Fractional order equivalent circuit model and battery state of charge estimation method

Abstract

The embodiment of the application discloses a fractional order equivalent circuit model and a battery state of charge estimation method, and the model comprises: a positive electrode end of a balance potential module is connected with a negative electrode end of a hysteresis voltage module; the positive electrode end of the hysteresis voltage module is connected with one end of a first resistor and one end of a second resistor respectively, the other end of the first resistor is connected with a negative electrode end of a first diode, the positive electrode end of the first diode is connected with one end of a magnetic flux module and a negative electrode end of a second diode respectively, and the positive electrode end of the second diode is connected with the other end of the second resistor; wherein the resistance value of the first resistor is not equal to the resistance value of the second resistor; the other end of the magnetic flux module, a first phase module, a second phase module and a negative electrode end of an impedance module are sequentially connected; the positive electrode end of the impedance module is a positive electrode end of a battery to be measured, and the negative electrode end of the balance potential module is a negative electrode end of the battery to be measured. The model precision of the model is higher than that of the prior art model, and the battery state of charge can be accurately estimated.

Description

Technical Field

[0001] This invention relates to the field of circuit technology, and in particular to a fractional-order equivalent circuit model and a method for estimating the state of charge of a battery. Background Technology

[0002] Equivalent circuit models are mainly divided into integer-order equivalent circuit models and fractional-order equivalent circuit models. Among them, the model accuracy of fractional-order equivalent circuit models is higher than that of integer-order equivalent circuit models. Therefore, fractional-order equivalent circuit models are often used to model batteries.

[0003] Currently, when using existing fractional-order equivalent circuit models to model batteries, the insufficient accuracy of these models leads to inaccurate estimation of the battery's state of charge, resulting in overcharging and over-discharging, which significantly reduces the battery's lifespan (by more than 20%). Summary of the Invention

[0004] Based on this, it is necessary to propose a fractional-order equivalent circuit model and a battery state-of-charge estimation method to address the above problems. This allows for accurate estimation of the battery state of charge, preventing overcharging and over-discharging, and effectively improving battery lifespan.

[0005] To achieve the above objectives, the present invention provides a fractional-order equivalent circuit model in a first aspect, the model comprising:

[0006] Open-circuit voltage module, charge / discharge module, magnetic flux module, first phase module, second phase module, impedance module;

[0007] The open-circuit voltage module includes a balanced potential module and a hysteresis voltage module, and the charge-discharge module includes a first resistor, a second resistor, a first diode, and a second diode;

[0008] The positive terminal of the balancing potential module is connected to the negative terminal of the hysteresis voltage module;

[0009] The positive terminal of the hysteresis voltage module is connected to one end of the first resistor and one end of the second resistor, respectively. The other end of the first resistor is connected to the negative terminal of the first diode. The positive terminal of the first diode is connected to one end of the magnetic flux module and the negative terminal of the second diode, respectively. The positive terminal of the second diode is connected to the other end of the second resistor. The resistance value of the first resistor is not equal to the resistance value of the second resistor.

[0010] The other end of the magnetic flux module, the first phase module, the second phase module, and the negative terminal of the impedance module are connected in sequence;

[0011] The positive terminal of the impedance module is the positive terminal of the battery under test, and the negative terminal of the equilibrium potential module is the negative terminal of the battery under test.

[0012] Optionally, the flux module includes an inductor, the first phase module includes a first constant phase element and a third resistor, the second phase module includes a second constant phase element and a fourth resistor, and the impedance module includes a Weber element;

[0013] One end of the inductor is connected to the positive terminal of the first diode;

[0014] The other end of the inductor is connected to one end of the first constant phase element and one end of the third resistor, respectively; the other end of the first constant phase element is connected to one end of the second constant phase element, one end of the fourth resistor, and the other end of the third resistor, respectively.

[0015] The other end of the second constant-phase element is connected to the negative terminal of the Weber element and the other end of the fourth resistor, respectively.

[0016] The positive terminal of the Weber element is the positive terminal of the battery under test.

[0017] Optionally, the expression for the first charging equation of the fractional-order equivalent circuit model is U. OCV(SOC，H，T) =U0-IR1-U L -U1-U2-U W The expression for the first discharge equation of the fractional-order equivalent circuit model is U. OCV(SOC，H，T) =U0+IR2+U L +U1+U2+U W ;

[0018] Among them, U OCV(SOC，H，T) U is the voltage of the open-circuit voltage module, U0 is the terminal voltage of the battery under test, R1 is the resistance of the first resistor, I is the current of the battery under test, and U L U1 is the voltage across the inductor, U2 is the voltage across the first constant-phase element and the third resistor, and U3 is the voltage across the second constant-phase element and the fourth resistor. W R1 is the voltage across the Weber impedance, and R2 is the resistance of the second resistor.

