CN116047304A - Combined estimation method for state of charge and state of health of energy storage battery - Google Patents

Combined estimation method for state of charge and state of health of energy storage battery Download PDF

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CN116047304A
CN116047304A CN202211637692.1A CN202211637692A CN116047304A CN 116047304 A CN116047304 A CN 116047304A CN 202211637692 A CN202211637692 A CN 202211637692A CN 116047304 A CN116047304 A CN 116047304A
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energy storage
storage battery
model
state
estimated value
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李泽文
王文
蔡雨思
邓芳明
高波
韩建
曾晗
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East China Jiaotong 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]
    • G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
    • G01R31/3842—Arrangements for monitoring battery or accumulator variables, e.g. SoC combining voltage and current 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
    • Y02E60/10—Energy storage using batteries

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Abstract

A method of joint estimation of state of charge and state of health of an energy storage battery, comprising: establishing an equivalent circuit model of the energy storage battery; performing parameter identification on the equivalent circuit model of the energy storage battery to obtain an estimated value of the parameter of the equivalent circuit model of the energy storage battery; when the electric quantity of the energy storage battery is larger than 0, acquiring an estimated value of the actual charged electric quantity by adopting an off-line established new battery OCV-SOC model according to the estimated value of the parameters of the equivalent circuit model of the energy storage battery, the new battery OCV-SOC model and an extended Kalman filtering algorithm; when the electric quantity of the energy storage battery is equal to 0, an OCV aging model is established, and an estimated value of the available capacity of the energy storage battery is obtained according to the OCV aging model and an extended Kalman filtering algorithm; and obtaining an estimated value of the SOC and an estimated value of the SOH according to the estimated value of the actual charge quantity and the estimated value of the available capacity of the energy storage battery. The estimated value of the SOC and the estimated value of the SOH obtained by the method are more accurate.

Description

Combined estimation method for state of charge and state of health of energy storage battery
Technical Field
The invention relates to the technical field of battery testing, in particular to a combined estimation method of the state of charge and the state of health of an energy storage battery.
Background
The investment of the energy storage battery maintains the stable operation of the new energy power generation system. The energy management of the energy storage battery is particularly important, and a reasonable energy storage battery model, accurate model parameter identification and battery state estimation are all preconditions for the energy management of the energy storage battery. The battery State of the energy storage battery includes State of Charge (SOC), state of Health (SOH). SOC reflects the remaining charge of the battery, SOH reflects the aging condition of the battery, and battery state estimation is the basis of battery energy management.
Conventional energy storage battery models (e.g., equivalent circuit models) often use a least squares method to perform model parameter identification, and use a kalman filter algorithm to estimate the state of charge. But offline least squares methods have difficulty characterizing the dynamic performance of battery parameters. In addition, a fixed OCV-SOC curve model is often used in the parameter identification, the estimation process of the state of charge and the state of health, and the aging degree of the battery is gradually increased along with the increment of the use times of the battery, so that the fixed OCV-SOC curve model can bring larger aging errors, and the estimation result of the state of charge and the state of health may be inaccurate.
Disclosure of Invention
The invention aims to provide a combined estimation method of the state of charge and the state of health of an energy storage battery, which is used for establishing an OCV aging model in consideration of the influence of battery aging on the state of charge estimation so as to accurately correct the aging error of SOC estimation according to the OCV aging model, so that the acquired estimated value of the SOC and the estimated value of SOH are more accurate.
A method of joint estimation of state of charge and state of health of an energy storage battery, comprising:
establishing an equivalent circuit model of the energy storage battery;
performing parameter identification on the equivalent circuit model of the energy storage battery to obtain an estimated value of the parameter of the equivalent circuit model of the energy storage battery;
when the electric quantity of the energy storage battery is larger than 0, acquiring an estimated value of the actual charged electric quantity by adopting an off-line established new battery OCV-SOC model according to the estimated value of the parameters of the equivalent circuit model of the energy storage battery, the new battery OCV-SOC model and an extended Kalman filtering algorithm; when the electric quantity of the energy storage battery is equal to 0, an OCV aging model is established, and an estimated value of the available capacity of the energy storage battery is obtained according to the OCV aging model and an extended Kalman filtering algorithm;
and obtaining an estimated value of the SOC and an estimated value of the SOH according to the estimated value of the actual charge quantity and the estimated value of the available capacity of the energy storage battery.
The method for jointly estimating the state of charge and the state of health of the energy storage battery, wherein the step of carrying out parameter identification on the equivalent circuit model of the energy storage battery to obtain the estimated value of the parameter of the equivalent circuit model of the energy storage battery specifically comprises the following steps:
acquiring parameters of an equivalent circuit model of the energy storage battery according to the equivalent circuit model of the energy storage battery;
acquiring a measured value of terminal voltage and a measured value of current of the energy storage battery under a charging working condition of the energy storage battery;
and obtaining an estimated value of a parameter of an equivalent circuit model of the energy storage battery through an extended Kalman filtering algorithm according to the measured value of the terminal voltage of the energy storage battery and the measured value of the current.
The method for jointly estimating the state of charge and the state of health of the energy storage battery, wherein the equivalent circuit model of the energy storage battery is a first-order circuit model, and acquiring parameters of the equivalent circuit model of the energy storage battery according to the equivalent circuit model of the energy storage battery specifically comprises:
obtaining a KVL equation of the first-order circuit model according to the first-order circuit model and kirchhoff's law;
discretizing the KVL equation of the first-order circuit model to obtain a terminal voltage expression of the first-order circuit model;
and acquiring parameters of the first-order circuit model according to the terminal voltage expression of the first-order circuit model, wherein the parameters of the equivalent circuit model of the energy storage battery comprise the parameter open-circuit voltage of the first-order circuit model.
