JP2021196302A - Estimation device - Google Patents

Abstract

To provide an internal state estimation device capable of achieving the acceleration of calculation of a thermal circuit network model or the like.SOLUTION: Information on a voltage command value of an IGBT 4, a current measured value and a case temperature measured value is inputted into an analyzer 2, respectively. The analyzer estimates a junction temperature (internal temperature) of the IGBT 4 by solving the simultaneous ordinary differential equations in an RC thermal network model 1. At this time, the simultaneous ordinary differential equations are simplified in advance and a portion in which the constant calculation can be performed shall be calculated in advance.SELECTED DRAWING: Figure 2

Description

The present invention relates to an estimation device that estimates an internal state from an input value, and is mainly used in an internal temperature estimation device or a vibration simulation device of a semiconductor device.

For example, the junction temperature (temperature of the silicon die in the package when power is supplied) of a semiconductor device such as an IGBT (Insulated Gate Bipolar Transistor) is important information in thermal design and the like.

Although semiconductor manufacturers hold detailed analysis information on junction temperatures, they are not always disclosed to users of semiconductor devices. Therefore, a method for measuring transient thermal resistance from the actual product has been standardized (JESD51-14 standard), and a method for generating a structural function corresponding to a ladder-shaped RC thermal network model using that method is also known (JESD51-14 standard). See Non-Patent Document 1).

An example of the RC thermal circuit model will be described with reference to FIG. The RC thermal network model 1 is configured by connecting the thermal resistance "R" and the thermal capacity "C" in a stepped manner, and from the correspondence between the heat flow, current, temperature, and voltage, simultaneous differential equations based on the conservation law, similar to the electric circuit. It is possible to calculate the temperature of each part by solving this.

Using this simultaneous differential equation, the temperature of each part including the _{junction temperature T 0} is measured from the measurable case temperature T and the input heat amount Q. This simultaneous differential equation can be described as Eqs. (1) and (2).

In equations (1) and (2), "x" indicates an internal state, "u" indicates an input, and "y" indicates an output, which are as follows.
・ X = ^t (T ₀ T ₁ T ₂ T ₃ T ₄ )
・ U = ^t (Q T)
・ Y = ^t (T ₀ )
-"A" and "B" in the formula (1) are shown in the formula (3).

_{"R 0 to} R ₄ " in the formula (3) indicate the thermal resistance, and "C _{0 to} C ₄ " indicate the heat capacity.

In FIG. 1 and equation (3), an RC thermal network model in which the thermal resistance “R” and the heat capacity “C” have five stages is shown. 1) The shape of (2) is the same. Further, since the equation (2) for obtaining "y" is a mere product-sum operation of a matrix, the equation (1) is important.

As described in Non-Patent Documents 2 to 4, the equation (1), which is a simultaneous ordinary differential equation, is generally a numerical value obtained by differentially approximating the differential and gradually integrating "x" from the initial value. Can be solved. At that time, the input "u" from the measured value is interpolated if necessary, and the value at that time is input for each step.

Takuya Shinoda Noritaka Inoue Tetsuya Ito “Proposals for International Standards for Semiconductor Device Thermal Resistance θJC”, Thermal Science & Engineering Vol.23 No.1 (2015) pp.1-4 [online] March 23, 2020 Search Internet <URL : Https://www.jstage.jst.go.jp/article/tse/23/1/23_1/_pdf/-char/ja> "Chapter 10 Ordinary Differential Equation (ODE) Solving Method and Its Application" [online] March 23, 2020 Search Internet <URL: http://www.nuce.nagoya-u.ac.jp/ e8 / Matsuoka / 070ctaveNum / LectureDocPub / 07CompA | go_05_pub.pdf> Search on June 8, 2020 “Scipy integrate.solve_ivp” [online] March 23, 2020 Search Internet <URL: https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html> "Ordinary differential equation / solver of initial value problem of ordinary differential equation" [online] March 23, 2020 Search Internet <URL: https://jp.mathworks.com/help/matlab/ordinary-differential-equations.html > "Chapter 6 Heat Dissipation Design Method" Fuji Electric Co., Ltd. [online] March 23, 2020 Search Internet <URL: https://www.fujielectric.co.jp/products/semiconductor/model/igbt/application/box/ doc / pdf / RH984b / RH984b_06.pdf>

The simultaneous differential equations of the RC thermal network model 1 shown in the equation (1) are generally called stiff because the thermal resistance R and the heat capacity C differ by 100 times or more between the junction side and the case side. The calculation does not converge unless the time interval for taking the difference is made considerably small.

Therefore, it is necessary to finely chop the calculation steps, which may take an excessive calculation time. For example, when 100,000 data (10 seconds) measured by 10 kHz sampling was used as an input and solved with numerical analysis software ("solve_inv" of "SciPy"), the solution became 500,000 steps or more, and the calculation time was 10 minutes or more. It also took.

