CN112685917A - Battery equalization modeling system and method based on nonlinear efficiency model - Google Patents

Abstract

The invention provides a battery equalization modeling method based on a nonlinear efficiency model, which comprises the following steps: s1, establishing a relation between the residual battery capacity and the balance current; s2, obtaining efficiency values under different balancing currents, and nonlinear relations between the efficiency and the balancing currents, establishing energy consumed by the jth battery in a balancing period in the balancing period, and obtaining a balancing loss objective function of the bus type balancing system in the balancing process; and S3, combining the residual electricity quantity change equations of the n batteries together to obtain a state space model of the bus type equalizing system according to the structure of the bus type equalizing system, then controlling the state space model of the bus type equalizing system by utilizing model prediction control, and establishing an equalizing model of nonlinear efficiency based on a model prediction control strategy. The invention greatly reduces the solving difficulty by utilizing the fusion of the linear efficiency model and the nonlinear efficiency model, so that the model applied to the dynamic battery equalization is more practical.

Description

Battery equalization modeling system and method based on nonlinear efficiency model

Technical Field

The invention relates to the field of automatic control, in particular to a battery equalization modeling system and method based on a nonlinear efficiency model.

Background

The model predictive control essentially belongs to the interdisciplinary discipline of optimization and control, and because the Model Predictive Control (MPC) is convenient to build a model, has low requirements on the model, adopts a rolling optimization strategy and has the characteristics of better dynamic control effect and the like, the application of the model predictive control on the dynamic battery balance can improve the balance performance;

however, most of the research in the battery equalization model is based on a linear model, and little research is on the nonlinear modeling of the battery equalization circuit; the efficiency of a practical equalizer is a non-linear function of the input current and the input-output voltage of the equalizer; under the equilibrium strategy of model predictive control, a large amount of nonlinear constraints exist especially when the number of batteries and the number of prediction steps are large, and the solution of an objective function is very troublesome; therefore, a trust domain reflection algorithm can be adopted, and the solving result of the objective function under the linear efficiency model is given to a trust domain reflection algorithm solver as an initial value, so that the difficulty of the optimization process is greatly reduced.

Disclosure of Invention

The invention aims to at least solve the technical problems in the prior art, and particularly provides a battery equalization modeling system and method based on a nonlinear efficiency model.

In order to achieve the above object of the present invention, the present invention provides a battery equalization modeling system based on a nonlinear efficiency model, comprising: the system comprises a charge-discharge module, n equalizers, n batteries and an energy bus;

the first end of the 1 st battery is connected with the first end of the charge-discharge module and the first end of the 1 st equalizer, the second end of the 1 st battery is connected with the second end of the 1 st equalizer, the first end of the 2 nd battery and the first end of the 2 nd equalizer, the third end of the 1 st equalizer is connected with the negative electrode of the energy bus, and the fourth end of the 1 st equalizer is connected with the positive electrode of the energy bus;

the first end of the 2 nd battery is connected with the second end of the 1 st battery, the second end of the 1 st equalizer and the first end of the 2 nd equalizer, the second end of the 2 nd battery is connected with the first end of the 3 rd battery, the first end of the 3 rd equalizer and the second end of the 2 nd equalizer, the third end of the 2 nd equalizer is connected with the negative electrode of the energy bus, and the fourth end of the 2 nd equalizer is connected with the positive electrode of the energy bus;

the first end of the 3 rd battery is connected with the second end of the 2 nd battery, the second end of the 2 nd equalizer and the first end of the 3 rd equalizer, the second end of the 3 rd battery is connected with the first end of the 4 th battery, the first end of the 4 th equalizer and the second end of the 3 rd equalizer, the third end of the 3 rd equalizer is connected with the negative electrode of the energy bus, and the fourth end of the 3 rd equalizer is connected with the positive electrode of the energy bus;

……；

the first end of the nth battery is connected with the second end of the nth-1 battery, the second end of the nth-1 equalizer and the first end of the nth equalizer, the second end of the nth battery is connected with the second end of the nth equalizer and the second end of the charge-discharge module, the third end of the nth equalizer is connected with the negative electrode of the energy bus, and the fourth end of the nth equalizer is connected with the positive electrode of the energy bus;

n is the total number of cells and is also the total number of equalizers corresponding to the cells.

Further, each equalizer includes:

a first end of the battery is connected with a first end of an inductor L1, a second end of the inductor L1 is connected with a first end of a capacitor C1 and a first end of a switch tube Q1, a second end of the battery is connected with a first end of the inductor L3, a second end of the inductor L3 is connected with a first end of a capacitor C2 and a second end of a switch tube Q1, a second end of the capacitor C1 is connected with a first end of a switch tube Q2 and a first end of the inductor L2, a second end of the capacitor C2 is connected with a second end of the switch tube Q2 and a first end of an inductor L4, and a second end of the inductor L2 is connected with a first end of a capacitor C2 and a_busIs connected to the energy bus, and a second terminal of the inductor L4 is connected to the capacitor C_busAnd the second end of the energy bus is connected with the energy bus.

The invention also provides a battery equalization modeling method based on the nonlinear efficiency model, which comprises the following steps:

s1, obtaining the relation between the SOC of the battery and the balance current in the bus type balance system according to an ampere-hour integral method, and accordingly establishing a relation between the residual electric quantity of the battery and the balance current;

s2, according to the structure of the bus type equalizing system, obtaining efficiency values under different equalizing currents through equipment, and establishing a nonlinear relation between the efficiency and the equalizing currents, and according to the nonlinear relation, establishing energy consumed by the jth battery in an equalizing cycle in the equalizing cycle, and obtaining an equalizing loss objective function of the bus type equalizing system in the equalizing cycle;

and S3, combining the residual electricity quantity change equations of the n batteries together to obtain a state space model of the bus type equalizing system according to the structure of the bus type equalizing system, then controlling the state space model of the bus type equalizing system by utilizing model prediction control, and establishing an equalizing model of nonlinear efficiency based on a model prediction control strategy.

Further, the solving of the non-linear efficiency model, which is the equilibrium model of the non-linear efficiency based on the model predictive control strategy in S3, belongs to the non-linear optimization, and includes:

firstly, setting the transmission efficiency of an equalizer as a constant, establishing a linear model, namely a linear efficiency model, solving an optimal solution through multi-target linear programming, and assigning the optimal solution to a trust domain reflection algorithm as an initial value so as to solve the optimal solution of a nonlinear efficiency model; the problem that the calculated amount is too large to solve is solved;

most of the constraints are nonlinear constraints, so that the solution is very difficult; solving the nonlinear objective function problem with nonlinear constraints is generally called nonlinear multi-objective programming problem; in multi-target planning with a large number of nonlinear constraints, a search algorithm or a confidence domain algorithm is commonly used, and an optimal value is usually found by gradient descent or confidence radius update through a given initial value; however, for a large optimization function, the search algorithm and the trust domain algorithm have the disadvantage that if the initial value is not selected properly, the global optimum value is difficult to obtain, and the problem is well solved by the proposed method.

Further, the S1 includes:

s1-1, establishing a relation between the SOC of the jth battery and the balance current according to the relation between the SOC of the jth battery and the balance current of the jth battery in the bus type balance system, so as to obtain a relation between the battery residual capacity and the balance current;

s1-2, adding the self-loss of the battery in the equation of the relation between the battery residual capacity and the equalizing current, and setting the residual capacity of the j-th battery as x_j＝Q_j*SOC_jAnd obtaining a complete equation of the relation between the residual battery capacity and the balance current.

