Method for estimating junction temperature online on IGBT power module

Abstract

A method for estimating the junction temperature on-line on an insulated gate bipolar transistor (IGBT) power module, including the following steps. Estimate the junction temperature by the temperature sensitive electrical parameter method, set the space thermal model of the extended state, and apply the Kalman filter to the junction temperature estimation. The temperature sensitive electrical parameter method estimates the junction temperature of the IGBT power module in real time, selects the IGBT conduction voltage drop V.sub.CE(ON) as the temperature sensitive electrical parameter, and provides a V.sub.CE(ON) on-line measuring circuit. The power loss of the diode and IGBT and the estimated value of junction temperature obtained by the temperature sensitive electrical parameter method are taken as the input of the Kalman filter, and measurement noise and process noise are considered to obtain an optimal estimated value of junction temperature.

Claims

1. A method for estimating junction temperature on-line on an insulated gate bipolar transistor (IGBT) power module, comprising the following steps executing by a processor: step 1: performing a control strategy of the IGBT power module and setting up a full-bridge inverter circuit and a V.sub.CE(ON) on-line measuring circuit based on a power electronic simulation software Saber, connecting two input terminals of the V.sub.CE(ON) on-line measuring circuit to a collector and an emitter of an IGBT of the full-bridge inverter circuit, thereby realizing connection between the full-bridge inverter circuit and the V.sub.CE(ON) on-line measuring circuit; step 2: obtaining IGBT conduction voltage drop V.sub.CE(ON) for the connected full-bridge inverter circuit and the V.sub.CE(ON) on-line measuring circuit, using a temperature sensitive electrical parameter method to obtain a calibration curve and a fitting relationship of the IGBT conduction voltage drop V.sub.CE(ON) and an IGBT power module junction temperature T.sub.j; step 3: based on the full-bridge inverter circuit set in step 1, setting a behavior model of the IGBT power module composed of an IGBT and a corresponding diode, wherein static and dynamic characteristics of the behavior model are simulated and analyzed to calculate switching loss and conduction loss of the IGBT, reverse recovery loss and conduction loss of the diode; step 4: considering a coupling effect between the IGBT and the diode in the IGBT power module of step 3, and setting a thermal model of an extended state space of the IGBT power module; step 5: setting a system model of the Kalman filter, the IGBT power module junction temperature obtained in the step 2, the switching loss and the conduction loss of the IGBT obtained in the step 3, the reverse recovery loss and the conduction loss of the diode obtained in the step 3 are used as filter inputs to calculate an optimal estimated value of the junction temperature; step 6: employing a physical IGBT power module in a power supplying circuit; and step 7: modifying an operation of the physical IGBT power module based on the optimal estimated value of the junction temperature.

2. The method for estimating junction temperature on-line on the IGBT power module according to claim 1, wherein setting the full-bridge inverter circuit in the step 1 comprises following steps executing by the processor: firstly setting a sinusoidal pulse width modulation (SPWM) control circuit, setting a dead-zone time, and then setting a gate driving circuit, wherein the gate driving circuit is modulated by the SPWM control circuit, an input terminal of the gate driving circuit is connected to an output terminal of the SPWM control circuit, and an output terminal of the gate driving circuit is connected to a gate of the IGBT of the IGBT power module; the full-bridge inverter circuit has four bridge arms, each of the bridge arms is composed of one SPWM control circuit, one gate driving circuit, one IGBT and one diode; then the V.sub.CE(ON) on-line measuring circuit is set, and finally the two input terminals of the V.sub.CE(ON) on-line measuring circuit are connected to the collector and emitter of the IGBT of one of the bridge arms of the full-bridge inverter circuit.

3. The method for estimating junction temperature on-line on the IGBT power module according to claim 1, wherein monitoring the junction temperature on-line by the temperature sensitive electrical parameter method comprises following steps executing by the processor: first, placing the IGBT in an incubator, and after the junction temperature of the IGBT power module being stabilized, injecting a small current I.sub.C of 100 mA-1A into the collector of the IGBT; then measuring a saturation conduction voltage drop V.sub.CE(ON) of IGBT, changing a temperature of the incubator and repeatedly measuring the saturation conduction voltage drop V.sub.CE(ON) of the IGBT in a range of 20° C.-150° C.; and finally taking the junction temperature T.sub.j as a dependent variable, and V.sub.CE(ON) as an independent variable, and linearly fitting the V.sub.CE(ON) to obtain a fitting relationship T.sub.j=f(v.sub.CE(ON)).

