CN115407205A - Multi-time scale SOC and SOH collaborative estimation method considering temperature influence - Google Patents

Multi-time scale SOC and SOH collaborative estimation method considering temperature influence Download PDF

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CN115407205A
CN115407205A CN202210985080.5A CN202210985080A CN115407205A CN 115407205 A CN115407205 A CN 115407205A CN 202210985080 A CN202210985080 A CN 202210985080A CN 115407205 A CN115407205 A CN 115407205A
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fitness
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高犇
昌诚程
赵万忠
周长志
章波
陈青云
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/374—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC] with means for correcting the measurement for temperature or ageing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/392—Determining battery ageing or deterioration, e.g. state of health

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Abstract

The invention discloses a multi-time scale SOC and SOH collaborative estimation method considering temperature influence, which comprises the following steps: constructing a lithium battery equivalent circuit model considering temperature influence; identifying the lithium battery equivalent circuit model by adopting a particle swarm optimization algorithm of dynamic inertia weight; inputting experimental data and identification results under the working condition of constant current pulse into a lithium battery equivalent circuit model for simulation verification; and constructing a cooperative estimator considering the temperature influence to estimate the SOC and the SOH of the lithium battery. The invention realizes the accurate calculation of the SOC and the SOH of the battery under the condition of changing the temperature of the battery, simultaneously realizes the cooperative calculation of the SOC and the SOH under the condition of different calculation periods of the same algorithm, and eliminates the influence between the calculation errors of the SOC and the SOH.

Description

Multi-time scale SOC and SOH collaborative estimation method considering temperature influence
Technical Field
The invention belongs to the technical field of battery management, and particularly relates to a multi-time scale SOC and SOH collaborative estimation method considering temperature influence.
Background
With the development of electric vehicles and the increasing market share, the technology of Battery Management System (BMS) for vehicles is also continuously developed. Among them, the State-of-charge (SOC) and State-of-health (SOH) of a battery are two key states in battery management, affecting the vehicle power output and the battery life. However, the existing sensors cannot directly measure the two states, so that the two states need to be estimated and calculated through an algorithm.
Temperature is an important influence factor in the practical use of the current electric automobile battery, so a battery model considering the temperature factor must be established. Meanwhile, most of the existing SOC and SOH estimation methods only consider the influence of single estimation of SOC, and ignore the mutual influence among the internal states of the battery. However, the state update period between SOC and SOH is not the same, and the estimation calculation cannot be performed using the same algorithm period.
In view of the above, the invention provides a SOC and SOH collaborative estimation method considering different temperature change influences and adopting a plurality of calculation time scales, which has important significance on battery life extension and energy efficiency and economy of electric vehicles.
Disclosure of Invention
In view of the above deficiencies of the prior art, the present invention aims to provide a multi-time scale SOC and SOH collaborative estimation method considering temperature influence, so as to solve the problem of inaccurate calculation caused by neglecting temperature influence in the existing battery model, and also solve the problem of different update periods of SOC and SOH states; the method realizes SOC and SOH collaborative estimation and reduces unnecessary calculation redundancy.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention discloses a multi-time scale SOC and SOH collaborative estimation method considering temperature influence, which comprises the following steps of:
1) Constructing a lithium battery equivalent circuit model considering temperature influence;
2) Identifying the lithium battery equivalent circuit model by adopting a particle swarm optimization algorithm of dynamic inertia weight;
3) Inputting experimental data under the working condition of constant current pulse and the identification result obtained in the step 2) into the lithium battery equivalent circuit model established in the step 1) for simulation verification;
4) And constructing a cooperative estimator considering the temperature influence to estimate the SOC and the SOH of the lithium battery.
Further, the method for constructing the equivalent circuit model of the lithium battery in the step 1) is as follows:
the discharge current is used as positive, and the space state equation of the double RC battery model is obtained by combining kirchhoff's law as follows:
Figure BDA0003801785680000021
in the formula of U OC Represents the open circuit voltage, R, of the battery 0 Represents the contact resistance between the internal structures of the battery, R 1 For electrochemical polarization resistance, R 2 For concentration polarization internal resistance, C 1 For electrochemical polarization of capacitance, C 2 Is a concentration polarization capacitor, U t Is terminal voltage of the battery, I L Is the load current;
converting U in the above formula (1) by Laplace oc The further derivation is:
Figure BDA0003801785680000022
the transfer equation for the battery model is:
Figure BDA0003801785680000023
in the formula, τ 1 ＝R 1 C 1 ；τ 2 ＝R 2 C 2 ；τ 1 And τ 2 Is the time constant of the RC polarized unit;
discretizing the transfer equation, and mapping the transfer equation from an S plane to a Z plane by adopting a bilinear transformation method;
Figure BDA0003801785680000024
in the formula, delta T is a sampling interval; z-1 is a delay factor;
the equation mapped onto the Z plane is:
Figure BDA0003801785680000025
transformation of the above formula (5) into the discrete time domain gives:
y k ＝U oc,k -U t,k ＝a 1 y k-1 +a 2 y k-2 +a 3 I k +a 4 I k-1 +a 5 I k-2 (6)
in the formula of U oc,k Open circuit voltage at time k, U t,k Terminal voltage at time k, y k Is the difference between the open circuit voltage at time k and the terminal voltage at time k, a 1 -a 5 Is an algebraic expression of the model parameters.
