CN107276171A - A kind of battery pack equilibrium method based on sliding formwork control - Google Patents
A kind of battery pack equilibrium method based on sliding formwork control Download PDFInfo
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- CN107276171A CN107276171A CN201710567058.8A CN201710567058A CN107276171A CN 107276171 A CN107276171 A CN 107276171A CN 201710567058 A CN201710567058 A CN 201710567058A CN 107276171 A CN107276171 A CN 107276171A
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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 kind of battery pack equilibrium method based on sliding formwork control.Special battery balanced topological structure is designed according to the unbalanced situation of series battery；Mathematical model is set up to battery balanced topological structure, and sets up the battery equalization system mathematical model that battery balanced topological structure and series battery are collectively constituted；Balance route is carried out with sliding mode controller with reference to battery equalization system mathematical model, the equilibrium treatment between each batteries in series battery is realized.The inventive method can carry out rapidly balanced, the effectively save energy to battery, improve battery life.
Description
Technical field
The present invention relates to a kind of battery algorithm, more particularly, to a kind of battery pack balancing side based on sliding formwork control
Method.
Background technology
Energy-conservation has become China Today with environmental protection so that the target that the whole world is made great efforts.Wherein, the extensive of battery pack should
With becoming a kind of beautiful of epoch.
Battery is unbalanced very common in battery system, is also a major issue of cell system lifetime.It is by two
Individual main classification causes, and they are respectively：The variance of the internal electric source, i.e. internal driving of the manufacture variance composition of physical size
With self-discharge rate difference；The hot-zone of external power source, such as packaging is other.The battery system of balancing technique is especially weighed in lithium battery
Will, because without that can make over-charging of battery if it, undercharge, or even mistake are put.
Battery pack is unbalanced to cause following harm：Due to battery premature degradation caused by overvoltage；Overcharge battery
Potential safety hazard；Capacity reduction caused by charging stops too early；Discharge premature end.
So the lithium battery group progress to series connection is battery balanced significant：Energy content of battery balance can effectively be maintained, prolonged
Long-life, raising discharging efficiency.
The content of the invention
In view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide a kind of lithium battery group equalization methods, the present invention is carried
Go out to devise battery equalization system model.Battery equalization system model is used as equalizing circuit, energy including two-way cuk converter circuits
Enough realize electric current transmission of the series battery two-by-two between battery.Lithium battery and equalizing circuit are modeled respectively simultaneously, then
Binding model obtains the overall model of system, and the stability and convergence property of whole batteries equalization methods can be divided accordingly
Analysis and assessment.The sliding mode control algorithm based on SOC is finally proposed, discontinuous current mode can be effectively directed to, it is equal to battery
Weighing apparatus process is controlled.
Technical scheme comprises the following steps：
1) special battery balanced topological structure is designed according to the unbalanced situation of series battery, specific implementation is with double
Battery balanced topological structure is constituted to cuk converters；
2) set up mathematical model to battery balanced topological structure, and set up battery balanced topological structure and series battery is common
With the battery equalization system mathematical model of composition；
3) Balance route is carried out with sliding mode controller with reference to battery equalization system mathematical model, realized each in series battery
Equilibrium treatment between batteries.
Technical scheme is mainly made up of battery equalization system model and control method.Battery equalization system model
It is, according to serial lithium battery feature, to design equalizing circuit, and for the equalizing circuit and lithium battery and equalizing circuit of lithium battery
The entirety of formation is modeled, and mathematics basis is provided for control algolithm.Control method is the sliding formwork control based on SOC (state-of-charge)
System, including qualifications and equalization target, the improvement sliding mode observer for SOC monitorings, the electricity limited by saturation euqalizing current
Pond equilibrium sliding mode controller.
Described battery is lithium battery.
Described step 1) in, it is connected between two adjacent cells of series battery as the two-way of equalizing circuit
Cuk converter circuits, and each equalizing circuit is all connected with a controller, between adjacent cell between equalizing circuit and
Its respective controller constitutes battery balanced topological structure.This structure can improve equalization efficiency, reduce the waste of energy.
In lithium battery group lithium battery be usually connect monomer battery pack form, lithium battery group constantly externally charging or
Electric discharge.According to this situation, if lithium battery group is in series by n single lithium battery, the present invention proposes to use battery balanced system
System such as Fig. 1.