4. The method for estimating junction temperature on-line on the IGBT power module according to claim 1, wherein the switching loss and the conduction loss of the IGBT, the reverse recovery loss and the conduction loss of the diode obtained through the calculation in the step 3 comprise following steps executing by the processor: using a IGBT Level-1 Tool modeling toolbox in Saber to set a simulation model for a specific structure and process of a device, thereby accurately representing the static and dynamic characteristics of the device, simulating a dynamic switching process of the IGBT power module, and obtaining a voltage and a current waveform of the IGBT when the IGBT is on and off, and a reverse recovery voltage and a current waveform of the diode, and a voltage and a current waveforms when the IGBT and the diode are turned on; wherein the loss of the IGBT is calculated as follows: $P_{on}=\frac{1}{t_{on}}{\int }_0^{t_{on}}{v}_{ce}\left(r\right)i_c\left(t\right)dt{P}_{off}=\frac{1}{t_{off}}{\int }_0^{t_{off}}{v}_{ce}\left(t\right)i_c\left(t\right)dt{P}_{\mathrm{cond}\mathrm{\_I}}=V_{ce\left(\mathrm{on}\right)}\times I_C\times {\delta }_1{P}_{\mathrm{IGBT}}=P_{on}+P_{off}+P_{\mathrm{cond}}$ wherein in the above equations, P.sub.on represents a turn-on loss of the IGBT; t.sub.on represents a turn-on time of the IGBT; v.sub.ce(t) represents a collector voltage of the IGBT during turn-on; i.sub.c(t) represents a collector current of the IGBT during turn-on; P.sub.off represents the IGBT turn-off loss; t.sub.off indicates a turn-off time of the IGBT; P.sub.cond_I indicates a conduction loss of the IGBT; V.sub.ce(on) indicates a conduction voltage drop of the IGBT; I.sub.C indicates a conduction current of the IGBT; and δ.sub.I indicates a duty ratio of a current operating state of the IGBT; P.sub.IGBT represents a total loss of the IGBT; t represents time; wherein the loss of the diode is calculated as follows: $P_{\mathrm{cond}\_D}=V_F\times I_F\times {\delta }_D{P}_{rec}=\frac{1}{t_{rr}}{\int }_0^{t_{rr}}{v}_f\left(t\right)i_f\left(t\right)\mathrm{dt}{P}_{\mathrm{DIODE}}=P_{\mathrm{cond}\_D}+P_{rec}$ wherein in the above equations, P.sub.cond_D represents a conduction loss of the diode; V.sub.F represents a conduction voltage drop of the diode; I.sub.F represents a conduction current of the diode; δ.sub.D represents a duty ratio of a current operating state of the diode; P.sub.rec represents a reverse recovery loss of the diode; t.sub.rr represents a reverse recovery time of the diode; v.sub.f(t) represents a voltage of the diode in reverse recovery; and i.sub.f(t) represents current when the diode is in reverse recovery; t represents time.