Further, the step 2) specifically includes:
21 Initialization;
defining and initializing various parameters in an iterative process; defining a flight speed interval of the particles, the upper limit value of the interval being the maximum flight speed v of the particles max (ii) a Minimum value of interval, i.e. minimum flying speed v of particle min (ii) a Setting the value range theta of the identification parameter according to the actual characteristics of the target system max 、θ min Preventing the result from overflowing; the number of particles is defined as N 1 Defining the maximum iteration number as M, and setting a numerical value according to actual needs; initial velocity v of the particles i,j＝0 And an initial position theta i,j＝0 Within the corresponding intervalRandomly selecting, wherein a subscript i represents a particle sequence, and j represents the current iteration number of the particle; position vector theta of particle i,j Parameter set [ R0, R1, R2, C1, C2 ] representing equivalent circuit model]；
Velocity v at initial time i,0 And the position theta of the initial time i,0 The value taking method comprises the following steps:
v i,0 ＝rand(0,1) (7)
θ i,0 ＝θ min +(θ max -θ min )*rand(0,1) (8)
in the formula, the function rand (0, 1) represents a random number that generates a uniform distribution between (0, 1);
22 Select and calculate a fitness function;
the fitness function is set as:
U RC (k)＝U OC (k)-U t (k) (9)
Figure BDA0003801785680000031
u in formula (9) RC (k) A fitness function corresponding to the particle i under the iteration number j, n is the length of test data, and y (k) is the position theta of the equivalent circuit model at the current particle i,j The difference between the open circuit voltage and the terminal voltage;
it is known that when a 1 -a 5 When represented by the identification parameter, y (k) can be calculated; order:
Figure BDA0003801785680000032
the following can be obtained:
fy k ＝aI k-2 +bI k-1 +cI k -dy k-2 -ey k-1 (12)
the specific expression of each coefficient is as follows:
Figure BDA0003801785680000041
during the iterative process of the algorithm, any particle passes through its position vector theta i,j Substituting each parameter in the above formula (13) to calculate a corresponding fitness function;
23 Individual optimal fitness update;
a position vector theta of the particle i under the current iteration number j i,j Substituting into fitness function, calculating specific value fitness (i, j) and matching with self-history optimal position
Figure BDA0003801785680000042
Corresponding fitness values fitness (i, best) are compared, and if the fitness (i, j) < fitness (i, best), the historical optimal position of the current particle is replaced by the position of the current particle
Figure BDA0003801785680000043
24 Update of population optimal fitness;
historical optimal fitness value fitness (i, best) and group optimal position theta of each particle under current iteration times best Comparing the corresponding fitness values fitness (best), and if the fitness (i, best) is less than the fitness (best), using the historical optimal position of the particle corresponding to the fitness (i, best)
Figure BDA0003801785680000044
Updating the population optimal position θ best ；
25 Particle velocity and position updates;
after completing one round of fitness updating, updating the speed of each particle:
Figure BDA0003801785680000045
in the formula, ω 1 And ω 2 Is an inertia weight factor for adjusting the search interval; m is the number of iterations, c 1 And c 2 Is the acceleration constant of the particles, and is usually in the range of [0,4%]Taking values; r is 1 And r 2 Is [0,1 ]]Random numbers between the two, which are used to ensure the randomness of particle search;
and (3) updating the position of the particle:
θ i,j+1 ＝θ i,j +v i,j+1 (15)；
26 Judging whether the particle swarm optimization algorithm is finished or not;
the end conditions of the particle swarm optimization algorithm are as follows: the current iteration times reach the maximum iteration times, and the optimal fitness function value of the group is smaller than a preset value; when any one of the two conditions is reached, the algorithm is terminated, and the output group optimal position theta is obtained best I.e. the optimal solution calculated this time, otherwise, returning to step 22).
Further, the step 3) specifically includes:
respectively obtaining parameters R under different cycles through parameter identification in the step 2) 0 ，R 1 ，R 2 ，C 1 ，C 2 The value of (d); under an MATLAB/Simulink environment, establishing the lithium ion battery equivalent circuit model which is set up in the step 1) and takes the temperature influence into consideration through a code and a Simulink module, and substituting experimental data under a constant current pulse working condition into calculation; wherein, the input is current and battery temperature; the output is terminal voltage; constant current pulse condition test is carried out at-10 deg.C, 0 deg.C, 10 deg.C, 20 deg.C, 30 deg.C, 40 deg.C]Simulations were performed at six temperatures.
