CN101692119B

CN101692119B - Method for measuring internal resistance of storage battery based on differential equation

Info

Publication number: CN101692119B
Application number: CN2009101802047A
Authority: CN
Inventors: 安凯; 安培亮; 王晓英
Original assignee: Individual
Current assignee: Individual
Priority date: 2009-10-09
Filing date: 2009-10-09
Publication date: 2012-01-04
Anticipated expiration: 2029-10-09
Also published as: CN101692119A

Abstract

The invention relates to a method for measuring internal resistance of a storage battery based on differential equation, which comprises the following steps: connecting a square wave generator, measuring voltages at two ends of the square wave generator at the moment when the connected square wave generator is about to be disconnected, voltages at two ends of the square wave generator when the disconnected square wave generator is about to be connected and voltage at the moment of the connection of the disconnected square wave generator, and calculating ohm internal resistance value and polarization resistance value of the storage battery through a formula to judge the failure degree of the storage battery. The method can reflect the change of the internal resistance of the storage battery more accurately so as to judge the failure degree of the storage battery more accurately. Compared with the prior measurement method, the calculation method of the invention is simpler and more convenient, and the measurement result is more reliable.

Description

Accumulator internal resistance measurement method based on the differential equation

(1), technical field

The present invention relates to a kind of accumulator internal resistance measurement method, specifically a kind of accumulator internal resistance measurement method based on the differential equation.

(2), background technology

Standby power supply when accumulator has a power failure as power-supply system is widely used in industries such as commercial production, traffic, communication.If battery failure or off-capacity; Just might cause a serious accident, so, the operational factor of accumulator is carried out comprehensive on-line monitoring; To the safe operation that improves straight-flow system, reliability and the automaticity that improves electric power system, crucial meaning is arranged.

It is exactly its internal resistance that accumulator uses one of important parameter of consumption state.No matter be that accumulator is about to inefficacy, off-capacity or discharges and recharges improperly, embody can both changing from its internal resistance.Therefore can its duty be assessed through measuring accumulator internal resistance.

At present, the on-line monitoring method of realization internal resistance of single cell mainly contains densimetry, open-circuit voltage method, direct-current discharge method and AC method etc.Densimetry is mainly estimated the internal resistance of accumulator through the density of measuring battery liquid, be usually used in the internal resistance measurement of open type lead-acid battery, is not suitable for the internal resistance measurement of sealed lead acid storage battery.The open-circuit voltage method is to estimate accumulator internal resistance through the terminal voltage of measuring accumulator; Precision is very poor; Even might derive a wrong conclusion, even because the accumulator that capacity has become very little, its terminal voltage still possibly show very normally under floating charge state.Through battery is carried out transient large current discharge, the transient voltage of measuring on the battery falls the direct-current discharge method, calculates the internal resistance of cell through Ohm law exactly.Though this method has also obtained using widely in practice; But also there are some shortcomings in it; As with this method accumulator internal resistance being detected must be under static state or off-line state, to carry out; Can't realize on-line measurement; And heavy-current discharge can cause bigger infringement to accumulator, thereby influences the capacity and the life-span of accumulator.AC method is measured the voltage responsive signal at accumulator two ends and both phase differential through accumulator is injected a constant ac current signal, is confirmed the internal resistance of accumulator by formula of impedance.This method does not need accumulator is discharged, and can realize the online detection internal resistance of cell of safety, so can the performance of accumulator not impacted.But this method need be measured the phase differential between ac current signal, voltage responsive signal and the voltage and current, and this method not only disturbing factor is many, and has increased the complicacy of system, has also influenced measuring accuracy simultaneously.

(3), summary of the invention

The present invention is intended to through a kind of accumulator internal resistance measurement method based on the differential equation is provided, to overcome the defective of existing accumulator internal resistance measurement method.First technical matters to be solved is: through connection side's wave producer; Measure the voltage that is about to break off its two ends of moment under the square-wave generator connection situation; Square-wave generator is about to connect the voltage at its two ends of moment when breaking off; Connect the voltage of moment under the square-wave generator disconnection; And pass through formula and calculate ohmic internal resistance value and the polarization resistance value that obtains accumulator, in order to judge the failure degree of accumulator.

