CN115128472A - Battery multi-state joint estimation method based on autoregressive equivalent circuit model - Google Patents

Battery multi-state joint estimation method based on autoregressive equivalent circuit model Download PDF

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CN115128472A
CN115128472A CN202210846129.9A CN202210846129A CN115128472A CN 115128472 A CN115128472 A CN 115128472A CN 202210846129 A CN202210846129 A CN 202210846129A CN 115128472 A CN115128472 A CN 115128472A
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battery
state
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soc
soh
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刘芳
苏卫星
朱天贺
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Tianjin Polytechnic University
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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]
    • G01R31/385—Arrangements for measuring battery or accumulator variables
    • G01R31/387—Determining ampere-hour charge capacity or SoC
    • G01R31/388—Determining ampere-hour charge capacity or SoC involving voltage measurements
    • 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 battery multi-state joint estimation method based on an autoregressive equivalent circuit model, which comprises the following steps of: step one, establishing a data acquisition module; step two, establishing a distinguishing model parameter identification module; step three, establishing an SOC and SOH estimation module; step four, establishing an SOP estimation module; step five, establishing an information display module; step six, multi-state joint estimation; the method aims at the problem of mutual coupling among three key states (state of charge-SOC, state of health-SOH and power state-SOP) of the battery, so that a multi-state online joint estimation method of the battery is provided; providing a brand-new battery equivalent circuit model based on the AR model by utilizing the advantage that the AR model is infinitely close to a true value; on the basis, the problem that the state equation is easy to be subjected to non-positive determination is considered, and the battery multi-state joint estimation is finally realized by adopting a square root unscented Kalman filtering (SR-UKF) algorithm, so that the joint estimation of the SOC, the SOH, the SOP and the ECM parameters of the battery is really realized.

Description

Battery multi-state joint estimation method based on autoregressive equivalent circuit model
Technical Field
The invention relates to the technical field of establishment of a battery model and battery state estimation, in particular to a battery multi-state joint estimation method based on an autoregressive equivalent circuit model.
Background
In order to ensure efficient, safe, and reliable stable operation of the Battery, a Battery Management System (BMS) plays a crucial role. Critical states of the battery: accurate estimation of state of charge, state of health, and power state is a primary task of BMS and is also an important basis for its ability to manage electric vehicle power cells. Currently, several methods have been developed for estimating the battery multi-state, which can be roughly divided into two categories: modeless methods and battery model-based methods.
In a model-free method, an open-circuit voltage method and an ampere-hour integration method are adopted for SOC estimation, and the method does not need to establish a battery ECM and is low in calculation complexity. However, these methods are open-loop methods, which are prone to accumulated errors and cannot be eliminated, and they need to be periodically corrected in combination with other methods. For the SOH estimation problem, the existing model-free methods mainly include a differential voltage analysis method, an incremental capacity analysis method and the like, and the aging degree of the battery is estimated according to the external electrical characteristic change rule of the battery in the aging process. The method has the advantages that the complicated internal mechanism change of the battery aging process is not required to be concerned, and the method is easy to understand. However, the estimation accuracy of the algorithm is directly influenced by the problems of poor consistency and the like brought by the battery production process. For the estimation of the SOP, there is few model methods, which are mostly calculated based on an accurate battery model.
Estimation of key states of a battery based on a battery model is a mainstream research idea at present. For example, a filter family method suitable for both SOC estimation and SOH estimation is widely concerned because it does not need an accurate initial state value due to a self-contained closed-loop self-correction link, but the estimation accuracy of such a filter family method is extremely sensitive to the accuracy of a battery model, so the accuracy of the battery model directly determines the battery state estimation accuracy based on the filter family method. For the estimation problem of the SOP, most of the estimation problem is obtained based on an accurate battery model and model parameters, and limitation calculation considering factors such as battery voltage, current and SOC is comprehensively considered. Therefore, for the estimation of the three key states of the battery based on the battery model, the accuracy of the battery model directly determines the estimation accuracy of the key states of the battery. There are many researchers working on the problem of battery model, and the widely accepted and widely used model is an n-order RC equivalent circuit model (nRC-ECM), which is characterized by being able to simulate the dynamic electrical characteristics of the battery by using the characteristics of the electrical components, and balance the accuracy and complexity of the battery equivalent circuit by setting the value of n, the number of series RC loops. Xiong et al indicate that when the value of n takes 1, the AIC criteria indicate that the battery ECM is optimal at this time. However, for applications such as electric vehicles with random charge and discharge and severe current fluctuation, the 1 st order RC-ECM accuracy is not ideal.
