Silicon carbide power device junction temperature online accurate extraction method based on double-sensor Kalman filtering weighted average algorithm

Abstract

The invention discloses a silicon carbide power device junction temperature online accurate extraction method based on a double-sensor Kalman filtering weighted average algorithm, and the method comprises the following steps: 1, enabling a loss model of a power device to receive the phase current, the DC bus voltage, the duty ratio, the phase current and the DC bus voltage from an inverter; the on resistance of the SIC MOSFET, the reference direct current bus voltage, the on loss energy and the off loss energy under the on current and the on threshold voltage of the Schottky diode are obtained from a data manual of the chip, and the gate driving resistor is used for extracting the junction temperature and monitoring operation in real time; and step 2, obtaining an estimated junction temperature through loss calculation of a power device and a thermal network model, and weighting the junction temperatures estimated at different measurement points through a Kalman filtering weighted average algorithm to obtain a more accurate junction temperature for next iterative calculation. According to the method, the limitation of a traditional single sensor in a dynamic working environment can be effectively compensated, and the accuracy and the real-time performance of junction temperature monitoring are improved.

Description

Technical Field

[0001] This invention relates to a method for extracting the junction temperature of silicon carbide power devices, specifically a method for online and accurate extraction of the junction temperature of silicon carbide power devices based on a dual-sensor Kalman filter weighted average algorithm. Background Technology

[0002] Silicon carbide (SiC) power devices, as important semiconductor devices in the current power electronics field, are widely used in power conversion systems under high-frequency, high-power, and high-temperature environments due to their high breakdown voltage, high-frequency response, low conduction loss, and excellent thermal stability. With the increasing demand for high power density and energy conservation in power electronic devices, SiC power devices have increasingly broad application prospects in smart grids, renewable energy, and electric vehicles. However, in these high-power-density application environments, junction temperature control of SiC power devices remains one of the core factors affecting their reliability and lifespan.

[0003] SiC power devices generate a significant amount of heat during operation. Excessive junction temperature can lead to performance degradation, accelerated aging, and even device failure. Therefore, accurate junction temperature monitoring and thermal management are essential for ensuring the normal operation of SiC power devices and extending their lifespan. Existing junction temperature monitoring technologies typically employ temperature sensors, thermal network models, and transient thermal impedance index fitting methods. While each method has its advantages and disadvantages, they still have many limitations in practical applications, necessitating the search for more accurate and reliable solutions.

[0004] Currently, junction temperature monitoring technology based on temperature sensors faces the following bottlenecks:

[0005] 1. While the built-in NTC temperature sensor can provide some temperature data, its measurement is usually limited to the case temperature and cannot accurately reflect the junction temperature inside the SiC power device. Because the performance of SiC power devices changes significantly at high temperatures, relying solely on surface temperature is insufficient to effectively determine the junction temperature state, leading to inaccurate monitoring.

[0006] 2. Existing thermal network models suffer from parameter deviations due to changes in the operating environment and device aging when using standardized thermal impedance parameters. This makes it impossible for the thermal impedance model to accurately estimate the junction temperature, resulting in measurement errors.

[0007] 3. While finite element method-based thermal analysis can provide relatively accurate junction temperature calculations, its calculation process is complex and resource-intensive, making it difficult to meet the needs of real-time online monitoring. In particular, for the dynamic changes of SiC power devices in practical applications, there is a lack of an efficient real-time correction scheme for junction temperature estimation errors. Summary of the Invention

[0008] To address the measurement errors that may arise from using a single sensor in dynamic environments in traditional junction temperature extraction methods, this invention provides an online accurate junction temperature extraction method for silicon carbide power devices based on a dual-sensor Kalman filter weighted averaging algorithm. This method proposes a dual-sensor Kalman filter weighted averaging algorithm that combines data from an external thermocouple sensor and a built-in NTC temperature sensor to accurately estimate the junction temperature of SiC power devices. By fusing the data from both types of sensors in real time and combining a thermal network model and transient thermal impedance index fitting, a high-precision junction temperature estimation method is formed. This method effectively compensates for the limitations of traditional single sensors in dynamic operating environments, improves the accuracy and real-time performance of junction temperature monitoring, and further enhances the operational stability and reliability of SiC power devices.

