A fast calculation method for IGBT transient temperature based on reduced-order method

Abstract

A fast calculation method for IGBT transient temperature based on order reduction method, firstly establishes the strong form of IGBT electrothermal coupling equation and its coupling mechanism, then establishes the finite-dimensional space finite element form of IGBT electrothermal coupling strong form and its coupling mechanism, then discretizes the finite-dimensional space finite element form, transforms the partial differential equation into a matrix equation, and collects the IGBT temperature sample matrix. X 2. Use singular value decomposition method to calculate the temperature sample matrix X 2 is reduced to a certain order and the number of eigenvalues is selected according to the truncation error to describe the entire temperature sample matrix X 2. Reduce the temperature sample matrix X Substituting 2 into the aforementioned matrix equation, reducing the matrix equation overall, and finally solving the reduced matrix equation, we can obtain the IGBT transient temperature. This method not only ensures calculation accuracy but also reduces the amount of calculation, significantly improving the efficiency of the IGBT's global transient temperature calculation.

Description

Technical Field

[0001] The present invention belongs to the technical field of semiconductor devices, and in particular relates to a method for quickly calculating the transient temperature of an IGBT based on a reduced-order method. Background Art

[0002] As the switching frequency of IGBT modules continues to increase, transient electromagnetic processes in IGBT power electronics systems have multi-timescale characteristics, raising a series of computational challenges related to circuit simulation and multi-physics coupling. IGBT transient temperature is a crucial parameter for determining IGBT health, but conventional calculation methods such as finite element methods are prohibitively time-consuming and expensive. Therefore, a method is urgently needed that can both ensure accuracy and significantly improve the efficiency of calculating the global transient temperature of IGBTs. Summary of the Invention

[0003] The purpose of the present invention is to overcome the above problems existing in the prior art and provide a method for fast calculation of IGBT transient temperature based on a reduced-order method, which can both ensure calculation accuracy and significantly improve calculation efficiency.

[0004] To achieve the above objectives, the present invention provides the following technical solutions:

[0005] A method for quickly calculating the transient temperature of an IGBT based on a reduced-order method, the method comprising the following steps in sequence:

[0006] S1. Establish the strong form of IGBT electrothermal coupling and its coupling mechanism;

[0007] S2. Establish the strong form of IGBT electrothermal coupling and its coupling mechanism in finite-dimensional space finite element form;

[0008] S3. Discretize the finite-dimensional space finite element form of the strong form of IGBT electrothermal coupling and its coupling mechanism, and transform it from a partial differential equation into a matrix equation;

[0009] S4. Collect the IGBT temperature sample matrix X2, then use the singular value decomposition method to reduce the order of the temperature sample matrix X2, and select the number of eigenvalues based on the truncation error to describe the entire temperature sample matrix X2;

[0010] S5. Substitute the reduced-order temperature sample matrix X2 into the matrix equation obtained in step S3, perform overall reduced-order processing on the matrix equation, and finally solve the overall reduced-order matrix equation to achieve rapid calculation of the IGBT transient temperature.

[0011] In step S1, the IGBT electrothermal coupling strong form and its coupling mechanism are:

[0012]

[0013]

[0014]

[0015] γ(T)=ρ0((1+α(TT ref ))

[0016] In the above formula, Indicates The vectors within this bounded region, is the gradient, for The potential at the point, ρ is the material density, C p is the specific heat at constant pressure, k is the thermal conductivity, t is the time, Indicates The temperature at the point where Q is the heat, γ is the conductivity, Respectively is the partial derivative of x, y, and z, γ(T) represents the conductivity at temperature T, ρ0 is the reference density, α is the temperature coefficient of resistance, T ref is the reference temperature.

