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

Battery pack balancing method based on sliding mode control Download PDF

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CN107276171B
CN107276171B CN201710567058.8A CN201710567058A CN107276171B CN 107276171 B CN107276171 B CN 107276171B CN 201710567058 A CN201710567058 A CN 201710567058A CN 107276171 B CN107276171 B CN 107276171B
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battery
current
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duty ratio
balancing
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CN107276171A (en
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陈剑
欧阳权
郭宣宏
郑剑
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Zhejiang University ZJU
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J7/00—Circuit arrangements for charging or depolarising batteries or for supplying loads from batteries
    • H02J7/0013—Circuit arrangements for charging or depolarising batteries or for supplying loads from batteries acting upon several batteries simultaneously or sequentially
    • H02J7/0014—Circuits for equalisation of charge between batteries
    • H02J7/0019—Circuits for equalisation of charge between batteries using switched or multiplexed charge circuits

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

Battery pack balancing method based on sliding mode control
Technical Field
The invention relates to a battery algorithm, in particular to a battery pack balancing method based on sliding mode control.
Background
Energy conservation and environmental protection have become the target of the world effort in China today. Among them, the wide application of the battery pack has become a standard of the times.
Battery imbalances are common in battery systems and are also a significant issue in battery system life. It is caused by two main categories, which are: an internal power supply consisting of manufacturing variance of the physical volume, i.e., variance of internal impedance and self-discharge rate difference; an external power source, such as a hot section of the package. Battery systems of the balancing technology are particularly important in lithium batteries, since without it the batteries would be overcharged, undercharged or even overdischarged.
Imbalance of the battery pack causes the following hazards: premature degradation of the battery due to overvoltage; potential safety hazards from overcharging the battery; capacity degradation due to premature charging shutdown; the discharge terminates prematurely.
Therefore, the battery equalization of the series lithium battery pack is significant: the energy balance of the battery can be effectively maintained, the service life is prolonged, and the discharge efficiency is improved.
Disclosure of Invention
The invention aims to provide a lithium battery pack balancing method aiming at the defects of the prior art, and provides a battery balancing system model. The battery equalization system model comprises a bidirectional cuk converter circuit as an equalization circuit, and can realize current transmission between every two batteries of the series battery pack. And simultaneously, the lithium battery and the equalizing circuit are respectively modeled, and then a model of the whole system is obtained by combining the models, so that the stability and the convergence of the equalizing method of the whole battery can be correspondingly analyzed and evaluated. Finally, a sliding mode control algorithm based on SOC is provided, and the battery equalization process can be effectively controlled aiming at a discontinuous current mode.
The technical scheme of the invention comprises the following steps:
1) designing a special battery balancing topological structure according to the unbalanced condition of the series battery pack, wherein the specific implementation is that a bidirectional cuk converter forms the battery balancing topological structure;
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;
3) 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 technical scheme of the invention mainly comprises a battery equalization system model and a control method. The battery equalization system model is characterized in that an equalization circuit is designed according to the characteristics of series-connected lithium batteries, modeling is carried out on the equalization circuit of the lithium batteries and the whole formed by the lithium batteries and the equalization circuit, and a mathematical basis is provided for a control algorithm. The control method is based on sliding mode control of SOC (state of charge), and comprises a limiting condition and an equalization target, an improved sliding mode observer for SOC monitoring, and a battery equalization sliding mode controller limited by saturation equalization current.
The battery is a lithium battery.
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 topology structure. The structure can improve the equalizing efficiency and reduce the waste of energy.
The lithium battery in the lithium battery pack is generally in a form of a series single battery pack, and the lithium battery pack is continuously charged or discharged. According to the situation, the lithium battery pack is formed by connecting n single lithium batteries in series, and the invention provides a battery equalization system as shown in figure 1.
The invention adopts the bidirectional cuk converter as a battery-to-battery equalizing circuit, and as shown in fig. 2, the method has the advantages of high speed, low energy consumption, easy operation and control, relatively high efficiency and the like. If the number of cells in the battery pack is increased or decreased, only the same number of inverters need to be increased or decreased, rather than adjusting the overall structure of the equalization system for the battery pack.
According to the invention, two adjacent batteries are connected in series by using the equalizing circuit, the equalizing circuit realizes energy transfer between the batteries, and the equalizing circuit is connected with an independent controller to control the equalizing circuit, so that a simple and rapid intelligent equalizing effect is realized.