[0009] The objective of this invention is achieved through the following technical solution:

[0010] A method for online accurate extraction of junction temperature of silicon carbide power devices based on a dual-sensor Kalman filter weighted averaging algorithm includes the following steps:

[0011] Step 1: The power device loss model receives the phase current, DC bus voltage, and duty cycle from the inverter, and obtains the on-resistance, on-state loss energy and off-state loss energy of the SiC MOSFET under the reference DC bus voltage and on-state current from the chip's datasheet, as well as the on-threshold voltage and gate drive resistance of the Schottky-Barrier Diode (SBD) for junction temperature extraction and real-time monitoring operation.

[0012] Step 2: The estimated junction temperature is obtained through power device loss calculation and thermal network model. Then, using a Kalman filter weighted averaging algorithm, the estimated junction temperatures from different measurement points are weighted to obtain a more accurate junction temperature for the next iteration calculation. The specific steps are as follows:

[0013] Step Two: Calculation of power device losses.

[0014] During inverter operation, the current flowing through S1 and VD1 is expressed as follows:

[0015]

[0016]

[0017]

[0018] In the formula, Is is the on-state current of the power device, I a Ivd is the phase current, and Rs and R are the on-state currents of VD1. VD The on-resistances of S1 and VD1 are respectively, V VD(TH)S1 is the turn-on threshold voltage of VD1, S1 is a SiC MOSFET, and VD1 is a Schottky diode;

[0019] Further calculations were performed to determine the conduction loss P of the SiC MOSFET during one switching cycle. S-CON With switching loss P S-SW :

[0020]

[0021]

[0022]

[0023] In the formula, I S (t) and I S (t+NT S T represents the current flowing through SiC sampled at the beginning and end of the cycle. S For the switching period, D1 and D N These represent the duty cycles of the first and last periods, R. S E is the on-resistance of SiC. SW (t) and E SW (t+NT S E represents the sum of the turn-on and turn-off energies of SiC at the beginning and end of the cycle, respectively. on(ref) and E off(ref) For SiC datasheets, select the collector current I ref Reference DC bus voltage V dc(ref) and reference junction temperature T ref The on and off energy, V dc(t) Here, a, b, and c represent the DC bus voltage, and T represents the temperature fitting coefficients. j For the junction temperature;

[0024] SBD conduction loss P in one switching cycle VD for:

[0025]

[0026] The sum of the conduction loss and switching loss of the power device, P total for:

[0027]

[0028] Step 22: Building the thermal network model:

[0029] Based on the principle of heat transfer, a Foster thermal network model of the SiC power device based on the junction temperature measured by a temperature sensor is drawn. Its mathematical model is as follows:

[0030]

[0031] In the formula, T j (t) represents the transient junction temperature, T c For ambient temperature, Z j-c The thermal impedance from the SiC chip to the casing of the power device is calculated. The thermal impedance parameters are fitted using the transient thermal impedance exponential fitting method. The fitting model is as follows:

[0032]

[0033] In the formula, t represents time, and n represents the order of the thermal network model. =R i C i R i C i These are the thermal resistance and heat capacity for each order, respectively;

[0034] Steps 2 and 3: Dual-sensor thermal network modeling and junction temperature estimation:

[0035] A dual-sensor temperature estimation structure is constructed based on an external thermocouple and an internal NTC temperature sensor of a SiC power device module. Two thermal impedance modeling paths are established to achieve junction temperature estimation. Specifically, the case temperature signal acquired by the thermocouple is combined with the heat conduction structure to establish a Foster-type thermal network model 1, thereby estimating the chip junction temperature T. j1 Using the internal temperature signal of the module collected by the NTC temperature sensor, and combining it with its heat conduction path, a Foster-type thermal network model 2 was established to estimate the chip junction temperature T. j2 ;

[0036] Step 2.4: Junction temperature estimation and fusion for junction temperature correction:

[0037] By combining Foster-type thermal network model 1 and Foster-type thermal network model 2 with the loss analysis model, junction temperature data observed through different paths are obtained. These data are then treated as data measured by different sensors and input into a Kalman filter weighted averaging algorithm for junction temperature correction. The specific steps are as follows:

[0038] The junction temperature T calculated using Foster-type thermal network model 1 and Foster-type thermal network model 2 j1 and T j2 The thermal impedance parameter Z was obtained through experiments. j-c The process noise covariance matrix Q, measurement noise covariance matrix R, state transition matrix F, and measurement matrix H are used to correct the chip junction temperature T by applying a Kalman filter weighted averaging algorithm. j To compensate for junction temperature deviation, its mathematical model is as follows:

[0039] Select state variables:

[0040]

[0041] In the formula, T j (k) is the estimated junction temperature. This represents the rate of change of junction temperature.