[0019] Optionally, the expression for the impedance of the inductor is: The expression for the impedance of the first constant-phase element is: The expression for the impedance of the second constant-phase element is: The expression for the impedance of the Weber element is as follows:

[0020] in, Let L be the impedance of the inductor. Q Let S be the fractional inductance value of the inductor, where S is the unit in the frequency domain, α1 is the order of the inductor, and Z is the fractional order inductance. CPE1 Let C1 be the impedance of the first constant-phase element, C2 be the capacitance of the first constant-phase element, and Z be the order of the first constant-phase element. CPE2 C1 is the impedance of the second constant-phase element, C2 is the capacitance of the second constant-phase element, α3 is the order of the second constant-phase element, and Z is the capacitance of the second constant-phase element. W Let W be the impedance of the Weber element, W be the capacitance of the Weber element, and β be the order of the Weber element.

[0021] Optionally, the expression for the second charging equation of the fractional-order equivalent circuit model is:

[0022]

[0023] The expression for the second discharge equation of the fractional-order equivalent circuit model is as follows:

[0024]

[0025] Among them, β = 0.5, U OCV(SOC，H，T ( ) U(0s) is the voltage of the open-circuit voltage module, U(0s) is the terminal voltage of the battery under test, I(s) is the current of the battery under test, R1 is the resistance of the first resistor, and L Q α1 is the fractional inductance value of the inductor, S is the unit in the frequency domain, α3 is the order of the inductor, R3 is the resistance value of the third resistor, C1 is the capacitance value of the first constant-phase element, α2 is the order of the first constant-phase element, R4 is the resistance value of the fourth resistor, C2 is the capacitance value of the second constant-phase element, α3 is the order of the second constant-phase element, W is the capacitance value of the Weber element, β is the order of the Weber element, and R2 is the resistance value of the second resistor.

[0026] Optionally, the expression for the fractional-order charging fractional-order differential equation of the fractional-order equivalent circuit model is:

[0027] (WD β +WR3R4C1C2D α2+α3+β +WR3C1D α2+β +WR4C2D α3+β )[U OCV(SOC，H，T) (t)-U(0t)]

[0028] =(-R1WD β +R1WR3R4C1C2D α2+α3+β +R1WR3C1D α2+β +R1WR4C2Dα3+β +L Q WD α1+β

[0029] +L Q WR3R4C1C2D α1+α2+α3+β +R3C1L Q WD α1+α2+β +L Q WR4C2D α1+α3+β +R3WD β +R4WD β

[0030] +R4WD β +WR3R4C2D α3+β +WR3R4C1D α2+β )I(t);

[0031] The expression for the discharge fractional differential equation of the fractional equivalent circuit model is as follows:

[0032] (WD β +WR3R4C1C2D α2+α3+β +WR3C1D α2+β +WR4C2D α3+β )[U OCV(SOC，H，T) (t)-U(0t)]

[0033] =(R2WD) β +R2WR3R4C1C2D α2+α3+β +R2WR3C1D α2+β +R2WR4C2D α3+β +L Q WD α1+β

[0034] +L Q WR3R4C1C2D α1+α2+α3+β +R3C1L Q WD α1+α2+β +L Q WR4C2D α1+α3+β +R3WD β +R4WD β

[0035] +R4WD β +WR3R4C2D α3+β +WR3R4C1D α2+β )I(t);

[0036] Among them, β = 0.5, U OCV(SOC，H，T ( )U(t) is the voltage of the open-circuit voltage module, U(0t) is the terminal voltage of the battery under test, I(t) is the current of the battery under test, and D is the unit of time domain.

[0037] Optionally, the four multidimensional variables of the GL fractional differential equation of the fractional equivalent circuit model are as follows:

[0038] a=(β, α2+α3+β, α2+β, α3+β);

[0039] p=(W, WR3R4C1C2, WR2C1, WR3C2);

[0040] b=(β, α2+α3+β, α2+β, α3+β, α1+β, α1+α2+α3+β, α1+α2+β, α1+α3+β, β, β, α3+β, α2+β);

[0041] q=(R2W, R2WR3R4C1C2, R2WR3C1, R2WR4C2, LW, LWR3R4C1C2, LWR4C2, R3W

[0042] , R4W, R4W, WR3R4C2, WR3R4C1);

[0043] Where β = 0.5.

[0044] Optionally, the expression for the fractional differential equation of the charging GL of the fractional equivalent circuit model is:

[0045]

[0046] The expression for the discharge GL fractional differential equation of the fractional equivalent circuit model is as follows:

[0047]

[0048] Where t is the computation time and h is the step size. a is the integer part of the quotient of the computation time and the step size. i p i b i q i Let be the values ​​of the i-th data among a, p, b, and q, respectively. For Newton's second degree.

[0049] Optionally, the voltage expression of the open-circuit voltage module is U. OCV(SOC，H，T) =EMF+U H The voltage expression for the balancing potential module is EMF = ηU charge +(1-η)U dischargeThe expression for the voltage of the hysteresis voltage module during charging is U. H =η(U charge -U discharge The expression for the voltage of the hysteresis voltage module during discharge is U. H =(1-η)(U charge -U discharge );

[0050] Among them, U OCV(SOC，H，T) U is the voltage of the open-circuit voltage module, EMF is the voltage of the equilibrium potential module, and U is the voltage of the open-circuit voltage module. H U is the hysteresis voltage module voltage during charging or discharging, with η ranging from [0.5, 1]. charge U is the equilibrium terminal voltage of the battery under test during charging. discharge The voltage at the equilibrium terminal of the battery under test during discharge is denoted as .

