CN103645372A - Method for quickly estimating open circuit voltage of secondary battery - Google Patents

Abstract

The invention discloses a method for quickly estimating an open circuit voltage of a secondary battery, which relates to the technical field of battery management. The method is used for solving the problems of the open circuit voltage of an existing battery of slow obtaining speed, poor universality and limitation caused by working temperature range. The method disclosed by the invention can be used for estimating the open circuit voltage of the battery by obtaining the time and the voltage data of the battery in an open circuit status within former few minutes and introducing the time and voltage data into a model of the invention. The method disclosed by the invention can be used for estimating the final open circuit voltage of the battery within several minutes. The method disclosed by the invention is suitable for quickly estimating the open circuit voltage of the secondary battery.

Description

A kind of secondary cell open-circuit voltage method for quick estimating

Technical field

The present invention relates to battery management technical field, be specifically related to a kind of secondary cell open-circuit voltage method of estimation.

Background technology

The open-circuit voltage of battery (OCV) has reacted the internal state of battery as the important parameter of battery, in the every field of battery technology, play an important role.Because the open-circuit voltage of battery depends on the activity substance content in battery electrode material and material, so the open-circuit voltage of battery not only can be used for analyzing the level characteristic of battery electrode, can also be used to estimate the dump energy state (SOC) of battery simultaneously.The open-circuit voltage of battery can also be used to estimate the health status (SOH) of battery, for example, in lithium ion battery, and aging along with battery, the open-circuit voltage of battery is only decayed in its high electric weight region.In addition the open-circuit voltage of battery or the important evidence of battery system equilibrium.So open-circuit voltage estimates it is the necessary guarantee of battery management and correlation technique thereof accurately.

Cell voltage only at battery in open-circuit condition, and sufficient standing is after its voltage discharges completely, just equals the open-circuit voltage of battery.In this process, the overpotential of battery constantly reduces, and cell voltage trends towards equilibrium state gradually, i.e. the open-circuit voltage of battery.But this process often needs long time, it is generally acknowledged more than 20 hours.General in order to obtain the open-circuit voltage of battery, can only wait for by long, but this long wait has seriously limited the online application of battery open circuit voltage.For this way to solve the problem, relevant research is also very limited.Only certain methods is the good dispose procedure of matching battery also, and this makes the estimation of its open-circuit voltage there will be certain error.

Summary of the invention

The present invention is slow in order to solve the acquisition speed of existing battery open circuit voltage, and versatility is poor, and the problem that is subject to operating temperature range restriction, thereby a kind of secondary cell open-circuit voltage method for quick estimating is provided.

A secondary cell open-circuit voltage method for quick estimating, it is realized by following steps:

In step 1, to battery after entering open-circuit condition front A minute, carry out voltage sample n time, obtain n open circuit time t _kwith magnitude of voltage U _{rLX, k}; A is positive number; K=1,2 ..., n, represents k sampled point; N is greater than 2 integer;

Step 2, set up open circuit time t _kwith by diffusion capacitance C _dwith diffusion resistance R _dthe relaxation time τ of the diffusion polarization link forming _dlinear function:

τ _d,k=αt _k+β

In formula: α and β are for characterizing the coefficient of linear relationship;

By in above-mentioned linear function substitution tradition second order equivalent model, obtain about battery release voltage U _rLXimproved model:

$U_{\mathrm{RLX},k}=U_{\mathrm{RLX},k-1}\×\exp \left[\frac{-(t_k-t_{k-1})}{\mathrm{\α}{t}_k+\mathrm{\β}}\right]-\mathrm{OCV}\×\exp \left[\frac{-(t_k-t_{k-1})}{\mathrm{\α}{t}_k+\mathrm{\β}}\right]+\mathrm{OCV},t_k>1\min$

In formula: the open-circuit voltage that OCV is battery; t ₀for initial time;

To above-mentioned about battery release voltage U _rLXimproved model arrange, obtain vector M=[the OCV α β] form about unknown variable ^tlinearized expression:

$\frac{(U_{\mathrm{RLX},k}+U_{\mathrm{RLX},k-1})(t_k-t_{k-1})}{2}={\left[\begin{array}{c}(t_k-t_{k-1})\\ -t_k(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})\\ -(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})\end{array}\right]}^T\left[\begin{array}{c}\mathrm{OCV}\\ \mathrm{\α}\\ \mathrm{\β}\end{array}\right],t_k>1\min$

