1])---\left(215\right)$

$\begin{array}{c}{P}_s[k+1|k+1]=(1-G[k+1\left]H\right[k+1\left]\right)P_s[k+1\left|k\right]{(1-G[k+1\left]H\right[k+1\left]\right)}^T\\ +G{[k+1]}^2{R}_{n_D}\left(0\right)\end{array}---\left(216\right)\left[2\right]$

C wherein _h[k] and it is respectively the latest estimated value of coulombmeter number system number and model parameter vector.Should describe and use state-space model (in 190) – (205) with carry out the importance of SOC tracking.Hysteresis can be considered to the error in OCV-SOC characteristic curve.It may be difficult to modeling and accurately estimate lag behind, because can change (referring to (178)) with previous electric current and SOC.Yet, can estimate true OCV-SOC relation.In fact, the V in (205) ₀(x _s[k]) based on true OCV-SOC model.For example, the hysteresis of supposing estimation is this means that wave filter " OCV of perception " and the true OCV of battery differ 10mV.For BFG algorithm, the OCV of perception, V ₀(x _s[k]), with SOC estimated value directly (and monotonously) is relevant.In other words, if the OCV of wave filter is different from actual OCV, wave filter estimated value so also the true SOC that is different from battery.Thereby, when wave filter is found its prediction terminal voltage in (212) decline 10mV, it can adjust its SOC estimated value in (215) make " the OCV error of perception " (or the hysteresis H estimating) (little by little) be adjusted into zero.Thereby the good indication of the normal operation of the method proposing is estimated all the time approach zero.

There is not reliable apparatus and the method for verifying in desired manner electric quantity metering algorithm.It is infeasible with simulation, assessing voltameter, in default of for example allowing the dynamic reliable mathematical model of simulated battery.For example, the self-correcting model of enhancing can not considered the impact of cell degradation.Due to the uncertainty in the true value of state of charge, battery capacity and internal resistance (all can be the amount of continuous drift), with single tolerance or verification method, verify that voltameter may be difficult to.Need to calculate the overall picture that a plurality of checkings measure to understand voltameter precision.

Next present disclosure is benchmark test, and it is from tolerance.In this exemplary concrete enforcement, described for verifying a plurality of reference test methods of the electric quantity metering algorithm of electrochemical energy storage device (battery).The cycle life that relatively accurate electric quantity metering (FG) can extend battery.This embodiment has also been described accurate and objective voltameter evaluation scheme.Tolerance as herein described is used in many aspects and measures FG precision and return at least one numeral that can indicate voltameter overall performance.Benchmark test as herein described can be applicable to multiple electric quantity metering algorithm.For example, being included in any concept described in the description that details in this embodiment can be called to name " method and apparatus that Methods and Apparatus Related to Tracking Battery State of Charge:A Reduced Order Filtering Approach(is relevant with following the tracks of battery state of charge: depression of order filtering method) " is combined.

Benchmark test described in this embodiment can be undertaken by being for example calculated as follows one or more in three kinds of tolerance of definition:

The first exemplary tolerance is a coulomb counting error.In conjunction with the understanding to the battery capacity of experiment and initial state of charge (SOC) point, coulombmeter counting method and/or equipment can provide the accurate estimation to battery state of charge.SOC estimation based on coulomb counting and the voltameter error (as root mean square (RMS)) between SOC estimation after a while can be used as the first tolerance of benchmark test.Error between SOC based on FG and the SOC based on coulomb counting may mean one or more problems relevant to the FG being verified:

-for the model possibility of open-circuit voltage state of charge (OCV-SOC) sign not accurate enough (supposing that FG adopts OCV-SOC to characterize)

-the battery capacity estimation of being undertaken by FG may be inaccurate

-dynamic equivalent circuit model may have problems aspect the Model Selection for FG and parameter estimation scheme.

The second exemplary tolerance is OCV-SOC error.The OCV-SOC of (can use one or more methods and/or equipment to carry out) battery characterizes the search program that can be provided for searching SOC.Thereby, by making battery in complete (or at least partly) static condition and by measuring the voltage of battery, voltameter can be estimated to compare to obtain error with OCV-SOC sign at the SOC of preset time.OCV-SOC error can be indicated one or more following problems of voltameter:

-may be invalid for the dynamic model of battery equivalent model

-minimum OCV-SOC error can indicate dynamic model used to mate well with the actual dynamic property of battery.

The 3rd exemplary tolerance reaches voltage time (TTV) error for predicting.Provide constant load/charging current, voltameter can (be used one or more methods and/or equipment), and prediction reaches a certain voltage spent time (TTV).Shut-in time (TTS) and completely duration of charging (TTF) can be the special circumstances that TTV estimates.Error during TTV estimates can be calculated after reaching considered virtual voltage.This TTV error can indicate relevant to evaluated voltameter following one or more:

The impedance estimation precision of-battery,

The battery capacity estimation precision of-voltameter,

-voltameter is to the understanding of battery SOC (as information),

The precision that-OCV-SOC characterizes.