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 Li1Inductor Li2Energy transfer capacitor CiMOSFET Qi1MOSFET Qi2Body diode di1And a body diode di2MOSFET tube Qi1And a body diode di1After being connected in parallel with an inductor Li1Connected in series at two ends of the ith battery, and provided with MOSFET tube Qi2And a body diode di2After being connected in parallel with an inductor Li2Are connected in series at two ends of the (i +1) th battery, and an energy transfer capacitor CiBoth ends of the inductor are connected in series with the inductor Li1And an inductance Li2To (c) to (d); therefore, n-1 bidirectional cuk converters are connected between the battery packs connected in series by the n batteries, and the circuit controls the on and off of the 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. The duty ratio of the PWM signal is used as a control variable for battery equalization and is respectively Di1，Di2The switching losses of the MOSFETs can be reduced by selecting a suitable duty cycle. For example, first, MOSFET transistor Qi1Turn-on and MOSFET transistor Qi2When the power supply is closed, the ith battery is enabled to firstly transmit to the energy transfer capacitor CiCharging; then, MOSFET transistor Qi2Turn-on and MOSFET transistor Qi1When turned off, causes the energy transfer capacitor CiCharging the (i +1) th battery.
The battery equalization topological structure formed by the equalization circuit has the following characteristics:
1. the bidirectional equalizing circuit is used, so that energy can be transferred from one battery to any other battery, and the problem of uneven energy distribution is solved. For example, an initial battery is charged to a next battery connected in series through the equalizing circuit, and then the next battery connected in series is charged to the next battery connected in series through the equalizing circuit, so that the initial battery is charged to any battery through the middle batteries connected in series, and the energy is transferred randomly.
2. On the basis of series connection of batteries, through designing an external circuit module, the current influence on the series connection of the batteries is not large, the hybrid power battery pack can cope with the complex environment of hybrid power, and the balance can be realized when the batteries work.
3. The battery and the equalizing circuit can be regarded as a whole, and the equalizing system uses n-1 bidirectional equalizing circuits aiming at n series batteries, so that the expansibility is good.
4. Relatively, modularization is obvious, and the equalization circuit can be abstracted out for modeling analysis. The portability of the system is very good, and the system is convenient to be applied to occasions with different battery management.
In the step 2), the battery equalization topological structure is modeled, and then a battery equalization system mathematical model is constructed by combining the battery equalization topological structure model, so that the stability and the convergence of the whole battery equalization method can be correspondingly analyzed and evaluated.
In the step 2), the mathematical model of the battery balancing topological structure is specifically as follows:
as shown in FIG. 1, the converter numbered i (1 ≦ i ≦ n-1) has a symmetrical structure, and can transfer energy between the ith battery and the (i +1) th battery in both directions. Therefore, the general loss is ignored, the energy is transferred from the ith battery to the (i +1) th battery, and meanwhile, according to the circuit of the ith bidirectional cuk circuit, the double circuit is driven by the PWM signal to control the on and off of the MOSFET. The duty ratio of the PWM signal is used as a control variable for battery equalization, and a calculation formula for obtaining the equalization current in the ith bidirectional cuk converter is as follows:
Figure BDA0001348650740000031
Figure BDA0001348650740000032
wherein, ILi1And ILi2Respectively representing a through inductance Li1And Li2The magnitude of the current determines how much to charge, Li1Denotes the inductance, L, connected to the ith battery in the ith bidirectional cuk converteri2Represents the inductance, P, connected to the (i +1) th battery in the ith bidirectional cuk converteriRepresents the current transfer efficiency, P, when the ith battery in the ith bidirectional cuk converter charges the (i +1) th batteryi' represents the current transfer efficiency of the i +1 th battery in the ith bidirectional cuk converter to the ith batterysIn order to be the time of sampling,
Figure BDA0001348650740000041
and
Figure BDA0001348650740000042
the terminal voltages of the ith and (i +1) th batteries respectively,
Figure BDA0001348650740000043
is the mean voltage of the capacitor, Di1Representing MOSFET tube Qi1Duty ratio control amount of upper PWM signal, Di2Representing MOSFET tube Qi2Duty ratio control quantity of the upper PWM signal;
the above formula is deformed to obtain two MOSFET tubesRespective corresponding duty ratio control quantity Di1And Di2The calculation formula of (a) is as follows:
Figure BDA0001348650740000044
Figure BDA0001348650740000045
according to the formula, the current I is equalized on the premise that the variables in the circuit are knownLi2Substituting into the control quantity D of duty ratio corresponding to two MOSFET tubesi1And Di2Value of (D), controlling the quantity D with a duty cyclei1And Di2And controlling two MOSFET tubes of the balancing circuit to realize the balancing of the battery.
