CN107276171B - Battery pack balancing method based on sliding mode control - Google Patents

Abstract

The invention discloses a sliding mode control-based battery pack balancing method. Designing a special battery balancing topological structure according to the unbalanced condition of the series battery pack; establishing a mathematical model for the battery balancing topological structure, and establishing a battery balancing system mathematical model formed by the battery balancing topological structure and the series battery pack; and (4) balance control is carried out by combining a mathematical model of the battery balance system and using a sliding mode controller, so that balance processing among all the batteries in the series battery pack is realized. The method can quickly balance the battery, effectively save energy and prolong the service life of the battery.

Description

A battery pack equalization method based on sliding mode control

technical field

The invention relates to a battery algorithm, in particular to a battery pack equalization method based on sliding mode control.

Background technique

Energy saving and environmental protection have become the goals of China and the world today. Among them, the wide application of battery packs has become a kind of Peugeot of the times.

Battery imbalance is common in battery systems and is an important issue for battery system life. It is caused by two main categories, which are: internal power sources, which consist of manufacturing variances of physical volume, i.e. variances in internal impedance and self-discharge rate differences; and external power sources, such as thermal differences in packaging. The battery system of equalization technology is especially important in lithium batteries, because without it, the battery will be overcharged, undercharged, or even overdischarged.

Unbalanced battery packs can cause the following hazards: premature battery degradation due to overvoltage; safety hazards of overcharged batteries; capacity reduction due to premature charging cessation; premature termination of discharge.

Therefore, it is of great significance to carry out battery balancing for lithium battery packs in series: it can effectively maintain battery energy balance, prolong life, and improve discharge efficiency.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a lithium battery pack balancing method in view of the deficiencies of the prior art, and the present invention proposes and designs a battery balancing system model. The battery balancing system model includes a bidirectional cuk converter circuit as a balancing circuit, which can realize current transmission between two batteries in a series battery pack. At the same time, the lithium battery and the balancing circuit are modeled separately, and then the overall model of the system is obtained by combining the models, which can analyze and evaluate the stability and convergence of the entire battery balancing method. Finally, a sliding mode control algorithm based on SOC is proposed, which can effectively control the battery balancing process for discontinuous current mode.

The technical scheme of the present invention comprises the following steps:

1) Design a special battery balancing topology structure according to the unbalanced situation of the series battery pack, and the specific implementation is to form a battery balancing topology structure with a bidirectional cuk converter;

2) Establish a mathematical model of the battery balancing topology, and establish a battery balancing system mathematical model composed of the battery balancing topology and the battery pack in series;

3) Combined with the mathematical model of the battery balancing system, the sliding mode controller is used for balancing control to realize the balancing processing among the cells in the series battery pack.

The technical solution of the present invention mainly consists of a battery balancing system model and a control method. The battery balance system model is to design the balance circuit according to the characteristics of the series lithium battery, and model the balance circuit of the lithium battery and the whole formed by the lithium battery and the balance circuit, so as to provide a mathematical basis for the control algorithm. The control method is a sliding mode control based on SOC (state of charge), including limiting conditions and equilibrium targets, an improved sliding mode observer for SOC monitoring, and a battery equilibrium sliding mode controller limited by saturated equilibrium current.

The battery is a lithium battery.

In the described step 1), a bidirectional cuk converter circuit as an equalization circuit is connected between two adjacent batteries in the series-connected battery pack, and each equalization circuit is connected to a controller, which is controlled by the difference between the adjacent batteries. The balancing circuits and their respective controllers constitute the cell balancing topology. This structure can improve the balance efficiency and reduce the waste of energy.

The lithium battery in the lithium battery pack is generally in the form of a single battery pack in series, and the lithium battery pack is continuously charged or discharged externally. According to this situation, it is assumed that the lithium battery pack is composed of n single lithium batteries connected in series, and the present invention proposes to use a battery balancing system as shown in Figure 1.

The present invention uses a bidirectional cuk converter as a battery-to-battery balancing circuit, as shown in Figure 2, the method has the advantages of high speed, low energy consumption, easy operation and control, and relatively high efficiency. If the number of cells in the battery pack increases or decreases, it is only necessary to increase or decrease the same number of inverters, rather than adjusting the overall structure of the balancing system for the battery pack.

