TW201437917A - Method for modeling equivalent circuit of Li-ion battery - Google Patents

Abstract

A method for modeling equivalent circuit of Li-ion battery is provided in the present invention. The model adopts a resistor connected to multiple parallel RC circuits to serve as an equivalent circuit to describe the static or dynamic electrical characteristics of the battery. When the charge current or discharge current thereof is vary, the terminal voltage of the battery would be affected by the contact area between the polar plates and electrolyte and the variation of the contact resistor such that the voltage curve thereof is as an attenuation exponential curve. Further, the voltage cannot be described by only one time constant. Thus, the battery model not only includes a series connection resistor but also includes more than one RC circuit. The key of the present invention is to design a method to obtain the different parameters for the RC circuits without using an expensive instrument, such as spectrum analyzers, impedance analyzer and so on.

Description

Circuit model construction method of lithium battery

The present invention relates to a method for simulating a battery, and more particularly to a circuit model construction method for a lithium battery.

Many different electrochemical cell models can be found in the literature, such as electrochemical models, behavioral models, and electric circuit models. Although the electrochemical model has high accuracy, the model itself is composed of many complex nonlinear differential equations [1]. In addition to computational complexity, it is necessary to have a deep understanding of the electrochemical reaction to construct such a model. The behavioral model uses a simplified equation to describe the relationship between battery power and other parameters such as current. The most famous behavioral model is Peukert's law, which evaluates the relationship between battery discharge time and discharge current. The circuit model uses circuit components such as capacitors, resistors, and voltage sources to form an equivalent circuit that represents the battery [2]. For power supply designers, the circuit model is the easiest to understand and the most convenient to operate.

As for the construction method of the circuit model, including electrochemical impedance spectroscopy (EIS) [3], this method needs to use an impedance analyzer to scan the impedance variation of the battery in multiple frequency bands, and then approximate the curve. , to derive the architecture of the circuit. The above method has another variant, that is, a Bode plot of the frequency response of the battery is drawn by an impedance analyzer, and then an equivalent circuit is obtained by the curve approximation method [4]. In addition, artificial intelligence, such as the neural network method [5], is used to find the correct circuit model parameters.

However, all of the above methods require considerable cost and relatively large resources. Based on this, the applicant proposed a method for accurately constructing a circuit model of a lithium battery using relatively limited resources.

Reference materials:

[1] DM Bernardi, H. Gu, AY Schoene, “Two-Dimensional Mathematical Model of a Lead-Acid Cell,” Journal of the Electrochemical Society, Vol. 140, No. 8, Aug. 1993, pp. 2250-2257 .

[2] L. Gao, S. Liu, and RA Dougal, “Dynamic Lithium-Ion Battery Model for System Simulation,” IEEE Trans. on Components and Packaging Technologies, Vol. 25, No. 3, Sep. 2002, pp. 495-505. 2 . M. Chen and GA Rincón-Mora, “Accurate Electrical Battery Model Capable of Predicting Runtime and IV Performance,” IEEE Trans. on Energy Conversion, Vol. 21, No. 2, Jun. 2006, pp. 504-511. 3 . M. Urbain, M. Hinaje, S Raël, B. Davat, and P. Desprez, “Energetical Modeling of Lithium-Ion Batteries Including Electrode Porosity Effects,” IEEE Trans. on Energy Conversion, Vol. 25 , No. 3, Sep. 2010, pp. 862-872.

[3] S. Buller, M. Thele, R WAA De Doncker, and E. Karden, “Impedance-Based Simulation Models of Supercapacitors and Li-Ion Batteries for Power Electronic Applications,” IEEE Trans. on Industry Applications, Vol. 41 , No. 3, May/Jun. 2005, pp. 742-747.

[4] J. Jang, and J. Yoo, “Equivalent Circuit Evaluation Method of Lithium Polymer Battery Using Bode Plot and Numerical Analysis,” IEEE Trans. on Energy Conversion, Vol. 26, No. 1, Mar. 2011, pp. 290-298.

[5] Y. Song and L. Gao, “Incremental Battery Model Using Wavelet-Based Neural Networks,” IEEE Trans. on Components, Packaging and Manufacturing Technology, Vol. 1, No. 7, Jul. 2011, pp. 1075- 1081.

It is an object of the present invention to provide a circuit model construction method for a lithium battery, whereby the battery is discharged in stages, and the internal parameters of the model are estimated using the battery standing voltage.

