energies Article
A High-Precision Adaptive Thermal Network Model for Monitoring of Temperature Variations in Insulated Gate Bipolar Transistor (IGBT) Modules Ning An 1 1
2
*
ID
, Mingxing Du 1, *, Zhen Hu 2 and Kexin Wei 1
Tianjin Key Laboratory of Control Theory & Applications in Complicated System, Tianjin University of Technology, Tianjin 300384, China;
[email protected] (N.A.);
[email protected] (K.W.) School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China;
[email protected] Correspondence:
[email protected]; Tel.: +86-22-6021-4268
Received: 20 January 2018; Accepted: 6 March 2018; Published: 8 March 2018
Abstract: This paper proposes a novel method for optimizing the Cauer-type thermal network model considering both the temperature influence on the extraction of parameters and the errors caused by the physical structure. In terms of prediction of the transient junction temperature and the steady-state junction temperature, the conventional Cauer-type parameters are modified, and the general method for estimating junction temperature is studied by using the adaptive thermal network model. The results show that junction temperature estimated by our adaptive Cauer-type thermal network model is more accurate than that of the conventional model. Keywords: insulated gate bipolar transistor (IGBT); thermal network; parameter identification; junction temperature
1. Introduction As a key component in the modern power-electronic system, insulated gate bipolar transistors (IGBTs) are widely used in high-reliability systems [1] and play a significant role in wind turbines [2,3], aircraft [3,4], electric vehicles [5–8], etc. The reason for the widespread application of IGBTs lies in IGBTs’ excellent performance in the aspects of switching frequency, energy efficiency, power density and cost effectiveness [9]. Simultaneously, ever more formidable working conditions and stricter operating conditions require higher quality. Almost 60% of power equipment failure results from higher junction temperatures caused by heat and increase of the thermal resistance or extra power loss, according to relevant data [10–12]. The reliability research of semiconductors depends on accurate measurement of the junction temperature. Consequently, the junction temperature of the IGBT is considered as one of important indices for its health and reliability. The accurate junction temperature is the important foundation of virtual simulation, precise design and practice. The main prediction methods of junction temperature involve infrared camera detection, thermal-sensitive electrical parameters (TSEPs) and electrothermal network models [13]. The most obvious advantage of infrared camera detection lies in the capturing of the temperature field; however, the IGBT’s package must be removed during the measuring [14,15]. Regarding the TSEPs, on-state voltage (Vce-on ) [16], gate threshold voltage (Vge ) [17], turn-on time (ton ) [18], turn-off time (toff ) [19] and other electrical parameters will contribute to the prediction of the junction temperature. However, circuitry design would be more complicated with the higher precision required, making this method quite expensive [20]. The last method, the use of the electrothermal network model, can provide accurate transient junction temperature and steady-state junction temperature information, Energies 2018, 11, 595; doi:10.3390/en11030595
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thereby enabling on-line monitoring of the junction temperature without a complicated measuring circuit. Hence, the electrothermal network model is extensively used and shows prospects for further development [21,22]. The current studies of the resistance-capacitance (RC) thermal network are divided into the use of the Foster-type and Cauer-type models; the Foster-type model is based on the measurement of the temperature dynamics of power devices [23], and the Cauer-type model is based on the physical structure of the device and is considered to be a relatively accurate model of the thermal behaviours of IGBTs [24,25]. In [26], a Foster-type model was introduced for the IGBTs used in a three-phase inverter. To solve the thermal coupling effects among the chips, the three-dimensional RC-lumped thermal networks were proposed [27,28]. As such, a dynamic electrothermal model extended to a paralleled system was proposed to establish a transient model to characterize the relationship between power losses and junction temperature [29]. One problem with the Foster-type thermal network is that its parameters are based on mathematical fitting of the measured/simulated junction temperature curves, and each of the RC-lumped elements in the Foster-type network has no physical meaning. Therefore, the Cauer-type model was proposed to obtain the temperature distribution of each layer. In [30], a Cauer-type model to monitor an IGBT’s health condition was presented. The thermal model consisting of a three-dimension network of RC cells constructed for time-dependent operation was proposed [31]. Malberti [32] introduced the Elmore delay equation to model the propagation delay times of the heat flux in the layers of IGBT. However, some problems were ignored in these studies: (a) based on the extraction of parameters at constant temperature, without considering the temperature dependence of the thermal conductivity and the specific heat capacity, the deviation of Cauer-type model will be amplified at certain temperatures; (b) the transient thermal behaviour of the IGBT is oversimplified by treating each layer as a block with uniform temperature distribution, resulting in poor prediction performance of the model. On the basis of the previous analysis, this paper proposes the optimization of the adaptive temperature Cauer-type network model. The optimization lies in: (a) (b)
Obvious improvement of the accuracy of the prediction of the steady-state junction temperature, considering the influence of temperature. Efficient improvement of the prediction performance of the transient junction temperature by redefining the hierarchical Cauer-type architecture for the internal structure of the module.