Further, the S1 includes:

in the bus-type equalization circuit, n represents the total number of cells,

representing the current between the jth cell and the equalizer,

representing the current between the energy bus and the jth equalizer, j e {1,2, …, n } is the battery number, and is also the equalizer number corresponding to the battery, v_jIs the voltage of the jth cell;

writing an SOC change equation of the j-th battery according to the relation between the residual capacity of the lithium ion battery and the balance current as follows:

wherein Q is_jThe capacity of the jth battery;

SOC_j(t) representing the SOC change equation of the jth battery at the moment of time t;

SOC_j(t₀) Is represented at time t₀At the moment, the SOC change equation of the j-th battery;

representing the current between the jth battery and the equalizer;

by differentiating equation (1), the following equation can be obtained:

wherein Q is_jThe capacity of the jth battery;

is SOC_jA differentiated form of (t);

representing the current between the jth battery and the equalizer;

for the completeness of the equation, adding the self-depletion of the battery in equation (2) yields the following equation:

wherein Q is_jThe capacity of the jth battery;

is SOC_jA differentiated form of (t);

τ is used to describe the self-discharge rate of the cell;

Q_jthe capacity of the jth battery;

SOC_jrepresents the percentage of the jth battery remaining capacity;

representing the current between the jth battery and the equalizer;

let the residual capacity x of the jth battery_j＝Q_j*SOC_jAnd obtaining the relation between the residual battery capacity and the balance current as follows:

wherein the content of the first and second substances,

is the remaining capacity x of the battery_jDifferentiation of (1);

τ is used to describe the self-discharge rate of the cell;

x_jthe residual capacity of the jth battery is;

representing the current between the jth battery and the equalizer;

a relationship between the remaining capacity of the battery and the equalizing current has been established so far.

Further, the S2 includes:

s2-1, for the jth equalizer, according to the nonlinear efficiency, the following equation can be obtained:

wherein the content of the first and second substances,

is the equalization efficiency between the equalizer and the battery;

indicating the jth batteryAnd the current between the equalizer;

v_jis the voltage of the jth cell;

representing the current between the energy bus and the jth equalizer;

v_busis the bus voltage;

wherein the content of the first and second substances,

representing the current between the jth battery and the equalizer;

v_jis the voltage of the jth cell;

is the efficiency of the equalization between the equalizer and the bus;

representing the current between the energy bus and the jth equalizer;

v_busis the bus voltage;

when energy is transferred from the battery to the energy bus, the input current of the equalizer is

When both the input voltage and the output voltage are constant,

only is and

(ii) related; can set

Wherein the content of the first and second substances,

representing the equilibrium current

And a nonlinear equation of relationship for efficiency; when energy is transferred from the bus to the battery, the input current of the equalizer is

When both the input voltage and the output voltage are constant,

only is and

(ii) related; can set

Wherein the content of the first and second substances,

expressed as the equilibrium current

And a nonlinear equation of relationship for efficiency;

to facilitate the expression, two variables u are redefined_j,1、u_j,2Control signals used to describe the solution to be solved; wherein u is_j,1、u_j,2The specific expression of (A) is shown as follows:

wherein u is_j,1Represents the current flowing from the energy bus to the jth equalizer;

representing the current between the energy bus and the jth equalizer;

wherein u is_j,2Represents the current flowing from the jth battery to the jth equalizer;

representing the current between the jth battery and the equalizer;

the default direction of the current is that the current flows from the bus to the equalizer and the current flows to the battery by the equalizer is positive, otherwise, the current is added with negative;

the battery balancing strategy is to achieve the purpose of SOC balancing by controlling the current flowing direction and the current flowing size between the battery and the energy bus;

when the battery is charged, the current flows into the battery through the equalizer via the bus, and the following formula can be obtained from formula (6):

wherein the content of the first and second substances,

representing the current between the jth battery and the equalizer;

is the efficiency of the equalization between the equalizer and the bus;

representing the current between the energy bus and the jth equalizer;

v_busis the bus voltage;

v_jis the voltage of the jth cell;

expressed as the equilibrium current

And a nonlinear equation of relationship for efficiency;

h(u_j,1) Represents the efficiency between the energy bus and the jth equalizer;

u_j,1represents the current flowing from the energy bus to the jth equalizer;

when the battery is discharged, the current is directly discharged from the battery, and the following formula can be obtained:

wherein the content of the first and second substances,

representing the current between the jth battery and the equalizer;

u_j,2represents the current flowing from the jth battery to the jth equalizer;

substituting equations (9) and (10) into equation (4) can yield the following equation:

wherein the content of the first and second substances,

indicates the remaining capacity x of the battery_jDifferentiation of (1);

τ is used to describe the self-discharge rate of the cell;

x_jrepresenting the residual capacity of the j-th battery;

h(u_j,1) Representing the energy bus and the jth equalizerEfficiency of the process;

v_busis the bus voltage;

u_j,1represents the current flowing from the energy bus to the jth equalizer;

v_jis the voltage of the jth cell;

u_j,2represents the current flowing from the jth battery to the jth equalizer;

s2-2, according to the above battery balancing model with non-linear efficiency, the energy consumed by the jth battery during a balancing cycle can be represented as follows:

wherein E represents the energy lost by the jth battery in the process of one balancing cycle;

t_eqrepresents an equalization period;

h(u_j,1) Represents the efficiency between the energy bus and the jth equalizer;

u_j,1represents the current flowing from the energy bus to the jth equalizer;

v_busis the bus voltage;

f(u_j,2) Is the efficiency between the jth battery and the jth equalizer;

u_j,2represents the current flowing from the jth battery to the jth equalizer;

v_jis the voltage of the jth cell;

therefore, an equalization loss objective function of the bus type equalization system in the equalization process is obtained.

Further, the S3 includes:

s3-1, combining the residual electricity quantity change equations of n batteries together to obtain a state space model of the bus type equalizing system according to the structure of the bus type equalizing system, discretizing the state space model to obtain a discrete state space model, and obtaining an equalizing loss target function and constraint of the target function in the discretization model;

s3-2, controlling the state space model of the bus type equalization system by using a model prediction control strategy, thereby obtaining a target function and a constraint condition thereof which enable equalization loss to be minimum in model prediction control, and according to the rule that the battery charge state changes along with time in the equalization process, the equalization speed is related to the area enclosed by a charge state change curve and a longitudinal axis in the equalization process, thereby combining time efficiency into the target function with minimum equalization loss.

Further, the S3-1 includes:

combining the remaining capacity change equations of the n batteries together to obtain a state space model of the bus type equalization system as shown in the following formula:

wherein the content of the first and second substances,

representing a state space model formed by combining equations of n batteries together;

A₀＝-τI_n×nis a matrix of n × n; τ is the self-discharge rate of the cell, I_n×nRepresenting an n × n identity matrix, n being the total number of cells;

x＝[x₁,x₂,…x_n]^Tis a state vector of n x 1 dimension, representing the residual capacity of all batteries in the equalizing system, x₁Indicates the remaining capacity, x, of the 1 st cell₂Indicates the remaining capacity, x, of the 2 nd battery_nRepresenting the residual capacity of the nth battery; a^TRepresenting a transpose;

u＝[u_1,1,u_1,2,u_2,1,u_2,2,…u_n,1,u_n,2,]^Tis a control input of 2n × 1 dimension, representing the control action of the equalizer on the battery, u_1,1Representing the current, u, of the energy bus flowing to the 1 st equalizer_1,2Representing the current, u, flowing from the 1 st cell to the 1 st equalizer_2,1Representing the current, u, of the energy bus flowing to the 2 nd equalizer_2,2Representing the current of the 2 nd battery to the 2 nd equalizer, u_n,1Representing the current of the energy bus flowing to the nth equalizer, u_n,2Representing the current of the nth battery flowing to the nth equalizer;