According to the above combined estimation method of the state of charge and the state of health of the energy storage battery, the obtaining the estimated value of the parameter of the equivalent circuit model of the energy storage battery by expanding a kalman filtering algorithm specifically includes:
according to the identification model of the parameters of the equivalent circuit model of the energy storage battery, establishing a state prediction equation of the parameters of the equivalent circuit model of the energy storage battery and a measurement equation of the parameters of the equivalent circuit model of the energy storage battery;
according to an extended Kalman filtering algorithm, inputting the measured value of the terminal voltage and the measured value of the current, combining a state prediction equation of parameters of an equivalent circuit model of the energy storage battery and a measurement equation of parameters of the equivalent circuit model of the energy storage battery, predicting through prior estimation, and calculating Kalman filtering gain of an identification model of the parameters of the equivalent circuit model of the energy storage battery;
updating through posterior estimation according to an extended Kalman filtering algorithm, updating Kalman filtering gain and posterior estimation covariance of an identification model of parameters of an equivalent circuit model of the energy storage battery, and correcting current parameter estimation by using the posterior estimation covariance to obtain an estimated value of the parameters of the equivalent circuit model of the energy storage battery.
The method for jointly estimating the state of charge and the state of health of the energy storage battery, wherein the method for acquiring the estimated value of the actual charge quantity by adopting the new battery OCV-SOC model established offline according to the estimated value of the parameters of the equivalent circuit model of the energy storage battery, the new battery OCV-SOC model and the extended Kalman filtering algorithm specifically comprises the following steps:
acquiring a state prediction equation of the actual charge quantity of the energy storage battery in a charging state;
an off-line established new battery OCV-SOC model is adopted, and a terminal voltage measurement model is established according to the estimated values of parameters of the new battery OCV-SOC model and an equivalent circuit model of the energy storage battery;
according to an extended Kalman filtering algorithm, inputting measured values of the terminal voltage, the measured values of the current and estimated values of parameters of an equivalent circuit model of the energy storage battery, predicting through prior estimation, and calculating Kalman filtering gain of charge quantity estimation; and updating through posterior estimation according to an extended Kalman filtering algorithm, updating Kalman filtering gain and posterior estimation covariance of the charge electric quantity estimation, and correcting the current electric quantity estimation by using the posterior estimation covariance to obtain an estimated value of the actual charge electric quantity.
The method for jointly estimating the state of charge and the state of health of the energy storage battery, wherein the establishment of the OCV aging model specifically comprises the following steps:
and under the full-discharge state, acquiring the open-circuit voltage of the instantaneous energy storage battery to be charged as a data sample, and fitting the data sample by adopting a least square method to acquire an OCV aging model.
The method for jointly estimating the state of charge and the state of health of the energy storage battery, wherein the obtaining the estimated value of the available capacity of the energy storage battery according to the OCV aging model and the extended Kalman filtering algorithm specifically comprises the following steps:
establishing a prediction equation of the available capacity of the energy storage battery;
establishing a terminal voltage measurement equation of the available capacity of the energy storage battery according to the OCV aging model;
according to an extended Kalman filtering algorithm, inputting the measured value of the terminal voltage and the measured value of the current, introducing an OCV aging model by using a partial differential equation method, predicting by prior estimation, and calculating Kalman filtering gain of the available capacity estimation of the energy storage battery; and updating through posterior estimation according to an extended Kalman filtering algorithm, updating Kalman filtering gain and posterior estimation covariance of the available capacity estimation of the energy storage battery, and correcting the current available capacity by using the posterior estimation covariance to obtain an estimated value of the available capacity of the energy storage battery.
The method for jointly estimating the state of charge and the state of health of the energy storage battery, wherein obtaining the estimated value of the SOC and the estimated value of the SOH according to the estimated value of the actual charge amount and the estimated value of the available capacity of the energy storage battery specifically includes:
acquiring an initial value of the residual electric quantity of the energy storage battery in a charging state, and acquiring an estimated value of the SOC according to the estimated value of the available capacity of the energy storage battery, the initial value of the residual electric quantity of the energy storage battery in the charging state and the estimated value of the actual charging electric quantity;
and acquiring a capacity value of a new battery, and acquiring an estimated value of the SOH according to the capacity value of the new battery and the estimated value of the available capacity of the energy storage battery.
The beneficial effects of the invention are as follows:
the invention adopts an extended Kalman filtering algorithm to carry out parameter identification, charge state estimation and health state estimation of an equivalent circuit model of the energy storage battery. The method for identifying the parameters has good online expression capability, solves the problem that the traditional least square method offline identification is difficult to reflect the actual condition of the current charge and discharge state, enables the parameter identification to be closer to the actual condition, and realizes the dynamic response of the parameters under the dynamic working condition. In addition, the estimation of the state of charge and the estimation method of the state of health provided by the invention take the influence of the aging of the energy storage battery on the OCV-SOC model into consideration, so that an OCV aging model is established for correcting aging errors caused by a fixed OCV-SOC curve. By combining a Kalman filtering algorithm, the SOC estimation value and the SOH estimation value obtained by the SOC estimation method are more true and accurate.
Drawings
FIG. 1 is a flow chart of a method for joint estimation of state of charge and state of health of an energy storage battery according to an embodiment;
FIG. 2 is a schematic diagram of the result of a first-order circuit model according to an embodiment;
FIG. 3 is a detailed flow chart of step 102;
FIG. 4 is a detailed flow chart of step 301;
FIG. 5 is a detailed flow chart of step 303;
FIG. 6 is a detailed flow chart of step 104;
FIG. 7 is a full-discharge open-circuit voltage U according to an embodiment OCV0 -C available Fitting a graph;
FIG. 8 is a detailed flow chart of step 105;
FIG. 9 is a detailed flow chart of step 106;
FIG. 10 is a waveform diagram of an input excitation current according to an embodiment;
FIG. 11 is a waveform diagram of an input voltage according to an embodiment;
FIG. 12 is R according to an embodiment 0 Is characterized by being a schematic diagram of different aging degree identification conditions;
FIG. 13 is R according to an embodiment p Is characterized by being a schematic diagram of different aging degree identification conditions;
FIG. 14 is a diagram of C according to an embodiment p Is characterized by being a schematic diagram of different aging degree identification conditions;
FIG. 15 is a U according to an embodiment ocv Is characterized by being a schematic diagram of different aging degree identification conditions;
fig. 16 is a schematic diagram of a charge capacity estimation case according to an embodiment.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Some embodiments of the present invention provide a method for jointly estimating a state of charge and a state of health of an energy storage battery, which adopts an extended kalman filtering algorithm to respectively perform parameter identification, estimation of the state of charge and estimation of the state of health of an equivalent circuit model of the energy storage battery.