The updated network not only strongly improves the accuracy of the estimated transient junction temperature variation for IGBTs but also highly contributes to optimizing the prediction performance of the steady-state junction temperature. This paper is organized as follows: Section 2 presents an analysis of the deviation of the model based on the materials properties and physical structures successively to perform optimization accordingly. Section 3 verifies the efficiency of the model via simulation experiments. Section 4 shows the validation of the simulation results in practice. 2. Methods The basic structure of IGBT and its conventional lumped Cauer-type thermal network model are shown in Figure 1. Figure 1a shows the seven-level sandwich structure of the IGBT module from chip to baseplate. Figure 1b shows a circuit used to establish a complete seven-order IGBT heat transfer network structure on the basis of the theory of electrothermal analogy. For each layer, the thermal resistance Rth and thermal capacitance Cth are calculated using the equations below: Rth =
Cth =
Z d 0
Z d 0
1 dz k· A(z)
(1)
c·ρ· A(z)dz
(2)
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where di is the thickness of the ith layer, ki is the thermal conductivity of the ith layer, ci is the specific heat capacity of the ith layer, ρi is the density of the ith layer material, and A(z) is the effective cross-sectional area ofPEER the ith layer and the heat spreading angle of each layer can be calculated Energies 2018, 11, x FOR REVIEW 3 of 16 by Equations (3) and (4) [33]: cross-sectional area of the ith layer and the heat spreading angle of each layer can be calculated by d λ= (3) Equations (3) and (4) [33]: a ( 𝑑 5.86 λ≤1 (3) 𝜆 ln = λ + 40.4, f (θ ) = (4) 𝑎 46.45 − 6.048·λ−0.969 , λ ≥ 1 𝑓(𝜃) = {
5.86 ln 𝜆 + 40.4,
𝜆≤1
(4)
− 6.048 𝜆−0.969 ≥1 where a is the contact area with adjacent46.45 layers, and θ∙ is the ,heat 𝜆spreading angle. Basedaon thecontact conventional the spreading improvedangle. method proposed in this where is the area withlumped adjacentCauer-type layers, and θmodel, is the heat paper is conducted using the following two steps: model, the improved method proposed in this Based on the conventional lumped Cauer-type
•
paper is conducted using the following two steps:
Establish the Cauer-type thermal network of the non-constant thermal conductivity and the
specific Establish the Cauer-type thermal network of the non-constant thermal conductivity and the heat capacity. specific heat capacity.
(a)
(b) Figure 1. (a) Sandwich structure of IGBT; (b) Cauer-type thermal model.
Figure 1. (a) Sandwich structure of IGBT; (b) Cauer-type thermal model.
The conventional lumped Cauer-type model does not take into account the effect of operating environment temperature on Cauer-type the internal model materialdoes properties. thermal resistance of of theoperating IGBT The conventional lumped not takeThe into account the effect power module is determined by thematerial thermal properties. conductivity, the thermal conductivity a environment temperature on the internal Theand thermal resistance of the IGBTispower variable related to the temperature. Similarly, the thermal capacitance is determined by the specific module is determined by the thermal conductivity, and the thermal conductivity is a variable related heat capacity, which is also a temperature-dependent variable. In the process of establishing the to the temperature. Similarly, the thermal capacitance is determined by the specific heat capacity, model, the effect of temperature on its parameters will be considered to improve the accuracy of the which is also a temperature-dependent variable. In the process of establishing the model, the effect prediction of the junction temperature. According to [34,35], the relationship between thermal of temperature on its parameters will be considered to improve the accuracy of the prediction of conductivity and specific heat capacity of different materials and temperature can be obtained. the junction temperature. According to [34,35], relationship between thermal conductivity After fitting the data with the least squares the method, the approximate expressions of thermaland specific heat capacity of different temperature can be obtained. After fitting the data conductivity and heat capacity ofmaterials materials and are obtained, as shown in Figures 2 and 3 below:
with the least squares method, the approximate expressions of thermal conductivity and heat capacity (5) 𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 of materials are obtained, as shown in Figures 2 and 3 below: 𝑦 = 𝑎𝑥 𝑏
(6)
y = ax2 + bx + c
(5)
Based on Figures 2 and 3, Equations (1) and (2) are improved to be: 𝑑
y = ax b1
𝑅𝑡ℎ = ∫
0
𝑘(𝑇) ∙ 𝐴(𝑧)
𝑑𝑧
(7)
(6)
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Based on Figures 2 and 3, Equations (1) and (2) are improved to be: Rth =
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Cth =
Z d 0
Z d 0
1 dz k( T )· A(z)
c( T )·ρ· A(z)dz
(7)
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(8)
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According to Equations (7) and (8), the𝑑 heat transfer network with non-constant thermal (8) 𝐶𝑡ℎ = ∫ 𝑑𝑐(𝑇) ∙ 𝜌 ∙ 𝐴(𝑧)𝑑𝑧 0 conductivity and specific heat capacity is 𝐶established; the accuracy of the model has been significantly (8) 𝑡ℎ = ∫ 𝑐(𝑇) ∙ 𝜌 ∙ 𝐴(𝑧)𝑑𝑧 0 to Equations (7) and (8), the heat transfer network with non-constant thermal structure improved. ToAccording further improve the accuracy of the model, this paper will optimize the physical According Equations (7)capacity and (8), istheestablished; heat transfer non-constant thermal conductivity andto specific heat thenetwork accuracywith of the model has been of the Cauer-type model.
•
conductivityimproved. and specific heat capacity accuracy the will model has been significantly To further improve is theestablished; accuracy of the model, thisofpaper optimize the significantly improved. To further improve the accuracy of the model, this paper will optimize the physical structure of the Cauer-type model. Optimization of the Cauer-type model based on the physical structure physical structure of the Cauer-type model. Optimization of the Cauer-type model based on the physical structure Optimization of the Cauer-type model based on the physical structure
Figure 2. The relationship between thermal conductivity and temperature of different materials.
Figure 2. Figure The relationship between thermal and temperature of different materials. 2. The relationship between thermalconductivity conductivity and temperature of different materials.
