**3. Thermal simulations of power semiconductors from rectifiers**

Further on, it presents the waveforms of input powers and junction temperatures of power semiconductors, diodes and thyristors, from different types of single-phase bridge rectifiers. Also, temperature waveforms in the case of steady state thermal conditions, are shown. Using PSpice software, a parametric simulation which highlights the influence of some parameter values upon temperature waveforms has been done.

On ordinate axis, the measurement unit in the case of input power waveforms, is the watt, and in the case of temperatures, the measurement unit is the 0C, unlike the volt one that appears on graphics. This apparent unconcordance between measurement units is because thermal phenomena had been simulated using electrical circuit analogy. The notations on the graphics P1, P2 and P3 mean input powers and T1, T2 and T3 temperatures, respectively.

#### **3.1 Single-phase uncontrolled bridge rectifier**

The waveforms of the input powers and junction temperatures of power diodes from the structure of a single-phase uncontrolled bridge rectifier are shown in the below diagrams.

Fig. 8. Input power waveforms at load resistance variation with 10, 20, 50Ω

From the above graphics, Fig. 8, the input power variation P1, P2 and P3 with the load resistance values can be noticed. The increase of load values leads to small input power values, and finally, to the decrease of junction temperature magnitudes, T1, T2 and T3, Fig. 9, and also to the decrease of temperature variations. In the case of quasi-steady state thermal conditions, Fig. 10, there are a clearly difference between temperatures waveforms variation. Also, the time variations of temperature values are insignificantly. The maximum value of T1 temperature, Fig. 10, outruns the maximum admissible value for power semiconductor junction, about 1250C. Therefore, it requires an adequate protection for the power diode or increasing of load resistance.

Thermal Analysis of Power Semiconductor Converters 141

 Time 0s 20ms 40ms 60ms 80ms 100ms

 Time 4.80s 4.85s 4.90s 4.95s 5.00s

 Time 0s 20ms 40ms 60ms 80ms 100ms

It has been done a parametric simulation both at firing angle variation of thyristors from semicontrolled bridge rectifier, Fig. 11…13, and at load inductance variation, Fig. 14…16. As in previous situation, the case with uncontrolled bridge rectifier, the variation of input power values depend on load inductance, Fig. 14. The increase of inductance value, from

Fig. 14. Input power waveforms at load inductance variation with 0.1, 10, 50mH

P3

P2

P1

Fig. 13. Temperature waveforms of quasi-steady state thermal conditions at firing angle

T3

T2

T1

Fig. 12. Temperature waveforms of thermal transient conditions at firing angle variation

T3

T2

T1

V(SUM1:OUT)

V(SUM1:OUT)

V(MULT1:OUT)

variation with 60, 90, 1200 el.

25.0V

50V

30V

0V

250V

500V

750V

75V

100V

with 60, 90, 1200 el.

31.3V

37.5V

43.8V

50.0V

Fig. 9. Temperature waveforms of thermal transient conditions at load variation with 10, 20, 50Ω

Fig. 10. Temperature waveforms of quasi-steady state thermal conditions at load variation with 10, 20,50Ω

#### **3.2 Single-phase semicontrolled bridge rectifier**

In the case of a single-phase semicontrolled bridge rectifier made with power diodes and thyristors, the time variations of input powers and temperatures are presented below.

Fig. 11. Input power waveforms at firing angle variation with 60, 90, 1200 el.

 Time 0s 20ms 40ms 60ms 80ms 100ms

Fig. 9. Temperature waveforms of thermal transient conditions at load variation with 10, 20,

 Time 4.80s 4.85s 4.90s 4.95s 5.00s

In the case of a single-phase semicontrolled bridge rectifier made with power diodes and thyristors, the time variations of input powers and temperatures are presented below.

 Time 0s 20ms 40ms 60ms 80ms 100ms

Fig. 11. Input power waveforms at firing angle variation with 60, 90, 1200 el.

P3

P2

P1

Fig. 10. Temperature waveforms of quasi-steady state thermal conditions at load variation

T3

T3

T2

T1

T2

T1

V(SUM1:OUT)

V(SUM1:OUT)

V(MULT1:OUT)

**3.2 Single-phase semicontrolled bridge rectifier** 

25.0V

50Ω

50V

with 10, 20,50Ω

0V

125V

250V

375V

100V

150V

37.5V

50.0V

62.5V

75.0V

Fig. 12. Temperature waveforms of thermal transient conditions at firing angle variation with 60, 90, 1200 el.

Fig. 13. Temperature waveforms of quasi-steady state thermal conditions at firing angle variation with 60, 90, 1200 el.