Battery can show different qualities in response to temperature variation.For example, the impedance of battery can be higher at low temperatures (thereby and available horsepower may be lower).In response to the load under lower SOC, to compare with under the identical load of higher SOC level, OCV rate of change may be large and nonlinearity.The voltameter of high-quality can have the ability of operational excellence in wide in range temperature and SOC horizontal extent.Benchmark test as herein described can be configured to guarantee during Performance Evaluation at least some in these key elements to include in test.

Below discuss and relate to the tolerance characterizing based on OCV-SOC.The state of charge of battery can be relevant with its open-circuit voltage (OCV) uniquely.An example of this type of relation is shown in Figure 14 is curve map.

Several different methods can be used for obtaining OCV characterization data.A kind of illustrative methods is summarized as follows:

1) from charging completely, complete standing battery

2) record its open-circuit voltage V _bAT=V _full

3) set i=1

4) record OCV (i)=V _bAT

Record SOC (i)=1

5) set i=i+1

6) use steady current I to make battery discharge reach the duration of Δ T

7) make battery sufficient standing (as at least 2 hours)

8) measure battery terminal voltage, V _bAT

9) record OCV (i)=V _bAT

Calculate SOC (i)=SOC (i-1)+c _hi (i) Δ T, wherein c _h=η/(3600C _batt), η is the constant of indication charge/discharge efficiency, C _battfor take the electric current that battery capacity that ampere hour (Ah) represents and I (i) be inflow battery.

10) repeating step 5 to 9 is closed voltage VSD until OCV (i) reaches battery.

Now, use { OCV (i); SOC (i) } right, can be for SOC ∈ [0; 1] obtaining OCV characterizes.

Note:

1) OCV-SOC characterizes and can change because temperature is different.(can calculate by some methods the OCV sign at any temperature place in certain usable range).

2) in some concrete enforcements, battery capacity C _battcan derive from manufacturer's tables of data or it can be estimated.

3) OCV-SOC sign can be unchanged, no matter and the tenure of use of battery.

4) use above-mentioned OCV-SOC to characterize, can calculate the OCV of the battery of given SOC s, write as υ=OCV(s).

5) use above-mentioned OCV-SOC to characterize, can calculate for given standing terminal voltage υ _rthe SOC of battery, write as s=OCV ^-1(υ _r).If the SOC estimated value at certain electric quantity metering algorithm at time k place is reported as corresponding error can be calculated as

${\&Element;}_{\mathrm{OCV}}={\hat{s}}_{\mathrm{FG}}\left[k\right]-{\mathrm{OCV}}^{-1}\left({\mathrm{\&upsi;}}_r\right[k\left]\right)---\left(217\right)$

υ wherein _r[k] is the terminal voltage at time k place (after battery standing).

Can use the checking characterizing based on OCV-SOC to calculate the OCV error (217) in whole temperature and/or SOC region.

Checking in relatively high SOC region can be by carrying out as follows: when first starting and applying from full rechargeable battery, varying duty reaches one section is enough to consume the time that (approximately) is less than 1/2 capacity of tested battery.Similarly, the checking in low SOC region can be by carrying out as follows: first from the battery after full rechargeable battery or high SOC checking, and apply the dynamic load that is enough to battery to take to lower SOC region.

Average OCV-SOC error (in %) can be calculated as

${\stackrel{\&OverBar;}{\&Element;}}_{\mathrm{OCV}}=[\frac{1}{8}\underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}{\&Element;}_{\mathrm{OCV}}(s_L,T_i)+{\&Element;}_{\mathrm{OCV}}(s_H,T_i)]100---\left(218\right)$

∈ OCV (s wherein _l, T _i) be illustrated in low SOC location and in temperature T _iunder the error that calculates.In some concrete enforcements, lower, FG algorithm is better.

The tolerance relating to based on relative coulomb of counting error is below discussed.Battery SOC can be counted (CC) by coulomb in the following manner and calculate:

${\hat{s}}_{\mathrm{CC}}\left[k\right]={\hat{s}}_{\mathrm{CC}}[k-1]+c_h{\&Integral;}_{t_{k-1}}^{t_k}I\left[t\right]\mathrm{dt}---\left(219\right)$

Suppose battery capacity C _battenough initial accurately known.Thereby, may be defined as with the FG error (in %) of coulomb enumeration correlation:

${\stackrel{\&OverBar;}{\&Element;}}_{\mathrm{CC}}=\frac{\sqrt{{\mathrm{\&Sigma;}}_{k=1}^T{\left({\hat{s}}_{\mathrm{CC}}\right[k]-{\hat{s}}_{\mathrm{FG}}[k\left]\right)}^2}}{T}100---\left(220\right)$

Wherein T is the duration (in second) of carrying out validation test.

1), in some concrete enforcements, some the comprised coulomb countings in battery metering outfit and/or method are as its ingredient.Yet above-mentioned tolerance still can be considered verification tool, this is to understand the initial of battery capacity and checking owing to supposing and FG method may not supposed this understanding.