B₀the matrix for n × 2n is as follows:

wherein, h (u)_1,1) Represents the efficiency between the energy bus and the 1 st equalizer;

v_busis the bus voltage;

v₁voltage of the 1 st battery;

h(u_2,1) Represents the efficiency between the energy bus and the 2 nd equalizer;

v₂the voltage of the 2 nd battery;

h(u_n,1) Representing the efficiency between the energy bus and the nth equalizer;

v_nis the voltage of the nth cell;

discretizing the formula (13) with kt as the sampling time₀-t₀Substituting the sampling instant into equation (13) may result in the following equation:

wherein the content of the first and second substances,

representing a time of kt₀-t₀The state space model of the bus type equalization system;

x(kt₀-t₀) Representing the battery at time kt₀-t₀The remaining amount of power of;

u(kt₀-t₀) Representing the battery at time kt₀-t₀To which is subjected toControl action, i.e. the magnitude of the equalizing current;

t₀the sampling time of the discretization of the continuous state space model, and the control signal is unchanged in a sampling period;

when t is₀Sufficiently small, then equation (15) may become the following equation:

wherein x (k) represents the remaining capacity of the battery at the kth sampling time;

x (k-1) represents the remaining capacity of the battery at the k-1 th sampling point;

t₀the sampling time of the discretization of the continuous state space model, and the control signal is unchanged in a sampling period;

x (k-1) represents the remaining capacity of the battery at the k-1 th sampling point;

u (k-1) represents a control signal at the k-1 th sampling point;

the equation (16) can be simplified as shown in the following equation:

x(k)＝(I_n×n+A₀t₀)x(k-1)+B₀t₀u(k-1) (17)

wherein x (k) represents the remaining capacity of the battery at the kth sampling time;

I_n×nan identity matrix of n × n;

t₀the sampling time of the discretization of the continuous state space model, and the control signal is unchanged in a sampling period;

x (k-1) represents the remaining capacity of the battery at the k-1 th sampling point;

u (k-1) represents a control signal at the k-1 th sampling point;

thus, a discretized model of equation (13) such as equation (17) can be obtained; for convenience of expression, let A be I_n×n+A₀t₀、B＝B₀t₀Wherein A is₀＝-τI_n×nIs an n x n matrix, and tau is the self of the cellDischarge rate, I_n×nRepresenting an n × n identity matrix, B₀Is a matrix of n × 2 n; for the discretized state space model, the time when equalization is completed is K, then the equalization loss objective function in the discretized state space model can be obtained according to equation (12) as shown in the following equation:

wherein E represents the energy lost by the jth battery in the process of one balancing cycle;

k represents the time when equalization is completed;

t₀a sampling time representing a discretization of the continuous state space model;

F₀(k) the F matrix at the 0 th step of the kth sampling moment is obtained;

u (k) represents the control action of the equalizer on the battery at the k sampling moment;

v_busis the bus voltage;

h[u_1,1(k)]representing the efficiency between the energy bus and the 1 st equalizer at the kth sampling instant;

h[u_n,1(k)]representing the efficiency between the energy bus and the nth equalizer at the kth sampling instant;

v₁voltage of the 1 st battery;

f[u_1,2(k)]the efficiency between the 1 st battery and the 1 st equalizer at the kth sampling moment is shown;

v_nis the voltage of the nth cell;

f[u_1,2(k)]the efficiency between the 1 st battery and the 1 st equalizer at the kth sampling moment is shown;

f[u_n,2(k)]the efficiency between the nth battery and the nth equalizer at the kth sampling moment is shown;

for optimization problems, it can be generally considered that the constraints on the state variables are soft constraints, the constraints on the control inputs belong to hard constraints, and the following constraints exist for equation (18): formula (19) is a soft constraint that the remaining capacity of each battery is equal at the time K of completing equalization, formula (20) is a hard constraint that the total current flowing into the bus and the total current flowing out of the bus are equal to ensure the bus voltage is stable during equalization, and formula (21) is a hard constraint on the control signal;

x₁(K)＝x₂(K)＝…＝x_n(K) (19)

wherein x is₁(K) Indicating the residual capacity of the 1 st battery at the moment K of finishing the balance;

x₂(K) indicating the residual capacity of the 2 nd battery at the moment K of finishing the balance;

x_n(K) indicating the residual capacity of the nth battery at the moment K of finishing the balance;

wherein u is_j,1(k) Is the current from the bus to the equalizer at the kth sampling instant;

u_j,2(k) efficiency between the equalizer and the battery at the kth sampling instant;

u_j,2(k) is the current from the battery to the equalizer at the kth sampling instant;

v_jis the voltage of the jth cell;

v_busis the bus voltage;

u_j,1(k)×u_j,2(k)＝0 k＝0,1,...,K-1,j＝1…,n (21)

wherein u is_j,1(k) Is the current from the bus to the equalizer at the kth sampling instant;

u_j,2(k) is the current from the battery to the equalizer at the kth sampling instant;

k is the time for completing the equalization;

n means n batteries;

and establishing the discrete state space model and corresponding constraint conditions of the discrete state space model.

Further, the S3-2 includes:

controlling a state space model of the bus type balance system by using a model prediction control strategy; and (3) controlling the balance system by adopting model prediction control, and obtaining the prediction state in the prediction step length according to the formula (17) as follows:

x(k+1|k)＝Ax(k)+Bu(k) (22)

the state for the next time is as follows:

x(k+2|k)＝Ax(k+1)+Bu(k+1) (23)

substituting equation (22) into equation (23) yields the following equation:

x(k+2|k)＝A²x(k)+ABu(k)+Bu(k+1) (24)

where u (k) means the control signal at the kth sampling instant, u (k +1) means the control signal at the (k +1) th sampling instant, and a ═ I_n×n+A₀t₀，B＝B₀t₀Wherein A is₀＝-τI_n×nIs a matrix of n × n, τ is the self-discharge rate of the cell, I_n×nRepresenting an n × n identity matrix, B₀Is a matrix of n × 2n, t₀Is the sampling time of the discretization of the continuous state space model; the step size of the model predictive control is in fact the time interval t between adjacent moments₀(ii) a x (k) and x (k +1) respectively represent the residual capacity of the battery at the k sampling moment and the residual capacity of the battery at the k +1 sampling moment; x (k +1| k) represents the residual capacity of the battery predicted in the step 1 at the k-th sampling moment, and x (k +2| k) represents the residual capacity of the battery predicted in the step 2 at the k-th sampling moment; similar iterations can result in the following prediction matrices:

wherein x (k +1| k) is the predicted state of step 1 at the kth sampling instant; x (k +2| k) is the predicted state of step 2 at the kth sampling instant; x (k + N | k) is the prediction state of the Nth step at the k sampling moment, namely the prediction step length is N; (.)²Represents the square, (.)^NDenotes the power of N, x (k + i | k) is inInterval kt₀The prediction state of the step i at the moment; u (k + i | k) is at time kt₀Inputting the prediction of the ith step at the moment;

b (k | k), u (k | k), B (k + N-1| k) are equations derived from the above equations:

from equation (13), u ═ u can be obtained_1,1,u_1,2,u_2,1,u_2,2,…u_n,1,u_n,2,]^TU (k | k) is the control input at the kth sampling moment, u (k +1| k) is the prediction input at the kth sampling moment and step 1; u (k + N-1| k) is the prediction input at step N-1 at the kth sampling instant;

represented by formula (17), wherein B is B₀t₀(ii) a From equation (14) the matrices B and h (u) can be seen_1,1)、h(u_2,1)…h(u_n,1) (ii) related; so the matrices B are also summed with u ═ u_1,1,u_1,2,u_2,1,u_2,2,…u_n,1,u_n,2,]^TTherefore, B (k | k) is a matrix obtained by substituting u (k | k) into the B matrix at the k-th sampling time; b (k + i | k) is a matrix obtained by substituting u (k + i | k) into the B matrix when predicting i steps at the kth sampling moment; b (k + N-1| k) is a matrix obtained by substituting u (k + N-1| k) into the B matrix when predicting the step N-1 at the kth sampling moment;

wherein k represents the kth sampling instant; n is the prediction step size, expressed for simplicity as:

wherein the content of the first and second substances,

for convenience of the following description, the following redefinitions are made; wherein the input variable matrix u (k) is a matrix of dimension (2 × N,1), the state variable X (k +1) is a matrix of dimension (N × N,1), and f (k) is a row vector of dimension (1,2 × N);

