Application of Kalman Filter to Estimate Junction Temperature in IGBT Power Modules

Knowledge of instantaneous junction temperature is essential for effective health management of power converters, enabling safe operation of the power semiconductors under all operating conditions. Methods based on fixed thermal models are typically unable to compensate for degradation of the thermal path resulting from aging and the effect of variable cooling conditions. Thermosensitive electrical parameters (TSEPs), on the other hand, can give an estimate of junction temperature TJ, but measurement inaccuracies and the masking effect of varying operating conditions can corrupt the estimate. This paper presents a robust and noninvasive real-time estimate of junction temperature that can provide enhanced accuracy under all operating and cooling conditions when compared to model-based or TSEP-based methods alone. The proposed method uses a Kalman filter to fuse the advantages of model-based estimates and an online measurement of TSEPs. Junction temperature measurements are obtained from an online measurement of the on-state voltage, VCE (ON), at high current and processed by a Kalman filter, which implements a predict-correct mechanism to generate an adaptive estimate of TJ. It is shown that the residual signal from the Kalman filter may be used to detect changes in thermal model parameters, thus allowing the assessment of thermal path degradation. The algorithm is implemented on a full-bridge inverter and the results verified with an IR camera.


Application of Kalman Filter to Estimate Junction
Temperature in IGBT Power Modules Mohd.Amir Eleffendi and C. Mark Johnson, Member, IEEE Abstract-Knowledge of instantaneous junction temperature is essential for effective health management of power converters, enabling safe operation of the power semiconductors under all operating conditions.Methods based on fixed thermal models are typically unable to compensate for degradation of the thermal path resulting from aging and the effect of variable cooling conditions.Thermosensitive electrical parameters (TSEPs), on the other hand, can give an estimate of junction temperature T J , but measurement inaccuracies and the masking effect of varying operating conditions can corrupt the estimate.This paper presents a robust and noninvasive real-time estimate of junction temperature that can provide enhanced accuracy under all operating and cooling conditions when compared to model-based or TSEP-based methods alone.The proposed method uses a Kalman filter to fuse the advantages of model-based estimates and an online measurement of TSEPs.Junction temperature measurements are obtained from an online measurement of the on-state voltage, V C E (O N ) , at high current and processed by a Kalman filter, which implements a predict-correct mechanism to generate an adaptive estimate of T J .It is shown that the residual signal from the Kalman filter may be used to detect changes in thermal model parameters, thus allowing the assessment of thermal path degradation.The algorithm is implemented on a full-bridge inverter and the results verified with an IR camera.

