CN103944235B - A kind of battery balanced time forecasting methods based on Fourier transformation - Google Patents

Abstract

The invention discloses a kind of battery balanced time forecasting methods based on Fourier transformation, it is adaptable to based on boosting inverter and the power battery equalization circuit of Sofe Switch.In a short period of time equalizing circuit is equivalent to the LC series resonance equivalent circuit with ac square wave input, set up the Fourier transformation model of the ac square wave input of series resonance equivalent circuit, and the expression formula of electric current it is equalized based on Fourier transformation, and then obtain the unit interval interior electricity transferring to the minimum battery cell of voltage from the battery cell that voltage is the highest, the final expression obtaining time for balance, show that time for balance t is proportional to R and C_q, it is inversely proportional to U_boostAnd λ, the conclusion unrelated with L, C.This method can the time for balance of Accurate Prediction battery, and determine the key factor affecting battery balanced speed, for improving balancing speed and the efficiency of equalizing circuit, reduce energy dissipation and provide strong theory support.

Description

A kind of battery balanced time forecasting methods based on Fourier transformation

Technical field

The present invention relates to a kind of battery balanced time forecasting methods based on Fourier transformation.

Background technology

Lithium ion battery is because of its high-energy-density, low discharge rate and does not has memory effect to be widely used in electric automobile and hybrid electrically In automobile.But, battery cell has limited voltage and capacity, it is necessary to used in groups by batteries monomer series and parallels up to a hundred To meet high power and the high energy demands of electric automobile.Such as, the electrokinetic cell of a BMW electric automobile is by 8088 economize on electricitys Pond monomer composition.But, serial lithium battery group brings a more acute problem: though battery cell in series battery Internal resistance or capacity there is fine difference, it is also possible to cause between battery cell voltage or SOC (SOC is the state-of-charge of battery, During SOC=100%, expression battery is full power state, and during SOC=0%, expression battery is electroless state) extreme unbalanced.This Outward, after charge and discharge cycles for several times, this unbalanced meeting is increasingly severe, greatly reduces the active volume of set of cells and follows The ring life-span.Even, security incident may be caused, such as blast, on fire etc..Therefore, battery balanced is indispensable. It is clear that as one of the key technology of battery management system, the efficient balance of series battery has become as a research heat Point.At present, equilibrium mainly has dissipation equilibrium, non-dissipation equilibrium and battery to select three major types.

Dissipate equilibrium (also referred to as cell bypass method equilibrium) by entering to the dissipating device in parallel of each battery cell in set of cells Row electric discharge shunting, thus realize the equilibrium of cell voltage.Dissipate to equalize and be divided into the most again two classes: passive equilibrium is with the most equal Weighing apparatus.Dissipation equalizing structure and control are simple, low cost, but the problem that there is energy dissipation and heat management.

Non-dissipate equilibrium use electric capacity, inductance etc. as energy-storage travelling wave tube, utilize common power converting circuit as underlying topology, Take dispersion or the structure concentrated, it is achieved unidirectional or two-way equalization scheme.According to balanced energy stream, non-dissipation equilibrium again can It is divided into following four: (1) cell to cell；(2)cell to pack；(3)pack to cell；(4)cell to pack to cell. For cell to pack or the equalization methods of pack to cell, when battery cell is carried out equalization discharge, set of cells simultaneously can be right This battery cell is charged；When battery cell is charged equilibrium, this battery cell can be discharged by set of cells simultaneously. Therefore, when target battery monomer is equalized by this equalization methods, charging and discharging is also deposited and is caused equalization efficiency low.And it is right In the equalization methods of cell to cell, energy directly can transfer to, from the battery cell that voltage is the highest, the battery cell that voltage is minimum, There is higher equalization efficiency, and be suitable for high voltage applications.Non-dissipation equilibrium exists that circuit structure is complicated, volume big, becomes The problems such as this height, time for balance length, high switching loss.

Battery selects equilibrium to refer to the battery cell structure set of cells consistent by experimental selection performance, typically has two step screening processes. The first step, under different discharge currents, selects the battery cell that battery average size is close to build set of cells；Second step, In the battery cell of first step screening, under different SOC, select that there is close cell voltage by pulse charge and discharge experiment and change The battery cell of amount.Owing to the self-discharge rate of battery cell is not quite similar, battery select equilibrium in the whole life cycle of battery not Be enough to keep battery to equalize always.It supplements equalization methods only as the one of other equalization methods.

The main cause that tradition equalization methods is not suitable for lithium ion battery is as follows:

1) open-circuit voltage of lithium ion battery is relatively flat when SOC is between 30%～70%, even if SOC differs greatly, The voltage difference of its correspondence is the least, additionally due to power electronic devices exists conduction voltage drop so that euqalizing current is very Little, in some instances it may even be possible to cause the power electronic devices can not normally；

2) there is conduction voltage drop due to power electronic devices, between battery cell, be difficulty with zero-voltage difference equilibrium.

Chinese invention patent application (application number 201310278475.2) proposes a kind of electrokinetic cell Zero Current Switch active equalization Circuit and implementation method, its can voltage is the highest and minimum in real-time judge set of cells battery cell, and it is carried out zero current Switch equilibrium, and two battery cells that equilibrium is both for voltage difference in set of cells maximum every time carry out peak load shifting, greatly Improve equalization efficiency, effectively reduce the discordance between battery cell.But, due to the power electronic devices used There is conduction voltage drop so that being extremely difficult to zero-voltage difference between battery cell, and euqalizing current is the least, time for balance is longer.

Summary of the invention

The present invention is to solve the problems referred to above, it is proposed that a kind of battery balanced time forecasting methods based on Fourier transformation, the party Method is disclosed based on boosting inverter and the power battery equalization circuit of Sofe Switch for application number 201320660950.8, for carrying The balancing speed of high circuit and efficiency, reduce energy dissipation and provide theory support.