U(k)＝[u(k|k),u(k+1|k),…,u(k+N-1|k)]^T (27)

X(k+1)＝[x(k+1|k),x(k+2|k),…,x(k+N|k)]^T (28)

F(k)＝[F₀(k|k),F₀(k+1|k),…,F₀(k+N-1|k)] (29)

wherein, F₀(k | k) denotes the matrix F, F at the prediction of step 0 at the k-th sampling instant₀(k +1| k) denotes the F matrix at the kth sampling instant during the 1 st prediction, F₀(k + N-1| k) represents the F matrix at the prediction of step N-1 at the kth sampling instant^TRepresenting a transpose; in order to minimize the loss during equalization, i.e., minimize equation (18); in the model predictive control strategy, it is equivalent to minimizing the loss within the whole prediction step; the objective function for minimizing the equalization loss in model predictive control can be obtained as follows:

mint₀F(k)U(k) (30)

t₀is the time interval between adjacent sampling instants of the discretization of the continuous state space model, f (k) is a row vector of dimension (1,2 × N), the variable matrix u (k) is a matrix of dimension (2 × N, 1);

meanwhile, the constraint of the discrete state space model under the model prediction control strategy can be obtained; as shown in equations (31) (32) (33) (34) (35); where equation (31) is the range limit for the input variable; equation (32) is the range limit for the state variables; equation (33) is the constraint that the current flowing into the bus is equal to the current flowing out of the bus in one equalization period; equation (34) is the limit for the battery charge to be equal after the equalization process is over; formula (35) is a constraint that the control signal has only one direction at a certain moment in the predicted step length;

0≤U(k)≤i^m (31)

x^l≤X(k+1)≤x^u (32)

x₁(k+N|k)＝x₂(k+N|k)＝…＝x_n(k+N|k) (34)

u_j,1(k+h|k)u_j,2(h|k)＝0 h＝0,1,…N-1,j＝1,…,n (35)

wherein i^mIs the maximum value of the input variable; x is the number of^l、x^uRespectively the minimum residual capacity and the maximum residual capacity allowed by the battery;

f[u_j,2(k+h|k)]the prediction efficiency of the h step between the jth battery and the jth equalizer at the kth sampling moment is shown; u. of_j,1(k + h | k) represents the prediction of the h step of the bus to equalizer current at the kth sample time; u. of_j,2(k + h | k) represents the current prediction of the h step between the jth battery and the jth equalizer at the kth sampling instant;

k represents the sampling time, j represents the j-th battery, N represents the total number of batteries, N represents the predicted step length, h represents the predicted step number at the k-th sampling time, v_busIs the bus voltage, v_jIs the voltage of the jth cell;

x₁(k + N | k) represents the remaining capacity of the 1 st battery at the k sampling moment when predicting N steps, x₂(k + N | k) represents the remaining capacity of the 2 nd battery at the k sampling moment when predicting N steps, x_n(k + N | k) represents the remaining capacity of the nth battery at the kth sampling moment when the nth battery predicts the N steps;

according to the rule that the state of charge of the battery changes along with time in the balancing process, the balancing speed is related to the area enclosed by a state of charge change curve and a longitudinal axis in the balancing process, and when the enclosed area is smaller, the balancing time is shorter, and the speed is faster, a target function related to time efficiency can be obtained as shown in the following formula:

wherein, beta is a weight coefficient, x (K +1) is the residual capacity of the battery at the (K +1) th sampling moment, K is the moment of completing equalization, K is the kth sampling moment, M₀＝[m₁,m₂,…,m_n]Wherein m is_jThe value of (j ═ 1,2 … n) is shown in the following formula：

M₀Is a defined coefficient matrix, m_nThe residual capacity of the nth battery is equal to the average residual capacity of the n batteries, and if the residual capacity of the nth battery is greater than the average residual capacity of the n batteries, m is_nIs 1, otherwise is-1; m is_jThe residual capacity of the j-th battery is equal to the average residual capacity of the j-th battery, and if the residual capacity of the j-th battery is larger than the average residual capacity of the j-th battery, the m_jIs 1, otherwise is-1; x is the number of_j、x_eqRespectively the residual capacity of the j-th battery and the average residual capacity of the n batteries;

according to the prediction step size of N, another coefficient matrix M ═ M₀,…,M₀]_(1,N×n)The objective function related to time efficiency can be obtained as shown in the following equation:

minβMX(k+1) (38)

wherein N is the total number of cells, β is a weight coefficient, and X (k +1) is a matrix with dimension (N × N, 1);

adding equation (30) to equation (38) results in a final objective function of time efficiency and loss efficiency, as shown in the following equation:

mint₀F(k)U(k)+βMX(k+1) (39)

the objective function can be reduced to min (F (k) t by the equations (26) and (39)₀+ β M (k) S (U) (k) +. β MRx (k), where t₀Is the interval duration between adjacent sampling points of the discretization of the continuous state space model, f (k) is a row vector with dimension (1,2 × N), the variable matrix u (k) is a matrix with dimension (2 × N,1), β is a weight coefficient, the state variable X (k +1) is a matrix with dimension (N × N,1), and since β mrx (k) belongs to a constant independent of the input u (k), the objective function can be simplified as shown in the following equation:

min(F(k)t₀+βMS)U(k) (40)

thus, an objective function of the equilibrium model based on the nonlinear efficiency of the model predictive control strategy and a constraint condition thereof are obtained.

In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:

1. under a model prediction control strategy, a nonlinear relation between the efficiency of an equalizer and an equalizing current is considered to model a bus type equalizing circuit, so that the model of the bus type equalizing circuit is more practical;

2. and (3) solving the multi-target nonlinear optimization problem, and taking the result of the linear model as the initial value of the nonlinear model optimization by utilizing the fusion of the linear efficiency model and the nonlinear efficiency model. The solving difficulty is greatly reduced.

Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention;

drawings

The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1 is a schematic diagram of a single improved bussed bi-directional Cuk circuit of the present invention;

FIG. 2 is a block diagram of a bus-based equalization system architecture of the present invention;

FIG. 3 is a graph of a non-linear function between equalization efficiency and equalization current of the present invention;

FIG. 4 is a graph of state of charge of a battery of the present invention over time;

FIG. 5 is a flowchart of the overall algorithm of the present invention;

FIG. 6 is a flow chart under the model predictive control strategy of the present invention;

FIG. 7 is a SOC curve under the model predictive control equalization strategy of the present invention.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout; the embodiments described below with reference to the drawings are illustrative only for the purpose of illustrating the invention and are not to be construed as limiting the invention;

in the description of the present invention, it is to be understood that the terms "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, and are used merely for convenience of description and for simplicity of description, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, are not to be construed as limiting the present invention.