In order to solve the problems of the technologies described above, the present invention has adopted following technical scheme.

A kind of accumulator internal resistance measurement method based on the differential equation is characterized in that carrying out according to following steps:

Connection side's wave producer between charger and accumulator, the anodal of three connects mutually, and negative pole also connects mutually;

Measure the voltage v that is about to break off its two ends of moment under the square-wave generator connection situation < > 3bb <> , square-wave generator is about to the voltage v at its two ends of closed circuit moment when breaking off < > 3kk <> , connect the voltage v of moment under the square-wave generator disconnection < > 3kb <>

Calculate the ohmic internal resistance R of accumulator < > 0 <> ,

R_{0} = \frac{V_{3 kk} - V_{3 kb}}{I},

In the formula, the measuring current when on behalf of square-wave generator, I connect;

And calculate the polarization resistance R of accumulator < > 2 <> ,

R_{2} = \frac{V_{3 kb} - V_{3 bb}}{I};

According to the ohmic internal resistance value of accumulator and the failure degree of polarization resistance value judgement accumulator.

Good effect of the present invention is: the present invention is on the basis of comprehensive traditional internal resistance of cell measuring method; Through the battery circuit differential equation group; Derive the computing formula of accumulator ohmic internal resistance and polarization resistance, and provide the measuring method of the measurement data that needs in the computing formula.

This method not only can calculate the ohmic internal resistance of accumulator, can also calculate the polarization resistance of accumulator.Therefore can reflect the variation of accumulator internal resistance more accurately, thereby judge the failure degree of accumulator more accurately.

On the other hand, compare with original measuring method, computing method of the present invention are easier, and measurement result is more reliable.

(4), description of drawings

Fig. 1 is the battery model synoptic diagram under the floating charge state of the present invention.

(5), embodiment

Below in conjunction with accompanying drawing and embodiment is provided, the present invention is further described.

Fig. 1 is the model of the accumulator under the floating charge state, and it is by charger 1, and square-wave generator 2 is formed with accumulator 3, and the anodal of them connects mutually, and negative pole also connects mutually.

Among the figure, E < > 1 <> Represent the voltage of charger, R < > 1 <> Represent the internal resistance of charger, I < > 1 <> Represent the electric current of charger, R < > 0 <> , R < > 2 <> Represent the resistance and the electric capacity of accumulator internal resistance equivalent electrical circuit, E respectively with C < > 2 <> Represent the electromotive force of accumulator, I < > 2 <> Represent the electric current of accumulator, I < > 3 <> Represent measuring current.

At first, record the voltage v that is about to break off its two ends of moment under the square-wave generator connection situation < > 3bb <> , square-wave generator is about to the voltage v at its two ends of closed circuit moment when breaking off < > 3kk <> , connect the voltage v of moment under the square-wave generator disconnection < > 3kb <>

Then, calculate the ohmic internal resistance R of accumulator < > 0 <> ,

R_{0} = \frac{V_{3 kk} - V_{3 kb}}{I},

And calculate the polarization resistance R of accumulator < > 2 <> ,

R_{2} = \frac{V_{3 kb} - V_{3 bb}}{I};

At last, the failure degree of judging accumulator according to the ohmic internal resistance value and the polarization resistance value of accumulator.The standard of international differentiation accumulator actual effect is that internal resistance surpasses 30% of new accumulator internal resistance, or internal resistance surpasses 30% of a group storage battery internal resistance mean value.

Below be the derivation of above-mentioned judgment formula:

Definition

I_{3} = \{\begin{matrix} I & on \\ 0 & off \end{matrix},

Then the no matter switching of measurement circuit always has

\{\begin{matrix} I_{1} + I_{2} = I_{3} \\ I_{1} R_{1} + V_{3} = E_{1} \\ R_{0} I_{2} + V_{3} = E_{2} - u \\ I_{2} = C \frac{du}{dt} + \frac{u}{R_{2}} \end{matrix}

I_{1} = I_{3} - I_{2} = I_{3} - (C \frac{du}{dt} + \frac{u}{R_{2}})

In the formula, u represents the voltage at capacitor two ends, and t represents the time;