To achieve these goals, the present invention adopts the following technical scheme that

A kind of battery balanced time forecasting methods based on Fourier transformation, comprise the following steps:

S1. the boosting inverter output voltage of equalizing circuit is modulated into a higher constant voltage, is equalized in a short period of time The voltage of the minimum battery cell of voltage can see a constant as, therefore can be equivalent to equalizing circuit to have The LC series resonant circuit of ac square wave input；

S2. Fourier transformation model and the AC impedance model of the equivalent AC square wave input of series resonance equivalent circuit are set up, It is equalized the expression formula of electric current, and derives battery cell transfer the highest from voltage in a switch periods To the electricity of the minimum battery cell of voltage, and then obtain electric quantity transfered in the unit interval；

S3. set up cell voltage and the piecewise linear model of SOC in balancing procedure, and be analyzed balancing procedure obtaining electricity Relation between pond monomer minimum voltage variable quantity and the variable quantity of ac square wave amplitude within the unit interval；

S4. derive the final expression formula of time for balance, obtain affecting the factor of balancing speed.

The concrete structure of LC series resonance equivalent circuit in described step S1, including equivalent AC square wave input f (t), equivalence is handed over The positive pole of stream square wave input takes back the negative pole of equivalent AC square wave input after being sequentially connected with inductance, electric capacity, resistance, wherein, inductance, Electric capacity, the capability value of resistance are respectively L, C, R.

In described step S2, the model of equivalent AC square wave input f (t) is:

$f\left(t\right)=\left\{\begin{array}{cc}\frac{U_{boost}-U_{min}\left(t\right)}{2}=A\left(t\right),& t\∈(kT,(k+\frac{1}{2}\left)T\right)\\ \frac{U_{\min }\left(t\right)-U_{boost}}{2}=-A\left(t\right),& t\∈\left(\right(k+\frac{1}{2})T,(k+1\left)T\right)\end{array}\right.---\left(1\right)$

In formula, f (t) is the equivalent AC square wave input of LC resonance circuit, and its amplitude is designated as A (t), is the function of time；T is MOSFET Switch periods, can be expressed asU_maxT () is largest battery monomer voltage, be the function of time；U_min(t) For minimum battery cell voltage, it is the function of time, in a cycle T, can see and be become a constant；U_boostFor BOOST The output voltage of boosting inverter, is a constant, meets relation U_boost＞ U_max(t)；[] is Gaussian function.

In described step S2, the Fourier transformation of equivalent AC square wave input f (t) is expressed as:

$f\left(t\right)=a_0+\underset{m=1}{\overset{\mathrm{\∞}}{\Σ}}{a}_{m}cos\left(\frac{2\mathrm{\π}mt}{T}\right)+\underset{m=1}{\overset{\mathrm{\∞}}{\Σ}}{b}_{m}sin\left(\frac{2\mathrm{\π}mt}{T}\right)---\left(2\right)$

In formula, a₀, a_m, b_mObtained by with following formula:

$a_0=\frac{1}{T}{\∫}_0^{T}f\left(t\right)dt---\left(3\right)$

$a_m=\frac{2}{T}{\∫}_0^{T}f\left(t\right)cos\frac{2\mathrm{\π}mt}{T}dt,m=1,2,3,\mathrm{...}---\left(4\right)$

$b_m=\frac{2}{T}{\∫}_0^{T}f\left(t\right)sin\frac{2\mathrm{\π}mt}{T}dt,m=0,1,2,\mathrm{...}---\left(5\right)$

Owing to switch periods T of MOSFET is the least, by A (t),Constant, i.e. etc. In A (kT), therefore Fourier coefficient a₀、a_m、b_mValue be calculated as:

a_m=0, m=0,1,2 ... (6)

$b_m=(1^m-{\left(-1\right)}^m)\frac{2A\left(kT\right)}{m\mathrm{\π}},m=0,1,\mathrm{2...}---\left(7\right).$

In sum, the expression formula of equivalent AC square wave input f (t) is:

$f\left(t\right)\≈\frac{4A\left(kT\right)}{\mathrm{\π}}\left(sin\right({\mathrm{\ω}}_{0}t)+\frac{sin\left(3{\mathrm{\ω}}_{0}t\right)}{3}+\frac{sin\left(5{\mathrm{\ω}}_{0}t\right)}{5}+\mathrm{...})---\left(8\right).$

In described step S2, the input AC impedance of series resonant circuit is expressed as:

Z=R+j (ω L-1/ ω C) (9).

In described step S2, the current amplitude I of m subharmonic_mIt is expressed as:

$I_m=\frac{4A\left(kT\right)}{m\mathrm{\π}R\sqrt{1+Q^2{(m-\frac{1}{m})}^2}}---\left(10\right)$

In formula, m is overtone order, and expression formula isω₀For the characteristic angular frequency of LC conversion, it is expressed as Q is the quality factor of resonance circuit, and expression formula isAs m=1, m ∈ N, I_mObtain maximum, represent ForIt will thus be seen that I₁Direct ratio and A (kT), inverse ratio and R, unrelated with L, C.