The present invention has speed using equalizing circuit of the two-way cuk converters as battery to battery, such as Fig. 2, this method
It hurry up, consumed energy is few, it is easy to which operation is with control, the advantages of efficiency is of a relatively high.If in battery pack number of batteries increase or
Person reduces, it is only necessary to increases or reduces the converter of identical quantity, rather than be the entirety of battery pack adjustment equalizing system
Structure.
The present invention is connected between the series connection of two adjacent sections battery with equalizing circuit, and equalizing circuit realizes the energy between battery
Transmission, connects a single controller in equalizing circuit and equalizing circuit is controlled, realize simple and rapid intelligence
Portfolio effect.
I-th pair is used as using the two-way cuk converters between the i-th batteries and i+1 batteries (1≤i≤n-1)
To cuk converters, particular circuit configurations are：Including inductance Li1, inductance Li2, energy transferring capacitor device Ci, MOSFET pipes Qi1、
MOSFET pipes Qi2, body diode di1With body diode di2, MOSFET pipes Qi1With body diode di1With inductance L after parallel connectioni1Together
It is connected on the two ends of the i-th batteries, MOSFET pipes Qi2With body diode di2With inductance L after parallel connectioni2I+1 section is connected on together
The two ends of battery, energy transferring capacitor device CiTwo ends are connected on inductance Li1With inductance Li2Between；So that the series connection of n batteries
N-1 two-way cuk converters are had between battery pack to be wherein connected, and circuit pwm signal drive control two
MOSFET pipes are opened and turned off to control the discharge and recharge between two batteries, to realize the balance of voltage between two batteries.
The dutycycle of pwm signal is used as battery balanced control variable, respectively Di1, Di2, by selecting suitable dutycycle to subtract
Few MOSFET switching loss.For example first, MOSFET pipes Qi1Open and MOSFET pipes Qi2During closing so that the i-th batteries are first
To energy transferring capacitor device CiCharging；Then, MOSFET pipes Qi2Open and MOSFET pipes Qi1During closing so that energy transferring capacitor
Device CiCharged to i+1 batteries.
The battery balanced topological structure that equalizing circuit of the present invention is constituted has following characteristics：
1st, using bidirectional equalization circuit so that during energy can be delivered to any another batteries from a batteries, solve
The problem of energy distribution is uneven.For example, an initial batteries are charged by equalizing circuit to the battery of next section series connection, Xia Yijie
The battery charging of series connection is charged by the battery of equalizing circuit next section series connection downwards again, so that in initial batteries warp
Between multi-section serial battery to any one batteries realize charge, complete energy any transmission.
2nd, by designing external circuit module on the basis of series-connected cell, on the electric current influence of series battery in itself not
Greatly, the complex environment of hybrid power can be tackled, equilibrium can also be realized when battery works.
3rd, battery and equalizing circuit are considered as an entirety, and equalizing system is for n series-connected cell, then using n-1
Two-way equalizing circuit, expansion is good.
4th, comparatively equalizing circuit substantially, can be abstracted, be modeled analysis by modularization.The transplantability of system
It is very good, it is easy in the occasion using different battery managements.
Described step 2) in, battery balanced topological structure is modeled, in conjunction with the mould of battery balanced topological structure
Type builds battery equalization system mathematical model, and the stability and convergence property of whole batteries equalization methods can be divided accordingly
Analysis and assessment.
Described step 2) in, the mathematical model of battery balanced topological structure is specially：
As shown in figure 1, the symmetrical configuration for the converter that numbering is i (1≤i≤n-1), can be by energy in the i-th batteries
The bi-directional between i+1 batteries.Therefore general loss is ignored, energy is transferred to i+1 batteries from the i-th batteries,
Simultaneously according to the circuit of i-th of two-way cuk circuit, double circuit is driven by pwm signal, and control MOSFET's opening and turning off.PWM
The dutycycle of signal obtains the meter of the euqalizing current in described i-th two-way cuk converter as battery balanced control variable
Calculate formula as follows：
Wherein, ILi1And ILi2Represent respectively by inductance Li1And Li2Euqalizing current, magnitude of current size determine charging much
It is few, Li1Represent to be connected to the inductance of the i-th batteries, L in i-th of two-way cuk converteri2Represent i-th of two-way cuk converter
In be connected to the inductance of i+1 batteries, PiThe i-th batteries in i-th of two-way cuk converter are represented to fill to i+1 batteries
Electric current efficiency of transmission when electric, Pi' represent in i-th of two-way cuk converter of table i+1 batteries to the i-th batteries charge when
Electric current efficiency of transmission, TsFor the sampling time,WithIt is the terminal voltage of i-th and i+1 batteries respectively,It is electricity
Hold average voltage, Di1Represent MOSFET pipes Qi1The Duty ratio control amount of upper pwm signal, Di2Represent MOSFET pipes Qi2Upper pwm signal
Duty ratio control amount；
Above-mentioned formula deformation obtains two MOSFET and manages each self-corresponding Duty ratio control amount Di1And Di2Calculation formula such as
Under：
According to above-mentioned formula, in known circuit on the premise of each variable, by euqalizing current ILi2Substitution can wherein be counted
Calculate and obtain two each self-corresponding Duty ratio control amount D of MOSFET pipesi1And Di2Value, with Duty ratio control amount Di1And Di2Control
Two MOSFET pipes of equalizing circuit realize the equilibrium of battery.
