CN105301504A - Lithium battery state of charge estimation method based on unit impulse response - Google Patents

Abstract

The invention relates to the field of electric automobile battery power, and provides a battery state of charge estimation method through estimation of current open-circuit voltage of a battery. The adopted technical scheme is the lithium battery state of charge estimation method based on unit impulse response. The method comprises the following steps that a group of N discrete points corresponding to various SOC levels of impulse response, i.e. a function, are calculated under the experiment condition of offline calibration firstly and then stored in a lookup table so that the full range of effective SOC values of the battery are evenly divided into n independent values, and each value is corresponding one definite impulse response hn[k]; after the lookup table of impulse response is completed, output voltage of the battery within the given time interval can be calculated via the measured values of working current and the convolution sum of all impulse response stored in the lookup table; and a group of n output voltage in total is calculated as for any one working current, and the SOC of the battery is determined. The lithium battery state of charge estimation method based on unit impulse response is mainly applied to design and manufacturing of the electric automobile battery.

Description

The method of lithium battery charge state is estimated based on unit impulse response

Technical field

The present invention relates to batteries of electric automobile dynamic field, particularly relate to the estimation problem of dynamic lithium battery state-of-charge when using state.Specifically, the method estimating lithium battery charge state based on unit impulse response is related to.

Technical background

In recent years, in order to solve the two fold problem of energy and environment, the electric automobile with low emission low noise becomes the focus of each large automaker's concern.In the power-supply management system of electric automobile, the state-of-charge (SoC, StateofCharge) of battery is very important key parameter because it characterize in battery store dump energy number.In general, the SoC of lithium ion battery is made to remain in a suitable scope, such as 20% ~ 95%, be conducive to the functional completeness protecting battery.

Open-circuit voltage method is a kind of very accurate SoC evaluation method relatively, because open-circuit voltage is all different in the gamut that SoC changes, show that open-circuit voltage and SoC exist quantitative linear relationship, therefore measure open-circuit voltage by discharge test and estimate corresponding SoC value.Open-circuit voltage method needs electric battery to experience a static state and deposits process and make its inside reach balance, therefore cannot be applied in the dynamic environment such as electric automobile.

Summary of the invention

For overcoming the deficiencies in the prior art, the open-circuit voltage that a kind of estimating battery is current is proposed, thus the method for the state-of-charge of estimating battery.For this reason, the technical scheme that the present invention takes is, the method of lithium battery charge state is estimated based on unit impulse response, comprise the steps, first, under the experiment condition of off-line calibration, calculate one group of corresponding impulse response of various SOC level and N number of discrete point of function, then they are stored in a look-up table, like this gamut of effective for battery SOC value are divided into n independent values, the corresponding impulse response h determined of each value _n[k]; After completing the look-up table of impulse response, in preset time interval battery output voltage can by the measured value of working current and look-up table in the Convolution sums of all impulse responses that stores calculate; One group of n output voltage is altogether calculated to any one working current, as shown in the formula:

$U_n\[k\]=i\[k\]*h_n\[k\]\⇒U_n\[k\]=\underset{j=1}{\overset{N}{\Σ}}i\[j\]*h_n\[k-j\]---\left(14\right)$

The convolution value that the measured value comparing wire-end voltage calculates with the impulse response in application look-up table, choose optimum matching, to determine the correct impulse response that this state of battery is corresponding, selected impulse response makes the error between the measured value of wire-end voltage and calculated value minimum; Because the SOC value of each impulse response of correspondence is known, so the SOC of battery just determines under state.

For obtaining the value of pulse width in engineering, regulation:

$Y\left(s\right)=\frac{\mathrm{\τ}}{1+\mathrm{\τ}\·s}-\frac{\mathrm{\τ}}{2!}\×\left(\frac{\mathrm{\Δ}s}{1+\mathrm{\τ}\·s}\right)---\left(9\right)$

$y\left(t\right)=e^{-\frac{t}{\mathrm{\τ}}}-\frac{\mathrm{\Δ}}{2!}(-\frac{1}{\mathrm{\τ}}{e}^{-\frac{t}{\mathrm{\τ}}})---\left(10\right)$

$e^{-\frac{t}{\mathrm{\τ}}}>90\%\×\[e^{-\frac{t}{\mathrm{\τ}}}+\frac{\mathrm{\Δ}}{2!\mathrm{\τ}}\left(e^{-\frac{t}{\mathrm{\τ}}}\right)\]---\left(11\right)$