The invention connects two adjacent batteries in series with an equalizing circuit, the equalizing circuit realizes the energy transfer between the batteries, and a separate controller is connected to the equalizing circuit to control the equalizing circuit, thereby realizing a simple and rapid intelligent equalizing effect .

The bidirectional cuk converter between the i-th battery and the i+1-th battery (1≤i≤n-1) is used as the i-th bidirectional cuk converter, and the specific circuit structure is: including an inductance L _i1 , an inductance L _i2 , energy transfer capacitor C _i , MOSFET tube Q _i1 , MOSFET tube Q _i2 , body diode d _i1 and body diode d _i2 , MOSFET tube Q _i1 and body diode d _i1 are connected in parallel with the inductor L _i1 and are connected in series in section i At both ends of the battery, the MOSFET Q _i2 and the body diode d _i2 are connected in parallel with the inductor L _i2 and are connected in series at the two ends of the i+1th battery, and the two ends of the energy transfer capacitor C _i are connected in series between the inductor L _i1 and the inductor L _i2 . There are n-1 bidirectional cuk converters connected in the battery pack with n batteries in series, and the circuit uses PWM signal to drive and control the turn-on and turn-off of the two MOSFET tubes to control the connection between the two batteries. charge and discharge to achieve voltage balance between the two batteries. The duty cycle of the PWM signal is used as a control variable for battery balancing, which are respectively D _i1 and D _i2 , and the switching loss of the MOSFET can be reduced by selecting an appropriate duty cycle. For example, first, when the MOSFET tube Q _i1 is turned on and the MOSFET tube Q _i2 is turned off, the i-th battery is charged to the energy transfer capacitor C _i first; then, when the MOSFET tube Q _i2 is turned on and the MOSFET tube Q _i1 is turned off, the energy transfer capacitor C is made to charge. _iCharge the i+1th battery.

The battery balancing topology formed by the balancing circuit of the present invention has the following characteristics:

1. Using a two-way balancing circuit, energy can be transferred from one battery to any other battery to solve the problem of uneven energy distribution. For example, the initial battery is charged to the next battery connected in series through the balancing circuit, and the next battery connected in series is charged through the balancing circuit to charge the next battery connected in series, so that the initial battery is connected in series through the middle battery. The battery can be charged to any battery to complete the arbitrary transfer of energy.

2. By designing external circuit modules on the basis of series-connected batteries, it has little effect on the current of the series-connected battery pack itself. It can cope with the complex environment of hybrid power, and can also achieve balance when the battery is working.

3. The battery and the equalizing circuit can be regarded as a whole. The equalizing system uses n-1 bidirectional equalizing circuits for n series batteries, which has good scalability.

4. Relatively speaking, the modularization is obvious, and the equalization circuit can be abstracted for modeling analysis. The portability of the system is very good, which is convenient for application in different battery management occasions.

In the step 2), the battery balancing topology is modeled, and the battery balancing system mathematical model is constructed in combination with the model of the battery balancing topology, so that the stability and convergence of the entire battery balancing method can be analyzed and analyzed accordingly. Evaluate.

In the described step 2), the mathematical model of the battery balancing topology is specifically:

As shown in Fig. 1, the structure of the converter numbered i (1≤i≤n-1) is symmetrical, which can transfer energy bidirectionally between the i-th battery and the i+1-th battery. Therefore, ignoring the general loss, the energy is transferred from the i-th battery to the i+1-th battery, and according to the circuit of the i-th bidirectional cuk circuit, the dual circuit is driven by the PWM signal to control the on and off of the MOSFET. The duty cycle of the PWM signal is used as a control variable for battery balancing, and the calculation formula for obtaining the balancing current in the i-th bidirectional cuk converter is as follows:

和

分别是第i和第i+1节电池的端电压，

是电容平均电压，D_i1表示MOSFET管Q_i1上PWM信号的占空比控制量，D_i2表示MOSFET管Q_i2上PWM信号的占空比控制量；Among them, I _Li1 and I _Li2 represent the balanced current through the inductors L _i1 and L _i2 respectively, the magnitude of the current determines how much to charge, L _i1 represents the inductance connected to the i-th battery in the i-th bidirectional cuk converter, and L _i2 represents the inductance of the i-th bidirectional cuk converter connected to the i+1th battery, P _i represents the current transfer efficiency of the i-th bidirectional cuk converter when the i-th battery is charging to the i+1th battery, P i _i ′ represents the current transfer efficiency of the i+1th battery in the i-th bidirectional cuk converter when charging the i-th battery, T _s is the sampling time,

and

are the terminal voltages of the i-th and i+1-th cells, respectively,

is the average voltage of the capacitor, D _i1 represents the duty cycle control amount of the PWM signal on the MOSFET tube Q _i1 , and D _i2 represents the duty cycle control amount of the PWM signal on the MOSFET tube Q _i2 ;