Test voltage V < > 3 <> Two kinds be expressed as

\{\begin{matrix} V_{3} = E_{1} - [I_{3} R_{1} - (C \frac{du}{dt} + \frac{u}{R_{2}}) R_{1}] \\ V_{3} = E_{2} - (C \frac{du}{dt} + \frac{u}{R_{2}}) R_{0} - u \end{matrix}

So have

\frac{du}{dt} + \frac{1}{C} (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}}) u = \frac{E_{2} - E_{1} + I_{3} R_{1}}{C (R_{0} + R_{1})}

Satisfy u(0)=u < > 0 <> General solution do

u (t) = (u_{0} - \frac{E_{2} - E_{1} + I_{3} R_{1}}{R_{0} + R_{1} + R_{2}} R_{2}) e^{- \frac{1}{C} (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}}) t} + \frac{E_{2} - E_{1} + I_{3} R_{1}}{R_{0} + R_{1} + R_{2}} R_{2}

And

C \frac{du}{dt} = [\frac{E_{2} - E_{1} + I_{3} R_{1}}{R_{0} + R_{1} + R_{2}} R_{2} - u (t)] (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}})

= \frac{E_{2} - E_{1} + I_{3} R_{1}}{R_{0} + R_{1}} - u (t) (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}})

(1) stable state reaches the moment of closing

P-wire open circuit, when reaching stable state

V_{2 kk} = E_{2} - \frac{u_{0}}{R_{2}} R_{0} - u_{0}

V_{3 kk} = E_{1} + \frac{u_{0}}{R_{2}} R_{1}

Thus

E_{2} - E_{1} = \frac{R_{0} + R_{1} + R_{2}}{R_{2}} u_{0}

u_{0} = \frac{E_{2} - E_{1}}{R_{0} + R_{1} + R_{2}} R_{2}

Note R < > 02 <>=R < > 0 <> +R < > 2 <> Then

V_{3 kk} = E_{2} - \frac{u_{0}}{R_{2}} R_{02} - - - (1)

Therefore after closed circuit

u (t) = (u_{0} - \frac{E_{2} - E_{1} + I_{3} R_{1}}{R_{0} + R_{1} + R_{2}} R_{2}) e^{- \frac{1}{C} (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}}) t} + \frac{E_{2} - E_{1} + I_{3} R_{1}}{R_{0} + R_{1} + R_{2}} R_{2}

C \frac{du}{dt} = \frac{E_{2} - E_{1} + {IR}_{1}}{R_{0} + R_{1}} - u (t) (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}})

{[C \frac{du}{dt}]}_{t = 0} = \frac{E_{2} - E_{1} + I R_{1}}{R_{0} + R_{1}} - u_{0} (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}})

Utilize

V_{3} = E_{2} - (C \frac{du}{dt} + \frac{u}{R_{2}}) R_{0} - u

Get

V_{3 kb} = E_{2} - [\frac{E_{2} - E_{1} + I R_{1}}{R_{0} + R_{1}} R_{0} - u_{0} R_{0} (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}})] - \frac{u_{0} R_{02}}{R_{2}} - - - (2)

Get by (1) and (2)

V_{3 kk} - V_{3 kb} = \frac{E_{2} - E_{1} + I R_{1}}{R_{0} + R_{1}} R_{0} - \frac{E_{2} - E_{1}}{R_{0} + R_{1} + R_{2}} R_{2} R_{0} \frac{R_{0} + R_{1} + R_{2}}{R_{2} (R_{0} + R_{1})})

= \frac{E_{2} - E_{1} + I R_{1}}{R_{0} + R_{1}} R_{0} - \frac{E_{2} - E_{1}}{R_{0} + R_{1}} R_{0}

= \frac{I R_{1}}{R_{0} + R_{1}} R_{0}

\approx I R_{0}

The moment of (two), opening after the closed circuit stable state

P-wire is closed circuit, when the T time reaches stable state

\{\begin{matrix} V_{3 bb} = E_{1} - I R_{1} + \frac{u (T)}{R_{2}} R_{1} \\ V_{3 bb} = E_{2} - \frac{u (T)}{R_{2}} R_{0} - u (T) \end{matrix} - - - (3)