In described step S2, contrast I₁And I_m(m ≠ 1), if Q is sufficiently large, along with the increase of overtone order m, resonance current Harmonic component in i is far below fundametal compoment, therefore, the resonance current i of LC resonance circuit can be considered as sine wave, obtains expression formula:

$i\≈\left(\frac{1}{R}\right)\frac{4A\left(kT\right)}{\mathrm{\π}}{\mathrm{sin\ω}}_{0}t---\left(11\right)$

According to (11), in switch periods T, transfer to, from the battery cell that voltage is the highest, the battery cell that voltage is minimum Electricity be expressed as:

${\mathrm{\Δq}}_T\≈{\∫}_0^{\frac{T}{2}}\frac{4A\left(t\right)}{\mathrm{\π}R}{\mathrm{sin\ω}}_{0}tdt\≈\frac{8A\left(kT\right)\sqrt{LC}}{\mathrm{\π}R}---\left(12\right)$

By above formula divided by T, obtain electric quantity transfered in the unit interval, be expressed as:

$\frac{\mathrm{\Δ}q}{\mathrm{\Δ}t}=\frac{{\mathrm{\Δq}}_T}{T}=\frac{4A\left(kT\right)}{{\mathrm{\π}}^{2}R}=\frac{I_1}{\mathrm{\π}}---\left(13\right)$

In formula, Δ q is electric quantity transfered in unit time Δ t.It will thus be seen that amplitude I of resonance current₁Determine balancing speed, and Balancing speed is unrelated with L, C.

In described step S3, in balancing procedure, cell voltage is expressed as with the piecewise linear relationship of SOC:

$\mathrm{\Δ}U=\mathrm{\λ}\mathrm{\Δ}SOC=\mathrm{\λ}\frac{\mathrm{\Δ}q}{C_q}=\frac{4\mathrm{\λ}A\left(kT\right)}{{\mathrm{\π}}^2{C}_{q}R}\mathrm{\Δ}t---\left(14\right)$

In formula, Δ U is the variable quantity of the cell voltage in unit time Δ t, and corresponding SOC variable quantity is Δ SOC；λ is linear at one The proportionality coefficient of voltage and SOC in section, and due in balancing procedure SOC change less, λ is considered a constant；

C_qRepresent the quantity of electric charge being stored in battery, it is possible to be converted into the battery capacity in units of Ah, be expressed as:

C_q=3600 C_Ah·f₁(Cycle)·f₂(Temp) (15) In formula, C_AhFor the battery standard capacity in units of Ah, f₁And f (Cycle)₂(Temp) the most relevant with cycle-index and temperature Coefficient, its value is 1.

Described step S3 method particularly includes: cell voltage variation delta U in unit interval Δ t and the change of ac square wave amplitude The relation of amount Δ A (t) can be expressed as:

$\mathrm{\Δ}U=2A\left(t\right)-2A(t+\mathrm{\Δ}t)=-2\mathrm{\Δ}A\left(t\right)=\frac{4\mathrm{\λ}A\left(t\right)}{{\mathrm{\π}}^2{C}_{q}R}\mathrm{\Δ}t---\left(16\right)$

In formula, Δ A (t) is ac square wave amplitude A (t) variable quantity within the unit interval.

Described step 4 method particularly includes: solve (16) formula, A (t) is expressed as with the relation of time for balance t:

$A\left(t\right)=A\left(0\right)e^{-\frac{2\mathrm{\λ}}{{\mathrm{\π}}^2{C}_{q}R}t}---\left(17\right)$

In formula, the initial magnitude of ac square wave when A (0) is equilibrium beginning.

(17) formula of solution, is equalized the final expression formula of time t:

$t=\frac{{\mathrm{\π}}^2{C}_{q}R}{2\mathrm{\λ}}ln\frac{A\left(0\right)}{A\left(t\right)}=\frac{{\mathrm{\π}}^2{C}_{q}R}{2\mathrm{\λ}}ln\frac{U_{boost}-U_{min}\left(0\right)}{U_{boost}-U_{\min }\left(t\right)}---\left(18\right)$

In formula, U_min(0) initial value of minimum cell voltage when starting for equilibrium.By (18) it can be seen that time for balance t is proportional to R And C_q, it is inversely proportional to U_boostAnd λ, and unrelated with L, C.Equivalent resistance R is the biggest, and time for balance t is the longest.

The present invention is applicable to the power battery equalization circuit based on boosting inverter and Sofe Switch, and described circuit include microcontroller, Switch module, BOOST boosting inverter module and LC resonance circuit, microcontroller connecting valve module, LC resonance circuit and BOOST boosting inverter module, BOOST boosting inverter module connects LC resonance circuit, and LC resonance circuit is by equilibrium bus even Connect switch module；Wherein, microcontroller includes analog-to-digital conversion module, drive circuit and general purpose I/O end；Analog-to-digital conversion module connects Battery cell, BOOST boosting inverter module, the pulse width modulation (PWM) signal output part of drive circuit connects BOOST liter Pressure conversion module；General purpose I/O end is connected with switch module.

Described equilibrium bus includes equalizing bus I and equilibrium bus II, and switch module includes switch module I and switch module II, equilibrium Bus I connects BOOST boosting inverter module and switch module I；Equilibrium bus II connecting valve module ii and LC resonance circuit.

The invention have the benefit that

1. can the time for balance of Accurate Prediction equalizing circuit based on LC quasi-resonance Zero Current Switch, and determine and affect battery The key factor of balancing speed, for improving balancing speed and the efficiency of equalizing circuit, reduces energy dissipation and provides by force Strong theory support.

Apply to Fourier conversion first, in the time for balance prediction of battery equalizing circuit, solve traditional method and be difficult to ask The problem that the complicated high-order of solution is micro-, integral equation even derives a wrong conclusion, provides one for analyzing equalizing circuit performance Plant effective approach.