5. The method for estimating junction temperature on-line on the IGBT power module according to claim 1, wherein setting the space thermal model of the extended state of the IGBT power module in the step 4 comprises following steps executing by the processor: first, simulating self-heating of the IGBT, and expressing its thermal resistance by the following equation:
Z.sub.θja(t)=(T.sub.j(t)−T.sub.a)/P.sub.IGBT wherein in the above equation, T.sub.j(t) represents an IGBT junction temperature; T.sub.a represents an ambient temperature at which the IGBT power module is located; Z.sub.θja(t) represents a thermal resistance; P.sub.IGBT represents a total loss of the IGBT; t represents time; wherein the above equation is expressed by an equivalent RC network, which is replaced by a Foster thermal network model, which is an RC loop composed of N thermal resistances and N thermal capacitances connected in parallel, a time response is expressed by the following series of exponential items: $Z_{\theta ja}\left(t\right)=\underset{i=1}{\overset{n}{.Math.}}{R}_i\left(1-e^{-t/R_i{C}_i}\right)$ performing the Laplace transform on the above equation, wherein the thermal resistance in a frequency domain is expressed as a partial fractional form: $Z_{\theta ja}\left(s\right)=\frac{k_1}{s+p_1}+\frac{k_2}{s+p_2}+.Math.+\frac{k_n}{s+p_n}$ wherein in the above two equations, i represents a network order of the Foster thermal network model; n represents a total network order of the Foster thermal network model; R.sub.i represents a thermal resistance in the Foster thermal network model; C.sub.i represents thermal capacitances in the Foster thermal network model; k.sub.i=1/C.sub.i; k.sub.n=1/C.sub.n; p.sub.i=1/R.sub.iC.sub.i, p.sub.n=1/R.sub.nC.sub.n; wherein a state space expression for the partial fraction of the above partial fractional form is: $\stackrel{.}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+Bu\left(t\right)T_j\left(t\right)=\mathrm{Cx}\left(t\right)+\mathrm{Du}\left(t\right)A=\left[\begin{array}{ccccc}\frac{1}{R_1{C}_1}& 0& 0& .Math.& 0\\ 0& \frac{1}{R_2{C}_2}& 0& .Math.& 0\\ 0& 0& \frac{1}{R_3{C}_3}& .Math.& 0\\ .Math.& .Math.& .Math.& \ddots & .Math.\\ 0& 0& 0& .Math.& \frac{1}{R_n{C}_n}\end{array}\right],B=\left[\begin{array}{cc}\frac{1}{C_1}& 0\\ \frac{1}{C_2}& 0\\ \frac{1}{C_3}& 0\\ .Math.& .Math.\\ \frac{1}{C_n}& 0\end{array}\right]C=\left[111.Math.1\right],D=\left[01\right]$ wherein x(t) represents an n-dimensional state vector; A.sub.n×n represents a system matrix of n rows and n columns, a diagonal matrix of which a main diagonal is p.sub.i; B.sub.n×2 represents an input matrix of n rows and 2 columns with a first column is k.sub.i; C.sub.l×n represents an output matrix of 1 row and n columns; D.sub.1×2 represents a feedforward matrix of 1 row and 2 columns; in addition, $u\left(t\right)=\left[\begin{array}{c}{P}_D\left(t\right)\\ T_a\end{array}\right]$ represents a system input vector, wherein P.sub.D(t) represents power loss of the IGBT power module; wherein considering the coupling effect of the diode, and the above state space model is extended as follows: $\left[\begin{array}{c}\stackrel{.}{x_{s1}}\\ .Math.\\ \stackrel{.}{x_{\mathrm{sn}}}\\ \stackrel{.}{x_{c1}}\\ .Math.\\ \stackrel{.}{x_{\mathrm{cn}}}\end{array}\right]=\left[\begin{array}{cccccc}{p}_{s1}& 0& 0& 0& .Math.& 0\\ 0& \ddots & 0& .Math.& .Math.& 0\\ .Math.& 0& p_{\mathrm{sn}}& 0& .Math.& 0\\ 0& .Math.& 0& p_{c1}& 0& .Math.\\ 0& .Math.& .Math.& 0& \ddots & 0\\ 0& .Math.& 0& 0& .Math.& p_{\mathrm{cn}}\end{array}\right]\left[\begin{array}{c}{x}_{s1}\\ .Math.\\ x_{\mathrm{sn}}\\ x_{c1}\\ .Math.\\ x_{\mathrm{cn}}\end{array}\right]+\left[\begin{array}{ccc}{k}_{s1}& 0& 0\\ .Math.& .Math.& .Math.\\ k_{\mathrm{sn}}& 0& 0\\ 0& k_{c1}& 0\\ .Math.& .Math.& .Math.\\ 0& k_{\mathrm{cn}}& 0\end{array}\right]\left[\begin{array}{c}{P}_{\mathrm{IGBT}}\\ P_{\mathrm{DIODE}}\\ T_a\end{array}\right]T_j=\left[111.Math.1\right]\left[\begin{array}{c}{x}_{s1}\\ .Math.\\ x_{\mathrm{sn}}\\ x_{c1}\\ .Math.\\ x_{\mathrm{cn}}\end{array}\right]+\left[001\right]\left[\begin{array}{c}{P}_{\mathrm{IGBT}}\\ P_{\mathrm{DIODE}}\\ T_a\end{array}\right]$ wherein x.sub.s1, . . . , x.sub.sn represents a state of self-heating impedance, x.sub.c1, . . . , x.sub.cn represents a state of coupling thermal impedance; P.sub.DIODE represents a power loss of the IGBT in the IGBT power module, P.sub.DIODE represents a power loss of the diode in the IGBT power module; $p_{s1}=\frac{1}{R_{S1}{C}_{S1}},p_{sn}=\frac{1}{R_{sn}{C}_{sn}};p_{c1}=\frac{1}{R_{c1}{C}_{c1}},p_{sn}=\frac{1}{R_{sn}{C}_{sn}};k_{s1}=\frac{1}{C_{S1}},k_{sn}=\frac{1}{C_{sn}};k_{c1}=\frac{1}{c_{c1}},k_{cn}=\frac{1}{c_{cn}};$ specifically, R.sub.s1 . . . R.sub.sn, C.sub.s1 . . . C.sub.sn represent thermal resistance thermal capacitances in the equivalent Foster thermal network model of the IGBT in the IGBT power module; R.sub.c1 . . . R.sub.cn, C.sub.c1 . . . C.sub.cn represent thermal resistance thermal capacitances in the equivalent Foster thermal network model of the diode in the IGBT power module.