As shown in fig. 1, the method may include steps 101 to 106.
And 101, establishing an equivalent circuit model of the energy storage battery.
Under the condition that the energy storage battery is a lithium ion battery, the charging and discharging process of the energy storage battery comprises a large amount of chemical reaction information, dozens of chemical reaction processes exist in the energy storage battery in the charging process, the amount of chemical active components in the energy storage battery is directly related to the capacity of the energy storage battery, the chemical reaction rate is closely connected with the internal resistance of the energy storage battery, a chemical model of the energy storage battery is established to be precise, a large amount of complex chemical reactions of the energy storage battery are difficult to model, and the difficulty of parameter identification is greatly increased due to the fact that the energy storage battery comprises more than 50 parameters to be identified. Therefore, considering the complexity and accuracy of the energy storage battery model, a first-order circuit model is established as an equivalent circuit model of the energy storage circuit, for example, the first-order circuit model may be as shown in fig. 2.
Step 102, performing parameter identification on the equivalent circuit model of the energy storage battery to obtain an estimated value of the parameter of the equivalent circuit model of the energy storage battery.
In some embodiments, as shown in fig. 3, the implementation method of step 102 may include steps 301 to 303.
Step 301, acquiring parameters of an equivalent circuit model of the energy storage battery according to the equivalent circuit model of the energy storage battery.
In some embodiments, in the case where the equivalent circuit model of the energy storage battery is a first-order circuit model, as shown in fig. 4, the implementation method of step 301 may include steps 401 to 403.
Step 401, obtaining a KVL equation of the first-order circuit model according to the first-order circuit model and kirchhoff's law.
The KVL equation for the first-order circuit model is shown in equation (1) according to kirchhoff's law.
Figure 559053DEST_PATH_IMAGE001
（1）
In the formula (1), U is represented as a terminal voltage value, U OCV Represents an open circuit voltage, i is current excitation, R 0 Is the internal resistance of the battery, U p For polarization voltage, R p For polarizing internal resistance C p Is the polarization capacitance, t is the time.
Step 402, discretizing a KVL equation of the first-order circuit model, and obtaining a terminal voltage expression of the first-order circuit model.
Discretizing the KVL equation of the first-order circuit model to obtain equation (2), wherein U k 、U k-1 In the discrete form of the k moment and the k-1 moment of U,
Figure 117073DEST_PATH_IMAGE002
is U (U) OCV In a discrete form at the time of k of (a),
Figure 505329DEST_PATH_IMAGE003
、
Figure 465195DEST_PATH_IMAGE004
u respectively p A discrete form of time k and time k-1; i.e k 、i k-1 In discrete form at times k and k-1 of the current i, respectively.
Figure 647915DEST_PATH_IMAGE005
（2）
Wherein, the liquid crystal display device comprises a liquid crystal display device,
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indicating the adoption interval between time k and time k-1.
The terminal voltage expression of the first-order circuit model is shown as the formula (3).
Figure 635910DEST_PATH_IMAGE007
（3）
In the formula (3), b 1 、b 0 A and U OCV Is a parameter of the first-order circuit model.
Step 403, obtaining parameters of the first-order circuit model according to a terminal voltage expression of the first-order circuit model; the parameters of the equivalent circuit model of the energy storage battery comprise the parameters of the first-order circuit model and the open-circuit voltage.
In the formula (3), parameters of the first-order circuit model are shown in the formula (4).
Figure 450283DEST_PATH_IMAGE008
（4）
Step 302, obtaining a measured value of a terminal voltage and a measured value of a current of the energy storage battery when the energy storage battery is in a charging working condition.
In some embodiments, a voltage sensor may be used to obtain a measurement of the terminal voltage of the energy storage battery and a current sensor may be used to obtain a measurement of the current of the energy storage battery.
Step 303, obtaining an estimated value of a parameter of an equivalent circuit model of the energy storage battery through an extended kalman filtering algorithm according to the measured value of the terminal voltage and the measured value of the current of the energy storage battery.
For example, the measured value of the current may be used as the input value of an extended kalman filter algorithm, and the estimated value of the parameter of the equivalent circuit model of the energy storage battery may be obtained through the extended kalman filter algorithm, and the estimated value of the parameter may be corrected according to the measured value of the terminal voltage of the energy storage battery. In some embodiments, as shown in fig. 5, the implementation method of step 303 may include steps 501 to 503.
And step 501, establishing a state prediction equation of the parameters of the equivalent circuit model of the energy storage battery and a measurement equation of the parameters of the equivalent circuit model of the energy storage battery according to the identification model of the parameters of the equivalent circuit model of the energy storage battery.
The parameter identification ARX model is shown in formula (5).
Figure 69483DEST_PATH_IMAGE009
（5）
In formula (5), y k For measurement of terminal voltage, phi k =[i k ，i k- ，U k- ]Representing discrete input vectors, θ k Is the parameter vector to be identified, and θ k =[b 1 ，b 0 ，ɑ，U OCV ] T K represents the current sampling time, and k or k-1 superscripts below represent discrete forms of parameters or variables at k time or k-1 time, which will not be described in detail.
The state prediction equation of the parameters of the equivalent circuit model of the energy storage battery is shown in formula (6).