Described step 2) in, battery equalization system mathematical model is specially：
For n batteries, the first batteries are individually only connected with final section battery with an equalizing circuit,
Other are all connected with two equalizing circuits.
For the Duty ratio control amount D of two MOSFET pipesi1And Di2Build respective switching variable γiWith γ 'i, represent
For：
Di1(k)Di2(k)=0
Because two MOSFET pipes can not be opened, D simultaneouslyi1(k)Di2(k)=0.
NoteIt is the monomer euqalizing current at i-th (2≤i≤n-1) batteries k moment,For Section 1 battery k
The monomer euqalizing current at moment,For the monomer euqalizing current at the n-th batteries k moment；
Each monomer euqalizing current calculation formula is as follows：
Wherein, k represents the sequence number in sampling time, γiWith γ 'i(1≤i≤n) is to be directed to Duty ratio control amount D respectivelyi1With
Di2Switching variable, piRepresent i-th piece of battery to i+1 block battery current efficiency of transmission, fi1(Di1And f (k)i2(Di2(k))(1
≤ i≤n) represent the transmission electric current of two MOSFET pipes and the duty cycle relationship of pwm signal, fi1(Di1(k) i-th piece) is represented
The Duty ratio control amount D at weighing apparatus circuit k momenti1Relation between transmission electric current, fi2(Di2(k) the dutycycle control at k moment) is represented
Amount D processedi2Relation between transmission electric current, transmission electric current refers to the electric current that i-th of battery is transmitted to i+1 battery；wi1
And w (k)i2(k) (1≤i≤n-1) represents model error of the monomer euqalizing current by i-th of two-way cuk converter respectively；
By the monomer euqalizing current at the i-th batteries k momentIt is reduced to：
Balanced for ease of being carried out for lithium battery group, the present invention is set for the SOC of lithium battery, the series connection of n batteries
The battery equalization system mathematical model of battery pack be expressed as：
Z (k+1)=z (k)+dB1(k)(u1(k)+w1(k))+dB2(k)(u2(k)+w2(k))-b(k)
Wherein, u1And u (k)2(k) represent that two section cells of two-way cuk converters to input side and outlet side are defeated respectively
The euqalizing current gone out, wi1And w (k)i2(k) first, second error foreign current, B are expressed as1(k) represent to be located at input side
All MOSFET pipes each efficiency, B2(k) each efficiency of all MOSFET pipes positioned at outlet side is represented, b (k) is represented
Foreign current affecting parameters；Z (k+1) represents the state-of-charge of k+1 moment each batteries, and z (k) represents k moment each batteries
State-of-charge；
In above-mentioned formula, z (k), u1(k)、u2(k)、B1(k)、B2(k) it is expressed as with b (k)：
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
B (k)=[dIs(k) … dIs(k)]T
Wherein, γiWith γ 'iIt is to be directed to Duty ratio control amount D respectivelyi1And Di2Switching variable, piRepresent i-th piece of battery
To i+1 block battery current efficiency of transmission, pi' represent i+1 block battery to i-th piece of battery current efficiency of transmission, Is(k) represent
Foreign current；D represents auxiliary variable,T is that the control sampling time is interval, CbRepresent battery capacity；f(n-1)1(D(n-1)1
(k) the Duty ratio control amount D at the (n-1)th block balance circuit k moment) is represented(n-1)1Relation between transmission electric current, f(n-1)2
(D(n-1)2(k) the Duty ratio control amount D at the (n-1)th block balance circuit k moment) is represented(n-1)2Relation between transmission electric current, zn
(k) state-of-charge of n-th batteries at the k moment is represented.