Another object of the present invention is to provide a circuit model construction method for a lithium battery, thereby understanding the dependence of the behavior of the battery on the state of charge ( SOC ) and temperature.

In view of the above, the present invention provides a circuit model construction method for a lithium battery. The circuit model construction method of the lithium battery includes the following steps: (Step A) discharging a fixed amount of electric power to a battery with a fixed current; (Step B) stopping discharging And standing for a predetermined time until the terminal voltage of the battery is stable; (step C) recording the voltage versus time curve of (step B); (step D) setting the voltage versus time curve of the step (step B) to a battery a function (step E) obtaining an initial change voltage of a voltage of the battery when the discharge is stopped; (step F) obtaining a maximum voltage of a terminal voltage of the battery during the rest process; (step G) assuming a natural function; (step H Using a curve matching method, according to the voltage versus time curve of the (step B) and the natural function, find a matching curve, a corresponding fitting curve function and a time constant; (step I) comparison The matching curve and the voltage versus time curve of the (step B) obtain an error versus time curve; (step J) provides an error threshold; (step K) find the error according to the error threshold In the time variation curve, the time point exceeding the error threshold is taken as a piece of time; (step L) the matching curve function is substituted into the initial time of the step (step B) to obtain an initial voltage; (step M) Dividing the initial voltage by the fixed current to obtain a resistance value; (step N) dividing the time constant by the first resistance to obtain a capacitance value; (step O) deducting the battery function from the fitting curve function, repeating (Step G) to (Step N) n times to obtain n resistance values, n capacitance values, and n time constants; and (step P) constructing a circuit model of the lithium battery based on the n resistance values, n capacitance values, and n time constants.

According to the circuit model construction method of the lithium battery according to the preferred embodiment of the present invention, the curve adaptation method of the above (step H) includes: a least square difference method. In addition, in the preferred embodiment, the above steps further include: (Step Q) returning (Step A), and repeating (Step A)~(Step Q) until the battery power is lower than a preset power. In a preferred embodiment, the resistance value of the voltage drop caused by the battery current can be obtained by subtracting the initial change voltage of the battery voltage at the time of discharging by the voltage drop of the battery current generated by the fixed current. . In addition, the step of (step D) setting the voltage versus time curve of the step (step B) to a battery function includes: subtracting the measured maximum open circuit voltage of the battery from the maximum voltage to obtain the (step B) Voltage vs. time curve.

The spirit of the present invention is to propose a new circuit model construction method for a lithium battery, which mainly discharges the battery in stages and estimates the internal parameters of the model by using the battery standing voltage. In the experimental example, the battery model is conceived as a resistor in series with three RC circuits to describe the dynamic electrical characteristics of the battery. This circuit model can be used to more accurately estimate the battery terminal voltage during charging and discharging of lithium-ion batteries, and is applied to battery power circuit design; or further applied to battery power estimation.

The above and other objects, features and advantages of the present invention will become more <RTIgt;

E ‧‧‧Battery internal electromotive force

R _t ‧‧‧resistance of voltage drop caused by battery current

V _t ‧‧‧ voltage drop caused by battery current

R _s ‧‧‧resistance of the first RC circuit

C _s ‧‧‧The capacitance of the first RC circuit

V _s ‧‧‧voltage drop of the first RC circuit

τ _s ‧‧‧ time constant of the first RC circuit

R _m ‧‧‧resistance of the second RC circuit

C _m ‧‧‧The capacitance of the second RC circuit

V _m ‧‧‧ voltage drop of the second stage RC circuit

τ _m ‧‧‧ time constant of the second RC circuit

R _f ‧‧‧resistance of the third stage RC circuit

C _f ‧‧‧The capacitance of the third stage RC circuit

V _f ‧‧‧ voltage drop of the third stage RC circuit

τ _f ‧‧‧ time constant of the third stage RC circuit

V _b ‧‧‧Battery external terminal voltage

i _b ‧‧‧Battery discharge voltage and current

SOC, θ ‧‧‧ battery remaining capacity

t ₁ ‧‧‧ Division 1

t ₂ ‧‧‧Section 2

t _end ‧‧‧Standing end point

FIG. 1 is a waveform diagram showing changes in battery terminal voltage versus time during intermittent discharge according to a preferred embodiment of the present invention.

FIG. 2 is a waveform diagram showing changes in terminal voltage versus time of a converted lithium battery according to a preferred embodiment of the present invention.