[0042] The state equation is:

[0043]

[0044] In the formula, f(x(k-1),u(k)) is a nonlinear function describing the junction temperature change, u(k) is the external input, and w(k) is the process noise;

[0045] After Taylor unfolds:

[0046]

[0047] In the formula, F(k) is the Jacobian matrix of the current state versus the state at the previous time step;

[0048] The measurement equation is:

[0049]

[0050]

[0051] In the formula, h1(x(k)) and h2(x(k)) are the nonlinear measurement functions of the internal and external temperature sensors, and v1(k) and v2(k) are the measurement noise;

[0052] The Kalman filter gain is:

[0053]

[0054] In the formula, P - H(k) is the prediction error covariance matrix, H(k) is the Jacobian matrix of the measurement matrix, and R(k) is the measurement noise covariance matrix.

[0055] Update status:

[0056]

[0057] In the formula, x - (k) represents the predicted state, y(k) represents the measured value, and h(x) represents the predicted state. - (k) represents the predicted value of the measurement function;

[0058] Update error covariance:

[0059]

[0060] In the formula, P(k) is the error covariance;

[0061] Weighted average algorithm:

[0062]

[0063] In the formula, The junction temperatures observed by sensors 1 and 2 are Kalman filtered, with α representing the weights, where 0 < α < 1.

[0064]

[0065] Where σ1 and σ2 are the standard deviations of the measurement noise of the built-in NTC sensor and the external thermocouple, respectively.

[0066] Compared with the prior art, the present invention has the following advantages:

[0067] 1. This invention can effectively fuse data from different sensors, optimize the data using the Kalman filter algorithm, and combine it with the weighted average method to significantly improve the accuracy and robustness of junction temperature estimation.

[0068] 2. This invention can monitor the junction temperature of power devices in real time and accurately, ensuring that they operate within a safe and efficient operating range, extending device life, and improving system reliability and performance. Attached Figure Description

[0069] Figure 1 This is a flowchart of the junction temperature extraction process, where R... g U is the gate resistor, U is the bus voltage, I includes the DC bus current and phase current, D is the duty cycle, and T is the phase current. j This is the corrected junction temperature, P. total Z represents the total loss of the power device. (j-c)1 and Z (j-c)2 These are the steady-state thermal impedances of thermal network model 1 and thermal network model 2, respectively.

[0070] Figure 2 This is a diagram showing the operating state of SiC power devices.

[0071] Figure 3 This is a physical structure diagram of a SiC MOSFET.

[0072] Figure 4 This is a diagram of the Foster thermal network model;

[0073] Figure 5 This is a flowchart of the Kalman filter weighted average algorithm. Detailed Implementation

[0074] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0075] This invention provides a method for online accurate extraction of junction temperature of silicon carbide power devices based on a dual-sensor Kalman filter weighted averaging algorithm. The junction temperature extraction flowchart is shown below. Figure 1 As shown, the power device loss model receives phase current, DC bus voltage, and duty cycle from the inverter, and obtains the on-resistance of the SiC MOSFET, the on-threshold voltage of the Schottky-Barrier Diode (SBD), and the gate drive resistance from the chip's datasheet for junction temperature extraction and real-time monitoring. The estimated junction temperature can be obtained through power device loss calculation and thermal network modeling. After weighted averaging using a Kalman filter, the estimated junction temperatures from different measurement points are weighted to obtain a more accurate junction temperature for the next iteration calculation.