In the step 2), the mathematical model of the battery equalization system is specifically as follows:
for n batteries, the first battery and the last battery are respectively and independently connected with only one equalizing circuit, and the other batteries are connected with two equalizing circuits.
Duty ratio control quantity D for two MOSFET tubesi1And Di2Construction of respective switching variables γiAnd gamma'iExpressed as:
Figure BDA0001348650740000046
Figure BDA0001348650740000047
Di1(k)Di2(k)＝0
since two MOSFET transistors cannot be turned on simultaneously, Di1(k)Di2(k)＝0。
Note the book
Figure BDA0001348650740000048
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),
Figure BDA0001348650740000049
the cell balance current at the moment k of the 1 st cell,
Figure BDA00013486507400000410
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:
Figure BDA0001348650740000051
Figure BDA0001348650740000052
Figure BDA0001348650740000053
where k denotes the number of sampling times, γiAnd gamma'i(1. ltoreq. i. ltoreq. n) is for the duty ratio control quantity D, respectivelyi1And Di2Of the switching variable, piRepresents the current transmission efficiency of the ith battery to the (i +1) th battery, fi1(Di1(k) And fi2(Di2(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, fi1(Di1(k) Represents the duty ratio control quantity D at the time of k of the ith block of the equalizer circuiti1And the relation between the transmitted current, fi2(Di2(k) Represents the duty ratio control quantity D at the time ki2And the transmission current, the transmission current refers to the current transmitted by the ith battery to the (i +1) th battery; w is ai1(k) And wi2(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
Figure BDA0001348650740000054
The method is simplified as follows:
Figure BDA0001348650740000055
Figure BDA0001348650740000056
in order to facilitate the equalization of the lithium battery pack, the SOC of the lithium battery is set, and a battery equalization system mathematical model 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 sidei1(k) And wi2(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)，……zn(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
Figure BDA0001348650740000061
Figure BDA0001348650740000062
b(k)＝[dIs(k) … dIs(k)]T
wherein, γiAnd gamma'iRespectively for duty ratio control quantity Di1And Di2Of the switching variable, piRepresents the current transmission efficiency of the ith battery to the (i +1) th battery, pi' represents the current transmission efficiency of the I +1 th battery to the I-th battery, Is(k) Represents an external current; d represents an auxiliary variable which is a variable of,
Figure BDA0001348650740000063
t is the control sampling time interval, CbRepresents 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, zn(k) Indicating the state of charge of the nth battery at time k.
The battery capacity C is known from the relevant literaturebAt 3600 amps, d is a very small constant.
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 obtainedi1And Di2。
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:
Figure BDA0001348650740000064
wherein the content of the first and second substances,
Figure BDA0001348650740000065
is the maximum allowable balancing current battery current limit in the bidirectional cuk converter, because the bidirectional cuk converter is used for working in the DICM state, and the over-charging and over-discharging current is harmful to the battery, so the current of the ith battery is kept at
Figure BDA0001348650740000066
Within the range.
Figure BDA0001348650740000067
Representing the maximum current allowed to pass by the battery in a bidirectional cuk converter, Is(k) Represents an external current;
and simultaneously satisfies the following formula:
Figure BDA0001348650740000071
from the above formula, ui(k) The current varies with the external current and is not constant.
Battery equalization target: the aim of battery balancing is to make the SOC of the lithium battery converge to a limit, and the state of charge between two batteries satisfies the following formula:
Figure BDA0001348650740000074
wherein z isi(k) Is the state of charge of the ith cell at time k, for all initial values zi(0) And zj(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.
According to the invention, the battery balancing sliding mode controller limited by the saturation balancing current is established by the battery limiting conditions and the battery balancing target, so that the balancing current can be as high as possible, and the balancing speed is improved.