Step 3, by the n obtaining in step 1 open circuit time t _kwith magnitude of voltage U _{rLX, k}the linearized expression that substitution step 2 obtains respectively, and simultaneous forms the linear overdetermined equation group about unknown variable:

Y=XM；

Wherein: $\left\{\begin{array}{c}M=\left[\begin{array}{c}\mathrm{OCV}\\ \mathrm{\α}\\ \mathrm{\β}\end{array}\right]\\ X=\left[\begin{array}{ccc}(t_1-t_0)& -t_1(U_{\mathrm{RLX},1}-U_{\mathrm{RLX},0})& -(U_{\mathrm{RLX},1}-U_{\mathrm{RLX},0})\\ .& .& .\\ .& .& .\\ .& .& .\\ (t_k-t_{k-1})& -t_k(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})& -(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})\end{array}\right]\\ Y=\left[\begin{array}{c}(U_{\mathrm{RLX},1}+U_{\mathrm{RLX},0})(t_1-t_0)/2\\ .\\ .\\ .\\ (U_{\mathrm{RLX},k}+U_{\mathrm{RLX},k-1})(t_k-t_{k-1})/2\end{array}\right]\end{array}\right.$

Then utilize M=[X ^tx] ^-1x ^ty solves the linear overdetermined equation group of unknown variable, obtains about open-circuit voltage OCV the solution at each interior unknown variable, using the solution of open-circuit voltage OCV as final estimated value, realizes the estimation to battery open circuit voltage.

Compared with prior art, the present invention has following beneficial effect:

1, avoid long wait, realize the fast prediction to battery open circuit voltage.

2, the calculated amount of method is little, is suitable for online use.

3, method does not need to carry out in advance characteristic test, and use cost is low.

4, method only needs to measure open circuit time and the magnitude of voltage of battery under open-circuit condition, and without other subsidiaries, hardware cost is low.

5, this method is applicable to all kinds of operating modes, and has broad operating temperature range.

Accompanying drawing explanation

Fig. 1 is the test pattern of the experiment in embodiment;

Fig. 2 is at 30 ℃, with the electric current of 2C, is discharged to the emulation schematic diagram of SOC=0.9 by SOC=1;

Fig. 3 is at 30 ℃, with FUDS state of cyclic operation, by SOC=0.9, is worked to the emulation schematic diagram of SOC=0.7;

Fig. 4 is at 50 ℃, with the electric current of 0.5C, is discharged to the emulation schematic diagram of SOC=0.4 by SOC=0.7;

Fig. 5 is at 10 ℃, is discharged to the emulation schematic diagram of SOC=0.3 with 0.5C electric current by SOC=0.4;

Fig. 6 is at 30 ℃, is charged to the emulation schematic diagram of SOC=0.5 with 1C electric current by SOC=0.3;

Fig. 7 is at 30 ℃, is charged to the emulation schematic diagram of SOC=0.8 with 1C electric current by SOC=0.5.

Embodiment

Embodiment one, a kind of secondary cell open-circuit voltage method for quick estimating, it is realized by following steps:

In step 1, to battery after entering open-circuit condition front A minute, carry out voltage sample n time, obtain n open circuit time t _kwith magnitude of voltage U _{rLX, k}; A is positive number; K=1,2 ..., n, represents k sampled point; N is greater than 2 integer;

Step 2, set up open circuit time t _kwith by diffusion capacitance C _dwith diffusion resistance R _dthe relaxation time τ of the diffusion polarization link forming _dlinear function:

τ _d,k=αt _k+β

In formula: α and β are for characterizing the coefficient of linear relationship;

By in above-mentioned linear function substitution tradition second order equivalent model, obtain about battery release voltage U _rLXimproved model:

$U_{\mathrm{RLX},k}=U_{\mathrm{RLX},k-1}\×\exp \left[\frac{-(t_k-t_{k-1})}{\mathrm{\α}{t}_k+\mathrm{\β}}\right]-\mathrm{OCV}\×\exp \left[\frac{-(t_k-t_{k-1})}{\mathrm{\α}{t}_k+\mathrm{\β}}\right]+\mathrm{OCV},t_k>1\min$