Further, the step 4) specifically includes:
41 Building a multi-time scale filtering algorithm model;
the model of the multi-time scale filtering algorithm containing the hidden state x and the parameter θ is as follows:
Figure BDA0003801785680000051
in the formula, x k,l Is t k,l ＝t k,0 +l×Δt,1≤l≤L Z The system state at a time, where the dual timescales k and L describe the macroscopic and microscopic timescales, respectively, L Z For scaling the limits, i.e. a macroThe viewing time scale is equal to L Z A microscopic time scale; u. u k,l Is t k,l Input information of a time system; y is k,l Is t k,l An observation matrix of the time system; w is a k,l Is a system state with a covariance of
Figure BDA0003801785680000052
p k Is parametric white noise with a covariance of
Figure BDA0003801785680000053
v k,l For measuring white noise, the covariance is R k,l (ii) a Estimating the system state by using the microscopic time scale and estimating the system parameters by using the macroscopic time scale; for system parameters, the macro scale is 0-L Z The value at 1 remains unchanged, i.e.
Figure BDA0003801785680000054
42 Multi-time scale filtering algorithm initialization;
separately set parameter observer HIF θ And the state observer AEKF x Initial parameter values of (a): theta 0 ，
Figure BDA0003801785680000055
λ θ ，S θ ，R 0 ，x 0，0 ，
Figure BDA0003801785680000056
R 0，0 Wherein, theta 0 ，
Figure BDA0003801785680000057
λ θ ，S θ Are respectively parameter observers HIF θ Initial parameter values, initial values of parameter estimation error covariance matrixes, initial values of system noise covariance matrixes, performance boundaries of parameter observers and self-defined matrixes; x is a radical of a fluorine atom 0，0 ，
Figure BDA0003801785680000058
R 0，0 Respectively being state observers AEKF x The initial state of the system, the initial value of a state estimation error covariance matrix, the initial value of a system noise covariance matrix and an observation noise covariance;
43 Parametric observer HIF based on macroscopic timescale θ Time update of (2);
Figure BDA0003801785680000061
performing a system parameter theta and a parameter estimation error covariance P θ To obtain corresponding estimated value
Figure BDA0003801785680000062
44 State observer AEKF based on microscopic time scales x Time update of (2);
Figure BDA0003801785680000063
start state observer AEKF x To obtain the prior estimated value of the system state X
Figure BDA0003801785680000064
And its error covariance P x Is estimated a priori
Figure BDA0003801785680000065
Priori estimated value based on available capacity of power battery
Figure BDA0003801785680000066
A priori estimates of sum states
Figure BDA0003801785680000067
Updating OCV value of power battery
Figure BDA0003801785680000068
45 Based onMicro time scale state observer AEKF x Updating the measurements of (1);
updating a state estimation innovation covariance matrix:
Figure BDA0003801785680000069
kalman gain matrix:
Figure BDA00038017856800000610
adaptive covariance matching:
Figure BDA00038017856800000611
noise covariance update:
Figure BDA00038017856800000612
Figure BDA00038017856800000613
and (3) correcting the estimated value of the system state:
Figure BDA00038017856800000614
state estimation error covariance update:
Figure BDA00038017856800000615
microscopic time scale cycle calculation l =1 Z And scale conversion:
Figure BDA0003801785680000071
Figure BDA0003801785680000072
Figure BDA0003801785680000073
Figure BDA0003801785680000074
completing the micro time scale cycle calculation under a macro time scale, and returning to the macro time scale to perform measurement updating of parameter estimation;
46 A state observer HIF based on macroscopic time scale θ Updating the measurement of (1):
Figure BDA0003801785680000075
h ∞ gain matrix:
Figure BDA0003801785680000076
correcting the system parameter estimation value:
Figure BDA0003801785680000077
updating an H-infinity feature matrix:
Figure BDA0003801785680000078
to this end, multi-time scale estimation of the parameters and states at time k is completed, state estimation at time (k + 1) is prepared, and the order is given
Figure BDA0003801785680000079
And obtaining the real-time estimation value of the available capacity and the SOC of the power battery.
The invention has the beneficial effects that:
the invention realizes the accurate calculation of the SOC and the SOH of the battery under the condition of changing the temperature of the battery, simultaneously realizes the cooperative calculation of the SOC and the SOH under the condition of different calculation periods of the same algorithm, and eliminates the influence between calculation errors of the SOC and the SOH.
Drawings
FIG. 1 is a schematic diagram of the method of the present invention.
FIG. 2 is a schematic diagram of an equivalent circuit of a lithium battery.
FIG. 3 is a graph of model estimated voltage versus test voltage.
