CN103293485A - Model-based storage battery SOC (state of charge) estimating method - Google Patents

Abstract

A model-based storage battery SOC estimating method relates to the technical field of batteries. The method comprises data acquisition, model selection, parameter identification, simulation verification and state estimation. The model-based storage battery SOC estimating method acquires current data and voltage data through a dynamic working condition experiment; selects an equivalent circuit model (a two-stage RC (resistor-capacitor) model) as a power battery model; utilizes an FFRLS (forgetting factor recursive least square) algorithm as a real-time parameter identification method; establishes a simulated battery model according to an identification result, utilizes an acquired current value as a known quantity to input into the model to obtain an estimated value of the terminal value of a battery, compares the estimated value with experimental data, completes the error analysis and verifies the rationality of the model and the accuracy of the identification method; and establishes a corresponding relationship between identification parameters and SOC and accordingly estimates the SOC of the battery through the real-time identification parameters. Besides, under the premise that the SOC of the battery is known, if an online identification parameter exceeds a corresponding reasonable parameter value range, the battery can be considered to be in a large degradation state and have potential security risks.

Description

Accumulator state-of-charge method of estimation based on model

Technical field

The present invention relates to the battery technology field, particularly relate to the estimation of power accumulator state-of-charge.

Background technology

Because accumulator has reliable operation, portable advantage is done the mode that power supply powers with accumulator and has been obtained using widely.As mobile phone and cells in notebook computer, automobile start battery, automobile power cell, satellite communication power supply and robot power supply etc.People wish that not only these batteries can provide reliable electric power supply, and wish can be at any time the dump energy of electrolytic cell, in order to rationally arrange stroke and duration of charging, bring into play the active volume of battery better.

Battery dump energy and the ratio of battery rated capacity are called the state-of-charge of battery, and (State of Charge SOC), is the data foundation of carrying out battery management, is the research focus in battery applications field always.The state-of-charge method of estimation comprises open-circuit voltage method, ampere-hour accumulative total method, neural net method and kalman filter method etc. at present.Wherein the open-circuit voltage method has influenced its online use owing to need deenergization to test; Ampere-hour accumulative total method is owing to need the continuous electric current that adds up in the charge and discharge process, even less current measuring error, in long-time, also cause bigger error easily, often need implement in conjunction with additive method such as open-circuit voltage method, and need have suitable method to carry out the correction of error; Neural net method needs a large amount of test figures that the factor that influences battery remaining power is carried out the training of weight coefficient usually, and needs to cover concrete usable range, so its use also is restricted; Kalman filter method is on to system input-output characteristic basis system to be carried out the estimation that parameter comprises battery charge state, but owing to need suppose the statistical property of system noise in real process, therefore in concrete the application, also need algorithm is adjusted.

Studies show that in a large number the circuit model of introducing battery can well address this problem.Equivalent-circuit model uses basic circuit elements forming circuits such as electric capacity, resistance to describe the operating characteristic of battery.Not only model parameter has good sign effect to the performance state of battery, and can estimate the state-of-charge that real-time online is estimated battery in conjunction with mathematical algorithm by battery model, has higher accuracy.

Summary of the invention

The method that the purpose of this invention is to provide the identification of a kind of power accumulator on-line parameter and state estimation.Simultaneously, designed the complete flow process of a cover, having comprised: data acquisition, model are chosen, parameter identification, simulating, verifying and state estimation 5 links, successively each link are described below.

1, data acquisition

To the battery model parameter identification, the electric current of needs collection battery and information of voltage are as the data vector of model.Consider the dynamic change of battery in real vehicle travels, we adopt mixed pulses power characteristic test (Hybrid Pulse Power Characterization is called for short HPPC) as the dynamic experiment of data acquisition.The HPPC test can obtain the discharge power under the different SOC, is used for judging whether electrokinetic cell satisfies the power demand of vehicle.

2, model is chosen

Battery model commonly used has: galvanochemistry model, equivalent-circuit model and neural network model etc.Wherein, equivalent-circuit model is based on the dynamic perfromance of battery, and the circuit that contains voltage source, resistance and electric capacity by foundation comes the duty of simulated battery.