The above formula is deformed to obtain the calculation formulas of the corresponding duty cycle control quantities D _i1 and D _i2 of the two MOSFET tubes as follows:

According to the above formula, under the premise of knowing the variables in the circuit, the equalizing current I _Li2 can be substituted into it to calculate and obtain the corresponding duty cycle control quantities D _i1 and D _i2 of the two MOSFET tubes. Quantities D _i1 and D _i2 control the two MOSFET tubes of the equalization circuit to realize the equalization of the battery.

In the described step 2), the mathematical model of the battery balancing system is specifically:

For n batteries, the first battery and the last battery are respectively connected to only one equalization circuit, and the others are connected to two equalization circuits.

The respective switching variables γ _i and γ′ _i are constructed for the duty cycle control quantities D _i1 and D _i2 of the two MOSFETs, which are expressed as:

D _i1 (k)D _i2 (k)=0

Since the two MOSFETs cannot be turned on at the same time, D _i1 (k)D _i2 (k)=0.

是第i(2≤i≤n-1)节电池k时刻的单体均衡电流，

为第1节电池k时刻的单体均衡电流，

为第n节电池k时刻的单体均衡电流；remember

is the cell equilibrium current at time k of the i-th (2≤i≤n-1) cell,

is the cell balancing current of the first cell at time k,

is the cell balancing current at time k of the nth battery;

The formula for calculating the equilibrium current of each cell is as follows:

Among them, k represents the sequence number of the sampling time, γ _i and γ′ _i (1≤i≤n) are the switching variables for the duty cycle control quantities D _i1 and D _i2 , respectively, and p _i indicates that the i-th battery is paired with the i+ The current transfer efficiency of a battery, f _i1 (D _i1 (k) and f _i2 (D _i2 (k)) (1≤i≤n) represent the relationship between the transmission current of the two MOSFETs and the duty cycle of the PWM signal, f _i1 (D _i1 (k)) represents the relationship between the duty ratio control amount D _i1 and the transmission current of the ith block equalizing circuit at time k, and f _i2 (D _i2 (k)) represents the duty ratio control amount at time k The relationship between D _i2 and the transmission current, the transmission current refers to the current transmitted by the i-th battery to the i+1-th battery; w _i1 (k) and w _i2 (k) (1≤i≤n-1) respectively Represents the model error of the single balancing current passing through the i-th bidirectional cuk converter;

简化为：Balance the current of the cell at time k of the i-th battery

Simplifies to:

In order to facilitate the balance of the lithium battery pack, the present invention sets the SOC of the lithium battery, and the mathematical model of the battery balance system of the battery pack with n cells connected in series is expressed as:

z(k+1)=z(k)+dB ₁ (k)(u ₁ (k)+w ₁ (k))+dB ₂ (k)(u ₂ (k)+w ₂ (k))- b(k)

Among them, u ₁ (k) and u ₂ (k) represent the balanced current output by the bidirectional cuk converter to the two single cells on the input side and the output side, respectively, and w _i1 (k) and w _i2 (k) are respectively expressed as The first and second error external currents, B ₁ (k) represents the respective efficiencies of all MOSFETs on the input side, B ₂ (k) represents the respective efficiencies of all MOSFETs on the output side, and b(k) represents the external current Influencing parameters; z(k+1) represents the state of charge of each battery at time k+1, and z(k) represents the state of charge of each battery at time k;