Figure 602095DEST_PATH_IMAGE010
（6）
In the formula (6), the amino acid sequence of the compound,
Figure 66575DEST_PATH_IMAGE011
process noise of the state equation is identified for the parameters,
Figure 984721DEST_PATH_IMAGE012
shows a gaussian normal distribution, Q 1 Is the process covariance of the parameter identification. f (f) 1 And the mapping relation between the input and the output in the parameter identification process model is represented.
The measurement equation of the parameters of the equivalent circuit model of the energy storage battery is shown in formula (7).
Figure 774822DEST_PATH_IMAGE013
（7）
In the formula (7), the amino acid sequence of the compound,
Figure 794731DEST_PATH_IMAGE014
for the observation noise of the parameter identification state equation, the subscript 1 indicates the first layer EKF1 operation, which accords with the Gaussian normal distribution
Figure 62901DEST_PATH_IMAGE015
，R 1 Observation protocol for parameter identificationThe variance. h is a 1 And the mapping relation between the input and the output in the parameter identification observation model is represented.
Step 502, according to the extended kalman filtering algorithm, the measured value of the voltage and the measured value of the current of the input end are combined with a state prediction equation of the parameters of the equivalent circuit model of the energy storage battery and a measurement equation of the parameters of the equivalent circuit model of the energy storage battery, prediction is performed through prior estimation, and the kalman filtering gain of the identification model of the parameters of the equivalent circuit model of the energy storage battery is calculated.
And 503, updating by posterior estimation according to an extended Kalman filtering algorithm, updating Kalman filtering gain and posterior estimation covariance of an identification model of parameters of an equivalent circuit model of the energy storage battery, and correcting current parameter estimation by using the posterior estimation covariance to obtain an estimated value of the parameters of the equivalent circuit model of the energy storage battery.
The following examples explain the methods of steps 502 and 503 in detail.
Prediction part:
the a priori estimate is shown in equation (8).
Figure 117445DEST_PATH_IMAGE016
（8）
The prior estimated covariance is shown in equation (9).
Figure 563601DEST_PATH_IMAGE017
（9）
An updating section:
the updated kalman filter gain is shown in equation (10).
Figure 70806DEST_PATH_IMAGE018
（10）
The superscript k-in equations (8) - (10) represents the left limit value at the time of parameter or variable k, and the following relevant definitions are consistent therewith and will not be described in detail.
Figure 877088DEST_PATH_IMAGE019
For a priori estimates of the parameters at time k,
Figure 786138DEST_PATH_IMAGE020
for a priori estimated covariance in the parameter estimation process,
Figure 386883DEST_PATH_IMAGE021
for the kalman filter gain of the layer EKF algorithm,
Figure 646963DEST_PATH_IMAGE022
for the translation vector of the EKF algorithm of this layer,
Figure 234765DEST_PATH_IMAGE023
is that
Figure 263901DEST_PATH_IMAGE024
Reverse amount of R 1 Observing covariance for parameter identification.
As can be seen from the kalman filter gain calculation formula,
Figure 35548DEST_PATH_IMAGE025
and (3) with
Figure 517345DEST_PATH_IMAGE026
In relation to the formula (9),
Figure 931009DEST_PATH_IMAGE025
and Q is equal to 1 、R 1 All related. By adjusting
Figure 549072DEST_PATH_IMAGE025
The value reaches the optimal value for estimation and measurement.
In the formula (10), the amino acid sequence of the compound,
Figure 773511DEST_PATH_IMAGE027
the method comprises the following steps of:
Figure 477025DEST_PATH_IMAGE028
、
Figure 428800DEST_PATH_IMAGE029
、
Figure 166949DEST_PATH_IMAGE030
、
Figure 545978DEST_PATH_IMAGE031
. Obtaining measurement noise variance R from steady-state measurements of battery voltage 1 ，Q 1 Represents an EKF-based adjustment parameter, Q 1 A trade-off is typically made between the tracking ability of parameter variations and noise attenuation.
The update posterior estimated covariance is shown in equation (11).
Figure 986055DEST_PATH_IMAGE032
（11）
In the formula (11), I is an identity matrix. The updated a priori estimated covariance can be used to verify the accuracy of the current filtered estimate correction and applied to the next time prediction.
The data is input to the EKF model, and the time update, the state update, and the correction estimation are performed as shown in expression (12).
Figure 741522DEST_PATH_IMAGE033
（12）
Step 103, determining whether the electric quantity of the energy storage battery is larger than 0; if yes, go to step 104, otherwise go to step 105.
And 104, acquiring an estimated value of the actual charged electric quantity by adopting an off-line established new battery OCV-SOC model according to the estimated value of the parameters of the equivalent circuit model of the energy storage battery, the new battery OCV-SOC model and an extended Kalman filtering algorithm.
In some embodiments, as shown in fig. 6, the implementation method of step 104 may include steps 601 to 603.
And 601, acquiring a state prediction equation of the actual charge quantity of the energy storage battery in a charged state.
During battery charging, the charge amount can be expressed by an integral expression of current as shown in expression (13). SOC (t) is a time expression form of SOC, SOC (0) is an initial time value of SOC,
Figure 334177DEST_PATH_IMAGE034
c for charging efficiency of lithium battery N For the nominal capacity of a lithium battery,
Figure 884107DEST_PATH_IMAGE035
for current i at [0, t]An integral expression of the time period.
Figure 827792DEST_PATH_IMAGE036
（13）
Further, the dynamic charge capacity in the battery charging process is obtained as shown in formula (14), and ΔC is the charge amount and is a dynamic change value.
Figure 855791DEST_PATH_IMAGE037
（14）
Taking the actual charge quantity delta C and the voltage U of the polarization circuit p Component state variable x= [ Δc, U p ] T And forming a state space expression by using a charge state ampere-hour integral equation and an equivalent circuit model voltage equation, and introducing random process noise and measurement noise as shown in a formula (15).
Figure 319265DEST_PATH_IMAGE038
（15）
The matrix form of formula (15) is shown as formula (16).
