CN116930772B - Battery SOC estimation method and device considering boundary constraint - Google Patents
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Abstract
The invention belongs to the technical field of battery state estimation, and particularly relates to a battery SOC estimation method and device considering boundary constraint, which are used for acquiring a relation curve between open-circuit voltage and residual battery capacity; selecting a Thevenin equivalent circuit model as a battery equivalent circuit model, and setting parameters to be identified and boundary constraint conditions of the residual quantity of the battery; setting a discrete transfer function of a battery equivalent circuit model, carrying out parameter identification by adopting a recursive total least square method to obtain a parameter estimation value to be identified, judging whether the parameter estimation value to be identified meets parameter boundary constraint conditions to be identified, and if not, correcting; based on a preset self-adaptive extended Kalman filter EKF algorithm, the battery residual capacity is estimated according to a Thevenin equivalent circuit model and boundary constraint conditions of the battery residual capacity, and the estimation accuracy of the battery SOC is improved.
Description
Technical Field
The invention belongs to the technical field of battery state estimation, and particularly relates to a battery SOC estimation method and device considering boundary constraint.
Background
The lithium ion battery has many advantages such as high specific energy and high specific power, and is widely applied to the fields of electric automobiles, energy storage systems and the like. The State of Charge (SOC) is a critical internal State of the battery, and indicates the remaining capacity of the battery, and the accuracy of estimation thereof is critical to the level of safety and efficient use of the battery. However, SOC, which is an implicit state of a battery, cannot generally be directly measured, but can only be indirectly inferred from data such as a measurable voltage, current, temperature, etc., is a difficulty in developing and designing a battery management system (Battery Management System, BMS).
Currently, the commonly used SOC estimation methods mainly comprise an ampere-hour integration method, an open-circuit voltage method, a data driving method and a model method. Among them, the modeling method generally uses a battery equivalent circuit model or an electrochemical model, and estimates the SOC by means of an extended kalman filter (Extended Kalman Filter, EKF), a leber observer, a lyapunov observer, or the like. Compared with other methods, the method is widely applied due to the characteristics of easy implementation, high precision, strong robustness and the like. Meanwhile, in consideration of the model uncertainty caused by the factors of environmental temperature, battery aging and the like, the aspects of sensor measurement errors, electromagnetic interference and the like, a method for jointly estimating some model parameters and SOC has been proposed.
However, at present, certain operation parameters of the battery system are not considered or fully utilized in the design of the methods, and only can be changed within a specific range, so that the SOC estimation accuracy needs to be further improved due to the fact that the prior known boundary constraint conditions are clear. For a battery system, its SOC value can only fluctuate in the range of 0% to 100%. The ohmic internal resistance, the polarized internal resistance and other parameters of the battery cannot be negative, and are influenced by the ambient temperature and the aging degree of the battery, the higher the temperature is, the smaller the internal resistance is, the heavier the aging degree is, and the larger the internal resistance is. The priori conditions are fully utilized, and the known priori information is added into the SOC algorithm design process, so that the battery SOC estimation accuracy can be effectively improved.
In order to solve the defects in the prior art, the prior known information of the battery SOC and the model parameters is fully considered, and the battery SOC estimation method considering boundary constraint is provided, so that the accuracy of battery SOC estimation can be effectively improved.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides a battery SOC estimation method and device considering boundary constraint.
The technical scheme for solving the technical problems is as follows:
in a first aspect, the present invention provides a battery SOC estimation method considering boundary constraints, including the steps of:
step 100, obtaining a relation curve between the open-circuit voltage of the battery and the residual electric quantity SOC of the battery, and establishing an OCV-SOC function;
step 200, selecting a Thevenin equivalent circuit model as a battery equivalent circuit model, and setting parameters to be identified and boundary constraint conditions of the residual electric quantity of the battery, wherein the parameters to be identified comprise: ohmic internal resistance of the battery, polarized internal resistance of the battery and polarized capacitance of the battery;
step 300, setting a discrete transfer function of the Thevenin equivalent circuit model, and converting the discrete transfer function into a discrete domain regression equation form; identifying parameters of the Thevenin equivalent circuit model by adopting a recursive total least square method to obtain a parameter estimation value to be identified, judging whether the parameter estimation value to be identified meets parameter boundary constraint conditions to be identified, and if not, correcting to obtain a parameter identification result to be identified;
step 400, estimating the residual battery power based on a preset self-adaptive extended Kalman filter EKF algorithm and according to a Thevenin equivalent circuit model and a boundary constraint condition of the residual battery power.