2) can, by battery is discharged to sky (or basic overhead) completely from full (or substantially full), pre-estimate for checking battery capacity.Or, can from full (or substantially full) to empty (or basic overhead) carry out validation test, and can upgrade with the battery capacity Cbatt of latest estimated in some concrete enforcements, can in the battery capacity estimation of this mode, consider to lag behind and relaxation factor.In some concrete enforcements, can forbid that FG algorithm does like this.

3) in some concrete enforcements, the temperature of the battery of just assessing whole (as, substantially whole) can keep constant in proof procedure.

Below discuss and relate to the tolerance based on reaching voltage time (TTV).If the SOC estimated value at the voltameter algorithm at time k place is s _fG[k], its time that reaches voltage υ needs can be write into following form:

$T_{\mathrm{FG},\mathrm{\&upsi;}}=\frac{[{\mathrm{OCV}}^{-1}\left(\mathrm{\&upsi;}\right)-s_{\mathrm{FG}}[k\left]\right]}{I}---\left(221\right)$

Wherein electric current I (in charging process in I>0 and discharge process I<0) keeps constant (or substantial constant) until reach voltage υ.

Once reach terminal voltage υ in operational process, can record the real time while reaching this voltage.When reaching voltage υ at special time, can calculate following TTV checking tolerance

${\&Element;}_{\mathrm{TTV}}=\frac{1}{T-k}\sqrt{{\mathrm{\&Sigma;}}_{i=k}^T{\left(\frac{T_{\mathrm{EG},\mathrm{\&upsi;}}\left[i\right]-T_{\mathrm{\&upsi;}}\left[i\right]}{T_{\mathrm{\&upsi;}}\left[i\right]}\right)}^2}---\left(222\right)$

T wherein _v[i]=T – i reaches from time i the real time that voltage υ needs.∈ _tTVvalue can minute meter.In some concrete enforcements, can calculate following tolerance (in %):

${\stackrel{\&OverBar;}{\&Element;}}_{\mathrm{TTV}}=\frac{{\&Element;}_{\mathrm{TTV}}}{T}100---\left(223\right)$

The tolerance of combination may be defined as:

${\stackrel{\&OverBar;}{\&Element;}}_{\mathrm{FG}}=\frac{{\stackrel{\&OverBar;}{\&Element;}}_{\mathrm{OCV}}+{\stackrel{\&OverBar;}{\&Element;}}_{\mathrm{CC}}+{\stackrel{\&OverBar;}{\&Element;}}_{\mathrm{TTV}}}{3}---\left(224\right)$

Wherein in %.In some concrete enforcements, this value is lower, and voltameter is better.

In some concrete enforcements, benchmark can be included as evaluated battery load reflection battery use (as, typical case uses) one or more different current loadings, and record SOC and the TTV reading of voltameter report.The method can be included under different temperatures and repeat these steps, until for example Table I, II and III are filled.

In some concrete enforcements, can in proof procedure, use simulation and actual loading curve.The advantage of fictitious load curve is to calculate the amount of the coulomb obtaining from battery (as, accurate amount), thereby can avoid due to the one or more errors due to sampling and current sense.This can be based on such supposition: load simulating device may not can be introduced one or more appreciable errors.Can create various actual loading curves and fictitious load curve.

Actual loading curve: can use for example smart phone as load, to create actual loading curve (as shown in Figure 15 A and 15B).When load is connected to the battery being verified, can carry out following activity: call (15 minutes), web surfing, read e-mail, play games etc. (20 minutes), send short messages (10 message), use loudspeaker listen to the music or see that video (30 minutes videos), the machine – for the treatment of enable cellular radio electrical communication base station (1 hour).

Load curve shown in Figure 15 A and 15B shows such scene, wherein can in single test, calculate three types tolerance (as, OCV tolerance 1505, TTV tolerance 1510 and CC tolerance 1515) in each a input.This test is from full rechargeable battery, and dynamically working load applies approximately 3 hours 15 minutes again.Battery was in leisure state 2 hours afterwards.5 hour-symbols provide calculating OCV-SOC error metrics ∈ _oCV(s _h, T _i) chance.Constant current load when test closes to an end allows to calculate ∈ _tTV(s _l, T _i).Can count and measure ∈ according to whole data calculating coulombmeter _cC(T _i).

Can use the load curve accounting temperature T shown in Figure 15 A and 15B _iunder following tolerance:

At the OCV-OSC of high SOC location error metrics ∈ _oCV(s _h, T _i)

At the TTC of low SOC location tolerance ∈ _tTV(s _l, T _i)

Coulomb count metric ∈ _cC(T _i)

Fictitious load curve: the piecewise constant current loading I that can use the different amplitudes in short duration Δ s _mcreate fictitious load curve.These segment load can be mixed and be connected together, thereby obtain the fictitious load curve shown in Figure 16 A and 16B.Note that fictitious load can occur between about 3.5 hours to 6.5 hours of test.This load curve can be used for example Δ s=2 second and I _m=40,120,130,160,300,400,440,520,600,640,800,880}(unit: Kikusui programmable load device mA) is simulated.