FIG. 3 illustrates a lithium ion battery model disclosed in accordance with a preferred embodiment of the present invention.

4 is a waveform diagram showing voltage changes of a stationary process terminal with respect to time in different state of charge ( SOC ) according to a preferred embodiment of the present invention.

FIG. 5 is a graph showing approximation of a standing voltage using three exponential functions according to a preferred embodiment of the present invention.

6 is a graph showing average values of square errors of different segmentation points according to a preferred embodiment of the present invention.

FIG. 7 is a flow chart of determining parameters according to a preferred embodiment of the present invention.

FIG. 8 is a diagram showing relationship between R _t and state of charge ( SOC ) according to a preferred embodiment of the present invention.

FIG. 9 is a diagram showing relationship between τ _s ^-1 and state of charge ( SOC ) according to a preferred embodiment of the present invention.

FIG. 10 is a diagram showing relationship between R _s and state of charge ( SOC ) according to a preferred embodiment of the present invention.

FIG. 11 is a diagram showing relationship between τ _m ^-1 and state of charge ( SOC ) according to a preferred embodiment of the present invention.

FIG. 12 is a diagram showing relationship between R _m and state of charge ( SOC ) according to a preferred embodiment of the present invention.

FIG. 13 is a diagram showing relationship between τ _f ^-1 and state of charge ( SOC ) according to a preferred embodiment of the present invention.

FIG. 14 is a diagram showing relationship between R _f and state of charge ( SOC ) according to a preferred embodiment of the present invention.

FIG. 15 is a flow chart showing a method for constructing a circuit model of a lithium battery according to a preferred embodiment of the present invention.

Since the internal chemical reaction of the battery is affected by factors such as the concentration of the reactants, the diffusion rate of the electrolyte, etc., there is not only an ohmic pressure drop at the electrode and the interface, but also an electrochemical polarization called concentration polarization. And phenomena such as electrochemical polarization. FIG. 1 is a waveform diagram showing changes in battery terminal voltage versus time during intermittent discharge according to a preferred embodiment of the present invention. Referring to Figure 1, the lithium battery is discharged for a period of time, the battery voltage will drop a steeply (as indicated by V _t in the figure), and then another voltage change similar to the exponential type; next to the stationary phase, the battery terminal voltage There will also be a sudden rise, followed by an exponential voltage recovery. E in Fig. 1 refers to the maximum voltage after being sufficiently left, and is generally referred to as a standing voltage. Since the battery voltage measurement value of this stationary process approximates the difference between a constant value and an exponential function, it is difficult to solve this type. For ease of analysis and illustration, the maximum open voltage E is subtracted from the measured open end voltage, and the resulting curve is presented as in FIG. FIG. 2 is a waveform diagram showing changes in terminal voltage versus time of a converted lithium battery according to a preferred embodiment of the present invention. The result approximates an exponentially decaying graph. The data point is the static voltage after conversion; the solid line is the result of approximating the exponential function as the trend line.

As can be seen from Fig. 2, if only a single exponential function is used for approximation, the change in the open circuit voltage cannot be reliably simulated. If the emphasis is on approximating the initial segment, the voltage decay will be much faster than it is; however, if the emphasis is on approximating the back-end data, the sharper portion of the previous segment will obviously be ignored. The invention therefore chooses to approximate the open circuit voltage by a function of three exponential decays, wherein the voltage variation simulated by each exponential function can be implemented on the circuit with a set of parallel capacitors and resistors. In addition, at the initial stage of standing, the ohmic voltage drop due to the change in the battery current can be simply achieved with a resistor. Therefore, the battery model is established as a circuit in which a resistor is connected in parallel with three RCs in parallel. As shown in FIG. 3, FIG. 3 illustrates a lithium ion battery model disclosed in a preferred embodiment of the present invention. In Fig. 3, the electromotive force E represents the voltage after the battery is fully rested, and is the battery terminal voltage, and the subscripts " s ", " m ", " f " represent "slow", "medium", "fast", respectively. That is, the time constant of the RC circuit is from the longest to the shortest. Since the three RC circuits mathematically represent only a linear combination of exponential functions of three different time constants, the relevant parameters of the three RC circuits cannot be separated by a simple curve fitting.