Thus

u (T) \frac{R_{0} + R_{1} + R_{2}}{R_{2}} = E_{2} - E_{1} + I R_{1}

u (T) = \frac{E_{2} - E_{1} + I R_{1}}{R_{0} + R_{1} + R_{2}} R_{2}

Therefore behind the open circuit

u (t) = (u_{0} - \frac{E_{2} - E_{1} + I_{3} R_{1}}{R_{0} + R_{1} + R_{2}} R_{2}) e^{- \frac{1}{C} (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}}) t} + \frac{E_{2} - E_{1} + I_{3} R_{1}}{R_{0} + R_{1} + R_{2}} R_{2}

{[C \frac{du}{dt}]}_{T} = \frac{E_{2} - E_{1}}{R_{0} + R_{1}} - u (T) (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}})

Utilize

V_{3} = E_{2} - (C \frac{du}{dt} + \frac{u}{R_{2}}) R_{0} - u

= E_{2} - C R_{0} \frac{du}{dt} - R_{02} \frac{u}{R_{2}}

V_{3 bk} = E_{2} - R_{0} C \frac{du}{dt} |_{T} - \frac{u (T)}{R_{2}} R_{02}

= E_{2} - R_{0} [\frac{E_{2} - E_{1}}{R_{0} + R_{1}} - u (T) (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}})] - \frac{u (T)}{R_{2}} R_{02}

= E_{2} - R_{0} \frac{E_{2} - E_{1}}{R_{0} + R_{1}} + u (T) R_{0} (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}}) - \frac{u (T)}{R_{2}} R_{02} - - - (4)

v < > 3bk <> Represent the voltage that breaks off moment under the square-wave generator connection situation;

Get by (3) and (4)

V_{3 bk} - V_{3 bb} = u (T) R_{0} (\frac{1}{R_{2}} + \frac{1}{R_{0} + R_{1}}) - R_{0} \frac{E_{2} - E_{1}}{R_{0} + R_{1}}

= \frac{E_{2} - E_{1} + I R_{1}}{R_{0} + R_{1} + R_{2}} R_{0} \frac{R_{0} + R_{1} + R_{2}}{R_{0} + R_{1}} - R_{0} \frac{E_{2} - E_{1}}{R_{0} + R_{1}}

= \frac{E_{2} - E_{1} + I R_{1}}{R_{0} + R_{1}} R_{0} - R_{0} \frac{E_{2} - E_{1}}{R_{0} + R_{1}}

= \frac{I R_{1}}{R_{0} + R_{1}} R_{0}

\approx I R_{0}

(3), the calculating of polarization resistance

Get by (1) and (3)

V_{3 kk} - V_{3 bb} = E_{1} - E_{2} + \frac{u_{0}}{R_{2}} R_{1} + \frac{u (T)}{R_{2}} R_{02}

= E_{1} - E_{2} + \frac{E_{2} - E_{1}}{R_{0} + R_{1} + R_{2}} R_{1} + \frac{E_{2} - E_{1} + I R_{1}}{R_{0} + R_{1} + R_{2}} R_{02}

= \frac{I R_{1}}{R_{0} + R_{1} + R_{2}} R_{02}

\approx I R_{02}

Therefore

R_{02} = \frac{V_{3 kk} - V_{3 bb}}{I}

R_{2} = R_{02} - R_{0} = \frac{V_{3 kk} - V_{3 bb}}{I} - \frac{V_{3 kk} - V_{3 kb}}{I} = \frac{V_{3 kb} - V_{3 bb}}{I}

Conclusion: ohmic internal resistance:

R_{0} = \frac{V_{3 kk} - V_{3 kb}}{I}

Polarization resistance:

R_{2} = \frac{V_{3 kb} - V_{3 bb}}{I} .

Claims

1. accumulator internal resistance measurement method based on the differential equation is characterized in that carrying out according to following steps:

Connection side's wave producer (2) between charger (1) and accumulator (3), the anodal of three connects mutually, and negative pole also connects mutually;

Record the voltage v that is about to break off its two ends of moment under the square-wave generator connection situation < > 3bb <> , square-wave generator is about to the voltage v at its two ends of closed circuit moment when breaking off < > 3kk <> , connect the voltage v of moment under the square-wave generator disconnection < > 3kb <>

Calculate the ohmic internal resistance R of accumulator < >0 <>,

And calculate the polarization resistance R of accumulator < >2 <>,