Fictitious load curve shown in Figure 16 A and 16B shows such scene, wherein can in single test, calculate three types tolerance (as, OCV tolerance 1605, TTV tolerance 1610 and CC tolerance 1615) in each a input.This test, from full rechargeable battery, and applies constant 500mA load approximately 1.5 hours.Battery, in leisure state 2 hours, then applies dynamic load curve 3 hours afterwards.3 hours again 15 minutes marks calculating OCV-SOC error metrics ∈ is provided _oCV(s _h, T _j) chance.Constant current load when test closes to an end allows to calculate ∈ _tTV(s _l, T _j).Can calculate a coulomb count metric ∈ according to whole data _cC(T _j).

In some concrete enforcements, can carry out accounting temperature T with the fictitious load curve shown in Figure 16 A and 16B _junder following tolerance:

At the OCV-OSC of high SOC location error metrics ∈ _oCV(s _h, T _i)

At the TTC of low SOC location tolerance ∈ _tTV(s _l, T _i)

Coulomb count metric ∈ _cC(T _i)

Above-mentioned exemplary concrete enforcement has been described the SOC that is applicable to battery powdered device (as, portable mobile device) and has been followed the tracks of.Described exemplary embodiment has realized linear method, and this linear method low cost and effectiveness of performance on calculating are better than the existing method for online Model Identification.Weighted least require method for parameter estimation has been described.Attested remarkable improvement in weight (based on variance) in the LS method of parameter estimation and parameter estimation has been described.Applicability for the different operational modes of battery comprises that identification represents four different equivalent models of the battery of representative cells operational mode, and sets up the framework that seamless SOC follows the tracks of.Described method is modeled as the error in open-circuit voltage (OCV) by hysteresis, thereby has eliminated the needs that hysteresis are modeled as to the function of SOC and load current.The method also contributes to from the wrong fast quick-recovery of SOC initialization.

Above-mentioned exemplary concrete enforcement has been described for battery capacity estimation to promote the feature of battery electric quantity metering progress.The weighting recurrence least square (RLS) with the capacity of accurate weight derivation is estimated.The formula of weight can calculate based on SOC tracking error covariance and current measurement errors standard deviation.TLS method for battery capacity real-time follow-up has been described.TLS estimated value is derived and can be used for coming self-adaptation to estimate by upgrading covariance matrix with Attenuation Memory Recursive with closed.The technology that the adaptive capacity that OCV based on resting batteries searches is estimated.Consider the source of the OCV seek error (hysteresiss) in deriving and described the method for the adaptive capacity estimation of searching by OCV.The method of having described the optimum fusion of the capacity estimation value obtaining by distinct methods based on capacity estimation value and evaluated error covariance, the method proposing is carried out adaptive optimal fusion by Kalman filter.

Above-mentioned exemplary concrete enforcement has been described the SOC that is applicable to battery powdered device (as, portable mobile device) and has been followed the tracks of.For high and effectiveness of performance is low on calculating by other nuisance parameter is stacked on to the routine techniques of estimating other nuisance parameter in state vector together with SOC.For fear of these problems, exemplary embodiment has been described depression of order Filtering Model, for the state-space model by new, carries out SOC tracking.The state-space model with decorrelation noise model has been described.SOC tracking problem relates to two measuring amount, i.e. voltage and current, and this just makes the state of SOC tracking problem and measures between noise model to have correlativity.The amended state space form of expression that has uncorrelated state and measure noise process has been described.Exemplary embodiment has been described the different operational modes of battery, and identifies at least four different equivalent models of the battery that represents representative cells operational mode, and sets up the framework that seamless SOC follows the tracks of.Exemplary embodiment has been described a kind of method, and the method is modeled as the error in open-circuit voltage (OCV) by hysteresis, thereby has eliminated the needs that hysteresis are modeled as to the function of SOC and load current.The method also contributes to from the wrong fast quick-recovery of SOC initialization.

Above-mentioned exemplary concrete enforcement has been described the SOC realizing by some strategies and has been followed the tracks of.First, by minimum battery modeling.The method that proposes is unique need to carry out off-line modeling to the open-circuit voltage of battery (OCV) characteristic.Every other desired parameters is estimated by firm means.Owing to being equipped with the single set of OCV parameter, the method proposing can be carried out SOC and follow the tracks of at any temperature, without any other parameter.The second, voltage drop observation model.The voltage drop model of observation allows online SOC to follow the tracks of, and needn't worry the lag element modeling to battery.This just makes proposed method can obtain better precision and robustness.The 3rd, by stability parameter, estimate.Identified the effect for the correlation noise structure of the least square model of parameter estimation.For parameter estimation algorithm, this has just obtained obviously better precision and has strengthened robustness.The 4th, pass through battery capacity estimation.The total least square for capacity estimation proposing (TLS) method has been guaranteed the excellent precision of capacity estimation.And last, by using filtering, depression of order EKF method is considered the correlativity (being followed the tracks of by deriving for SOC) of noise process in state-space model and is applied and suitable goes correlation filter so that the error minimize of SOC in following the tracks of.