Accompanying drawing explanation

Fig. 1 is power battery equalization circuit structural representation based on boosting inverter and Sofe Switch；

Fig. 2 is the LC resonance circuit charging fundamental diagram of the present invention；

Fig. 3 is the LC resonance circuit electric discharge fundamental diagram of the present invention；

Fig. 4 is charging and discharging currents oscillogram based on boosting inverter and the power battery equalization circuit of Sofe Switch；

Fig. 5 is the series resonance schematic equivalent circuit with ac square wave input；

Fig. 6 is quality factor q when being respectively 1,3,5, the current amplitude schematic diagram of m subharmonic；

Fig. 7 is the relation schematic diagram of open-circuit voltage OCV Yu SOC；

Fig. 8 is that balancing procedure analyzes schematic diagram；

Fig. 9 is under different L, C, the simulation waveform figure of resonance current i and capacitance voltage Uc；

Figure 10 is under different R, the simulation waveform figure of resonance current i and capacitance voltage Uc；

Figure 11 is under different R, L and C, the balancing procedure figure of 8 batteries monomer voltages；

(a)U_boost=7.5V, R=0.01 Ω, C=10 μ F, L=10 μ H；

(b)U_boost=15V, R=0.01 Ω, C=10 μ F, L=10 μ H；

(c)U_boost=15V, R=0.1 Ω, C=10 μ F, L=10 μ H；

(d)U_boost=7.5V, R=0.01 Ω, C=20 μ F, L=5 μ H；

Figure 12 is under different C, L and R, resonance current i and capacitance voltage U_cExperimental waveform figure；

(a)U_boost=7.5V, R_extra=0 Ω, C=10.9 μ F, L=9.5 μ H；

(b)U_boost=7.5V, R_extra=0 Ω, C=51.2 μ F, L=50.3 μ H；

(c)U_boost=7.5V, R_extra=0 Ω, C=93.6 μ F, L=200.8 μ H；

(d)U_boost=7.5V, R_extra=1.08 Ω, C=10.9 μ F, L=9.5 μ H；

(e)U_boost=7.5V, R_extra=2.09 Ω, C=10.9 μ F, L=9.5 μ H；

Wherein, 1, switch module I；2, equilibrium bus II；3, battery cell；4, equilibrium bus I；5, microcontroller；6、 BOOST boosting inverter module；7, LC resonance circuit；8, drive circuit；9, multi-channel gating switch；10, voltage detecting electricity Road；11, switch module II；R_extraFor outer meeting resistance.

Detailed description of the invention:

The invention will be further described with embodiment below in conjunction with the accompanying drawings.

1. based on boosting inverter and the operation principle of the power battery equalization circuit of Sofe Switch

As it is shown in figure 1, microcontroller is numbered according to the battery cell that high monomer voltage is corresponding with minimum monomer voltage, Jing Guotong With IO end encoded control switch module, battery cell the highest and minimum for the voltage of optional position in set of cells is gated to equalizing mother On line；Then, battery cell the highest for voltage is boosted to a higher electricity by microprocessor controls BOOST boosting inverter module Pressure；Microcontroller sends the complementary pwm signal of a pair state and controls LC resonance circuit simultaneously so that it is alternation in charging and Discharge two states, as shown in Figure 4.Especially, the PWM frequency sent when microcontroller is equal to the intrinsic of LC resonance circuit During resonant frequency, it is possible to achieve Zero Current Switch equalizes, and equilibrium be both for that voltage difference in set of cells is maximum two every time Battery cell carries out peak load shifting.

It is assumed hereinafter that B₁For the battery cell 3, B that voltage is the highest₄For as a example by the battery cell 3 that voltage is minimum, operation principle is entered one Step explanation.

First, microcontroller 5, by analog-to-digital conversion module, obtains each monomer voltage of electrokinetic cell, so that it is determined that high monomer electricity The battery cell 3 of pressure and minimum monomer voltage and correspondence is numbered, and judges whether maximum voltage difference is more than battery balanced threshold value, If more than, start equalizing circuit, and gating switch module I 1 (S '₂、Q’₂) and (S of switch module II 11₅、Q₅) and Keep its conducting state until this equilibrium terminates, respectively by battery cell B the highest for voltage₁The battery cell minimum with voltage B₄Gating is to equilibrium bus I 4 and equalizes on bus II 2.

Under equilibrium state, microcontroller 5 uses PID controller control, and BOOST boosting inverter module 6 is the highest by voltage Battery cell B₁Boost to about 7.5V.

Meanwhile, control LC resonance circuit 7 and make its alternation in two states of charging and discharging, thus realize the not stealpass of energy Pass.

As in figure 2 it is shown, work as M₁And M₂During conducting, M₃And M₄Turn off, LC resonance circuit 7 and BOOST boosting inverter mould Block 6 is in parallel.C_b, inductance L become a resonant tank with electric capacity C-shaped, now charge, resonance current i is just, electric capacity C two The voltage V of end_cBegin to ramp up until resonance current i becomes negative value, as seen from Figure 4, V_cDelayed resonance current i tetra-/ One cycle, and waveform is sine wave.This moment, due to M₃And M₄It is off state, battery cell B₄Open circuit, institute To flow into B₄Electric current i_B4It is zero；Again because microcontroller 5 controls BOOST boosting inverter module 6 output voltage stabilization and exists About 7.5V, so the resonance current i flowing into LC is outflow battery cell B₁Electric current, and rated current flow out battery Just it is during monomer, therefore available B shown in state I as shown in Figure 4₁And B₄Current waveform.

As it is shown on figure 3, work as M₃And M₄During conducting, M₁And M₂Turning off, LC resonance circuit 7 passes through switch module I 1, opens Close the battery cell B that module ii 11 is minimum with voltage₄In parallel.B₄, L become a resonant tank with C-shaped, now discharge, humorous The electric current i that shakes is negative, the voltage V at electric capacity C two ends_cBegin to decline until resonance current become on the occasion of.Because BOOST boosting inverter Module 6 is in open-circuit condition, thus flows out battery cell B₁Electric current i_B1It is zero；This moment resonance current i is exactly B simultaneously₄ Charging current, therefore available B as shown in Fig. 4 state II₁And B₄Current waveform.