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 formulai1(Di1(k) And f) andi2(Di2(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 fi1(Di1(k) And f) andi2(Di2(k) the following formula is adopted to carry out reverse calculation to obtain the duty ratio control quantity Di1And Di2Controlling each equalization circuit:
Figure BDA0001348650740000072
Figure BDA0001348650740000073
in the series battery pack, the bidirectional cuk converter circuit is adopted between every two batteries as the equalizing circuit, and the battery pack and the equalizing circuit form a battery-to-battery equalizing topological structure. The lithium battery and the equalizing circuit are respectively modeled, and then the model of the whole system is obtained by combining the models, so that the stability and the convergence of the equalizing method of the whole battery can be correspondingly analyzed and evaluated.
The invention has the beneficial effects that:
the invention adopts a sliding mode control method and limits the range, so that the maximum allowable current of the balance compensation is changed along with the external current instead of being fixed at a constant value, and the current of the battery can be prevented from exceeding the limit.
The discrete sliding mode control is carried out through the battery balancing sliding mode controller with saturated balancing current limitation, so that the robustness to unknown interference is very good, and simulation proves that the SOC of the battery in the battery pack can be converged more rapidly and well than other methods.
Finally, the method is proved by mathematics using Lyapunov analysis that the SOC difference between n series-connected single batteries can be converged to a small range. Different from the prior method of only balancing two single batteries, the algorithm can be applied to balancing more than two batteries and has good balancing effect.
Simulation and experiments prove that the design of the invention can quickly balance the battery, effectively save energy and prolong the service life of the battery.
Drawings
FIG. 1 is a schematic diagram of a series battery pack having an equalization circuit;
FIG. 2 is a block diagram of the bidirectional cuk converter of the present invention;
FIG. 3 is a graph of the inductor current of a bidirectional cuk converter;
fig. 4 is a graph showing the result of the sliding mode control in the present embodiment, (a) is a graph showing the SOC value of each battery, and (b) is a graph showing the PWM duty ratio change under the sliding mode control.
Detailed Description
The effectiveness of the lithium battery equalization method proposed by the present invention is demonstrated by an example below.
1. Experimental equipment
1) A battery:
experiments were performed using a battery consisting of four NCR 18650(MH12210-3400mAh) lithium cells, as shown in fig. 2. After several cycles of charge and discharge experiments, the electric capacity of these batteries was found to be approximately 3.1Ah and Cb ═ 3.1 × 3600.
Figure BDA0001348650740000081
And
Figure BDA0001348650740000082
are calculated to be 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 fig. 1, a 4-bit serial battery pack needs to include 3 bidirectional cuk converters. The relevant accessory parameters were chosen as follows:
Li1＝Li2＝100μH，C＝470μF
the MOSFET of NTD6416AN-1G model is driven by PWM wave signal with 7kHz frequency.
Correlation experiments were performed to determine the performance of the bidirectional cuk converter. The final voltages of the adjacent batteries are VB 1-3.93V and VB 2-3.62V, respectively. The duty ratio of the PWM wave is set to 0.3. The current curve of the inductor is shown in fig. 3.
The maximum allowable current of the battery is IBmax3A. Maximum equalizing current is set to I in DICM modeDmax0.9A. The control time is T-1 s. The initial SOC of each battery of the battery pack is respectively as follows:
SOC1(0)＝74％，SOC2(0)＝82％，SOC3(0)＝71％，and SO4(0)＝80％
with the sliding mode control setting, the process of cell balancing will stop when the SOC difference between the cells is less than 2%.
For the sliding mode control algorithm, the gain is set to η -0.01, and ξ -3
2. Results of the experiment
The result of the sliding mode control is shown in fig. 4. The time required for equalization is 1138s, which is much shorter than the previously proposed sliding mode control. The corresponding PWM wave duty cycle is shown in fig. 4.
Therefore, the method has a good balancing effect, can effectively prevent the current of the battery from exceeding the limit, has good robustness for unknown interference, realizes the purpose of rapidly balancing the battery, effectively saves energy and prolongs the service life of the battery, and has remarkable technical effects.