. . Figure 3. The relationship between specific heat capacity and temperature of different materials. Figure 3. The relationship between specific heat capacity and temperature of different materials.
Figure 3. The relationship between specific heat capacity and temperature of different materials.
Although the seven-layer Cauer-type model established by the seven-layer physical structure the seven-layer model established by the the higher seven-layer physical structure of theAlthough IGBT power module has Cauer-type a high computational efficiency, thermal resistance and of the the IGBT power module has a high computational efficiency, higher resistance and higher thermal capacitance of the ceramic layerestablished and the baseplate inthermal the thermal network Although seven-layer Cauer-type model bythe thelayer seven-layer physical structure of higher lead thermal capacitance of the ceramic andresults the baseplate layer in the the model thermal network to a longer constant, which,layer in turn, in prediction IGBT model power module has atime high computational efficiency, thea decrease higher thermal resistance and higher model lead to a longer time constant, which, in turn, results in a decrease in the model prediction
the thermal capacitance of the ceramic layer and the baseplate layer in the thermal network model lead
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to a longer time constant, which, in turn, results in a decrease in the model prediction performance of thetemperature; overall junction as anot result, it does not accurately capture the of the performance overall junction as atemperature; result, it does accurately capture the dynamic junction dynamic junction temperature changes of the IGBT module during the power cycle. Based on the temperature changes of the IGBT module during the power cycle. Based on the seven-layer Cauer-type seven-layer thermal network structure of the analyses IGBT module, this papercharacteristics analyses the of a thermal network Cauer-type structure of the IGBT module, this paper the operating operating characteristics of a single-layer RC network and compares the interaction between the single-layer RC network and compares the interaction between the layers of different time scales to layers of different time scales to establish the accurate prediction of the IGBT transient junction establish the accurate prediction of the IGBT transient junction temperature using the heat transfer temperature using the heat transfer model. The single-level Cauer-type model is shown in Figure 4 model.below. The single-level Cauer-type model is shown in Figure 4 below.
Figure 4. Single-layer Cauer-type thermal network.
Figure 4. Single-layer Cauer-type thermal network. By using the electrothermal analogy method, the complete response of the first order equation of the single-layer Cauer-type analogy thermal network is the as follows: By using the electrothermal method, complete response of the first order equation of
the single-layer Cauer-type thermal network is as follows: =
−
=(
−
) 1−
( js)−( T)c Tjc = Tj − Tc = = T
(9)
t
1 − e− τ
(10)
(9)
Tjs is the steady-state junction temperature, Tjc is the temperature difference between the chip τ =TcRis( Tthe )Ccase ( T ) temperature, and τ is the time constant. (10) and the case, Tj is the junction temperature, According to Equation (9), the time required for junction temperature to reach steady state is given Tjs is the steady-state junction temperature, Tjc is the temperature difference between the chip by:
and the case, Tj is the junction temperature, Tc is the case temperature, and τ is the time constant. − According to Equation (9), the time required temperature to reach steady state is(11) given by: = for − lnjunction 1− −
!
Tj −state; Tc thus: When Tjc = 0.98Tjs, the system is defined as the steady ts = −τ ln 1 −
(11)
Tjs − Tc = − ln0.02
(12)
On this basis, different combinations of RC and power loss are simulated by PLECS, and the duty cycle set is 0.5, Tc = 25 °C. The results are shown in Table 1. Where ts1 is acquired in PLECS, ts2 is the calculation time using Equation (12).
When Tjc = 0.98Tjs , the system is defined as the steady state; thus: ts = −τ ln 0.02
Table 1. Characteristics of single layer when the thermal resistance and capacitance different.
(12)
On this basis, different combinations of RC and power loss are simulated by PLECS, and the duty Rth (°C/W) Cth (J/°C) Power (W) Tjcs (°C) ts1 (ms) ts2 (ms) cycle set is 0.5, Tc = 25 ◦ C. The results are shown in Table 1. Where ts1 is acquired in PLECS, ts2 is the 0.03 0.50 50 1.5 58.7 58.7 calculation time using Equation (12).0.30 0.05 50 2.5 58.7 58.7 0.06
0.30
50
3
70.4
70.4
Table 1. Characteristics layer when capacitance different. 0.10 of single 0.10 100the thermal 10 resistance 39.1 and39.1 Rth (◦ C/W)
0.30 ◦ 0.50 C th (J/ C)
0.05 100 0.03 Power (W) 100
30
0.03
0.50
50
1.5
58.7
58.7
0.06 0.10 0.30 0.50
0.30 0.10 0.05 0.03
50 100 100 100
3 10 30 50
70.4 39.1 58.7 58.7
70.4 39.1 58.7 58.7
Tjcs 50 (◦ C)
58.7 58.7 58.7ts1 (ms) 58.7
ts2 (ms)
According the characteristics layer thermal58.7 network are obtained: 0.05 to Table 1,0.30 50 of the single2.5 58.7
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According to Table 1, the characteristics of the single layer thermal network are obtained: (a)
Tjcs is determined by the power loss when the time constant is same. The larger power loss, Energies 2018, 11, x FOR PEER REVIEW 6 of 16 the higher Tjcs .