2. time for balance based on Fourier transformation prediction

According to the operation principle of the present invention, the voltage of BOOST boosting inverter is modulated into a constant voltage, and battery cell voltage Also being able to be seen as a constant an extremely short time, therefore, the equalizing circuit of Fig. 1 equivalence can become tool as shown in Figure 5 There is the series resonance equivalent circuit that ac square wave inputs.

It is below the primary symbols explanation of the present invention:

The switch periods of T:MOSFET, is expressed as:

$T=2\mathrm{\π}\sqrt{LC}---\left(1\right)$

ω₀: the characteristic angular frequency of LC conversion, it is expressed as:

${\mathrm{\ω}}_0=\frac{2\mathrm{\π}}{T}=\frac{1}{\sqrt{LC}}---\left(2\right)$

M: overtone order, is expressed as:

$m=\frac{\mathrm{\ω}}{{\mathrm{\ω}}_0}---\left(3\right)$

U_max(t): largest battery monomer voltage；

U_minT (): minimum battery cell voltage, in a cycle T, it is possible to regard a constant as；

U_boost: the output voltage of BOOST boosting inverter, generally one constant, meet following relation:

U_boost＞ U_max(t) (4)

The equivalent AC square wave input of f (t): LC resonance circuit, its amplitude is designated as A (t), is the function of time, and meet with Lower relation:

$f\left(t\right)=\left\{\begin{array}{cc}\frac{U_{boost}-U_{min}\left(t\right)}{2}=A\left(t\right),& t\∈(kT,(k+\frac{1}{2}\left)T\right)\\ \frac{U_{\min }\left(t\right)-U_{boost}}{2}=-A\left(t\right),& t\∈\left(\right(k+\frac{1}{2})T,(k+1\left)T\right)\end{array}\right.---\left(5\right)$

In formula,[] is Gaussian function.

The Fourier transformation of ac square wave f (t) is expressed as:

$f\left(t\right)=a_0+\underset{m=1}{\overset{\mathrm{\∞}}{\Σ}}{a}_{m}cos\left(\frac{2\mathrm{\π}mt}{T}\right)+\underset{m=1}{\overset{\mathrm{\∞}}{\Σ}}{b}_{m}sin\left(\frac{2\mathrm{\π}mt}{T}\right)---\left(6\right)$

In formula, a₀, a_m, b_mCan be obtained by with following formula:

$a_0=\frac{1}{T}{\∫}_0^{T}f\left(t\right)dt---\left(7\right)$

$a_m=\frac{2}{T}{\∫}_0^{T}f\left(t\right)cos\frac{2\mathrm{\π}mt}{T}dt,m=1,2,3,\mathrm{...}---\left(8\right)$

$b_m=\frac{2}{T}{\∫}_0^{T}f\left(t\right)sin\frac{2\mathrm{\π}mt}{T}dt,m=0,1,2,\mathrm{...}---\left(9\right)$

Owing to switch periods T of MOSFET is the least, can by A (t),It is approximately permanent Value A (kT) is so that calculating, therefore Fourier coefficient a₀、a_m、b_mValue can be calculated as:

a_m=0, m=0,1,2 ... (10)

$b_m=(1^m-{\left(-1\right)}^m)\frac{2A\left(kT\right)}{m\mathrm{\π}},m=0,1,\mathrm{2...}---\left(11\right)$

After all coefficients obtaining (6), (6) can be rewritten as:

$f\left(t\right)\≈\frac{4A\left(kT\right)}{\mathrm{\π}}\left(sin\right({\mathrm{\ω}}_{0}t)+\frac{sin\left(3{\mathrm{\ω}}_{0}t\right)}{3}+\frac{sin\left(5{\mathrm{\ω}}_{0}t\right)}{5}+\mathrm{...})---\left(12\right)$

As it is shown in figure 5, the input AC impedance of series resonant circuit can be expressed as:

Z=R+j (ω L-1/ ω C) (13)

By (12) divided by (13), the current amplitude I of available m subharmonic_m:

$I_m=\frac{4A\left(kT\right)}{m\mathrm{\π}R\sqrt{1+Q^2{(m-\frac{1}{m})}^2}}---\left(14\right)$

In formula, Q is the quality factor of resonance circuit, has a following relation:

$Q=\frac{{\mathrm{\ω}}_{0}L}{R}=\frac{1}{{\mathrm{\ω}}_{0}CR}---\left(15\right)$

For (14), as m=1, m ∈ N, I_mObtain maximum, be represented by:

$\underset{m=1,2,\mathrm{3...}}{max}\left\{I_m\right\}=I_1=\frac{4A\left(kT\right)}{\mathrm{\π}R}---\left(16\right)$

By (16) it can be seen that I₁Direct ratio and A (kT), inverse ratio and R, unrelated with L, C.

Under reasonably assuming: R=0.3 Ω, A (kT)=0.1V, when quality factor q is respectively 1,3,5, by m subharmonic Current amplitude I_mIt is drawn in Fig. 6.Contrast I₁And I_m(m ≠ 1), if Q is sufficiently large, along with the increase of overtone order m, resonance electricity Harmonic component in stream i is far below fundametal compoment, and therefore, the resonance current i of LC resonance circuit is in close proximity to sine wave, can approximate It is expressed as:

$i\≈\left(\frac{1}{R}\right)\frac{4A\left(kT\right)}{\mathrm{\π}}{\mathrm{sin\ω}}_{0}t---\left(17\right)$

According to (17), in switch periods T, transfer to, from the battery cell that voltage is the highest, the battery cell that voltage is minimum Electricity can approximate and be expressed as:

${\mathrm{\Δq}}_T\≈{\∫}_0^{\frac{T}{2}}\frac{4A\left(t\right)}{\mathrm{\π}R}{\mathrm{sin\ω}}_{0}tdt\≈\frac{8A\left(kT\right)\sqrt{LC}}{\mathrm{\π}R}---\left(18\right)$

By (18) divided by T, electric quantity transfered in the available unit interval, it is expressed as:

$\frac{\mathrm{\Δ}q}{\mathrm{\Δ}t}=\frac{{\mathrm{\Δq}}_T}{T}=\frac{4A\left(kT\right)}{{\mathrm{\π}}^{2}R}=\frac{I_1}{\mathrm{\π}}---\left(19\right)$

In formula, Δ q is electric quantity transfered in unit time Δ t.(19) show that the amplitude of resonance current determines balancing speed, and equilibrium Speed is unrelated with L, C.