Battery capacity C is known by pertinent literaturebDuring=3600 peace times, d is a very small constant.
Described step 3) in, for step 2) build battery balanced topological structure mathematical model and battery balanced system
Unite mathematical model, carry out Balance route is carried out using sliding mode control algorithm, calculate and obtain that two MOSFET pipe is each self-corresponding to be accounted for
Sky is than controlled quentity controlled variable Di1And Di2。
In described sliding mode control algorithm, following battery qualifications and battery balanced target are set up：
Battery qualifications：Controlled euqalizing current u in i-th of equalizing circuit1And u (k)2(k) meet：
Wherein,It is euqalizing current battery current limitation maximum allowable in two-way cuk converters, because two-way cuk
Converter is used to work under DICM states, overcharges and crosses the current versus cell put and be harmful to, so the electric current of the i-th batteries will quilt
It is maintained atIn the range of.Representing battery in two-way cuk converters allows the maximum current passed through, Is(k) represent outer
Portion's electric current；
While meeting below equation：
From above formula, ui(k) change with the change of outside electric current, not constant.
Battery balanced target：Battery balanced target is so that the SOC of lithium battery converges on a limit, two batteries it
Between state-of-charge meet equation below：
Wherein, zi(k) it is state-of-charge of i-th batteries at the k moment, to all initial value ziAnd z (0)j(0) 1 is met
≤ i, j≤n, i ≠ j, ε are receptible maximum state-of-charge deviations between battery, and k represents the moment, when τ is the balance of battery
Between.
The present invention sets up the battery limited by saturation euqalizing current by above battery qualifications and battery balanced target
Balanced sliding mode controller, enables to euqalizing current as high as possible, to improve balancing speed.
The equal of cells output is saved calculating to obtain by sliding mode control algorithm to the two of input side and outlet side respectively
Weigh electric current u1(k)、u2(k) below equation, is recycled to calculate the duty for transmitting electric current and pwm signal for obtaining two MOSFET pipes
Than relation fi1(Di1) and f (k)i2(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) duty cycle relationship f is recycledi1(Di1) and f (k)i2(Di2(k)) opposite calculate is carried out using below equation to obtain
Duty ratio control amount Di1And Di2Control each equalizing circuit：
The present invention is that in series battery, battery is with battery between any two using two-way cuk converter circuits as equal
Weigh circuit, and battery pack and equalizing circuit constitute battery to battery balanced topological structure, and which can improve equalization efficiency, reduce
The waste of energy.Lithium battery and equalizing circuit are modeled respectively, the overall model of system is obtained in conjunction with model, can be right
The stability and convergence property of whole batteries equalization methods analyze and assess accordingly.
The beneficial effects of the invention are as follows：
The present invention uses after sliding-mode control and limits scope so that balanced compensated maximum allowed current is with external electrical
Rheology rather than fixed constant value, can so prevent battery current from being limited more than it.
The present invention carries out discrete sliding mode control by the battery balanced sliding mode controller limited with saturation euqalizing current,
So there is extraordinary robustness for unknown interference, and proved by emulating, the SOC of battery in battery pack can be than it
The more rapid good convergence of his method.
The inventive method is eventually passed between the mathematical proof using Lyapunov analysis, n series connection cell
SOC gaps can converge to the scope of a very little.With conventional individually only balanced two cell differences, this algorithm can be applied
With it is more than two battery balanced, and possess good portfolio effect.
Through emulation and it is demonstrated experimentally that the present invention is designed to rapidly carry out battery equilibrium, the effectively save energy improves electricity
The pond life-span.
Brief description of the drawings
Fig. 1 is that have equalizing circuit series battery schematic diagram；
Fig. 2 is the two-way cuk transformer configurations figure of the present invention；
Fig. 3 is the inductive current curve map of two-way cuk converters；
Fig. 4 is the result figure of the sliding formwork control in this implementation, and (a) figure is the SOC value of each batteries, and (b) figure is sliding formwork control
PWM duty cycle change under system.
Embodiment
The validity of lithium battery equalization methods proposed by the present invention is proved with an example below.