Further, the setting of the boundary constraint condition of the parameter to be identified in the step 200 specifically includes: testing brand-new batteries and retired batteries at different environment temperatures and battery residual amounts to obtain test data, and fitting a Thevenin equivalent circuit model by utilizing a MATLAB curve fitting tool box to obtain boundary constraint conditions of parameters to be identified; the boundary constraint conditions of the parameters to be identified are as follows:
in the method, in the process of the invention,representing ohmic internal resistance +.>Lower bound of->Respectively express ohmic internal resistance +.>The upper boundary of the upper limit,；/>representing the internal resistance of battery polarization>Lower bound of->Representing the internal resistance of battery polarization>The upper boundary of the upper limit,；/>representing battery polarization capacitance +.>Lower bound of->Representing battery polarization capacitance +.>Is defined by the upper bound of (c),。
further, the boundary constraint condition for setting the remaining battery power in the step 200 specifically includes: because the SOC value of the battery residual power fluctuates in the range from 0% to 100%, the boundary constraint conditions of the battery residual power are further set according to the use ranges of the battery residual power in different application scenes, and the set boundary constraint conditions of the battery residual power are as follows:
in the method, in the process of the invention,lower bound representing remaining battery power, +.>Indicating the upper bound of the remaining battery power,。
further, the setting a discrete transfer function of the Thevenin equivalent circuit model in the step 300 specifically includes:
order theThe continuous transfer function G(s) of the Thevenin equivalent circuit model is expressed as:
in the method, in the process of the invention,representing battery terminal voltagesDomain expression, metropolis (L.) Roxb>Representing open circuit voltage of batterysDomain expression is carried out by a method of,srepresenting complex variables in the laplace transform; />Representing the voltage difference between the battery terminal and the open circuitsDomain expression; />Representing battery currentsDomain expression;
performing bilinear transformation on the transfer function G(s), and performingLine discretization of discrete transfer functionExpressed as:
in the method, in the process of the invention,the period of the sampling is indicated and,d 1 、d 2 、d 3 、d 4 is a coefficient, wherein->，，/>。
Further, the step 300 converts the discrete domain regression equation form, specifically including:
order theRepresentation->Noise of the time voltage measurement signal, +.>Representation->The real value of the battery terminal voltage and the expression of the real current of the battery are written as:
in the above-mentioned method, the step of,representation ofkTrue value of battery terminal voltage at moment, +.>Representation ofkTime of day using measured battery terminal voltage value of voltage sensor,/->Representation ofkReal current flowing through the battery at any time; />Representation ofkThe battery current value measured by the current sensor is utilized at any moment;
order the，/>Then get->；
In the above-mentioned method, the step of,representation ofkThe difference between the battery terminal voltage and the open circuit voltage measured at the moment; />Representation ofkThe voltage value of the battery terminal actually measured by the voltage sensor is utilized at any moment; />Representation ofkBattery open circuit voltage at time; />Representation ofkActually measuring an input vector at any moment; />Representation ofk-Cell terminal voltage and open circuit voltage measured at time 1Is a difference in (2); />Representation ofkThe current flowing through the battery is actually measured by a current sensor at any moment; />Representation ofk-At time 1 the current flowing through the battery measured by means of the current sensor,/->，/>Representation ofkAnd a parameter vector to be identified at the moment.
Further, in the step 300, the identifying of the parameters of the Thevenin equivalent circuit model by adopting a recursive total least square method, and the obtaining of the parameter estimation value to be identified specifically includes:
the model parameter vector is initialized offline, the overall least square method with forgetting factors is adopted to identify the parameters of the lithium battery model, and the overall least square method parameter estimation formula is as follows:
in the method, in the process of the invention,representation->Gain at time; />Representation ofkTime error covariance matrix,>representation ofk-1 moment error covariance matrix; />Is forgetting factorIndicating the forgetting degree of the historical data, wherein the value is between 0 and 1;；/>is a noise covariance matrix; />Representing the vector +.>1 st to->Sub-vectors formed by individual elements,>for the number of parameters to be identified, +.>Representation->Is a function of the estimated value of (2); />Representation ofk-1 transposition of the estimated values of the parameter vector to be identified at moment; />The expression is represented by->Column vector consisting of sum-1, +.>Is made of->Further calculatedkValues of time column vector->Representing the vector +.>Is the first of (2)n+Values of 1 element;
the estimated value of the parameter to be identified is:
in the method, in the process of the invention,representing ohmic internal resistance +.>Estimated value of ∈10->Representing the internal resistance of battery polarization>Estimated value of ∈10->Representing battery polarization capacitance +.>Estimated value of ∈10->Representation->Estimated value of ∈10->Representation->Estimated value of ∈10->Representation->Is used for the estimation of the estimated value of (a).
Further, in the step 300, it is determined whether the parameter estimation value to be identified meets the parameter boundary constraint condition to be identified, which specifically includes:
performing rationality judgment on the parameter estimation value to be identified, and judging whether the estimation value of the battery model parameter meets the parameter boundary constraint condition to be identified;
if not, taking the parameter as the average value of the upper and lower boundaries of the parameter; and further calculate by using the modified estimated value of the parameter to be identifiedThe method includes the steps that the method participates in a subsequent recursive calculation process; the average value of the upper and lower boundaries of the parameters to be identified is as follows:
in the method, in the process of the invention,representing a union operation.