In summary, in the practical application of the battery, the accuracies of the ECM, SOC, SOH, and SOP are coupled to each other: battery aging can potentially affect the estimation of SOC or lead to too high/too low SOP estimates; variations in ECM parameters and SOC have a significant effect on SOP. Considering the close relationship among ECM, SOC, SOH and SOP, joint estimation is essential in practical engineering applications and research on a single problem does not meet practical requirements.
Disclosure of Invention
The present invention aims to provide a battery multi-state joint estimation method based on an autoregressive equivalent circuit model, so as to solve the problems proposed in the background art.
In order to achieve the purpose, the invention provides the following technical scheme: the battery multi-state joint estimation method based on the autoregressive equivalent circuit model comprises the following steps: step one, establishing a data acquisition module; step two, establishing a distinguishing model parameter identification module; establishing an SOC and SOH estimation module; step four, establishing an SOP estimation module; step five, establishing an information display module; step six, multi-state joint estimation;
in the first step, firstly, a data acquisition module with a current acquisition unit and a voltage acquisition unit is established;
in the second step, a differential model parameter identification module with a slow and fast time-varying parameter identification unit is established; the estimation of the slow time-varying parameters needs to judge whether the collected current and voltage data reach the standard or not, and the calculation mode is as follows:
first, the collected voltage coverage is calculated:
ΔU d ＝|U d (1)-U d (k)|； (1)
the judgment rule is then as follows:
Figure BDA0003728505580000031
wherein U is d Is the terminal voltage of the battery, Δ U set To set a voltage span range, and consider Δ U set ≥0.85*(U max -U min ) Wherein U is max And U min Respectively the cut-off voltage of the charge and discharge of the battery;
in the third step, the SOC and SOH estimation module with the modeling unit based on the AR model, the state value initialization unit, and the state value online correction unit, then the modeling unit based on the AR model: firstly, a brand new equivalent circuit model is established, and U in the brand new equivalent circuit model n Represents the internal voltage drop of the cell; r represents the ohmic resistance inside the battery, U AR Representing the internal polarization voltage, U, of the cell OCV Represents the open circuit voltage, U, of the battery d Represents a terminal voltage of the battery; and the relation among the voltages of all parts is as follows:
U d (k)＝U OCV (k)-RI(k)-U AR (k) (3)
in the formula of U d (k)、U OCV (k)、U AR (k) Respectively representing a battery terminal voltage value, an open-circuit voltage value and an internal polarization voltage value at the moment k; i (k) represents the current at time k, defined here as charging negative and discharging positive;
it is then fitted using an AR model with current i (k) as input, which is:
Figure BDA0003728505580000032
wherein p is the order of the model, a i (i 1.. p) is an AR model coefficient, and accordingly, formula (3) is rewritten as follows：
Figure BDA0003728505580000041
Wherein the formula (5) is an AR model-based all-new ECM (AR-ECM) expression proposed in the present invention; as can be seen from the observation of the formula (5), wherein
Figure BDA0003728505580000042
The actual characterization of the cell internal voltage drop at time k is:
Figure BDA0003728505580000043
further, the expression at time k +1 is given as:
Figure BDA0003728505580000044
in the formulae (6) and (7), U n (k)、U n (k +1) represents the voltage in the battery at the time k and the time k +1, respectively; the internal voltage drop U of the battery can be obtained by the formulas (7) to (6) n The recursive expression of (c):
Figure BDA0003728505580000045
wherein Δ I (k +1-I) ═ I (k +1-I) -I (k-I); when i is 0, a 0 Represents ohmic internal resistance; a is 0 ＝R；a i P represents the AR model coefficients for standard polarization voltage drop;
the SOH, which reflects the degree of battery aging, is considered to be in a long-term gradual change state, which only varies in the range of [0.8,1] over the full life cycle of the battery; therefore, it can be considered that the SOH of the battery remains unchanged for the two preceding and following sampling instants, that is:
L SOH (k+1)＝L SOH (k) (9)
wherein L is SOH (k +1) and L SOH (k) Respectively representing the SOH value of the battery at the k +1 moment and the k moment(ii) a The recursive expression of the SOC of the battery given by the ampere-hour integration method is as follows:
Figure BDA0003728505580000051
in the formula (10), L SOC (k +1) and L SOC (k) Respectively representing SOC values at the k +1 moment and the k moment; Δ t is the sampling period; c n Is the nominal capacity of the battery; η represents a coefficient relating to temperature and charge/discharge rate; based on SOC, SOH and U of the battery n For a hidden state, the state space discrete equation of the battery is given as follows:
Figure BDA0003728505580000052
wherein, the state variable x (k) is set as [ L ] SOH (k) L SOC (k) U n (k)] T Control quantity u (k) ═ I (k +1),.. I (k +1-p)] T (ii) a Selecting terminal voltage U d As observed variables, the observed equation can be derived:
U d (k)＝Gx(k)+U OCV (L SOC (K))+υ k (12)
in the above formula, G ═ 00-1]；υ k For observation noise, its covariance is R; open circuit voltage U OCV Can be expressed as a battery state of charge L SOC Function of (c):
Figure BDA0003728505580000053
in the formula k 0 -k 4 Is a parameter to be identified; the complete state equation for AR-ECM is given up to this:
Figure BDA0003728505580000061
in the formula, w k Is system noise, with covariance Q; f (-) represents the negation of the state variable x (k) and the controlled variable u (k) given by the formula (11)A linear functional relation, h (-) represents a nonlinear functional relation between the state variable x (k) and the controlled variable u (k) given by the formula (12);
in the fourth step, the SOP estimation module is provided with an SOP estimation unit under multi-constraint limitation;
in the fifth step, an information display module with a battery key state output display unit is arranged;
in the sixth step, after real-time current and voltage data are collected from the vehicle-mounted battery, the vehicle-mounted battery enters a differentiated model parameter identification module, and the module carries out a fast time-varying or slow time-varying parameter identification strategy on the model parameters by identifying different characteristics of the model parameters; and then, obtaining a model parameter result as the input of an SOC and SOH estimation module, then combining the three-dimensional state space model and an SR-UKF algorithm to obtain an estimation result of the SOC and the SOH, using the model parameter and the SOC as the input of the SOP estimation module, further obtaining an SOP estimation result under multiple constraints, and finally outputting the results of all the battery key states estimated by the method.
Preferably, in the first step, the input ends of the current collecting unit and the voltage collecting unit are connected with the output end of the vehicle-mounted power battery.
Preferably, in the second step, the input ends of the slow time-varying parameter identification unit and the fast time-varying parameter identification unit are connected with the output ends of the current acquisition unit and the voltage acquisition unit in the first step.
Preferably, in the third step, the input end of the modeling unit based on the AR model is connected to the output end of the fast and slow time-varying parameter identification unit in the second step, and the output end of the modeling unit based on the AR model is connected to the input end of the state value initialization unit; the output end of the state value initialization unit is connected with the input end of the state value online correction unit.
Preferably, in the fourth step, the input end of the SOP estimation unit under the multiple constraint limits is connected to the output end of the fast and slow time-varying parameter identification unit in the second step; the input end of the SOP estimation unit under multiple constraints is connected with the output end of the state value online correction unit in the step three.
Preferably, in the fifth step, the input end of the battery key state output display unit is connected with the output end of the state value online correction unit in the third step; the input end of the battery key state output display unit is connected with the output end of the SOP estimation unit under the multi-constraint limit in the step four.
Compared with the prior art, the invention has the beneficial effects that:
1) the ECM utilizes the AR model to simulate a polarization voltage drop part highly related to the current change rate in the battery so as to realize the purpose of simulating the dynamic characteristics of the battery with high precision under the condition of severe current fluctuation, so that the ECM is more suitable for the battery multi-state joint estimation problem in the random charge and discharge application scene;
2) the method is based on the completely new ECM, and a state space equation representing SOC, SOH and battery model parameters is deduced; considering the requirements of practical engineering application on algorithm calculation speed and complexity, comprehensively analyzing different parameter characteristics and change rules in the battery model, and giving a differentiated updating strategy;
3) the invention considers the problem that a state matrix is uncertain easily appearing in the state estimation of a filter family algorithm under a multi-state, and proposes a multi-state joint estimation algorithm based on SR-UKF to realize the joint state estimation of SOH, SOC and the internal pressure drop of a battery; meanwhile, an SOC estimation value and a battery internal voltage drop value are integrated to an SOP estimator, so that SOP on-line estimation under multiple constraints is realized; finally, an AR-ECM-based battery multi-state joint estimator is formed.