[0051] To achieve the above objectives, the present invention provides a method for estimating the state of charge of a battery in a second aspect, the method comprising:

[0052] Establish a fractional-order equivalent circuit model as described in the first aspect;

[0053] Charging and discharging experiments were conducted on the battery under test to determine the two-dimensional relationship curve between the state of charge of the battery under test and the voltage of the open circuit voltage module at the same temperature, and to determine the three-dimensional relationship curve between the state of charge of the battery under test, the voltage of the open circuit voltage module, and the temperature at different temperatures.

[0054] The state of charge of the battery under test is estimated based on the fractional-order equivalent circuit model, the two-dimensional relationship curve, the three-dimensional relationship curve, the terminal voltage of the battery under test, and the current of the battery under test.

[0055] The embodiments of the present invention have the following beneficial effects: the positive terminal of the balancing potential module is connected to the negative terminal of the hysteresis voltage module; the positive terminal of the hysteresis voltage module is connected to one end of the first resistor and one end of the second resistor, the other end of the first resistor is connected to the negative terminal of the first diode, the positive terminal of the first diode is connected to one end of the magnetic flux module and the negative terminal of the second diode, and the positive terminal of the second diode is connected to the other end of the second resistor; wherein, the resistance value of the first resistor is not equal to the resistance value of the second resistor; the other end of the magnetic flux module, the negative terminal of the first phase module, the second phase module, and the impedance module are connected in sequence; the positive terminal of the impedance module is the positive terminal of the battery under test, and the negative terminal of the balancing potential module is the negative terminal of the battery under test. The above model reflects the hysteresis characteristics of the battery under test through a hysteresis voltage module, and reflects the inconsistent ohmic internal resistance of the battery under test during charging and discharging through a first resistor, a first diode, a second resistor, and a second diode (i.e., two resistors with different resistance values ​​are used when the battery under test is charging and discharging). In other words, by considering the hysteresis characteristics and the inconsistent ohmic internal resistance of the battery under test during charging and discharging, the model accuracy of this model is higher than that of existing models. Therefore, it can accurately estimate the battery state of charge (with high model accuracy, the estimation of battery state of charge is also accurate), and will not lead to overcharging and over-discharging of the battery, thus effectively improving the battery's lifespan. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] in:

[0058] Figure 1 This is a schematic diagram of the structure of a fractional-order equivalent circuit model in an embodiment of this application;

[0059] Figure 2 This is another structural schematic diagram of a fractional-order equivalent circuit model in an embodiment of this application;

[0060] Figure 3 This is another structural schematic diagram of a fractional-order equivalent circuit model in an embodiment of this application;

[0061] Figure 4 This is a flowchart illustrating a battery state of charge estimation method according to an embodiment of this application. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] Please see Figure 1 The diagram below is a schematic diagram of a fractional-order equivalent circuit model in an embodiment of this application. The model includes: an open-circuit voltage module 110, a charge-discharge module 120, a magnetic flux module 130, a first phase module 140, a second phase module 150, and an impedance module 160.

[0064] The open-circuit voltage module 110 includes a balanced potential module 111 and a hysteresis voltage module 112, and the charge-discharge module 120 includes a first resistor 121, a second resistor 122, a first diode 123, and a second diode 124.

[0065] In one feasible implementation, the positive terminal of the balancing potential module 111 is connected to the negative terminal of the hysteresis voltage module 112; the positive terminal of the hysteresis voltage module 112 is connected to one end of the first resistor 121 and one end of the second resistor 122, the other end of the first resistor 121 is connected to the negative terminal of the first diode 123, the positive terminal of the first diode 123 is connected to one end of the magnetic flux module 130 and the negative terminal of the second diode 124, and the positive terminal of the second diode 124 is connected to the other end of the second resistor 122; wherein, the resistance value of the first resistor 121 is not equal to the resistance value of the second resistor 122; the other end of the magnetic flux module 130, the negative terminals of the first phase module 140, the second phase module 150, and the impedance module 160 are connected in sequence; the positive terminal of the impedance module 160 is the positive terminal of the battery under test, and the negative terminal of the balancing potential module 111 is the negative terminal of the battery under test.

[0066] The battery under test is a battery, which can be any type of battery; there are no restrictions here.

[0067] It should be noted that all batteries have hysteresis characteristics (i.e., hysteresis voltage). However, existing models ignore the hysteresis characteristics of batteries, resulting in only one open-circuit voltage (i.e., the voltage of the equilibrium potential module 111 in this application) during battery charging and discharging. The voltage influence caused by hysteresis voltage is not considered, which reduces the accuracy of existing models. The model in this application uses the hysteresis voltage module 112 to simulate the hysteresis voltage of the battery, making the model accuracy of this application higher than that of existing models.

[0068] It should be further explained that, since the flow directions of the positive and negative electrodes of the battery are different during charging and discharging, and the chemical substances of the positive electrode material and the negative electrode material are different, meaning the chemical flow directions are different during charging and discharging, the ohmic internal resistance of the battery is inconsistent during charging and discharging. In existing models, the inconsistent characteristics of the ohmic internal resistance during charging and discharging are ignored, resulting in only one resistor in the existing models for charging and discharging, without considering the impedance effect caused by the inconsistent characteristics of the ohmic internal resistance during charging and discharging, thus reducing the model accuracy of the existing models. The model of this application uses a first resistor 121, a first diode 123, a second resistor 122, and a second diode 124, that is, two resistors with different resistance values, to simulate the inconsistent characteristics of the ohmic internal resistance during charging and discharging, so that the model accuracy of the model of this application is higher than that of the existing models.

