CN110412471B - Construction method of composite electrochemical polarization model of lithium ion battery pack - Google Patents

Abstract

The invention discloses a method for constructing a composite electrochemical polarization model of a lithium ion battery pack, which comprises the following steps: s1, establishing an equivalent circuit model of the lithium ion battery pack; s2, constructing a state space equation of the equivalent circuit model based on the kirchhoff circuit law; s3, calculating the closed circuit voltage U of the lithium ion battery pack at the moment k according to the state space equation of the equivalent circuit model_L(k) The discrete expression of (1); s4, solving the closed circuit voltage U of the lithium ion battery pack at the moment k by adopting a least square method_L(k) The discrete expression of (a) is required to identify the parameters. According to the invention, the accurate description of the working state of the lithium ion battery pack is realized by comprehensively considering the representation accuracy and the calculation complexity and combining the advantages of different equivalent circuit models.

Description

Construction method of composite electrochemical polarization model of lithium ion battery pack

Technical Field

The invention relates to the technical field of charge state estimation of lithium ion battery packs, in particular to a construction method of a composite electrochemical polarization model of a lithium ion battery pack.

Background

The power battery system is one of the most important components, and has great influence on the performance and safety of the whole machine, and the lithium ion battery becomes the most widely used power battery for the machine at present by virtue of excellent performance; for a lithium ion Battery, not only a Battery core material with excellent performance needs to be continuously searched, but also a Battery Management System (BMS) needs to manage the Battery core material so as to prevent dangerous conditions such as spontaneous combustion and spontaneous explosion of the lithium ion Battery under certain extreme working conditions; the SOC (State of Charge) estimation of the battery is the basis of the BMS, the estimation precision is an important basis for judging the quality of a battery management system, the accurate SOC estimation is favorable for the full and reasonable use of the battery, the service life of the battery is prolonged, and the safety of the battery is improved; the accurate lithium ion battery model is the premise of improving the SOC estimation precision, so the accurate establishment of the battery model is the key of a battery management system; the battery is a nonlinear system, a common battery model can be divided into an electrochemical model and an equivalent circuit model, the electrochemical model is modeled according to an electrochemical reaction mechanism, the internal action of the battery is described through a mathematical relationship, and the internal action of the battery is described through pure mathematics to fully describe the characteristics of the battery, but the traditional pure electrochemical model is difficult to simulate the dynamic performance of the battery; the equivalent circuit model is established by forming a circuit network by using a resistor, a capacitor and a voltage source according to the dynamic characteristics and the working principle of the battery; however, for most equivalent circuit models, the Open Circuit Voltage (OCV) is directly measured or several estimated specified SOC values are measured in experiments, so that in the equivalent circuit model, simply using OCV as a function of SOC is not only time-consuming and labor-consuming, but is even prone to error; worse yet, the discrete representation of the OCV over multiple SOCs is not intuitive for kalman filtering or kalman filtering-based SOC estimation techniques.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: aiming at the problem that the SOC value cannot be accurately estimated due to insufficient accuracy of the existing lithium ion battery model, the construction method of the composite electrochemical polarization model of the lithium ion battery pack is provided.

The technical scheme adopted by the invention is as follows:

a construction method of a composite electrochemical polarization model of a lithium ion battery pack comprises the following steps:

s1, establishing an equivalent circuit model of the lithium ion battery pack;

s2, constructing a state space equation of the equivalent circuit model based on the kirchhoff circuit law;

s3, calculating the closed circuit voltage U of the lithium ion battery pack at the moment k according to the state space equation of the equivalent circuit model_L(k) The discrete expression of (1);

s4, solving the closed circuit voltage U of the lithium ion battery pack at the moment k by adopting a least square method_L(k) The parameters to be identified in the discrete expression are solved to calculate the parameters in the state space equation of the equivalent circuit model, so as to obtain the composite electrochemical polarization model of the lithium ion battery pack.