Drawings
FIG. 1 is a block diagram of the structural principle of the present invention;
FIG. 2 is a schematic diagram of an autoregressive model-based equivalent circuit model of a battery according to the present invention;
FIG. 3 is a schematic diagram of a differentiated model parameter identification strategy according to the present invention;
FIG. 4 is a flow chart of the method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-4, an embodiment of the present invention is shown: the battery multi-state joint estimation method based on the autoregressive equivalent circuit model comprises the following steps: step one, establishing a data acquisition module; step two, establishing a distinguishing model parameter identification module; establishing an SOC and SOH estimation module; step four, establishing an SOP estimation module; step five, establishing an information display module; step six, multi-state joint estimation;
in the first step, firstly, a data acquisition module with a current acquisition unit and a voltage acquisition unit is established, and the input ends of the current acquisition unit and the voltage acquisition unit are connected with the output end of a vehicle-mounted power battery;
in the second step, a differential model parameter identification module with a slow and fast time-varying parameter identification unit is established; the input ends of the slow time-varying parameter identification unit and the fast time-varying parameter identification unit are connected with the output ends of the current acquisition unit and the voltage acquisition unit in the step one, wherein the estimation of the slow time-varying parameter needs to judge whether the acquired current and voltage data cover the standard, and the calculation mode is as follows:
first, the collected voltage coverage is calculated:
ΔU d ＝|U d (1)-U d (k)|； (1)
the judgment rule is then as follows:
Figure BDA0003728505580000081
wherein U is d Is the terminal voltage of the battery, Δ U set To set a voltage span range, and consider Δ U set ≥0.85*(U max -U min ) Wherein U is max And U min Respectively is the cut-off voltage of the charge and discharge of the battery;
in the third step, an SOC and SOH estimation module with an AR model-based modeling unit, a state value initialization unit and a state value online correction unit is provided, wherein the input end of the AR model-based modeling unit is connected with the output ends of the fast and slow time-varying parameter identification units in the second step, and the output end of the AR model-based modeling unit is connected with the input end of the state value initialization unit; the output end of the state value initialization unit is connected with the input end of the state value online correction unit, and then the modeling unit based on the AR model: firstly, a brand new equivalent circuit model is established, the brand new equivalent circuit model is as shown in FIG. 2, and U in the brand new equivalent circuit model n Represents the internal voltage drop of the cell; r represents the ohmic resistance inside the battery, U AR Representing the internal polarization voltage, U, of the cell OCV Represents the open circuit voltage, U, of the battery d Represents a terminal voltage of the battery; and the relation among the voltages of all parts is as follows:
U d (k)＝U OCV (k)-RI(k)-U AR (k) (3)
in the formula of U d (k)、U OCV (k)、U AR (k) Respectively representing a battery terminal voltage value, an open-circuit voltage value and an internal polarization voltage value at the moment k; i (k) represents the current at time k, defined here as charging negative and discharging positive;
it is then fitted using an AR model with current i (k) as input, which is:
Figure BDA0003728505580000091
wherein p is the order of the model, a i (i 1.. p) are AR model coefficients, from which formula (3) is rewritten as follows:
Figure BDA0003728505580000092
wherein formula (5) is an AR model-based all-new ECM (AR-ECM) expression proposed in the present invention; as can be seen from the following formula (5), wherein
Figure BDA0003728505580000093
The internal voltage drop of the cell at the moment k is actually characterized, namely:
Figure BDA0003728505580000101
further, the expression at time k +1 is given as:
Figure BDA0003728505580000102
in the formulae (6) and (7), U n (k)、U n (k +1) represents the voltage in the battery at the time k and the time k +1, respectively; the internal voltage drop U of the battery can be obtained by the formulas (7) to (6) n The recursive expression of (c):
Figure BDA0003728505580000103
wherein Δ I (k +1-I) ═ I (k +1-I) -I (k-I); when i is 0, a 0 Represents ohmic internal resistance; a is 0 ＝R；a i I 1.. p represents AR model coefficients of standard polarization voltage drop;
the SOH, which reflects the degree of battery aging, is considered to be in a long-term gradual change state, which only varies in the range of [0.8,1] over the full life cycle of the battery; therefore, it can be considered that the SOH of the battery remains unchanged for the two preceding and following sampling instants, that is:
L SOH (k+1)＝L SOH (k) (9)
wherein L is SOH (k +1) and L SOH (k) Respectively representing the SOH value of the battery at the k +1 moment and the K moment; the recursive expression of the SOC of the battery given by the ampere-hour integration method is as follows:
Figure BDA0003728505580000104
in the formula (10), L SOC (k +1) and L SOC (k) Respectively represent kSOC values at +1 time and k time; Δ t is the sampling period; c n Is the nominal capacity of the battery; η represents a coefficient relating to temperature and charge/discharge rate; based on SOC, SOH and U of the battery n For a hidden state, the state space discrete equation of the battery is given as follows:
Figure BDA0003728505580000111
wherein, the state variable x (k) is L SOH (k) L SOC (k) U n (k)] T Control quantity u (k) ═ I (k +1),.. I (k +1-p)] T (ii) a Selecting terminal voltage U d As observed variables, the observed equation can be derived:
U d (k)＝Gx(k)+U OCV (L SOC (K))+υ k (12)
in the above formula, G ═ 00-1]；υ k For observation noise, its covariance is R; open circuit voltage U OCV Can be expressed as a battery state of charge L SOC Function of (c):
Figure BDA0003728505580000112
in the formula k 0 -k 4 Is a parameter to be identified; the AR-ECM complete state equation is given up to this:
Figure BDA0003728505580000113
in the formula, w k Is system noise, with covariance Q; f (-) represents the nonlinear functional relation between the state variable x (k) and the controlled variable u (k) given by the formula (11), and h (-) represents the nonlinear functional relation between the state variable x (k) and the controlled variable u (k) given by the formula (12);
in the fourth step, an SOP estimation module with an SOP estimation unit under multiple constraint limits is provided, and the input end of the SOP estimation unit under multiple constraint limits is connected with the output ends of the fast and slow time-varying parameter identification units in the second step; the input end of the SOP estimation unit under multiple constraints is connected with the output end of the state value online correction unit in the third step;
in the fifth step, an information display module with a battery key state output display unit is arranged; the input end of the battery key state output display unit is connected with the output end of the state value online correction unit in the step three; the input end of the battery key state output display unit is connected with the output end of the SOP estimation unit under the multi-constraint limit in the step four;
in the sixth step, after real-time current and voltage data are collected from the vehicle-mounted battery, a distinguishing model parameter identification module is entered, and the distinguishing model parameter identification module carries out a fast time-varying or slow time-varying parameter identification strategy on the model parameters by identifying different characteristics of the model parameters; and then, obtaining a model parameter result as the input of an SOC and SOH estimation module, then combining the three-dimensional state space model and an SR-UKF algorithm to obtain an estimation result of the SOC and the SOH, using the model parameter and the SOC as the input of the SOP estimation module, further obtaining an SOP estimation result under multiple constraints, and finally outputting the results of all the battery key states estimated by the method.