In the description of the present invention, unless otherwise specified and limited, it is to be noted that the terms "mounted," "connected," and "connected" are to be construed broadly, and can be, for example, a mechanical or electrical connection, a communication between two elements, a direct connection, or an indirect connection via an intermediate medium, and the specific meaning of the terms can be understood by those skilled in the art according to specific situations.

FIG. 1 shows a single improved bussed bi-directional Cuk circuit diagram structure, namely the equalizer portion of FIG. 2: a first end of the battery is connected with a first end of an inductor L1, a second end of the inductor L1 is connected with a first end of a capacitor C1 and a first end of a switch tube Q1, a second end of the battery is connected with a first end of the inductor L3, a second end of the inductor L3 is connected with a first end of a capacitor C2 and a second end of a switch tube Q1, a second end of the capacitor C1 is connected with a first end of a switch tube Q2 and a first end of the inductor L2, a second end of the capacitor C2 is connected with a second end of the switch tube Q2 and a first end of an inductor L4, and a second end of the inductor L2 is connected with a first end of a capacitor C2 and a_busIs connected to the energy bus, and a second terminal of the inductor L4 is connected to the capacitor C_busAnd the second end of the energy bus is connected with the energy bus.

Fig. 2 shows a bus-based equalization system obtained by a cell-pack-cell method, in which a battery with a high state of charge is charged by an equalizer through a bus to a battery with a lower state of charge. The bus here mainly serves as an energy schedule. According to the remaining capacity of the batteryAnd the balance current, obtaining a relation formula of the residual capacity of the battery and the balance current, wherein Q is shown in the following formula_jThe capacity of the jth battery.

Therein, SOC_j(t) represents the SOC variation equation of the j-th battery at the time t,

is SOC_jA differentiated form of (t);

representing the current between the jth battery and the equalizer;

in the above equation, plus the self-loss of the cell, the following equation can be obtained, where τ is used to describe the self-discharge rate of the cell, and τ is a very small number.

Q SOC in the above formula_jThe remaining capacity of the battery. Let the residual capacity x of the jth battery_j＝Q_j*SOC_jWherein, SOC_jRepresents the percentage of the jth battery remaining capacity; the relationship between the remaining battery capacity and the balance current can be obtained as shown in the following formula:

fig. 3 shows a non-linear function between equalization efficiency and equalization current. Can be measured using a dedicated device and then a function fit is used to obtain a non-linear function between the equalizer efficiency and the equalizer current. Wherein the relationship between equalizer to battery current and equalizer efficiency is shown as:

y₁＝-0.0002x₁ ⁴+0.0043x₁ ³-0.0317x₁ ²+0.0897x₁+0.8113

the relationship between bus to equalizer current and equalizer efficiency is shown as follows:

y₂＝0.0003x₂ ⁴-0.0038x₂ ³-0.0019x₂ ²+0.0949x₂+0.6878

fig. 4 shows a graph of the state of charge of a battery over time. The upper graph is a plot of the SOC of the cell over time in a standard cell balancing problem. In the same battery state, it is apparent that the equalization time t indicated by the broken line_eq1Less than the equalisation time t indicated by the solid line_eq2. The essence of the method is that the area enclosed by the dotted line and the coordinate axes is smaller than the area enclosed by the solid line and the coordinate axes. From the principle of minimum area and minimum time, the objective function related to time efficiency can be obtained as shown in the following formula:

wherein, beta is a weight coefficient, x (K +1) is the residual capacity of the battery at the (K +1) th sampling moment, K is the moment of completing equalization, K is the kth sampling moment, M₀＝[m₁,m₂,…,m_n]Wherein m is_jThe value of (j ═ 1,2 … n) is shown by the following formula:

since the prediction step is N, another coefficient matrix M is [ M ═ M₀,…,M₀]_(1,N×n)The objective function related to time efficiency can be obtained as shown in the following equation:

minβMX(k+1)

where N is the total number of cells, β is a weight coefficient, and X (k +1) is a matrix with dimension (N × N, 1).

Fig. 5 shows the present inventionAnd (3) an explicit overall algorithm flow chart. In order to solve the problem that the calculated amount is too large to solve, the invention firstly sets the transmission efficiency of the equalizer as a constant, thereby establishing a linear model and solving the optimal solution u through multi-objective linear programming₀And then assigning the optimal solution to a trust domain reflection algorithm of a discrete state space model of the nonlinear equilibrium system as an initial value, thereby solving the optimal solution u of the nonlinear efficiency model₀. The solving difficulty of the confidence domain reflection algorithm can be greatly reduced by utilizing the fusion of the linear model and the nonlinear model.

Fig. 6 shows a specific algorithm flow chart of the model-based prediction strategy. The key of the model predictive control is to use the first control action in the optimal solution as the input of the current control object. In fact, in the next sampling period, the measured value at the next time is used again, and the measured value at the next time is used for solving the control input at the next time, so that the model predictive control has the function of feedback correction.

S-A, initializing A sampling time K to be 0, and setting the time K for completing the equalization to be K;

S-B, obtaining an optimal value u according to a linear model₀；，

S-C, reaction of u₀As an initial value of the nonlinear multi-objective optimization;

S-D, solving the problem of multi-target nonlinear programming under the constraint condition to obtain an optimal solution U (k), wherein U (k) is an input variable matrix;

S-E, the value of k is equal to the last k plus 1;

S-F, taking the first control action in the optimal solution U (k) as input;

S-G, judging whether K is less than or equal to K, if so, skipping to execute S-D; if not, executing S-H;

and S-H, finishing.

FIG. 7 shows a simulation diagram of a bus-based equalization model solution for nonlinear efficiency under a model predictive control strategy. The selected simulation parameters are: the number of cells n is 5, and the sampling time of the discretization of the continuous state space model, namely the interval time t between two adjacent sampling moments₀30, prediction step N100, electricityCell self-discharge rate τ 10^-8And the capacity Q of the battery is [ 20; 20; 20; 20; 20]X 3600, initial remaining capacity x of battery₀＝[0.45；0.51；0.55；0.57；0.65]X 20X 3600, lowest state of charge SOC of battery_min0.3, maximum state of charge SOC of battery_maxVoltage v of battery 0.7_j＝[3.0；3.1；3.3；3.4；3.2]Bus voltage v_bus＝8。

In the figure, the upper half and the lower half represent SOC equalization results when the weighting coefficients of the equalization speed are β 0.01 and β 0, respectively. As can be seen from the figure, when the equalization speed weight coefficient β is 0, equalization is achieved at a time of 3000 s. When the weighting coefficient β of the equalizing speed is 0.01, that is, the equalizing speed efficiency is considered in the objective function, and only about 1050s is needed to achieve equalization.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (9)