6. The method for estimating junction temperature on-line on the IGBT power module according to claim 1, wherein setting the system model of the Kalman filter in the step 5 comprises following steps executing by the processor: introducing a system of a discrete control process based on the space thermal model of the extended state as follows:
x.sub.k=Fx.sub.k−1+Gu.sub.k+w.sub.k
T.sub.k=Hx.sub.k+Ju.sub.k+v.sub.k wherein in the above equation, k represents a time step; x.sub.k−1 represents a state variable, i.e., the thermal resistance of the IGBT power module, at time (k−1); x.sub.k represents the state variable, i.e., the thermal resistance of the IGBT power module, at time k; F and G respectively represent a system matrix and a control matrix; u.sub.k represents a system input vector, including a IGBT power module loss and an ambient temperature of the IGBT power module; w.sub.k and v.sub.k respectively represent process noise and measurement noise, and assuming that both are Gaussian white noise, a covariance of the process noise w.sub.k and the measurement noise v.sub.k are Q and R respectively; T.sub.k represents a junction temperature observation value of the IGBT power module at time k; H and J respectively represent an observation matrix and a direct matrix; wherein a Kalman filtering algorithm flow is described as follows: (1) predicting a thermal resistance value {circumflex over (x)}.sub.(k|k−1) of the IGBT power module at time k from an optimal thermal resistance estimated value {circumflex over (x)}.sub.(k−1|k−1) of the IGBT power module at time (k−1):
{circumflex over (x)}.sub.(k|k−1)=F{circumflex over (x)}.sub.(k−1|k−1)+Gu.sub.k (2) calculating the predicted value of the junction temperature of the IGBT power module at time k:
{circumflex over (T)}.sub.(k|k−1)=H{circumflex over (x)}.sub.(k|k−1)+Iu.sub.k (3) measuring the covariance P.sub.(k|k−1) at time k by the covariance P.sub.(k−1|k−1) between the observed value and the predicted value of the IGBT power module junction temperature at time (k−1):
P.sub.(k|k−1)=FP.sub.(k−1|k−1)F.sup.T+Q (4) calculating a Kalman filter gain:
K.sub.(k)=P.sub.(k|k−1)H.sup.T[HP.sub.(k|k−1).sup.−1H.sup.T+R].sup.−1 wherein K.sub.(k) represents the Kalman filter gain; (5) calculating an optimal estimated value of the system:
{circumflex over (x)}.sub.(k|k)={circumflex over (x)}.sub.(k|k−1)+K.sub.(k)(T.sub.k−{circumflex over (T)}.sub.(k|k−1)) wherein {circumflex over (x)}.sub.(k|k) represents an optimal estimated value of the thermal resistance of the IGBT power module at time k; (6) updating an inverse operation of the optimal junction temperature value of the IGBT power module in the next step at time (k+1), which is updating the covariance:
P.sub.(k|k)=[I−K.sub.(k)H]P.sub.(k|k−1) wherein P.sub.(k|k) represents an updated covariance after time k, and I represents a unity matrix; (7) returning to step (1) from step (6), performing a loop until a final result achieves a desired effect.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a flow chart of a method for estimating junction temperature on-line on an IGBT power module according to the present invention.

(2) FIG. 2 is a circuit diagram of a full-bridge inverter.

(3) FIG. 3 is a schematic diagram showing principle of the SPWM control strategy.

(4) FIG. 4 shows the V.sub.CE(ON) on-line measuring circuit.

(5) FIG. 5 is a schematic diagram of the operating signals of the V.sub.CE(ON) on-line measuring circuit.

(6) FIG. 6 is a multi-layer structure diagram of an IGBT power module.

(7) FIG. 7 is a diagram of an electrically equivalent Foster thermal network model.

(8) FIG. 8 is a flow chart of the Kalman filter algorithm.

DESCRIPTION OF THE EMBODIMENTS

(9) The present invention will be further described below with reference to specific embodiments and the accompanying drawings.

(10) As shown in FIG. 1, the present invention provides a method for estimating the junction temperature on-line on an IGBT power module. The implementation process of the method is described in detail below by taking the full-bridge inverter circuit shown in FIG. 3 as an example. The specific implementation steps are as follows:

(11) Step 1. Set up a full-bridge inverter circuit, a V.sub.CE(ON) on-line measuring circuit, a SPWM control circuit and a gate driving circuit in Saber, and connect the two input terminals of the V.sub.CE(ON) on-line measuring circuit to the collector and emitter of an IGBT of the full-bridge inverter, thereby implementing the connection of the full-bridge inverter circuit to the V.sub.CE(ON) on-line measuring circuit, as shown in FIG. 2.