Further, the equivalent circuit model is composed of: polarization resistance R_PAnd a polarization capacitor C_PForming a first-order RC circuit; internal resistance to charging R_cAnd internal discharge resistance R_dRespectively reverse-serially connected with diodes D_cAnd a diode D_dThen connected in parallel, and then sequentially connected in series with a first-order RC circuit, an ohmic internal resistance Ro and an open-circuit voltage U of the lithium ion battery pack_OC(ii) a The closed circuit voltage of the equivalent circuit model is U_L。

Further, in S2, based on kirchhoff' S circuit law, a state space equation for constructing the equivalent circuit model is:

in the formula, R₀Ohmic internal resistance of the lithium ion battery pack; r_PIs the polarization resistance of the lithium ion battery pack; c_PIs the polarization capacitance of the lithium ion battery pack; r_cdIs the internal resistance of the lithium ion battery pack during charging and discharging, R_cd＝R_cAt discharge time R_cd＝R_d(ii) a k is the time of SOC estimation of the lithium ion battery pack; u shape_L(k) The closed circuit voltage of the lithium ion battery pack at the moment k is obtained; i is_L(k) The output current of the lithium ion battery pack at the moment k is obtained; u shape_P(k) Is a polarization resistance R_PThe voltage at the moment k at both ends; open circuit voltage U of lithium ion battery pack_OCEquivalence by Nernst model, K₁、K₂、K₃For the three constants selected by the Nernst model, SOC (k) is the SOC estimate for the lithium ion battery pack at time k;

further, in step S3, the closed-circuit voltage U of the lithium ion battery pack at time k is calculated according to the state space equation of the equivalent circuit model_L(k) The discrete formula of (2) is as follows:

s3-1, polarization resistance R in the state space equation_PVoltage U across the terminals at time k_P(k) By first order backward difference instead, to obtain U_P(k) The discretized equivalent differential equation of (1):

in the formula of U_P(k) And U_P(k-1) are respectively a polarization resistance R_PVoltages of two ends at the time k and the time k-1, wherein T is a parameter detection period of the lithium ion battery pack, namely a signal sampling time interval;

s3-2, combined with equivalent U_P(k) Is differential expression and U_P(k) Obtaining the polarization resistance R by the discretization equivalent differential formula_PVoltage U across the terminals at time k_P(k) The discrete equation of (c):

in the formula I_L(k) And I_L(k-1) respectively representing the output current of the lithium ion battery pack at the k moment and the k-1 moment;

s3-3, polarization resistance R_PVoltage U across the terminals at time k_P(k) Substituting the discrete expression into the state space equation to obtain the closed circuit voltage U of the lithium ion battery pack at the moment k_L(k) The discrete equation of (c):

U_L(k)＝a₁+a₂U_L(k-1)+a₃ln(SOC(k))+a₄ln(1-SOC(k))+a₅I_L(k)+a₆I_L(k-1)

in the formula, the parameter a to be identified₁、a₂、a₃、a₄、a₅、a₆The development of (a) is as follows:

further, in step S4, the closed-circuit voltage U of the lithium ion battery pack at time k is solved by using a least square method_L(k) The parameters to be identified in the discrete expression are solved to obtain the parameters to be identified, and the parameters in the state space equation of the equivalent circuit model are calculated by using the parameters to be identified, so that the process of obtaining the composite electrochemical polarization model of the lithium ion battery pack is as follows:

s4-1, the closed circuit voltage U of the lithium ion battery pack at the moment k is measured_L(k) The discrete expression of (a) is regarded as a six-element set consisting of independent variables and dependent variables, each element contains N units, and N is 1,2,3, …, k:

{U_L(k)U_L(k-1)SOC(k)SOC(k-1)I_L(k)I_L(k-1)}

wherein the matrix of dependent variables is: y ═ U_L(1)U_L(2)…U_L(N)]^T(ii) a The matrix of arguments is: x ═ β (1) β (2) … β (N)]^T；

S4-2, according to U_L(k) The discrete expression of (a) can be obtained:

β(k)＝[1U_L(k-1)ln(SOC(k))ln(1-SOC(k))I_L(k)I_L(k-1)]

then there is a parameter matrix to be identified: a ═ a₁a₂a₃a₄a₅a₆]^T；

S4-3, estimating by using a least square method, and solving a parameter matrix A (X) needing to be identified^TX)^-1X^TY＝X^-1Y, obtaining the parameter a to be identified₁、a₂、a₃、a₄、a₅、a₆；

S4-4, identifying the parameter a according to the requirement₁、a₂、a₃、a₄、a₅、a₆The expansion form of the equivalent circuit model is further deformed to obtain a parameter calculation formula in a state space equation of the equivalent circuit model:

solving the obtained parameters a needing to be identified₁、a₂、a₃、a₄、a₅、a₆Substituting the calculation result into the state space equation of the equivalent circuit model to obtain the composite electrochemical polarization model of the lithium ion battery pack.