In order to control the cause of the change, the batteries to be tested are placed in the temperature control box, and the influence of temperature is first excluded. Then explore the impact of battery state of charge ( SOC ) on the parameters. The battery is first charged in a fixed condition, for example, the embodiment of the invention is charged at a constant current of 0.1 A. When the battery terminal voltage reaches the rated voltage, it is switched to a constant voltage of 4.2V for charging; when the charging current is less than 0.01A, the battery is considered to be fully charged. The battery is repeatedly discharged at a fixed current with a fixed current and is left open for a period of time (for example, 30 minutes). As shown in FIG. 4, FIG. 4 illustrates different states of charge ( SOC ) disclosed in a preferred embodiment of the present invention. Waveform of the change of voltage at the end of the stationary process. Please refer to FIG. 4, because each time the battery releases a fixed amount of electricity, in Figure 4, each of the stationary curves represents a resting curve at a different state of charge ( SOC ). Then analyze the static curve to find out the relationship between the parameters and the battery state ( SOC ). In order to avoid excessive discharge, affecting the cycle life of the battery, it is necessary to set a safe cut-off voltage (for example, lithium-ion battery is about 3.2V), and the discharge should not be lower than this cut-off voltage.

Following the practice of Figure 2, the maximum voltage after sufficient rest is assumed to be the electromotive force E , and the measured battery terminal voltage is v _b ( t ). The terminal voltage measured by subtracting the static voltage is obtained as v ₂ ( t ), that is, v ₂ ( t )= E - v _b ( t ), and then approximated by three exponential functions, and the result is shown in FIG. 5 . FIG. 5 is a graph showing approximation of a standing voltage using three exponential functions according to a preferred embodiment of the present invention. Referring to Fig. 5, V _t is the instantaneous change of voltage at the start of static operation, that is, the voltage on the resistor R _t in the model of Fig. 3, so the following equation can be obtained to obtain R _t : R _t = V _t /i _b ( 1)

The mathematical formulas of the exponential functions v _s ( t ), v _m ( t ), v _f ( t ) of the other three analog voltages are:

Where τ _s = R _s C _s , τ _m = R _m C _m , τ _f = R _f C _f .

As mentioned above, although the time constants of the three exponential functions are different, they have the exact same mathematical form, so the parameter values cannot be found directly in the curve matching manner. We observe the change of the curve and find that since τ _s is the largest time constant, v _s decays the slowest. Therefore, at some point in time, after t ₂ , the other two voltages, v _f and v _m , have decayed to zero, leaving v _s alone. Using the voltage data of the t ₂ - t _end period, ie v ₂ ( t | t ₂ t t _end ), perform the following curve fitting analysis to obtain the exponential function The initial value V _s and the time constant τ _s .

Formula (4) indicates the matching curve The sum of the squared differences between the measured values v ₂ ( t ), if the sum of the squared differences is the smallest, indicates that the best fit curve has been obtained. For example, in Matlab's mathematical software, there is a function fminsearch( fun, [ x, y, ...]), which can be used to solve the minimum value of a multivariable function, which can be used to conveniently obtain the parameter value of this matching curve. . In other words, such a technique can be implemented programmatically or in hardware. Next, the obtained v _s ( t ) is extrapolated to obtain v _s ( t | t ₀ t t ₂₎ value, and let _{v 1 (t) = v 2} (t) - v s (t); i.e., the removal of the _{v 2 (t) v s (} t) from the measured values. At this point, you can repeat the previous process, so that at some point in time, such as after t ₁ , v _f has decayed to zero, leaving v _m alone. Using the voltage data of the t ₁ - t ₂ period, ie v ₁ ( t | t ₁ t t ₂ ), curve matching analysis, you can get the exponential function The initial value V _m and the time constant τ _m . Once the same procedure is repeated again, the minimum time constants V _f and τ _{f can be found} .

As for the selection method of the above t ₁ and t ₂ , the least square difference is used again, as shown in FIG. 6. 6 is a graph showing average values of square errors of different segmentation points according to a preferred embodiment of the present invention. Please refer to Figure 6, which shows v _x ( t | t _y t t _end ) is obtained by exponential function and then the average of the squared difference between v _x ( t ) is obtained. Where v _x may be v ₁ or v ₂ ; and t _y is gradually incremented from t ₀ to t _end . It can be seen from the figure that there will be a large square difference at the beginning; but since t _cut , the square error is no longer reduced and remains almost unchanged. As long as t ₁ and t ₂ are selected at times greater than t _cut , the correct fit curve can be obtained.