1st, experimental facilities
1) battery：
Using by four (MH12210-3400mAh) lithium battery groups of NCR 18650 into battery pack tested, such as Fig. 2
It is shown.By a few wheel charge-discharge tests, the capacitance for obtaining these batteries is probably 3.1Ah and Cb=3.1 × 3600.WithBe can calculate obtain be respectively for the relevant parameter of 3.23 and 0.8948. models：
R0i=0.206 Ω, Rsi=0.0158 Ω,
Csi=12340F, Rfi=0.01509 Ω, and Cfi=1584F.
2) two-way cuk converters：
As shown in figure 1, the battery pack of 4 metasequences needs one to include 3 two-way cuk converters.Selection correlation is matched somebody with somebody
Part parameter is as follows：
Li1=Li2=100 μ H, C=470 μ F
The MOSFET pipes of NTD6416AN-1G models are driven by the PWM ripple signals of 7kHz frequencies.
Related experiment is carried out to determine the performance of two-way cuk converters.The final voltage of adjacent cell is VB1=respectively
3.93V and VB2=3.62V.The dutycycle of PWM ripples is arranged to 0.3.The current curve of inductance such as Fig. 3.
The maximum allowed current of battery is IBmax=3A.Maximum euqalizing current is set as I under DICM patternsDmax=
0.9A.Control time is T=1s.The initial SOC of each batteries of battery pack is respectively：
SOC1 (0)=74%, SOC2 (0)=82%, SOC3 (0)=71%, and SO4 (0)=80%
Set by sliding formwork control, when the SOC differences between battery are smaller than 2%, battery balanced process will stop.
For sliding formwork control control algolithm, gain is set as η=0.01, sets ξ=3
2nd, experimental result
The result of sliding formwork control such as Fig. 4.The time is 1138s required for balanced, and the sliding formwork control than proposing in the past contracts significantly
It is short.Its corresponding PWM ripples dutycycle is shown in Fig. 4.
As can be seen here, the inventive method has good portfolio effect, can effectively prevent battery current from being limited more than it, right
There is extraordinary robustness in unknown interference, balanced, the effectively save energy and raising can be carried out to battery rapidly by realizing
Battery life, significant technique effect is protruded with it.
Claims (8)
1. a kind of battery pack equilibrium method based on sliding formwork control, it is characterised in that：
1) special battery balanced topological structure is designed according to the unbalanced situation of series battery；
2) mathematical model is set up to battery balanced topological structure, and sets up battery balanced topological structure and common group of series battery
Into battery equalization system mathematical model；
3) Balance route is carried out with sliding mode controller with reference to battery equalization system mathematical model, realizes in series battery and respectively economize on electricity
Equilibrium treatment between pond.
2. a kind of battery pack equilibrium method based on sliding formwork control according to claim 1, it is characterised in that：Described step
It is rapid 1) in, the two-way cuk converter circuits as equalizing circuit are connected between two adjacent cells of series battery, and
And each equalizing circuit is all connected with a controller, between adjacent cell between equalizing circuit and its respective controller structure
Into battery balanced topological structure.
3. a kind of battery pack equilibrium method based on sliding formwork control according to claim 2, it is characterised in that：With the i-th section
The two-way cuk converters between battery and i+1 batteries (1≤i≤n-1) are used as i-th of two-way cuk converter, tool
Body circuit structure is：Including inductance Li1, inductance Li2, energy transferring capacitor device Ci, MOSFET pipes Qi1, MOSFET pipes Qi2, the pole of body two
Pipe di1With body diode di2, MOSFET pipes Qi1With body diode di1With inductance L after parallel connectioni1The i-th batteries are connected on together
Two ends, MOSFET pipes Qi2With body diode di2With inductance L after parallel connectioni2The two ends of i+1 batteries are connected on together, and energy is passed
Pass capacitor CiTwo ends are connected on inductance Li1With inductance Li2Between；So that having n-1 between the battery pack of n batteries series connection
Individual two-way cuk converters are connected wherein, and circuit with two MOSFET pipes of pwm signal drive control open with shut-off come
The discharge and recharge between two batteries is controlled, to realize the balance of voltage between two batteries.