The present invention has been made to solve such a conventional problem, and an object of the present invention is to speed up the calculation of junction temperature estimation of a semiconductor device.

(1) One aspect of the present invention is
A device that estimates the internal state of the unit based on the input data.
Collect the external force data group and input it as the input data at any time.
By solving the equation of motion for the input data, the value of the internal state is calculated.
The feature is that the equation of motion is simplified and the part where the constant can be calculated is calculated in advance.

(2) Another aspect of the present invention is a device that estimates the internal temperature of a semiconductor device based on an RC thermal network model in which thermal resistance and heat capacity are connected in a stepped manner.
While the information of the voltage command value, the current measurement value, and the case temperature measurement value of the semiconductor device is input, the internal temperature is estimated by solving the simultaneous ordinary differential equations of the RC thermal network model.
The simultaneous equations are simplified in advance to equation (10).
It is characterized in that the part where the constant can be calculated shown in the equations (8) and (9) is calculated in advance.

-U (t) = input-x (t) = internal temperature-A and B are as shown in equation (3).

-R _{0 to} R ₄ = thermal resistance-C _{0 to} C ₄ = heat capacity (3) Another object of the present invention is an RC thermal circuit network in which the internal temperature of a semiconductor device is connected in a stepwise manner by thermal resistance and heat capacity. It is a device that estimates based on a model.
While the voltage command value, current measurement value, and case temperature information of the semiconductor device are input, while
The input data is linearly approximated, and the internal temperature is estimated by solving the simultaneous ordinary differential equations of the RC thermal circuit model.
When solving the simultaneous ordinary differential equations, equations (15) to (17) are used.

・ A and B are as shown in equation (3).

-R _{0 to} R ₄ = thermal resistance-C _{0 to} C ₄ = thermal capacity (4) In yet another aspect of the present invention, time-series data of an external force generated by an abnormality in the primary vibration system is prepared, and the external force is applied. It is a device that estimates the mass point vibration when series data is given and creates simulated vibration data.
The vibration data is acquired by solving the equation of motion of the mass point of the primary vibration system by inputting the external force time series data.
In solving the equation of motion, equations (19) and (20) are used.

In Equation 19, "x" indicates a mass point (internal state and output) of the one-dimensional vibration system, and "u" indicates an input.

According to the present invention, it is possible to speed up the calculation of junction temperature estimation of a semiconductor device.

The block diagram which shows an example of the RC thermal network model. The block diagram of Example 1. The block diagram of Example 2. The block diagram of Example 3.

Hereinafter, the estimation device according to the embodiment of the present invention will be described with reference to Examples 1 to 3.

(1) Configuration Example The configuration of the first embodiment will be described with reference to FIG. This embodiment constitutes a junction temperature estimation device that frequently measures the current value, voltage command value, and case temperature directly under the chip flowing through the element of the IGBT 4, and estimates the junction temperature in real time based on these measurement information.

Reference numeral 2 in FIG. 2 shows an analysis device constituting the junction temperature estimation device. The analysis device 2 is configured by a computer, and the following information A to C collected at high frequency is input at any time.
A: Voltage command value from the control device 3 to the IGBT 4 B: Current value flowing through the IGBT 4 measured by the ammeter 5 C: Measured value of the case temperature measured by the thermometer 6 directly under the IGBT 4 Here, the constituent function of the IGBT 4. Is measured in advance by the method of Non-Patent Document 1 or the like, and it is assumed that an RC thermal network model has been created. Specifically, the analysis device 2 collects the data of the information (A to C) by sampling with a period of about 10 kHz, and estimates the temperature based on the collected data.

At this time, it is assumed that the structural function required for temperature estimation is separately measured in advance and incorporated in the analysis device 2. Further, the junction temperature estimation by the analysis device 2 is performed by solving the simultaneous ordinary differential equations of the equation (1).

The heat input Q to the RC thermal network model is calculated using the data sheet of the IGBT 4. That is, the voltage value of the device is read from the current value measured using the correlation table of "current = device voltage". In addition, the due diligence ratio determined from the voltage command value and the voltage / current value of the device are used to obtain the conduction loss.

Further, the switching loss is also read from the correlation table with the current, and the total loss obtained by adding them is the input heat amount Q. Since the device characteristics of the IGBT 4 and the like have a part that changes depending on the junction temperature, the junction temperature is required to read the correlation table. For this junction temperature, the measured value of the case temperature measured by the thermometer 6 is used at the first time, and the junction temperature estimated last time is used thereafter. At this time, since the IGBT 4 is in a switching operation, it is “Q = 0” at the timing when the IGBT 4 is not conducting (see Non-Patent Document 5).