[0076] 1. Since junction temperature extraction requires loss data of the inverter's operating state, and the three-phase inverter consists of six identical power devices, analysis of the losses of these power devices is sufficient. The losses of the power devices mainly consist of the conduction and switching losses of SiC and SBD, and their operating states are as follows: Figure 2 As shown, Figure 2 In this diagram, S1 is a SiC MOSFET, and VD1 is a Schottky diode. Because the SiC MOSFET has bidirectional conduction characteristics, when the power device is in the on state (a), and the phase current flows through the upper bridge arm to the motor load, S1 is in the forward conduction state, and diode VD1 is in the reverse cutoff state. When the power device is in the reverse freewheeling state (b), the phase current flows from the motor to the upper bridge arm. Since S1 is in the on state, VD1 requires a certain forward voltage to conduct, and the initial freewheeling current will flow entirely through S1. When the forward voltage drop generated by the freewheeling current flowing through S1 reaches the turn-on threshold voltage VD1... VD(TH) Subsequently, S1 and VD1 are connected in parallel to provide freewheeling current, and the freewheeling current flowing through S1 and VD1 is determined by their respective on-resistances. The current flowing through S1 and VD1 during inverter operation can be expressed as:

[0077]

[0078]

[0079]

[0080] In the formula, Is is the on-state current of the power device, which can be replaced by the corresponding phase current collected in actual operation.a Ivd is the phase current, and Ivd is the conduction current of VD1. Alternatively, the corresponding phase current collected can be used instead. R VD and R S The on-resistances of S1 and VD1 are respectively, V VD(TH) This is the turn-on threshold voltage of VD1.

[0081] Then the conduction loss P of the SiC MOSFET in one switching cycle can be further calculated. S-CON With switching loss P S-SW :

[0082]

[0083]

[0084]

[0085] In the formula, I S (t) and I S (t+NT S T represents the current flowing through SiC sampled at the beginning and end of the cycle. S For the switching cycle, D1 and D N These represent the duty cycles of the first and last periods, R. S E represents the on-resistance of SiC. SW (t) and E SW (t+NT S E represents the sum of the turn-on and turn-off energies of SiC at the beginning and end of the cycle, respectively. on(ref) and E off(ref) For SiC datasheets, select the collector current I ref Reference DC bus voltage V dc(ref) and reference junction temperature T ref The on and off energy, V dc(t) Here, a, b, and c represent the DC bus voltage, and T represents the temperature fitting coefficients. j This is the junction temperature. Where R... S E off(ref) E off(ref) I ref V dc(ref) T ref a, b, and c can all be obtained by fitting using the double-pulse experimental method with the help of the datasheet.

[0086] Since the SBD has no switching losses and reverse recovery losses, and only generates conduction losses during the freewheeling period, the conduction loss P of the SBD in one switching cycle can be calculated. VD for:

[0087]

[0088] In the formula R VD 、V VD(TH) It can be obtained from the datasheet.

[0089] The sum of the conduction loss and switching loss of the power device, P total for:

[0090]

[0091] 2. Build a heat network model

[0092] Figure 3 The diagram shows the heat conduction process of SiC power devices. Based on the principle of heat transfer, the following diagram can be drawn: Figure 4 The power device SiC shown uses a Foster thermal network model based on a temperature sensor to estimate the junction temperature. Its mathematical model is as follows:

[0093]

[0094] In the formula, T j (t) represents the transient junction temperature, T c For ambient temperature, Z j-c The thermal impedance from the SiC chip to the casing of the power device is calculated. The thermal impedance parameters are fitted using the transient thermal impedance exponential fitting method. The fitting model is as follows:

[0095]

[0096] In the formula, t represents time, and n represents the order of the thermal network model. =R i C i R i C i These represent the thermal resistance and heat capacity for each order.

[0097] Starting from zero power, a certain amount of heat is suddenly applied (e.g., through a heating element with a constant current), and then the power is kept constant. The temperature change of the system is observed, and the thermal impedance parameter between the two is obtained by fitting a multi-order exponential curve.

[0098] 3. Dual-sensor thermal network modeling

[0099] A dual-sensor temperature estimation structure is constructed based on an external thermocouple and an internal NTC temperature sensor of the SiC power device module. Two thermal impedance modeling paths are established to achieve junction temperature estimation. Path 1 utilizes the case temperature signal acquired by the thermocouple and combines it with the heat conduction structure to establish a Foster-type thermal network model 1 to estimate the chip junction temperature T. j1 Paths 2 and 3 utilize the internal temperature signals of the module acquired by the NTC temperature sensor, and combine them with the heat conduction path to establish a Foster-type thermal network model 2, thereby estimating the chip junction temperature T.j2 The two paths described above provide junction temperature estimation results with complementary characteristics based on the thermal inertia and response characteristics of different measurement points.