[0069] Furthermore, each module in the model of this application is determined based on the spectrum diagram of the battery. It can be understood that the magnetic flux module 130 is used to reflect the inductive characteristics of the battery, the first phase module 140 is used to reflect the transport characteristics of the solid electrolyte interface film of the battery, the second phase module 150 is used to reflect the activation polarization characteristics of the battery, and the impedance module 160 is used to reflect the concentration polarization characteristics of the battery. That is, by considering the inductive characteristics, transport characteristics, activation polarization characteristics, and concentration polarization characteristics of the battery, the model accuracy of the model of this application is higher than that of the model of the prior art.

[0070] It should also be noted that the serial order of the modules in this application model can be varied. That is, without affecting the normal use of this application model, the positions of the modules in this application model can be interchanged. For another feasible implementation, please refer to [link / reference needed]. Figure 2 This is another structural schematic diagram of a fractional-order equivalent circuit model in an embodiment of this application. The connection order of the charging / discharging module 120 and the magnetic flux module 130 has been changed, which does not affect the normal use of the model in this application.

[0071] In this embodiment, the hysteresis voltage module 112 reflects the hysteresis characteristics of the battery under test, and the first resistor 121, the first diode 123, the second resistor 122, and the second diode 124 (i.e., two resistors with different resistance values ​​are used when the battery is charging and discharging) reflect the inconsistent ohmic internal resistance characteristics of the battery during charging and discharging. By considering the voltage effect caused by the battery's hysteresis characteristics and the impedance caused by the inconsistent ohmic internal resistance during charging and discharging, the accuracy of this model is higher than that of existing models. This allows for accurate estimation of the battery's state of charge (high model accuracy leads to accurate estimation of the battery's state of charge), preventing overcharging and over-discharging, and effectively improving battery lifespan. It is understood that the model accuracy determines the accuracy of the battery's state of charge estimation; higher model accuracy results in more accurate estimation of the battery's state of charge.

[0072] Please see Figure 3 The diagram below shows another structural schematic of a fractional-order equivalent circuit model in an embodiment of this application. The flux module 130 includes an inductor 131, the first phase module 140 includes a first constant-phase element 141 and a third resistor 142, the second phase module 150 includes a second constant-phase element 151 and a fourth resistor 152, and the impedance module 160 includes a Weber element 161.

[0073] In one feasible implementation, one end of inductor 131 is connected to the positive terminal of first diode 122; the other end of inductor 131 is connected to one end of first constant phase element 141 and one end of third resistor 142 respectively; the other end of first constant phase element 141 is connected to one end of second constant phase element 151, one end of fourth resistor 152 and the other end of third resistor 142 respectively; the other end of second constant phase element 151 is connected to the negative terminal of Weber element 161 and the other end of fourth resistor 152 respectively; the positive terminal of Weber element 161 is the positive terminal of the battery under test.

[0074] It should be noted that the impedance spectrum of a battery during charging and discharging has three parts: high frequency, mid frequency, and low frequency. The approximately straight line in the high-frequency part represents the inductive characteristics of the battery; the small semicircle in the high-frequency part represents the transport characteristics of the solid electrolyte interface film; the semicircle in the mid-frequency part represents the activation polarization characteristics; and the diagonal line in the low-frequency part represents the concentration polarization characteristics. This application simulates the high-frequency, mid-frequency, and low-frequency parts of the impedance spectrum of a battery during charging and discharging by using an inductor 131, a first constant-phase element 141 and a third resistor 142 in parallel, a second constant-phase element 151 and a fourth resistor 152 in parallel, and a Weber element 161. The selection and connection relationship of the inductor 131, the first constant-phase element 141 and the third resistor 142 in parallel, the second constant-phase element 151 and the fourth resistor 152 in parallel, and the Weber element 161 can be determined during the test based on the impedance spectrum of the elements. This reflects the inductive characteristics of the battery, the transport characteristics of the solid electrolyte interface film, the activation polarization characteristics, and the concentration polarization characteristics. In the existing model, the influence of the transport characteristics of the solid electrolyte interface film of the battery is not considered, which reduces the accuracy of the existing model. This model, by considering the transport characteristics of the solid electrolyte interface film of the battery, makes the accuracy of the model higher than that of the existing model.

[0075] In this embodiment, the impedance spectrum of a battery during charging and discharging is simulated using an inductor 131, a first constant-phase element 141 connected in parallel with a third resistor 142, a second constant-phase element 151 connected in parallel with a fourth resistor 152, and a Weber element 161. This simulates the high-frequency, mid-frequency, and low-frequency components of the impedance spectrum, reflecting the battery's inductive characteristics, the transport characteristics of the solid electrolyte interface film, the activation polarization characteristics, and the concentration polarization characteristics. By considering the influence of these characteristics, the model's accuracy is higher than that of existing models, allowing for accurate estimation of the battery's state of charge. This prevents overcharging and over-discharging, effectively improving battery lifespan.