(2) Junction temperature estimation process As described above, the junction temperature estimation by the analyzer 2 is performed by solving the simultaneous ordinary differential equations of the equation (1). At that time, it is assumed that the part that can be calculated as a constant is calculated first by solving it at the mathematical formula level in advance and simplifying it. The details will be described below.

First, the general solution of the simultaneous ordinary differential equations given by Eq. (1) is Eq. (4).

"C" in the equation (4) is a Sekibunkan constant. When this "C" is determined from the value "x (t _{0 )" at the time "t 0} ", the equation (5) is obtained.

Here, _{assuming that the interval between "t 0} " and "t" is about the data measurement cycle and the value of "u (s)" is constant during that period, the equation (5) is transformed into the equation (6). can do.

Since the integral in the equation (6) can be calculated, it becomes the equation (7).

Here, if "t-t ₀ = T" is constant, the equations (8) and (9) become time-independent constant line examples, and can be calculated before the calculation data is given.

As a result, the calculation when the measurement data is given is a simple product-sum operation of the equation (10) and the matrix.

Then, the analysis device 2 can calculate the internal state (internal temperature) “x (t)” of the IGBT 4 from the input “u (t)” by the equation (10). At this time, the analysis device 2 shall obtain in advance "R" and "S" in the solution of the simultaneous ordinary differential equations of the IGBT 4 from the structural function by the equations (8) and (9). Further, for the first "x (t ₀ )", it is assumed that all the internal temperatures of the IBBT 4 are initialized with the measured values of the case temperature.

Then, the operation of acquiring a new input "u (t)" in the period S and calculating the latest internal temperature "x (t)" by the equation (10) from _{this and the previous "x (t 0)".} Is repeated, and the calculation result is estimated as the junction temperature. Since the calculation in this case is a simple matrix product-sum operation, it is very fast, and in this respect, it is possible to speed up the junction temperature calculation.

For example, when 100,000 data (for 10 seconds) measured by 10 kHz sampling were collectively calculated for input, it was possible to calculate in 2 seconds including the calculation of the input heat amount Q from the input measurement data. When the internal temperature is estimated (calculated) in real time from the measured value, although the efficiency is slightly reduced, sufficient real-time processing is possible.

Here, the exponential function of the matrix appearing in "R = exp (TA)" of the equation (8) is the one in which the matrix TA is substituted into the tailor series of the exponential function, and is approximated by a finite sum up to an appropriate number of terms. Can be calculated. Further, when "A" in the formula (7) ^{can be diagonalized to "A = PDP-1} ", the above "R = exp (TA)" can be expressed as the formula (11).

Since "D" in equation (11) is a diagonal matrix, the same "exe (TD)" is an exponential function of the corresponding diagonal component arranged for each diagonal component, and the Taylor series of the exponential function is appropriate. It is much easier than calculating up to the number of terms, which also contributes to speeding up. However, it is assumed that the calculation of the equation (11) is executed only at the time of initialization.

As described above, according to the first embodiment, when solving the simultaneous ordinary differential equations of the equation (1), the part that can be solved in advance at the mathematical expression level and simplified to the equation (10) to calculate the constants shown in the equations (8) and (9). By calculating in advance, it is possible to estimate the internal temperature at each time at a very high speed.

The second embodiment will be described with reference to FIG. The analysis device 2 of this embodiment frequently measures the current value, the voltage command value, and the case temperature directly under the chip that flow through the element of the IGBT 4, stores them in the database 8, and estimates the junction temperature based on the stored data. Configure a junction estimation device.

Here, the data of the information (A to C) measured with high frequency (for example, 10 kHz sampling) is stored in the database 8. At this time, it is assumed that the structural function of the IGBT 4 is measured in advance by a method such as Non-Patent Document 1 as in the first embodiment, and an RC thermal network model is created.

Then, the analysis device 2 acquires the data of the information (A to C) from the database 8 as time series data, and estimates the junction temperature. However, the database 8 is not limited to a system managed by a DBMS (DataBase Management System) as long as it can store and store the data of the information (A to C), and may be a file / file group or the like. Specifically, the junction temperature estimation of the analysis device 2 may be calculated in the same manner as in the first embodiment, but the accuracy can be improved by adopting the method of the present embodiment.

In Example 1, "u (s)" was considered to be constant in the integration interval [t _{0, t] of the equation (5).} On the other hand, in this embodiment, the following linear approximation is considered between "u (s)" and "u (t ₀ )" and "u (t)".

Substituting equation (12) into equation (5) yields equation (13).

When the second term of the equation (13) is integrated by using integration by parts, the equation (14) is obtained.

Substituting the equation (14) into the equation (13) and rearranging it gives the equation (15).

However, "V" and "W" in the equation (15) are time-independent constant matrices as shown in the equations (16) and (17), and the calculation is completed before the measurement data is given. Can be left.