[0100] 4. Junction temperature estimation is combined with estimation correction.

[0101] By combining thermal network models 1 and 2 with the loss analysis model, junction temperature data observed through different paths can be obtained. These data can then be treated as data measured by different sensors and input into the Kalman filter weighted average algorithm.

[0102] like Figure 5 As shown, the junction temperature T is calculated using a thermal network model. j1 and T j2 The thermal impedance parameter Z was obtained through experiments. j-c The process noise covariance matrix Q, measurement noise covariance matrix R, state transition matrix F, and measurement matrix H are used to correct the chip junction temperature T by applying a Kalman filter weighted averaging algorithm. j To compensate for junction temperature deviation, its mathematical model is as follows:

[0103] Select state variables:

[0104]

[0105] In the formula, T j (k) is the estimated junction temperature. This represents the rate of change of junction temperature.

[0106] The state equation is:

[0107]

[0108] In the formula, f(x(k-1),u(k)) is a nonlinear function describing the junction temperature change, u(k) is the external input, and w(k) is the process noise.

[0109] After Taylor unfolds:

[0110]

[0111] In the formula, F(k) is the Jacobian matrix of the current state versus the state at the previous time step, which describes the linear approximation of the nonlinear system.

[0112] The measurement equation is:

[0113]

[0114]

[0115] In the formula, h1(x(k)) and h2(x(k)) are nonlinear measurement functions of the internal and external temperature sensors, representing the relationship between the sensor measurements and the junction temperature. v1(k) and v2(k) are measurement noises, assumed to be zero-mean Gaussian noise.

[0116] The Kalman filter gain is:

[0117]

[0118] In the formula, P - H(k) is the prediction error covariance matrix, H(k) is the Jacobian matrix of the measurement matrix, representing the linearization of the measurement equation with respect to the state, and R(k) is the measurement noise covariance matrix.

[0119] Update status:

[0120]

[0121] In the formula, x - (k) represents the predicted state, y(k) represents the measured value, and h(x) represents the predicted state. - (k) represents the predicted value of the measurement function.

[0122] Update error covariance:

[0123]

[0124] In the formula, p(k) is the error covariance.

[0125] Weighted average algorithm:

[0126]

[0127] In the formula, Let be the junction temperature values ​​observed by sensors 1 and 2 after Kalman filtering, and α be a weight dynamically adjusted based on factors such as the sensor's signal-to-noise ratio and measurement error, with a value satisfying 0 < α < 1.

[0128]

[0129] Where σ1 and σ2 are the standard deviations of the measurement noise of the built-in NTC sensor and the external thermocouple, respectively.

Claims

1. A method for online accurate extraction of junction temperature of silicon carbide power devices based on a dual-sensor Kalman filter weighted averaging algorithm, characterized in that... The method includes the following steps: Step 1: The power device loss model receives the phase current, DC bus voltage, and duty cycle from the inverter, and obtains the on-resistance, on-state loss energy and off-state loss energy of the SiC MOSFET under the reference DC bus voltage and on-state current, the on-threshold voltage of the Schottky diode, and the gate drive resistance from the chip's datasheet for junction temperature extraction and real-time monitoring operation. Step 2: The estimated junction temperature is obtained through power device loss calculation and thermal network model. After weighting the estimated junction temperature at different measurement points using Kalman filtering weighted averaging algorithm, a more accurate junction temperature is obtained for the next iteration calculation.