$1>0.9\×(1+\frac{\mathrm{\Δ}}{2\mathrm{\τ}})---\left(12\right)$

Then:

$\frac{\mathrm{\&Delta;}}{\mathrm{\&tau;}}<\frac{2}{9}---\left(13\right)$

。

Compared with the prior art, technical characterstic of the present invention and effect:

The present invention make use of the state-of-charge that open-circuit voltage method carrys out estimating battery, therefore has open-circuit voltage method and estimates advantage accurately.And utilize the unit impulse response of battery, real-time current and wire-end voltage the acquisition of open-circuit voltage can be made not need battery static state to place to the open-circuit voltage calculating battery, thus solve open-circuit voltage method and can not be used for the problem of real-time estimation battery charge state.Use the mode of look-up table to carry out the state-of-charge of estimating battery, whole method is simple.

Accompanying drawing explanation

The thevenin equivalent circuit model of Fig. 1 battery.

A kind of typical input pulse waveform of Fig. 2.

Fig. 3 process flow diagram of the present invention.

Embodiment

Set up a rational battery model exciter response relation of analog simulation battery and raising SOC estimation precision are of great significance.Equivalent-circuit model structure is clear, explicit physical meaning, is convenient to emulate dynamic response characteristic or mathematically calculate its state space equation, is thus widely used in current research.Thevenin equivalent circuit model is a kind of classical field formalism of equivalent-circuit model.Fig. 1 is the thevenin equivalent circuit model of battery, R ₄represent electrode and the packaged resistance of battery; R ₅represent the internal resistance of battery, define the releasable maximum current of battery, cause discharge and recharge loss simultaneously; C ₅be the electric capacity of battery, the double layer capacitor series connection be made up of every a pair battery unit is formed, and represents the electric charge of the limited quantity of inside battery storage; U ₇₈represent the open-circuit voltage of battery.

Investigate the single order RC model shown in Fig. 1, we can suppose that the mathematical model of this first-order linear time-invariant system has following form:

$\frac{dy\left(t\right)}{dt}+\frac{1}{\mathrm{\&tau;}}y\left(t\right)=f\left(t\right)---\left(1\right)$

Wherein y (t) exports, and f (t) is input, and τ is the minimum time constant of system.Through Laplace transform, the transition function of system should be expressed as:

$H\left(s\right)=\frac{\mathrm{\&tau;}}{1+\mathrm{\&tau;}\&CenterDot;s}---\left(2\right)$

The waveform making input f (t) of system as shown in Figure 2, is expressed as:

$f\left(t\right)=\frac{1}{\mathrm{\&Delta;}}\&lsqb;u\left(t\right)-u(t-\mathrm{\&Delta;})\&rsqb;---\left(3\right)$

The Laplace transform of f (t) is as follows:

$F\left(s\right)=\frac{1}{\mathrm{\&Delta;}s}(1-e^{-\mathrm{\&Delta;}s})---\left(4\right)$

By e in formula 4 ^{-Δ s}item is launched into Taylor series at s=0 place:

$F\left(s\right)=\frac{1}{\mathrm{\&Delta;}s}\&lsqb;1-(1+(-\mathrm{\&Delta;}s)+\frac{{(-\mathrm{\&Delta;}s)}^2}{2!}+\frac{{(-\mathrm{\&Delta;}s)}^3}{3!}+\mathrm{...})\&rsqb;$

$=1-\frac{\mathrm{\&Delta;}s}{2!}+\frac{{(-\mathrm{\&Delta;}s)}^2}{3!}-\frac{{(-\mathrm{\&Delta;}s)}^3}{4!}+\mathrm{...}---\left(5\right)$

Then response Y (s) of system to F (s) is:

$\begin{array}{c}Y\left(s\right)=F\left(s\right)\&CenterDot;H\left(s\right)\\ =\frac{\mathrm{\&tau;}}{1+\mathrm{\&tau;}.s}\&times;\&lsqb;1-\frac{\mathrm{\&Delta;}.s}{2!}+\frac{{(-\mathrm{\&Delta;}.s)}^2}{3!}-\frac{(-\mathrm{\&Delta;}.s)}{4!}+\mathrm{...}\&rsqb;\\ =\frac{\mathrm{\&tau;}}{1+\mathrm{\&tau;}.s}-\frac{\mathrm{\&tau;}}{2!}\&times;\left(\frac{\mathrm{\&Delta;}.s}{1+\mathrm{\&tau;}.s}\right)+\frac{\mathrm{\&tau;}(\mathrm{\&Delta;}.s)}{3!}\&times;\left(\frac{\mathrm{\&Delta;}.s}{1+\mathrm{\&tau;}.s}\right)-\\ \frac{\mathrm{\&tau;}{(\mathrm{\&Delta;}.s)}^2}{4!}\&times;\left(\frac{\mathrm{\&Delta;}.s}{1+\mathrm{\&tau;}.s}\right)+\mathrm{...}\end{array}---\left(6\right)$

Make f (t) meet the character of uni-impulse function, system must be made equal with the impulse response of system to the response of f (t), that is:

$Y\left(s\right)=F\left(s\right)\&CenterDot;H\left(s\right)=H\left(s\right)=\frac{x}{1+x\&CenterDot;s}---\left(7\right)$

Item in this formula 6 except Section 1 should be all 0, has:

$\frac{\mathrm{\&Delta;}s}{1+\mathrm{\&tau;}\&CenterDot;s}\&RightArrow;0\&DoubleRightArrow;\mathrm{\&Delta;}<<\mathrm{\&tau;}---\left(8\right)$

So far demonstrate: if the pulse width Δ of input f (t) is much smaller than the minimum time constant τ of system, then can think that f (t) is an engineering approximation of unit impulse function, s represents the complex frequency domain variable of Laplace transformation.

Continue the relation that pulse width and system minimum time constant are discussed below, to quantize the standard of current pulse width further.First two in investigation formula (6), think that all the other higher order terms are very little and can ignore.Now specify, Section 2 also can be neglected when the contribution of Section 2 to time domain response is less than 10% of total time domain response, this means:

$Y\left(s\right)=\frac{\mathrm{\&tau;}}{1+\mathrm{\&tau;}\&CenterDot;s}-\frac{\mathrm{\&tau;}}{2!}\&times;\left(\frac{\mathrm{\&Delta;}s}{1+\mathrm{\&tau;}\&CenterDot;s}\right)---\left(9\right)$

$y\left(t\right)=e^{-\frac{t}{\mathrm{\&tau;}}}-\frac{\mathrm{\&Delta;}}{2!}(-\frac{1}{\mathrm{\&tau;}}{e}^{-\frac{t}{\mathrm{\&tau;}}})---\left(10\right)$

$e^{-\frac{t}{\mathrm{\&tau;}}}>90\%\&times;\&lsqb;e^{-\frac{t}{\mathrm{\&tau;}}}+\frac{\mathrm{\&Delta;}}{2!\mathrm{\&tau;}}\left(e^{-\frac{t}{\mathrm{\&tau;}}}\right)\&rsqb;---\left(11\right)$

$1>0.9\&times;(1+\frac{\mathrm{\&Delta;}}{2\mathrm{\&tau;}})---\left(12\right)$

$\frac{\mathrm{\&Delta;}}{\mathrm{\&tau;}}<\frac{2}{9}---\left(13\right)$

This calculating more clearly explains the relation such as not in formula (8).In fact, the minimum time constant of cells known system allows our strobe pulse electric current better, to realize being similar to the better of impulse response.

Under the condition that temperature is certain, the impulse response of lithium ion battery depends on the SOC level of the battery in other words of residual charge quantity in battery, the impulse response that the SOC of varying level is corresponding different.Consider that the Li-ion battery model that we select is its thevenin equivalent circuit, above-mentioned conclusion is not difficult to explain.This battery model contains the voltage source of a characterizing battery open-circuit voltage, when applying current impulse to this model and encouraging and investigate the transient response of its wire-end voltage, this voltage responsive is inevitable has inseparable contacting with the parameter of voltage source and the open-circuit voltage of battery.To sum up, the algorithm estimated lithium ion battery SOC based on impulse response concept that this method is studied is that the one of open-circuit voltage method is improved in essence.