Figure 40096DEST_PATH_IMAGE039
（16）
In the formula (16), the amino acid sequence of the compound,
Figure 471078DEST_PATH_IMAGE040
、
Figure 302767DEST_PATH_IMAGE041
is that
Figure 870015DEST_PATH_IMAGE042
And (3) with
Figure 11015DEST_PATH_IMAGE043
Is a differential version of random disturbance
Figure 929293DEST_PATH_IMAGE044
Is a state vector
Figure 299094DEST_PATH_IMAGE045
Random Gaussian disturbance process with zero mean value accords with Gao Sixie variance matrix
Figure 720848DEST_PATH_IMAGE046
Wherein q is Q 、q U Respectively is
Figure 49061DEST_PATH_IMAGE047
、
Figure 923476DEST_PATH_IMAGE048
A corresponding Gao Sixie variance matrix.
And 602, adopting an off-line established new battery OCV-SOC model, and establishing a terminal voltage measurement model according to the estimated values of parameters of the new battery OCV-SOC model and an equivalent circuit model of the energy storage battery.
The new battery OCV-SOC model may be a fixed OCV-SOC curve model as used in the prior art.
And according to the OCV-SOC model of the new battery, the SOC pre-estimation model is shown in a formula (17).
Figure 113280DEST_PATH_IMAGE049
（17）
In the formula (17), A k 、B k Discrete system states respectivelyA spatial coefficient matrix, an input coefficient matrix, each coefficient matrix may be expressed as equation (17-1).
Figure 655120DEST_PATH_IMAGE050
For the measurement equation, the calculation content is equation (18).
Figure 888655DEST_PATH_IMAGE051
（17-1）
Calculated to obtain
Figure 515946DEST_PATH_IMAGE052
The method realizes the connection between the first layer of EKF parameter identification model and the current layer of EKF online electric quantity estimation model, and can obtain the identified parameters from the parameter identification module and estimate the electric quantity and the state of charge of the identified parameters.
Establishing a measurement model of the terminal voltage as shown in (18), and randomly generating noise
Figure 227550DEST_PATH_IMAGE053
Is scalar noise of the measurement matrix, is also independent and conforms to Gaussian noise process, conforms to variance R 2 。
Figure 623896DEST_PATH_IMAGE054
（18)
In this step, it is worth noting that the estimated battery state quantity is actually the current charge change capacity of the battery, equivalent to a real-time on-line battery charge estimator. While
Figure 543179DEST_PATH_IMAGE055
Corresponding to new batteries
Figure 392187DEST_PATH_IMAGE056
Curve relation, knowing the nominal charge of the new battery, can be used to
Figure 173061DEST_PATH_IMAGE057
Conversion to
Figure 423914DEST_PATH_IMAGE058
The process is carried out hereEKFAnd predicting the electric quantity of the algorithm, and predicting the current electric quantity when the health state soh=1.
Step 603, according to the extended kalman filtering algorithm, the measured value of the voltage and the measured value of the current of the input end and the estimated value of the parameter of the equivalent circuit model of the energy storage battery are predicted through prior estimation, and the kalman filtering gain of the charge quantity estimation is calculated; and updating through posterior estimation according to an extended Kalman filtering algorithm, updating Kalman filtering gain and posterior estimation covariance of the charge electric quantity estimation, and correcting the current electric quantity estimation by using the posterior estimation covariance to obtain an estimated value of the actual charge electric quantity.
The following examples explain the method of step 603 in detail.
Prediction part:
the a priori estimate is shown in equation (19).
Figure 264831DEST_PATH_IMAGE059
（19）
The prior estimated covariance matrix is shown in equation (20).
Figure 351867DEST_PATH_IMAGE060
（20）
In the formula (20), Q 2 Is a state perturbation covariance matrix; in the formulae (18) to (20),
Figure 670852DEST_PATH_IMAGE061
for prior estimation of the state vector in the k-state at the left limit moment of the k moment, according to the estimated value of the state vector at the last moment
Figure 41791DEST_PATH_IMAGE062
With current i at the previous moment k-1 Calculated, A k-1 、B k-1 A discrete state space coefficient matrix for the previous moment,The matrix of coefficients is input and,
Figure 788030DEST_PATH_IMAGE063
for a priori estimated covariance in the parameter estimation process,
Figure 611630DEST_PATH_IMAGE064
covariance is estimated for the a posteriori in the k-1 state.
An updating section:
the state of charge estimate Ji Kaer Manfiltered gain matrix is shown in equation (21).
Figure 734306DEST_PATH_IMAGE065
（21）
The vector form is calculated as shown in formula (22).
Figure 214878DEST_PATH_IMAGE066
（22）
State estimation error posterior covariance matrix
Figure 132019DEST_PATH_IMAGE067
As shown in formula (23).
Figure 708494DEST_PATH_IMAGE068
（23）
State update, posterior estimation
Figure 369282DEST_PATH_IMAGE069
As shown in formula (24).
Figure 449233DEST_PATH_IMAGE070
（24）
Figure 553587DEST_PATH_IMAGE071
For the kalman filter gain of the layer EKF algorithm,
Figure 351779DEST_PATH_IMAGE072
the conversion vector of the EKF algorithm of the layer is obtained by solving the bias derivative of the state vector by an observation equation about a nonlinear output gradient model near the prior state estimation value,
Figure 550679DEST_PATH_IMAGE073
is that
Figure 750716DEST_PATH_IMAGE072
Is the inverse vector of (c).
In the formula (24), the amino acid sequence of the compound,
Figure 275238DEST_PATH_IMAGE074
the prior prediction error used for observation correction can obtain noise variance by measuring the steady state value of the voltage of the battery terminal, the EKF algorithm adjusts the state estimation value by adjusting the noise covariance matrix, and the diagonal element of the covariance matrix is the expected state disturbance variance value and can be regarded as an ideal value between the tracking capacity of the layer estimator and noise suppression in the estimation state.