FIG. 4 is a diagram illustrating model identification errors.
Fig. 5 is a schematic flow chart of a multi-time scale filtering algorithm.
Fig. 6 is a diagram of SOC estimation results.
Fig. 7 is a diagram showing the SOH estimation result.
Detailed Description
In order to facilitate understanding of those skilled in the art, the present invention will be further described with reference to the following examples and drawings, which are not intended to limit the present invention.
Referring to fig. 1, the method for cooperatively estimating SOC and SOH on multiple time scales with consideration of temperature influence includes the following steps:
1) Constructing a lithium battery equivalent circuit model considering temperature influence, and referring to fig. 2;
specifically, the method for constructing the equivalent circuit model of the lithium battery in the step 1) comprises the following steps:
the discharge current is used as positive, and the space state equation of the double RC battery model is obtained by combining kirchhoff's law as follows:
Figure BDA0003801785680000081
in the formula of U OC Indicating open circuit of batteryPressure, R 0 Represents the contact resistance between the internal structures of the battery, R 1 For electrochemical polarization resistance, R 2 For concentration polarization internal resistance, C 1 For electrochemical polarization of capacitance, C 2 Is a concentration polarization capacitor, U t Is the terminal voltage of the battery, I L Is the load current;
the conversion of UO in the above formula (1) by Laplace transform c The further derivation is:
Figure BDA0003801785680000082
the transfer equation for the cell model is:
Figure BDA0003801785680000083
in the formula, τ 1 ＝R 1 C 1 ；τ 2 ＝R 2 C 2 ；τ 1 And τ 2 Is the time constant of the RC polarized unit;
discretizing the transfer equation, and mapping the transfer equation from an S plane to a Z plane by adopting a bilinear transformation method;
Figure BDA0003801785680000084
in the formula, delta T is a sampling interval; z-1 is a delay factor;
the equation mapped onto the Z plane is:
Figure BDA0003801785680000091
transformation of the above formula (5) into the discrete time domain yields:
y k ＝U oc,k -U t,k ＝a 1 y k-1 +a 2 y k-2 +a 3 I k +a 4 I k-1 +a 5 I k-2 (6)
in the formula of U oc,k Open circuit voltage at time k, U t,k Terminal voltage at time k, y k Is the difference between the open circuit voltage at time k and the terminal voltage at time k, a 1 -a 5 Is an algebraic expression of the model parameters.
2) Identifying the lithium battery equivalent circuit model by adopting a particle swarm optimization algorithm of dynamic inertia weight; the method specifically comprises the following steps:
21 Initialization;
defining and initializing various parameters in an iterative process; the flight speed interval of the particles is limited, and the upper limit value of the interval is the maximum flight speed v of the particles max (it cannot be too large, otherwise it is prone to loss of the optimum value in the iteration); minimum value of interval, i.e. minimum flying speed v of particle min (it must not be too small, otherwise the iteration efficiency of the algorithm is reduced); setting the value range theta of the identification parameter according to the actual characteristics of the target system max 、θ min Preventing the result from overflowing; the number of particles is defined as N 1 Defining the maximum iteration number as M, and setting a numerical value according to actual needs; initial velocity v of the particles i,j＝0 And an initial position theta i,j＝0 Randomly selecting in a corresponding interval, wherein a subscript i represents a particle sequence, and j represents the current iteration times of the particles; position vector theta of particle i,j Parameter set [ R0, R1, R2, C1, C2 ] representing equivalent circuit model]；
Velocity v at initial time i,0 And the position theta of the initial time i,0 The value taking method comprises the following steps:
v i,0 ＝rand(0,1) (7)
θ i,0 ＝θ min +(θ max -θ min )*rand(0,1) (8)
in the formula, the function rand (0, 1) represents a random number that generates a uniform distribution between (0, 1);
22 Select and calculate a fitness function;
the fitness function is set as:
U RC (k)＝U OC (k)-U t (k) (9)
Figure BDA0003801785680000092
u in formula (9) RC (k) Is a fitness function corresponding to the particle i under the iteration number j, n is the length of the test data, and y (k) is the position theta of the equivalent circuit model at the current particle i,j The difference between the open circuit voltage and the terminal voltage;
it is known that when a 1 -a 5 When the identification parameter represents, y (k) can be calculated; order:
Figure BDA0003801785680000101
the following can be obtained:
fy k ＝aI k-2 +bI k-1 +cI k -dy k-2 -ey k-1 (12)
the specific expression of each coefficient is as follows:
Figure BDA0003801785680000102
during the iterative process of the algorithm, any particle passes through its position vector theta i,j Substituting each parameter in the above formula (13) to calculate a corresponding fitness function;
23 Individual optimal fitness update;
the position vector theta of the particle i under the current iteration number j i,j Substituting into fitness function, calculating specific value fitness (i, j) and matching with self-history optimal position
Figure BDA0003801785680000103
Corresponding fitness values fitness (i, best) are compared, and if fitness (i, j) < fitness (i, best), the historical optimal position of the current particle is replaced by the position of the current particle
Figure BDA0003801785680000104
24 Update of population optimal fitness;
the historical optimal fitness value fitness (i, best) and the group optimal position theta of each particle under the current iteration number best Comparing the corresponding fitness values fitness (best), and if the fitness (i, best) is smaller than the fitness (best), using the historical optimal position of the particle corresponding to the fitness (i, best)
Figure BDA0003801785680000105
Updating the population optimal position θ best ；
25 Particle velocity and position updates;
after completing one round of fitness updating, updating the speed of each particle:
Figure BDA0003801785680000111
in the formula, ω 1 And ω 2 Is used as an inertia weight factor to adjust the search window (take ω 1 ＝0.4，ω 2 = 0.9); m is the number of iterations, c 1 And c 2 Is the acceleration constant of the particles, and is usually in the range of [0,4%]Value between (take c) 1 ＝c 2 ＝2)；r 1 And r 2 Is [0,1 ]]Random number between the two, which is used to ensure the randomness of particle search;
and (3) updating the position of the particle:
θ i,j+1 ＝θ i,j +v i,j+1 (15)；
26 Judging whether the particle swarm optimization algorithm is finished or not;
the end conditions of the particle swarm optimization algorithm are as follows: the current iteration times reach the maximum iteration times, and the optimal fitness function value of the group is smaller than a preset value; when any one of the two conditions is reached, the algorithm is terminated, and the output group optimal position theta is obtained best I.e. the optimal solution calculated this time, otherwise, the step 22) is returned to.
3) Inputting experimental data under the working condition of constant current pulse and the identification result obtained in the step 2) into the lithium battery equivalent circuit model established in the step 1) for simulation verification;
respectively obtaining parameters R under different cycles through parameter identification in the step 2) 0 ，R 1 ，R 2 ，C 1 ，C 2 The value of (d); under an MATLAB/Simulink environment, establishing the lithium ion battery equivalent circuit model which is set up in the step 1) and takes the temperature influence into consideration through a code and a Simulink module, and substituting experimental data under the working condition of constant current pulse into calculation; wherein, the input is current and battery temperature; the output is terminal voltage; constant current pulse condition test is carried out at-10 deg.C, 0 deg.C, 10 deg.C, 20 deg.C, 30 deg.C, 40 deg.C]Simulations were performed at six temperatures.
Taking the temperature of 40 ℃ as an example: comparing the measured voltage with the simulated voltage as shown in fig. 3 and 4; and the corresponding error is obtained to be basically within 0.005, as shown in figure 4; the errors at other temperatures (10 ℃, 0 ℃, 10 ℃, 20 ℃, 30 ℃) are respectively [0.007, 0.008, 0.006, 0.004, 0.008, 0.009].
4) Constructing a cooperative estimator considering the temperature influence to estimate the SOC and the SOH of the lithium battery; referring to fig. 5, specifically, the following are:
41 Building a multi-time scale filtering algorithm model;
the model of the multi-time scale filtering algorithm containing the hidden state x and the parameter θ is as follows:
Figure BDA0003801785680000112
in the formula, x k,l Is t k,l ＝t k,0 +l×Δt,1≤l≤L Z The system state at a time, where the dual timescales k and L describe the macroscopic and microscopic timescales, respectively, L Z For scale-conversion limits, i.e. a macroscopic time scale equal to L Z A microscopic time scale; u. of k,l Is t k,l Input information of a time system; y is k,l Is t k,l An observation matrix of the time system; w is a k,l Is a system state with a covariance of
Figure BDA0003801785680000121
p k Is parametric white noise with a covariance of
Figure BDA0003801785680000122
v k,l For measuring white noise, the covariance is R k,l (ii) a Estimating the system state by using the microscopic time scale and estimating the system parameters by using the macroscopic time scale; for system parameters, the macro scale is 0-L Z The value at 1 remains unchanged, i.e.