4. a kind of battery pack equilibrium method based on sliding formwork control according to claim 1, it is characterised in that：Described step
It is rapid 2) in, the mathematical model of battery balanced topological structure is specially：
The calculation formula of euqalizing current in i-th of two-way cuk converter is as follows：
Wherein, ILi1And ILi2Represent respectively by inductance Li1And Li2Euqalizing current, Li1Represent in i-th of two-way cuk converter
It is connected to the inductance of the i-th batteries, Li2Represent to be connected to the inductance of i+1 batteries, P in i-th of two-way cuk converteriGeneration
In i-th of two-way cuk converter of table the i-th batteries to i+1 batteries charge when electric current efficiency of transmission, Pi' represent table i-th
In individual two-way cuk converters i+1 batteries to the i-th batteries charge when electric current efficiency of transmission, TsFor the sampling time,
WithIt is the terminal voltage of i-th and i+1 batteries respectively,It is capacitor averaging voltage, Di1Represent MOSFET pipes Qi1Upper PWM
The Duty ratio control amount of signal, Di2Represent MOSFET pipes Qi2The Duty ratio control amount of upper pwm signal；
Above-mentioned formula deformation obtains two MOSFET and manages each self-corresponding Duty ratio control amount Di1And Di2Calculation formula it is as follows：
According to above-mentioned formula, in known circuit on the premise of each variable, by euqalizing current ILi2Substitution, which can wherein be calculated, to be obtained
Obtain two MOSFET and manage each self-corresponding Duty ratio control amount Di1And Di2Value, with Duty ratio control amount Di1And Di2Control is balanced
Two MOSFET pipes of circuit realize the equilibrium of battery.
5. a kind of battery pack equilibrium method based on sliding formwork control according to claim 1, it is characterised in that：Described step
It is rapid 2) in, battery equalization system mathematical model is specially：
For the Duty ratio control amount D of two MOSFET pipesi1And Di2Build respective switching variable γiWith γ 'i, it is expressed as：
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Di1(k)Di2(k)=0
NoteIt is the monomer euqalizing current at i-th (2≤i≤n-1) batteries k moment,For Section 1 battery k moment
Monomer euqalizing current,For the monomer euqalizing current at the n-th batteries k moment；
Each monomer euqalizing current calculation formula is as follows：
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</msub>
<mrow>
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</msubsup>
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</msubsup>
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</msub>
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</mtd>
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</mfenced>
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</mfenced>
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<mi>I</mi>
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<mi>eq</mi>
<mi>n</mi>
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</msub>
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</mrow>
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</mrow>
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</mtd>
</mtr>
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</mrow>
Wherein, k represents the sequence number in sampling time, γiWith γ 'i(1≤i≤n) is to be directed to Duty ratio control amount D respectivelyi1And Di2's
Switching variable, piRepresent i-th piece of battery to i+1 block battery current efficiency of transmission, fi1(Di1) and f (k)i2(Di2(k))(1≤i
≤ n) represent the transmission electric current of two MOSFET pipes and the duty cycle relationship of pwm signal, fi1(Di1(k) the i-th block balance electricity) is represented
The Duty ratio control amount D at road k momenti1Relation between transmission electric current, fi2(Di2(k) the Duty ratio control amount at k moment) is represented
Di2Relation between transmission electric current, transmission electric current refers to the electric current that i-th of battery is transmitted to i+1 battery；wi1(k) and
wi2(k) (1≤i≤n-1) represents model error of the monomer euqalizing current by i-th of two-way cuk converter respectively；
By the monomer euqalizing current at the i-th batteries k momentIt is reduced to：
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</mrow>
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</mrow>
</msub>
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</msub>
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</mrow>
</mrow>
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</mrow>
The battery equalization system mathematical model of the battery pack of n batteries series connection is expressed as：
Z (k+1)=z (k)+dB1(k)(u1(k)+w1(k))+dB2(k)(u2(k)+w2(k))-b(k)
Wherein, u1And u (k)2(k) represent that two-way cuk converters save cells output to the two of input side and outlet side respectively
Euqalizing current, wi1And w (k)i2(k) first, second error foreign current, B are expressed as1(k) institute positioned at input side is represented
There are each efficiency of MOSFET pipes, B2(k) each efficiency of all MOSFET pipes positioned at outlet side is represented, b (k) represents outside
Electric current affecting parameters；Z (k+1) represents the state-of-charge of k+1 moment each batteries, and z (k) represents the charged of k moment each batteries
State；
In above-mentioned formula, z (k), u1(k)、u2(k)、B1(k)、B2(k) it is expressed as with b (k)：
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
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<mi>B</mi>
<mn>1</mn>
</msub>
<mrow>
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<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<msub>
<mi>&gamma;</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
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<mn>0</mn>
</mtd>
</mtr>
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<mtd>
<mrow>
<msub>
<mi>&gamma;</mi>
<mn>1</mn>
</msub>
<msub>
<mi>p</mi>
<mn>1</mn>
</msub>
</mrow>
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<mtd>
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</msub>