Step 105, establishing an OCV aging model; and obtaining an estimated value of the available capacity of the energy storage battery according to the OCV aging model and the extended Freeman filtering algorithm.
In some embodiments, an implementation method for establishing an OCV aging model may include: and under the full-discharge state, obtaining the open-circuit voltage of the instantaneous energy storage battery to be charged as a data sample, and fitting the data sample by adopting a least square method to obtain the OCV aging model.
For example, the experimental data of the battery B0005 in the NASA battery data set is selected, the initial charging voltage in each full-charge state, namely the open-circuit voltage of the battery at the moment of charging, is taken as a data sample, and the variation trend of the full-charge voltage in different aging conditions under the life scale of the lithium battery is researched. And carrying out interpolation fitting on the data samples to obtain a full life cycle model of the OCV aging scale, wherein the full life cycle model is fitted into a 5-order polynomial, a fitting curve is selected by using the principle of minimum deviation square sum, and the fitting is carried out by adopting a polynomial equation method, wherein the fitting formula is shown as a formula (25).
Figure 29568DEST_PATH_IMAGE075
（25）
In the formula (25), the fitting y value is the full-release open-circuit voltage U OCV0 The value x is the remaining available capacity C of the battery under different times of cyclic charge and discharge available ，
Figure 812585DEST_PATH_IMAGE076
、
Figure 601549DEST_PATH_IMAGE077
、
Figure 31393DEST_PATH_IMAGE078
Representing the fitting coefficients, n being the order of the fitting polynomial. The fitted curve is shown in fig. 7.
In this case, in some embodiments, as shown in fig. 8, the implementation method of step 105 may include steps 801 to 803.
Step 801, a prediction equation of the available capacity of the energy storage battery is established.
The SOH prediction equation is shown in equation (26).
Figure 804177DEST_PATH_IMAGE079
（26）
And step 802, establishing a terminal voltage observation model of the available capacity of the energy storage battery according to the OCV aging model.
An observation model of the available capacity of the energy storage battery is shown in formula (27).
Figure 876039DEST_PATH_IMAGE080
（27）
Thus, the layer EKF prediction and observation model expression is shown in equation (28).
Figure 270242DEST_PATH_IMAGE081
（28）
Remaining usable capacity C of battery available In the short-term "c",
Figure 136567DEST_PATH_IMAGE082
、
Figure 131068DEST_PATH_IMAGE083
is a discrete expression of the k moment and the k-1 moment of the available capacity of the state quantity,
Figure 741040DEST_PATH_IMAGE084
、
Figure 770176DEST_PATH_IMAGE085
disturbance in the processes of a prediction equation and an observation equation respectively accords with the process noise and the observed noise covariance Q of the EKF of the layer 3 And R is 3 。z k Is an observation function representing the voltage of a battery terminal and is a state vector
Figure 541823DEST_PATH_IMAGE086
Input vector
Figure 538467DEST_PATH_IMAGE087
Is a functional expression of (2).
Step 803, according to the extended Kalman filtering algorithm, the measured value of the voltage and the measured value of the current of the input end are introduced into an OCV aging model by using a partial differential equation method, prediction is carried out through priori estimation, and Kalman filtering gain of available capacity estimation is calculated; and updating through posterior estimation according to an extended Kalman filtering algorithm, updating Kalman filtering gain and posterior estimation covariance of the available capacity estimation, and correcting the current available capacity by using the posterior estimation covariance to obtain an estimated value of the available capacity of the energy storage battery.
The following examples explain the method of step 803 in detail.
Prediction part:
the state estimation a priori estimates are shown in equation (29).
Figure 686552DEST_PATH_IMAGE088
（29）
The state estimation error a priori covariance matrix is shown in equation (29).
Figure 570194DEST_PATH_IMAGE089
（30）
In the formula (30), Q 3 Is the state perturbation covariance matrix.
Figure 512742DEST_PATH_IMAGE090
The left limit transient state estimated value at k moment in the discrete system is equal to the state estimated value at the previous moment k-1.
Figure 481835DEST_PATH_IMAGE091
For a priori estimated covariance in the parameter estimation process in the k-1 state,
Figure 184343DEST_PATH_IMAGE092
covariance is estimated for the a posteriori in the k-1 state.
An updating section:
the updated kalman filter gain matrix is shown in equation (31).
Figure 656913DEST_PATH_IMAGE093
（31）
Figure 301521DEST_PATH_IMAGE094
Is the Kalman filtering gain of the EKF algorithm of the layer. In the formula (31),
Figure 757910DEST_PATH_IMAGE095
about the estimated state around the a priori state estimate
Figure 247797DEST_PATH_IMAGE096
Nonlinear output gradient mode of (a)Model, mathematically, is a gradient equation around the estimated state, due to the residual capacity c k And terminal voltage U k The mapping relation between the two is not clear, so that a partial differential equation is used for deducing the function relation between the two to reflect the change condition of state estimation. And (3) calculating:
Figure 840452DEST_PATH_IMAGE097
（32）
according to the conversion vector
Figure 905229DEST_PATH_IMAGE098
Defining (32) a conversion vector in the calculation of the available capacity estimation step
Figure 317756DEST_PATH_IMAGE098
. And the state matrix x in the observation equation k- The state estimation matrix in the charge state estimation step is a state estimation matrix in which the relation between the current father C and the residual available capacity C is not clear, so that a partial differential equation method is selected to deduce the functional relation between the father C and the residual available capacity C, and the change condition of state estimation is reflected. According to the established OCV aging model, the open-circuit voltage is selected as an intermediate parameter of a partial differential equation, so that the relation between the current electric quantity and the open-circuit voltage and the relation between the open-circuit voltage and the available electric quantity need to be defined in gradient coefficient calculation. The relationship between the current electric quantity and the open-circuit voltage selected by the EKF of the layer and the relationship between the open-circuit voltage and the available electric quantity are shown in a formula (33).