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

according to the method, the representation accuracy and the calculation complexity of the lithium ion battery pack are comprehensively considered, the advantages of different equivalent circuit models are combined, and a lithium ion battery pack composite electrochemical polarization model is provided and constructed in a mode of combining electrochemistry and equivalent circuits; the provided composite electrochemical polarization model of the lithium ion battery pack realizes accurate mathematical expression of working conditions and working processes of the lithium ion battery pack by simulating different effects in the lithium ion battery pack in group cascade connection; a lithium ion battery parameter identification method based on a least square method of a lithium ion battery pack composite electrochemical polarization model is provided; provides a useful reference and reference for the combined application of the electrochemical model and the equivalent circuit model in the battery management.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.

Fig. 1 is a flow chart of a method for constructing a composite electrochemical polarization model of a lithium ion battery pack according to the present invention.

Fig. 2 is a schematic diagram of an equivalent circuit model of the lithium ion battery pack according to the present invention.

Detailed Description

The features and properties of the present invention are described in further detail below with reference to examples.

The method for constructing a lithium ion battery pack composite Electrochemical Polarization Model (S-EPM Model) provided in this embodiment, as shown in fig. 1, includes:

s1, establishing an equivalent circuit model of the lithium ion battery pack; as shown in fig. 2, the equivalent circuit model is composed of: polarization resistance R_PAnd a polarization capacitor C_PForming a first-order RC circuit; internal resistance to charging R_cAnd internal discharge resistance R_dRespectively reverse-serially connected with diodes D_cAnd a diode D_dThen connected in parallel, and then sequentially connected in series with a first-order RC circuit, an ohmic internal resistance Ro and an open-circuit voltage U of the lithium ion battery pack_OC(ii) a The closed circuit voltage of the equivalent circuit model isU_L。

S2, constructing a state space equation of the equivalent circuit model based on the Kirchoff circuit law:

in the formula, R₀The ohmic internal resistance of the lithium ion battery pack can represent the voltage drop of the two ends of the positive electrode and the negative electrode caused by the ohmic effect in the charging and discharging processes of the lithium ion battery pack; r_PIs the polarization resistance, C, of a lithium ion battery pack_PIs the polarization capacitance, R, of a lithium ion battery pack_PAnd C_PThe formed first-order RC circuit represents the relaxation effect in the charge and discharge process of the lithium ion battery pack, and further realizes the expression of the transient response of the lithium ion battery pack; r_cdIs the internal resistance of the lithium ion battery pack during charging and discharging, R_cd＝R_cAt discharge time R_cd＝R_d(ii) a k is the time of SOC estimation of the lithium ion battery pack; u shape_L(k) The closed circuit voltage of the lithium ion battery pack at the moment k is obtained; i is_L(k) The output current of the lithium ion battery pack at the moment k is obtained; u shape_P(k) Is a polarization resistance R_PThe voltage at the moment k at both ends; open circuit voltage U of lithium ion battery pack_OCThe Nernst model is used for equivalence, the Nernst model can provide a good fitting effect in the whole charging and discharging process of the lithium ion battery pack, and K is₁、K₂、K₃The three constants selected by the Nernst model can be determined by different combination tests according to the special working conditions of the grouped work of the lithium ion battery pack; SOC (k) is the SOC estimated value of the lithium ion battery pack at the time k.

S3, calculating the closed circuit voltage U of the lithium ion battery pack at the moment k according to the state space equation of the equivalent circuit model_L(k) The discrete expression of (1);

s3-1, polarization resistance R in the state space equation_PVoltage U across the terminals at time k_P(k) By first order backward difference instead, to obtain U_P(k) The discretized equivalent differential equation of (1):

in the formula of U_P(k) And U_P(k-1) are respectively a polarization resistance R_PVoltages of two ends at the time k and the time k-1, wherein T is a parameter detection period of the lithium ion battery pack, namely a signal sampling time interval;

s3-2, combined with equivalent U_P(k) Is differential expression and U_P(k) Obtaining the polarization resistance R by the discretization equivalent differential formula_PVoltage U across the terminals at time k_P(k) The discrete equation of (c):

in the formula I_L(k) And I_L(k-1) respectively representing the output current of the lithium ion battery pack at the k moment and the k-1 moment;

s3-3, polarization resistance R_PVoltage U across the terminals at time k_P(k) Substituting the discrete expression into the state space equation to obtain the closed circuit voltage U of the lithium ion battery pack at the moment k_L(k) The discrete equation of (c):