Further, in the step 400, based on a preset adaptive extended kalman filter EKF algorithm, estimating the remaining battery power according to the Thevenin equivalent circuit model and the boundary constraint condition of the remaining battery power specifically includes:
discrete state space expression of Thevenin equivalent circuit model:
in the method, in the process of the invention,representation->System matrix of time-of-day state space expressions, +.>Representation->An input matrix of the time state space expression; />Representation->State vector of time of day->Representation->A state vector of time; />Representation->Output vector of time,/->Is->An output vector of the moment; />Is->Input vector of moment; />Representation->A time nonlinear measurement function; />Representation->Battery polarization capacitance +.>The polarization voltage at both ends of the substrate,U p,k+1 representation ofkBattery polarization capacitance at +1 moment->Polarization voltage at two ends; />Representation->Time capacitor->The current flowing through the battery at the two ends discharges positively and charges negatively; />Representation ofk+Time 1 capacitor->Current flowing through the battery at both ends; />Representation->Battery remaining capacity of battery at moment,/>Representation->The battery residual capacity of the battery at the moment; />Representing a sampling period; />Representing coulombic efficiency; />Indicating the available capacity of the battery; />Representing the terminal voltage of the battery;
based on the state space expression, the state vector is predicted in one step:
in the method, in the process of the invention,representation ofkA priori estimates of the time state vector, +.>Representation ofkA priori error covariance matrix of time state vector,/>Represented ask-1 state vector estimate after constraint condition determination processing,/time->Representation ofk-error covariance matrix after constraint condition judgment processing at moment-1,/error covariance matrix after constraint condition judgment processing at moment-1>Is thatk-a process noise covariance matrix at time-1;representation->System matrix of time-of-day state space expressions, +.>Representation->Input matrix of the time state space expression, +.>Is->Input vector of moment;
and carrying out rationality judgment on the prior state vector: due to state vectorThe battery remaining capacity information of the battery is contained, and the boundary constraint condition of the battery remaining capacity is further rewritten as:
in the method, in the process of the invention,，/>；
judgingIf the formula is satisfied, the treatment is not needed, and the +.>The method comprises the steps of carrying out a first treatment on the surface of the If not, then the quadratic programming problem shown in the following formula is solved to project the quadratic programming problem into a constraint range, namely
In the method, in the process of the invention,is the estimated value of the state vector after constraint processing; />Is an arbitrary positive weighting matrix, ifThen, for the least squares constraint estimation,Irepresenting the identity matrix; if->Constraint estimation under the maximum probability is performed;
the estimation value of the state vector is updated in a posterior mode, and a specific calculation formula is as follows:
in the method, in the process of the invention,representation ofkA time nonlinear measurement function; />Representation ofkThe kalman gain matrix of the moment in time,representing the value of the state vector prior estimation value after constraint judgment processing,/and the like>Representing a priori error covariance matrix,>represented askPosterior estimate of time state vector, +.>Represented askA posterior error covariance matrix of the time-of-day state vector,representation ofkMeasurement noise covariance moment at time-1Array (S)>Expressed as a unitary matrix; />Representation ofkOutputting the value of the matrix at the moment; />Representation ofkThe value of the moment innovation matrix; />Representation ofkA value of a time nonlinear measurement function;
using noise information covariance matching algorithm to adaptively adjust covariance matrix, wherein the calculation formula is as follows
In the method, in the process of the invention,for the size of the window, +.>Representing an innovation covariance matrix derived from a windowed estimation principle,/>Representing a process noise covariance matrix derived from a windowed estimation principle,/>Representing the measurement noise covariance matrix obtained by the windowing estimation principle,/>Representation ofiThe value of the moment innovation matrix;
and (3) judging rationality of posterior state vector estimation: judgingWhether the rewritten battery residual capacity boundary constraint condition is satisfied, if so, the processing is not needed, and the +.>The method comprises the steps of carrying out a first treatment on the surface of the If not, it is constrained within the boundary range.
Further, if in the rationality judgment of posterior state vector estimationThe method does not meet the boundary constraint condition of the residual electric quantity of the battery, adopts a probability density function truncation method to process, and comprises the following specific processes:
the following transformation relationship is defined:
in the method, in the process of the invention,and->All are->Orthogonal matrix of->Representation of the diagonal matrix +.>Is the inverse of the square root matrix of (a);representing transformed +.>Is a column vector of (2);
matrix arrayAnd->Is->Is decomposed, i.e., satisfies the following formula:
for orthogonal matrixObtained by using Gram-Schmidt orthogonalization method, and the following formula is satisfied:
using the above relation, the battery remaining capacity boundary constraint is further converted into a normalized scalar constraint represented by the following formula:
in the method, in the process of the invention,，/>；
according to constraintsThe value of (2) is->And->And removing probability density function parts outside the constraint boundary, and normalizing to obtain a truncated probability density function as follows:
in the method, in the process of the invention,representing the probability density function after truncation, +.>，；
It is thus possible to obtain,the first element of (2) being constraint-processed with the mean +.>Sum of variances->The calculation is as follows:
after the processing of the constraint condition, the processing method,mean vector of>And covariance matrix->The method comprises the following steps of:
in the method, in the process of the invention,the expression is represented by->And 1;
finally, carrying out inverse transformation on the transformation relation to obtain state estimation and covariance which meet boundary constraint conditions, wherein the state estimation and covariance are respectively as follows:
。
in a second aspect, the present invention provides a battery SOC estimation apparatus considering boundary constraints, comprising: a processor, a memory, and a program; the program is stored in the memory, and the processor invokes the memory-stored program to perform the method of the first aspect.
Compared with the prior art, the invention has the following technical effects:
aiming at the problem that the prior known information (including battery model parameters and SOC) of a battery system is not considered or fully utilized in the design of the traditional battery SOC estimation method, the invention provides a battery SOC estimation method considering boundary constraint, and the battery SOC estimation precision is effectively improved. The method is characterized by comprising two aspects: in the aspect of model parameter identification, based on a large amount of battery test data, boundary constraint conditions of parameters such as ohmic internal resistance, polarization internal resistance and polarization capacitance of the battery are established, and the constraint conditions are considered, so that the values of the recursive total least square online identification model parameters are correspondingly processed, and higher parameter identification precision is realized; in the aspect of SOC estimation, reasonable SOC boundary constraint conditions are set according to actual application scenes, and based on the reasonable SOC boundary constraint conditions, estimated values of state vectors are reasonably adjusted in a one-step prediction stage and a posterior updating stage.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions and advantages of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are only some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a pseudo-random sequence signal according to the present invention;
FIG. 2 is a schematic diagram of a Thevenin equivalent circuit model of the present invention;
FIG. 3 is a flow chart of the present invention.