In embodiment, the reference test method of the battery electric quantity metering algorithm based at least three assessment tolerance has been described.The first assessment tolerance can characterize by the open-circuit voltage (OCV) based on battery.The second assessment tolerance can be based on voltameter relative coulomb of counting error, and the 3rd benchmark can reach the specific voltage calculating of required time based on battery.Each checking tolerance can be included in various SOC levels, different temperatures and/or voltage regime, and some tolerance is calculated at place like that.

Some SOC trackings comprise at least following weak point: (1) some models are only considered resistance, are not suitable for dynamic load; (2) they adopt nonlinear method to carry out system identification; (3) need to estimate for the initial parameter of method of model identification; (4) suppose that single dynamic equivalent model represents all battery operation patterns; (5) importance of unresolved online capacity estimation; (6) existing online battery capacity estimation technology is subject to the impact of SOC and parameter estimating error, and they are built on the sand; (7), except SOC, they also adopt the on-line tracing (this causes having increased computational complexity and has reduced SOC tracking accuracy) of many amount of redundancys; (8) they need to lag behind and carry out independent modeling battery, and it is the function (being therefore unlimited model) of SOC and load current that battery lags behind, and only may carry out approximate modeling to lagging behind; (9) anyly in existing method all do not recognize this process and measure noise process and have correlativity; And any not fact of adaptive all these conditions of variation in the battery behavior causing due to temperature, aging, SOC and load variations and single equivalent model of all not recognizing in (10) existing method.

Therefore, concrete enforcement as herein described can have short design time (a couple of days in), can have comparatively faster algorithm convergence, and in " real world " service condition, can have about 1% SOC and the precision of battery capacity report precision.In some concrete enforcements, (or seldom) need to not customize battery model or data, and can comprise having the adaptive learning algorithm that relatively very fast SOC follows the tracks of convergence.Some concrete enforcements can comprise automatic temperature-adjusting, tenure of use and load compensation.

Some concrete enforcements can be estimated and real time capacity estimation based on for example reduced-order EKF device, correlated measurement noise decoupling, online electrical model parameters.

Depression of order Kalman filter can comprise that the accurate SOC that relates to four different parameters of common estimation estimates (trackings): SOC, flows through electric current and the hysteresis of two different resistors in dynamic equivalent model, and all these can change during in load/charging at battery.This relates to the complex matrix operation that is commonly referred to recursive filtering.This depression of order filtering method is simplified by this way: by recursive filtering program, only estimate SOC.Three other parameters by mathematical operation by marginalisation.One or more SOC track algorithms of gained are feasible now in voltameter SOC on calculating.

Correlated measurement noise decoupling can comprise Kalman filter, and it moves with measuring the incoherent hypothesis of noise based on process noise.In voltameter application, in current measurement, intrinsic measurement noise can be coupled to measurement noise and the process noise of SOC and voltage quantities in depression of order EKF.Adopted a kind of peculiar methods, the method is by the process noise decoupling of electric current induced noise and Kalman filter.

Online electrical model parameters estimates to comprise the dynamic estimation of model parameter (coefficient).The dynamic estimation of model parameter (coefficient) can comprise when its estimation during with SOC, changing currents with time load curve, temperature, charge-discharge cycles and/or variation like that.EKF wave filter is suitable for, and precondition is that the model parameter of the dynamic equivalent circuit of battery is known, yet equivalent electrical circuit represents the inner member of battery; These model parameters also can be estimated with the measured value that can derive from battery: voltage and current.Solution as herein described is with real-time mode estimation model parameter, thereby can use kalman filter method.

Real-time or online capacity estimation can comprise based on upgrading actual service conditions, load, temperature, tenure of use one or more algorithms of (as, continuous updating) active volume.Some concrete enforcements can comprise coulombmeter counting method, and the method compares the SOC of FG report and the SOC calculating based on coulomb counting (bookkeeping method).Some concrete enforcements can comprise that TTE(electric power uses up the time) method, the method can be predicted TTE and compare with actual conditions with FG.Some concrete enforcements can comprise SOC/OCV curve lookup method, and the method can compare SOC and the SOC/OCV curve of FG report.

In some concrete enforcements, can support various batteries, it has chemical composition, battery manufacturers and/or the aging data of multiple particular battery model and every kind of battery, like that.In some concrete enforcements, voltameter appraisal procedure can change.For example, state of charge precision assessment method and test procedure, dynamic load and/or detailed test request, like that variation.In some concrete enforcements, for example, to requiring the feedback of specification (key system perameter and accuracy requirement and/or system integration requirement, like that) to change.In some concrete enforcements, operating system drives requirement to change.

Figure 17 shows the schematic diagram that example system realizes.System 1700 comprises voltameter evaluation module 1705, battery 1710, battery electric quantity meter 1715 and calculation element 1715.Voltameter evaluation module 1705 can be embodied as software module or the ASIC in BMS110.In other words, voltameter evaluation module 1705 can be code, and this code storage is carried out in storer 230 and by processor 235 and/or another module relevant to BMS110.Calculation element 1715 can and be presented at (as shown in figure 18) graphic user interface by this information from voltameter evaluation module 1705 reception information.