I. INTRODUCTION
P OWER converters that use insulated gate bipolar transistors (IGBT) modules are becoming more common in automotive and rail-traction applications where the combination of environmental and load-derived thermal cycling can result in large and unpredictable fluctuations in junction temperature [1].In renewable energy applications, the unpredictable mission profiles again result in large amplitude temperature cycles; for example, in the case of wind power turbines, thermal cycles emerge from variations of wind speed [2].In such conditions, the need for the knowledge of junction temperature becomes vital.In addition, there is a tradeoff between converter size and its heat transfer capabilities.Smaller sizes are desirable for reduced cost but have increased susceptibility to thermal cycling.Therefore, the knowledge of junction temperature becomes more important.
Accurate knowledge of junction temperature plays a major role in the control and health management algorithms, which have been recently proposed to monitor and extend the reliability of IGBT power modules under in-service conditions.Methods for implementing real-time health management for applications with uncertain mission profiles have been demonstrated [3], [4].These methods rely on estimates of the junction temperature profile and cycle-counting algorithms to yield equivalent thermal cycle parameters, which are then applied to lifetime reliability models.
Similarly, junction temperature can be used in the active thermal management algorithms to reduce the effects of thermal cycling in power modules and to improve reliability.Power dissipation can be controlled through regulating the current limit, switching frequency and dc-link voltage in a way that limits temperature variations [5]- [7].Dynamic cooling of power modules is another way to reduce temperature variations [8].
Real-time knowledge of junction temperature is vital for condition monitoring and prognostics of power converter since it can facilitate the identification of competing wear-out mechanisms [9].For example, in cases, where wire-bond lift-off and solder fatigue happen simultaneously, it is not clear whether changes in the on-state voltage are due to an increase in electrical resistance (wire bond lift) or an increase in thermal resistance (solder fatigue leading to increased temperature and changes in voltage).Therefore, knowledge of junction temperature is essential to discriminate between the thermal aging effects and the wire-bond failures [3].According to [10], the accuracy of the junction temperature estimate should be within 1 °C for successful application in condition monitoring.In addition, it is suggested in [11] that a continuous monitoring of junction temperature as a failure indicator is required to enable effective IGBT prognostics.An example of IGBT prognostic where junction temperature is required can be found in [12].
One way to obtain an online measurement of IGBT temperature is via integrated sensors.Two types of sensors are typically integrated into power modules, NTC resistors, and on-chip diodes.While NTC resistors are fixed on the DBC substrate and return baseplate temperature with a time constant in the range of few seconds [13], on-chip diodes are integrated within the IGBT chip itself and return the local chip temperature with a time constant of about 1 ms [14].Both types require special consideration during design and manufacturing process to ensure electrical isolation from HV traces on the substrate and require additional external pins and separate copper traces, which might increase manufacturing cost and give rise to new reliability issues.In the absence of direct measurements, RC equivalent thermal models can provide a simplified and efficient way to obtain junction temperature estimates for IGBT modules.Reduced order models of the thermal conduction path can be used to get an estimate of junction temperature in real time [15].However, even with accurate precharacterization of the junction-to-case thermal impedance, large uncertainties in the thermal interfacing and heat sink reduces the applicability of those models [16].Therefore, thermal characterization of the complete thermal path, by measuring junction-to-ambient thermal impedance, is often needed to achieve more accurate models.Furthermore, these models are generally defined under known boundary condition of a constant ambient or coolant temperature.Any variation in the coolant flow rate results in a variation in the heat transfer coefficient, and consequently, varies the thermal resistance of the heat sink [17].One solution is a multimodel approach, which considers the effect of variable cooling on the thermal impedance by generating multiple models for multiple cooling rates [18].This procedure complicates the modeling process and still cannot cope with degradation of the thermal path.
The aging effect of power modules reduces model validity over time, for example, where gradual degradation of the thermal path due to solder fatigue increases thermal resistance [19].Therefore, adaptive thermal models were proposed to quantify the change in the thermal resistance and update model parameters accordingly [20], [21].Nonetheless, those models suffer some drawbacks: the method described in [20] requires modification of gate drive to extend the turn-on time of the semiconductor to allow making online measurement of threshold voltage, whereas the method in [21] is intrusive and requires temperature sensors positioned on the baseplate to detect the change of temperature nonuniformity and is highly sensitive to the locations of those sensors.
In this paper, a real-time, noninvasive method to estimate the junction temperature (T J ) of IGBT power modules is proposed, which combines measurements of a temperature sensitive parameter with a thermal model.The approach is shown in Fig. 1 is based on the external measurement of the on-state voltage V CE(ON) , at high current, without the need to modify the gate drive circuit or disturb the normal switching cycles of the IGBT.The V CE(ON) measurement is translated into a junction temperature measurement T J using a look-up table.The resulting T J measurement can be very noisy due to V CE(ON) measurement inaccuracies and the low sensitivity of V CE(ON) to temperature.Therefore, a Kalman filter is introduced to improve accuracy and eliminate noise and intermittency in the T J measurement.The Kalman filter [22] is a model-based approach that uses a thermal model of the heat conduction path to process the T J measurements resulting from V CE(ON) .A power loss model, based on the measured current, is used to calculate power dissipation, which is then used as an input to the Kalman filter.The adaptive property of Kalman filter allows consistent and accurate estimates of junction temperature to be obtained in the presence of aging effects and variable cooling conditions.In addition, examination of the residual error allows the quality of the estimate to be assessed and provides a mechanism for detecting changes in the thermal path.A simulation study of the proposed method was presented previously in [23].This paper presents the practical implementation and experimental verification of the proposed method for multichip IGBT modules.In Section II, the measurement circuit of V CE(ON) for T J measurement is presented.Section III introduces the development of the state-space thermal model.Section IV explains the algorithm of Kalman filter.Test setup and experimental results are presented in Section V. Conclusion is in Section VI.