[0076] In one feasible implementation, the expression for the first charging equation of the fractional-order equivalent circuit model is U. OCV(SOC，H，T) =U0-IR1-U L -U1-U2-U W The expression for the first discharge equation of the fractional-order equivalent circuit model is U. OCV(SOC，H，T) =U0+IR2+U L +U1+U2+U W Among them, U OCV(SOC，H，T) U is the voltage of the open-circuit voltage module 110, U0 is the terminal voltage of the battery under test, R1 is the resistance of the first resistor 121, I is the current of the battery under test, and UL U1 is the voltage across inductor 131, U2 is the voltage across the first constant-phase element 141 and the third resistor 142, and U3 is the voltage across the second constant-phase element 151 and the fourth resistor 152. W R1 is the voltage across the Weber impedance, and R2 is the resistance of the second resistor 122.

[0077] It should be noted that, based on the circuit structure of the model in this application and Kirchhoff's voltage law, the expressions for the first charging equation and the first discharging equation of the model in this application can be determined.

[0078] In this embodiment, the differences in terminal voltage during charging and discharging of the battery under test are determined by the expressions of the first charging equation and the first discharging equation of the model. This reflects the inconsistent characteristics of the ohmic internal resistance of the battery under test during charging and discharging, thus more accurately representing the actual circuit state of the battery under test. This results in higher model accuracy, enabling accurate estimation of the battery's state of charge and preventing overcharging and over-discharging, thereby effectively improving the battery's lifespan.

[0079] In one feasible implementation, the expression for the impedance of inductor 131 is: The expression for the impedance of the first constant-phase element 141 is: The expression for the impedance of the second constant-phase element 151 is: The expression for the impedance of a Weber element is: in, The impedance of inductor 131, L Q S represents the fractional order inductance of inductor 131, where S is the unit in the frequency domain, α1 is the order of inductor 131, and Z is the fractional order inductance of inductor 131. CPE1 Let C1 be the impedance of the first constant-phase element 141, C2 be the capacitance of the first constant-phase element 141, and Z be the order of the first constant-phase element 141. CPE2 C1 is the impedance of the second constant-phase element 151, C2 is the capacitance of the second constant-phase element 151, α3 is the order of the second constant-phase element, and Z is the capacitance of the second constant-phase element 151. W Let W be the impedance of the Weber element, W be the capacitance of the Weber element, and β be the order of the Weber element.

[0080] It should be noted that, based on the circuit structure, basic circuit principle, and working principle of the fractional-order energy storage element of the model in this application, the expressions for the impedance of inductor 131, the impedance of the first constant-phase element 141, the impedance of the second constant-phase element 151, and the impedance of the Weber element can be determined.

[0081] Furthermore, it should be noted that the capacitance values ​​of the first constant-phase element 141, the second constant-phase element 151, and the Weber element actually refer to the parameter values ​​of the first constant-phase element 141, the second constant-phase element 151, and the Weber element themselves. It can be understood that when the first constant-phase element 141, the second constant-phase element 151, and the Weber element are capacitors, then their parameter values ​​are capacitance values. If they are other elements, their parameter values ​​can also be other parameter values.

[0082] In this embodiment, the impedances of inductor 131, first constant-phase element 141, second constant-phase element 151, and Weber element in the model of this application are calculated using the expressions for the impedances of inductor 131, first constant-phase element 141, second constant-phase element 151, and Weber element, which is convenient for technicians to use directly.

[0083] In one feasible implementation, the expression for the second charging equation of the fractional-order equivalent circuit model is:

[0084]

[0085]

[0086] The expression for the second discharge equation of the fractional-order equivalent circuit model is:

[0087]

[0088] Among them, β = 0.5, U OCV(SOC，H，T ( ) U(0s) is the voltage of the open-circuit voltage module 110, U(0s) is the terminal voltage of the battery under test, I(s) is the current of the battery under test, R1 is the resistance of the first resistor 121, and L Q α1 is the fractional order inductance value of inductor 131, S is the unit in the frequency domain, α1 is the order of inductor 131, R3 is the resistance value of the third resistor 142, C1 is the capacitance value of the first constant phase element 141, α2 is the order of the first constant phase element 141, R4 is the resistance value of the fourth resistor 152, C2 is the capacitance value of the second constant phase element 151, α3 is the order of the second constant phase element, W is the capacitance value of the Weber element, β is the order of the Weber element, and R2 is the resistance value of the second resistor 122.

[0089] It should be noted that, considering the model of this application as a fractional-order system, and after performing a Laplace transform on the transfer function of the model of this application, i.e., the expression after the Laplace transform (the numerator is the output, the denominator is the input; in this application, the input is the current of the battery under test, and the output is the difference between the voltage of the open-circuit voltage module 110 and the terminal voltage of the battery under test), based on the expressions of the first charging equation and the first discharging equation of the model of this application, the expression of the impedance of the inductor 131, the expression of the impedance of the first constant-phase element 141, the expression of the impedance of the second constant-phase element 151, the expression of the impedance of the Weber element, and the principle of series and parallel resistors, the expressions of the second charging equation and the second discharging equation of the model of this application can be determined.