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 Li1Inductor Li2Energy transfer capacitor CiMOSFET Qi1MOSFET Qi2Body diode di1And a body diode di2MOSFET tube Qi1And a body diode di1After being connected in parallel with an inductor Li1Connected in series at two ends of the ith battery, and provided with MOSFET tube Qi2And a body diode di2After being connected in parallel with an inductor Li2Are connected in series at two ends of the (i +1) th battery, and an energy transfer capacitor CiBoth ends of the inductor are connected in series with the inductor Li1And an inductance Li2To (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 tubesi1And Di2Construction of respective switching variables γiAnd gamma'iExpressed as:
Figure FDA0002362886500000011
Figure FDA0002362886500000012
Di1(k)Di2(k)＝0
note the book
Figure FDA0002362886500000015
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),
Figure FDA0002362886500000013
the cell balance current at the moment k of the 1 st cell,
Figure FDA0002362886500000014
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:
Figure FDA0002362886500000021
Figure FDA0002362886500000022
Figure FDA0002362886500000023
where k denotes the number of sampling times, γiAnd gamma'i(1. ltoreq. i. ltoreq. n) is for the duty ratio control quantity D, respectivelyi1And Di2Of the switching variable, piRepresents the current transmission efficiency of the ith battery to the (i +1) th battery, fi1(Di1(k) And f) andi2(Di2(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, fi1(Di1(k) Represents the duty ratio control quantity D at the time of k of the ith block of the equalizer circuiti1And the relation between the transmitted current, fi2(Di2(k) Represents the duty ratio control quantity D at the time ki2And 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 ai1(k) And wi2(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
Figure FDA0002362886500000024
The method is simplified as follows:
Figure FDA0002362886500000025
Figure FDA0002362886500000026
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)，……zn(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
Figure FDA0002362886500000031
Figure FDA0002362886500000032
b(k)＝[dIs(k)…dIs(k)]T
wherein, γiAnd gamma'iRespectively for duty ratio control quantity Di1And Di2Of the switching variable, piRepresents the current transmission efficiency of the ith battery to the (i +1) th battery, pi' represents the current transmission efficiency of the I +1 th battery to the I-th battery, Is(k) Represents an external current; d represents an auxiliary variable which is a variable of,
Figure FDA0002362886500000033
t is the control sampling time interval, CbRepresents 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, zn(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 obtainedi1And Di2；
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:
Figure FDA0002362886500000034
wherein the content of the first and second substances,
Figure FDA0002362886500000036
is the maximum allowable equalization current battery current limit in the bi-directional cuk converter,
Figure FDA0002362886500000037
representing the maximum current allowed to pass by the battery in a bidirectional cuk converter, Is(k) Represents an external current;
battery equalization target: the state of charge between the two batteries satisfies the following formula:
Figure FDA0002362886500000035
wherein z isi(k) Is the state of charge of the ith cell at time k, for all initial values zi(0) And zj(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:
Figure FDA0002362886500000041
Figure FDA0002362886500000042
wherein, ILi1And ILi2Respectively representing a through inductance Li1And Li2Of the equalizing current, Li1Denotes the inductance, L, connected to the ith battery in the ith bidirectional cuk converteri2Represents the inductance, P, connected to the (i +1) th battery in the ith bidirectional cuk converteriRepresents the current transfer efficiency, P, when the ith battery in the ith bidirectional cuk converter charges the (i +1) th batteryi' represents the current transfer efficiency of the i +1 th battery in the ith bidirectional cuk converter to the ith batterysIn order to be the time of sampling,
Figure FDA0002362886500000043
and
Figure FDA0002362886500000044
the terminal voltages of the ith and (i +1) th batteries respectively,
Figure FDA0002362886500000045
is the mean voltage of the capacitor, Di1Representing MOSFET tube Qi1Duty ratio control amount of upper PWM signal, Di2Representing MOSFET tube Qi2Duty 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 deformationi1And Di2The calculation formula of (a) is as follows:
Figure FDA0002362886500000046
Figure FDA0002362886500000047
according to the formula, the current I is equalized on the premise that the variables in the circuit are knownLi2Substituting into the control quantity D of duty ratio corresponding to two MOSFET tubesi1And Di2Value of (D), controlling the quantity D with a duty cyclei1And Di2And 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 formulai1(Di1(k) And f) andi2(Di2(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 fi1(Di1(k) And f) andi2(Di2(k) the following formula is adopted to carry out reverse calculation to obtain the duty ratio control quantity Di1And Di2Controlling each equalization circuit:
Figure FDA0002362886500000051
Figure FDA0002362886500000052
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