1. A battery equalization modeling system based on a nonlinear efficiency model is characterized by comprising: the system comprises a charge-discharge module, n equalizers, n batteries and an energy bus;

the first end of the 1 st battery is connected with the first end of the charge-discharge module and the first end of the 1 st equalizer, the second end of the 1 st battery is connected with the second end of the 1 st equalizer, the first end of the 2 nd battery and the first end of the 2 nd equalizer, the third end of the 1 st equalizer is connected with the negative electrode of the energy bus, and the fourth end of the 1 st equalizer is connected with the positive electrode of the energy bus;

the first end of the 2 nd battery is connected with the second end of the 1 st battery, the second end of the 1 st equalizer and the first end of the 2 nd equalizer, the second end of the 2 nd battery is connected with the first end of the 3 rd battery, the first end of the 3 rd equalizer and the second end of the 2 nd equalizer, the third end of the 2 nd equalizer is connected with the negative electrode of the energy bus, and the fourth end of the 2 nd equalizer is connected with the positive electrode of the energy bus;

the first end of the 3 rd battery is connected with the second end of the 2 nd battery, the second end of the 2 nd equalizer and the first end of the 3 rd equalizer, the second end of the 3 rd battery is connected with the first end of the 4 th battery, the first end of the 4 th equalizer and the second end of the 3 rd equalizer, the third end of the 3 rd equalizer is connected with the negative electrode of the energy bus, and the fourth end of the 3 rd equalizer is connected with the positive electrode of the energy bus;

……；

the first end of the nth battery is connected with the second end of the nth-1 battery, the second end of the nth-1 equalizer and the first end of the nth equalizer, the second end of the nth battery is connected with the second end of the nth equalizer and the second end of the charge-discharge module, the third end of the nth equalizer is connected with the negative electrode of the energy bus, and the fourth end of the nth equalizer is connected with the positive electrode of the energy bus;

n is the total number of cells and is also the total number of equalizers corresponding to the cells.

2. The nonlinear efficiency model-based battery equalization modeling system of claim 1 wherein each equalizer comprises:

a first terminal of the battery is connected to a first terminal of the inductor L1, a second terminal of the inductor L1 is connected to a first terminal of the capacitor C1 and a first terminal of the switching tube Q1, a second terminal of the battery is connected to a first terminal of the inductor L3, a second terminal of the inductor L3 is connected to a first terminal of the capacitor C2The second end of the switch tube Q1 is connected, the second end of the capacitor C1 is connected with the first end of the switch tube Q2 and the first end of the inductor L2, the second end of the capacitor C2 is connected with the second end of the switch tube Q2 and the first end of the inductor L4, and the second end of the inductor L2 is connected with the capacitor C2_busIs connected to the energy bus, and a second terminal of the inductor L4 is connected to the capacitor C_busAnd the second end of the energy bus is connected with the energy bus.

3. A battery equalization modeling method based on a nonlinear efficiency model is characterized by comprising the following steps:

s1, obtaining the relation between the SOC of the battery and the balance current in the bus type balance system according to an ampere-hour integral method, and accordingly establishing a relation between the residual electric quantity of the battery and the balance current;

s2, according to the structure of the bus type equalizing system, obtaining efficiency values under different equalizing currents through equipment, and establishing a nonlinear relation between the efficiency and the equalizing currents, and according to the nonlinear relation, establishing energy consumed by the jth battery in an equalizing cycle in the equalizing cycle, and obtaining an equalizing loss objective function of the bus type equalizing system in the equalizing cycle;

and S3, combining the residual electricity quantity change equations of the n batteries together to obtain a state space model of the bus type equalizing system according to the structure of the bus type equalizing system, then controlling the state space model of the bus type equalizing system by utilizing model prediction control, and establishing an equalizing model of nonlinear efficiency based on a model prediction control strategy.

4. The battery equalization modeling method based on nonlinear efficiency model according to claim 3, wherein the solving of the nonlinear efficiency model based on nonlinear efficiency of model predictive control strategy in S3 belongs to nonlinear optimization, and comprises:

the transmission efficiency of the equalizer is set as a constant, a linear model, namely a linear efficiency model, is established, an optimal solution is solved through multi-objective linear programming, and the optimal solution is assigned to a trust domain reflection algorithm to be used as an initial value, so that the optimal solution of the nonlinear efficiency model is solved.

5. The battery equalization modeling method based on the nonlinear efficiency model according to claim 3, wherein the S1 includes:

s1-1, establishing a relation between the SOC of the jth battery and the balance current according to the relation between the SOC of the jth battery and the balance current of the jth battery in the bus type balance system, so as to obtain a relation between the battery residual capacity and the balance current;

s1-2, adding the self-loss of the battery in the equation of the relation between the battery residual capacity and the equalizing current, and setting the residual capacity of the j-th battery as x_j＝Q_j*SOC_jObtaining a complete equation of the relation between the residual battery capacity and the balance current;

writing an SOC change equation of the j-th battery according to the relation between the residual capacity of the lithium ion battery and the balance current as follows:

wherein Q is_jThe capacity of the jth battery;

SOC_j(t) representing the SOC change equation of the jth battery at the moment of time t;

SOC_j(t₀) Is represented at time t₀At the moment, the SOC change equation of the j-th battery;

representing the current between the jth battery and the equalizer;

by differentiating equation (1), the following equation can be obtained:

wherein Q is_jThe capacity of the jth battery;

is SOC_jA differentiated form of (t);

representing the current between the jth battery and the equalizer;

for the completeness of the equation, adding the self-depletion of the battery in equation (2) yields the following equation:

wherein Q is_jThe capacity of the jth battery;

is SOC_jA differentiated form of (t);

τ is used to describe the self-discharge rate of the cell;

Q_jthe capacity of the jth battery;

SOC_jrepresents the percentage of the jth battery remaining capacity;

representing the current between the jth battery and the equalizer;

let the residual capacity x of the jth battery_j＝Q_j*SOC_jAnd obtaining the relation between the residual battery capacity and the balance current as follows:

wherein the content of the first and second substances,

is the remaining capacity x of the battery_jDifferentiation of (1);

τ is used to describe the self-discharge rate of the cell;

x_jthe residual capacity of the jth battery is;

representing the current between the jth battery and the equalizer;

a relationship between the remaining capacity of the battery and the equalizing current has been established so far.

6. The battery equalization modeling method based on the nonlinear efficiency model according to claim 3, wherein the S2-1 comprises:

wherein the content of the first and second substances,

representing the current between the jth battery and the equalizer;

v_jis the voltage of the jth cell;

is the efficiency of the equalization between the equalizer and the bus;

representing the current between the energy bus and the jth equalizer;

v_busis the bus voltage;

when energy is transferred from the battery to the energy bus, the input current of the equalizer is

When both the input voltage and the output voltage are constant,

only is and

(ii) related; setting up

Wherein the content of the first and second substances,

representing the equilibrium current

And a nonlinear equation of relationship for efficiency; when energy is transferred from the bus to the battery, the input current of the equalizer is

When both the input voltage and the output voltage are constant,

only is and

(ii) related; can set

Wherein the content of the first and second substances,

expressed as the equilibrium current

And a nonlinear equation of relationship for efficiency;

to facilitate the expression, two variables u are redefined_j,1、u_j,2Control signals used to describe the solution to be solved; wherein u is_j,1、u_j,2The specific expression of (A) is shown as follows:

wherein u is_j,1Represents the current flowing from the energy bus to the jth equalizer;

representing the current between the energy bus and the jth equalizer;

wherein u is_j,2Represents the current flowing from the jth battery to the jth equalizer;

representing the current between the jth battery and the equalizer;

the default direction of the current is that the current flows from the bus to the equalizer and the current flows to the battery by the equalizer is positive, otherwise, the current is added with negative;

the battery balancing strategy is to achieve the purpose of SOC balancing by controlling the current flowing direction and the current flowing size between the battery and the energy bus;

when the battery is charged, the current flows into the battery through the equalizer via the bus, and the following formula can be obtained from formula (6):

wherein the content of the first and second substances,

representing the current between the jth battery and the equalizer;

is the efficiency of the equalization between the equalizer and the bus;

representing the current between the energy bus and the jth equalizer;

v_busis the bus voltage;

v_jis the voltage of the jth cell;

expressed as the equilibrium current

And a nonlinear equation of relationship for efficiency;

h(u_j,1) Represents the efficiency between the energy bus and the jth equalizer;

u_j,1representing the current flowing from the energy bus to the jth equalizer.

