Fractional order thermal network model modeling and parameter identification method of IGBT module

Abstract

The invention discloses a fractional order thermal network model modeling and parameter identification method for an IGBT module, and the method is characterized in that the method comprises the following steps: S1, building a fractional order thermal network model of the thermal impedance of the IGBT module based on the mathematical function operation relation between the heat transfer mechanism of the IGBT module and the fractional order calculus; s2, based on a junction-shell transient thermal impedance curve given in a data manual of an IGBT module of any model, identifying a fractional order thermal capacity C, an order alpha, a thermal resistance R and a time constant tau in the fractional order thermal network model; the fractional order thermal network model provided by the invention can accurately describe a time-varying curve of thermal impedance of the IGBT module, so that a reference basis can be provided for design and reliability analysis of a circuit system containing such elements.

Description

Technical Field

[0001] The invention relates to the technical field of reliability and thermal aging analysis of power electronic devices, and in particular to a fractional-order thermal network modeling and parameter identification method for an IGBT module. Background Art

[0002] Insulated Gate Bipolar Transistors (IGBTs) have the characteristics of high power density, high voltage, high frequency and low loss, and are therefore widely used in various applications, such as variable frequency speed regulation, inverters, power transmission and distribution, etc. However, the junction-case temperature of the IGBT module rises during operation, which will cause the module to be subjected to high thermal stress, thus causing the module to fail. Therefore, effectively monitoring the junction temperature change trend of the IGBT module and accurately describing the thermal characteristics of the module are very important for improving the reliability of power electronic systems using such devices (Reference 1 "Xu Zhiliang, Ge Xinglai, Li Jin, et al. Calculation of IGBT junction temperature considering the flow-heat coupling thermal network model [J]. Journal of Electrical Engineering, 2022, 17(02): 19-26.").

[0003] At present, the commonly used methods for identifying the junction temperature of IGBT modules are: physical contact method, temperature-sensitive electrical parameter method, optical measurement method and thermal model method.

[0004] The physical contact method mainly uses thermal elements such as thermistors and thermocouples to directly contact the chip surface to obtain the junction temperature of the chip. The physical contact method can have a higher spatial resolution, so that the temperature of the target position can be accurately obtained, but this method is costly and requires direct contact with the object to be measured, so the IGBT module needs to be unsealed for measurement.

[0005] The temperature-sensitive electrical parameter method is a method of indirectly obtaining the junction temperature of the IGBT module by measuring temperature-sensitive electrical parameters. Many external electrical parameters in power devices are temperature-sensitive electrical parameters, such as collector-emitter voltage, threshold voltage, and switching time, which are all related to temperature. By measuring these temperature-sensitive electrical parameters and combining the relationship between these temperature-sensitive electrical parameters and chip temperature, the junction temperature of the device can be obtained. However, this method is usually more complicated to operate, and the device under test needs to be calibrated before testing, and complex and expensive circuits are required to monitor small drifts of thermal parameters and resist interference from noisy backgrounds.

[0006] The optical measurement method uses a focused light beam to measure the junction temperature of the IGBT module, which is a non-contact measurement method. However, in the actual measurement process, the measurement equipment involved in the optical measurement method is expensive, and the IGBT module needs to be unsealed for measurement.

[0007] The thermal model method is usually used to simulate the dynamic thermal behavior of IGBT modules to predict the junction temperature. There are three typical thermal models, namely numerical models, analytical models and thermal network models. The numerical model mainly uses the finite element method as the numerical simulation method. In professional simulation software such as COMSOL and ANSYS, the high-precision temperature distribution inside the IGBT module is simulated according to the detailed internal structure and material properties of the IGBT module and the actual working conditions. However, the simulation and calculation of this type of model takes a long time and has high requirements on computer hardware. The analytical model describes the heat transfer process in the model by establishing heat conduction diffusion expressions in different dimensions. It can consider the influence of multiple parameters. The simulation and calculation process is relatively simple, but there are simplifications in the modeling process, and the dynamic simulation of the thermal behavior of the IGBT module cannot be completed.