In formula: the open-circuit voltage that OCV is battery; t ₀for initial time;

To above-mentioned about battery release voltage U _rLXimproved model arrange, obtain vector M=[the OCV α β] form about unknown variable ^tlinearized expression:

$\frac{(U_{\mathrm{RLX},k}+U_{\mathrm{RLX},k-1})(t_k-t_{k-1})}{2}={\left[\begin{array}{c}(t_k-t_{k-1})\\ -t_k(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})\\ -(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})\end{array}\right]}^T\left[\begin{array}{c}\mathrm{OCV}\\ \mathrm{\α}\\ \mathrm{\β}\end{array}\right],t_k>1\min$

Step 3, by the n obtaining in step 1 open circuit time t _kwith magnitude of voltage U _{rLX, k}the linearized expression that substitution step 2 obtains respectively, and simultaneous forms the linear overdetermined equation group about unknown variable:

Y=XM；

Wherein: $\left\{\begin{array}{c}M=\left[\begin{array}{c}\mathrm{OCV}\\ \mathrm{\α}\\ \mathrm{\β}\end{array}\right]\\ X=\left[\begin{array}{ccc}(t_1-t_0)& -t_1(U_{\mathrm{RLX},1}-U_{\mathrm{RLX},0})& -(U_{\mathrm{RLX},1}-U_{\mathrm{RLX},0})\\ .& .& .\\ .& .& .\\ .& .& .\\ (t_k-t_{k-1})& -t_k(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})& -(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})\end{array}\right]\\ Y=\left[\begin{array}{c}(U_{\mathrm{RLX},1}+U_{\mathrm{RLX},0})(t_1-t_0)/2\\ .\\ .\\ .\\ (U_{\mathrm{RLX},k}+U_{\mathrm{RLX},k-1})(t_k-t_{k-1})/2\end{array}\right]\end{array}\right.$

Then utilize M=[X ^tx] ^-1x ^ty solves the linear overdetermined equation group of unknown variable, obtains about open-circuit voltage OCV the solution at each interior unknown variable, using the solution of open-circuit voltage OCV as final estimated value, realizes the estimation to battery open circuit voltage.

Because the present invention has only used open circuit time and the battery voltage value of battery under open-circuit condition, so use of the present invention does not rely on advanced testing apparatus, also do not rely on any characteristic test in early stage, while method is applicable to various working conditions and temperature conditions.

Below with concrete experiment, effect of the present invention is verified:

Ferric phosphate lithium cell is carried out to the experiment of various operating modes and temperature, comprising:

(a), at 30 ℃, with the electric current of 2C, by SOC=1, be discharged to SOC=0.9; Simulation result as shown in Figure 2;

(b), at 30 ℃, with FUDS state of cyclic operation, by SOC=0.9, worked to SOC=0.7; Simulation result as shown in Figure 3;

(c), at 50 ℃, with the electric current of 0.5C, by SOC=0.7, be discharged to SOC=0.4; Simulation result as shown in Figure 4;

(d), at 10 ℃, with 0.5C electric current, by SOC=0.4, be discharged to SOC=0.3; Simulation result as shown in Figure 5;

(e), at 30 ℃, with 1C electric current, by SOC=0.3, charge to SOC=0.5; Simulation result as shown in Figure 6;

(f), at 30 ℃, with 1C electric current, by SOC=0.5, charge to SOC=0.8; Simulation result as shown in Figure 7.

The measurement result of each experimentation curve as shown in Figure 1, wherein: 111,121,131,141,151 and 161 is current curve, and 112,122,132,142,152 and 162 is voltage curve.

Voltage after each experimental cell open circuit and the open circuit time of correspondence be take to 2s as the cycle gathers, obtain 201,301,401,501,601 and 701 6 voltage data curves in Fig. 2 to Fig. 7.

Adopt the front 20min data of experiment to be brought into X, in Y.

Recycling M=[X ^tx] ^-1x ^ty obtains the value of vector M.First variable of getting M is method and estimates the open-circuit voltage values obtaining, as shown in 203 in Fig. 2 to Fig. 7,303,403,503,603 and 703.Meanwhile, other two variable α and the β value of M also provide respectively in Fig. 2 to 7.