(12) Specifically, step 1 in the embodiment includes the following process:

(13) 1-1. Referring to the schematic diagram showing the principle of the sinusoidal pulse width modulation shown in FIG. 3, the most common strategy for controlling the power transmitted to the load is pulse width modulation (PWM), and one method of generating the PWM signal is to compare the sine wave v.sub.sin having a frequency of f.sub.L with the sawtooth wave v.sub.t having a switching frequency of f.sub.s, and then the gate driving circuit switch is controlled according to v.sub.sin and v.sub.t. The gate driving circuit is modulated by the SPWM control circuit, and the input terminal of the gate driving circuit is connected to the output terminal of the SPWM control circuit. The output terminal of the gate driving circuit is connected to the gate of the IGBT of the IGBT power module. The full-bridge inverter circuit has four bridge arms, and each of the bridge arms is composed of an SPWM control circuit, a gate driving circuit, an IGBT and a diode. Then the V.sub.CE(ON) on-line measuring circuit is set, and finally the two input terminals of the V.sub.CE(ON) on-line measuring circuit are connected to the collector and emitter of the IGBT of one of the bridge arms of the full-bridge inverter circuit. In order to prevent that the two IGBTs in the upper and lower bridge arms of the full-bridge inverter are simultaneously turned on due to the switching speed problem of the gate driving circuit, it is required to set a reasonable dead-zone time.

(14) 1-2. Referring to the V.sub.CE(ON) on-line measuring circuit shown in FIG. 4, the two input terminals of the V.sub.CE(ON) on-line measuring circuit are respectively connected to the collector and emitter of the IGBT, and the resistor R.sub.1, R.sub.2 and R.sub.3, R.sub.4 in the V.sub.CE(ON) on-line measuring circuit are proportionally divided to reach the input voltage range of the operational amplifier U1; the output terminal of U1 is connected to a falling edge detector, and the output voltage of U1 is compared with a set voltage to detect the falling edge of the IGBT collector-emitter voltage V.sub.CE, and the monoflop is triggered so that the monoflop changes from steady state to transient state. The delay time of the monoflop is set as 100 μs, when the monoflop is recovered from the temporary steady state to the steady state, the monoflop triggers sampling. The sampling signal is modulated through the high frequency signal and transmitted through the isolation barrier (capacitor C in FIG. 4), and then demodulated at the output terminal of the operational amplifier U2 in FIG. 5, thereby recovering the sampling signal. A 16-bit analog-to-digital converter (ADC) with a range of ±5V is utilized to obtain the IGBT conduction voltage drop V.sub.CE(ON) value on the measurement side (i.e., the output terminal of the V.sub.CE(ON) on-line measuring circuit).

(15) 1-3, FIG. 5 shows the operating signal of the V.sub.CE(ON) on-line measuring circuit, wherein V.sub.CE_UI represents the output voltage of the operational amplifier U1; S/H represents the sampling and retaining signal used to obtain the IGBT conduction voltage drop V.sub.CE(ON) value; t.sub.d is the delay time of the monoflop.

(16) Step 2: Obtain the IGBT conduction voltage drop V.sub.CE(ON) for the connected full-bridge inverter circuit and the V.sub.CE(ON) on-line measuring circuit, and obtain the calibration curve and fitting relationship of IGBT conduction voltage drop V.sub.CE(ON) and IGBT power module junction temperature T.sub.j by using the temperature sensitive electrical parameter method. Firstly, the IGBT is placed in the incubator, and the small current I.sub.C (100 mA-1 A) is injected into the collector of the IGBT after the junction temperature of the IGBT power module is stabilized. Then, the saturation conduction voltage drop V.sub.CE(ON) of the IGBT is measured, and the temperature of the incubator is changed, the saturation conduction voltage drop V.sub.CE(ON) of the IGBT is repeatedly measured in the range of 20° C.-150° C. Finally the junction temperature T.sub.j serves as the dependent variable, V.sub.CE(ON) serves as the independent variable, and the V.sub.CE(ON) is linearly fitted to obtain the fitting relationship T.sub.j=f(V.sub.CE(ON)).

(17) Step 3. Set up a full-bridge inverter model in Saber, set a behavior model of an IGBT power module composed of an IGBT and a corresponding diode, simulate and analyze its static and dynamic characteristics of the behavior model, and calculate the switch loss and conduction loss of the IGBT as well as reverse recovery loss and conduction loss of the diode.

(18) The IGBT Level-1 Tool modeling toolbox in Saber is utilized to set the simulation model for the specific structure and process of the device, thereby accurately representing the static and dynamic characteristics of the device, simulating the dynamic switching process of the IGBT power module, and obtaining the voltage and current waveform of the IGBT when the IGBT is on and off, and reverse recovery voltage and current waveform of diode, and voltage and current waveforms when IGBT and diode are turned on.