[0008] Finally, the most widely used method is the thermal network model. The basic principle of the thermal network model is to construct a thermal circuit network from the junction temperature to the known temperature node based on the thermoelectric analogy theory, so as to achieve the effect of online monitoring and prediction of the junction temperature. As a junction temperature monitoring method recommended by device manufacturers, this method has low hardware requirements, is simple and easy to implement, and has the characteristics of low implementation cost and fast response. At present, a variety of thermal network models of IGBT modules have been proposed, among which the two most commonly used combinations are the Cauer thermal network model and the Foster thermal network model, both of which can reflect the changes in the junction temperature of the IGBT module when the power changes (Reference 2 "Fan Peng. Research on electrothermal modeling and junction temperature control methods of IGBT power electronic systems [D]. Hunan University, 2020.").

[0009] However, both the Cauer thermal network model and the Foster thermal network model use multiple parameters to describe the thermal impedance characteristics of the IGBT module. In the IGBT module manuals of internationally renowned manufacturers, the Foster thermal network structure is commonly used to describe the thermal impedance Z of the IGBT module. th Characteristics, for example: Infineon IGBT module data sheet gives the IGBT module junction-to-case transient thermal impedance Z thjc curve, and a list of parameters based on the Foster thermal network model, such as Figure 1 The figure shows the junction-to-case transient thermal impedance curve of the Infineon FF100R12KS4 IGBT module.

[0010] It can be seen that the model based on the Foster thermal network uses 8 parameters to describe the thermal impedance characteristics of the IGBT module. It is foreseeable that adding more thermal resistance R i , heat capacity C iComponents can further improve the prediction accuracy of the model. However, more thermal resistance and thermal capacitance components in the Foster thermal network model will increase the complexity of the model and make it difficult to identify the model parameters. Summary of the invention

[0011] The purpose of the present invention is to overcome the above-mentioned shortcomings and provide a fractional-order thermal network modeling and parameter identification method for an IGBT module, thereby reducing the parameters of the existing IGBT module thermal impedance model based on the Cauer thermal network and the Foster thermal network, and reducing the complexity of model parameter identification, thereby improving the efficiency of junction temperature monitoring and thermal characteristics investigation of the IGBT module.

[0012] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for modeling and parameter identification of a fractional-order thermal network model of an IGBT module, characterized in that it comprises the following steps:

[0013] S1. Based on the mathematical function operation relationship between the heat transfer mechanism of the IGBT module and fractional calculus, a fractional-order thermal network model of the thermal impedance of the IGBT module is established, and the time domain expression of its transient thermal impedance is:

[0014]

[0015] Among them, fractional heat capacity C, order α, thermal resistance R and time constant τ are the parameters to be identified of the model;

[0016] S2. Based on the junction-to-case transient thermal impedance curve given in the data sheet of any type of IGBT module, identify the fractional heat capacity C, order α, thermal resistance R and time constant τ in the fractional thermal network model.

[0017] Furthermore, the step S1 comprises:

[0018] S11. Based on the mathematical function operation relationship between the heat transfer mechanism of the IGBT module and fractional calculus, a fractional-order thermal network model of the thermal impedance of the IGBT module is established;

[0019] S12. Based on the thermoelectric analogy theory, the complex domain transfer function expression of the fractional-order thermal network model is obtained:

[0020]

[0021] Where C is the fractional heat capacity, α is the order, R is the thermal resistance, C1 is the heat capacity, and S is the complex domain operator.

[0022] S13. Perform a Lapse inverse transformation on the complex domain transfer function expression of the fractional-order thermal network model to obtain the time domain expression of the transient thermal impedance of the fractional-order thermal network model:

[0023]

[0024] Let τ = RC1, we get:

[0025]

[0026] Where C is the fractional heat capacity, α is the order, R is the thermal resistance, τ is the time constant, t is the time, and Γ(.) is the gamma function.