[0090] In this embodiment, the expressions for the charging equation and the discharging equation after Laplace transformation in the model of this application, namely the expressions for the second charging equation and the second discharging equation, are used to determine the differences in the signs (negative sign during charging and positive sign during discharging) and resistances (first resistance 121 during charging and second resistance 122 during discharging) of the battery under test during charging and discharging, thereby reflecting the inconsistent characteristics of the ohmic internal resistance of the battery under test during charging and discharging.

[0091] In one feasible implementation, the expression for the fractional-order differential equation of the charging circuit model is:

[0092] (WD β +WR3R4C1C2D α2+α3+β +WR3C1D α2+β +WR4C2D α3+β )[U OCV(SOC，H，T) (t)-U(0t)]

[0093] =(-R1WD β +R1WR3R4C1C2D α2+α3+β +R1WR3C1D α2+β +R1WR4C2D α3+β +L Q WD α1+β

[0094] +L Q WR3R4C1C2D α1+α2+α3+β +R3C1L Q WD α1+α2+β +L Q WR4C2D α1+α3+β +R3WD β +R4WD β

[0095] +R4WD β+WR3R4C2D α3+β +WR3R4C1D α2+β )I(t);

[0096] The expression for the fractional-order differential equation of discharge in the fractional-order equivalent circuit model is as follows:

[0097] (WD β +WR3R4C1C2D α2+α3+β +WR3C1D α2+β +WR4C2D α3+β )[U OCV(SOC，H，T) (t)-U(0t)]

[0098] =(R2WD) β +R2WR3R4C1C2D α2+α3+β +R2WR3C1D α2+β +R2WR4C2D α3+β +L Q WD α1+β

[0099] +L Q WR3R4C1C2D α1+α2+α3+β +R3C1L Q WD α1+α2+β +L Q WR4C2D α1+α3+β +R3WD β +R4WD β

[0100] +R4WD β +WR3R4C2D α3+β +WR3R4C1D α2+β )I(t);

[0101] Among them, β = 0.5, U OCV(SOC，H，T ( ) U(t) is the voltage of the open-circuit voltage module 110, U(0t) is the terminal voltage of the battery under test, I(t) is the current of the battery under test, and D is the unit of time domain.

[0102] It should be noted that after converting the expressions of the second charging equation and the second discharging equation of the model in this application to the time domain, that is, replacing the frequency domain unit S with the time domain unit D, the expressions of the fractional differential equations of charging and discharging of the model in this application can be determined.

[0103] In the embodiments of this application, after converting the expressions of the second charging equation and the second discharging equation in the model of this application to the time domain, the expressions of the fractional differential equations of charging and discharging are obtained, which are convenient for technicians to use directly.

[0104] In one feasible implementation, the four multidimensional variables of the GL fractional differential equation of the fractional equivalent circuit model are as follows:

[0105] a=(β, α2+α3+β, α2+β, α3+β);

[0106] p=(W, WR3R4C1C2, WR2C1, WR3C2);

[0107] b=(β, α2+α3+β, α2+β, α3+β, α1+β, α1+α2+α3+β, α1+α2+β, α1+α3+β, β, β, α3+β, α2+β);

[0108] q=(R2W, R2WR3R4C1C2, R2WR3C1, R2WR4C2, LW, LWR3R4C1C2, LWR4C2, R3W

[0109] , R4W, R4W, WR3R4C2, WR3R4C1);

[0110] Where β = 0.5.

[0111] It should be noted that this application adopts the definition method of GL fractional differential equation, that is, it is necessary to first define four multidimensional variables (a, p, b, q) of GL fractional differential equation; where a, p, and q are the degree and coefficient of the polynomial in the denominator of the expression after Laplace transform, respectively, and b and q are the degree and coefficient of the polynomial in the numerator and denominator of the expression after Laplace transform, respectively. That is, the four multidimensional variables of GL fractional differential equation are determined according to the expression of the second charging equation and / or the expression of the second discharging equation, and a, p, and q are the degree and coefficient of the polynomial in the denominator of the expression of the second charging equation and / or the expression of the second discharging equation, respectively, and b and q are the degree and coefficient of the polynomial in the numerator and denominator of the expression of the second charging equation and / or the expression of the second discharging equation, respectively.

[0112] In the embodiments of this application, four multidimensional variables are defined in the GL fractional differential equation of this application model to facilitate direct use by those skilled in the art.

[0113] In one feasible implementation, the expression for the fractional-order differential equation of the charging GL in the fractional-order equivalent circuit model is:

[0114]

[0115] The expression for the fractional differential equation of discharge GL in the fractional equivalent circuit model is as follows:

[0116]

[0117] Where t is the computation time and h is the step size. a is the integer part of the quotient of the computation time and the step size. i p i b i q i Let be the values ​​of the i-th data among a, p, b, and q, respectively. For Newton's second degree.

[0118] The step size is consistent with the sampling time.

[0119] It should be noted that after defining the four multidimensional variables of the GL fractional differential equation, the charging GL fractional differential equation and the discharging GL fractional differential equation can be determined according to the theory of fractional differential equations.

[0120] In the embodiments of this application, by determining the fractional differential equations of charging GL and discharging GL, it is convenient for technicians to use directly.