(19) The loss of the IGBT is calculated as follows:

(20) $P_{\mathrm{on}}=\frac{1}{t_{\mathrm{on}}}\stackrel{t_{\mathrm{on}}}{\underset{0}{\int }}{v}_{\mathrm{ce}}\left(t\right)i_c\left(t\right)\mathrm{dt}$$P_{\mathrm{off}}=\frac{1}{t_{\mathrm{off}}}\stackrel{t_{\mathrm{off}}}{\underset{0}{\int }}{v}_{\mathrm{ce}}\left(t\right)i_c\left(t\right)\mathrm{dt}$$P_{\mathrm{cond}\_I}=V_{\mathrm{ce}\left(\mathrm{on}\right)}\times I_C\times {\delta }_I$$P_{\mathrm{IGBT}}=P_{\mathrm{on}}+P_{\mathrm{off}}+P_{\mathrm{cond}}$

(21) In the above equations, P.sub.on represents the turn-on loss of the IGBT; t.sub.on represents the turn-on time of the IGBT; v.sub.ce(t) represents the collector-emitter voltage of the IGBT during turn-on; i.sub.c(t) represents the collector current of the IGBT during turn-on; P.sub.off represents the IGBT turn-off loss; t.sub.off indicates the turn-off time of the IGBT; P.sub.cond_I indicates the conduction loss of the IGBT; V.sub.ce(on) indicates the conduction voltage drop of the IGBT; I.sub.C indicates the conduction current of the IGBT; and δ.sub.1 indicates the duty ratio of the current operating state of the IGBT; P.sub.IGBT represents the total loss of the IGBT; t represents time.

(22) The loss of the diode is calculated as follows:

(23) $P_{\mathrm{cond}\_D}=V_F\times I_F\times {\delta }_D$$P_{\mathrm{rec}}=\frac{1}{t_{\mathrm{rr}}}\stackrel{t_{\mathrm{rr}}}{\underset{0}{\int }}{v}_f\left(t\right)i_f\left(t\right)\mathrm{dt}$$P_{\mathrm{DIODE}}=P_{\mathrm{cond}\_D}+P_{\mathrm{rec}}$

(24) In the above equations, P.sub.cond_D represents the conduction loss of the diode; V.sub.F represents the conduction voltage drop of the diode; I.sub.F represents the conduction current of the diode; δ.sub.D represents the duty ratio of the current operating state of the diode; P.sub.rec represents the reverse recovery loss of the diode; t represents the reverse recovery time of the diode; v.sub.f(t) represents the voltage of the diode in reverse recovery; and i.sub.f(t) represents the current when the diode is in reverse recovery; t represents time.

(25) Step 4. Consider the coupling effect between the IGBT and the diode in the IGBT power module of step 3, and set a space thermal model of extended state of the IGBT power module.

(26) FIG. 6 shows a multilayer structure of IGBTs made up of different materials, with power transmitted from the top to the bottom. The thermal resistance is regarded as a step response of the junction temperature to the input power. The equation is as follows:
Z.sub.θja(t)=(T.sub.j(t)−T.sub.a)/P.sub.IGBT

(27) In the equation, T.sub.j(t) represents the IGBT junction temperature; T.sub.a represents the ambient temperature at which the IGBT power module is located; Z.sub.θja(t) represents the IGBT thermal resistance; P.sub.IGBT represents the total loss of the IGBT; t represents time.

(28) FIG. 7 shows the Foster thermal network model, which uses a series of RC components to characterize the thermal resistance. The time response can be expressed as:
Z.sub.θja(t)=Σ.sub.i=1.sup.nR.sub.i(1−e.sup.−t/R.sup.i.sup.C.sup.i)

(29) The Laplace transform is performed on the above equation, and the thermal resistance in the frequency domain is expressed as a partial fractional form:

(30) 0$Z_{\theta ja}\left(s\right)=\frac{k_1}{s+p_1}+\frac{k_2}{s+p_2}+.Math.+\frac{k_n}{s+p_n}$

(31) In the above two equations, i represents the network order of the Foster thermal network model; n represents the total network order of the Foster thermal network model; R.sub.i represents the thermal resistance in the Foster thermal network model; C.sub.i represents the thermal capacitances in the Foster thermal network model; t represents time; k.sub.i=1/C.sub.i; k.sub.n=1/C.sub.n; p.sub.i=1/R.sub.iC.sub.i, p.sub.n=1/R.sub.nC.sub.n.