The equivalent-circuit model that this method is chosen is the Order RC model, and this model is made up of a resistance and two RC modules, as shown in Figure 1.Wherein, U _OCBe ideal voltage source, the open-circuit voltage of expression battery; R ₀It is the battery ohmic internal resistance; R ₁And R ₂The polarization resistance of expression battery, C ₁And C ₂The polarization capacity of expression battery, two reinforced concrete structures are represented the polarization reaction of battery; I is the ohmic internal resistance R that flows through ₀Electric current; U can survey battery terminal voltage.

3, parameter identification

The present invention adopts and contains genic least square (Forgetting Factor Recursive Least Square, FFRLS) algorithm carries out the Order RC identification of Model Parameters, exactly the battery under the duty is considered as a dynamic system, electric current I is imported u as system, voltage U is exported y as system, to the so single output of single input (Single Input Single Output, SISO) system carries out System Discrimination, obtain containing the difference equation coefficient of model parameter, thereby try to achieve the battery model parameter.Concrete solution is as follows:

The circuit relationships of Order RC model as shown in Figure 1 can get the state equation under the frequency domain:

$U\left(s\right)-U_{\mathrm{OC}}\left(s\right)=-I\left(s\right)(R_0+\frac{R_1}{R_1{C}_{1}s+1}+\frac{R_2}{R_2{C}_{2}s+1})---\left(1\right)$

In the formula: s is frequency domain symbol; U (s) is the frequency domain form of terminal voltage; U _OC(s) be the frequency domain form of open-circuit voltage; I (s) is the frequency domain form of electric current.

Make U ' (s)=U (s)-U _OC(s), then can obtain corresponding transport function, as follows:

$G\left(s\right)=\frac{U^{\′}\left(s\right)}{I\left(s\right)}=-(R_0+\frac{R_1}{R_1{C}_{1}s+1}+\frac{R_2}{R_2{C}_{2}s+1})---\left(2\right)$

(2) formula is carried out the z conversion, can pass through bilater substitution

(T is the sampling time) realizes:

$G\left(z^{-1}\right)=\frac{U^{\′}\left(z^{-1}\right)}{I\left(z^{-1}\right)}=\frac{k_3+k_4{z}^{-1}+k_5{z}^{-2}}{1-k_1{z}^{-1}-k_2{z}^{-2}}---\left(3\right)$

In the formula, k ₁, k ₂, k ₃, k ₄And k ₅Be undetermined coefficient.

Can be obtained the difference equation form of model state equation by formula (3):

U'(k)=k ₁U'(k-1)+k ₂U'(k-2)+k ₃I(k)+k ₄I(k-1)+k ₅(k-2) （4）

In the formula: k, k-1, k-2 represent k item value, k-1 item value and the k-2 item value of voltage or electric current respectively.

Because the open-circuit voltage U of battery _OCWith state-of-charge SOC, work temperature em and life-span L very strong relevance is arranged, and these three amounts are the function of time t, therefore define U _OCBe the function of SOC, Tem and L, as shown in the formula:

U _OC=f(SOC(t),Tem(t),L(t)) （5）

Differentiate gets to time t:

$\frac{{\mathrm{dU}}_{\mathrm{OC}}}{\mathrm{dt}}=\frac{\∂U_{\mathrm{OC}}}{\∂\mathrm{SOC}}\frac{\∂\mathrm{SOC}}{\∂t}+\frac{{\∂U}_{\mathrm{OC}}}{\∂\mathrm{Tem}}\frac{\∂\mathrm{Tem}}{\∂t}+\frac{\∂U_{\mathrm{OC}}}{\∂L}\frac{\∂L}{\∂t}---\left(6\right)$

At this, make the following assumptions:

1. the electric weight of electrokinetic cell unit's sampling time T internal consumption or regeneration is compared rated capacity and can be left in the basket, therefore

Set up;

2. the working temperature of electrokinetic cell arranges under the rational situation in ventilation and cooling infrastructure owing to being subjected to battery management system monitoring in real time and being controlled effectively, and the temperature variation of electrokinetic cell is slower, can be considered constant in the single sampling time T, that is,

3. the sampling time T of unit also is negligible compared to battery life L.Thereby

Set up.