Figure 18 shows to realize with system the schematic diagram of the user interface being combined with.Figure 19 A and 19B comprise that showing exemplary sparking voltage/current curve searches the figure of checking 1905 and TTS test 1910 to illustrate SOC.Figure 20 A and 20B illustrate exemplary CC appraisal procedure to illustrate voltameter algorithm 2005 and a coulomb figure for the proximity of counting 2010.Figure 21 A and 21B are the schematic diagram that TTS appraisal procedure is shown, and it illustrates the obvious overlapping and TTS error 2115 of voltameter 2105 and actual SOC2110.

Some in above-mentioned exemplary embodiment are described to the process shown in process flow diagram or method.Although process flow diagram is described as sequential process by operation, many operations can walk abreast, concurrent or execution simultaneously.In addition, can rearrange order of operation.These processes can stop when completing its operation, but also can have the other step that figure does not comprise.These processes can be corresponding to method, function, program, subroutine, subroutine etc.

Said method (some of them are illustrated by process flow diagram) can be realized by hardware, software, firmware, middleware, microcode, hardware description language or their any combination.When realizing with software, firmware, middleware or microcode, carry out the program code of necessary task or code segment and can be stored in machine or computer-readable medium for example in storage medium.Can carry out necessary task by one or more processors.

Concrete structure disclosed herein and function detail are only representational, to describe exemplary embodiment.Yet exemplary embodiment is embodied as many alternative forms and should not be construed as the embodiment that only limits to provide herein.

Although should be appreciated that term first, second etc. can be in this article for describing various elements, these elements should not be subject to the restriction of these terms.These terms are only for separating an element and another element region.For example, the first element can be called the second element, and similarly, the second element can be called the first element, and does not depart from the scope of exemplary embodiment.As used herein, term "and/or" comprises the one or more any and all combinations in the continuous item of listing.

Should be appreciated that when element is called as " connection " or " coupling " to another element, it can directly connect or be coupled to this another element maybe can there is intermediary element.On the contrary, when element is called as " directly connection " or " direct-coupling " to another element, there is not intermediary element.For other words of describing the relation between element should explain in a similar manner (as, " and between ... between " with " and directly between ... between ", " adjacent " and " direct neighbor " etc.).

Should also be noted that at some and substitute in concrete enforcement, function/action of pointing out can occur not according to order pointed in figure.For example, two figure that illustrate in a continuous manner can in fact concurrent execution or sometimes can inverted order be carried out, and specifically depend on related function/action.

The concrete enforcement of various technology as herein described can realize in Fundamental Digital Circuit or in computer hardware, firmware, software or in their combination.Concrete enforcement can be embodied as computer program, be tangible being embodied in information carrier, as the computer program in machine-readable storage device (computer-readable medium, non-provisional computer-readable recording medium, tangible computer-readable recording medium) or in the signal of propagating, for for example, processing by data processing equipment (programmable processor, computing machine or many computing machines), or control the operation of described data processing equipment.Computer program for example above-mentioned one or more computer program can any programming language form (comprising compiling or interpretative code) be write, and can dispose in any form, comprise stand-alone program or be applicable to module, assembly, subroutine or other unit of computing environment.

Each several part in above-mentioned exemplary embodiment and corresponding embodiment represents to propose according to the software of the operation in the data bit in computer memory or algorithm and symbol.Algorithm (when this term use herein and when it uses with general fashion) be envisioned for draw results needed be certainly in harmony sequence of steps.These steps are that the step of physical manipulation is carried out in requirement to physical quantity.Conventionally, although dispensable, the form of light signal, electric signal or magnetic signal that this tittle adopts and can store, shifts, combines, compares and otherwise handles.Confirmed sometimes more conveniently, particularly for general reason, these signals have been called to bit, value, element, symbol, character, item, numeral etc.

In above exemplary embodiment, the operation of the be embodied as program module of mentioning or function course (as, action in a flowchart) and symbol represent to comprise the routine carrying out specific tasks or realize concrete abstract data type, program, object, assembly, data structure etc., and can describe and/or realize by the existing hardware at existing structure element place.Some existing hardwares can comprise one or more CPU (central processing unit) (CPU), digital signal processor (DSP), special IC, field programmable gate array (FPGA) computing machine etc.

Yet, should remember that all these are relevant to suitable physical quantity with similar terms, and be only the label that facilitates that is applicable to this tittle.Unless otherwise specified, otherwise as can obviously find out from discuss, term for example " processing " or " calculating " (computing) or " calculating " (calculating) or " determining " or " demonstration " etc. refer to action and the process of computer system or similar computing electronics, the data manipulation that the physics with in computer system RS, amount of electrons are represented and be transformed into other data that represent with the physical quantity in computer system memory or register or other this type of information storages, transmission or display device similarly.

The aspect being realized by software that it shall yet further be noted that exemplary embodiment is conventionally encoded on the non-provisional program recorded medium of certain form or realizes on the transmission medium of certain type.Program recorded medium can be magnetic (as, floppy disk or hard disk drive) or optics (as, compact disc read-only memory, or " CDROM "), and be read-only or random-access.Similarly, transmission medium can be twisted-pair feeder, concentric cable, optical fiber or some other suitable transmission mediums.Exemplary embodiment is not subject to the restriction of concrete these aspects implemented of any appointment.