Fig. 14. Input power waveforms at load inductance variation with 0.1, 10, 50mH

It has been done a parametric simulation both at firing angle variation of thyristors from semicontrolled bridge rectifier, Fig. 11…13, and at load inductance variation, Fig. 14…16. As in previous situation, the case with uncontrolled bridge rectifier, the variation of input power values depend on load inductance, Fig. 14. The increase of inductance value, from

Thermal Analysis of Power Semiconductor Converters 143

power rectifier. The temperatures have been measured using proper iron-constantan thermocouples fixed on the case of power semiconductor devices. The measurements have been done both for the firing angle values of 60, 90 and 1200 el., and load inductance values

 Time 0s 20ms 40ms 60ms 80ms 100ms

 Time 0s 20ms 40ms 60ms 80ms 100ms

Fig. 18. Temperature waveforms of thermal transient conditions at firing angle variation

 Time 4.80s 4.85s 4.90s 4.95s 5.00s

Fig. 19. Temperature waveforms of quasi-steady state thermal conditions at firing angle

Fig. 17. Input power waveforms at firing angle variation with 60, 90, 1200 el.

P3

T3

T2T1 T3

T2

T1

P2

P1

of 0.1, 10 and 50mH. The results are shown in Fig. 20 and Fig. 21.

V(MULT1:OUT)

V(SUM1:OUT)

V(SUM1:OUT)

variation with 60, 90, 1200 el.

0V

37.5V

50V

30V

75V

100V

with 60, 90, 1200 el.

50.0V

62.5V

250V

500V

750V

0.1mH to 50mH, leads not only to input power decreasing, P3 < P2 < P1, but also its shape changing. The same thing can be observed at firing angle variation, Fig. 11...13. Hence, the increase of the firing angle from 60 to 1200 el., leads to decrease of input power values P3 < P2 < P1. Also, the increase of load inductance leads to decrease of temperature values, T3 < T2 < T1, as shown in Fig. 15 and Fig. 16. The steady state thermal conditions allow to highlight the temperature differences in the case of firing angle variation, T3 < T2 < T1, Fig. 13, and load variation, T3 < T2 < T1, Fig. 16.

Fig. 15. Temperature waveforms of thermal transient conditions at load inductance variation with 0.1, 10, 50mH

Fig. 16. Temperature waveforms of quasi-steady state thermal conditions at load inductance variation with 0.1, 10, 50mH

#### **3.3 Single-phase controlled bridge rectifier**

Next diagrams present input power variation and temperature values in the case of a singlephase controlled bridge rectifier made with power thyristors.

As in the case of single-phase semicontrolled bridge rectifier, a parametric simulation for firing angle variation has been done. It can be noticed that increasing of firing angle leads to input power and temperature decrease, Fig. 17 and Fig. 18. The quasi-steady state thermal conditions highlight the differences between temperature values and their variations, Fig. 19. In order to validate the thermal simulations some experimental tests have been done. It was recorded the temperature rise on the case of the thyristors used for semi-controlled

0.1mH to 50mH, leads not only to input power decreasing, P3 < P2 < P1, but also its shape changing. The same thing can be observed at firing angle variation, Fig. 11...13. Hence, the increase of the firing angle from 60 to 1200 el., leads to decrease of input power values P3 < P2 < P1. Also, the increase of load inductance leads to decrease of temperature values, T3 < T2 < T1, as shown in Fig. 15 and Fig. 16. The steady state thermal conditions allow to highlight the temperature differences in the case of firing angle variation, T3 < T2 < T1, Fig. 13, and

 Time 0s 20ms 40ms 60ms 80ms 100ms

Fig. 15. Temperature waveforms of thermal transient conditions at load inductance variation

 Time 4.80s 4.84s 4.88s 4.92s 4.96s 5.00s

Fig. 16. Temperature waveforms of quasi-steady state thermal conditions at load inductance

Next diagrams present input power variation and temperature values in the case of a single-

As in the case of single-phase semicontrolled bridge rectifier, a parametric simulation for firing angle variation has been done. It can be noticed that increasing of firing angle leads to input power and temperature decrease, Fig. 17 and Fig. 18. The quasi-steady state thermal conditions highlight the differences between temperature values and their variations, Fig. 19. In order to validate the thermal simulations some experimental tests have been done. It was recorded the temperature rise on the case of the thyristors used for semi-controlled

T3

T2 T1

T3 T2

T1

load variation, T3 < T2 < T1, Fig. 16.

V(SUM1:OUT)

V(SUM1:OUT)

**3.3 Single-phase controlled bridge rectifier** 

phase controlled bridge rectifier made with power thyristors.

variation with 0.1, 10, 50mH

25.0V

50V

75V

100V

with 0.1, 10, 50mH

37.5V

50.0V

60.0V

power rectifier. The temperatures have been measured using proper iron-constantan thermocouples fixed on the case of power semiconductor devices. The measurements have been done both for the firing angle values of 60, 90 and 1200 el., and load inductance values of 0.1, 10 and 50mH. The results are shown in Fig. 20 and Fig. 21.