U_L(k)＝a₁+a₂U_L(k-1)+a₃ln(SOC(k))+a₄ln(1-SOC(k))+a₅I_L(k)+a₆I_L(k-1)

in the formula, the parameter a to be identified₁、a₂、a₃、a₄、a₅、a₆The development of (a) is as follows:

s4, solving the closed circuit voltage U of the lithium ion battery pack at the moment k by adopting a least square method_L(k) The parameters to be identified in the discrete expression are calculated by utilizing the parameters to be identified obtained by solvingObtaining parameters in a state space equation of the effective circuit model to obtain a lithium ion battery pack composite electrochemical polarization model:

s4-1, the closed circuit voltage U of the lithium ion battery pack at the moment k is measured_L(k) The discrete expression of (a) is regarded as a six-element set consisting of independent variables and dependent variables, each element contains N units, and N is 1,2,3, …, k:

{U_L(k)U_L(k-1)SOC(k)SOC(k-1)I_L(k)I_L(k-1)}

wherein the matrix of dependent variables is: y ═ U_L(1)U_L(2)…U_L(N)]^T(ii) a The matrix of arguments is: x ═ β (1) β (2) … β (N)]^T；

S4-2, according to U_L(k) The discrete expression of (a) can be obtained:

β(k)＝[1U_L(k-1)ln(SOC(k))ln(1-SOC(k))I_L(k)I_L(k-1)]

then there is a parameter matrix to be identified: a ═ a₁a₂a₃a₄a₅a₆]^T；

S4-3, estimating by using a least square method, and solving a parameter matrix A (X) needing to be identified^TX)^-1X^TY＝X^-1Y, obtaining the parameter a to be identified₁、a₂、a₃、a₄、a₅、a₆；

S4-4, identifying the parameter a according to the requirement₁、a₂、a₃、a₄、a₅、a₆The expansion form of the equivalent circuit model is further deformed to obtain a parameter calculation formula in a state space equation of the equivalent circuit model:

solving the obtained parameters a needing to be identified₁、a₂、a₃、a₄、a₅、a₆Parameter calculation substituted into the state space equation of the equivalent circuit modelAnd substituting the calculation result into a state space equation of the equivalent circuit model to obtain the composite electrochemical polarization model of the lithium ion battery pack.

In conclusion, the invention comprehensively considers the representation accuracy and the calculation complexity of the lithium ion battery pack, combines the advantages of different equivalent circuit models, and provides and constructs the composite electrochemical polarization model of the lithium ion battery pack by combining electrochemistry and equivalent circuits; the provided composite electrochemical polarization model of the lithium ion battery pack realizes accurate mathematical expression of working conditions and working processes of the lithium ion battery pack by simulating different effects in the lithium ion battery pack in group cascade connection, and experiments show that the error can be controlled within 0.5 percent, and the precision is higher; a lithium ion battery parameter identification method based on a least square method of a lithium ion battery pack composite electrochemical polarization model is provided; provides a useful reference and reference for the combined application of the electrochemical model and the equivalent circuit model in the battery management.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (2)

1. A construction method of a composite electrochemical polarization model of a lithium ion battery pack is characterized by comprising the following steps:

s1, establishing an equivalent circuit model of the lithium ion battery pack;

s2, constructing a state space equation of the equivalent circuit model based on the kirchhoff circuit law;

s3, calculating the closed circuit voltage U of the lithium ion battery pack at the moment k according to the state space equation of the equivalent circuit model_L(k) The discrete expression of (1);

s4, solving the closed circuit voltage U of the lithium ion battery pack at the moment k by adopting a least square method_L(k) The parameters to be identified in the discrete expression are obtained by calculating the parameters in the state space equation of the equivalent circuit model by using the parameters to be identified obtained by solvingA lithium ion battery pack composite electrochemical polarization model;

the equivalent circuit model comprises the following components: polarization resistance R_PAnd a polarization capacitor C_PForming a first-order RC circuit; internal resistance to charging R_cAnd internal discharge resistance R_dRespectively reverse-serially connected with diodes D_cAnd a diode D_dThen connected in parallel, and then sequentially connected in series with a first-order RC circuit, an ohmic internal resistance Ro and an open-circuit voltage U of the lithium ion battery pack_Oc(ii) a The closed circuit voltage of the equivalent circuit model is U_L；