In order to verify the effectiveness and the practicability of the AR-ECM-based Battery multi-state joint estimation algorithm, the charging and discharging data of an A123 Battery in an open data set of a CALCE Battery Research Group of the university of Maryland under the working condition of a Dynamic Stress Test (DST) are selected for experimental verification, and the specifications of the A123 Battery are as follows:
type (B) Nominal voltage (V) Nominal capacity (Ah) Charging/dischargingCut-off voltage (V) Maximum discharge current (A)
LiFePO 4 3.3 1.1 3.6/2.0 30
And the experiment verifies that the specific steps are as follows:
the method comprises the following steps: based on the autoregressive equivalent circuit model and the charging and discharging data of the A123 battery, a recursive least square algorithm is adopted, and a differentiated model parameter identification strategy is used for updating parameters, wherein the specific strategy is shown in figure 3; the parameters to be identified in this example include two types, one is a slowly time-varying parameter, that is, equation (13) represents the open-circuit voltage U of the battery OCV Coefficient k in function of SOC 0 ,...,k 4 (ii) a The other is a fast time-varying parameter, namely formula (8) for representing the internal voltage drop U of the battery n Coefficient of function relation with current I-AR model coefficient a i ,i＝0,1,...,p；
Step two: the obtained model parameter result is used as the input of an SOC and SOH estimation module, the estimation of the SOC and the SOH is realized by adopting an SR-UKF algorithm, and the specific steps of the SR-UKF algorithm are as follows:
1) initializing a state value:
Figure BDA0003728505580000131
x 0 denotes a state x ═ L given randomly at the initial time SOH L SOC U n ] T An initial value of (1);
2) cholesky decomposition:
Figure BDA0003728505580000132
wherein chol (·) represents a Cholesky decomposition operation; s 0 Cholesky factor representing state error covariance matrix;
3) build a Sigma point set:
Figure BDA0003728505580000133
wherein the content of the first and second substances,
Figure BDA0003728505580000134
represents the ith Sigma point at the k-1 moment; n is the state dimension; λ ═ α 2 (n + k) -n, k is a scaling factor, usually taken as 0 or 3-n, α reflects the deviation of the Sigma spot around the mean, S k-1|k-1 Cholesky factor representing the state error covariance matrix at time k-1;
4) and (3) state one-step prediction:
Figure BDA0003728505580000135
Figure BDA0003728505580000136
Figure BDA0003728505580000137
Figure BDA0003728505580000138
wherein
Figure BDA0003728505580000141
To represent
Figure BDA0003728505580000142
The one-step estimation value of (1);
Figure BDA0003728505580000143
to represent
Figure BDA0003728505580000144
1.., 2 n; w is a m ，w c Mean weight and variance weight, respectively:
Figure BDA0003728505580000145
Figure BDA0003728505580000146
in the formula w m ，w c The superscript i of (a) represents a weight corresponding to the ith Sigma point; QR (-) denotes a QR decomposition function; s k|k-1 Represents a one-step estimate of the Cholesky factor;
Figure BDA0003728505580000147
the superscripts of (1) respectively represent the ith weight value or one-step estimated state value, i ═ 1.., 2 n; choleupdate (·) represents the update function of Cholesky decomposition;
5) and (3) observation estimation value calculation:
Figure BDA0003728505580000148
Figure BDA0003728505580000149
Figure BDA00037285055800001410
Figure BDA00037285055800001411
Figure BDA00037285055800001412
wherein the content of the first and second substances,
Figure BDA00037285055800001413
a one-step estimate representing the observed value;
Figure BDA00037285055800001414
to represent
Figure BDA00037285055800001415
Weighted observation estimates, i ═ 1, ·,2 n;
Figure BDA00037285055800001416
1, 2n one-step estimates representing the observed values; s yk Cholesky factor which is the observed error covariance; p xk,yk Is a cross covariance matrix;
6) and (3) state correction:
K k ＝(P xk,yk /S yk T )/S yk (27)
Figure BDA0003728505580000151
U＝K k S yk (29)
S k|k ＝cholupdate{S k|k-1 ,U,-1} (30)
wherein K k Kalman gain at time k;
Figure BDA0003728505580000152
is the corrected state value; y is k Is an observation vector at the k moment; s k|k Cholesky factor at time k;
step three: obtaining peak current results under voltage limit, SOC limit and battery design current limit based on the model parameter identification result, the SOC estimation result and the battery specification limit, and finally obtaining an SOP estimation result under multiple constraints; the parameter limits under the cell design in this example are shown in the following table:
parameter(s) Maximum value Minimum value
SOC(％) 15 100
Current I (A) -30 30
Voltage U d (V) 2 3.6
In conclusion, the multi-state joint estimation of the SOC, the SOH and the SOP of the battery is finally realized.