If the three exponentially decaying adaptation curves obtained above are extrapolated back to t ₀ , the initial voltage values of the three RC circuits at the interruption of the discharge current are obtained, that is, v _s ( t ₀ ), v _m ( t ₀ ) and v _f ( t ₀ ). Since the battery is discharged with a fixed DC current i _b for a long time before the current is interrupted; that is, the capacitances C _s , C _m and C _f in the model are in a steady state, and the capacitor voltage is before and after the interruption of the discharge current. The voltage is continuous. When the capacitor is in DC steady state, it can be regarded as an open state; that is, at the moment before t ₀ , current i _b flows through R _s , R _m and R _f , respectively, to generate v _s ( t ₀ ), v _m The pressure drop of ( t ₀ ) and v _f ( t ₀ ). From this observation, we can further separate the resistance and capacitance values in the RC circuit: R _x = V _x /i _b (6)

C _x = τ _x /R _x (7)

Where x represents the above s , m , or f .

Through the above process, the parameter value of the battery equivalent circuit under a certain state of charge ( SOC ) can be obtained. Continue to use the same procedure to analyze the battery terminal voltage of other static processes to obtain the parameter distribution of the equivalent circuit of the battery under different state of charge ( SOC ).

FIG. 7 is a flow chart of determining parameters according to a preferred embodiment of the present invention. This method of obtaining parameters comprises the following steps: Step S701,: E stand process obtaining the maximum voltage changes and the initial voltage V _t.

Step S702: Setting v ₂ (t)= E - v _b ( t ). Thus, the voltage versus time variation of Figure 2 can be obtained.

Step S703: using v ₂ ( t | t ₂ t t _end ), find V _s and τ _s .

Step S704: setting v ₁ ( t )= v ₂ ( t )- v _s ( t ).

Step S705: using v ₁ ( t | t ₁ t t ₂ ), find V _m and τ _m .

Step S706: setting v ₀ ( t )= v ₁ ( t )- v ₂ ( t ).

Step S707: using v ₀ ( t | t ₀ t t ₁ ), find V _f and τ _f .

Step S708: Find R _t , R _s , R _m , R _f according to the current i _b .

Step S709: The resistance _{R s, R m, R f} , to obtain _{C s, C m, C f} .

In this embodiment, for a lithium-ion battery of a brand 8.5Ah, the battery model parameters are obtained by using the foregoing procedure, and the distribution of the parameter to the state of charge ( SOC ) is respectively shown in FIG. 8 to FIG. It can be seen from Fig. 8 that R _t has no obvious relationship with the state of charge ( SOC ), so R _t is set to a fixed value. In FIGS. 9 to 14, τ _s ^-1 , R _s , R _m , τ _m ^-1 , τ _f ^-1 , and R _f all exhibit an ω shape relationship with respect to the state of charge ( SOC ), so these parameters are selected separately. The minimum error at each time point is found in the least squares method for the state of charge ( SOC ) and approximates two concave quadratic curves. The curve equations of the approximate parameters are organized as follows, where θ represents the state of charge (SOC): R _t (θ)=5.570319 (8)

τ _s ^-1 (θ)=9.74θ ² -14.01θ+6.09 52%<θ

τ _s ^-1 (θ)=8.03θ ² -5.15θ+1.91 θ≦52% (9)

R _s (θ)=72.42θ ² -104.15θ+39.51 52%<θ

R _s (θ)=96.57θ ² -67.64θ+13.69 θ≦52% (10)

τ _m ^-1 (θ)=-20.94θ ² +34.57θ-2.65 52%<θ

τ _m ^-1 (θ)=57.47θ ² -56.42θ+23.74 θ≦52% (11)

R _m (θ)=48.98θ ² -74.24θ+30.12 52%<θ

R _m (θ)=23.28θ ² -16.18θ+5.24 θ≦52% (12)

τ _f ^-1 (θ)=240.43θ ² -371.62θ+220.03 52%<θ

τ _f ^-1 (θ)=451.9θ ² -383.26θ+156.8 θ≦52% (13)

R _f (θ)=11.76θ ² -17.59θ+9.78 52%<θ

R _f (θ)=1.41θ ² -1.72θ+2.11 θ≦52% (14)

It should be understood by those skilled in the art that although the above embodiments are three RC circuits connected in series, those skilled in the art should understand that the more RC circuits, the more accurate the circuit model of the battery. In addition, the method of the present invention can also be applied to a battery model in which two RC circuits or two or more RC circuits are constructed. Therefore, the invention is not limited thereto.