[0017] Step S2 is performed in the following steps:

[0018] S21, based on the strong form of IGBT electrothermal coupling and its coupling mechanism T∈H 1 (Ω), the infinite-dimensional space finite element form of the strong form of IGBT electrothermal coupling and its coupling mechanism is derived. The infinite-dimensional space finite element form is:

[0019]

[0020]

[0021]

[0022] (Tt, v2)+a(T, v2)=(Q, v2)

[0023]

[0024] (Tt, v2) = ∫ Ω ρC p T·v2dxdydz

[0025]

[0026] In the above formula, (Q, v2) represents the inner product of Q and v2, H is the Hilbert space, H 1The (Ω) superscript indicates that the original function and its first-order derivative are square-integrable. middle The subscript indicates that v1 is in H 1 (Ω) boundary is 0, The subscript indicates that v2 is in H 1 (Ω) boundary is 0, represents electric potential, v1 is the electric potential test function, v2 is the temperature test function, Q represents heat, k represents the coefficient of the temperature equation, represents the temperature change, Represents the change in potential test function, Indicates the change in temperature test function, T t Derivative of temperature T with respect to time t;

[0027] S22, introduction time T1, Infinite-dimensional space finite element method based on the strong form of IGBT electrothermal coupling and its coupling mechanism T 1h ∈U 2h , and derive its finite-dimensional space finite element form, which is:

[0028]

[0029]

[0030] (T t , v 2h )+a(T,v 2h )=(Q,v 2h )

[0031]

[0032] In the above formula, Indicates that in U 1h The electric potential in this space-time, v 1h Indicates U 2h The potential test function in this space-time space, v 2h Indicates U 2h The temperature test function in this space-time space, is the finite element subspace, Indicates U 2h From 0 to T1 in U 1h The space-time of space, T 1h Indicates that in U 2h The temperature of this spacetime, φ j represents the finite element node value, Ns is the total number of finite element nodes, T j is the temperature of node j, express The inner product with t, is the node potential, Indicates v 1h in U 2h The boundary is 0, Indicates v 2h in U 2h The boundary is 0.

[0033] Step S3 is performed in the following steps:

[0034] S31. Select test function V 1h , v 2h =φ i (i=1, 2, ..., Ns), numerically integrate the finite-dimensional space finite element form of the IGBT electrothermal coupling equation and its coupling mechanism obtained in step S2, and obtain the following equation through numerical integration:

[0035]

[0036] In the above formula, c1 and c2 are equation coefficients, T j 、 Represent the temperature and potential of the finite element node j, For the test function φ i The gradient, For the test function φ j The gradient of T j (t) represents T at time t j ;

[0037] S32. Based on the equation obtained by numerical integration, define the potential stiffness matrix A1, the temperature stiffness matrix A2, the mass matrix M about temperature, and the heat source load vector Among them, the potential stiffness matrix A1 is:

[0038]

[0039] The temperature stiffness matrix A2 is:

[0040]

[0041] The mass matrix M with respect to temperature is:

[0042]

[0043] The heat source load vector for:

[0044]

[0045] S33, first the potential stiffness matrix A1, the temperature stiffness matrix A2, the mass matrix M about temperature, the heat source load vector Substitute into the matrix equation of the scalar potential and the ordinary differential equation of temperature, then use the backward Euler method to discretize the ordinary differential equation of temperature to obtain equation 1, sort equation 1 to obtain equation 2, and multiply equation 2 by Δt on both sides to obtain the matrix equation. The matrix equation of the scalar potential is:

[0046] A1X1=0

[0047] In the above formula,

[0048] The ordinary differential equation for temperature is:

[0049]

[0050] In the above formula, X2(t) represents the temperature vector at time t, and X2′(t) represents the first-order derivative of the temperature vector at time t.

[0051] The equation 1 is specifically:

[0052]

[0053] In the above formula, Δt represents the time difference from time m to time m+1. represents the temperature vector at time m+1, represents the temperature vector at time m, p m -1 is the termination time, A(t m+1 ) is the temperature stiffness matrix at time m+1, is the heat source load vector at time m+1;

[0054] The second equation is:

[0055]

[0056] The matrix equation is:

[0057]

[0058] Step S4 is performed in the following steps:

[0059] S41, collecting IGBT temperature sample matrix X2, the temperature sample matrix X2 is:

[0060]

[0061] In the above formula, Indicates the Nth S Node N tThe temperature of the moment;