2. The method for online accurate extraction of junction temperature of silicon carbide power devices based on dual-sensor Kalman filter weighted averaging algorithm according to claim 1, characterized in that... The specific steps of step two are as follows: Step Two: Calculation of power device losses. During inverter operation, the current flowing through S1 and VD1 is expressed as follows: In the formula, Is is the on-state current of the power device, I a Ivd is the phase current, and Rs and R are the on-state currents of VD1. VD The on-resistances of S1 and VD1 are respectively, V VD(TH) S1 is the turn-on threshold voltage of VD1, S1 is a SiC MOSFET, and VD1 is a Schottky diode; Further calculations were performed to determine the conduction loss P of the SiC MOSFET during one switching cycle. S-CON With switching loss P S-SW : In the formula, I S (t) and I S (t+NT S T represents the current flowing through SiC sampled at the beginning and end of the cycle. S For the switching period, D1 and D N These represent the duty cycles of the first and last periods, R. S E is the on-resistance of SiC. SW (t) and E SW (t+NT S E represents the sum of the turn-on and turn-off energies of SiC at the beginning and end of the cycle, respectively. on(ref) and E off(ref) For SiC datasheets, select the collector current I ref Reference DC bus voltage V dc(ref) and reference junction temperature T ref The on and off energy, V dc(t) Here, a, b, and c represent the DC bus voltage, and T represents the temperature fitting coefficients. j For the junction temperature; SBD conduction loss P in one switching cycle VD for: The sum of the conduction loss and switching loss of the power device, P total for: Step 22: Building the thermal network model: Based on the principle of heat transfer, a Foster thermal network model of the SiC power device based on the junction temperature measured by a temperature sensor is drawn. Its mathematical model is as follows: In the formula, T j (t) represents the transient junction temperature, T c For ambient temperature, Z j-c The thermal impedance from the SiC chip to the casing of the power device is calculated. The thermal impedance parameters are fitted using the transient thermal impedance exponential fitting method. The fitting model is as follows: In the formula, t represents time, and n represents the order of the thermal network model. =R i C i R i 、C i These are the thermal resistance and heat capacity for each order, respectively; Steps 2 and 3: Dual-sensor thermal network modeling and junction temperature estimation: A dual-sensor temperature estimation structure is constructed based on an external thermocouple and an internal NTC temperature sensor of a SiC power device module. Two thermal impedance modeling paths are established to achieve junction temperature estimation. Specifically, the case temperature signal acquired by the thermocouple is combined with the heat conduction structure to establish a Foster-type thermal network model 1, thereby estimating the chip junction temperature T. j1 Using the internal temperature signal of the module collected by the NTC temperature sensor, and combining it with its heat conduction path, a Foster-type thermal network model 2 was established to estimate the chip junction temperature T. j2 ; Step 2.4: Junction temperature estimation and fusion for junction temperature correction: By combining Foster-type thermal network model 1 and Foster-type thermal network model 2 with the loss analysis model, junction temperature data observed through different paths are obtained. These data are then treated as data measured by different sensors and input into the Kalman filter weighted average algorithm for junction temperature correction.

3. The method for online accurate extraction of junction temperature of silicon carbide power devices based on dual-sensor Kalman filter weighted averaging algorithm according to claim 2, characterized in that... The specific steps of step two or four are as follows: The junction temperature T calculated using Foster-type thermal network model 1 and Foster-type thermal network model 2 j1 and T j2 The thermal impedance parameter Z was obtained through experiments. j-c The process noise covariance matrix Q, measurement noise covariance matrix R, state transition matrix F, and measurement matrix H are used to correct the chip junction temperature T by applying a Kalman filter weighted averaging algorithm. j To compensate for junction temperature deviation, its mathematical model is as follows: Select state variables: In the formula, T j (k) is the estimated junction temperature. This represents the rate of change of junction temperature. The state equation is: In the formula, f(x(k-1),u(k)) is a nonlinear function describing the junction temperature change, u(k) is the external input, and w(k) is the process noise; After Taylor unfolds: In the formula, F(k) is the Jacobian matrix of the current state versus the state at the previous time step; The measurement equation is: In the formula, h1(x(k)) and h2(x(k)) are the nonlinear measurement functions of the internal and external temperature sensors, and v1(k) and v2(k) are the measurement noise; The Kalman filter gain is: In the formula, P - H(k) is the prediction error covariance matrix, H(k) is the Jacobian matrix of the measurement matrix, and R(k) is the measurement noise covariance matrix. Update status: In the formula, x - (k) represents the predicted state, y(k) represents the measured value, and h(x) represents the predicted state. - (k) represents the predicted value of the measurement function; Update error covariance: In the formula, P(k) is the error covariance; Weighted average algorithm: In the formula, The junction temperatures observed by sensors 1 and 2 are Kalman filtered, with α representing the weights, where 0 < α < 1. Where σ1 and σ2 are the standard deviations of the measurement noise of the built-in NTC sensor and the external thermocouple, respectively.

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