(b)
Compared with the results aboutloss ts1 ,when the deviation of ts2 calculated bylarger Equation (12) is the always (a) Tjcs is determined by the power the time constant is same. The power loss, kepthigher in a small Tjcs. range. (b) Compared with the results about ts1, the deviation of ts2 calculated by Equation (12) is always
This kept paper SKM75GB12T4 module of SEMIKRON Company as the research object. in atakes smallthe range. The specific dimensions of the module and the material properties including thermal resistance and This paper takes the SKM75GB12T4 module of SEMIKRON Company as the research object. thermal capacitance calculated by constant thermal conductivity and specific heat capacity (25 ◦ C) The specific dimensions of the module and the material properties including thermal resistance and which can be improved in this paper are shown in Table 2. thermal capacitance calculated by constant thermal conductivity and specific heat capacity (25 °C) which can be improved in this paper are shown in Table 2 Table 2. Parameters of the IGBT module (SKM75GM12T4). Table 2. Parameters of the IGBT module (SKM75GM12T4).
Material Thickness Density Length 3) Thickness(kg/mDensity Length LayerMaterial (mm) (mm) Layer (mm) (kg/m3) (mm) Silicon 0.15 2329 7.24 Silicon 0.15 2329 7.24 Solder 0.12 7300 7.24 Solder 0.12 7300 7.24 Copper 0.3 8960 28.5 Copper 0.3 8960 28.5 Alumina 0.38 3780 30.65 Alumina 0.38 3780 30.65 Copper 0.3 8960 28.5 28.5 SolderCopper 0.12 0.3 7300 8960 28.5 CopperSolder 2.8 0.12 8960 7300 91.4 28.5 Copper 2.8 8960 91.4
Width Width (mm) (mm) 6.9 6.9 6.9 6.9 25.8 25.8 28 28 25.8 25.8 31.4 25.8 31.4
◦ Rth Rth( C/W)
(°C/W) 1.65e−2 1.65e-2 2.26e−2 2.26e-2 9.17e−3 9.17e-3 0.112 0.112 8.18e−3 8.18e-3 1.93e−2 7.71e−2 1.93e-2 7.71e-2
Cth (J/◦ C) Cth (J/°C) 2.60e−2 2.60e-2 9.51e−3 9.51e-3 8.55e−2 8.55e-20.104 0.104 9.56e−2 9.56e-2 1.12e−2 1.12e-21.44 1.44
Based on Equations (7) and (8), the values and distribution of the time constant of each layer Based on Equations (7) and (8), the values and distribution of the time constant of each layer ◦ C) are shown in Figure 5. underunder ambient temperature (25(25 ambient temperature °C) are shown in Figure 5.
Figure 5. Time constant of each layer.
Figure 5. Time constant of each layer.
In the heat transfer model, the RC is a constant for the transition time of the network and is the
In the heat transferreflecting model, the is required a constant for the transition time the network and physical parameter theRC time to transfer the heat over theoflayer. The larger theis the timeparameter constant is,reflecting the longerthe thetime time required it takes to to transfer the the heatheat overover the layer. Equation is used physical transfer the layer. The (12) larger the time to solve the valuesthe and distribution the timethe constant for each layer Equation to obtain (12) the steady-state constant is, the longer time it takes tooftransfer heat over the layer. is used to solve under ambient temperature (25 °C), as shown in Figure 6. the values and distribution of the time constant for each layer to obtain the steady-state under ambient temperature (25 ◦ C), as shown in Figure 6.
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Figure 6. Time to reach steady-state of each layer.
Figure 6. Time to reach steady-state of each layer.
According to the analysis of the data available in the figures, the times of the ceramic layer and According themuch analysis ofthan the data in layers. the figures, the times thetransfer ceramictime layer the baseplatetoare longer thoseavailable of the other The much longerofheat is and in these two than in than the other the predictive performance the transient the baseplate are layers much longer thoselayers of thereduces other layers. The much longer heatoftransfer time is in temperature innerlayers layer reduces structuresthe of predictive thermal model network, thereby degradingjunction the thesejunction two layers than in in thethe other performance of the transient overall performance of capturing the transient junction temperature of the IGBT power module. To temperature in the inner layer structures of thermal model network, thereby degrading the overall improve the performance of the lumped Cauer-type thermal network model, the prediction performance of capturing the transient junction temperature of the IGBT power module. To improve accuracy can be improved by the fine stratification of the ceramic layer and the baseplate layer. the performance of the lumped Cauer-type thermal network model, the prediction accuracy can be With the increase of the number of layers, Equation (10) can be rewritten as Equation (13) where n improved by the fine stratification of the ceramic layer and the baseplate layer. With the increase of the is the number of sublayers. The thermal resistance and thermal capacitance decrease with a trend of number of layers, Equationand (10)the can be constant rewrittenofas Equation where with n is the number of sublayers. positive ratio function, time new sublayer(13) decreases a trend of quadratic. The thermal resistance and(12), thermal capacitance a trend of are positive ratio function, According to Equation the ceramic layerdecrease and the with baseplate layer divided into several and the time constant of new sublayer decreases with a trend of quadratic. According to Equation smaller sublayers that can reach the steady-state in a shorter period, and the time of each layer after (12), the ceramic layer and baseplate layer are divided several smaller can reach the re-division is the in the same level, ensuring theinto smaller time span sublayers to requiredthat achieve the the optimization of the thermal The data in Figures is 5 in andthe 6 same can belevel, steady-state in a shorter period,network and the model time ofperformance. each layer after the re-division calculated by Equations (7), (8)toand (12). The ceramic layer can be divided intothermal three sublayers ensuring the smaller time span required achieve the optimization of the networkand model the copper baseplate can be divided into four sublayers to ensure the time of all layers can be kept performance. The data in Figures 5 and 6 can be calculated by Equations (7), (8) and (12). The ceramic thebe same level. into In addition, the transient milliseconds determined by layeratcan divided three sublayers andtemperature the copper difference baseplate in can be dividedisinto four sublayers the thermal behaviour of chips. To better express the transient characteristics, chips are divided into to ensure the time of all layers can be kept at the same level. In addition, the transient temperature three layers to improve the transient performance of the Cauer-type models:
difference in milliseconds is determined by the thermal behaviour of chips. To better express the 1 1 1 transient characteristics, chips are divided into to improve the transient performance of (13) 𝜏 = 𝑅(𝑇) ∙ three 𝐶(𝑇) =layers 𝑅(𝑇)𝐶(𝑇) 𝑛 𝑛 𝑛2 the Cauer-type models: Redefining the stratification of1 the Cauer-type model of IGBT can effectively improve the 1 1 τ = R(junction T )· C ( T ) = 2 R( Tchanges. )C ( T ) The proposed multi-layered (13) performance of capturing the dynamic temperature n n n
thermal network model is compared with the conventional model, and the results are shown below Redefining the stratification of the Cauer-type model of IGBT can effectively improve the in Figure 7. performance of capturing the dynamic junction temperature changes. The proposed multi-layered Analysis of Figure 7 shows that the method of subdividing the layer structure not only thermal network model is compared with the conventional model, and the results are shown below in effectively improves the performance of the model in capturing the transient junction temperature Figure but7.also largely reduces the error caused by ignoring the slope of the temperature distribution of Analysis Figure thatarea, the method of subdividing the layer structure effectively the layers,ofthat is the7 shows triangular thus achieving more accurate calculation of not the only heat inside improves the performance of the model in capturing the transient junction temperature but also largely each layer, thereby ensuring the accuracy of extracting thermal capacitance parameters of the model to accurately predict by the ignoring transient the junction Therefore, the improved reduces the error caused slope temperature. of the temperature distribution of theCauer-type layers, that is
the triangular area, thus achieving more accurate calculation of the heat inside each layer, thereby ensuring the accuracy of extracting thermal capacitance parameters of the model to accurately predict the transient junction temperature. Therefore, the improved Cauer-type thermal network model has been effectively improved in the prediction performance of transient junction temperature.
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thermal network model has been effectively improved in the prediction performance of transient junction temperature. thermal network model has been effectively improved in the prediction performance of transient From thethe above, the the Cauer-type thermal network model established on theonbasis the proposed From above, Cauer-type thermal network model established the of basis of the junction temperature. method, the performance of conventional Cauer-type model is optimized both in predicting proposed method, the performance of conventional Cauer-type model is optimized both inthe From the above, the Cauer-type thermal network model established on the basis of the transient junction temperature andtemperature the steady-state junction temperature of theaccuracy IGBT power predicting the transient junction and the steady-state junctionaccuracy temperature of proposed method, the performance of conventional Cauer-type model is optimized both in the IGBT power module; remarkable results have been achieved. module; remarkable results have been achieved. predicting the transient junction temperature and the steady-state junction temperature accuracy of the IGBT power module; remarkable results have been achieved.
Figure 7. Comparison of two models. Figure 7. Comparison of two models. Figure 7. Comparison of two models.
3. Simulation Validation 3. Simulation Validation 3. Simulation Validation A commercial SKM75GB12T4IGBT module made by SEMIKRON Company (Nürnberg, A commercial SKM75GB12T4IGBT made by Germany) was studied to verify the module effectiveness of SEMIKRON the proposedCompany method.(Nürnberg, According Germany) to the A commercial SKM75GB12T4IGBT module made by According SEMIKRON Company (Nürnberg, was studied to verify the effectiveness of the proposed method. to the geometric information geometric information provided in Table 1 and the material properties of each layer, the finite Germany) was studied to verify the effectiveness of the proposed method. According to the provided Table 1 and themodel material each layer, the finite elementsoftware analysis (FEA) model elementinanalysis (FEA) of properties the IGBT ofmodule in PRO/ENGINEER (PROE3.0, geometric information provided in Table 1 and the material properties of each layer, the finite of Needham, the IGBT module in PRO/ENGINEER software (PROE3.0, Needham, MA, USA) is established, MA, USA) is established, as shown in Figure 8. element analysis (FEA) model of the IGBT module in PRO/ENGINEER software (PROE3.0, as shown in Figure 8. Needham, MA, USA) is established, as shown in Figure 8.
(a) (a)
(b) (b)FEA model with a cold plate. Figure 8. (a) IGBT module; (b) Figure 8. (a) IGBT module; (b) FEA model with a cold plate. Figure 8. (a) IGBT module; (b) FEA model with a cold plate.
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Energies 2018, 11, xmodel, FOR PEER REVIEW In the FEA the heat sink
surface9 of of16the
is simplified as an aluminium block, the bottom In the FEA model, the heat sink is simplified as an aluminium block, the bottom surface of the heat sink is set as a heat dissipative surface and the temperature of the bottom is set as a constant. heat In sink set as a heatthe dissipative and the ofblock, the bottom is set surface as a constant. theisFEA model, heat sinksurface is simplified as temperature an aluminium the bottom of the The power loss is generated inside the chip near the surface; thus, the power loss is simulated on the The power is agenerated inside the chip and nearthe thetemperature surface; thus, is as simulated on heat sink is loss set as heat dissipative surface of the power bottomloss is set a constant. chip surface, and the power loss set is set shown in Figure 9. The temperature distribution of the IGBT the chip surface, and the power loss is shown in Figure 9. The temperature distribution of the The power loss is generated inside the chip near the surface; thus, the power loss is simulated on module is obtained as shown shown in Figure 10. Therefore, the temperature information of different layers IGBT module is obtained in set Figure 10. Therefore, information of different the chip surface, and the as power loss is shown in Figurethe 9. temperature The temperature distribution of the of IGBT the IGBT power module can be accurately mastered by the finite model. layers of the IGBT power as module can accurately mastered by the element finite element model.of different module is obtained shown in be Figure 10. Therefore, the temperature information layers of the IGBT power module can be accurately mastered by the finite element model.