In order to enable those skilled in the art to understand the spirit of the present invention, the present embodiment further provides a flowchart of a circuit model construction method for a lithium battery, and FIG. 15 illustrates a circuit of a lithium battery disclosed in a preferred embodiment of the present invention. Flow chart of the model construction method. Referring to FIG. 15, the steps of the circuit model construction method of the lithium battery include the following steps: Step S1501: discharging a fixed amount of power to a battery with a fixed current.

Step S1502: The discharge is stopped and left for a predetermined time until the terminal voltage of the battery is stabilized.

Step S1503: Record the voltage versus time curve of (step S1502). as shown in picture 2.

Step S1504: The voltage versus time curve of the (step S1502) is set to be a battery function.

Step S1505: Acquire the initial change voltage V _t of the voltage of the battery when the discharge is stopped. When V _{t is} obtained, the above R _t can be obtained by R _t = V _t /i _b .

Step S1506: Acquire the maximum voltage E of the terminal voltage of the battery in the above-described stationary process.

Step S1507: Assuming a natural function. E.g, .

Step S1508: Using a curve matching method, according to the voltage versus time curve of the (step S1502) and the natural function, find a matching curve, a corresponding fitting curve function corresponding thereto, and a time constant. Such as the above .

Step S1509: Compare the matching curve with the voltage versus time curve of the (step S1502) to obtain an error versus time curve. As shown in Figure 6.

Step S1510: Provide an error threshold.

Step S1511: According to the error threshold, find a time point in the error versus time variation curve that exceeds the error threshold as a segment time. From t _cut to t _{end in} Figure 6, it can be seen that this segment is the natural function that best fits the above, that is, the most stable segment of error. In other words, as long as the threshold is set, it is easy to find the segmentation point.

Step S1512: Substituting the fitting curve function into the initial time v _s ( t ₀ ) of the step (step S1502) to obtain an initial voltage V _s .

Step S1513: dividing the initial voltage V _s by the fixed current i _b to obtain a resistance value R _s . Please refer to the above formula (6) R _s = V _s /i _b .

Step S1514: Dividing the time constant τ _s by the first resistance R _s to obtain a capacitance value C _s . Please refer to the above formula (7) C _s = τ _s /R _s .

Step S1515: Deducting the fitting curve function from the battery function, repeating (step S1507) to (step S1514) n times to obtain n resistance values, n capacitance values, and n time constants. From the above embodiment, a total of three times are performed back and forth, and C _s , τ _s , R _s , C _m , τ _m , R _m , C _f , τ _f , R _{f are obtained} .

Step S1516: Construct a circuit model of the lithium battery according to the n resistance values, n capacitance values, and n time constants. As shown in Figure 3, the circuit model can be built.

Step S1517: Returning (step S1501), the execution is repeated (step S1501) to (step S1517) until the battery power is lower than a predetermined power amount. Due to the above steps S1501 to S1516, only the circuit model of the lithium battery for establishing the remaining battery capacity ( SOC ) is established. However, when the lithium battery power ( SOC ) changes, the circuit model of the lithium battery also changes, and only one execution is performed, which may be insufficient. To correctly describe the behavior of the battery. Therefore, the above steps need to be performed multiple times in order to effectively and accurately obtain the function of the circuit model of the lithium battery to the remaining battery capacity ( SOC ), and also correctly describe the behavior of the battery.

From the above several embodiments, it will be apparent to those skilled in the art that this method can be easily implemented on a circuit in addition to accurately constructing a circuit model for battery remaining capacity ( SOC ). In other words, as long as the battery is connected to a fixed switch, a fixed discharge load, a waveform recorder for measuring the voltage of the battery, and an arithmetic unit for performing calculations of the time constant and the adaptive curve, a battery-free battery model can be realized. Construction. Therefore, the present invention is not a simple mathematical method but a battery model construction method having industrial applicability. In particular, battery manufacturers or mobile device manufacturers can use this method to construct or test battery models to determine whether a batch of batteries is in compliance.