[0027] Furthermore, the step S2 comprises:

[0028] S21. Extract the data of the junction-case transient thermal impedance curve in the data sheet of any type of IGBT module to obtain the data of the junction-case thermal impedance value of any type of IGBT module changing with time:

[0029] Z thjc = {Z thjc (t i )|i=1,2,…,N} (5)

[0030] Among them, Z thjc (t i ) is represented by the junction-to-case thermal impedance corresponding to the time at the i-th point, i is a positive integer, and there are N time points in total;

[0031] S22. According to S1, the Laplace inverse transform is performed on the complex domain transfer function expression of the fractional-order thermal network model to obtain the relationship between the thermal impedance of the fractional-order thermal network model and time as follows:

[0032]

[0033] Among them, Z thc (t i ) represents the thermal impedance of the fractional-order thermal network model corresponding to the time at the i-th point;

[0034] S23. Use the mean square error (MSE) of the thermal impedance of the fractional-order thermal network model and the junction-case thermal impedance in the data sheet of any type of IGBT module corresponding to N-point data to construct the objective function of the parameter identification method:

[0035]

[0036] Among them, ΔZ th (t i ) is expressed as the error between the junction-to-case thermal impedance corresponding to the time at the ith point in the data sheet and the thermal impedance of the fractional-order thermal network model;

[0037] S24. According to the number of parameters to be estimated in the model in S1, the number of iterations and the number of parameters to be optimized are selected, the value of parameter α is limited, and the objective function (7) is fitted to obtain a set of model parameters [C, α, R, τ] under the condition of fitting convergence.

[0038] Furthermore, in step S24, the number of iterations is selected to be 500, the number of optimization parameters is selected to be 4, and the value of parameter α is limited to 0<α<2.

[0039] Beneficial effects of the present invention:

[0040] 1. The fractional-order thermal network model established by the present invention is simpler than the traditional Foster thermal network model and Cauer thermal network model, and only has four parameters to be identified, namely, fractional-order heat capacity C, order α, thermal resistance R and time constant τ, thereby improving the efficiency of thermal analysis of the IGBT module.

[0041] 2. The fractional-order thermal network model proposed in the present invention can accurately describe the curve of the thermal impedance of the IGBT module changing with time, thereby providing a reference for the design and reliability analysis of circuit systems containing such components.

[0042] 3. The present invention reduces the parameters of the existing IGBT module thermal impedance model based on the Cauer thermal network and the Foster thermal network, reduces the complexity of model parameter identification, and thus improves the efficiency of junction temperature monitoring and thermal characteristic investigation of the IGBT module. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is the thermal impedance curve of Infineon FF100R12KS4 IGBT module;

[0044] Figure 2 It is a diagram of the fractional-order thermal network model;

[0045] Figure 3 This is the flow chart for identifying the thermal impedance characteristic parameters of the IGBT module;

[0046] Figure 4 GetData obtains a sample graph of thermal impedance curve data points in the data sheet;

[0047] Figure 5 It is a comparison chart between the data sheet curve and the fractional-order thermal network model curve;

[0048] Figure 6 This is the error diagram between the data sheet curve and the fractional-order thermal network model curve. DETAILED DESCRIPTION

[0049] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0050] Example 1: Figure 2 and Figure 3 As shown, a method for modeling and parameter identification of a fractional-order thermal network model of an IGBT module includes the following steps:

[0051] S1. Based on the mathematical function operation relationship between the heat transfer mechanism of the IGBT module and fractional calculus, a fractional-order thermal network model of the thermal impedance of the IGBT module is established, and the time domain expression of its transient thermal impedance is: The fractional heat capacity C, order α, thermal resistance R1 and time constant τ are parameters to be identified in the model, and step S1 includes:

[0052] S11, such as Figure 2 As shown, based on the mathematical function operation relationship between the heat transfer mechanism of the IGBT module and fractional-order calculus, a fractional-order thermal network model of the thermal impedance of the IGBT module is established.