Detailed Description
In order to further describe the technical means and effects adopted by the present invention to achieve the preset purpose, the following detailed description is given below of the specific implementation, structure, features and effects of the technical solution according to the present invention with reference to the accompanying drawings and preferred embodiments. The particular features, structures, or characteristics of one or more embodiments may be combined in any suitable manner. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
In one embodiment of the present invention, referring to fig. 3, there is provided a battery SOC estimation method considering boundary constraints, including the steps of:
step 100, obtaining a relation curve between the open circuit voltage (Open Circuit Voltage, OCV) of the battery and the residual electric quantity SOC of the battery, and establishing an OCV-SOC function.
Under the condition of a specific ambient temperature, discharging the lithium ion battery at a 1/3C multiplying power, and then charging the battery with a small multiplying power constant current (such as 1/30C) until the battery reaches a charging cut-off voltage to obtain a battery terminal voltage change curve in a charging process; standing for 2 hours, discharging the battery at the same multiplying power (such as 1/30C) and obtaining a battery terminal voltage change curve in the discharging process. Wherein, the multiplying power is 1C, namely 1 hour is full, and the amount of C is 1 hour of full; such as 2C, which is 0.5 hours full, 1/3C, which is 3 hours full, and so on.
In order to reduce the influence of hysteresis effect, taking the average value of the two curves, establishing an analytic relationship between the open-circuit voltage of the battery and the residual electric quantity of the battery, wherein the analytic relationship is shown in the following formula:
（1）
in the method, in the process of the invention,indicating the open circuit voltage of the battery,SOCindicating the remaining battery power, ">Representing polynomial order +.>Representing the coefficients of a polynomial fit,irepresenting the variable.
Step 200, selecting a Thevenin equivalent circuit model as a battery equivalent circuit model, and setting parameters to be identified and boundary constraint conditions of the residual electric quantity of the battery, wherein the parameters to be identified comprise: ohmic internal resistance of the battery, polarized internal resistance of the battery and polarized capacitance of the battery.
Referring to fig. 2, the thevenin equivalent circuit model can be expressed as:
（2）
in the above-mentioned method, the step of,U p representing the polarization voltage of the battery,I L the current is represented by a value representing the current,R o represents the ohmic internal resistance of the battery,R p represents the polarization internal resistance of the battery,C p representing the polarization capacitance of the battery,U t representing the terminal voltage of the battery,U oc indicating the open circuit voltage of the battery.
Testing brand-new batteries and retired batteries at different environment temperatures and battery residual amounts by using the pseudo-random sequence signals shown in fig. 1, obtaining test data, and fitting the Thevenin equivalent circuit model shown in fig. 2 by using a MATLAB curve fitting tool box, wherein boundary constraint conditions of parameters to be identified can be obtained are shown as follows:
（3）
in the method, in the process of the invention,representing ohmic internal resistance +.>Lower bound of->Respectively express ohmic internal resistance +.>The upper boundary of the upper limit,；/>representing the internal resistance of battery polarization>Lower bound of->Representing the internal resistance of battery polarization>The upper boundary of the upper limit,；/>representing battery polarization capacitance +.>Lower bound of->Representing battery polarization capacitance +.>Is defined by the upper bound of (c),。
due to the remaining capacity of the batterySOCThe value of the battery residual capacity fluctuates within the range of 0% to 100%, and reasonable battery residual capacity boundary constraint conditions are set according to the battery residual capacity use ranges of different application scenes such as a hybrid electric vehicle, an energy storage power station and the like, and can be written as follows:
（4）
in the method, in the process of the invention,lower bound representing remaining battery power, +.>Indicating the upper bound of the remaining battery power,。
step 300, setting a discrete transfer function of the Thevenin equivalent circuit model, identifying parameters of the Thevenin equivalent circuit model by adopting a recursive total least square method, obtaining parameter estimated values to be identified, judging whether the parameter estimated values to be identified meet parameter boundary constraint conditions to be identified, and if not, correcting to obtain parameter identification results to be identified.
Step 310, setting a discrete transfer function of a Thevenin equivalent circuit model;
order theThe continuous transfer function G(s) of the Thevenin equivalent circuit model can be expressed as:
（5）
in the method, in the process of the invention,representing battery terminal voltagesDomain expression, metropolis (L.) Roxb>Representing open circuit voltage of batterysDomain expression is carried out by a method of,srepresenting complex variables in the laplace transform; />Representing the voltage difference between the battery terminal and the open circuitsDomain expression; />Representing battery currentsDomain expression.
The transfer function G(s) is subjected to bilinear transformation and discretization, and the discrete transfer function can be obtainedCan be expressed as: />
（6）
In the method, in the process of the invention,the period of the sampling is indicated and,d 1 、d 2 、d 3 、d 4 as a coefficient, z is a complex variable, where,，/>，/>。
step 320, converting into a discrete domain regression equation form;
order the，/>Then can be obtained by the above formula->。
In the above-mentioned method, the step of,representation ofkInputting the value of the vector at the moment, wherein +.>Representation ofk-Difference between battery terminal voltage and open circuit voltage at time 1, < >>Representation->Current flowing through the battery at a time; />Representation ofk-1 a current flowing through the battery; />Representation ofkParameter vector to be identified at the moment, < > and the like>Representation ofkThe difference between the battery terminal voltage and the open circuit voltage difference at the moment.
Taking into consideration the influence of measurement errors of current and voltage sensors and ambient environment interference in the practical application environment, the method comprises the following steps ofRepresentation->Time voltage measurement signalNoise of->Representation->The noise of the current measurement signal at the moment, the expressions of the measured current and the measured voltage signal can be written as:
（7）
in the above-mentioned method, the step of,representation ofkTrue value of battery terminal voltage at moment, +.>Representation ofkTime of day using measured battery terminal voltage value of voltage sensor,/->Representation->Real current flowing through the battery at any time; />Representation ofkAnd the battery current value measured by the current sensor at the moment.