II. USING THERMOSENSITIVE ELECTRICAL PARAMETERS
TO ESTIMATE JUNCTION TEMPERATURE Many recent researches focused on the online measurement of thermosensitive electrical parameters (TSEPs) to resolve temperature information during converter operation.IGBTTSEPs such as on-state voltage V CE(ON) [24], threshold voltage V TH [25], and gate resistance R G [26] and turn-off timing [27] can be used to estimate junction temperature in real time.Resolving T J information from TSEPs can be challenging due to the low sensitivity of those TSEPs to T J and their dependence on the loading conditions of power converters.In addition, the harsh working environment of power modules adds lot of inaccuracies to the measurement.Those inaccuracies originate from the switching and modulation signals and the EMI from the environment, which increases error margins in the resulting T J measurement [9].In addition, some TSEPs are affected by the progressive degradation of power modules.For example, onstate voltage V CE(ON) is affected by wire-bond liftoff.The loss of wire-bond shifts up the value of V CE(ON) as a result of electrical resistance increment [28], which can lead to large errors in the measured T J using that TSEP.In this paper, the on-state voltage V CE(ON) is used to get T J measurements during normal operation of the power converter.

A. Temperature Dependence of the On-State Voltage V CE(ON)
The relationship of V CE(ON) to temperature is dependent on current and has a nonlinear temperature coefficient.Fig. 2 shows the I-V characteristic of 1.2-kV/400-A IGBT module at multiple temperatures, which describes that relationship.It is clear that the temperature coefficient of V CE(ON) is a function of current, where at low currents, V CE(ON) has a negative temperature coefficient, and at high currents, it has a positive temperature coefficient.The point where temperature coefficient changes  sign is the inflection point and here V CE(ON) becomes independent of temperature.For the example module under test, the negative temperature coefficient of V CE(ON) below inflection point is found to have a maximum value of 1.23 mV/°C at 8 A, which decreases in magnitude toward inflection point.Above that point temperature coefficient becomes positive and increases with current to reach 2.68 mV/°C at 180 A.

B. Online Measurement of the On-State Voltage V CE(ON)
Online measurement of the on-state voltage V CE(ON) for temperature measurement, during normal operation of power converters, can be a challenge.The voltage across the IGBT device has a wide dynamic range (between dc-link voltage and onstate voltage) and must be captured with millivolt.Precise timing, synchronized to the device switching instants, is required in order to capture a consistent representation of V CE(ON) .In addition, electrical isolation is required between power converter and the processing end point.Therefore, a dedicated measurement circuit is developed to meet these requirements.Fig. 2 shows a schematic of the measurement circuit.The voltage dividers R1-R2 and R3-R4 scale down V CE voltage to the acceptable range of the U1 inputs.The op-amp U1 is a precision amplifier in a differential configuration.During the off-state of the IGBT V CE voltage equals V DC and the output of the U1 is saturated.However, no measurement is required during IGBT off-state.U1 has a short recovery time so that when the IGBT switches ON, it recovers from saturation and settles to the value of V CE(ON) .U1 inputs are protected by ESD diodes against high-voltage spikes.Capacitors in parallel to the resistors R1-R4 can be used to improve the frequency response of the voltage dividers if  necessary.The falling edge detector compares the output of U1 with a predefined voltage to detect the falling edge of V CE and triggers the monostable multivibrator to enable the sampling circuit after a 100 μs of the trigger giving sufficient time for V CE to stabilize.This delay time can be tuned by choosing the appropriate values for the multivibrator components.The capacitive isolation is achieved using an isolation amplifier where the sampled signal is modulated using a high frequency signal and is sent through the isolation barrier (capacitors).It is then demodulated at the other end and the original signal is recovered.A 16-bit analog-to-digital converter (ADC) with a range of ±5 V is used to acquire V CE(ON) value at the measurement side, which gives a resolution of 0.15 mV.
Every switching cycle, a single sample is captured and held until the next switching cycle.The operation of the circuit is depicted in Fig. 4 where the output of the differential amplifier U1 and the sample and hold signal S/H is shown.The circuit is verified in a full-bridge inverter, where it is connected to the power terminals of the high-side device.Fig. 5 shows the load current signal and the correspondingly measured V CE(ON) signal.

III. DEVELOPMENT OF A STATE-SPACE THERMAL MODEL
Typically, a power module includes a combination of IGBTs and diodes, which form multiple heat sources that contribute to the total heat generation in a module.Fig. 6 shows the halfbridge power module used in this study, where four IGBTs and two free-wheeling diodes are connected in parallel on each substrate tile.The temperature of IGBTs on a single substrate tile is affected by the adjacent diodes on same substrate tile and by the chips on the other substrate tile.In this paper, the cross coupling between diodes and IGBTs on the same substrate tile is considered in the modeling process, whereas the relatively small cross coupling between the two substrate tiles is ignored.