Figure 876913DEST_PATH_IMAGE099
（33）
The equation on the left of equation (33) expresses the state quantity
Figure 589654DEST_PATH_IMAGE100
And open circuit voltage
Figure 310486DEST_PATH_IMAGE101
Partial differential relation, full open circuit voltage
Figure 226620DEST_PATH_IMAGE102
And available capacity c k The right-hand approximate equation is a mathematical approximation of the partial differential equation, introducing a gradient equation for the offline OCV-SOC aging curve. Substituting equation (33) into equation (32) to calculate the observation matrix
Figure 323889DEST_PATH_IMAGE103
。
Updating posterior covariance matrix
Figure 625558DEST_PATH_IMAGE104
As shown in equation (34).
Figure 782869DEST_PATH_IMAGE105
（34）
State update, posterior estimation
Figure 169988DEST_PATH_IMAGE106
As shown in formula (35).
Figure 337794DEST_PATH_IMAGE107
（35）
And 106, acquiring an estimated value of the SOC and an estimated value of the SOH according to the estimated value of the actual charge quantity and the estimated value of the available capacity of the energy storage battery.
Numerous studies have shown that there is a coupling relationship between battery state of charge, SOC, and state of health, SOH, and in some embodiments, as shown in fig. 9, the method of implementing step 106 may include steps 901-902.
Step 901, obtaining an initial value of the remaining capacity of the energy storage battery in a charging state, and obtaining an estimated value of the SOC according to the estimated value of the available capacity of the energy storage battery, the initial value of the remaining capacity of the energy storage battery in the charging state and the estimated value of the actual charged capacity.
Illustratively, the SOC is defined from a volumetric perspective, as shown in equation (36).
Figure 759548DEST_PATH_IMAGE108
（36）
In the formula (36), C 0 C is the estimated value of the actual charged electric quantity, C is the initial value of the residual electric quantity of the battery in the charged state available And the initial value of the residual electric quantity of the energy storage battery in a charged state.
Step 902, obtaining a capacity value of the new battery, and obtaining an estimated value of SOH according to the capacity value of the new battery and the estimated value of the available capacity of the energy storage battery.
Illustratively, SOH is defined from a volumetric perspective as shown in equation (37).
Figure 822182DEST_PATH_IMAGE109
（37）
In the formula (37), C new The capacity value for the new battery is a known quantity.
According to the method for jointly estimating the state of charge and the state of health of the energy storage battery, provided by the embodiment of the invention, the three-layer extended Kalman filtering algorithm is established to respectively realize the first-order equivalent circuit parameter identification, the state of charge SOC estimation and the state of health SOH estimation of the lithium battery. The method comprises the steps that EKF1 solves the problem of off-line identification of a traditional least square method, and sets open-circuit voltage OCV as a state variable to obtain real-time tracked battery circuit open-circuit voltage dynamic data, and the battery circuit open-circuit voltage dynamic data is input into a lower-layer EKF model to participate in on-line state estimation, so that parameter identification is closer to a real condition, and parameter dynamic response under a dynamic working condition is realized; since the effect of aging on OCV-SOC is considered herein, U is established OCV0 -C available An open circuit voltage aging model for correcting aging error caused by fixed OCV-SOC curve, U OCV0 -C available The open-circuit voltage aging model participates in the aging available capacity estimation of the EKF3 model, so that once the battery is charged in a full-discharge state, the EKF3 model carries out the aging available capacity re-estimation, and the state of health SOH of the battery is updated; available battery after being updatedThe capacity is applied to the state of charge estimation of an EKF2 model, errors caused by aging are corrected, the EKF2 uses an open-circuit voltage curve of a new battery to estimate the SOC value of a real-time state, the SOC is overlapped with an aging correction part in the new state, and the estimation accuracy of the experimental verification SOC is effectively improved. Meanwhile, the noise covariance realizes the update of the state vector and time, and avoids the larger influence caused by inaccurate initial value.
The above method is described below for experimental verification.
When the method is used for verification, pulse charge and discharge excitation shown in fig. 10 and 11 is used, charge and discharge is carried out 27600 times until the service life of the battery is ended, and experimental results prove that after the method for jointly estimating the charge state and the health state of the energy storage battery provided by the embodiment of the invention is used, parameter identification errors influenced by aging are well corrected, parameter identification conditions of different aging degrees are different, and identification results are shown in fig. 12 to 15. FIG. 12 shows R 0 Is identified for different aging levels. FIG. 13 shows R p Is identified for different aging levels. FIG. 14 shows C p Identifying conditions of different aging degrees; FIG. 15 shows U ocv The battery aging is combined with the different aging degree identification conditions of the battery to correct the current capacity of the battery, so that the error of the state of charge estimation is reduced well, the current electric quantity estimation value is calibrated essentially, the battery capacity estimation error is reduced to 0.08%, and the capacity estimation condition is shown in fig. 16. The OCV-SOC aging dynamic model provided by the invention has the advantages that the estimation error of aging to the state of charge is better improved, and the output result of the estimation model is more real and accurate.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means 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 present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. 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 present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.

Claims (8)

1. A method for joint estimation of state of charge and state of health of an energy storage battery, comprising:
establishing an equivalent circuit model of the energy storage battery;
performing parameter identification on the equivalent circuit model of the energy storage battery to obtain an estimated value of the parameter of the equivalent circuit model of the energy storage battery;
when the electric quantity of the energy storage battery is larger than 0, acquiring an estimated value of the actual charged electric quantity by adopting an off-line established new battery OCV-SOC model according to the estimated value of the parameters of the equivalent circuit model of the energy storage battery, the new battery OCV-SOC model and an extended Kalman filtering algorithm; when the electric quantity of the energy storage battery is equal to 0, an OCV aging model is established, and an estimated value of the available capacity of the energy storage battery is obtained according to the OCV aging model and an extended Kalman filtering algorithm;
and obtaining an estimated value of the SOC and an estimated value of the SOH according to the estimated value of the actual charge quantity and the estimated value of the available capacity of the energy storage battery.