Further, let the，/>Then it can be obtained。
In the above-mentioned method, the step of,representation ofkBattery terminal electricity actually measured at momentThe difference between the voltage and the open circuit voltage; />Representation ofkThe voltage value of the battery terminal actually measured by the voltage sensor is utilized at any moment; />Representation ofkBattery open circuit voltage at time; />Representation ofkActually measuring an input vector at any moment; />Representation ofk-1, the difference value between the battery terminal voltage and the open circuit voltage measured at the moment; />Representation ofkThe current flowing through the battery is actually measured by a current sensor at any moment; />Representation ofk-The current flowing through the battery is actually measured by a current sensor at the time 1.
Step 330, online identifying parameters of the battery Thevenin equivalent circuit model by using a recursive total least square method, and obtaining estimated values of the parameters to be identified;
in the invention, the model parameter vector is initialized off-line, and the overall least square method with forgetting factors is adopted to identify the parameters of the lithium battery model, and the estimation formula of the overall least square method parameter is as follows:
(8)
in the method, in the process of the invention,representation->Gain at time; />Representation ofkTime error covariance matrix,>representation ofk-1 moment error covariance matrix; />The forgetting factor is used for indicating the forgetting degree of historical data, and the value is between 0 and 1;；/>is a noise covariance matrix; />Representing the vector +.>Is>To->Sub-vectors formed by individual elements,>is the number of parameters to be identified, in this example 3; />Representation->Is a function of the estimated value of (2); />Representation ofk-1 transposition of the estimated values of the parameter vector to be identified at moment; />The expression is represented by->Column vector consisting of sum-1, +.>Is made of->Further calculatedkValues of time column vector->Representing the vector +.>Is the first of (2)n+Values of 1 element;
further, by using the formula (8)Is estimated to be +.>Estimate of +.>Estimate of +.>Then the estimated values of the parameters to be identified are:
（9）
in the method, in the process of the invention,representing ohmic internal resistance +.>Estimated value of ∈10->Representing the internal resistance of battery polarization>Estimated value of ∈10->Representing battery polarization capacitance +.>Estimated value of ∈10->Representation->Estimated value of ∈10->Representation->Estimated value of ∈10->Representation->Is used for the estimation of the estimated value of (a).
And 340, carrying out rationality judgment on the parameter estimated value to be identified, and judging whether the estimated value of the battery model parameter meets the parameter boundary constraint condition to be identified.
If not, taking the average value of the upper and lower boundaries of the parameter as shown in the following formula, and further calculating by using the modified estimated value of the parameter to be identifiedWhich participates in the subsequent recursive computation. />
(10)
In the method, in the process of the invention,representing a union operation.
Step 400, estimating the residual battery power based on a preset self-adaptive extended Kalman filter EKF algorithm and according to a Thevenin equivalent circuit model and a boundary constraint condition of the residual battery power.
Discrete state space expression of thevenin equivalent circuit model:
(11)
in the method, in the process of the invention,representation->System matrix of time-of-day state space expressions, +.>Representation->An input matrix of the time state space expression; />Representation->State vector of time of day->Representation->A state vector of time; />Representation->Time of day deliveryGo out vector (I),>is->An output vector of the moment; />Is->The input vector of the moment (actually representing +.>Current flowing through the battery at the moment); />Representation->A time nonlinear measurement function; />Representation->Battery polarization capacitance +.>Polarization voltage at both ends->Representation ofkBattery polarization capacitance at +1 moment->Polarization voltage at two ends; />Representation->Time capacitor->The current flowing through the battery at the two ends discharges positively and charges negatively; />Representation ofk+Capacitor at time 1Current flowing through the battery at both ends; />Representation->Battery remaining capacity of battery at moment,/>Representation->The battery residual capacity of the battery at the moment; />Representing a sampling period; />Representing coulombic efficiency; />Indicating the available capacity of the battery; />Representing the terminal voltage of the battery.
Step 420, predicting the state vector;
based on the state space expression, the state vector is predicted in one step:
(12)
in the method, in the process of the invention,representation ofkA priori estimates of the time state vector, +.>Representation ofkA priori error covariance matrix of time state vector,/>Represented ask-1 state vector estimate after constraint condition determination processing,/time->Representation ofk-error covariance matrix after constraint condition judgment processing at moment-1,/error covariance matrix after constraint condition judgment processing at moment-1>Is thatk-a process noise covariance matrix at time-1; />Representation->System matrix of time-of-day state space expressions, +.>Representation->Input matrix of the time state space expression, +.>Is->Input vector of time of day.
And 430, performing rationality judgment on the prior state vector.
Due to state vectorBattery remaining power information of the batteryThe battery remaining capacity boundary constraint condition (4) can be further rewritten as:
(13)
in the method, in the process of the invention,，/>。
judgingIf the formula is satisfied, the treatment is not needed, and the +.>The method comprises the steps of carrying out a first treatment on the surface of the If not, then the quadratic programming problem shown in the following formula is solved to project the quadratic programming problem into a constraint range, namely
（14）
In the method, in the process of the invention,is the estimated value of the state vector after constraint processing; />Is an arbitrary positive weighting matrix, ifThen, for the least squares constraint estimation,Iexpressed as a unitary matrix; if->Then the constraint estimate at maximum probability is made.
Step 440, updating the posterior of the estimated value of the state vector, wherein the specific calculation formula is as follows:
(15)
in the method, in the process of the invention,representation ofkA time nonlinear measurement function; />Representation ofkThe kalman gain matrix of the moment in time,representing the value of the state vector prior estimation value after constraint judgment processing,/and the like>Representing a priori error covariance matrix,>represented askPosterior estimate of time state vector, +.>Represented askPosterior error covariance matrix of moment state vector,/->Representation ofk-measurement noise covariance matrix at time-1, < ->Expressed as a unitary matrix; />Representation ofkOutputting the value of the matrix at the moment;representation ofkThe value of the moment innovation matrix; />Representation ofkThe value of the time of day measurement function.