[0062] S42. Express the temperature sample matrix X2 in the form of T=Uα, and use the singular value decomposition method to select the first Nd eigenvalues of the temperature sample matrix X2 to represent the reduced-order temperature sample matrix X2. U is the standard orthogonal basis formed by the eigenvectors obtained in the previous section. Specifically, U is:

[0063]

[0064] In the above formula, u NsNd Expressed as a feature vector with Ns rows and Nd columns;

[0065] α is the temperature vector after reduction, and α is specifically:

[0066]

[0067] In the above formula, is the temperature vector that decreases from Ns rows to Nd rows;

[0068] The reduced-order temperature sample matrix X2 is specifically:

[0069]

[0070] Step S5 is performed in the following steps:

[0071] S51, the reduced-order temperature sample matrix X2 is used as Substituting the matrix equation obtained in step S3 into equation 3, the equation 3 is:

[0072]

[0073] S52. Multiply Equation 3 by U on the left T , U T is the transpose of U, so that the overall order of the matrix equation is reduced to Nd, and equation 4 is obtained, which is:

[0074]

[0075] S53. Solve the reduced-order temperature vector α according to Equation 4, and then calculate the transient temperature according to T=Uα.

[0076] Compared with the prior art, the present invention has the following beneficial effects:

[0077] In a method for quickly calculating the transient temperature of an IGBT based on an order reduction method, the present application first establishes a strong form of the electrothermal coupling equation of the IGBT and its coupling mechanism, then establishes a finite-dimensional space finite element form of the strong form of the electrothermal coupling of the IGBT and its coupling mechanism, then discretizes the finite-dimensional space finite element form, converts the partial differential equation into a matrix equation, collects the IGBT temperature sample matrix X2, uses the singular value decomposition method to reduce the order of the temperature sample matrix X2, and selects the number of eigenvalues according to the truncation error to describe the entire temperature sample matrix X2, substitutes the reduced-order temperature sample matrix X2 into the aforementioned matrix equation, and then performs overall order reduction on the matrix equation, and finally solves the overall reduced-order matrix equation to obtain the IGBT transient temperature. This method can not only ensure calculation accuracy but also reduce the amount of calculation, thereby greatly improving the global transient temperature calculation efficiency of the IGBT. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0079] The present invention will be further described below with reference to the accompanying drawings and specific implementation methods.

[0080] See also Figure 1 A method for quickly calculating the transient temperature of an IGBT based on a reduced-order method is provided. The method is performed in the following steps:

[0081] S1. Establishing the strong form of IGBT electrothermal coupling and its coupling mechanism

[0082] The strong form of IGBT electrothermal coupling and its coupling mechanism are:

[0083]

[0084]

[0085]

[0086] γ(T)=ρ0((1+α(TT ref ))

[0087] In the above formula, Indicates The vectors in this bounded region, is the gradient, for The potential at the point, ρ is the material density, C p is the specific heat at constant pressure, k is the thermal conductivity, t is the time, Indicates The temperature at the point, Q is the heat, γ is the conductivity, Respectively is the partial derivative of x, y, and z, γ(T) represents the conductivity at temperature T, ρ0 is the reference density, α is the temperature coefficient of resistance, T ref is the reference temperature;

[0088] S2. Establish the strong form of IGBT electrothermal coupling and its coupling mechanism in finite-dimensional space finite element form

[0089] S21, based on the strong form of IGBT electrothermal coupling and its coupling mechanism T∈H 1 (Ω), the infinite-dimensional space finite element form of the strong form of IGBT electrothermal coupling and its coupling mechanism is derived. The infinite-dimensional space finite element form is:

[0090]

[0091]

[0092] (Tt, v2)+a(T, v2)=(Q, v2)

[0093]

[0094]

[0095] (Tt, v2) = ∫ Ω ρC p T·v2dxdydz

[0096]

[0097] In the above formula, (Q, v2) represents the inner product of Q and v2, H is the Hilbert space, H 1 The (Ω) superscript indicates that the original function and its first-order derivative are square-integrable. middle The subscript indicates that v1 is in H 1 (Ω) boundary is 0, middle The subscript indicates that v2 is in H 1 (Ω) boundary is 0, represents electric potential, v1 is the electric potential test function, v2 is the temperature test function, Q represents heat, k represents the coefficient of the temperature equation, represents the temperature change, Represents the change in potential test function, Indicates the change in temperature test function, T t Derivative of temperature T with respect to time t;