Figure BDA0003801785680000123
42 Multi-time scale filtering algorithm initialization;
respectively setting parameter observers HIF θ And state observer AEKF x Initial parameter values of (a): theta.theta. 0 ，
Figure BDA0003801785680000124
λ θ ，S θ ，R 0 ，x 0，0 ，
Figure BDA0003801785680000125
R 0，0 Wherein, theta 0 ，
Figure BDA0003801785680000126
λ θ ，S θ Are respectively parameter observers HIF θ Initial parameter values, initial values of parameter estimation error covariance matrixes, initial values of system noise covariance matrixes, performance boundaries of parameter observers and self-defined matrixes; x is the number of 0，0 ，
Figure BDA0003801785680000127
R 0，0 Respectively state observer AEKF x The system initial state, the initial value of the state estimation error covariance matrix, the initial value of the system noise covariance matrix and the observation noise covariance;
43 Parametric observer HIF based on macroscopic timescale θ Time update (a priori estimate);
Figure BDA0003801785680000128
performing a system parameter theta and a parameter estimation error covariance P θ To obtain a corresponding estimated value
Figure BDA0003801785680000129
44 State observer AEKF based on microscopic time scales x Time update (a priori estimate);
Figure BDA00038017856800001210
start state observer AEKF x To obtain the prior estimated value of the system state X
Figure BDA00038017856800001211
And its error covariance P x Is estimated a priori
Figure BDA00038017856800001212
Priori estimated value based on available capacity of power battery
Figure BDA00038017856800001213
A priori estimates of sum states
Figure BDA00038017856800001214
Updating OCV value of power battery
Figure BDA00038017856800001215
45 State observer AEKF based on microscopic time scales x Measurement update (a posteriori estimation);
updating a state estimation innovation covariance matrix:
Figure BDA00038017856800001216
kalman gain matrix:
Figure BDA0003801785680000131
adaptive covariance matching (voltage estimation error window function):
Figure BDA0003801785680000132
noise covariance update:
Figure BDA0003801785680000133
Figure BDA0003801785680000134
and (3) correcting the estimated value of the system state:
Figure BDA0003801785680000135
state estimation error covariance update:
Figure BDA0003801785680000136
microscopic time scale cycle calculation l =1 Z And scale conversion (when L = L) Z When:
Figure BDA0003801785680000137
Figure BDA0003801785680000138
Figure BDA0003801785680000139
Figure BDA00038017856800001310
so far, the micro time scale cycle calculation under a macro time scale is completed, and then the measurement updating (posterior estimation) of parameter estimation is carried out by returning to the macro time scale;
46 A state observer HIF based on macroscopic time scale θ Measurement update (a posteriori estimation):
Figure BDA00038017856800001311
h ∞ gain matrix:
Figure BDA00038017856800001312
and (3) correcting the estimated value of the system parameter:
Figure BDA00038017856800001313
updating an H-infinity feature matrix:
Figure BDA00038017856800001314
to this end, multi-time scale estimation of the parameters and states at time k is completed, state estimation at time (k + 1) is prepared, and the order is given
Figure BDA0003801785680000141
And obtaining the real-time estimation value of the available capacity and the SOC of the power battery.
As shown in fig. 6 and 7, the method of the present invention can stably estimate the values of SOC and SOH, and the SOC estimation error is 1.5%, and the SOH estimation error is within 1%, thereby verifying the validity and accuracy of the estimation method of the present invention.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (5)

1. A multi-time scale SOC and SOH collaborative estimation method considering temperature influence is characterized by comprising the following steps:
1) Constructing a lithium battery equivalent circuit model considering temperature influence;
2) Identifying the lithium battery equivalent circuit model by adopting a particle swarm optimization algorithm of dynamic inertia weight;
3) Inputting experimental data under the working condition of constant current pulse and the identification result obtained in the step 2) into the lithium battery equivalent circuit model established in the step 1) for simulation verification;
4) And constructing a cooperative estimator for estimating the SOC and the SOH of the lithium battery by considering the temperature influence.
2. The method for the multi-time scale SOC and SOH collaborative estimation considering temperature influence according to claim 1, wherein the step 1) lithium battery equivalent circuit model is constructed by the following steps:
the discharge current is used as positive, and the space state equation of the double RC battery model is obtained by combining kirchhoff's law as follows:
Figure FDA0003801785670000011
in the formula of U OC Represents the open circuit voltage, R, of the battery 0 Denotes the contact resistance between the internal structures of the battery, R 1 For electrochemical polarization resistance, R 2 Is concentratedDifferential internal resistance to polarization, C 1 For electrochemical polarization of capacitance, C 2 Is a concentration polarization capacitor, U t Is terminal voltage of the battery, I L Is the load current;
converting U in the above formula (1) by Laplace oc The further derivation is:
Figure FDA0003801785670000012
the transfer equation for the battery model is:
Figure FDA0003801785670000013
in the formula, τ 1 ＝R 1 C 1 ；τ 2 ＝R 2 C 2 ；τ 1 And τ 2 Is the time constant of the RC polarized unit;
discretizing the transfer equation, and mapping the transfer equation from an S plane to a Z plane by adopting a bilinear transformation method;
Figure FDA0003801785670000021
in the formula, delta T is a sampling interval; z is a radical of -1 Is a delay factor;
the equation mapped onto the Z plane is:
Figure FDA0003801785670000022
transformation of the above formula (5) into the discrete time domain yields:
y k ＝U oc,k -U t,k ＝a 1 y k-1 +a 2 y k-2 +a 3 I k +a 4 I k-1 +a 5 I k-2 (6)
in the formula (I), the compound is shown in the specification,U oc,k open circuit voltage at time k, U t,k Terminal voltage at time k, y k Is the difference between the open circuit voltage at time k and the terminal voltage at time k, a 1 -a 5 Is an algebraic expression of the model parameters.