A. Modeling the Self-Heating of the IGBT
The thermal path between the semiconductor chip in a power module and the convective surface of the heat sink consists of a stack of layers of different materials as shown in Fig. 7(a).This thermal path can be characterized by the junction-to-ambient thermal impedance Z θj a (t) which is defined as the step response of the junction temperature to a power input.It is described by the ratio of the difference between the junction temperature T j (t) and a constant ambient temperature T a to the step power input P D .
Z θj a (t) = (T j (t) − T a ) /P D . ( An electrical equivalent RC network can be used to describe this function Z θj a (t) with a number of RC elements, forming a Foster network as shown in Fig. 7(b).The time response of the Foster network is described by a series of exponential terms of the following form: ( Taking the Laplace transformation of (2) gives the partial fraction expansion form of the transfer function of the thermal impedance in the frequency domain.
where k i and p i are the residues and poles of the transfer function, respectively, and s is the complex variable.By algebraic manipulation, it can be found that poles and residues are related to the RC components by the following formulas: It should be noted that these RC elements have no correlation to the physical nature of the thermal path because a Foster network is only a behavioral model of the thermal system [29].The partial fraction expansion form in (3) can be easily transferred into a state-space model of the parallel form with a diagonal system matrix, where the poles p i form the elements of the main diagonal while the residues k i form the elements of the input matrix [30].The resulting state-space representation for a Foster  network thermal model is where A n×n is the system matrix, B n×2 is the input matrix, C l×n is the output matrix, and D 1×2 is the feed-forward matrix.The state vector x(t) represents the differential temperatures across RC elements, u(t) = [P D (t), T a ] is the system input vector, where P D (t) is the power dissipation and T a is the ambient temperature.The output equation gives the junction temperature T J (t), which is the total sum of system states and the constant ambient temperature.According to [15], the ambient temperature can be considered additive to the output when the variations in the ambient temperature is slow in comparison to the slowest dynamics in thermal system.

B. Modeling the Diode Cross-Coupling Effect
By accepting negative values of RC components, the Foster network in Fig. 7(b) can be used to model the cross-coupling effect [31].Therefore, the state-space model in ( 5) is suitable to represent both the self-heating and cross-coupling thermal impedances individually.
Therefore, an extended model that represents both impedances can be constructed by combining a state-space model of order n for the self-heating impedance with a model of order m for the cross-coupling impedance.This results in a model that describes the thermal behavior of the IGBT dies on one substrate tile.A similar modeling procedure can be used to construct a model for the diode junction temperature.But for simplicity, only the junction temperature of the IGBT is considered here.The complete state-space model description for IGBT junction temperature becomes  where x s1 , . . ., x sn are the states of the self-heating impedance, and p s1 , . . ., p sn and k s1 , . . ., k sn are the poles and residues of the self-heating impedance, respectively.Similarly, x c1 , . . ., x cm are the states of the cross-coupling impedance, whereas p c1 , . . ., p cm and k c1 , . . ., k cm are the poles and residues of the self-heating impedance, respectively.T J is the IGBT junction temperature.T a is the ambient temperature, P IGBT and P Diode are the power dissipation of the IGBT and diode, respectively.

C. Identification of Model Parameters
Fig. 8 shows the measured self-heating and cross-coupling junction-to-ambient thermal impedance curves for one side of the half-bridge module.Thermal impedance curves were obtained by measuring the cooling curve of the IGBT using the voltage drop V CE across the IGBT at a current of 40 mA as a TSEP.A calibrated relationship T j = f (V CE ) is then used to convert the voltage into a temperature measurement.The thermal propagation time which is the time necessary for the heat generated by the diodes to reach the adjacent IGBTs is about 0.1 s as it is seen on the diode cross-coupling impedance.
It is found that a fourth order model is a good approximation for both self-heating and cross-coupling impedances.By least-square fitting of (2) to the measured data shown in Fig. 8, the RC component values are determined.The resulting fitting parameters are shown in Table I.