The specific implementation process of this algorithm is as shown in Figure 3: first, under the experiment condition of off-line calibration, calculate the impulse response (N number of discrete point of function) of one group of corresponding various SOC level, then they are stored in a look-up table, gamut by the effective SOC value of battery is divided into n independent values, the corresponding impulse response (h determined of each value _n[k]); After completing the look-up table of impulse response, in preset time interval battery output voltage can by the measured value of working current and look-up table in the Convolution sums of all impulse responses that stores calculate.Like this, one group of n output voltage altogether can be calculated to any one working current, as shown in the formula:

$U_n\&lsqb;k\&rsqb;=i\&lsqb;k\&rsqb;*h_n\&lsqb;k\&rsqb;\&DoubleRightArrow;U_n\&lsqb;k\&rsqb;=\underset{j=1}{\overset{N}{\&Sigma;}}i\&lsqb;j\&rsqb;*h_n\&lsqb;k-j\&rsqb;---\left(14\right)$

Wherein, U _n[k] represents wire-end voltage, and i [k] represents electric current, and k represents discrete time.

The convolution value that the measured value comparing wire-end voltage calculates with the impulse response in application look-up table, choose optimum matching, just can determine the correct impulse response that this state of battery is corresponding, selected impulse response makes the error between the measured value of wire-end voltage and calculated value minimum.Because the SOC value of each impulse response of correspondence is known, so the SOC of battery just determines under state.

The SoC key of lithium battery is choosing of response pulse duration Δ to use this method to estimate, due to the time constant of lithium battery in the value of different SoC level greatly between 30 ~ 60s, therefore can choose Δ=1s intensity of impulse is 1A.SoC is divided into 100 states, respectively impulse response experiment is carried out to battery, record the impulse response of battery under different SoC.During actual use battery, obtain different wire-end voltages with the electric current recorded from the impulse response convolution under each SoC level, and compare with the current wire-end voltage of actual measurement, choose optimum matching, thus determine the state-of-charge of present battery.

Claims (2)

1. estimate the method for lithium battery charge state based on unit impulse response for one kind, it is characterized in that, comprise the steps, first, under the experiment condition of off-line calibration, calculate one group of corresponding impulse response of various SOC level and N number of discrete point of function, then they are stored in a look-up table, like this gamut of effective for battery SOC value is divided into n independent values, the corresponding impulse response h determined of each value _n[k]; After completing the look-up table of impulse response, in preset time interval battery output voltage can by the measured value of working current and look-up table in the Convolution sums of all impulse responses that stores calculate; One group of n output voltage is altogether calculated to any one working current, as shown in the formula:

$U_n\&lsqb;k\&rsqb;=i\&lsqb;k\&rsqb;*h_n\&lsqb;k\&rsqb;\&DoubleRightArrow;U_n\&lsqb;k\&rsqb;=\underset{j=1}{\overset{N}{\&Sigma;}}i\&lsqb;j\&rsqb;*h_n\&lsqb;k-j\&rsqb;---\left(14\right)$

The convolution value that the measured value comparing wire-end voltage calculates with the impulse response in application look-up table, choose optimum matching, to determine the correct impulse response that this state of battery is corresponding, selected impulse response makes the error between the measured value of wire-end voltage and calculated value minimum; Because the SOC value of each impulse response of correspondence is known, so the SOC of battery just determines under state.

2. estimate the method for lithium battery charge state as claimed in claim 1 based on unit impulse response, it is characterized in that, for obtaining the value of pulse width in engineering, regulation:

$Y\left(s\right)=\frac{\mathrm{\&tau;}}{1+\mathrm{\&tau;}\&CenterDot;s}-\frac{\mathrm{\&tau;}}{2!}\&times;\left(\frac{\mathrm{\&Delta;}s}{1+\mathrm{\&tau;}\&CenterDot;s}\right)---\left(9\right)$

$y\left(t\right)=e^{-\frac{t}{\mathrm{\&tau;}}}-\frac{\mathrm{\&Delta;}}{2!}(-\frac{1}{\mathrm{\&tau;}}{e}^{-\frac{t}{\mathrm{\&tau;}}})---\left(10\right)$

$e^{-\frac{t}{\mathrm{\&tau;}}}>90\%\&times;\&lsqb;e^{-\frac{t}{\mathrm{\&tau;}}}+\frac{\mathrm{\&Delta;}}{2!\mathrm{\&tau;}}\left(e^{-\frac{t}{\mathrm{\&tau;}}}\right)\&rsqb;---\left(11\right)$

$1>0.9\&times;(1+\frac{\mathrm{\&Delta;}}{2\mathrm{\&tau;}})---\left(12\right)$

Then:

$\frac{\mathrm{\&Delta;}}{\mathrm{\&tau;}}<\frac{2}{9}---\left(13\right).$