In the above formula, z(k), u ₁ (k), u ₂ (k), B ₁ (k), B ₂ (k) and b(k) are expressed as:

z(k)=[z ₁ (k), z ₂ (k), ... z _n (k)]

u ₁ (k)=[f ₁₁ (D ₁₁ (k)). …, f _(n-1)1 (D _(n-1)1 (k))] ^T

u ₂ (k)=[f ₁₂ (D ₁₂ (k)), ..., f _(n-1)2 (D _(n-1)2 (k))] ^T

b(k)=[dI _s (k) … dI _s (k)] ^T

T是控制采样时间区间，C_b表示电池容量；f_(n-1)1(D_(n-1)1(k))表示第n-1块均衡电路k时刻的占空比控制量D_(n-1)1和传输电流之间的关系，f_(n-1)2(D_(n-1)2(k))表示第n-1块均衡电路k时刻的占空比控制量D_(n-1)2和传输电流之间的关系，z_n(k)表示第n节电池在k时刻的荷电状态。Among them, γ _i and γ′ _i are switching variables for the duty cycle control quantities D _i1 and D _i2 respectively, pi represents the current transfer efficiency of the _i -th battery to the i+1-th battery, and pi ' represents the _i +th battery The current transfer efficiency of one battery to the i-th battery, I _s (k) represents the external current; d represents the auxiliary variable,

T is the control sampling time interval, C _b represents the battery capacity; f _(n-1)1 (D _(n-1)1 (k)) represents the duty cycle control amount D ₍ The relationship between _n-1)1 and the transmission current, f _(n-1)2 (D _(n-1)2 (k)) represents the duty ratio control amount D ₍ The relationship between _n-1)2 and the transmission current, z _n (k) represents the state of charge of the nth battery at time k.

It is known from the relevant literature that when the battery capacity C _b =3600 ampere, d is a very small constant.

In the described step 3), for the mathematical model of the battery balancing topology and the mathematical model of the battery balancing system constructed in step 2), a sliding mode control algorithm is used to carry out balancing control, and the corresponding duty ratios of the two MOSFET tubes are obtained by calculation. Control quantities D _i1 and D _i2 .

In the described sliding mode control algorithm, the following battery limiting conditions and battery balancing goals are established:

Battery Constraints: The controlled balancing currents u ₁ (k) and u ₂ (k) in the i-th balancing circuit satisfy:

是双向cuk变换器中最大允许的均衡电流电池电流限制，因为双向cuk变换器用于在DICM状态下工作，过充和过放的电流对电池有害，所以第i节电池的电流要被保持在

范围内。

代表双向cuk变换器中电池允许通过的最大电流，I_s(k)表示外部电流；in,

is the maximum allowable balancing current battery current limit in the bidirectional cuk converter, because the bidirectional cuk converter is used to work in the DICM state, the current of overcharge and overdischarge is harmful to the battery, so the current of the i-th battery should be kept at

within the range.

Represents the maximum current allowed by the battery in the bidirectional cuk converter, I _s (k) represents the external current;

and also satisfy the following formulas:

It can be seen from the above formula that u _i (k) changes with the change of the external current and is not constant.

Battery balancing goal: The goal of battery balancing is to make the SOC of the lithium battery converge to a limit, and the state of charge between the two batteries satisfies the following formula:

Among them, _zi (k) is the state of charge of the i-th battery at time k, and for all initial values _zi (0) and z _j (0) satisfy 1≤i, j≤n, i≠j, ε is the maximum acceptable state-of-charge deviation between batteries, k is the time instant, and τ is the balancing time of the batteries.

The present invention establishes a battery balancing sliding mode controller limited by the saturated balancing current through the above battery limiting conditions and the battery balancing target, which can make the balancing current as high as possible to improve the balancing speed.

After calculating the balanced currents u ₁ (k) and u ₂ (k) output to the two single cells on the input side and the output side by the sliding mode control algorithm, the transmission currents of the two MOSFETs are obtained by calculating the following formulas. And the duty cycle relationship f _i1 (D _i1 (k)) and f _i2 (D _i2 (k)) of the PWM signal:

u ₁ (k)=[f ₁₁ (D ₁₁ (k))......., f _(n-1)1 (D _(n-1)1 (k))] ^T

u ₂ (k)=[f ₁₂ (D ₁₂ (k)), ..., f _(n-1)2 (D _(n-1)2 (k))] ^T

3.2) Then use the duty ratio relationship f _i1 (D _i1 (k)) and f _i2 (D _i2 (k)) to perform the reverse calculation with the following formula to obtain the duty cycle control quantities D _i1 and D _i2 to control each equalizing circuit:

In the present invention, in a series battery pack, a bidirectional cuk converter circuit is used as a balance circuit between the batteries and the battery pack. The battery pack and the balance circuit form a battery-to-battery balance topology structure, which can improve the balance efficiency and reduce energy consumption. waste. Model the lithium battery and the balancing circuit separately, and then combine the models to obtain the overall model of the system, which can analyze and evaluate the stability and convergence of the entire battery balancing method.