IV. FORMULATION OF KALMAN FILTER
A Kalman filter is a model-based state estimator, which estimates the temperature of an IGBT utilizing a linear model of thermal path given inaccurate power dissipation as an input and an inaccurate measurement of junction temperature.The continuous state-space model in ( 6) is first discretized with a time step t s using the Euler backward method, resulting in a discrete state-space model with a time step k and F and G as the state transition matrix and input matrix respectively.Then, a process noise w k and a measurement noise v k are added to the model to account for inaccuracies in modeling, power dissipation, and measurement signal.Noise terms are assumed to be uncorrelated white Gaussian noise with known covariances Q and R for process and measurement noise, respectively, whereas H is the process noise gain matrix.The resulting discrete model is written as The Kalman filter works in two recursive predict-correct steps in order to minimize the mean squared error of the estimate.In the prediction step, the model is used to calculate the predicted states x− k using the present calculated power dissipation u k and the corrected states x+ k −1 from the previous step.The predicted error covariance P − k is calculated as well.When a measurement T k becomes available, the correction step is implemented and the residual e k is obtained by the difference between the measurement T k and the estimate Tk .The corrected state x+ k is calculated by updating the predicted state with the residual e k using the calculated Kalman gain matrix K k .This process is depicted by the following relationships, which explain the recursive implementation of algorithm.Predict Correct The filter is tuned by varying Q and R to get the best performance [22].The parameter a in (15) takes the value 1 when a measurement T k is available otherwise it takes the value 0. That makes the corrected state x+ k equal to the predicted state x− k and ensures the continuity of the estimate in the absence of the measurement, which is the case when the IGBT is not conducting.In other words, during the availability of the T k measurement both predict and correct steps are implemented, otherwise only the predict step is carried out as depicted in Fig. 9.

A. Power Loss Calculation
Kalman filter requires an input of the IGBT and diode power dissipation.The total power dissipation of the IGBT P IGBT is the summation of conduction loss P cond and switching loss P sw , where the conduction loss is calculated by the multiplication of loading current I L and the on-state voltage V CE(ON) .The switching loss consists of turn-on and turn-off losses represented by E on and E off , respectively, and f sw is the switching frequency [32].The power loss is calculated according to the following formulas: A look-up table is used to calculate the switching losses, utilizing the load current, dc-link voltage V DC , and the junction temperature.Fig. 10 shows the look-up table for the IGBT switching losses P sw at a constant V DC = 100 V. Similarly, the power dissipation of the diode P DIODE , consisting of conduction loss and reverse recovery loss, is calculated using another look-up table.

B. T J Measurement Signal
The measurement of T J obtained from V CE(ON) constitutes the measurement signal of Kalman filter.This measurement as explained in Section II can be informative only above a certain current level [24].Therefore, the measurement signal becomes intermittent if current level varies over a wide range as is typical in an inverter.A look-up table is used to replicate the I-V characteristic of the IGBT.The data for the look-up table are collected by a curve tracer and the realization of the look-up table is shown in Fig. 11.It is this look-up table used to obtain T J measurement utilizing the measurement circuit explained in Section II.

V. EXPERIMENTAL VERIFICATION
Experimental verification of the algorithm is performed on a full-bridge inverter with the junction temperature of the highside IGBT in one half bridge.The system utilizes two 1.2-kV/400-A half-bridge IGBT power modules.The modules are uncovered and sprayed in black to allow thermal imaging with an infrared camera for verification.The modules are fixed on a copper water cooled heat sink and are connected to an inductive load of 300 μH.A current transducer is used to measure the load current and the on-state voltage is measured using the circuit described in Section II, which is connected to the power terminals of the high side IGBT.The measurement circuit is connected to a dSPACE digital system, which utilizes a 16-bit ADC with a range of ±5 V provides a resolution of 0.1 mV for V CE(ON) measurement.The load current is controlled by a PI current controller, which, along with the Kalman filter and PWM generator, is implemented on the dSPACE system.A unipolar switching scheme is used to generate a 3-kHz PWM switching signals taking into consideration the blanking time required to prevent short circuiting of upper and lower devices, which is about t B = 0.1 μs.A combination of optical and capacitive isolation ensures a complete electrical isolation between the inverter and the digital system.The inverter test rig is shown in Fig. 12 and a block diagram of the setup is shown in Fig. 13.For experimental verification of junction temperature estimate, it is necessary to understand the representative temperature estimated by V CE(ON) .In [33], it is found that the temperature measured by the voltage drop V CE represents a weighted average of chip temperatures where the weighting vector is proportional to the current density such that areas on the chip with the highest current density and highest temperature dominate the measurement of V CE .Similarly, in [34], it is reported that the voltage drop across multiple paralleled IGBTs operating at different temperatures is a temperature weighted average with the hottest chip being the most influential.
Therefore, the maximum temperature among the monitored IGBTs is selected for comparison.An infrared camera with an accuracy of ±1 °C and a sampling frequency of 50 Hz is used to measure the temperature at the top surface of the IGBTs during inverter operation.Fig. 14 shows the thermal image of the monitored IGBTs of the high side of one leg in the inverter.The maximum temperature on each chip is found by examining the temperature profile across the chip diagonal, and then, the maximum temperature among the chips is chosen for comparison.