Based on the above, the invention has the advantages that the invention comprises a data acquisition module with a current and voltage acquisition unit, a differentiated model parameter identification module with a slow and fast time-varying parameter identification unit, an SOC and SOH estimation module with an AR model-based modeling unit, a state value initialization unit and a state value online correction unit, an SOP estimation module with an SOP estimation unit under multi-constraint limitation, and an information display module with a battery key state output display unit; when real-time current and voltage data are acquired from the vehicle-mounted battery, the data enter a differentiated model parameter identification module, and the module carries out a fast time-varying or slow time-varying parameter identification strategy on the model parameters by identifying different characteristics of the model parameters; then, the obtained model parameter result is used as the input of an SOC and SOH estimation module, and the estimation results of the SOC and the SOH are obtained by combining the three-dimensional state space model provided by the method and an SR-UKF algorithm; the model parameters and the SOC are used as the input of the SOP estimation module, so that an SOP estimation result under multiple constraints is obtained, the requirements of practical engineering application on algorithm calculation speed and complexity are considered, different parameter characteristics and change rules in the battery model are comprehensively analyzed, and a differentiated updating strategy is provided.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Claims (6)

1. The battery multi-state joint estimation method based on the autoregressive equivalent circuit model comprises the following steps: step one, establishing a data acquisition module; step two, establishing a distinguishing model parameter identification module; establishing an SOC and SOH estimation module; step four, establishing an SOP estimation module; step five, establishing an information display module; step six, multi-state joint estimation; the method is characterized in that:
in the first step, firstly, a data acquisition module with a current acquisition unit and a voltage acquisition unit is established;
in the second step, a differential model parameter identification module with a slow time-varying parameter identification unit and a fast time-varying parameter identification unit is established; the estimation of the slow time-varying parameters needs to judge whether the acquired current and voltage data reach the standard or not, and the calculation mode is as follows:
first, the collected voltage coverage is calculated:
ΔU d ＝|U d (1)-U d (k)|； (1)
the judgment rule is then as follows:
Figure FDA0003728505570000011
wherein U is d Is the terminal voltage of the battery, Δ U set To set a voltage span range, and consider Δ U set ≥0.85*(U max -U min ) Wherein U is max And U min Respectively is the cut-off voltage of the charge and discharge of the battery;
in the third step, the SOC and SOH estimation module with the modeling unit based on the AR model, the state value initialization unit, and the state value online correction unit, then the modeling unit based on the AR model: firstly, a brand new equivalent circuit model is established, and U in the brand new equivalent circuit model n Represents the internal voltage drop of the cell; r represents the ohmic resistance inside the battery, U AR Representing the internal polarization voltage, U, of the cell OCV Represents the open circuit voltage, U, of the battery d Represents a terminal voltage of the battery; and the relation among the voltages of all parts is as follows:
U d (k)＝U OCV (k)-RI(k)-U AR (k) (3)
in the formula of U d (k)、U OCV (k)、U AR (k) Respectively representing a battery terminal voltage value, an open-circuit voltage value and an internal polarization voltage value at the moment k; i (k) represents the current at time k, defined here as charging negative and discharging positive;
it is then fitted using an AR model with current i (k) as input, which is:
Figure FDA0003728505570000021
wherein p is the order of the model, a i (i 1.. p) are AR model coefficients, from which formula (3) is rewritten as follows:
Figure FDA0003728505570000022
wherein formula (5) is an AR model-based all-new ECM (AR-ECM) expression proposed in the present invention; as can be seen from the observation of the formula (5), wherein
Figure FDA0003728505570000023
The internal voltage drop of the cell at the moment k is actually characterized, namely:
Figure FDA0003728505570000024
further, the expression at time k +1 is given as:
Figure FDA0003728505570000025
in the formulae (6) and (7), U n (k)、U n (k +1) represents the voltage in the battery at the time k and the time k +1, respectively; the internal voltage drop U of the battery can be obtained by the formulas (7) to (6) n The recursive expression of (c):
Figure FDA0003728505570000031
wherein Δ I (k +1-I) ═ I (k +1-I) -I (k-I); when i is 0, a 0 Represents ohmic internal resistance; a is 0 ＝R；a i P represents the AR model coefficients for standard polarization voltage drop;
the SOH reflecting the aging degree of the battery belongs to a long-term gradual change state, and the change range of the SOH within the whole life cycle of the battery is only [0.8,1 ]; therefore, it can be considered that the SOH of the battery remains unchanged for the two preceding and following sampling instants, that is:
L SOH (k+1)＝L SOH (k) (9)