[0053] S12. According to Figure 2 , based on the thermoelectric analogy theory, the complex domain transfer function expression of the fractional-order thermal network model can be obtained:

[0054]

[0055] Where C is the fractional heat capacity, α is the order, R is the thermal resistance, C1 is the heat capacity, and S is the complex domain operator.

[0056] S13. By performing a Lapse inverse transformation on the complex domain transfer function expression of the fractional-order thermal network model, the time domain expression of the transient thermal impedance of the fractional-order thermal network model can be obtained:

[0057]

[0058] Let τ = RC1, we get:

[0059]

[0060] Where C is the fractional heat capacity, α is the order, R is the thermal resistance, τ is the time constant, t is the time, and Γ(.) is the gamma function.

[0061] S2, based on the junction-to-case transient thermal impedance curve given in the Infineon FF100R12KS4 IGBT module data sheet, identify the fractional-order heat capacity C, order α, thermal resistance R and time constant τ in the fractional-order thermal network model, the step S2 includes:

[0062] S21. Obtain the thermal impedance characteristic curve from the Infineon FF100R12KS4 IGBT module data sheet. The data sheet curve is as follows: Figure 1 As shown. Figure 4 The GetData image data acquisition software shown in the figure obtains the data points of the thermal impedance curve in the data sheet and represents them as Z thjc :

[0063] Z thjc = {Z thjc (t i )|i=1,2,…,N}

[0064] Among them, Z thjc (t i ) is expressed as the junction-to-case thermal impedance corresponding to the i-th point in time, i is a positive integer, and there are N time points in total.

[0065] S22. According to S1, the Laplace inverse transform is performed on the complex domain transfer function expression of the fractional-order thermal network model to obtain the relationship between the thermal impedance of the fractional-order thermal network model and time as follows:

[0066]

[0067] Among them, Z thc (t i ) is represented by the thermal impedance of the fractional-order thermal network model corresponding to the time at the i-th point.

[0068] S23. The objective function of the parameter identification method is constructed by using the mean square error (MSE) of the thermal impedance of the fractional-order thermal network model and the junction-case thermal impedance corresponding to N points in the data sheet of the Infineon FF100R12KS4 IGBT module:

[0069]

[0070] Among them, ΔZ th (t i ) is expressed as the error between the junction-to-case thermal impedance corresponding to the i-th point in the data sheet and the thermal impedance of the fractional-order thermal network model.

[0071] S24. For the number of parameters to be estimated in the model in S1, the number of iterations is selected as 500, the number of optimal parameters is selected as 4, the value of parameter α is limited to 0<α<2, and the objective function (13) is fitted to obtain a set of model parameters [87.78904, 0.17268, 0.14367, 0.03964] under the condition of fitting convergence.

[0072] like Figure 5As shown, the thermal impedance change curve fitted by the fractional-order thermal network model is compared with the junction-case transient thermal impedance curve on the data sheet of the Infineon FF100R12KS4 IGBT module. The black solid line represents the junction-case transient thermal impedance curve on the data sheet of the Infineon FF100R12KS4 IGBT module, and the red dashed line represents the thermal impedance change curve fitted by the fractional-order thermal network model. Figure 6 This is the error diagram of the junction-to-case transient thermal impedance curve in the Infineon FF100R12KS4 data sheet and the thermal impedance curve of the fractional-order thermal network model, where ΔZ th It is expressed as the error between the junction-to-case thermal impedance in the Infineon FF100R12KS4 data sheet and the thermal impedance of the fractional-order thermal network model, and its calculation formula is:

[0073] ΔZ th =Z thjc -Z thc

[0074] from Figure 5 and Figure 6 It can be seen that the error ΔZ between the thermal impedance change curve fitted by the fractional-order thermal network model and the junction-to-case transient thermal impedance curve in the data sheet is th The results are basically in the range of [-0.006, 0.006] K / W, and the fitting effect is good, which shows that the method proposed in the present invention is effective.