[0121] In one feasible implementation, the voltage of the open-circuit voltage module 110 is expressed as U. OCV(SOC，H，T) =EMF+U H The expression for the voltage of the balancing potential module 111 is EMF = ηU charge +(1-η)U discharge The expression for the voltage of the hysteresis voltage module 112 during charging is U. H =η(U charge -U discharge The expression for the voltage of the hysteresis voltage module 112 during discharge is U. H =(1-η)(U charge -U discharge ); where U OCV(SOC，H，T) U is the voltage of open-circuit voltage module 110, EMF is the voltage of balanced potential module 111, and U... H The voltage of the hysteresis voltage module 112 during charging or discharging, η, has a value range of [0.5, 1]. charge U is the equilibrium terminal voltage of the battery under test during charging. discharge This is the equilibrium terminal voltage of the battery under test during discharge.

[0122] It should be noted that the hysteresis voltage module 112 uses different voltage calculations when the battery under test is charging and discharging in order to solve the voltage hysteresis problem of the battery under test.

[0123] In this embodiment of the application, by determining the expressions for the voltage of the open-circuit voltage module 110, the voltage of the equilibrium potential module 111, the voltage of the charging hysteresis voltage module 112, and the voltage of the discharging hysteresis voltage module 112, it is convenient for technicians to use directly.

[0124] Please see Figure 4 The diagram below illustrates a method for estimating the state of charge of a battery according to an embodiment of this application. The method includes:

[0125] Step 410: Establish a fractional-order equivalent circuit model.

[0126] It is understandable that, since the model accuracy of this application is higher than that of the existing technology model, it can accurately estimate the state of charge of the battery. Therefore, the model of this application is used to estimate the state of charge of the battery under test.

[0127] Step 420: Conduct charging and discharging experiments on the battery under test to determine the two-dimensional relationship curve between the state of charge of the battery under test and the voltage of the open circuit voltage module at the same temperature, and to determine the three-dimensional relationship curve between the state of charge of the battery under test, the voltage of the open circuit voltage module, and the temperature at different temperatures.

[0128] It should be noted that the electrochemical process of the battery under test is quite sensitive to temperature. Therefore, the state of charge of the battery under test is different at the same temperature and at different temperatures. Furthermore, the voltage of the open-circuit voltage module and the state of charge of the battery under test are also different when the battery is charging and discharging. Therefore, it is necessary to conduct charging and discharging experiments on the battery under test to determine the two-dimensional relationship curve between the state of charge of the battery under test and the voltage of the open-circuit voltage module at the same temperature, and to determine the three-dimensional relationship curve between the state of charge of the battery under test, the voltage of the open-circuit voltage module, and the temperature at different temperatures.

[0129] Furthermore, in charging and discharging experiments on the battery under test, it may only be necessary to determine the correspondence between the state of charge (SOC) of the battery under test and the voltage of the open-circuit voltage module at the same temperature, and the correspondence between the SOC, the voltage of the open-circuit voltage module, and the temperature at different temperatures. In other words, obtaining two-dimensional and three-dimensional relationship curves is not necessary. It is understandable that obtaining two-dimensional and three-dimensional relationship curves is for the purpose of facilitating the estimation of the SOC of the battery under test.

[0130] Step 430: Estimate the state of charge of the battery under test based on the fractional equivalent circuit model, two-dimensional relationship curve, three-dimensional relationship curve, terminal voltage of the battery under test, and current of the battery under test.

[0131] It should be noted that, based on the model of this application, expressions related to estimating the state of charge (SOC) of a battery using the model of this application can be derived. It can be understood that, based on the model of this application, the two-dimensional relationship curves, the three-dimensional relationship curves, the terminal voltage of the battery under test, and the current of the battery under test, the SOC of the battery under test can be estimated. It can also be understood that, based on the model of this application, the two-dimensional relationship curves, the three-dimensional relationship curves, the terminal voltage of the battery under test, and the current of the battery under test, parameters of the model of this application can be identified, thereby estimating the SOC of the battery under test.

[0132] In the embodiments of this application, when estimating the state of charge of the battery under test using the model of this application, the influence of temperature, hysteresis characteristics, inductance characteristics, transport characteristics of the solid electrolyte interface film, activation polarization characteristics, and concentration polarization characteristics of the battery under test is considered. This makes the model accuracy of the model of this application higher than that of the prior art model, so that the state of charge of the battery can be accurately estimated, avoiding overcharging and over-discharging of the battery, and effectively improving the battery life.

[0133] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0134] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A fractional-order equivalent circuit model, characterized in that, The model includes: Open-circuit voltage module, charge / discharge module, magnetic flux module, first phase module, second phase module, impedance module; The open-circuit voltage module includes a balanced potential module and a hysteresis voltage module, and the charge-discharge module includes a first resistor, a second resistor, a first diode, and a second diode; The positive terminal of the balancing potential module is connected to the negative terminal of the hysteresis voltage module; The positive terminal of the hysteresis voltage module is connected to one end of the first resistor and one end of the second resistor, respectively. The other end of the first resistor is connected to the negative terminal of the first diode. The positive terminal of the first diode is connected to one end of the magnetic flux module and the negative terminal of the second diode, respectively. The positive terminal of the second diode is connected to the other end of the second resistor. The resistance value of the first resistor is not equal to the resistance value of the second resistor. The other end of the magnetic flux module, the first phase module, the second phase module, and the negative terminal of the impedance module are connected in sequence; The positive terminal of the impedance module is the positive terminal of the battery under test, and the negative terminal of the equilibrium potential module is the negative terminal of the battery under test.