In summary, the spirit of the present invention is to propose a new circuit model for constructing a lithium battery, which mainly discharges the battery in stages and estimates the internal parameters of the model by using the battery standing voltage. In the experimental example, the battery model is conceived as a resistor in series with three RC circuits to describe the dynamic electrical characteristics of the battery. This circuit model can be used to more accurately estimate the battery terminal voltage during charging and discharging of lithium-ion batteries, and is applied to battery power circuit design; or further applied to battery power estimation. Especially in recent years, lithium batteries have gradually been applied to electric vehicles. In the face of high-power, variable-load applications such as electric vehicles, the use of simple static models may not be sufficient to properly characterize the behavior of the battery, thus affecting the overall design of the vehicle. Therefore, the method for constructing the battery dynamic model disclosed by the present invention will be of considerable benefit to industrial applications.

The specific embodiments of the present invention are intended to be illustrative only and not to limit the invention to the above embodiments, without departing from the spirit of the invention and the following claims. The scope of the invention and the various changes made are within the scope of the invention. Therefore, the scope of the invention is defined by the scope of the appended claims.

E ‧‧‧Battery internal electromotive force

R _t ‧‧‧resistance of voltage drop caused by battery current

V _t ‧‧‧ voltage drop caused by battery current

R _s ‧‧‧resistance of the first RC circuit

C _s ‧‧‧The capacitance of the first RC circuit

V _s ‧‧‧voltage drop of the first RC circuit

R _m ‧‧‧resistance of the second RC circuit

C _m ‧‧‧The capacitance of the second RC circuit

V _m ‧‧‧ voltage drop of the second stage RC circuit

R _f ‧‧‧resistance of the third stage RC circuit

C _f ‧‧‧The capacitance of the third stage RC circuit

V _f ‧‧‧ voltage drop of the third stage RC circuit

V _b ‧‧‧Battery external terminal voltage

i _b ‧‧‧Battery discharge voltage and current

Claims (6)

A circuit model construction method for a lithium battery, comprising: (Step A) discharging a fixed amount of electric power to a battery with a fixed current; (Step B) stopping discharging, and allowing to stand for a predetermined time until the terminal voltage of the battery is stable; Step C) recording the voltage versus time curve of (step B); (step D) setting the voltage versus time curve of the step (step B) as a battery function; (step E) obtaining the voltage of the battery at the time of stopping the discharge Initial variation voltage; (step F) obtaining the maximum voltage of the terminal voltage of the battery in the above-mentioned stationary process; (step G) assuming a natural function; (step H) using a curve matching method according to the voltage pair of (step B) a time variation curve and the natural function, finding a matching curve, a corresponding fitting curve function corresponding thereto, and a time constant; (Step I) comparing the matching curve with the voltage versus time curve of the (Step B) Obtaining an error versus time curve; (Step J) providing an error threshold; (Step K) according to the error threshold, finding a time point in the error versus time variation curve that exceeds the error threshold as a segment Room; (Step L) The initial time the fit of the curve function is substituted (step B) to obtain an initial voltage; (Step M) dividing the initial voltage by the fixed current to obtain a resistance value; (Step N) dividing the time constant by the first resistance to obtain a capacitance value; (Step O) deducting the battery function from the distribution a suitable curve function, repeating (step G) to (step N) n times to obtain n resistance values, n capacitance values, and n time constants; and (step P) according to the above-mentioned n resistance values, n capacitance values, and n A time constant is constructed to construct a circuit model of the lithium battery, wherein n is a natural number. The circuit model construction method for a lithium battery according to the first aspect of the invention, wherein the curve adaptation method of the (step H) comprises: a least square difference method. For example, the circuit model construction method of the lithium battery described in claim 1 further includes: (step Q) returning (step A), repeating execution (step A) to (step Q) until the battery power is lower than one Default power. The circuit model construction method of the lithium battery according to the first aspect of the invention, wherein the resistance value of the voltage drop caused by the battery current can be obtained by dividing the initial voltage of the voltage of the battery at the time of stopping the discharge by the solid The constant current obtains the resistance value of the voltage drop caused by the battery current. The method for constructing a circuit model of a lithium battery according to the first aspect of the invention, wherein the step (step D) of setting the voltage versus time curve of the step (step B) to a battery function comprises: subtracting the maximum voltage The measured open-circuit voltage of the battery obtains the voltage versus time curve of this (step B). A circuit model construction method for a lithium battery as recited in claim 5, wherein the natural function of "(Step G) assuming a natural function;" is assumed to be: Where V _{x is} the initial voltage and τ _{x is} the time constant.