As it is shown in fig. 7, cell voltage becomes piecewise linear relationship with SOC, can be expressed as:

$\mathrm{\Δ}U=\mathrm{\λ}\mathrm{\Δ}SOC=\mathrm{\λ}\frac{\mathrm{\Δ}q}{C_q}=\frac{4\mathrm{\λ}A\left(kT\right)}{{\mathrm{\π}}^2{C}_{q}R}\mathrm{\Δ}t---\left(20\right)$

In formula, Δ U is the variable quantity of the cell voltage in unit time Δ t, and corresponding SOC variable quantity is Δ SOC.λ is linear at one The proportionality coefficient of voltage and SOC in section, and due in balancing procedure SOC change less, λ can be considered a constant.C_q Represent the quantity of electric charge being stored in battery, it is possible to be converted into the battery capacity in units of Ah, can be expressed as:

C_q=3600 C_Ah·f₁(Cycle)·f₂(Temp) (21)

In formula, C_AhFor the battery standard capacity in units of Ah.f₁And f (Cycle)₂(Temp) the most relevant with cycle-index and temperature Coefficient.In general, the cycle-index of battery keeps constant in balancing procedure, and battery is usually operated in an experiment Under temperature constant state.Therefore, f₁And f (Cycle)₂(Temp) being generally independent of cycle-index and the constant of temperature, its value is 1.

As shown in Figure 8, by the analysis to balancing procedure, cell voltage variation delta U in unit interval Δ t and ac square wave The relation of variation delta A (t) of amplitude can be expressed as:

$\mathrm{\Δ}U=2A\left(t\right)-2A(t+\mathrm{\Δ}t)=-2\mathrm{\Δ}A\left(t\right)=\frac{4\mathrm{\λ}A\left(t\right)}{{\mathrm{\π}}^2{C}_{q}R}\mathrm{\Δ}t---\left(22\right)$

In formula, Δ A (t) is ac square wave amplitude A (t) variable quantity within the unit interval.

Solving (22), the relation of A (t) and time for balance t can be expressed as:

$A\left(t\right)=A\left(0\right)e^{-\frac{2\mathrm{\λ}}{{\mathrm{\π}}^2{C}_{q}R}t}---\left(23\right)$

In formula, the initial magnitude of ac square wave when A (0) is equilibrium beginning.

Solve (23), be equalized the final expression formula of time t:

$t=\frac{{\mathrm{\π}}^2{C}_{q}R}{2\mathrm{\λ}}ln\frac{A\left(0\right)}{A\left(t\right)}=\frac{{\mathrm{\π}}^2{C}_{q}R}{2\mathrm{\λ}}ln\frac{U_{boost}-U_{min}\left(0\right)}{U_{boost}-U_{\min }\left(t\right)}---\left(24\right)$

In formula, U_min(0) initial value of minimum cell voltage when starting for equilibrium.

By (24) it can be seen that time for balance t is proportional to R and C_q, it is inversely proportional to U_boostAnd λ, and unrelated with L, C.Equivalence Resistance R is the biggest, and time for balance t is the longest.Therefore, it should select have low conducting internal resistance electronic devices and components (MOSFET, two Pole pipe, inductance and electric capacity etc.).

Fig. 9 and Figure 10 points out at U_boost=3.6V, U_minDuring=3.4V, the impact that resonance current amplitude is produced by different L, C, R. The major parameter of Fig. 9 is respectively set to L=5 μ H, C=5 μ F, R=0.3 Ω and L=5 μ H, C=10 μ F, R=0.3 Ω and L=10 μ H, C=10 μ F, R=0.3 Ω.The major parameter of Figure 10 is respectively set to L=5 μ H, C=10 μ F, R=0.2 Ω and L=5 μ H, C=10 μ F, R=0.3 Ω and L=5 μ H, C=10 μ F, R=0.4 Ω.Switch periods T of equalizing circuit is determined by formula (1), PWM duty cycle It is set to 0.5.

From Fig. 9 and Figure 10 it can be seen that resonance current i is sinusoidal wave form, its corresponding capacitance voltage V_cIt it is an advanced resonance electricity Flow a sinusoidal wave form of i, and its peak value occurs exactly at electric current i zero crossing.MOSFET turns on and off generation at electric current Zero crossing, the least switching loss.

Fig. 9 points out when changing the value of L, C, amplitude I of resonance current keeps constant, it was demonstrated that formula (16): I₁Size with L, C are unrelated.

Figure 10 point out when change equivalent internal resistance R from 0.2 Ω to 0.3 Ω again to 0.4 Ω time, resonance current amplitude I become more and more less, this Also consistent with formula (16): resonance current amplitude I inverse ratio and equivalent internal resistance R.

Figure 11 shows under different R, L and C, the balancing procedure of 8 batteries monomer voltages.8 batteries monomers initial Voltage is respectively set to 3.63V, 3.60V, 3.61V, 3.59V, 3.62V, 3.58V, 3.64V and 3.57V.Figure 11 (a) (b) show that time for balance is with U_boostChange big and reduce.Figure 11 (b) and (c) show that equivalent internal resistance R is the biggest, equilibrium Time is the longest.Figure 11 (a) and (d) show at R and U_boostKeep constant in the case of, the change of L, C is to time for balance Without impact.