Figure 9. The input of heat flow. Figure 9. The input of heat flow. Figure 9. The input of heat flow.
(a) (a)
(b) (b) (a) Vertical view; (b) Cross-sectional view. Figure 10. Temperature distribution in IGBT: Figure 10. Temperature distribution in IGBT: (a) Vertical view; (b) Cross-sectional view. Figure 10. Temperature distribution in IGBT: (a) Vertical view; (b) Cross-sectional view.
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OnOn this basis, the networkmodel modeland andthe theimproved improved thermal this basis, theconventional conventionalCauer-type Cauer-type thermal thermal network thermal network model are simulated, and the power loss, case temperature and ambient temperature as input network model are simulated, and the power loss, case temperature and ambient temperature as parameters are inputare to input obtaintothe temperature curve ofcurve each of module of IGBTofpower module. And the input parameters obtain the temperature each module IGBT power module. parameters of the two of models in models different are shown Table in 3. Table 3. And the parameters the two in condition different condition areinshown ◦ C/W; J/◦ C). Table 3. The RCRC parameters ofofthe (R; C, C, °C/W; Table 3. The parameters thetwo twomodels modelsin indifferent different condition condition (R; J/°C).
Chip Substrate Copper Copper Ceramic Ceramic Copper Copper Substrate Solder Solder Solder 0.112; 1.65 × 10−2 ; 2.26 × 10−2 ; 9.17 × 10−3 ; 8.18 × 10−3 ; 1.93 × 10−2 ; −2; −2; −3; −3; Convention − 2 − 3 − 2 − 2 −−2 2 ; 1.65 × 10 2.26 × 10 9.17 × 10 0.112; 8.18 × 10 1.93 10 0.104 9.51 × 10 8.55 × 10 9.56 × 10 1.12 ××10 Convention 2.60 × 10 −2 −3 −2 −2 −2 2.60−×2 10 9.51 −×2 10 8.55 ×−310 0.104 9.56 ×−310 1.12 × 10 − 2 Improved 0.126; 1.86 × 10 ; 2.31 × 10 ; 9.27 × 10 ; 8.27 × 10 ; 1.97 × 10 ; −2 −2 −3 −3 −2 ◦ 2 2 −2 ; Improved ×310 ; 8.699.27 ; 0.108 0.126; 9.728.27 ; 1.97××1010 (50 C) 2.72 1.86 × 10−×210 ; 9.51 2.31 × 10− × 10×−10 × 10×−10 1.12 −2 −3 −2 −2 −2 (50 ° C) 2.72 × 10 9.51 × 10 8.69 × 10 0.108 9.72 × 10 1.12 × 10 − 2 − 2 − 3 − 3 − Improved 0.151; 2.21 × 10 ; 2.43 × 10 ; 9.42 × 10 ; 8.41 × 10 ; 2.07 × 10 2 ; ◦ − 2 − 3 − 2 − 2 − 2 −2 −2 −3 −3 −2 (100 C) 2.90 2.21 × 10 × 10 ; 9.51 2.43 × 10 × 10 ; 8.909.42 × 10× 10 ; 0.114 × 10× 10 ; 1.12 Improved 0.151; 9.968.41 2.07××1010 ; (100 °C) 2.90 × 10−2 9.51 × 10−3 8.90 × 10−2 0.114 9.96 × 10−2 1.12 × 10−2 Model Model
ChipChip
Chip Solder
Baseplate Baseplate 7.71 × 10−2 ;
7.711.44 × 10−2; 1.44 7.80 × 10−2 ; 7.801.47 × 10−2; 7.931.47 × 10−2 ; 7.931.50 × 10−2; 1.50
The forecast results of junction temperature are compared with the results in the finite element The forecast results of junction temperature are compared with the results in the finite element analysis model. The comparison results are shown in Figure 11. analysis model. The comparison results are shown in Figure 11.
(a)
(b) Figure 11. Junction temperature Tj as a function of time for the SKM75GB12T4 module during the Figure 11. Junction temperature Tj as a function of time for the SKM75GB12T4 module during the variable heat flow test estimated from two thermal models: (a) the ambient temperature is 50 °C; (b) variable heat flow test estimated from two thermal models: (a) the ambient temperature is 50 ◦ C; (b) the the ambient temperature is 100 °C. ambient temperature is 100 ◦ C.