A. Verification of T J Measurement Obtained From V CE(ON)
As explained in the previous section, the measurement of V CE(ON) can be translated into a measurement of T J utilizing a look-up table and the load current.Fig. 15 shows the measurement of T J obtained from the on-state voltage V CE(ON)  compared to the IR camera measurement along with the corresponding sinusoidal load current and on-state voltage.It is obvious that T J measurement has a large spread due to measurement noise inherited from V CE(ON) , which is estimated to be 14 mVpp.The intermittency that disturbs the continuity of the T J measurement signal in comparison to IR measurement happens when the current changes direction and when the current value goes below a specific limit, in this case, about 80 A.

B. Verification of Kalman Filter Estimate of Junction Temperature
Fig. 16(a) shows the T J estimate given by the Kalman filter in comparison to the IR camera measurement and the T J measurement obtained from V CE(ON) .It is evident that the estimate of T J given by the Kalman filter tracks the IR camera measurement accurately during both heating and cooling regimes with a maximum error of 3.4%.The error between the T J estimate and the IR camera measurement is shown in Fig. 16(b).The difference between the two signals at the peaks of temperature  profile which is about 1.3 °C can be attributed to many factors.First, the IR camera measures the temperature at the top surface of the IGBT, whereas V CE(ON) indicates the temperature at the intrinsic body region buried inside the IGBT.Second, the presence of the wire-bonds on the top of the chip prevents the IR camera from obtaining the maximum temperature due to the shading effect and the measured temperature could, therefore, be lower than reality [35].In addition, calibration of look-up table is done under isothermal conditions, while in practice, there are temperature gradients across the module.Since V CE(ON) is measured across the power terminals, the measurement includes the voltage drop across the packaging resistance, which is affected by temperature gradients.This results in a mismatch with the calibration.On the other hand, the difference between IR camera and T J estimate in the cooling regime, which shows a maximum of 1.5 °C, is justified by the fact that no V CE(ON) data are available for T J measurement and the correction step of the Kalman filter implementation is not carried out.As a result, Fig. 18.IR camera measurement and T J estimate when modulation frequency is changed from 0.5 to 1 Hz as can be seen in the load current.
the estimate in this regime is purely dependent on the thermal model.The difference is then linked to errors inherited from the modeling process.
Compared to the T J measurement, the estimate is noise free and continuity of the signal is preserved.To evaluate the improvement in the T J estimate over the T J measurement, the mean absolute error (MAE) and standard deviation (σ) of the error is examined.The errors of the T J estimate and the T J measurement are acquired by subtracting the T J estimate and the T J measurement from the IR camera measurement.Table II shows the statistics of the two error signals.It is evident that the accuracy of T J estimate has improved compared to T J measurement obtained by V CE(ON) with 53% less MAE and 30% less spread.
Inverter modulation frequency and amplitude both affect the junction temperature response.To demonstrate the consistency of the T J estimate under variable operating conditions, the load current is varied in the inverter.Fig. 18 shows the T J estimate response at the instant when the modulation frequency changes from 0.5 to 1 Hz with constant amplitude 150 A. The agreement of the T J estimate with the IR camera measurements is maintained.It is seen that the ripple ΔT in T J is reduced when the frequency is increased whereas the mean temperature T m is nearly constant in agreement with IR camera measurement as can be seen in Table III.This is to be expected since the frequency response of the thermal system replicates a low-pass filter.
Fig. 17 shows T J estimate when current amplitude is increased from 120 to 160 A with a modulation frequency of 0.5 Hz.The increment in the mean temperature and the ripple is evident in Table IV for both IR measurement and T J estimate.