It should be noted that, the setting of the noise covariance matrix has a great influence on the estimation accuracy of the algorithm, and inappropriate parameter setting may even cause divergence of the estimation result.
For this purpose, a noise information covariance matching algorithm is used in the present invention to adaptively adjust the covariance matrix. The calculation formula is as follows
(16)
In the method, in the process of the invention,for the size of the window, +.>Representing an innovation covariance matrix derived from a windowed estimation principle,/>Representing a process noise covariance matrix derived from a windowed estimation principle,/>Representing the measurement noise covariance matrix obtained by the windowing estimation principle,/>Representation ofiThe value of the moment innovation matrix.
And 450, judging the rationality of the posterior state vector estimation.
JudgingWhether the rewritten battery remaining capacity boundary constraint condition (13) is satisfied, if so, directly making +.>The method comprises the steps of carrying out a first treatment on the surface of the If not, it is constrained within the boundary range.
In the invention, a probability density function truncation method is adopted for processing, and the specific process is as follows:
a) The following transformation relationship is defined:
(17)
in the method, in the process of the invention,and->All are->Orthogonal matrix of->Representation of the diagonal matrix +.>Is the inverse of the square root matrix of (a);z k representing transformed +.>Is a column vector of (a).
Matrix arrayAnd->Is->Is decomposed by the approximate specification, i.e. satisfies the following formula
(18)
For orthogonal matrixCan be obtained by using Gram-Schmidt orthogonalization method and satisfies the following formula
(19)
b) Using the above relationship, equation (13) can be further converted into a normalized scalar constraint represented by the following equation:
(20)
in the method, in the process of the invention,，/>。
it can be seen that onlyIs constrained so that truncating its probability density function becomes a one-dimensional density function truncate. />According to the first element of (2)N(0, 1) distribution (before being constrained), but according to the constraint +.>The value of (2) is->And->And removing probability density function parts outside the constraint boundary, and normalizing to obtain the truncated probability density function as follows: />
(21)
In the method, in the process of the invention,representing probability density function after truncationCount (n)/(l)>，Wherein r represents an integral variable, +.>Representing the variable.
It is thus possible to obtain,the first element of (2) being constraint-processed with the mean +.>Sum of variances->It can be calculated as:
(22)
it is further available that, after constraint processing,mean vector of>And covariance matrix->Respectively is
(23)
In the method, in the process of the invention,the expression is represented by->And 1.
Finally, performing inverse transformation on the formula (17) to obtain state estimation and covariance meeting boundary constraint conditions, wherein the state estimation and covariance are respectively as follows:
(24)
it should be noted that, in the present invention, constraint processing is performed on the prior estimation value and the posterior estimation value of the state vector, and the algorithm can be simplified by considering the aspects of complexity, estimation precision, calculation cost and the like of the algorithm, and only the prior or posterior estimation is processed.
Aiming at the problem that the prior known information (including battery model parameters and SOC) of a battery system is not considered or fully utilized in the design of the traditional battery SOC estimation method, the invention provides a battery SOC estimation method considering boundary constraint, and the battery SOC estimation precision is effectively improved. The method is characterized by comprising two aspects: in the aspect of model parameter identification, based on a large amount of battery test data, boundary constraint conditions of parameters such as ohmic internal resistance, polarization internal resistance and polarization capacitance of the battery are established, and the constraint conditions are considered, so that the values of the recursive total least square online identification model parameters are correspondingly processed, and higher parameter identification precision is realized; in the aspect of SOC estimation, reasonable SOC boundary constraint conditions are set according to actual application scenes, and based on the reasonable SOC boundary constraint conditions, estimated values of state vectors are reasonably adjusted in a one-step prediction stage and a posterior updating stage.
In an embodiment of the present invention, there is also provided a battery SOC estimation apparatus considering boundary constraints, including: a processor, a memory, and a program; the program is stored in the memory, and the processor calls the program stored in the memory to execute the battery SOC estimation method considering the boundary constraint as described above.
In the implementation of the battery SOC estimation apparatus based on considering boundary constraints, the memory and the processor are electrically connected directly or indirectly to achieve data transmission or interaction. For example, the elements may be electrically connected to each other via one or more communication buses or signal lines, such as through a bus connection. The memory stores computer-executable instructions for implementing the data access control method, including at least one software functional module that may be stored in the memory in the form of software or firmware, and the processor executes the software programs and modules stored in the memory to perform various functional applications and data processing.