The beneficial effects of the present invention are:

The invention adopts the sliding mode control method and limits the range, so that the maximum allowable current of the balance compensation changes with the external current instead of a fixed constant value, which can prevent the battery current from exceeding its limit.

The invention performs discrete sliding mode control through a battery balancing sliding mode controller with saturated balancing current limit, which has very good robustness to unknown disturbances, and it is proved by simulation that the SOC of the battery in the battery pack can be compared with other The method converges more quickly and well.

The method of the present invention finally proves that the SOC gap between n series single cells can converge to a very small range through the mathematical proof by using Lyapunov analysis. Different from only balancing two single cells in the past, this algorithm can be applied to more than two cells balancing, and has a good balancing effect.

It is proved by simulation and experiments that the design of the present invention can quickly balance the battery, effectively save energy and improve battery life.

Description of drawings

Figure 1 is a schematic diagram of a battery pack connected in series with an equalizing circuit;

Fig. 2 is the bidirectional cuk converter structural diagram of the present invention;

Fig. 3 is the inductor current curve diagram of the bidirectional cuk converter;

Fig. 4 is a result graph of the sliding mode control in this embodiment, (a) graph is the SOC value of each battery, (b) graph is the PWM duty ratio change under the sliding mode control.

Detailed ways

An example is used below to demonstrate the effectiveness of the lithium battery balancing method proposed by the present invention.

1. Experimental equipment

1) Battery:

和

是可以计算得到为3.23和0.8948.模型的相关参数分别为：The experiments were carried out using a battery pack consisting of four NCR 18650 (MH12210-3400mAh) lithium cells, as shown in Figure 2. After several rounds of charge-discharge experiments, the electric capacity of these batteries is about 3.1Ah and Cb=3.1×3600.

and

can be calculated as 3.23 and 0.8948. The relevant parameters of the model are:

R0i=0.206Ω, Rsi=0.0158Ω,

Csi=12340F, Rfi=0.01509Ω, and Cfi=1584F.

2) Bidirectional cuk converter:

As shown in Figure 1, a 4-element battery pack requires a 3-way bidirectional cuk converter. Select the relevant accessories parameters as follows:

Li1=Li2=100μH, C=470μF

The MOSFET of NTD6416AN-1G is driven by a PWM wave signal with a frequency of 7kHz.

Experiments were carried out to determine the performance of the bidirectional cuk converter. The final voltages of the adjacent cells are VB1=3.93V and VB2=3.62V, respectively. The duty cycle of the PWM wave is set to 0.3. The current curve of the inductor is shown in Figure 3.

The maximum allowable current of the battery is _IBmax =3A. The maximum equalizing current in DICM mode is set to I _Dmax =0.9A. The control time is T=1s. The initial SOC of each cell in the battery pack is:

SOC1(0)=74%, SOC2(0)=82%, SOC3(0)=71%, and SO4(0)=80%

With the sliding mode control setting, when the SOC difference between the cells is less than 2%, the process of cell balancing will stop.

For the sliding mode control algorithm, set the gain as η=0.01 and set ξ=3

2. Experimental results

The result of sliding mode control is shown in Fig. 4. The time required for equalization is 1138s, which is much shorter than the sliding mode control proposed previously. Its corresponding PWM wave duty cycle is shown in Figure 4.

It can be seen that the method of the present invention has a good balancing effect, can effectively prevent the battery current from exceeding its limit, has very good robustness against unknown interference, and realizes the ability to quickly balance the battery, effectively save energy and improve the battery. life, has its outstanding technical effect.