Under the situation that above-mentioned hypothesis is set up, formula (6) can be reduced to:

$\frac{d{U}_{\mathrm{OC}}}{\mathrm{dt}}=\frac{U_{\mathrm{OC}}\left(k\right)-U_{\mathrm{OC}}(k-1)}{T}=\frac{U_{\mathrm{OC}}(k-1)-U_{\mathrm{OC}}(k-2)}{T}\≈0---\left(7\right)$

ΔU _OC(k)=U _OC(k)-U _OC(k-1)=U _OC(k-1)-U _OC(k-2)≈0 （8）

Then formula (4) arrangement can get:

U(k)=(1-k ₁-k ₂)U _OC(k)+k ₁U(k-1)+k ₂U(k-2)+k ₃I(k)+k ₄I(k-1)+k ₅(k-2) （9）

Formula (9) can be write as least squares formalism:

θ=[(1-k ₁-k ₂)U _OC,k ₁,k ₂,k ₃,k ₄,k ₅] ^T （12）

In the formula,

(k) be data vector, θ is coefficient vector to be estimated.

Can be estimated θ by the FFRLS algorithm, thereby try to achieve k ₁, k ₂, k ₃, k ₄And k ₅:

$\widehat{\mathrm{\θ}}\left(k\right)=\widehat{\mathrm{\θ}}(k-1)+K\left(k\right)e\left(k\right)---\left(13\right)$

In the formula: e (k) is the evaluated error of U (k);

(k) be the estimated value of θ; K (k) is the algorithm gain; P (k) is covariance matrix; λ is gene, and generally speaking, 0.98. is got in λ=0.95～1 in examples of implementation

By k ₁, k ₂, k ₃, k ₄And k ₅Can get with the relation of battery model parameter:

${\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="HDA00003334608400012.png,HDA00003334608400021.png"\; state="\{\{state\}\}">R</figure-callout>}}_0=\frac{-k_3+k_4-k_5}{1+k_1-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003334608400032.png,HDA00003334608400051.png"\; state="\{\{state\}\}">k</figure-callout>}}_2},$ $R_1{C}_1{R}_2{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA00003334608400032.png,HDA00003334608400051.png"\; state="\{\{state\}\}">C</figure-callout>}}_2=\frac{T^2(1+k_1-k_2)}{4(1-k_1-k_2)},$ $R_1{C}_1+R_2{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA00003334608400032.png,HDA00003334608400051.png"\; state="\{\{state\}\}">C</figure-callout>}}_2=\frac{T(1+k_2)}{1-k_1-k_2}$ (14)

${\mathrm{<figure-callout\; id="0"\; label="R"\; filenames="HDA00003334608400012.png,HDA00003334608400021.png"\; state="\{\{state\}\}">R</figure-callout>}}_0+R_1+{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA00003334608400032.png,HDA00003334608400051.png"\; state="\{\{state\}\}">R</figure-callout>}}_2=\frac{-k_3-k_4-k_5}{1-k_1-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003334608400032.png,HDA00003334608400051.png"\; state="\{\{state\}\}">k</figure-callout>}}_2},$ $R_0{R}_1{C}_1+R_0{R}_2{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA00003334608400032.png,HDA00003334608400051.png"\; state="\{\{state\}\}">C</figure-callout>}}_2+R_2{R}_1{C}_1+R_1{R}_2{\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA00003334608400032.png,HDA00003334608400051.png"\; state="\{\{state\}\}">C</figure-callout>}}_2=\frac{T(k_5-k_3)}{1+k_1-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003334608400032.png,HDA00003334608400051.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}$

In order to solve the many solutions problem that occurs in the calculation of parameter, make τ ₁=R ₁C ₁, τ ₂=R ₂C ₂, τ ₁Get the minimal value of trying to achieve time constant, τ ₂Get maximum value.So far, finish the battery model parameters R ₀, R ₁, R ₂, C ₁And C ₂Identification.