For the accuracy of analyzing novel methods estimation, here by the long-time standing actual value that obtains open-circuit voltage, respectively as shown in Fig. 2 to 7 202,302,402,502,602 and 702.

Contrast six resulting estimated values of experiment and actual value, the error in 20 minutes is respectively: (a) 0.3mV, (b)-0.7mV, (c) 0.9mV, (d)-1.7mV, (e) 0.6mV and (f) 0.5mV.And use the error of traditional wait method to be respectively: (a) – 3.2mV, (b)-9.6mV, (c) – 2.6mV, (d)-18.4mV, (e) 4.9mV and (f) 4.1mV.

By above experiment, the feasibility of new method and the accuracy of estimated result have fully been confirmed.

Claims (2)

1. a secondary cell open-circuit voltage method for quick estimating, is characterized in that: it is realized by following steps:

In step 1, to battery after entering open-circuit condition front A minute, carry out voltage sample n time, obtain n open circuit time t _kwith magnitude of voltage U _{rLX, k}; A is positive number; K=1,2 ..., n, represents k sampled point; N is greater than 2 integer;

Step 2, set up open circuit time t _kwith by diffusion capacitance C _dwith diffusion resistance R _dthe relaxation time τ of the diffusion polarization link forming _dlinear function:

τ _d,k=αt _k+β

In formula: α and β are for characterizing the coefficient of linear relationship;

By in above-mentioned linear function substitution tradition second order equivalent model, obtain about battery release voltage U _rLXimproved model:

$U_{\mathrm{RLX},k}=U_{\mathrm{RLX},k-1}\×\exp \left[\frac{-(t_k-t_{k-1})}{\mathrm{\α}{t}_k+\mathrm{\β}}\right]-\mathrm{OCV}\×\exp \left[\frac{-(t_k-t_{k-1})}{\mathrm{\α}{t}_k+\mathrm{\β}}\right]+\mathrm{OCV},t_k>1\min$

In formula: the open-circuit voltage that OCV is battery;

To above-mentioned about battery release voltage U _rLXimproved model arrange, obtain vector M=[the OCV α β] form about unknown variable ^tlinearized expression:

$\frac{(U_{\mathrm{RLX},k}+U_{\mathrm{RLX},k-1})(t_k-t_{k-1})}{2}={\left[\begin{array}{c}(t_k-t_{k-1})\\ -t_k(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})\\ -(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})\end{array}\right]}^T\left[\begin{array}{c}\mathrm{OCV}\\ \mathrm{\α}\\ \mathrm{\β}\end{array}\right],t_k>1\min$

Step 3, by the n obtaining in step 1 open circuit time t _kwith magnitude of voltage U _{rLX, k}the linearized expression that substitution step 2 obtains respectively, and simultaneous forms the linear overdetermined equation group about unknown variable:

Y=XM；

Wherein: $\left\{\begin{array}{c}M=\left[\begin{array}{c}\mathrm{OCV}\\ \mathrm{\α}\\ \mathrm{\β}\end{array}\right]\\ X=\left[\begin{array}{ccc}(t_1-t_0)& -t_1(U_{\mathrm{RLX},1}-U_{\mathrm{RLX},0})& -(U_{\mathrm{RLX},1}-U_{\mathrm{RLX},0})\\ .& .& .\\ .& .& .\\ .& .& .\\ (t_k-t_{k-1})& -t_k(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})& -(U_{\mathrm{RLX},k}-U_{\mathrm{RLX},k-1})\end{array}\right]\\ Y=\left[\begin{array}{c}(U_{\mathrm{RLX},1}+U_{\mathrm{RLX},0})(t_1-t_0)/2\\ .\\ .\\ .\\ (U_{\mathrm{RLX},k}+U_{\mathrm{RLX},k-1})(t_k-t_{k-1})/2\end{array}\right]\end{array}\right.$

Then utilize M=[X ^tx] ^-1x ^ty solves the linear overdetermined equation group of unknown variable, obtains about open-circuit voltage OCV the solution at each interior unknown variable, using the solution of open-circuit voltage OCV as final estimated value, realizes the estimation to battery open circuit voltage.

2. a kind of secondary cell open-circuit voltage method for quick estimating according to claim 1, is characterized in that battery is ferric phosphate lithium cell.

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