Claims (3)
1. The battery SOC estimation method taking boundary constraint into consideration is characterized by comprising the following steps of:
step 100, obtaining a relation curve between the open-circuit voltage of the battery and the residual electric quantity SOC of the battery, and establishing an OCV-SOC function;
step 200, selecting a Thevenin equivalent circuit model as a battery equivalent circuit model, and setting parameters to be identified and boundary constraint conditions of the residual electric quantity of the battery, wherein the parameters to be identified comprise: ohmic internal resistance of the battery, polarized internal resistance of the battery and polarized capacitance of the battery;
step 300, setting a discrete transfer function of the Thevenin equivalent circuit model, and converting the discrete transfer function into a discrete domain regression equation form; identifying parameters of the Thevenin equivalent circuit model by adopting a recursive total least square method to obtain a parameter estimation value to be identified, judging whether the parameter estimation value to be identified meets parameter boundary constraint conditions to be identified, and if not, correcting to obtain a parameter identification result to be identified;
step 400, estimating the residual battery power based on a preset self-adaptive extended Kalman filter EKF algorithm and according to a Thevenin equivalent circuit model and boundary constraint conditions of the residual battery power;
the setting of the boundary constraint condition of the parameter to be identified in the step 200 specifically includes: testing brand-new batteries and retired batteries at different environment temperatures and battery residual amounts to obtain test data, and fitting a Thevenin equivalent circuit model by utilizing a MATLAB curve fitting tool box to obtain boundary constraint conditions of parameters to be identified; the boundary constraint conditions of the parameters to be identified are as follows:
in the method, in the process of the invention,representing ohmic internal resistance +.>Lower bound of->Respectively express ohmic internal resistance +.>The upper boundary of the upper limit,；/>representing the internal resistance of battery polarization>Lower bound of->Representing the internal resistance of battery polarization>The upper boundary of the upper limit,；/>representing battery polarization capacitance +.>Lower bound of->Representing battery polarization capacitance +.>Is defined by the upper bound of (c),；
the boundary constraint conditions for setting the remaining battery power in the step 200 specifically include: because the SOC value of the battery residual power fluctuates in the range from 0% to 100%, the boundary constraint conditions of the battery residual power are further set according to the use ranges of the battery residual power in different application scenes, and the set boundary constraint conditions of the battery residual power are as follows:
in the method, in the process of the invention,lower bound representing remaining battery power, +.>Upper bound representing the remaining battery power, +.>；
The step 300 of setting the discrete transfer function of the Thevenin equivalent circuit model specifically includes:
order theThe continuous transfer function G(s) of the Thevenin equivalent circuit model is expressed as:
in the method, in the process of the invention,representing battery terminal voltagesDomain expression, metropolis (L.) Roxb>Representing open circuit voltage of batterysDomain expression is carried out by a method of,srepresenting complex variables in the laplace transform; />Representing the voltage difference between the battery terminal and the open circuitsDomain expression; />Representing battery currentsDomain expression;
performing bilinear transformation on the transfer function G(s), discretizing, and discretizing the transfer functionExpressed as:
in the method, in the process of the invention,the period of the sampling is indicated and,d 1 、d 2 、d 3 is a coefficient, wherein->，，/>；
In the step 300, the identifying of the parameters of the Thevenin equivalent circuit model is performed by adopting a recursive total least square method, and the obtaining of the parameter estimation value to be identified specifically comprises the following steps:
the model parameter vector is initialized offline, the overall least square method with forgetting factors is adopted to identify the parameters of the lithium battery model, and the overall least square method parameter estimation formula is as follows:
in the method, in the process of the invention,representation->Gain at time; />Representation ofkTime error covariance matrix,>representation ofk-1 moment error covariance matrix; />The forgetting factor is used for indicating the forgetting degree of historical data, and the value is between 0 and 1;；/>is a noise covariance matrix; />Representing the vector +.>1 st to->Sub-vectors formed by individual elements,>for the number of parameters to be identified, +.>Representation->Is a function of the estimated value of (2); />Representation ofk-1 transposition of the estimated values of the parameter vector to be identified at moment; />The expression is represented by->Column vector consisting of sum-1, +.>Is made of->Further calculatedkValues of time column vector->Representing the vector +.>Is>The values of the individual elements;
the estimated value of the parameter to be identified is:
in the method, in the process of the invention,representing ohmic internal resistance +.>Estimated value of ∈10->Representing the internal resistance of battery polarization>Estimated value of ∈10->Representing battery polarization capacitance +.>Estimated value of ∈10->Representation->Estimated value of ∈10->Representation->Estimated value of ∈10->Representation->Is a function of the estimated value of (2);
in the step 300, it is determined whether the parameter estimation value to be identified meets the parameter boundary constraint condition to be identified, which specifically includes:
performing rationality judgment on the parameter estimation value to be identified, and judging whether the estimation value of the battery model parameter meets the parameter boundary constraint condition to be identified;
if not, taking the parameter as the average value of the upper and lower boundaries of the parameter; and further calculate by using the modified estimated value of the parameter to be identifiedThe method includes the steps that the method participates in a subsequent recursive calculation process; the average value of the upper and lower boundaries of the parameters to be identified is as follows:
in the method, in the process of the invention,representing a union operation;
in the step 400, based on a preset adaptive extended kalman filter EKF algorithm, estimating the remaining battery power according to a Thevenin equivalent circuit model and a boundary constraint condition of the remaining battery power specifically includes:
discrete state space expression of Thevenin equivalent circuit model:
in the method, in the process of the invention,representation->System matrix of time-of-day state space expressions, +.>Representation->An input matrix of the time state space expression; />Representation->State vector of time of day->Representation->A state vector of time; />Representation->Output vector of time,/->Is->An output vector of the moment; />Is->Input vector of moment; />Representation->A time nonlinear measurement function; />Representation->Battery polarization capacitance +.>Polarization voltage at both ends->Representation ofkBattery polarization capacitance at +1 moment->Polarization voltage at two ends; />Representation->Time capacitor->The current flowing through the battery at the two ends discharges positively and charges negatively; />Representation ofk+Time 1 capacitor->Current flowing through the battery at both ends; />Representation ofBattery remaining capacity of battery at moment,/>Representation->The battery residual capacity of the battery at the moment; />Representing a sampling period; />Representing coulombic efficiency; />Indicating the available capacity of the battery; />Representing the terminal voltage of the battery;