[0098] S22, introduction time T1, Infinite-dimensional space finite element method based on the strong form of IGBT electrothermal coupling and its coupling mechanism T 1h ∈U 2h , the finite-dimensional space finite element form of the strong form of IGBT electrothermal coupling and its coupling mechanism is derived, specifically:

[0099]

[0100]

[0101] (T t , v 2h )+a(T,V 2h )=(Q,V 2h )

[0102]

[0103] In the above formula, Indicates that in U 1h The electric potential in this space-time, v 1h Indicates U 2h The potential test function in this space-time space, v 2h Indicates U 2h The temperature test function in this space-time space, is the finite element subspace, Indicates U 2h From 0 to T1 in U 1h The space-time of space, T 1h Indicates that in U 2h The temperature of this spacetime, φ j represents the finite element node value, Ns is the total number of finite element nodes, T j is the temperature of node j, express The inner product with t, is the node potential, Indicates v 1h in U 2h The boundary is 0, Indicates v 2h in U 2h The boundary of is 0;

[0104] S3. Discretize the finite-dimensional finite element form of the strong form of IGBT electrothermal coupling and its coupling mechanism, and transform it from a partial differential equation into a matrix equation

[0105] S31. Select test function V 1h , v 2h =φ i(i=1, 2, ..., Ns), numerically integrate the finite-dimensional space finite element form of the IGBT electrothermal coupling equation and its coupling mechanism obtained in step S2 to obtain the following equation:

[0106]

[0107] In the above formula, c1 and c2 are the coefficients of the partial differential equation, T j 、 Represent the temperature and potential of the finite element node j, For the test function φ i The gradient, For the test function φ j The gradient of T j (t) represents T at time t j ;

[0108] S32. Based on the equation obtained by numerical integration, define the potential stiffness matrix A1, the temperature stiffness matrix A2, the mass matrix M about temperature, and the heat source load vector Among them, the potential stiffness matrix A1 is:

[0109]

[0110] The temperature stiffness matrix A2 is:

[0111]

[0112] The mass matrix M with respect to temperature is:

[0113]

[0114] The heat source load vector for:

[0115]

[0116] S33, first the potential stiffness matrix A1, the temperature stiffness matrix A2, the mass matrix M about temperature, the heat source load vector Substitute into the matrix equation of the scalar potential and the ordinary differential equation of temperature, and then use the backward Euler method to discretize the ordinary differential equation of temperature to obtain equation 1. The matrix equation of the scalar potential is:

[0117] A1X1=0

[0118] In the above formula,

[0119] The ordinary differential equation for temperature is:

[0120]

[0121] In the above formula, X2(t) represents the temperature vector at time t, and X2′(t) represents the first-order derivative of the temperature vector at time t.

[0122] The equation 1 is specifically:

[0123]

[0124] In the above formula, Δt represents the time difference from time m to time m+1. represents the temperature vector at time m+1, represents the temperature vector at time m, p m -1 is the termination time, A(t m+1 ) is the temperature stiffness matrix at time m+1, is the heat source load vector at time m+1;

[0125] Then, equation 1 is sorted to obtain equation 2, which is:

[0126]

[0127] Finally, multiply Equation 2 by Δt on both sides to obtain the matrix equation, which is:

[0128]

[0129] S4, collect the IGBT temperature sample matrix X2, and then use the singular value decomposition method to reduce the order of the temperature sample matrix X2, and select the number of eigenvalues based on the truncation error to describe the entire temperature sample matrix X2

[0130] S41, collecting IGBT temperature sample matrix X2, the temperature sample matrix X2 is:

[0131]

[0132] In the above formula, Indicates the Nth S Node N t The temperature of the moment;

[0133] S42. Express the temperature sample matrix X2 in the form of T=Uα, and use the singular value decomposition method to select the first Nd eigenvalues of the temperature sample matrix X2 to represent the reduced-order temperature sample matrix X2. When determining the number Nd, the rate at which the singular values decrease should be considered to ensure the calculation accuracy without increasing the calculation burden. U is the standard orthogonal basis formed by the eigenvectors obtained in the previous section. Specifically, U is:

[0134]

[0135] In the above formula, u NsNd Expressed as a feature vector with Ns rows and Nd columns;

[0136] α is the temperature vector after reduction, and α is specifically:

[0137]

[0138] In the above formula, is the temperature vector that decreases from Ns rows to Nd rows;

[0139] The reduced-order temperature sample matrix X2 is specifically:

[0140]

[0141] S5. Substitute the temperature sample matrix X2 after the order reduction process into the matrix equation obtained in step S3, perform overall order reduction on the matrix equation, and finally solve the matrix equation after the overall order reduction process to achieve rapid calculation of the IGBT transient temperature.

[0142] S51, the reduced-order temperature sample matrix X2 is used as Substituting the matrix equation obtained in step S3 into equation 3, the equation 3 is:

[0143]

[0144] S52. Multiply Equation 3 by U on the left T , U T is the transpose of U, so that the overall order of the matrix equation is reduced to Nd, and equation 4 is obtained, which is:

[0145]

[0146] S53. Solve the reduced-order temperature vector α according to Equation 4, and then calculate the transient temperature according to T=Uα.

Claims

1. A method for fast calculation of IGBT transient temperature based on a reduced-order method, characterized by: The calculation method comprises the following steps in sequence: S1. Establish the strong form of IGBT electrothermal coupling and its coupling mechanism; S2. Establish the strong form of IGBT electrothermal coupling and its coupling mechanism in finite-dimensional space finite element form; S3. Discretize the finite-dimensional space finite element form of the strong form of IGBT electrothermal coupling and its coupling mechanism, and transform it from a partial differential equation into a matrix equation; S4. Collect the IGBT temperature sample matrix X2, then use the singular value decomposition method to reduce the order of the temperature sample matrix X2, and select the number of eigenvalues based on the truncation error to describe the entire temperature sample matrix X2; S5. Substitute the reduced-order temperature sample matrix X2 into the matrix equation obtained in step S3, perform overall reduced-order processing on the matrix equation, and finally solve the overall reduced-order matrix equation to achieve rapid calculation of the IGBT transient temperature.

2. The method for rapidly calculating IGBT transient temperature based on a reduced-order method according to claim 1, characterized in that: In step S1, the IGBT electrothermal coupling strong form and its coupling mechanism are: γ(T)=ρ0((1+α(TT ref )) In the above formula, Indicates The vectors in this bounded region, is the gradient, for The potential at the point, ρ is the material density, C p is the specific heat at constant pressure, k is the thermal conductivity, t is the time, Indicates The temperature at the point, Q is the heat, γ is the conductivity, Respectively is the partial derivative of x, y, and z, γ(T) represents the conductivity at temperature T, ρ0 is the reference density, α is the temperature coefficient of resistance, T ref is the reference temperature.

3. The method for rapidly calculating IGBT transient temperature based on a reduced-order method according to claim 2, characterized in that: Step S2 is performed in the following steps: S21, based on the strong form of IGBT electrothermal coupling and its coupling mechanism The infinite-dimensional space finite element form of the strong form of IGBT electrothermal coupling and its coupling mechanism is derived, and the infinite-dimensional space finite element form is: (T t ,v2)+α(T,v2)=(Q,v2) (T t ,v2)=∫ Ω ρC p T·v2dxdydz In the above formula, (Q, v2) represents the inner product of Q and v2, H is the Hilbert space, H 1 The (Ω) superscript indicates that the original function and its first-order derivative are square-integrable. middle The subscript indicates that v1 is in H 1 (Ω) boundary is 0, middle The subscript indicates that v2 is in H 1 (Ω) boundary is 0, represents electric potential, v1 is the electric potential test function, v2 is the temperature test function, Q represents heat, k represents the coefficient of the temperature equation, represents the temperature change, Represents the change in potential test function, Indicates the change in temperature test function, T t Derivative of temperature T with respect to time t; S22, introduction time T1, Infinite-dimensional space finite element method based on the strong form of IGBT electrothermal coupling and its coupling mechanism T 1h ∈U 2h , and derive its finite-dimensional space finite element form, which is: (T t ,v 2h )+α(T,v 2h )=(Q,v 2h ) In the above formula, Indicates that in U 1h The electric potential in this space-time, v 1h Indicates U 2h The potential test function in this space-time space, v 2h Indicates U 2h The temperature test function in this space-time space, is the finite element subspace, Indicates U 2h From 0 to T1 in U 1h The space-time of space, T 1h Indicates that in U 2h The temperature of this spacetime, φ j represents the finite element node value, Ns is the total number of finite element nodes, T j is the temperature of node j, express The inner product with t, is the node potential, Indicates v 1h in U 2h The boundary is 0, Indicates v 2h in U 2h The boundary is 0.