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The details of the simulation of Figure 11 are presented in Table 4. In a period of junction temperature fluctuation, the peak-to-valley value in the FEM model is 4.99 ◦ C and 5.38 ◦ C for 50 ◦ C and 100 ◦ C, respectively. The peak-to-valley value of the improved Cauer-type model is 4.35 ◦ C and 4.96 ◦ C for 50 ◦ C and 100 ◦ C, respectively. However, the peak-to-valley value of the conventional Cauer-type model is 3.68 ◦ C and 3.71 ◦ C for 50 ◦ C and 100 ◦ C, respectively. Therefore, the average change rate of junction temperature of the improved Cauer-type model is closer to the change rate of the junction temperature in the FEM model, showing that the modified Cauer-type model effectively improves the transient temperature prediction performance. Overall, the junction temperature value of the Cauer-type thermal network model is always greater than that of the conventional Cauer-type model and is closer to the predicting junction temperature in the FEM. Moreover, in the different ambient temperatures, the deviation prediction of the junction temperature from the improved Cauer-type model proposed in this paper is always kept in a small range, in good agreement with the results from the FEM model, indicating that the improved Cauer-type model has excellent prediction performance of steady-state junction temperature. With the continuous change of the working state of the IGBT power module, the junction temperature is increasing. The higher junction temperature will lead to the decrease of material thermal conductivity, leading to the increase of thermal resistance inside the package. Similarly, with the increase of junction temperature caused by the influence of specific heat capacity, the thermal capacitance in the package also increases. Thus, the increase of thermal resistance and thermal capacitance is the main reason for the difference between both of them in the predicted steady-state junction temperature. Moreover, with the increase of thermal capacitance and thermal resistance, the model cannot accurately simulate the law of the junction temperature, mainly including switching process, rise and fall time and so on. On the basis of guaranteeing the precision of prediction of steady-state junction temperature, the reasonable layering allows the improved Cauer-type model to realize the accurate simulation of the operating law of the junction temperature. Table 4. Comparison of two models. Model
Peak-to-Valley Value (◦ C)
Average Rate of Change (◦ C/s)
FEM Improved Convention
4.99; 5.38 4.35; 4.96 3.68; 3.71
9.98; 10.76 8.7; 9.92 7.36; 7.42
In summary, the improved Cauer-type thermal network model proposed in this paper modifies the conventional Cauer-type model from two aspects, namely, prediction of the transient junction temperature and prediction of the steady-state junction temperature, and the two aspects of optimization achieved notable results. The establishment of the temperature adaptive Cauer-type thermal network model is completed. 4. Experimental Validation 4.1. Experiment Setup The improved method is further verified by experimental studies in accordance with Figure 12. Figure 12 shows the experimental setup, which consists of a high-DC power for supplying test current, a gate driver for generating gate signal for the test IGBT module, a recorder for electrical signal acquisition (such as Vce and Ic ), an infrared camera for real-time collection of the junction temperature, a and National Instruments (NI) data acquisition instrument with a LabVIEW system for acquiring the Tc , which is measured by using precise fine-wire thermocouple.
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(a)
(b) Figure 12. Experimental setup: (a) schematic; (b) actual setup. Figure 12. Experimental setup: (a) schematic; (b) actual setup.
4.2. Variable Current Test 4.2. Variable Current Test On this basis, the thermal network models are examined; the upper surface temperature On this for basis, the thermal models examined; upperinsurface temperature distribution the IGBT module network obtained using theare infrared imagerthe is shown Figure 13. To allow distribution the IGBT module obtained thetemperature, infrared imager is shown infrom Figure To allow the infraredfor camera accurately capture the using junction the silicon gels the13. surface of theinfrared IGBT module be removed the camerathe should begels aimed at the the surface centre ofof the camerashould accurately capturedeliberately the junctionand temperature, silicon from theIGBT chip after it is should calibrated. The temperature rangeand measured herein withinbe150 °C and the centre effect of the module be removed deliberately the camera should aimed at the of ◦ emissivity is small, can be neglected. the chip after it is calibrated. The temperature range measured herein within 150 C and the effect of emissivity is small, can be neglected.
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Figure 13. The temperature distribution of IGBT taken by the infrared imager. Figure 13. The temperature distribution of IGBT taken by the infrared imager. Figure 13. The temperature distribution of IGBT taken by the infrared imager.
In addition, the gate drive voltage is set as VG = 15 V to set the IGBT in a constant conduction state. The current is shown in Figureis14. power of set the the IGBT, which be integrated by In addition, theset gate drive voltage setThe as V = 15loss V to IGBT in awill constant conduction In addition, the gate drive voltage is set as VG G = 15 V to set the IGBT in a constant conduction Vce The and Icurrent c, is regarded as the input power unit ofpower thermal network. Obtaining thewill real-time Tc by theby state. set is shown in Figure 14. The loss of the IGBT, which be integrated state. The current set is shown in Figure 14. The power loss of the IGBT, which will be integrated by will beastaken as thepower baseplate input Obtaining of thermal network. VceVthermocouple and I , is regarded the input unittemperature of thermal unit network. the real-time Tc by ce andc Ic, is regarded as the input power unit of thermal network. Obtaining the real-time Tc by thethe thermocouple will be taken as the baseplate temperature unit input of thermal network. thermocouple will be taken as the baseplate temperature unit input of thermal network.
Figure 14. The input of the collector current. Figure 14. The input of the collector current.