(32) The state space expression for the partial fraction of the above partial fractional form is:

(33) $\stackrel{.}{x}\left(t\right)=\mathrm{Ax}\left(t\right)+\mathrm{Bu}\left(t\right)\left(\mathrm{equation}\mathrm{of}\mathrm{state}\right)T_j\left(t\right)=\mathrm{Cx}\left(t\right)+\mathrm{Du}\left(t\right)\left(\mathrm{output}\mathrm{equation}\right)A=\left[\begin{array}{ccccc}\frac{1}{R_1{C}_1}& 0& 0& .Math.& 0\\ 0& \frac{1}{R_2{C}_2}& 0& .Math.& 0\\ 0& 0& \frac{1}{R_3{C}_3}& .Math.& 0\\ .Math.& .Math.& .Math.& \ddots & .Math.\\ 0& 0& 0& .Math.& \frac{1}{R_n{C}_n}\end{array}\right],b=\left[\begin{array}{cc}\frac{1}{C_1}& 0\\ \frac{1}{C_2}& 0\\ \frac{1}{C_3}& 0\\ .Math.& .Math.\\ \frac{1}{C_n}& 0\end{array}\right]C=\left[111.Math.1\right],D=\left[01\right]$

(34) Specifically, x(t) represents an n-dimensional state vector; t represents time; A.sub.n×n represents a system matrix of n rows and n columns; B.sub.n×2 represents an input matrix of n rows and 2 columns; C.sub.l×n represents the output matrix of l row and n columns; D.sub.1×2 represents the feedforward matrix of 1 row and 2 columns. In addition,

(35) $u\left(t\right)=\left[\begin{array}{c}{P}_D\left(T\right)\\ T_a\end{array}\right]$
represents the system input vector, wherein P.sub.D(t) represents power loss of the IGBT power module.

(36) Consider the coupling effect of the diode, and the above state space model is extended as follows:

(37) $\left[\begin{array}{c}\stackrel{.}{x_{s1}}\\ .Math.\\ \stackrel{.}{x_{\mathrm{sn}}}\\ \stackrel{.}{x_{c1}}\\ .Math.\\ \stackrel{.}{x_{\mathrm{cn}}}\end{array}\right]=\left[\begin{array}{cccccc}{p}_{s1}& 0& 0& 0& .Math.& 0\\ 0& \ddots & 0& .Math.& .Math.& 0\\ .Math.& 0& p_{\mathrm{sn}}& 0& .Math.& 0\\ 0& .Math.& 0& p_{c1}& 0& .Math.\\ 0& .Math.& .Math.& 0& \ddots & 0\\ 0& .Math.& 0& 0& .Math.& p_{\mathrm{cn}}\end{array}\right]\left[\begin{array}{c}{x}_{s1}\\ .Math.\\ x_{\mathrm{sn}}\\ x_{c1}\\ .Math.\\ x_{\mathrm{cn}}\end{array}\right]+\left[\begin{array}{ccc}{k}_{s1}& 0& 0\\ .Math.& .Math.& .Math.\\ k_{\mathrm{sn}}& 0& 0\\ 0& k_{c1}& 0\\ .Math.& .Math.& .Math.\\ 0& k_{\mathrm{cn}}& 0\end{array}\right]\left[\begin{array}{c}{P}_{\mathrm{IGBT}}\\ P_{\mathrm{DIODE}}\\ T_a\end{array}\right]T_j=\left[111.Math.1\right]\left[\begin{array}{c}{x}_{s1}\\ .Math.\\ x_{\mathrm{sn}}\\ x_{c1}\\ .Math.\\ x_{\mathrm{cn}}\end{array}\right]+\left[001\right]\left[\begin{array}{c}{P}_{\mathrm{IGBT}}\\ P_{\mathrm{DIODE}}\\ T_a\end{array}\right]$

(38) Specifically, x.sub.s1, . . . , x.sub.sn represents the state of self-heating impedance, x.sub.c1, . . . , x.sub.cn represents the state of the coupling thermal impedance; P.sub.IGBT represents the power loss of the IGBT in the IGBT power module, P.sub.DIODE represents the power loss of the diode in the IGBT power module;

(39) $p_{s1}=\frac{1}{R_{s1}{C}_{s1}},p_{sn}=\frac{1}{R_{sn}{C}_{sn}};p_{c1}=\frac{1}{R_{c1}{C}_{c1}},p_{sn}=\frac{1}{R_{sn}{C}_{sn}};k_{s1}=\frac{1}{C_{\mathrm{s1}}},k_{sn}=\frac{1}{C_{sn}};k_{c1}=\frac{1}{c_{\mathrm{c1}}},k_{cn}=\frac{1}{c_{cn}};$
specifically, R.sub.s1 . . . R.sub.sn, C.sub.s1 . . . C.sub.sn represent the thermal resistance thermal capacitances in the equivalent Foster thermal network model of the IGBT in the IGBT power module; R.sub.c1 . . . R.sub.cn, C.sub.c1 . . . C.sub.cn represent the thermal resistance thermal capacitances in the equivalent Foster thermal network model of the diode in the IGBT power module.