Figure 12 is under different C, L and R, resonance current i and capacitance voltage V_cExperimental waveform figure.From Figure 12 (a)～(c) Can be seen that resonance current amplitude I is substantially if neglecting the impact of the different equivalent internal resistance R due to different L, C introductions Equal.From Figure 12 (a), (d), (e) is it can be seen that external series resistance R_extra1.08 Ω are changed to again to 2.09 Ω from 0, Resonance circuit amplitude I is reduced to 0.64A again to 0.48A from 0.86A, and this also demonstrates resonance current amplitude and is inversely proportional to internal resistance.

Although the detailed description of the invention of the present invention is described by the above-mentioned accompanying drawing that combines, but not limit to scope System, one of ordinary skill in the art should be understood that on the basis of technical scheme, and those skilled in the art need not pay Go out various amendments or deformation that creative work can make still within protection scope of the present invention.

Claims (10)

1. battery balanced time forecasting methods based on Fourier transformation, the structure of equalizing circuit be microcontroller according to The battery cell numbering that high monomer voltage is corresponding with minimum monomer voltage, through general purpose I/O end encoded control switch module, will The battery cell gating that in set of cells, the voltage of optional position is the highest and minimum is to equalizing on bus；Then, microprocessor controls Battery cell the highest for voltage is boosted to a higher voltage by BOOST boosting inverter module；Microcontroller sends a pair simultaneously The pwm signal control LC series resonant circuit that state is complementary so that it is alternation is gone here and there at two states of charging and discharging, LC Connection resonance circuit includes that the inductance L of series connection and electric capacity C, the inductance L and electric capacity C of series connection are connected to switch mosfet and constitute Bridge circuit midpoint on；

It is characterized in that: comprise the following steps:

S1. the boosting inverter output voltage of equalizing circuit is modulated into a higher constant voltage, is equalized in a short period of time The voltage of the battery cell that voltage is minimum can see a constant as, and therefore equalizing circuit can be equivalent to have ac square wave input LC series resonant circuit；

S2. Fourier transformation model and the AC impedance model of the equivalent AC square wave input of series resonance equivalent circuit are set up, will The resonance current of LC series resonant circuit is considered as sine wave, is equalized the expression formula of electric current, calculate in a switch periods from The battery cell that voltage is the highest transfers to the electricity of the minimum battery cell of voltage, and then obtains electric quantity transfered in the unit interval；

S3. cell voltage and the piecewise linear model of SOC in balancing procedure are set up, by cell voltage and SOC in a linearity range Proportionality coefficient be considered as constant, the quantity of electric charge being stored in battery is converted into battery capacity, statement battery cell minimum voltage exists The relation between variable quantity and the variable quantity of ac square wave amplitude in unit interval；

S4. derive the final expression formula of time for balance, obtain affecting the factor of balancing speed.

A kind of battery balanced time forecasting methods based on Fourier transformation, is characterized in that: described The concrete structure of LC series resonant circuit in step S1, including equivalent AC square wave input f (t), equivalent AC square wave input Positive pole takes back the negative pole of equivalent AC square wave input, wherein, inductance, electric capacity, resistance after being sequentially connected with inductance, electric capacity, resistance Capability value be respectively L, C, R.

A kind of battery balanced time forecasting methods based on Fourier transformation, is characterized in that: described In step S2, the model of equivalent AC square wave input f (t) is:

$f\left(t\right)=\left\{\begin{array}{cc}\frac{U_{boost}-U_{min}\left(t\right)}{2}=A\left(t\right),& t\∈(kT,(k+\frac{1}{2})T)\\ \frac{U_{\min }\left(t\right)-U_{boost}}{2}=-A\left(t\right),& t\∈\left(\right(k+\frac{1}{2})T,(k+1)T)\end{array}\right.---\left(1\right)$

In formula, f (t) is the equivalent AC square wave input of LC series resonant circuit, and its amplitude is designated as A (t), is the function of time；T is The switch periods of MOSFET, is expressed asU_minT () is minimum battery cell voltage, be the function of time, In a cycle T, it is seen as a constant；U_boostFor the output voltage of BOOST boosting inverter, it is a constant, meets Relation U_boost＞ U_max(t)；[] is Gaussian function.

A kind of battery balanced time forecasting methods based on Fourier transformation, is characterized in that: described In step S2, the Fourier transformation of equivalent AC square wave input f (t) is expressed as:

$f\left(t\right)=a_0+\underset{m=1}{\overset{\mathrm{\∞}}{\Σ}}{a}_{m}cos\left(\frac{2\mathrm{\π}mt}{T}\right)+\underset{m=1}{\overset{\mathrm{\∞}}{\Σ}}{b}_{m}sin\left(\frac{2\mathrm{\π}mt}{T}\right)---\left(2\right)$

In formula, a₀, a_m, b_mObtained by with following formula:

$a_0=\frac{1}{T}{\∫}_0^{T}f\left(t\right)dt---\left(3\right)$

$a_m=\frac{2}{T}{\∫}_0^{T}f\left(t\right)cos\frac{2\mathrm{\π}mt}{T}dt,m=1,2,3,...---\left(4\right)$

$b_m={\∫}_0^{T}f\left(t\right)sin\frac{2\mathrm{\π}mt}{T}dt,m=1,2,...---\left(5\right)$

Owing to switch periods T of MOSFET is the least, by A (t),Constant, i.e. etc. In A (kT), therefore Fourier coefficient a₀、a_m、b_mValue be calculated as:

a_m=0, m=1,2,3 ... (6)

$b_m=(1^m-{\left(-1\right)}^m)\frac{2A\left(kT\right)}{m\mathrm{\π},}m=1,2,...---\left(7\right)$

In sum, the Fourier transformation of equivalent AC square wave input f (t) is expressed as:

$f\left(t\right)\≈\frac{4A\left(kT\right)}{\mathrm{\π}}\left(sin\right({\mathrm{\ω}}_{0}t)+\frac{sin\left(3{\mathrm{\ω}}_{0}t\right)}{3}+\frac{sin\left(5{\mathrm{\ω}}_{0}t\right)}{5}+...)---\left(8\right).$

A kind of battery balanced time forecasting methods based on Fourier transformation, is characterized in that: described In step S2, the input AC impedance of LC series resonant circuit is expressed as:

Z=R+j (ω L-1/ ω C) (9).