based on the state space expression, the state vector is predicted in one step:
in the method, in the process of the invention,representation ofkA priori estimates of the time state vector, +.>Representation ofkA priori error covariance matrix of time state vector,/>Represented ask-1 state vector estimate after constraint condition determination processing,/time->Representation ofkError cooperative prescription after constraint condition judgment processing at moment-1Difference matrix, < >>Is thatk-a process noise covariance matrix at time-1; />Representation->System matrix of time-of-day state space expressions, +.>Representation->Input matrix of the time state space expression, +.>Is->Input vector of moment;
and carrying out rationality judgment on the prior state vector: due to state vectorThe battery remaining capacity information of the battery is contained, and the boundary constraint condition of the battery remaining capacity is further rewritten as:
in the method, in the process of the invention,，/>；
judgingIf the formula is satisfied, the treatment is not needed, and the +.>The method comprises the steps of carrying out a first treatment on the surface of the If not, then the quadratic programming problem shown in the following formula is solved to project the quadratic programming problem into a constraint range, namely
In the method, in the process of the invention,is the estimated value of the state vector after constraint processing; />Is an arbitrary positive weighting matrix, if +.>Then, for the least squares constraint estimation,Irepresenting the identity matrix; if->Constraint estimation under the maximum probability is performed;
the estimation value of the state vector is updated in a posterior mode, and a specific calculation formula is as follows:
in the method, in the process of the invention,representation ofkA time nonlinear measurement function; />Representation ofkTime-of-day Kalman gain matrix, +.>Representing the value of the state vector prior estimation value after constraint judgment processing,/and the like>Representing a priori error covariance matrix,>represented askPosterior estimate of time state vector, +.>Represented askPosterior error covariance matrix of moment state vector,/->Representation ofk-measurement noise covariance matrix at time-1, < ->Expressed as a unitary matrix; />Representation ofkOutputting the value of the matrix at the moment; />Representation ofkThe value of the moment innovation matrix; />Representation ofkA value of a time nonlinear measurement function; />Representation ofkAn output vector of the moment;is thatkInput vector of moment;
using a noise information covariance matching algorithm, and adaptively adjusting a covariance matrix, wherein the calculation formula is as follows:
in the method, in the process of the invention,for the size of the window, +.>Representing an innovation covariance matrix derived from a windowed estimation principle,/>Representing a process noise covariance matrix derived from a windowed estimation principle,/>Representing the measurement noise covariance matrix obtained by the windowing estimation principle,/>Representation ofiThe value of the moment innovation matrix;
and (3) judging rationality of posterior state vector estimation: judgingWhether the rewritten battery residual capacity boundary constraint condition is satisfied, if so, the processing is not needed, and the +.>The method comprises the steps of carrying out a first treatment on the surface of the If not, the method is restricted in the boundary range;
if in the rationality judgment of posterior state vector estimationThe method does not meet the boundary constraint condition of the residual electric quantity of the battery, adopts a probability density function truncation method to process, and comprises the following specific processes:
the following transformation relationship is defined:
in the method, in the process of the invention,and->All are->Orthogonal matrix of->Representation of the diagonal matrix +.>Is the inverse of the square root matrix of (a); />Representing transformed +.>Is a column vector of (2);
matrix arrayAnd->Is->Is decomposed, i.e., satisfies the following formula:
for orthogonal matrixObtained by using Gram-Schmidt orthogonalization method, and the following formula is satisfied:
using the above relation, the battery remaining capacity boundary constraint is further converted into a normalized scalar constraint represented by the following formula:
in the method, in the process of the invention,，/>；
according to constraintsThe value of (2) is->And->And removing probability density function parts outside the constraint boundary, and normalizing to obtain a truncated probability density function as follows:
in the method, in the process of the invention,representing the probability density function after truncation, +.>，；
It is thus possible to obtain,the first element of (2) being constraint-processed with the mean +.>Sum of variances->The calculation is as follows:
after the processing of the constraint condition, the processing method,mean vector of>And covariance matrix->The method comprises the following steps of:
in the method, in the process of the invention,the expression is represented by->And 1;
finally, carrying out inverse transformation on the transformation relation to obtain state estimation and covariance which meet boundary constraint conditions, wherein the state estimation and covariance are respectively as follows:
。
2. the method for estimating SOC of a battery in consideration of boundary constraint according to claim 1, wherein the converting in step 300 into a discrete domain regression equation form specifically includes:
order theRepresentation->Noise of the time voltage measurement signal, +.>Representation->The real value of the battery terminal voltage and the expression of the real current of the battery are written as:
in the above-mentioned method, the step of,representation ofkTrue value of battery terminal voltage at moment, +.>Representation ofkTime of day using measured battery terminal voltage value of voltage sensor,/->Representation ofkReal current flowing through the battery at any time; />Representation ofkThe battery current value measured by the current sensor is utilized at any moment;
order the，/>Then get->；
In the above-mentioned method, the step of,representation ofkThe difference between the battery terminal voltage and the open circuit voltage measured at the moment; />Representation ofkThe voltage value of the battery terminal actually measured by the voltage sensor is utilized at any moment; />Representation ofkBattery open circuit voltage at time; />Representation ofkActually measuring an input vector at any moment; />Representation ofk-1, the difference value between the battery terminal voltage and the open circuit voltage measured at the moment; />Representation ofkThe current flowing through the battery is actually measured by a current sensor at any moment; />Representation ofk-The current flowing through the battery measured by the current sensor at time 1,，/>representation ofkAnd a parameter vector to be identified at the moment.
3. A battery SOC estimation apparatus considering boundary constraints, comprising: a processor, a memory, and a program; the program is stored in the memory, and the processor invokes the memory-stored program to perform the method of any one of claims 1-2.
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