(40) Step 5. Set a system model of the Kalman filter (i.e., the Kalman filter):

(41) A system of a discrete control process is introduced based on a space thermal model of the extended state in step 4 as follows:
x.sub.k=Fx.sub.k−1+Gu.sub.k+w.sub.k
T.sub.k=Hx.sub.k+Ju.sub.k+v.sub.k

(42) In the above equation, k represents the time step; x.sub.k−1 represents the state variable at time (k−1) (i.e., the thermal resistance of the IGBT power module); x.sub.k represents the state variable at time k (i.e., the thermal resistance of the IGBT power module); F and G respectively represent the system matrix and control matrix; u.sub.k represents the system input vector (the IGBT power module loss and the ambient temperature of the IGBT power module); w.sub.k and v.sub.k respectively represent the process noise and measurement noise. Assume that both are Gaussian white noise, the covariance of which are Q and R respectively; T.sub.k represents the junction temperature observation value of IGBT power module at time k; H and J respectively represent the observation matrix and direct matrix.

(43) As shown in FIG. 8, the Kalman filtering algorithm flow is described as follows:

(44) (1) Predict the thermal resistance value {circumflex over (x)}.sub.(k|k−1) of IGBT power module at time k from the optimal thermal resistance estimated value {circumflex over (x)}.sub.(k−1|k−1) of the IGBT power module at time (k−1):
{circumflex over (x)}.sub.(k|k−1)=F{circumflex over (x)}.sub.(k−1|k−1)+Gu.sub.k

(45) (2) Calculate the predicted value of the junction temperature of the IGBT power module at time k:
{circumflex over (T)}.sub.(k|k−1)=H{circumflex over (x)}.sub.(k|k−1)+Iu.sub.k

(46) (3) Measure the covariance P.sub.(k|k−1) at time k by the covariance P.sub.(k−1|k−1) between the observed value and the predicted value of the IGBT power module junction temperature at time (k−1):
P.sub.(k|k−1)=FP.sub.(k−1|k−1)F.sup.T+Q

(47) (4) Calculate the Kalman filter gain:
K.sub.(k)=P.sub.(k|k−1)H.sup.T[HP.sub.(k|k−1).sup.−1H.sup.T+R].sup.−1

(48) Specifically, K.sub.(k) represents the Kalman filter gain.

(49) (5) Calculate the optimal estimated value of the system:
{circumflex over (x)}.sub.(k|k)={circumflex over (x)}.sub.(k|k−1)+K.sub.(k)(T.sub.k−{circumflex over (T)}.sub.(k|k−1))

(50) Specifically, {circumflex over (x)}.sub.(k|k) represents the optimal estimated value of the thermal resistance of the IGBT power module at time k.

(51) (6) Update the inverse operation of the optimal junction temperature value of the IGBT power module in the next step at time (k+1), that is, update the covariance:
P.sub.(k|k)=[I−K.sub.(k)H]P.sub.(k|k−1)

(52) Specifically, P.sub.(k|k) represents the updated covariance after time k, and I represents the unity matrix.

(53) Return to step (1) from step (6), perform a loop until the final result achieves the desired effect.

(54) Table 1 compares the statistical error of estimated value of the junction temperature T.sub.j before and after the application of the Kalman filter, which fully demonstrates the superiority of the present invention.

(55) Table 1 statistical error of estimated value of the junction temperature T.sub.j before and after the application of the Kalman filter

(56) TABLE-US-00001 Average absolute error Standard deviation Before application 1.42 2.05 After application 0.76 0.61

(57) The equation for calculating the average absolute error is as follows:

(58) $\mathrm{MAE}=\frac{1}{N}\underset{t=1}{\overset{N}{.Math.}}.Math.x_t-y_t.Math.$

(59) The equation for calculating the standard deviation is as follows:

(60) $\sigma =\sqrt{\frac{1}{N}\underset{t=1}{\overset{N}{.Math.}}{\left(x_t-\mu \right)}^2}$

(61) In the above two equations, MAE represents the average absolute error; a represents the standard deviation; t represents the serial number of each estimated value of junction temperature; N represents the total number of estimated values of junction temperature; x.sub.t represents each estimated value of junction temperature; and y.sub.t represents each junction temperature value obtained through measurement by the infrared thermal imager; μ represents the average of N estimated values of junction temperature.

(62) It is apparent that the above-described embodiments are merely illustrative of the invention and are not intended to limit the embodiments of the invention. Other variations or modifications of the various forms may be made by those skilled in the art in light of the above description. Obvious changes or variations that come within the spirit of the invention are still within the scope of the invention.