4, simulating, verifying

By dynamic operation condition experiment and identification of Model Parameters, the model parameter in the time of can obtaining under the variable working condition.Otherwise, after obtaining model parameter, set up realistic model, can estimate the terminal voltage of battery by real-time current.The virtual voltage that the terminal voltage of estimating is gathered with dynamic operation condition contrasts, and carries out error analysis, but both rationality of certificate parameter discrimination method, but the also accuracy of assessment models is the terminal voltage relative method.

Error analysis comprises: least absolute error, maximum absolute error, minimum relative error, maximum relative error and root-mean-square-deviation.Wherein, absolute error and relative error are used for describing the accuracy between estimated value and the actual value, and root-mean-square-deviation is the degree of accuracy of describing between estimated value and the actual value.

5, state estimation

The model parameter of electrokinetic cell can change along with the difference of state-of-charge (SOC), by setting up the model parameter database corresponding with SOC, both can be linked together.By real-time identification of Model Parameters, with identified parameters and database information comparison, judge battery state-of-charge of living in again.

So far, be concrete grammar of the present invention and detailed flow process.

Description of drawings

Fig. 1 is Order RC precircuit schematic diagram

Fig. 2 is HPPC measuring current-time curve

Fig. 3 is HPPC test voltage-time curve

Fig. 4 is HPPC test SOC-time curve

When Fig. 5 is HPPC test SOC=0.9, big current disturbing stage electric current-time curve

When Fig. 6 is HPPC test SOC=0.9, big current disturbing stage voltage-time curve

When Fig. 7 is HPPC test SOC=0.9, the comparison curves of experimental voltage and estimated voltage

Fig. 8 is that the parameter identification active component is with the graph of a relation of SOC

Fig. 9 is that the parameter identification capacitive part is with the graph of a relation of SOC

Embodiment

Further illustrate outstanding feature of the present invention below by embodiment, only be to illustrate implementation content of the present invention and be not limited to the present invention.

Embodiment 1

Select 20Ah for use, 3.2V LiFePO4 (LiFePO ₄) battery is as experimental subjects of the present invention, carries out the HPPC test, electric current, voltage data that the acquisition parameter identification is required.HPPC test performance curve is shown in accompanying drawing 2-6.Wherein, Fig. 2,3,4 are respectively electric current-time curve, volt-time curve and the SOC time curve of HPPC test.Fig. 5,6 when being respectively SOC=0.9, electric current-time curve and the voltage-time curve of big current disturbing part.

Select for use the Order RC model as the equivalent-circuit model of this battery, utilize the FFRLS algorithm that real time data is carried out the on-line parameter identification, obtain identified parameters.Recycling identification gained result, set up the emulation battery model, to test the current value of collection as the known quantity input model, can obtain corresponding terminal voltage estimated value, comparative experiments data and emulated data, carry out error analysis, can verify the rationality of Order RC model and the accuracy of FFRLS algorithm parameter identification.

The Order RC model error was analyzed when table 1 was tested SOC=0.9 for HPPC.When accompanying drawing 7 is SOC=0.9, experimental data under the terminal voltage relative method and the comparison diagram of emulated data, can visually see in conjunction with chart: experimental data overlaps substantially with emulated data, and error less (in reasonable range ± 0.032V), show that the Order RC model can embody the dynamic perfromance of electrokinetic cell well, and the FFRLS algorithm to carry out the real-time parameter identification accurately feasible.

The Order RC model error is analyzed during table 1HPPC experiment SOC=0.9

After checking is finished, identified parameters with SOC opening relationships, is obtained the curve that model parameter changes with SOC.Shown in accompanying drawing 8,9, be respectively the graph of a relation of battery model parameter active component and capacitive part and SOC.By the corresponding relation of model parameter and SOC, we can estimate the state-of-charge of battery by the parameter of real-time identification, the present duty of electrolytic cell.