7. The battery equalization modeling method based on the nonlinear efficiency model according to claim 3, wherein the S3 includes:

s3-1, combining the residual electricity quantity change equations of n batteries together to obtain a state space model of the bus type equalizing system according to the structure of the bus type equalizing system, discretizing the state space model to obtain a discrete state space model, and obtaining an equalizing loss target function and constraint of the target function in the discretization model;

s3-2, controlling the state space model of the bus type equalization system by using a model prediction control strategy, thereby obtaining a target function and a constraint condition thereof which enable equalization loss to be minimum in model prediction control, and according to the rule that the battery charge state changes along with time in the equalization process, the equalization speed is related to the area enclosed by a charge state change curve and a longitudinal axis in the equalization process, thereby combining time efficiency into the target function with minimum equalization loss.

8. The battery equalization modeling method based on the nonlinear efficiency model according to claim 7, wherein the S3-1 comprises:

combining the remaining capacity change equations of the n batteries together to obtain a state space model of the bus type equalization system as shown in the following formula:

wherein the content of the first and second substances,

representing a state space model formed by combining equations of n batteries together;

A₀＝-τI_n×nis a matrix of n × n; τ is the self-discharge rate of the cell, I_n×nRepresenting an n × n identity matrix, n being the total number of cells;

x＝[x₁,x₂,…x_n]^Tis a state vector of n x 1 dimension, representing the residual capacity of all batteries in the equalizing system, x₁Indicates the remaining capacity, x, of the 1 st cell₂Indicates the remaining capacity, x, of the 2 nd battery_nRepresenting the residual capacity of the nth battery; a^TRepresenting a transpose;

u＝[u_1,1,u_1,2,u_2,1,u_2,2,…u_n,1,u_n,2,]^Tis a control input of 2n x 1 dimensions,represents the control action of the equalizer on the battery, u_1,1Representing the current, u, of the energy bus flowing to the 1 st equalizer_1,2Representing the current, u, flowing from the 1 st cell to the 1 st equalizer_2,1Representing the current, u, of the energy bus flowing to the 2 nd equalizer_2,2Representing the current of the 2 nd battery to the 2 nd equalizer, u_n,1Representing the current of the energy bus flowing to the nth equalizer, u_n,2Representing the current of the nth battery flowing to the nth equalizer;

B₀the matrix for n × 2n is as follows:

wherein, h (u)_1,1) Represents the efficiency between the energy bus and the 1 st equalizer;

v_busis the bus voltage;

v₁voltage of the 1 st battery;

h(u_2,1) Represents the efficiency between the energy bus and the 2 nd equalizer;

v₂the voltage of the 2 nd battery;

h(u_n,1) Representing the efficiency between the energy bus and the nth equalizer;

v_nis the voltage of the nth cell;

discretizing the formula (13) with kt as the sampling time₀-t₀Substituting the sampling instant into equation (13) may result in the following equation:

wherein the content of the first and second substances,

representing a time of kt₀-t₀The state space model of the bus type equalization system;

x(kt₀-t₀) Representing the battery at time kt₀-t₀The remaining amount of power of;

u(kt₀-t₀) Representing the battery at time kt₀-t₀The magnitude of the balancing current;

t₀the sampling time of the discretization of the continuous state space model, and the control signal is unchanged in a sampling period;

when t is₀Sufficiently small, then equation (15) may become the following equation:

wherein x (k) represents the remaining capacity of the battery at the kth sampling time;

x (k-1) represents the remaining capacity of the battery at the k-1 th sampling point;

t₀the sampling time of the discretization of the continuous state space model, and the control signal is unchanged in a sampling period;

x (k-1) represents the remaining capacity of the battery at the k-1 th sampling point;

u (k-1) represents a control signal at the k-1 th sampling point;

the equation (16) can be simplified as shown in the following equation:

x(k)＝(I_n×n+A₀t₀)x(k-1)+B₀t₀u(k-1) (17)

wherein x (k) represents the remaining capacity of the battery at the kth sampling time;

I_n×nan identity matrix of n × n;

t₀the sampling time of the discretization of the continuous state space model, and the control signal is unchanged in a sampling period;

x (k-1) represents the remaining capacity of the battery at the k-1 th sampling point;

u (k-1) represents a control signal at the k-1 th sampling point;

thus, the discretization model of equation (13) can be obtainedThe type is shown as formula (17); a ═ I_n×n+A₀t₀、B＝B₀t₀Wherein A is₀＝-τI_n×nIs a matrix of n × n, τ is the self-discharge rate of the cell, I_n×nRepresenting an n × n identity matrix, B₀Is a matrix of n × 2 n; for the discretized state space model, the time when equalization is completed is K, and the equalization loss objective function in the discretized state space model can be obtained as shown in the following formula:

wherein E represents the energy lost by the jth battery in the process of one balancing cycle;

k represents the time when equalization is completed;

t₀a sampling time representing a discretization of the continuous state space model;

F₀(k) the F matrix at the 0 th step of the kth sampling moment is obtained;

u (k) represents the control action of the equalizer on the battery at the k sampling moment;

v_busis the bus voltage;

h[u_1,1(k)]representing the efficiency between the energy bus and the 1 st equalizer at the kth sampling instant;

h[u_n,1(k)]representing the efficiency between the energy bus and the nth equalizer at the kth sampling instant;

v₁voltage of the 1 st battery;

f[u_1,2(k)]the efficiency between the 1 st battery and the 1 st equalizer at the kth sampling moment is shown;

v_nis the voltage of the nth cell;

f[u_1,2(k)]the efficiency between the 1 st battery and the 1 st equalizer at the kth sampling moment is shown;

f[u_n,2(k)]the efficiency between the nth battery and the nth equalizer at the kth sampling moment is shown;

the constraints on the state variables are soft constraints, the constraints on the control inputs belong to hard constraints, and for equation (18) the following constraints exist: formula (19) is a soft constraint that the remaining capacity of each battery is equal at the time K of completing equalization, formula (20) is a hard constraint that the total current flowing into the bus and the total current flowing out of the bus are equal to ensure the bus voltage is stable during equalization, and formula (21) is a hard constraint on the control signal;

x₁(K)＝x₂(K)＝…＝x_n(K) (19)

wherein x is₁(K) Indicating the residual capacity of the 1 st battery at the moment K of finishing the balance;

x₂(K) indicating the residual capacity of the 2 nd battery at the moment K of finishing the balance;

x_n(K) indicating the residual capacity of the nth battery at the moment K of finishing the balance;

wherein u is_j,1(k) Is the current from the bus to the equalizer at the kth sampling instant;

u_j,2(k) efficiency between the equalizer and the battery at the kth sampling instant;

u_j,2(k) is the current from the battery to the equalizer at the kth sampling instant;

v_jis the voltage of the jth cell;

v_busis the bus voltage;

u_j,1(k)×u_j,2(k)＝0 k＝0,1,...,K-1,j＝1…,n (21)

wherein u is_j,1(k) Is the current from the bus to the equalizer at the kth sampling instant;

u_j,2(k) is the current from the battery to the equalizer at the kth sampling instant;

k is the time for completing the equalization;

n means n batteries;

and establishing the discrete state space model and corresponding constraint conditions of the discrete state space model.