C. T J Estimate Under Unstable Boundary Condition
As discussed before, large variations in heat transfer coefficient can result from deviations of coolant flow rate.For examination of these effects on the T J estimate, the water flow in the heat sink is blocked completely by switching the water pump OFF during inverter operation.Water blockage prevents heat removal by convection at the baseplate and increases the thermal resistance of the heat sink [17].Fig. 19(a) shows the T J estimate compared to the IR camera measurement along with the baseplate temperature T C in Fig. 19(b) when the water pump is stopped after reaching thermal equilibrium.The baseplate temperature T C is measured with a thermocouple fixed to the back side of the baseplate facing the coolant.The water pump is stopped for 84 s, where upon the peak junction, temperature increases from 42 to 58 °C, whereas the baseplate temperature increases correspondingly from 32 to 43 °C.The pump is turned ON again and T J goes down back to 43 °C after 52 s in good agreement with IR camera measurement, whereas T C falls back to 32 °C.
The difference between the IR camera measurements and the T J estimate is shown in Fig. 19(c).A gradual increment in error margins during the transient state with a slight shift in the mean value can be clearly seen.However, regardless of the growing error, which remains within 3.6%, the adaptive property of Kalman filter preserves estimate consistency and robustness by the predict-correct mechanism.The T J measurement derived from V CE(ON) is utilized to update the T J estimate and keep it in track with the true value obtained from the IR camera as can be seen from Fig. 19(a).

D. Detecting Thermal Resistance Change Using the Residual Signal
The growing error in Fig. 19(c) is justified by the degraded performance of the Kalman filter due to changes in the thermal model parameters.As water flow rate is brought down to zero, the convective coefficient of heat transfer in the heat sink  decreases, which increases the thermal resistance of the heat sink.As a consequence, the junction-to-ambient thermal impedance modeled by the RC network is no longer valid.The degraded performance can be quantified by the examination of the estimate residual produced by the Kalman filter [36], where the residual is the difference between the T J estimate and the T J measurement derived from V CE(ON) .Fig. 20 shows the statistical distribution of the normalized residual before and after the pump shutdown.It is evident that the statistical distribution of the residual exhibits a change when the thermal system is altered.Fig. 21 shows the time evolution of residual mean value, which ramps up from −0.515 to 0.06 following the change in the thermal resistance of the heat sink, and then, falls back to its original value when water flows again in the heat sink.The initial value of the residual mean −0.515 indicates an initial mismatch between the thermal model and the real thermal path, which can be a result of modeling errors.The negative sign indicates that the model underestimates the junction temperature, which is corrected by the Kalman filter.
Degradation of the thermal path increases the residual mean indicating an increased thermal resistance.This correlation between the residual mean and the thermal resistance enables using the residual as a failure indictor of the thermal path.It allows monitoring the state of the thermal path to detect any increment in thermal resistance that might result from solder fatigue.Residual evaluation can be achieved by statistical classification and machine learning methods.Learning the behavior of the residual signal under different healthy and faulty conditions can enable the decision-making process about an ongoing degradation, which can trigger an alarm indicating a potential failure.It is important for the residual evaluation method to provide a reliable and fast detection of any deviation in the residual from its healthy conditions.
Since the residual signal is indicative of a mismatch between the thermal model and the measurement different reasons can cause it to deviate from its original characteristic: a change in the thermal impedance Z θj a or a change in the measurement signal of V CE(ON) due to measurement circuit malfunction or wire-bond liftoff.
Wire-bond liftoffs can lead to wrong estimate of T J since V CE(ON) will deviate from its normal value as a result of wirebond liftoff.However, this can still be detected by the evaluation of the residual signal.Alternatively, an alternative TSEP, which is not affected by wire-bond liftoffs such as threshold voltage (V th ) can be used instead of V CE(ON) .Nevertheless, it is required to obtain more measurements from the IGBT in order to enable more efficient diagnosis of system failures and identify the true reason behind a change in residual characteristic.