Compared with experimental results the conventional Cauer-type model and the Figure results, 14. The the input of theof collector current. improved Cauer-type model are obtained, as shown in Figure 15. Compared with experimental results, the results of the conventional Cauer-type model and the The details of Figure 15 are given in Table 5. As the current changes, the junction temperature of Compared with experimental results, the resultsinofFigure the conventional Cauer-type model and the improved Cauer-type model are obtained, as shown 15. the IGBT is constantly changing. Compared with the conventional Cauer-type model, the deviation TheCauer-type details of Figure 15are are obtained, given in Table 5. As the current15. changes, the junction temperature of improved model as shown in Figure of the prediction of the junction temperature from that of the improved Cauer-type model proposed theThe IGBT is constantly Compared with thethe conventional Cauer-type model, the deviation of details of Figurechanging. 15 are given in Table 5. As current changes, the junction temperature in this paper is always kept in a small range. Figure 15b compares the values of the junction of the prediction of the junction temperature from that of the improved Cauer-type model proposed the IGBT is constantly changing. Compared with the conventional Cauer-type model, the deviation temperature estimation errors of the conventional Cauer-type model and those of the improved this paper isofalways kept in a small range. Figure compares the values ofmodel the junction of in the prediction junction that by of15b the Cauer-type modelthe with respecttemperature to the resultsfrom obtained the improved IR camera.Cauer-type As demonstrated inproposed Figure temperature estimation errors of the conventional Cauer-type model and those of the improved in this paper is always kept in a small range. Figure 15b compares the values of the junction 15b, the maximum deviation between the actual temperature and the junction temperature Cauer-type estimation model with errors respectof to the the conventional results obtained by the IR camera. As demonstrated Figure temperature Cauer-type model and those of thein improved predicted by the improved Cauer-type thermal network is 2.34 °C, whereas the maximum deviation 15b, the maximum deviation between the actual temperature and the junction temperature Cauer-type model with respect to themodel resultsisobtained the IRiscamera. As demonstrated Figure 15b, of the conventional Cauer-type 5.88 °C, by which approximately 2.5 times in that of the predicted by the improved Cauer-type thermal network is 2.34 °C, whereas the maximum deviation theimproved maximumCauer-type deviation between the actual temperature and the junctionΔError temperature predicted model. After optimization, the error fluctuation c is 2.3 °C and 4.25by°Cthe of the conventional Cauer-type model is 5.88 °C, which is approximately 2.5 times that of the improved network is 2.34 ◦ C, whereas the maximumindicating deviationthat of the for the Cauer-type thermal model and the conventional model, respectively, theconventional improved improved Cauer-type model. After optimization, the error fluctuation ΔErrorc is 2.3 °C and 4.25 °C ◦ Cauer-type model is 5.88 C, which is approximately 2.5 times that of the improved Cauer-type Cauer-type model performs better in transient junction temperature prediction. Moreover,model. the for the Cauer-type model and the conventional model, respectively, indicating that the improved After optimization, the error fluctuation ∆Errorc is 2.3 ◦ C and 4.25 ◦ C for the Cauer-type model Cauer-type model performs better in transient junction temperature prediction. Moreover, the
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and the conventional respectively, indicating that the improved Cauer-type model14performs Energies 2018, 11, x FORmodel, PEER REVIEW of 16 better in transient junction temperature prediction. Moreover, the average deviation of the improved averagemodel deviation of the Cauer-type model, model isindicating only 33%that of the model, Cauer-type is only 33%improved of the conventional the conventional prediction performance indicating that the prediction performance of steady-state junction temperature is effectively of steady-state junction temperature is effectively improved. improved.
(a)
(b) Figure 15. Comparison of the junction temperature estimated by two models: (a) Tj(t); (b) errors
Figure 15.respect Comparison the junction temperature estimated by two models: (a) Tj (t); (b) errors with with to the IRofcamera. respect to the IR camera. Table 5. Comparison of the two models with respect to the IR camera.
Table 5. Comparison of the two models with respect to the IR camera.
Model Maximum Deviation (°C) Error Fluctuation (°C) Average Deviation (°C) Improved 2.34 2.30 1.03 Model (◦ C) Error Fluctuation (◦ C) Average Deviation (◦ C) Convention Maximum Deviation 5.88 4.25 3.13
Improved 2.34 2.30 1.03 From the above, the improved effectively Convention 5.88 Cauer-type thermal network 4.25 proposed in this paper3.13 corrects the conventional Cauer-type thermal network from two aspects, namely, prediction of the transient junction temperature and prediction of the steady-state junction temperature, making the From the above, the model improved Cauer-type network inexperimental this paper effectively improved Cauer-type predicted junctionthermal temperature curveproposed close to the data. corrects the conventional Cauer-type network from two aspects,performance namely, prediction Moreover, the improved Cauer-typethermal model also has excellent prediction in variableof the transient junction temperature and prediction of the steady-state junction temperature, making current conditions. As the result, the law of junction temperature can be captured accurately. The the establishment of temperature-adaptive Cauer-type thermal network model is completed. improved Cauer-type model predicted junction temperature curve close to the experimental data.
Moreover, the improved Cauer-type model also has excellent prediction performance in variable current conditions. As the result, the law of junction temperature can be captured accurately. The establishment of temperature-adaptive Cauer-type thermal network model is completed.
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5. Conclusions In this paper, a method to improve the conventional Cauer-type thermal network model of an IGBT by considering both the temperature influence on the extraction of parameters and the error caused by physical structure was presented. Furthermore, the efficiency of this model was verified through simulation and experiment on a commercial IGBT module. The improved Cauer-type thermal network modifies the convention model both in prediction of the transient junction temperature and in the steady-state junction temperature accuracy. Both modified models have remarkable effects, indicating the excellent prediction performance of the junction temperature. Based on the high-precision prediction performance, the temperature adaptive Cauer-type model was established. Acknowledgments: The authors wish to acknowledge the financial support of National Key R&D Program of China (No. 2017YFB0102500) and Tianjin Natural Science Foundation of China (No. 17JCYBJC21300). Thanks to Prof. Hurley William Gerard from Electrical Engineering with the National University of Ireland, Galway, Ireland. Author Contributions: Ning An: Operation of experiments, analysis and writing of article; Mingxing Du: Guidance of experiments and modification of manuscript and reply of comments; Zhen Hu: Support of simulations and experiments; Kexin Wei: Assistance of analysis in simulation part. Conflicts of Interest: The authors declare no conflict of interest.
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