Although it is as described herein that some feature of described concrete enforcement has been shown as, those skilled in the art now can expect many modifications, substitute, change and equivalents.Therefore, should be appreciated that appended claims is intended to contain all these type of modification and the change form in the scope that falls into concrete enforcement.Should be appreciated that described embodiment only presents by way of example rather than in the mode limiting, and can aspect form and details, carry out various changes.Arbitrary part of device as herein described and/or method can be combined with any combination, but the except combinations of mutually repelling.Concrete enforcement as herein described can comprise various combinations and/or the sub-portfolio of concrete function, parts and/or the feature of implementing of described difference.

Claims (40)

1. a method, comprising:

In the very first time, calculate first of battery and estimate state of charge (SOC);

In the second time, receive the magnitude of voltage of the measuring voltage that represents described battery two ends;

At described the second Time Calculation filter gain; And

In described the second time, based on described first, estimate that SOC, described magnitude of voltage and described filter gain calculate second of described battery and estimate SOC.

2. method according to claim 1, also comprises:

By described second, estimate that SOC is stored in impact damper; And

Before calculating the described second estimation SOC of described battery, from described impact damper, read described first and estimate SOC.

3. method according to claim 1, also comprises:

By described first, estimate that SOC is stored in impact damper, calculate described battery described second estimate SOC before, from described impact damper, read described first and estimate that SOC is as one of following:

The vector of at least two SOC,

The array of at least two SOC,

At least two SOC average and

The average of at least two SOC.

4. method according to claim 1, also comprises: from impact damper, read and estimate SOC variance, wherein said filter gain is based on described estimation SOC variance.

5. method according to claim 1, wherein, calculating filter gain comprises: use at least one in weighting recurrence least square (RLS) algorithm and total least square (TLS) algorithm to calculate at least one capability value.

6. method according to claim 1, wherein, calculating filter gain comprises: use the weighting RLS algorithm based on SOC tracking error covariance and current measurement errors standard deviation to carry out calculated capacity value.

7. method according to claim 1, wherein, calculating filter gain comprises: the TLS algorithm of using the recurrence based on covariance matrix to upgrade carrys out calculated capacity value.

8. method according to claim 1, wherein, calculating filter gain comprises: use open-circuit voltage (OCV) to search calculated capacity value.

9. method according to claim 1, wherein

Described second estimates that SOC equals described filter gain and is multiplied by described magnitude of voltage and adds the above and first estimate SOC.

10. method according to claim 1, also comprises:

At least one in voltage time (TTV) error metrics that reach based on coulomb counting error metrics, OCV-SOC error metrics and prediction, estimates that to described second SOC carries out benchmark test.

11. 1 kinds of systems, comprising:

Battery; And

Battery electric quantity meter module, it is configured to use Reduced Order Filter to calculate the estimation state of charge (SOC) of described battery, described Reduced Order Filter is single state filter, and the SOC estimated value that described single state filter is configured to based on calculating before to estimate SOC described in recursive calculation.

12. systems according to claim 11, wherein, described battery electric quantity meter comprises:

Voltage drop prediction module, it is configured to come calculating voltage to fall based on described estimation SOC;

Model estimation module, its equivalent model being configured to based on representing described battery calculates at least one voltage drop model parameter; And

Tracking module, it is configured to make described at least one voltage drop model parameter to change to remove instantaneous lagging.

13. systems according to claim 11, wherein, described battery electric quantity meter comprises capacity module, total least square (TLS) algorithm that described capacity module is configured to use the recurrence based on covariance matrix to upgrade calculates the capability value of described battery.

14. systems according to claim 11, wherein, described battery electric quantity meter comprises capacity module, described capacity module is configured to use open-circuit voltage (OCV) to search to calculate the capability value of described battery.

15. systems according to claim 11, wherein

Described battery electric quantity meter comprises impact damper, and described impact damper is configured to store at least one and estimates SOC value, and

The SOC estimated value calculating before described reads from described impact damper.

16. systems according to claim 11, also comprise data-carrier store, described data-carrier store is configured to store OCV parameter, voltage measurement error standard deviation and current measurement errors standard deviation, and wherein at least one voltage drop model parameter relevant to described Reduced Order Filter defined by one of described OCV parameter, described voltage measurement error standard deviation and described current measurement errors standard deviation.

17. systems according to claim 11, also comprise: display, described display is configured to show described estimation SOC.

18. 1 kinds of computer-readable mediums, comprise code segment, and described code segment, when being carried out by processor, makes described processor:

Calculate the estimation state of charge (SOC) of battery;

Described estimation SOC is stored in to impact damper; And

Use Reduced Order Filter to calculate the estimation SOC after the renewal of described battery, described Reduced Order Filter is single state filter, the estimation SOC after described single state filter is configured to upgrade described in recursive calculation based on described estimation SOC.