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<mo>...</mo>
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</msub>
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<mi>p</mi>
<mn>2</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
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<mn>3</mn>
</msub>
</mrow>
</mtd>
<mtd>
<mo>...</mo>
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<mtd>
<mn>0</mn>
</mtd>
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<mtr>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
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</mtd>
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</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
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<mn>0</mn>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
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</mrow>
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<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
<mrow>
<msub>
<mi>B</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
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<mtd>
<mrow>
<mo>-</mo>
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<mn>1</mn>
<mo>&prime;</mo>
</msubsup>
<msubsup>
<mi>p</mi>
<mn>1</mn>
<mo>&prime;</mo>
</msubsup>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<msubsup>
<mi>&gamma;</mi>
<mn>1</mn>
<mo>&prime;</mo>
</msubsup>
</mtd>
<mtd>
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<mo>-</mo>
<msubsup>
<mi>&gamma;</mi>
<mn>2</mn>
<mo>&prime;</mo>
</msubsup>
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<mo>&prime;</mo>
</msubsup>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<msubsup>
<mi>&gamma;</mi>
<mn>2</mn>
<mo>&prime;</mo>
</msubsup>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<msubsup>
<mi>&gamma;</mi>
<mn>3</mn>
<mo>&prime;</mo>
</msubsup>
<msubsup>
<mi>p</mi>
<mn>3</mn>
<mo>&prime;</mo>
</msubsup>
</mrow>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mo>...</mo>
</mtd>
<mtd>
<msubsup>
<mi>&gamma;</mi>
<mrow>
<mi>n</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mo>&prime;</mo>
</msubsup>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
B (k)=[dIs(k) … dIs(k)]T
Wherein, γiWith γ 'iIt is to be directed to Duty ratio control amount D respectivelyi1And Di2Switching variable, piRepresent i-th piece of battery to i-th+
1 piece of battery current efficiency of transmission, pi' represent i+1 block battery to i-th piece of battery current efficiency of transmission, Is(k) external electrical is represented
Stream；D represents auxiliary variable,T is that the control sampling time is interval, CbRepresent battery capacity；f(n-1)1(D(n-1)1(k)) table
Show the Duty ratio control amount D at the (n-1)th block balance circuit k moment(n-1)1Relation between transmission electric current, f(n-1)2(D(n-1)2(k))
Represent the Duty ratio control amount D at the (n-1)th block balance circuit k moment(n-1)2Relation between transmission electric current, zn(k) n-th is represented
State-of-charge of the batteries at the k moment.
6. a kind of battery pack equilibrium method based on sliding formwork control according to claim 1, it is characterised in that：Described step
It is rapid 3) in, for step 2) build battery balanced topological structure mathematical model and battery equalization system mathematical model, use
Sliding mode control algorithm carries out carry out Balance route, calculates and obtains two each self-corresponding Duty ratio control amount D of MOSFET pipesi1With
Di2。
7. a kind of battery pack equilibrium method based on sliding formwork control according to claim 6, it is characterised in that：Described cunning
In mould control algolithm, following battery qualifications and battery balanced target are set up：
Battery qualifications：Controlled euqalizing current u in i-th of equalizing circuit1And u (k)2(k) meet：
<mrow>
<msub>
<mi>u</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>,</mo>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>&le;</mo>
<mi>min</mi>
<mo>{</mo>
<msub>
<mi>I</mi>
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<mi>D</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
</mrow>
</msub>
<mo>,</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>I</mi>
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<mi>B</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
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<mo>-</mo>
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<mi>I</mi>
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<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
<mo>|</mo>
<mo>)</mo>
</mrow>
<mo>}</mo>
</mrow>
Wherein,It is euqalizing current battery current limitation maximum allowable in two-way cuk converters,Represent two-way
Battery allows the maximum current passed through, I in cuk converterss(k) foreign current is represented；
While meeting below equation：
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<mi>u</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
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<mo>,</mo>
<msub>
<mi>u</mi>
<mn>2</mn>
</msub>
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<mo>(</mo>
<mi>k</mi>
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<mo>&le;</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>B</mi>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
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<mo>-</mo>
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<mi>I</mi>
<mi>S</mi>
</msub>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
<mo>|</mo>
<mo>)</mo>
</mrow>
</mrow>
Battery balanced target：State-of-charge between two batteries meets equation below：
<mrow>
<mo>|</mo>
<msub>
<mi>z</mi>
<mi>i</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>z</mi>
<mi>j</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<mo>&le;</mo>
<mi>&epsiv;</mi>
<mo>,</mo>
<mo>&ForAll;</mo>
<mi>k</mi>
<mo>&GreaterEqual;</mo>
<mi>&tau;</mi>
</mrow>
Wherein, zi(k) it is state-of-charge of i-th batteries at the k moment, to all initial value ziAnd z (0)j(0) 1≤i is met,
J≤n, i ≠ j, ε are receptible maximum state-of-charge deviations between battery, and k represents the moment, and τ is the equilibration time of battery.