VI. CONCLUSION
The instantaneous junction temperature of an IGBT power module is estimated in real time.Online measurements of the on-state voltage V CE(ON) , obtained at high current during normal operation of power converter, are used as a TSEP to get a measurement of T J .No modification of the control strategy of the power converter is necessary to make the measurement.A Kalman filter is then applied to the resulting T J measurement to reduce noise and eliminate the effects of intermittency of the V CE(ON) measurement by constraining the measurement signal to a thermal model in a predict-correct manner.A statespace representation of the thermal model is developed to derive a Kalman filter utilizing the junction-to-ambient thermal impedance measurement of IGBT self-heating and diode cross coupling.The proposed method is implemented on a full-bridge inverter and is verified with an IR camera measurement of the IGBT module during normal operation of the inverter.Excellent matching is achieved between the T J estimate and the IR camera measurement under different loading and cooling conditions, demonstrating the ability of the method to adapt to variations in the operating conditions of power converter.An improved accuracy is obtained by the Kalman filter compared to T J measurement obtained by V CE(ON) alone.The use of the residual signal to detect a change in the thermal resistance is demonstrated, which offers a potential means to monitor the gradual degradation in the thermal path, for example, due to solder fatigue.This method can form part of a real-time health management or active control system for power converters and can be easily integrated within existing power converter control elements.

Fig. 1 .
Fig. 1.Block diagram of the complete method for IGBT junction temperature estimation.

Fig. 2 .
Fig. 2. Schematic of the online measurement circuit of V C E (O N ) .

Fig. 3 .
Fig. 3. Operating signals of V C E (O N ) measuement circuit.(a) Output of the differential amplifier U1 where V H U 1 is the saturation voltage of the op-amp.(b) Sample and hold signal used to capture V C E (O N ) value where t d is delay time between V C E falling edge and sampling instant.

Fig. 4 .
Fig. 4. I-V characteristic of a 1.2-kV/400-A IGBT power module at multiple temperatures explains temperature dependence of the on-state voltage V C E (O N ) .

Fig. 5 .
Fig. 5. Online measurement of load current and V C E (O N ) during inverter operation.

Fig. 6
Fig. 6. 1.2-kV/400-A half-bridge power module used in the test.Each substrate tile contains four IGBTs and two freewheeling diodes.

Fig. 7 .
Fig. 7. (a) Multilayered structure of the thermal path of a power module.(b) Electrical equivalent Foster model of a thermal path.

Fig. 9 .
Fig. 9. Sequence of Kalman filter predict and correct steps is dependent of the availability of T k measurement.

Fig. 10 .
Fig. 10.Switching power loss model of the IGBT at V D C = 100 V.

Fig. 11 .
Fig. 11.Look-up table used to get T J using measurement of V C E (O N ) and current.

Fig. 12 .
Fig. 12. Image of the full-bridge inverter showing the power modules, gate drives, current sensor, and V C E (O N ) measurement circuit.

Fig. 13 .
Fig. 13.Block diagram of the experimental setup used for algorithm verification.A full-bridge inverter is controlled by a digital system.

Fig. 14 .
Fig. 14.Thermal image of the high-side IGBT during inverter operation.

Fig. 15
Fig. 15 Online measurements of load current I L , V C E (O N ) , and T J measurement compared to IR camera measurement.

Fig. 16 (
Fig. 16 (a) Kalman estimate of junction temperate compared to IR camera measurement and T J measurement by V C E (O N ) .(b) Difference between IR camera measurement and T J estimate.

Fig. 17 .
Fig.17.IR camera measurement and T J estimate when current amplitude is changed from 120 to 160 A as can be seen in the load current.

Fig. 19 .
Fig. 19.(a) IR camera measurement and T J estimate over the duration of water flow blockage.(b) Corresponding baseplate temperature T C .(c) Difference between IR camera measurement and T J estimate.

Fig. 20 .
Fig. 20.Statistical distribution of the residual clearly indicates a change in thermal system parameters as R th increases after water pump is stopped.

Fig. 21 .
Fig. 21.Time evolution of the mean value of the residual follows the direction of the change in thermal resistance.This can be used as a failure indicator for thermal path degradation.

TABLE I IDENTIFIED
THERMAL MODEL PARAMETERS

TABLE II ERROR
STATISTICS OF T J MEASUREMENT AND T J ESTIMATE

TABLE III T
J PROFILE PARAMETERS FOR IR CAMERA AND T J ESTIMATE UNDER A CHANGE IN MODULATION FREQUENCY

TABLE IV T
J PROFILE PARAMETERS FOR IR CAMERA AND T J ESTIMATE UNDER A CHANGE IN CURRENT AMPLITUDE