19. computer-readable mediums according to claim 18, also comprise code segment, and described code segment makes described processor:

Based on described estimation SOC calculating voltage, fall;

Equivalent model based on representing described battery calculates at least one voltage drop model parameter; And

Change open-circuit voltage (OCV) error that described at least one voltage drop model parameter lags behind to reduce indication.

20. computer-readable mediums according to claim 18, also comprise: code segment, and described code segment makes described processor:

Capacity based on described battery and at least one voltage drop model parameter are carried out calculating filter gain, and wherein said Reduced Order Filter calculates the estimation SOC after described renewal based on described filter gain and described estimation SOC.

21. 1 kinds of methods, comprising:

In storer, storage represents the storehouse of the equivalent-circuit model of battery;

Based on the load relevant to described battery, determine the operational mode of battery;

Based on determined operational mode, select one of described equivalent-circuit model; And

With selected equivalent-circuit model, calculate the state of charge (SOC) of described battery.

22. methods according to claim 21, wherein

The high voltage load of described operational mode based on consuming variable current,

Described operational mode comprises corresponding equivalent-circuit model, and described equivalent-circuit model comprises the first resistance-electric current (RC) circuit and the 2nd RC circuit.

23. methods according to claim 21, wherein

Described operational mode is based on variable voltage load,

Described operational mode comprises corresponding equivalent-circuit model, and described equivalent-circuit model comprises resistance-electric current (RC) circuit.

24. methods according to claim 21, wherein

Described operational mode is based on variable voltage load,

Described operational mode comprises corresponding equivalent-circuit model, and described equivalent-circuit model comprises resistor and biasing element.

25. methods according to claim 21, wherein

Described operational mode is based on low-voltage load,

Described operational mode comprises corresponding equivalent-circuit model, and described equivalent-circuit model comprises resistor.

26. methods according to claim 21, wherein

At least one in described equivalent-circuit model comprises lag element, and

Described lag element is modeled as open-circuit voltage (OCV) error of calculation.

27. methods according to claim 21, also comprise:

At battery eliminator interdischarge interval, measure the terminal voltage of described battery eliminator;

Terminal voltage based on measured is determined linear equation; And

Based on described linear equation, with weighted least square algorithm, calculate at least one parameter, to the calculating of the described SOC of described battery based on described at least one parameter.

28. methods according to claim 21, also comprise:

At least one in voltage time (TTV) error metrics that reach based on coulomb counting error metrics, OCV-SOC error metrics and prediction, carries out benchmark test to described SOC.

29. 1 kinds of systems, comprising:

Data-carrier store, it is configured to the storehouse that storage represents the equivalent-circuit model of battery;

Model Selection module, its operational mode being configured to based on described battery is selected equivalent-circuit model; And

Filter module, it is configured to calculate based on selected equivalent-circuit model the estimation state of charge (SOC) of described battery.

30. systems according to claim 29, also comprise:

Operational mode module, its be configured in electric current based on relevant to described battery and the voltage relevant with described battery at least one determine the operational mode of described battery.

31. systems according to claim 29, wherein

The high voltage load of described operational mode based on consuming variable current,

Described operational mode comprises corresponding equivalent-circuit model, and described equivalent-circuit model comprises the first resistance-electric current (RC) circuit and the 2nd RC circuit.

32. systems according to claim 29, wherein

Described operational mode is based on variable voltage load,

Described operational mode comprises corresponding equivalent-circuit model, and described equivalent-circuit model comprises resistance-electric current (RC) circuit.

33. systems according to claim 29, wherein

Described operational mode is based on variable voltage load,

Described operational mode comprises corresponding equivalent-circuit model, and described equivalent-circuit model comprises resistor and biasing element.

34. systems according to claim 29, wherein

Described operational mode is based on low-voltage load,

Described operational mode comprises corresponding equivalent-circuit model, and described equivalent-circuit model comprises resistor.

35. according to the method for claim 29, wherein

At least one in described equivalent-circuit model comprises lag element, and

Described lag element is modeled as open-circuit voltage (OCV) error of calculation.

36. systems according to claim 29, also comprise:

Model estimation module, the selected equivalent model that described model estimation module is configured to based on representing described battery calculates at least one voltage drop model parameter, and wherein said estimation SOC calculates based on described at least one voltage drop model parameter.

37. according to the system of claim 29, also comprises display, and described display is configured to show described estimation SOC.

38. 1 kinds of computer-readable mediums, comprise code segment, and described code segment, when being carried out by processor, makes described processor:

Operational mode based on described battery is selected equivalent-circuit model from represent the storehouse of equivalent-circuit model of battery; And

With selected equivalent-circuit model, calculate the state of charge (SOC) of described battery.

39. according to the computer-readable medium described in claim 38, also comprises code segment, and described code segment makes described processor:

Based on selected equivalent model, calculate at least one voltage drop model parameter, wherein said SOC calculates based on described at least one voltage drop model parameter.

40. according to the computer-readable medium described in claim 38, and at least one in wherein said equivalent-circuit model comprises lag element, and described code segment also makes described processor:

Based on selected equivalent model, calculate at least one voltage drop model parameter; And

Change open-circuit voltage (OCV) error that described at least one voltage drop model parameter lags behind to reduce indication.