Here, it is assumed that the analysis device 2 obtains “R”, “V”, and “W” in the solution of the simultaneous ordinary differential equations of the IGBT 4 shown in the equation (15) from the structural function in advance.
_{Further, regarding "x (t 0} )" in the equation (15), it is assumed that all the internal temperatures are initially initialized with the measured values of the case temperature.

After that, the input "u (t)" of the time and the previous input "u (t ₀ )" are prepared in the cycle S, and the equation (15) is used from _{this and the previous input "x (t 0)".} Then, the operation of calculating the latest internal temperature "x (t)" is repeated, and the calculation result is estimated as the junction temperature. According to the second embodiment, the estimation accuracy can be improved by linearly approximating the input data without increasing the amount of calculation so much.

Example 3 will be described with reference to FIG. This embodiment shows an application example to mass point simulation in a one-dimensional vibration system as an example other than the RC thermal network model.

For example, when evaluating the vibration technology of a machine or equipment, there is a demand to simulate the vibration data of the machine or equipment. Therefore, in this embodiment, external force time-series data generated by an abnormality in a simple one-dimensional vibration system is prepared, and qualitative vibration when the external force time-series data is given is estimated and simulated vibration data is created. ..

That is, the time-series data of the external force is stored in the database 9 in advance, and the analysis device 2 takes the complementary data of the database 9 as input and solves the simultaneous ordinary differential equations to obtain the time-series data of the displacement, velocity, and acceleration of the mass point.

Here, the equation of motion of the mass point "x" of the one-dimensional vibration system in which the external force "u (t)" acts is given by the equation (18).

Equation (18) is a second-order ODE, but it can be made into a simultaneous ODE of Eq. (19) by introducing an additional variable "v = (d / dt) x".

In the formula (19), "internal state and output x = ^t (x, v)" is shown, "input u = ^t (u (t))" is shown, and "A" and "B" are shown in the formula ( 20).

As a result, the format is the same as that used in Examples 1 and 2, and by solving in the same way, the time-series value of the mass point position and velocity when the time-series data "u (t)" of the external force is given can be obtained. Also, the acceleration can be obtained by differentiating the velocity with respect to time. As a result, not only the first-order ordinary differential equation but also the second-order or higher-order ordinary differential equation can be processed in the same manner. It should be noted that the present invention is not limited to the above embodiment, and can be modified and implemented within the scope described in each claim.

1 ... RC thermal network model 2 ... Analytical device (estimating device)
3 ... Control device 4 ... IGBT (semiconductor device)
5 ... Ammeter 6 ... Thermometer 7 ... AC power supply 8, 9 ... Database

Claims (5)

A device that estimates the internal state of the unit based on the input data.
Collect the external force data group and input it as the input data at any time.
By solving the equation of motion for the input data, the value of the internal state is calculated.
An estimation device characterized in that the equation of motion is simplified in advance and a part that can be calculated as a constant is calculated in advance. The estimation device according to claim 1, wherein the input data is linearly approximated. A device that estimates the internal temperature of a semiconductor device based on an RC thermal network model in which thermal resistance and heat capacity are connected in a stepped manner.
While the information of the voltage command value, the current measurement value, and the case temperature measurement value of the semiconductor device is input, the internal temperature is estimated by solving the simultaneous ordinary differential equations of the RC thermal network model.
The simultaneous equations are simplified in advance to equation (10).
An estimation device characterized in that a portion capable of calculating a constant shown in equations (8) and (9) is calculated in advance.

-U (t) = input-x (t) = internal temperature-A and B are as shown in equation (3).

・ R _{0 to} R ₄ = thermal resistance ・ C _{0 to} C ₄ = heat capacity A device that estimates the internal temperature of a semiconductor device based on an RC thermal network model in which thermal resistance and heat capacity are connected in a stepped manner.
While the voltage command value, current measurement value, and case temperature information of the semiconductor device are input, while
The input data is linearly approximated, and the internal temperature is estimated by solving the simultaneous ordinary differential equations of the RC thermal circuit model.
An estimation device characterized in that equations (15) to (17) are used when solving simultaneous ordinary differential equations.

・ A and B are as shown in equation (3).

・ R _{0 to} R ₄ = thermal resistance ・ C _{0 to} C ₄ = heat capacity It is a device that prepares time-series data of external force generated by an abnormality in the primary vibration system, estimates the mass point vibration when the external force time-series data is given, and creates simulated vibration data.
The vibration data is acquired by solving the equation of motion of the mass point of the primary vibration system by inputting the external force time series data.
An estimation device characterized in that equations (19) and (20) are used in solving the equation of motion.

In Equation 19, "x" indicates a mass point (internal state and output) of the one-dimensional vibration system, and "u" indicates an input.

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