Simultaneously, under the prerequisite of cells known state-of-charge, if when line identification parameter has surpassed the Reasonable Parameters value scope corresponding with it (for example: on-line identification gained ohmic internal resistance R ₀Value surpasses corresponding Reasonable Parameters value 20%), we can think that battery occurs than the great depression phenomenon, have potential safety hazard, should carry out further fault diagnosis, with the generation of accident prevention.

Claims (2)

1. based on the accumulator state-of-charge method of estimation of model, it is characterized in that:

1) data acquisition

To the battery model parameter identification, the electric current of needs collection battery and information of voltage are as the data vector of model; Consider the dynamic change of battery in real vehicle travels, adopt mixed pulses power characteristic test HPPC as the dynamic experiment of data acquisition;

2) model is chosen

The equivalent-circuit model that this method is chosen is the Order RC model, and this model is made up of a resistance and two RC modules;

3) parameter identification

The present invention's employing contains genic least-squares algorithm and carries out the Order RC identification of Model Parameters, exactly the battery under the duty is considered as a dynamic system, electric current I is imported u as system, voltage U is exported y as system, such single-input single-output system is carried out System Discrimination, obtain containing the difference equation coefficient of model parameter, thereby try to achieve the battery model parameter;

4) simulating, verifying

By dynamic operation condition experiment and identification of Model Parameters, the model parameter in the time of can obtaining under the variable working condition; Otherwise, after obtaining model parameter, set up realistic model, can estimate the terminal voltage of battery by real-time current; The virtual voltage that the terminal voltage of estimating is gathered with dynamic operation condition contrasts, and carries out error analysis, but both rationality of certificate parameter discrimination method, but the also accuracy of assessment models is the terminal voltage relative method;

5) state estimation

The model parameter of electrokinetic cell can change along with the difference of state-of-charge SOC, by setting up the model parameter database corresponding with SOC, both can be linked together; By real-time identification of Model Parameters, with identified parameters and database information comparison, judge battery state-of-charge of living in again.

2. the accumulator state-of-charge method of estimation based on model according to claim 1 is characterized in that parameter identification is specific as follows in the step 3):

According to the circuit relationships of Order RC model, get the state equation under the frequency domain:

$U\left(s\right)-U_{\mathrm{OC}}\left(s\right)=-I\left(s\right)(R_0+\frac{R_1}{R_1{C}_{1}s+1}+\frac{R_2}{R_2{C}_{2}s+1})---\left(1\right)$

In the formula: s is frequency domain symbol; U (s) is the frequency domain form of terminal voltage; U _OC(s) be the frequency domain form of open-circuit voltage; I (s) is the frequency domain form of electric current;

Make U ' (s)=U (s)-U _OC(s), then can obtain corresponding transport function, as follows:

$G\left(s\right)=\frac{U^{\&prime;}\left(s\right)}{I\left(s\right)}=-(R_0+\frac{R_1}{R_1{C}_{1}s+1}+\frac{R_2}{R_2{C}_{2}s+1})---\left(2\right)$

(2) formula is carried out the z conversion, can pass through bilater substitution

(T is the sampling time) realizes:

$G\left(z^{-1}\right)=\frac{U^{\&prime;}\left(z^{-1}\right)}{I\left(z^{-1}\right)}=\frac{k_3+k_4{z}^{-1}+k_5{z}^{-2}}{1-k_1{z}^{-1}-k_2{z}^{-2}}---\left(3\right)$

In the formula, k ₁, k ₂, k ₃, k ₄And k ₅Be undetermined coefficient;

Can be obtained the difference equation form of model state equation by formula (3):

U′(k)=k ₁U'(k-1)+k ₂U'(k-2)+k ₃I(k)+k ₄I(k-1)+k ₅(k-2) （4）

In the formula: k, k-1, k-2 represent k item value, k-1 item value and the k-2 item value of voltage or electric current respectively;

Because the open-circuit voltage U of battery _OCWith state-of-charge SOC, work temperature em and life-span L very strong relevance is arranged, and these three amounts are the function of time t, therefore define U _OCBe the function of SOC, Tem and L, as shown in the formula:

U _OC=f(SOC(t),Tem(t),L(t)) （5）

Differentiate gets to time t:

$\frac{d{U}_{\mathrm{OC}}}{\mathrm{dt}}=\frac{\&PartialD;U_{\mathrm{OC}}}{\&PartialD;\mathrm{SOC}}\frac{\&PartialD;\mathrm{SOC}}{\&PartialD;t}+\frac{\&PartialD;U_{\mathrm{OC}}}{\&PartialD;\mathrm{Tem}}\frac{\&PartialD;\mathrm{Tem}}{\&PartialD;t}+\frac{\&PartialD;U_{\mathrm{OC}}}{\&PartialD;L}\frac{\&PartialD;L}{\&PartialD;t}---\left(6\right)$

At this, make the following assumptions:

1. the electric weight of electrokinetic cell unit's sampling time T internal consumption or regeneration is compared rated capacity and can be left in the basket, therefore

Set up;

2. the working temperature of electrokinetic cell arranges under the rational situation in ventilation and cooling infrastructure owing to being subjected to battery management system monitoring in real time and being controlled effectively, and the temperature variation of electrokinetic cell is slower, can be considered constant in the single sampling time T, that is,

3. the sampling time T of unit also is negligible compared to battery life L; Thereby

Set up;

Under the situation that above-mentioned hypothesis is set up, formula (6) can be reduced to:

$\frac{d{U}_{\mathrm{OC}}}{\mathrm{dt}}=\frac{U_{\mathrm{OC}}\left(k\right)-U_{\mathrm{OC}}(k-1)}{T}=\frac{U_{\mathrm{OC}}(k-1)-U_{\mathrm{OC}}(k-2)}{T}\&ap;0---\left(7\right)$

ΔU _OC(k)=U _OC(k)-U _OC(k-1)=U _OC(k-1)-U _OC(k-2)≈0 （8）

Then formula (4) arrangement can get:

U(k)=(1-k ₁-k ₂)U _OC(k)+k ₁U(k-1)+k ₂U(k-2)+k ₃I(k)+k ₄I(k-1)+k ₅(k-2) （9）

Formula (9) can be write as least squares formalism:

θ=[(1-k ₁-k ₂)U _OC,k ₁,k ₂,k ₃,k ₄,k ₅] ^T （12）

In the formula,

(k) be data vector, θ is coefficient vector to be estimated;

Can be estimated θ by the FFRLS algorithm, thereby try to achieve k ₁, k ₂, k ₃, k ₄And k ₅:

$\widehat{\mathrm{\&theta;}}\left(k\right)=\widehat{\mathrm{\&theta;}}(k-1)+K\left(k\right)e\left(k\right)---\left(13\right)$

In the formula: e (k) is the evaluated error of U (k);

(k) be the estimated value of θ; K (k) is the algorithm gain; P (k) is covariance matrix; λ is gene, λ=0.95～1;

By k ₁, k ₂, k ₃, k ₄And k ₅Can get with the relation of battery model parameter:

$R_0=\frac{-k_3+k_4-k_5}{1+k_1-k_2},$ $R_1{C}_1{R}_2{C}_2=\frac{T^2(1+k_1-k_2)}{4(1-k_1-k_2)},$ $R_1{C}_1+R_2{C}_2=\frac{T(1+k_2)}{1-k_1-k_2}$ （14）

$R_0+R_1+R_2=\frac{-k_3-k_4-k_5}{1-k_1-k_2},$ $R_0{R}_1{C}_1+R_0{R}_2{C}_2+R_2{R}_1{C}_1+R_1{R}_2{C}_2=\frac{T(k_5-k_3)}{1+k_1-k_2}$

In order to solve the many solutions problem that occurs in the calculation of parameter, make τ ₁=R ₁C ₁, τ ₂=R ₂C ₂, τ ₁Get the minimal value of trying to achieve time constant, τ ₂Get maximum value; So far, finish the battery model parameters R ₀, R ₁, R ₂, C ₁And C ₂Identification.

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