The S2, based on kirchhoff circuit law, constructs a state space equation of the equivalent circuit model as:

in the formula, R₀Ohmic internal resistance of the lithium ion battery pack; r_PIs the polarization resistance of the lithium ion battery pack; c_PIs the polarization capacitance of the lithium ion battery pack; r_cdIs the internal resistance of the lithium ion battery pack during charging and discharging, R_cd＝R_cAt discharge time R_cd＝R_d(ii) a k is the time of SOC estimation of the lithium ion battery pack; u shape_L(k) The closed circuit voltage of the lithium ion battery pack at the moment k is obtained; i is_L(k) The output current of the lithium ion battery pack at the moment k is obtained; u shape_P(k) Is a polarization resistance R_PThe voltage at the moment k at both ends; open circuit voltage U of lithium ion battery pack_OCEquivalence by Nernst model, K₁、K₂、K₃For the three constants selected by the Nernst model, SOC (k) is the SOC estimate for the lithium ion battery pack at time k;

in the step S3, the closed-circuit voltage U of the lithium ion battery pack at the time k is calculated according to the state space equation of the equivalent circuit model_L(k) The discrete formula of (2) is as follows:

s3-1, polarization resistance R in the state space equation_PVoltage U across the terminals at time k_P(k) By first order backward difference instead, to obtain U_P(k) The discretized equivalent differential equation of (1):

in the formula of U_P(k) And U_P(k-1) are respectively a polarization resistance R_PVoltages of two ends at the time k and the time k-1, wherein T is a parameter detection period of the lithium ion battery pack, namely a signal sampling time interval;

s3-2, combined with equivalent U_P(k) Is differential expression and U_P(k) Obtaining the polarization resistance R by the discretization equivalent differential formula_PVoltage U across the terminals at time k_P(k) The discrete equation of (c):

in the formula I_L(k) And I_L(k-1) respectively representing the output current of the lithium ion battery pack at the k moment and the k-1 moment;

s3-3, polarization resistance R_PVoltage U across the terminals at time k_P(k) Substituting the discrete expression into the state space equation to obtain the closed circuit voltage U of the lithium ion battery pack at the moment k_L(k) The discrete equation of (c):

U_L(k)＝a₁+a₂U_L(k-1)+a₃ln(SOC(k))+a₄ln(1-SOC(k))+a₅I_L(k)+a₆I_L(k-1)

in the formula, the parameter a to be identified₁、a₂、a₃、a₄、a₅、a₆The development of (a) is as follows:

2. the lithium ion battery composite electrochemical of claim 1The method for constructing the chemical polarization model is characterized in that in step S4, the closed-circuit voltage U of the lithium ion battery pack at the time k is solved by using a least square method_L(k) The parameters to be identified in the discrete expression are solved to obtain the parameters to be identified, and the parameters in the state space equation of the equivalent circuit model are calculated by using the parameters to be identified, so that the process of obtaining the composite electrochemical polarization model of the lithium ion battery pack is as follows:

s4-1, the closed circuit voltage U of the lithium ion battery pack at the moment k is measured_L(k) The discrete expression of (a) is considered to be a six-element set consisting of independent variables and dependent variables, each element contains N units, N is 1,2, 3.

{U_L(k)U_L(k-1)SOC(k)SOC(k-1)I_L(k)I_L(k-1)}

Wherein the matrix of dependent variables is: y ═ U_L(1)U_L(2)…U_L(N)]^T(ii) a The matrix of arguments is: x ═ β (1) β (2) … β (N)]^T；

S4-2, according to U_L(k) The discrete expression of (a) can be obtained:

β(k)＝[1U_L(k-1) ln(SOC(k)) ln(1-SOC(k))I_L(k)I_L(k-1)]

then there is a parameter matrix to be identified: a ═ a₁a₂a₃a₄a₅a₆]^T；

S4-3, estimating by using a least square method, and solving a parameter matrix A (X) needing to be identified^TX)^-1X^TY＝X^-1Y, obtaining the parameter a to be identified₁、a₂、a₃、a₄、a₅、a₆；

S4-4, identifying the parameter a according to the requirement₁、a₂、a₃、a₄、a₅、a₆The expansion form of the equivalent circuit model is further deformed to obtain a parameter calculation formula in a state space equation of the equivalent circuit model:

solving the obtained parameters a needing to be identified₁、a₂、a₃、a₄、a₅、a₆Substituting the calculation result into the state space equation of the equivalent circuit model to obtain the composite electrochemical polarization model of the lithium ion battery pack.

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