Claims (3)

1. A battery pack balancing method based on sliding mode control is characterized in that:

1) designing a battery balancing topological structure according to the unbalanced condition of the series battery pack;

in the step 1), a bidirectional cuk converter circuit serving as an equalizing circuit is connected between two adjacent batteries of the series battery pack, each equalizing circuit is connected with a controller, and the equalizing circuit between the adjacent batteries and the controllers thereof form a battery equalizing topological structure;

the bi-directional cuk converter between the ith battery and the (i +1) th battery (i is more than or equal to 1 and less than or equal to n-1) is used as the ith bi-directional cuk converter, and the specific circuit structure is as follows: comprising an inductance L_i1Inductor L_i2Energy transfer capacitor C_iMOSFET Q_i1MOSFET Q_i2Body diode d_i1And a body diode d_i2MOSFET tube Q_i1And a body diode d_i1After being connected in parallel with an inductor L_i1Connected in series at two ends of the ith battery, and provided with MOSFET tube Q_i2And a body diode d_i2After being connected in parallel with an inductor L_i2Are connected in series at two ends of the (i +1) th battery, and an energy transfer capacitor C_iBoth ends of the inductor are connected in series with the inductor L_i1And an inductance L_i2To (c) to (d); therefore, n-1 bidirectional cuk converters are connected between the battery packs connected in series by n batteries, and the circuit controls the on and off of two MOSFET tubes by PWM signal drive to control the charge and discharge between the two batteries so as to realize the voltage balance between the two batteries;

2) establishing a mathematical model for the battery balancing topological structure, and establishing a battery balancing system mathematical model formed by the battery balancing topological structure and the series battery pack;

in the step 2), the mathematical model of the battery equalization system is specifically as follows:

duty ratio control quantity D for two MOSFET tubes_i1And D_i2Construction of respective switching variables γ_iAnd gamma'_iExpressed as:

D_i1(k)D_i2(k)＝0

note the book

Is the monomer balance current of the battery k at the ith (i is more than or equal to 2 and less than or equal to n-1),

the cell balance current at the moment k of the 1 st cell,

balancing current for the cell at the k moment of the nth cell;

the calculation formula of the equilibrium current of each monomer is as follows:

where k denotes the number of sampling times, γ_iAnd gamma'_i(1. ltoreq. i. ltoreq. n) is for the duty ratio control quantity D, respectively_i1And D_i2Of the switching variable, p_iRepresents the current transmission efficiency of the ith battery to the (i +1) th battery, f_i1(D_i1(k) And f) and_i2(D_i2(k) (i is more than or equal to 1 and less than or equal to n) represents the duty ratio relation between the transmission current of the two MOSFET tubes and the PWM signal, f_i1(D_i1(k) Represents the duty ratio control quantity D at the time of k of the ith block of the equalizer circuit_i1And the relation between the transmitted current, f_i2(D_i2(k) Represents the duty ratio control quantity D at the time k_i2And the relation between the transmission current, which is the transmission of the ith battery to the (i +1) th batteryThe current of (a); w is a_i1(k) And w_i2(k) (i is more than or equal to 1 and less than or equal to n-1) respectively represents the model error of the monomer equalizing current passing through the i bidirectional cuk converter;

equalizing current of the ith battery at the time of k

The method is simplified as follows:

the mathematical model of the battery equalization system of the battery pack with n batteries connected in series is represented as follows:

z(k+1)＝z(k)+dB₁(k)(u₁(k)+w₁(k))+dB₂(k)(u₂(k)+w₂(k))-b(k)

wherein u is₁(k) And u₂(k) Respectively representing the balance current, w, output by the bidirectional cuk converter to the two single batteries at the input side and the output side₁(k) And w₂(k) Respectively expressed as first and second error external currents, B₁(k) Representing the respective efficiencies of all MOSFET transistors at the input side, B₂(k) Representing the respective efficiencies of all MOSFET tubes at the output side, b (k) representing the external current influencing parameter; z (k +1) represents the state of charge of each battery at the moment k +1, and z (k) represents the state of charge of each battery at the moment k;

in the above formulas, z (k), u₁(k)、u₂(k)、B₁(k)、B₂(k) And b (k) is represented by:

z(k)＝[z₁(k)，z₂(k)，……z_n(k)]

u₁(k)＝[f₁₁(D₁₁(k)).……，f_(n-1)1(D_(n-1)1(k))]^T

u₂(k)＝[f₁₂(D₁₂(k))，……，f_(n-1)2(D_(n-1)2(k))]^T

b(k)＝[dI_s(k)…dI_s(k)]^T

wherein, γ_iAnd gamma'_iRespectively for duty ratio control quantity D_i1And D_i2Of the switching variable, p_iRepresents the current transmission efficiency of the ith battery to the (i +1) th battery, p_i' represents the current transmission efficiency of the I +1 th battery to the I-th battery, I_s(k) Represents an external current; d represents an auxiliary variable which is a variable of,

t is the control sampling time interval, C_bRepresents the battery capacity; f. of_(n-1)1(D_(n-1)1(k) Represents the duty ratio control quantity D at the k moment of the n-1 th equalizing circuit_(n-1)1And the relation between the transmitted current, f_(n-1)2(D_(n-1)2(k) Represents the duty ratio control quantity D at the k moment of the n-1 th equalizing circuit_(n-1)2And the relation between the transmitted current, z_n(k) Representing the state of charge of the nth battery at the moment k;