2. The model according to claim 1, characterized in that, The flux module includes an inductor, the first phase module includes a first constant phase element and a third resistor, the second phase module includes a second constant phase element and a fourth resistor, and the impedance module includes a Weber element. One end of the inductor is connected to the positive terminal of the first diode; The other end of the inductor is connected to one end of the first constant phase element and one end of the third resistor, respectively; the other end of the first constant phase element is connected to one end of the second constant phase element, one end of the fourth resistor, and the other end of the third resistor, respectively. The other end of the second constant-phase element is connected to the negative terminal of the Weber element and the other end of the fourth resistor, respectively. The positive terminal of the Weber element is the positive terminal of the battery under test.

3. The model according to claim 2, characterized in that, The expression for the first charging equation of the fractional-order equivalent circuit model is: The expression for the first discharge equation of the fractional-order equivalent circuit model is as follows: ; in, The voltage of the open-circuit voltage module. The terminal voltage of the battery under test is... Let be the resistance value of the first resistor. The current of the battery under test is... The voltage across the inductor. The voltage between the first constant-phase element and the third resistor. The voltage between the second constant-phase element and the fourth resistor. The voltage of the Weber element. The resistance value is the value of the second resistor.

4. The model according to claim 2, characterized in that, The expression for the impedance of the inductor is: The expression for the impedance of the first constant-phase element is: The expression for the impedance of the second constant-phase element is: The expression for the impedance of the Weber element is: ; in, The impedance of the inductor is... The fractional inductance value of the inductor. Units in the frequency domain. Let be the order of the inductor. Let be the impedance of the first constant-phase element. The capacitance value of the first constant-phase element. Let be the order of the first constant-phase element. The impedance of the second constant-phase element is given. The capacitance value of the second constant-phase element. Let be the order of the second constant phase. The impedance of the Weber element is given. Let be the capacitance value of the Weber element. Let be the order of the Weber element.

5. The model according to claim 2, characterized in that, The expression for the second charging equation of the fractional-order equivalent circuit model is: ； The expression for the second discharge equation of the fractional-order equivalent circuit model is as follows: ； in, , The voltage of the open-circuit voltage module. The terminal voltage of the battery under test is... The current of the battery under test is... Let be the resistance value of the first resistor. The fractional inductance value of the inductor. Units in the frequency domain. Let be the order of the inductor. The resistance value of the third resistor. The capacitance value of the first constant-phase element. Let be the order of the first constant-phase element. The resistance value of the fourth resistor is... The capacitance value of the second constant-phase element. Let be the order of the second constant phase. Let be the capacitance value of the Weber element. Let the order of the Weber element be denoted by . The resistance value is the value of the second resistor.

6. The model according to claim 5, characterized in that, The expression for the fractional-order differential equation of the charging circuit model is as follows: ； The expression for the discharge fractional differential equation of the fractional equivalent circuit model is as follows: ； in, , The voltage of the open-circuit voltage module. The terminal voltage of the battery under test is... The current of the battery under test is... For the time domain.

7. The model according to claim 5, characterized in that, The four multidimensional variables of the GL fractional differential equation of the fractional equivalent circuit model are as follows: ； ； ； ； in, .

8. The model according to claim 7, characterized in that, The expression for the fractional-order differential equation of the charging GL of the fractional-order equivalent circuit model is as follows: ； The expression for the discharge GL fractional differential equation of the fractional equivalent circuit model is as follows: ； in, For computation time, Step size, It is the integer part of the quotient of the computation time and the step size. , , , They are respectively , , , The value of the i-th data in the data, , For Newton's second degree.

9. The model according to any one of claims 1 to 8, characterized in that, The expression for the voltage of the open-circuit voltage module is as follows: The expression for the voltage of the balancing potential module is: The expression for the voltage of the hysteresis voltage module during charging is: The expression for the voltage of the hysteresis voltage module during discharge is: ; in, The voltage of the open-circuit voltage module. The voltage of the equilibrium potential module is... The voltage of the hysteresis voltage module during charging or discharging. The value range is [0.5, 1]. The equilibrium terminal voltage of the battery under test during charging. The voltage at the equilibrium terminal of the battery under test during discharge is denoted as .

10. A method for estimating the state of charge of a battery, characterized in that, The method includes: Establish a fractional-order equivalent circuit model as described in any one of claims 1 to 9; Charging and discharging experiments were conducted on the battery under test to determine the two-dimensional relationship curve between the state of charge of the battery under test and the voltage of the open circuit voltage module at the same temperature, and to determine the three-dimensional relationship curve between the state of charge of the battery under test, the voltage of the open circuit voltage module, and the temperature at different temperatures. The state of charge of the battery under test is estimated based on the fractional-order equivalent circuit model, the two-dimensional relationship curve, the three-dimensional relationship curve, the terminal voltage of the battery under test, and the current of the battery under test.

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