2. The method for jointly estimating a state of charge and a state of health of an energy storage battery according to claim 1, wherein performing parameter identification on an equivalent circuit model of the energy storage battery to obtain an estimated value of a parameter of the equivalent circuit model of the energy storage battery specifically comprises:
acquiring parameters of an equivalent circuit model of the energy storage battery according to the equivalent circuit model of the energy storage battery;
acquiring a measured value of terminal voltage and a measured value of current of the energy storage battery under a charging working condition of the energy storage battery;
and obtaining an estimated value of a parameter of an equivalent circuit model of the energy storage battery through an extended Kalman filtering algorithm according to the measured value of the terminal voltage of the energy storage battery and the measured value of the current.
3. The method for jointly estimating a state of charge and a state of health of an energy storage battery according to claim 2, wherein the equivalent circuit model of the energy storage battery is a first-order circuit model, and acquiring parameters of the equivalent circuit model of the energy storage battery according to the equivalent circuit model of the energy storage battery specifically comprises:
obtaining a KVL equation of the first-order circuit model according to the first-order circuit model and kirchhoff's law;
discretizing the KVL equation of the first-order circuit model to obtain a terminal voltage expression of the first-order circuit model;
and acquiring parameters of the first-order circuit model according to the terminal voltage expression of the first-order circuit model, wherein the parameters of the equivalent circuit model of the energy storage battery comprise the parameter open-circuit voltage of the first-order circuit model.
4. The method for jointly estimating a state of charge and a state of health of an energy storage battery according to claim 2, wherein obtaining, by an extended kalman filter algorithm, an estimated value of a parameter of an equivalent circuit model of the energy storage battery according to a measured value of the terminal voltage and a measured value of the current of the energy storage battery specifically comprises:
according to the identification model of the parameters of the equivalent circuit model of the energy storage battery, establishing a state prediction equation of the parameters of the equivalent circuit model of the energy storage battery and a measurement equation of the parameters of the equivalent circuit model of the energy storage battery;
according to an extended Kalman filtering algorithm, inputting the measured value of the terminal voltage and the measured value of the current, combining a state prediction equation of parameters of an equivalent circuit model of the energy storage battery and a measurement equation of parameters of the equivalent circuit model of the energy storage battery, predicting through prior estimation, and calculating Kalman filtering gain of an identification model of the parameters of the equivalent circuit model of the energy storage battery;
updating through posterior estimation according to an extended Kalman filtering algorithm, updating Kalman filtering gain and posterior estimation covariance of an identification model of parameters of an equivalent circuit model of the energy storage battery, and correcting current parameter estimation by using the posterior estimation covariance to obtain an estimated value of the parameters of the equivalent circuit model of the energy storage battery.
5. The method for jointly estimating the state of charge and the state of health of an energy storage battery according to claim 2, wherein the obtaining the estimated value of the actual charge amount according to the estimated value of the parameters of the equivalent circuit model of the energy storage battery, the new battery OCV-SOC model and the extended kalman filter algorithm by using an off-line established new battery OCV-SOC model specifically comprises:
acquiring a state prediction equation of the actual charge quantity of the energy storage battery in a charging state;
an off-line established new battery OCV-SOC model is adopted, and a terminal voltage measurement model is established according to the estimated values of parameters of the new battery OCV-SOC model and an equivalent circuit model of the energy storage battery;
according to an extended Kalman filtering algorithm, inputting measured values of the terminal voltage, the measured values of the current and estimated values of parameters of an equivalent circuit model of the energy storage battery, predicting through prior estimation, and calculating Kalman filtering gain of charge quantity estimation; and updating through posterior estimation according to an extended Kalman filtering algorithm, updating Kalman filtering gain and posterior estimation covariance of the charge electric quantity estimation, and correcting the current electric quantity estimation by using the posterior estimation covariance to obtain an estimated value of the actual charge electric quantity.
6. The method for joint estimation of state of charge and state of health of an energy storage battery according to claim 2, wherein establishing the OCV aging model specifically comprises:
and under the full-discharge state, acquiring the open-circuit voltage of the instantaneous energy storage battery to be charged as a data sample, and fitting the data sample by adopting a least square method to acquire an OCV aging model.
7. The method for jointly estimating a state of charge and a state of health of an energy storage battery according to claim 6, wherein obtaining an estimate of the available capacity of the energy storage battery according to the OCV aging model and the extended kalman filter algorithm specifically comprises:
establishing a prediction equation of the available capacity of the energy storage battery;
establishing a terminal voltage measurement equation of the available capacity of the energy storage battery according to the OCV aging model;
according to an extended Kalman filtering algorithm, inputting the measured value of the terminal voltage and the measured value of the current, introducing an OCV aging model by using a partial differential equation method, predicting by prior estimation, and calculating Kalman filtering gain of the available capacity estimation of the energy storage battery; and updating through posterior estimation according to an extended Kalman filtering algorithm, updating Kalman filtering gain and posterior estimation covariance of the available capacity estimation of the energy storage battery, and correcting the current available capacity by using the posterior estimation covariance to obtain an estimated value of the available capacity of the energy storage battery.
8. The method of claim 1, wherein obtaining the estimated value of SOC and the estimated value of SOH according to the estimated value of the actual charge amount and the estimated value of the available capacity of the energy storage battery specifically comprises:
acquiring an initial value of the residual electric quantity of the energy storage battery in a charging state, and acquiring an estimated value of the SOC according to the estimated value of the available capacity of the energy storage battery, the initial value of the residual electric quantity of the energy storage battery in the charging state and the estimated value of the actual charging electric quantity;
and acquiring a capacity value of a new battery, and acquiring an estimated value of the SOH according to the capacity value of the new battery and the estimated value of the available capacity of the energy storage battery.
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* Cited by examiner, † Cited by third party
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