3) balance control is carried out by combining a mathematical model of a battery balance system through a sliding mode controller, and balance processing among all the batteries in the series battery pack is realized;

in the step 3), balance control is performed on the mathematical model of the battery balance topological structure and the mathematical model of the battery balance system constructed in the step 2) by adopting a sliding mode control algorithm, and duty ratio control quantity D corresponding to the two MOSFET tubes is calculated and obtained_i1And D_i2；

In the sliding mode control algorithm, the following battery limiting conditions and battery balancing targets are established:

battery limiting conditions: controlled equalizing current u in the ith equalizing circuit₁(k) And u₂(k) Satisfies the following conditions:

wherein,

is the maximum allowable equalization current battery current limit in the bi-directional cuk converter,

representing the maximum current allowed to pass by the battery in a bidirectional cuk converter, I_s(k) Represents an external current;

battery equalization target: the state of charge between the two batteries satisfies the following formula:

wherein z is_i(k) Is the state of charge of the ith cell at time k, for all initial values z_i(0) And z_j(0) I is more than or equal to 1, j is less than or equal to n, i is not equal to j, epsilon is the maximum acceptable state of charge deviation between batteries, k represents the moment, and tau is the balancing time of the batteries.

2. The sliding-mode-control-based battery pack balancing method according to claim 1, characterized in that: in the step 2), the mathematical model of the battery balancing topological structure is specifically as follows:

the calculation formula of the equalizing current in the ith bidirectional cuk converter is as follows:

wherein, I_Li1And I_Li2Respectively representing a through inductance L_i1And L_i2Of the equalizing current, L_i1Denotes the inductance, L, connected to the ith battery in the ith bidirectional cuk converter_i2Represents the inductance, P, connected to the (i +1) th battery in the ith bidirectional cuk converter_iRepresents the current transfer efficiency, P, when the ith battery in the ith bidirectional cuk converter charges the (i +1) th battery_i' represents the current transfer efficiency of the i +1 th battery in the ith bidirectional cuk converter to the ith battery_sIn order to be the time of sampling,

and

the terminal voltages of the ith and (i +1) th batteries respectively,

is the mean voltage of the capacitor, D_i1Representing MOSFET tube Q_i1Duty ratio control amount of upper PWM signal, D_i2Representing MOSFET tube Q_i2Duty ratio control quantity of the upper PWM signal;

the duty ratio control quantity D corresponding to the two MOSFET tubes is obtained by the formula deformation_i1And D_i2The calculation formula of (a) is as follows:

according to the formula, the current I is equalized on the premise that the variables in the circuit are known_Li2Substituting into the control quantity D of duty ratio corresponding to two MOSFET tubes_i1And D_i2Value of (D), controlling the quantity D with a duty cycle_i1And D_i2And controlling two MOSFET tubes of the balancing circuit to realize the balancing of the battery.

3. The sliding-mode-control-based battery pack balancing method according to claim 1, characterized in that: the method comprises the steps of obtaining balanced currents u output to two single batteries on the input side and the output side respectively through calculation of a sliding mode control algorithm₁(k)、u₂(k) And calculating and obtaining the duty ratio relation f between the transmission current of the two MOSFET tubes and the PWM signal by using the following formula_i1(D_i1(k) And f) and_i2(D_i2(k))：

u₁(k)＝[f₁₁(D₁₁(k)).......，f_(n-1)1(D_(n-1)1(k))]^T

u₂(k)＝[f₁₂(D₁₂(k))，......，f_(n-1)2(D_(n-1)2(k))]^T

3.2) reuse duty ratio relationship f_i1(D_i1(k) And f) and_i2(D_i2(k) the following formula is adopted to carry out reverse calculation to obtain the duty ratio control quantity D_i1And D_i2Controlling each equalization circuit:

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