3. The method for multi-time scale SOC and SOH collaborative estimation considering temperature influence according to claim 2, wherein the step 2) specifically includes:
21 Initialization;
defining and initializing various parameters in an iterative process; the flight speed interval of the particles is limited, and the upper limit value of the interval is the maximum flight speed v of the particles max (ii) a Minimum value of interval, i.e. minimum flying speed v of particle min (ii) a Setting the value range theta of the identification parameter according to the actual characteristics of the target system max 、θ min Preventing the result from overflowing; the number of particles is defined as N 1 Defining the maximum iteration number as M, and setting a numerical value according to actual needs; initial velocity v of the particles i,j＝0 And an initial position theta i,j＝0 Randomly selecting in a corresponding interval, wherein a subscript i represents a particle sequence, and j represents the current iteration times of the particles; position vector theta of particle i,j Parameter set [ R0, R1, R2, C1, C2 ] representing equivalent circuit model]；
Velocity v at initial time i,0 And the position theta of the initial time i,0 The value taking method comprises the following steps:
v i,0 ＝rand(0,1) (7)
θ i,0 ＝θ min +(θ max -θ min )*rand(0,1) (8)
in the formula, the function rand (0, 1) represents a random number that generates a uniform distribution between (0, 1);
22 Select and calculate a fitness function;
the fitness function is set as:
U RC (k)＝U OC (k)-U t (k) (9)
Figure FDA0003801785670000031
u in formula (9) RC (k) Is a fitness function corresponding to the particle i under the iteration number j, n is the length of the test data, and y (k) is the position theta of the equivalent circuit model at the current particle i,j The difference between the open circuit voltage and the terminal voltage;
it is known that when a 1 -a 5 When represented by the identification parameter, y (k) can be calculated; order:
Figure FDA0003801785670000032
the following can be obtained:
fy k ＝aI k-2 +bI k-1 +cI k -dy k-2 -ey k-1 (12)
the specific expression of each coefficient is as follows:
Figure FDA0003801785670000033
during the algorithm iteration, any particle passes through its position vector θ i,j Substituting each parameter in the above formula (13) to calculate a corresponding fitness function;
23 Individual optimal fitness update;
the position vector theta of the particle i under the current iteration number j i,j Substituting into fitness function, calculating specific value fitness (i, j) and matching with self-history optimal position
Figure FDA0003801785670000034
Corresponding fitness values fitness (i, best) are compared, and if fitness (i, j) < fitness (i, best), the historical optimal position of the current particle is replaced by the position of the current particle
Figure FDA0003801785670000035
24 Update of population optimal fitness;
historical optimal fitness value fitness (i, best) and group optimal position theta of each particle under current iteration times best Comparing the corresponding fitness values fitness (best), and if the fitness (i, best) is less than the fitness (best), using the historical optimal position of the particle corresponding to the fitness (i, best)
Figure FDA0003801785670000036
Updating the population optimum position θ best ；
25 Particle velocity and position updates;
after completing one round of fitness updating, updating the speed of each particle:
Figure FDA0003801785670000041
in the formula, ω 1 And ω 2 Is an inertia weight factor for adjusting the search interval; m is the number of iterations, c 1 And c 2 Is the acceleration constant of the particles, and is usually in the range of [0,4%]Taking values; r is 1 And r 2 Is [0,1 ]]Random numbers between the two, which are used for ensuring the randomness of particle searching;
and (3) updating the position of the particle:
θ i,j+1 ＝θ i,j +v i,j+1 (15)；
26 Judging whether the particle swarm optimization algorithm is finished or not;
the end conditions of the particle swarm optimization algorithm are as follows: the current iteration times reach the maximum iteration times and the group optimal fitness function value is smaller than a preset value; when any one of the two conditions is reached, the algorithm is terminated, and the output group optimal position theta is obtained best I.e. the optimal solution calculated this time, otherwise, the step 22) is returned to.
4. The method for multi-time scale SOC and SOH collaborative estimation considering temperature influence according to claim 3, wherein the step 3) specifically includes:
respectively obtaining parameters R under different cycles through parameter identification in the step 2) 0 ，R 1 ，R 2 ，C 1 ，C 2 The value of (d); under an MATLAB/Simulink environment, establishing the lithium ion battery equivalent circuit model which is set up in the step 1) and takes the temperature influence into consideration through a code and a Simulink module, and substituting experimental data under the working condition of constant current pulse into calculation; wherein, the input is current and battery temperature; the output is terminal voltage; constant current pulse condition test is carried out at-10 deg.C, 0 deg.C, 10 deg.C, 20 deg.C, 30 deg.C, 40 deg.C]Simulations were performed at six temperatures.