[0075] The above embodiments are only preferred technical solutions of the present invention and should not be regarded as limiting the present invention. The protection scope of the present invention shall be the technical solutions recorded in the claims, including equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A method for modeling and parameter identification of a fractional-order thermal network model of an IGBT module, characterized in that: It includes the following steps: S1. Based on the mathematical function operation relationship between the heat transfer mechanism of the IGBT module and fractional calculus, a fractional-order thermal network model of the thermal impedance of the IGBT module is established, and the time domain expression of its transient thermal impedance is: Among them, fractional heat capacity C, order α, thermal resistance R and time constant τ are the parameters to be identified of the model; S2. Based on the junction-to-case transient thermal impedance curve given in the data sheet of any type of IGBT module, identify the fractional heat capacity C, order α, thermal resistance R and time constant τ in the fractional thermal network model.

2. The method for modeling and parameter identification of a fractional-order thermal network model of an IGBT module according to claim 1, characterized in that: The step S1 comprises: S11. Based on the mathematical function operation relationship between the heat transfer mechanism of the IGBT module and fractional calculus, a fractional-order thermal network model of the thermal impedance of the IGBT module is established; S12. Based on the thermoelectric analogy theory, the complex domain transfer function expression of the fractional-order thermal network model is obtained: Where C is the fractional heat capacity, α is the order, R is the thermal resistance, C1 is the heat capacity, and S is the complex domain operator. S13. Perform a Lapse inverse transformation on the complex domain transfer function expression of the fractional-order thermal network model to obtain the time domain expression of the transient thermal impedance of the fractional-order thermal network model: Let τ = RC1, we get: Where C is the fractional heat capacity, α is the order, R is the thermal resistance, τ is the time constant, t is the time, and Γ(.) is the gamma function.

3. The method for modeling and parameter identification of a fractional-order thermal network model of an IGBT module according to claim 1, characterized in that: The step S2 comprises: S21. Extract the data of the junction-case transient thermal impedance curve in the data sheet of any type of IGBT module to obtain the data of the junction-case thermal impedance value of any type of IGBT module changing with time: Z thjc ={ Z thjc (t i )|i=1,2,…,N} (5) Among them, Z thjc (t i ) is represented by the junction-to-case thermal impedance corresponding to the time at the i-th point, i is a positive integer, and there are N time points in total; S22. According to S1, the Laplace inverse transform is performed on the complex domain transfer function expression of the fractional-order thermal network model to obtain the relationship between the thermal impedance of the fractional-order thermal network model and time as follows: Among them, Z thc (t i ) represents the thermal impedance of the fractional-order thermal network model corresponding to the time at the i-th point; S23. Use the mean square error (MSE) of the thermal impedance of the fractional-order thermal network model and the junction-case thermal impedance in the data sheet of any type of IGBT module corresponding to N-point data to construct the objective function of the parameter identification method: Among them, ΔZ th (t i ) is expressed as the error between the junction-to-case thermal impedance corresponding to the time at the ith point in the data sheet and the thermal impedance of the fractional-order thermal network model; S24. According to the number of parameters to be estimated in the model in S1, the number of iterations and the number of parameters to be optimized are selected, the value of parameter α is limited, and the objective function (7) is fitted to obtain a set of model parameters [C, α, R, τ] under the condition of fitting convergence.

4. The method for modeling and parameter identification of a fractional-order thermal network model of an IGBT module according to claim 3, characterized in that: In step S24, the number of iterations is selected to be 500, the number of optimization parameters is selected to be 4, and the value of parameter α is limited to 0<α<2.

Images