8. a kind of battery pack equilibrium method based on sliding formwork control according to claim 6, it is characterised in that：Passing through cunning
Mould control algolithm calculates the euqalizing current u for obtaining two section cell outputs respectively to input side and outlet side1(k)、u2(k),
Below equation is recycled to calculate the duty cycle relationship f for transmitting electric current and pwm signal for obtaining two MOSFET pipesi1(Di1(k)) and
fi2(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) duty cycle relationship f is recycledi1(Di1) and f (k)i2(Di2(k) opposite calculate) is carried out using below equation and obtains duty
Than controlled quentity controlled variable Di1And Di2Control each equalizing circuit：
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<mrow>
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</mrow>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<msub>
<mi>L</mi>
<mrow>
<mi>i</mi>
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</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
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<msub>
<mi>c</mi>
<mi>i</mi>
</msub>
</msub>
<mo>-</mo>
<msub>
<mi>V</mi>
<mrow>
<msub>
<mi>B</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>.</mo>
</mrow>
4
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Cited By (5)
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| CN107732331A (en) * | 2017-09-11 | 2018-02-23 | 浙江大学 | A kind of serial lithium battery group SOC balance control method of global optimization control |
| CN108649674A (en) * | 2018-06-05 | 2018-10-12 | 北京师范大学珠海分校 | Double-direction radio charging circuit, method and system |
| CN110297452A (en) * | 2019-07-15 | 2019-10-01 | 福州大学 | A kind of equal balance system of the adjacent type of battery group and its forecast Control Algorithm |
| CN113452108A (en) * | 2021-05-14 | 2021-09-28 | 国网浙江省电力有限公司杭州供电公司 | Device and method for active equalization hierarchical control of power battery pack |
| CN115360793A (en) * | 2022-09-15 | 2022-11-18 | 湖北亿纬动力有限公司 | Battery pack balancing method and device, battery system and storage medium |
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| CN105226744A (en) * | 2015-09-10 | 2016-01-06 | 广西大学 | A kind of power battery pack balance charge/discharge control method based on SOC and system |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107732331A (en) * | 2017-09-11 | 2018-02-23 | 浙江大学 | A kind of serial lithium battery group SOC balance control method of global optimization control |
| CN108649674A (en) * | 2018-06-05 | 2018-10-12 | 北京师范大学珠海分校 | Double-direction radio charging circuit, method and system |
| CN110297452A (en) * | 2019-07-15 | 2019-10-01 | 福州大学 | A kind of equal balance system of the adjacent type of battery group and its forecast Control Algorithm |
| CN110297452B (en) * | 2019-07-15 | 2021-11-02 | 福州大学 | Storage battery adjacent type equalization system and prediction control method thereof |
| CN113452108A (en) * | 2021-05-14 | 2021-09-28 | 国网浙江省电力有限公司杭州供电公司 | Device and method for active equalization hierarchical control of power battery pack |
| CN113452108B (en) * | 2021-05-14 | 2024-02-02 | 国网浙江省电力有限公司杭州供电公司 | Device and method for active equalization layered control of power battery pack |
| CN115360793A (en) * | 2022-09-15 | 2022-11-18 | 湖北亿纬动力有限公司 | Battery pack balancing method and device, battery system and storage medium |
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