9. The battery equalization modeling method based on the nonlinear efficiency model according to claim 7, wherein the S3-2 comprises:

controlling a state space model of the bus type balance system by using a model prediction control strategy; and (3) controlling the balance system by adopting model prediction control, and obtaining the prediction state in the prediction step length according to the formula (17) as follows:

x(k+1|k)＝Ax(k)+Bu(k) (22)

the state for the next time is as follows:

x(k+2|k)＝Ax(k+1)+Bu(k+1) (23)

substituting equation (22) into equation (23) yields the following equation:

x(k+2|k)＝A²x(k)+ABu(k)+Bu(k+1) (24)

where u (k) means the control signal at the kth sampling instant, u (k +1) means the control signal at the (k +1) th sampling instant, and a ═ I_n×n+A₀t₀，B＝B₀t₀Wherein A is₀＝-τI_n×nIs a matrix of n × n, τ is the self-discharge rate of the cell, I_n×nRepresenting an n × n identity matrix, B₀Is a matrix of n × 2n, t₀Is the sampling time of the discretization of the continuous state space model; the step size of the model predictive control is in fact the time interval t between adjacent moments₀(ii) a x (k) and x (k +1) respectively represent the residual capacity of the battery at the k sampling moment and the residual capacity of the battery at the k +1 sampling moment; x (k +1| k) represents the residual capacity of the battery predicted in the step 1 at the k-th sampling moment, and x (k +2| k) represents the residual capacity of the battery predicted in the step 2 at the k-th sampling moment; similar iterations can result in the following prediction matrices:

wherein x (k +1| k) is the predicted state of step 1 at the kth sampling instant; x (k +2| k) is the predicted state of step 2 at the kth sampling instant; x (k + N | k) is the prediction state of the Nth step at the k sampling moment, namely the prediction step length is N; (.)²Represents the square, (.)^NRepresenting the power of N, x (k + i | k) being at time kt₀The prediction state of the step i at the moment; u (k + i | k) is at time kt₀Inputting the prediction of the ith step at the moment;

b (k | k), u (k | k), B (k + N-1| k) are equations derived from the above equations:

from equation (13), u ═ u can be obtained_1,1,u_1,2,u_2,1,u_2,2,…u_n,1,u_n,2,]^TU (k | k) is the control input at the kth sampling moment, u (k +1| k) is the prediction input at the kth sampling moment and step 1; u (k + N-1| k) is the prediction input at step N-1 at the kth sampling instant;

represented by formula (17), wherein B is B₀t₀(ii) a From equation (14) the matrices B and h (u) can be seen_1,1)、h(u_2,1)…h(u_n,1) (ii) related; so the matrices B are also summed with u ═ u_1,1,u_1,2,u_2,1,u_2,2,…u_n,1,u_n,2,]^TTherefore, B (k | k) is a matrix obtained by substituting u (k | k) into the B matrix at the k-th sampling time; b (k + i | k) is a matrix obtained by substituting u (k + i | k) into the B matrix when predicting i steps at the kth sampling moment; b (k + N-1| k) is a matrix obtained by substituting u (k + N-1| k) into the B matrix when predicting the step N-1 at the kth sampling moment;

wherein k represents the kth sampling instant; n is the prediction step size, expressed for simplicity as:

wherein the content of the first and second substances,

for convenience of the following description, the following redefinitions are made; wherein the input variable matrix u (k) is a matrix of dimension (2 × N,1), the state variable X (k +1) is a matrix of dimension (N × N,1), and f (k) is a row vector of dimension (1,2 × N);

U(k)＝[u(k|k),u(k+1|k),…,u(k+N-1|k)]^T (27)

X(k+1)＝[x(k+1|k),x(k+2|k),…,x(k+N|k)]^T (28)

F(k)＝[F₀(k|k),F₀(k+1|k),…,F₀(k+N-1|k)] (29)

wherein, F₀(k | k) denotes the matrix F, F at the prediction of step 0 at the k-th sampling instant₀(k +1| k) denotes the F matrix at the kth sampling instant during the 1 st prediction, F₀(k + N-1| k) represents the F matrix at the prediction of step N-1 at the kth sampling instant^TRepresenting a transpose; in order to minimize the loss during equalization, i.e., minimize equation (18); in the model predictive control strategy, it is equivalent to minimizing the loss within the whole prediction step; the objective function for minimizing the equalization loss in model predictive control can be obtained as follows:

mint₀F(k)U(k) (30)

t₀is the time interval between adjacent sampling instants of the discretization of the continuous state space model, f (k) is a row vector of dimension (1,2 × N), the variable matrix u (k) is a matrix of dimension (2 × N, 1);

meanwhile, obtaining the constraint of the discrete state space model under a model prediction control strategy; as shown in equations (31) (32) (33) (34) (35); where equation (31) is the range limit for the input variable; equation (32) is the range limit for the state variables; equation (33) is the constraint that the current flowing into the bus is equal to the current flowing out of the bus in one equalization period; equation (34) is the limit for the battery charge to be equal after the equalization process is over; formula (35) is a constraint that the control signal has only one direction at a certain moment in the predicted step length;

0≤U(k)≤i^m (31)

x^l≤X(k+1)≤x^u (32)

x₁(k+N|k)＝x₂(k+N|k)＝…＝x_n(k+N|k) (34)

u_j,1(k+h|k)u_j,2(h|k)＝0 h＝0,1,…N-1,j＝1,…,n (35)

wherein i^mIs the maximum value of the input variable; x is the number of^l、x^uRespectively the minimum residual capacity and the maximum residual capacity allowed by the battery;

f[u_j,2(k+h|k)]the prediction efficiency of the h step between the jth battery and the jth equalizer at the kth sampling moment is shown; u. of_j,1(k + h | k) represents the prediction of the h step of the bus to equalizer current at the kth sample time; u. of_j,2(k + h | k) represents the current prediction of the h step between the jth battery and the jth equalizer at the kth sampling instant;

k represents the sampling time, j represents the j-th battery, N represents the total number of batteries, N represents the predicted step length, h represents the predicted step number at the k-th sampling time, v_busIs the bus voltage, v_jIs the voltage of the jth cell;

x₁(k + N | k) represents the remaining capacity of the 1 st battery at the k sampling moment when predicting N steps, x₂(k + N | k) represents the remaining capacity of the 2 nd battery at the k sampling moment when predicting N steps, x_n(k + N | k) represents the remaining capacity of the nth battery at the kth sampling moment when the nth battery predicts the N steps;

according to the prediction step size of N, another coefficient matrix M ═ M₀,…,M₀]_(1,N×n)The objective function related to time efficiency can be obtained as shown in the following equation:

minβMX(k+1) (38)

wherein N is the total number of cells, β is a weight coefficient, and X (k +1) is a matrix with dimension (N × N, 1);

adding equation (30) to equation (38) results in a final objective function of time efficiency and loss efficiency, as shown in the following equation:

mint₀F(k)U(k)+βMX(k+1) (39)

the objective function can be reduced to min (F (k) t by the equations (26) and (39)₀+ β M (k) S (U) (k) +. β MRx (k), where t₀Is the interval duration between adjacent sampling points of the discretization of the continuous state space model, f (k) is a row vector with dimension (1,2 × N), the variable matrix u (k) is a matrix with dimension (2 × N,1), β is a weight coefficient, the state variable X (k +1) is a matrix with dimension (N × N,1), and since β mrx (k) belongs to a constant independent of the input u (k), the objective function can be simplified as shown in the following equation:

min(F(k)t₀+βMS)U(k) (40)

thus, an objective function of the equilibrium model based on the nonlinear efficiency of the model predictive control strategy and a constraint condition thereof are obtained.

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