A kind of battery balanced time forecasting methods based on Fourier transformation, is characterized in that: described In step S2, the current amplitude I of m subharmonic_mIt is expressed as:

$I_m=\frac{4A\left(kT\right)}{m\mathrm{\π}R\sqrt{1+Q^2{(m-\frac{1}{m})}^2}}---\left(10\right)$

In formula, m is overtone order, and expression formula is:ω₀For the characteristic angular frequency of LC series resonant circuit, it is expressed as:Q is the quality factor of humorous LC series resonant circuit, and expression formula is:As m=1, M ∈ N, I_mObtain maximum, be expressed as:It will thus be seen that I₁Direct ratio and A (kT), inverse ratio With R, unrelated with L, C.

A kind of battery balanced time forecasting methods based on Fourier transformation, is characterized in that: described In step S2, contrast I₁And I_m, wherein, m ≠ 1, if Q is sufficiently large, along with the increase of overtone order m, in resonance current i Harmonic component is far below fundametal compoment, therefore, the resonance current i of LC series resonant circuit is considered as sine wave, obtains expression formula:

$i\≈\left(\frac{1}{R}\right)\frac{4A\left(kT\right)}{\mathrm{\π}}{\mathrm{sin\ω}}_{0}t---\left(11\right)$

According to (11) formula, in switch periods T, transfer to, from the battery cell that voltage is the highest, the battery list that voltage is minimum The electricity of body is expressed as:

${\mathrm{\Δq}}_T\≈{\∫}_0^{\frac{T}{2}}\frac{4A\left(t\right)}{\mathrm{\π}R}{\mathrm{sin\ω}}_{0}tdt\≈\frac{8A\left(kT\right)\sqrt{LC}}{\mathrm{\π}R}---\left(12\right)$

By above formula divided by T, obtain electric quantity transfered in the unit interval, be expressed as:

$\frac{\mathrm{\Δ}q}{\mathrm{\Δ}t}=\frac{{\mathrm{\Δq}}_T}{T}=\frac{4A\left(kT\right)}{{\mathrm{\π}}^{2}R}=\frac{I_1}{\mathrm{\π}}---\left(13\right)$

In formula, Δ q is electric quantity transfered in unit time Δ t, it will thus be seen that amplitude I of resonance current₁Determine balancing speed, and Balancing speed is unrelated with L, C.

A kind of battery balanced time forecasting methods based on Fourier transformation, is characterized in that: described In step S3, in balancing procedure, the piecewise linear relationship of cell voltage U with SOC is expressed as:

$\mathrm{\Δ}U=\mathrm{\λ}\mathrm{\Δ}SOC=\mathrm{\λ}\frac{\mathrm{\Δ}q}{C_q}=\frac{4\mathrm{\λ}A\left(kT\right)}{{\mathrm{\π}}^2{C}_{q}R}\mathrm{\Δ}t---\left(14\right)$

In formula, Δ U is the variable quantity of the cell voltage in unit time Δ t, and corresponding SOC variable quantity is Δ SOC；λ is at a line Property section in the proportionality coefficient of voltage and SOC, and due in balancing procedure SOC change less, λ is considered a constant； C_qRepresent the quantity of electric charge being stored in battery, it is possible to be converted into the battery capacity in units of Ah, be expressed as:

C_q=3600 C_Ah·f₁(Cycle)·f₂(Temp) (15)

In formula, C_AhFor the battery standard capacity in units of Ah, f₁And f (Cycle)₂(Temp) the most relevant with cycle-index and temperature Coefficient, its value is 1.

A kind of battery balanced time forecasting methods based on Fourier transformation, is characterized in that: described Step S3 method particularly includes: cell voltage variation delta U in unit interval Δ t and variation delta A (t) of ac square wave amplitude Relation be expressed as:

$\mathrm{\Δ}U=2A\left(t\right)-2A(t+\mathrm{\Δ}t)=-2\mathrm{\Δ}A\left(t\right)=\frac{4\mathrm{\λ}A\left(t\right)}{{\mathrm{\π}}^2{C}_{q}R}\mathrm{\Δ}t---\left(16\right)$

In formula, Δ A (t) is ac square wave amplitude A (t) variable quantity within the unit interval.

A kind of battery balanced time forecasting methods based on Fourier transformation, is characterized in that: institute Stating step S4 method particularly includes: solve (16) formula, A (t) is expressed as with the relation of time for balance t:

$A\left(t\right)=A\left(0\right)e^{-\frac{2\mathrm{\λ}}{{\mathrm{\π}}^2{C}_{q}R}t}---\left(17\right)$

In formula, the initial magnitude of ac square wave when A (0) is equilibrium beginning；

Solve (17) formula, be equalized the final expression formula of time t:

$t=\frac{{\mathrm{\π}}^2{C}_{q}R}{2\mathrm{\λ}}ln\frac{A\left(0\right)}{A\left(t\right)}=\frac{{\mathrm{\π}}^2{C}_{q}R}{2\mathrm{\λ}}ln\frac{U_{boost}-U_{min}\left(0\right)}{U_{boost}-U_{min}\left(t\right)}---\left(18\right)$

In formula, U_min(0) initial value of minimum cell voltage when starting for equilibrium.