wherein L is SOH (k +1) and L SOH (k) Respectively representing the SOH value of the battery at the k +1 moment and the K moment; the recursive expression of the SOC of the battery given by the ampere-hour integration method is as follows:
Figure FDA0003728505570000032
in the formula (10), L SOC (k +1) and L SOC (k) Respectively representing SOC values at the k +1 moment and the k moment; Δ t is the sampling period; c n Is the nominal capacity of the battery; η represents a coefficient relating to temperature and charge/discharge rate; based on SOC, SOH and U of the battery n For a hidden state, the state space discrete equation of the battery is given as follows:
Figure FDA0003728505570000033
wherein, the state variable x (k) is set as [ L ] SOH (k) L SOC (k) U n (k)] T Control quantity u (k) ═ I (k +1),.. I (k +1-p)] T (ii) a Selecting terminal voltage U d As observed variables, the observed equation can be derived:
U d (k)＝Gx(k)+U OCV (L SOC (K))+υ k (12)
in the above formula, G ═ 00-1]；υ k For observation noise, its covariance is R; open circuit voltage U OCV Can be expressed as a battery state of charge L SOC Function of (c):
Figure FDA0003728505570000041
in the formula k 0 -k 4 Is a parameter to be identified; the complete state equation for AR-ECM is given up to this:
Figure FDA0003728505570000042
in the formula, w k Is system noise, with covariance Q; f (-) represents the nonlinear functional relationship between the state variable x (k) and the controlled variable u (k) given by the formula (11), h (-) represents the state variable x (k) and the controlled variable u (k) given by the formula (12)The non-linear functional relationship of (a);
in the fourth step, the SOP estimation module is provided with an SOP estimation unit under multi-constraint limitation;
in the fifth step, an information display module with a battery key state output display unit is arranged;
in the sixth step, after real-time current and voltage data are collected from the vehicle-mounted battery, a distinguishing model parameter identification module is entered, and the distinguishing model parameter identification module carries out a fast time-varying or slow time-varying parameter identification strategy on the model parameters by identifying different characteristics of the model parameters; and then, obtaining a model parameter result as the input of an SOC and SOH estimation module, then combining the three-dimensional state space model and an SR-UKF algorithm to obtain an estimation result of the SOC and the SOH, using the model parameter and the SOC as the input of the SOP estimation module, further obtaining an SOP estimation result under multiple constraints, and finally outputting the results of all the battery key states estimated by the method.
2. The battery multi-state joint estimation method based on the autoregressive equivalent circuit model according to claim 1, characterized in that: in the first step, the input ends of the current acquisition unit and the voltage acquisition unit are connected with the output end of the vehicle-mounted power battery.
3. The battery multi-state joint estimation method based on the autoregressive equivalent circuit model according to claim 1, characterized in that: in the second step, the input ends of the slow time-varying parameter identification unit and the fast time-varying parameter identification unit are connected with the output ends of the current acquisition unit and the voltage acquisition unit in the first step.
4. The battery multi-state joint estimation method based on the autoregressive equivalent circuit model according to claim 1, characterized in that: in the third step, the input end of the modeling unit based on the AR model is connected with the output ends of the fast and slow time-varying parameter identification units in the second step, and the output end of the modeling unit based on the AR model is connected with the input end of the state value initialization unit; the output end of the state value initialization unit is connected with the input end of the state value online correction unit.
5. The battery multi-state joint estimation method based on the autoregressive equivalent circuit model according to claim 1, characterized in that: in the fourth step, the input end of the SOP estimation unit under the multi-constraint limit is connected with the output end of the fast and slow time-varying parameter identification unit in the second step; the input end of the SOP estimation unit under multiple constraints is connected with the output end of the state value online correction unit in the step three.
6. The battery multi-state joint estimation method based on the autoregressive equivalent circuit model according to claim 1, characterized in that: in the fifth step, the input end of the battery key state output display unit is connected with the output end of the state value online correction unit in the third step; the input end of the battery key state output display unit is connected with the output end of the SOP estimation unit under the multi-constraint limit in the fourth step.
CN202210846129.9A 2022-07-04 2022-07-04 Battery multi-state joint estimation method based on autoregressive equivalent circuit model Pending CN115128472A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116204387A (en) * 2023-04-26 2023-06-02 之江实验室 Chip current prediction method and device, medium and electronic equipment
CN116204387B (en) * 2023-04-26 2023-07-21 之江实验室 Chip current prediction method and device, medium and electronic equipment

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