5. The method for multi-time scale SOC and SOH collaborative estimation considering temperature influence according to claim 4, wherein the step 4) specifically comprises:
41 Building a multi-time scale filtering algorithm model;
the model of the multi-time scale filtering algorithm containing the hidden state x and the parameter θ is as follows:
Figure FDA0003801785670000042
in the formula, x k,l Is t k,l ＝t k,0 +l×Δt,1≤l≤L Z The system state at a time, where the dual timescales k and L describe the macroscopic and microscopic timescales, respectively, L Z For scale-conversion limits, i.e. one macroscopic timescale equal to L Z A microscopic time scale; u. of k,l Is t k,l Input information of a time system; y is k,l Is t k,l An observation matrix of the time system; w is a k,l Is a system state with a covariance of
Figure FDA0003801785670000051
p k Is parametric white noise with a covariance of
Figure FDA0003801785670000052
v k,l For measuring white noise, the covariance is R k,l (ii) a Estimating the system state by using the microscopic time scale and estimating the system parameters by using the macroscopic time scale; for system parameters, the macro scale is 0-L Z The value at 1 remains unchanged, i.e.
Figure FDA0003801785670000053
42 Multi-time scale filtering algorithm initialization;
separately set parameter observer HIF θ And the state observer AEKF x Initial parameter values of (a): theta 0 ，
Figure FDA0003801785670000054
λ θ ，S θ ，R 0 ，x 0，0 ，
Figure FDA0003801785670000055
R 0，0 Wherein, theta 0 ，
Figure FDA0003801785670000056
λ θ ，S θ Are respectively parameter observers HIF θ Initial parameter values, initial values of parameter estimation error covariance matrixes, initial values of system noise covariance matrixes, performance boundaries of parameter observers and self-defined matrixes; x is a radical of a fluorine atom 0，0 ，
Figure FDA0003801785670000057
R 0，0 Respectively state observer AEKF x The initial state of the system, the initial value of a state estimation error covariance matrix, the initial value of a system noise covariance matrix and an observation noise covariance;
43 Parametric observer HIF based on macroscopic timescale θ Time update of (2);
Figure FDA0003801785670000058
performing a system parameter theta and a parameter estimation error covariance P θ To obtain a corresponding estimated value
Figure FDA0003801785670000059
44 State observer AEKF based on microscopic time scales x Time update of (2);
Figure FDA00038017856700000510
start state observer AEKF x To obtain the prior estimated value of the system state X
Figure FDA00038017856700000511
And its error covariance P x Is estimated a priori
Figure FDA00038017856700000512
Priori estimated value based on available capacity of power battery
Figure FDA00038017856700000513
A priori estimates of sum states
Figure FDA00038017856700000514
Updating OCV value of power battery
Figure FDA00038017856700000515
45 State observer AEKF based on microscopic time scales x Updating the measurements of (1);
updating a state estimation innovation covariance matrix:
Figure FDA00038017856700000516
kalman gain matrix:
Figure FDA00038017856700000517
adaptive covariance matching:
Figure FDA0003801785670000061
noise covariance update:
Figure FDA0003801785670000062
Figure FDA0003801785670000063
and (3) correcting the estimated value of the system state:
Figure FDA0003801785670000064
state estimation error covariance update:
Figure FDA0003801785670000065
microscopic time scale cycle calculation l =1 Z And scale conversion:
Figure FDA0003801785670000066
Figure FDA0003801785670000067
Figure FDA0003801785670000068
Figure FDA0003801785670000069
completing the micro time scale cycle calculation under a macro time scale, and returning to the macro time scale to perform measurement updating of parameter estimation;
46 A state observer HIF based on macroscopic time scale θ Updating the measurement of (1):
Figure FDA00038017856700000610
h ∞ gain matrix:
Figure FDA00038017856700000611
and (3) correcting the estimated value of the system parameter:
Figure FDA00038017856700000612
updating an H-infinity feature matrix:
Figure FDA00038017856700000613
to this end, a multi-time scale estimation of the parameters and states at time k is completed, a state estimation at time (k + 1) is prepared, and the state estimation at time (k + 1) is performed
Figure FDA0003801785670000071
Obtain power electricityThe pool available capacity and real-time SOC estimate.
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CN116339153A (en) * 2023-05-22 2023-06-27 科大智能物联技术股份有限公司 Lime kiln control method based on particle swarm optimization
CN116339153B (en) * 2023-05-22 2023-09-01 科大智能物联技术股份有限公司 Lime Kiln Control Method Based on Particle Swarm Optimization
CN116449222A (en) * 2023-06-19 2023-07-18 中国第一汽车股份有限公司 Battery parameter determining method and device, processor and vehicle
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