4. The method for rapidly calculating IGBT transient temperature based on a reduced-order method according to claim 3, characterized in that: Step S3 is performed in the following steps: S31. Select test function V 1h , V 2h =φ i (i=1, 2, ..., Ns), numerically integrate the finite-dimensional space finite element form of the IGBT electrothermal coupling equation and its coupling mechanism obtained in step S2, and obtain the following equation through numerical integration: In the above formula, c1 and c2 are equation coefficients, T j 、 Represent the temperature and potential of the finite element node j, For the test function φ i The gradient, For the test function φ j The gradient of T j (t) represents T at time t j ; S32. Based on the equation obtained by numerical integration, define the potential stiffness matrix A1, the temperature stiffness matrix A2, the mass matrix M about temperature, and the heat source load vector Among them, the potential stiffness matrix A1 is: The temperature stiffness matrix A2 is: The mass matrix M with respect to temperature is: The heat source load vector for: S33, first the potential stiffness matrix A1, the temperature stiffness matrix A2, the mass matrix M about temperature, the heat source load vector Substitute into the matrix equation of the scalar potential and the ordinary differential equation of temperature, then use the backward Euler method to discretize the ordinary differential equation of temperature to obtain equation 1, sort equation 1 to obtain equation 2, and multiply equation 2 by Δt on both sides to obtain the matrix equation. The matrix equation of the scalar potential is: A1X1=0 In the above formula, The ordinary differential equation for temperature is: In the above formula, X2(t) represents the temperature vector at time t, and X2′(t) represents the first-order derivative of the temperature vector at time t. The equation 1 is specifically: In the above formula, Δt represents the time difference from time m to time m+1. represents the temperature vector at time m+1, represents the temperature vector at time m, p m -1 is the termination time, A(t m+1 ) is the temperature stiffness matrix at time m+1, is the heat source load vector at time m+1; The second equation is: The matrix equation is:

5. The method for rapidly calculating IGBT transient temperature based on a reduced-order method according to claim 4, characterized in that: Step S4 is performed in the following steps: S41, collecting IGBT temperature sample matrix X2, the temperature sample matrix X2 is: In the above formula, Indicates the Nth S Node N t The temperature of the moment; S42. Express the temperature sample matrix X2 in the form of T=Uα, and use the singular value decomposition method to select the first Nd eigenvalues of the temperature sample matrix X2 to represent the reduced-order temperature sample matrix X2. U is the standard orthogonal basis formed by the eigenvectors obtained in the previous section. Specifically, U is: In the above formula, u NsNd Expressed as a feature vector with Ns rows and Nd columns; α is the temperature vector after reduction, and α is specifically: In the above formula, is the temperature vector that decreases from Ns rows to Nd rows; The reduced-order temperature sample matrix X2 is specifically:

6. The method for rapidly calculating IGBT transient temperature based on a reduced-order method according to claim 5, characterized in that: Step S5 is performed in the following steps: S51, the reduced-order temperature sample matrix X2 is used as Substituting the matrix equation obtained in step S3 into equation 3, the equation 3 is: S52. Multiply Equation 3 by U on the left T , U T is the transpose of U, so that the overall order of the matrix equation is reduced to Nd, and equation 4 is obtained, which is: S53. Solve the reduced-order temperature vector α according to Equation 4, and then calculate the transient temperature according to T=Uα.

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