Fig. 17. Input power waveforms at firing angle variation with 60, 90, 1200 el.

Fig. 18. Temperature waveforms of thermal transient conditions at firing angle variation with 60, 90, 1200 el.

Fig. 19. Temperature waveforms of quasi-steady state thermal conditions at firing angle variation with 60, 90, 1200 el.

Thermal Analysis of Power Semiconductor Converters 145

values resulted from experimental tests (60el.exp, 90el.exp and 120el.exp from Fig. 20 and L1exp, L2exp, L3exp as shown in Fig. 21) with respect to simulations (60el.sim, 90el.sim and 120el.sim from Fig. 20 and L1sim, L2sim, L3sim as in Fig. 21), because of measurement errors, thermal model simplifications and mounting test conditions. Anyway, the maximum

During former work, (Chung, 1999; Allard et al., 2005), because of limited computer capabilities, the authors had to concentrate on partial problems or on parts of power semiconductors geometry. The progress in computer technology enables the modelling and simulation of more and more complex structures in less time. It has therefore been the aim of this work to develop a 3D model of a power thyristor as main component part from

The starting point is the power balance equation for each volume element dV, in the integral

( ) *<sup>j</sup> <sup>T</sup> dV c dV div gradT dV*

The left term of before equation (it exists only in the device conductor elements), denotes the heating power from the current flow. It is in balance with the heat stored by temporal change of temperature, and the power removed from the element by thermal conduction. For the steady state temperature calculation, the heat storage term is zero, and the equation

> ( ) *<sup>j</sup> dV div*

Taking one's stand on the above thermal equations, first of all a 3D model for a power thyristor has been developed using a specific software, the Pro-ENGINEER, an integrated

It has been considered an application which includes a bidirectional bridge equiped with power thyristors type AT505, with the average direct current of 430A and an internal resistance of 0.68m. The current which flows through the converter branches is about 315A. This value allows computing the power loss for each tyristor, which results in 67.47W. The material properties of every component part of the thyristor are described in the Table 2 and the 3D thermal models of the thyristor with its main component parts and together with

*gradT dV*

(20)

2

thermal design tool for all type of accurate thermal analysis on devices.

its heatsinks for both sides cooling are shown in Fig. 22, respectively, Fig. 23.

 

(19)

*t* 

difference between experimental and simulation results is less than 3ºC.

**3.4 D thermal modelling and simulations of power semiconductors** 

2

power semiconductor converters.

T means the temperature of element [ºC];

j – current density [A/m2];

σ – electrical conductivity [1/Ωm]; ρ – material density [kg/m3]; c – specific heat [J/kgºC];

λ – thermal conductivity [W/mºC].

formulation:

(19) becomes,

where:

Fig. 20. Comparison between simulation and experimental temperature rise of the case at firing angle variation

Fig. 21. Comparison between simulation and experimental temperature rise of the case at inductance load variation

In both cases, at firing angle and load inductance variation, it ca be noticed closer values between simulation results and measurements. Of course, there are different temperature values resulted from experimental tests (60el.exp, 90el.exp and 120el.exp from Fig. 20 and L1exp, L2exp, L3exp as shown in Fig. 21) with respect to simulations (60el.sim, 90el.sim and 120el.sim from Fig. 20 and L1sim, L2sim, L3sim as in Fig. 21), because of measurement errors, thermal model simplifications and mounting test conditions. Anyway, the maximum difference between experimental and simulation results is less than 3ºC.

#### **3.4 D thermal modelling and simulations of power semiconductors**

During former work, (Chung, 1999; Allard et al., 2005), because of limited computer capabilities, the authors had to concentrate on partial problems or on parts of power semiconductors geometry. The progress in computer technology enables the modelling and simulation of more and more complex structures in less time. It has therefore been the aim of this work to develop a 3D model of a power thyristor as main component part from power semiconductor converters.

The starting point is the power balance equation for each volume element dV, in the integral formulation:

$$\iiint \frac{\dot{j}^2}{\sigma}dV = \iiint \rho \mathbf{c} \frac{\partial T}{\partial t}dV - \iiint \text{div}(\mathcal{k} \cdot \mathbf{grad}T)dV\tag{19}$$

where:

144 Power Quality Harmonics Analysis and Real Measurements Data

0 100 200 300 400 500 600 700 **t[s]**

60el.sim 90el.sim 120el.sim 60el.exp 90el.exp 120el.exp

0 100 200 300 400 500 600 700 **t[s]**

Fig. 21. Comparison between simulation and experimental temperature rise of the case at

In both cases, at firing angle and load inductance variation, it ca be noticed closer values between simulation results and measurements. Of course, there are different temperature

L1sim L2sim L3sim L1exp L2exp L3exp

Fig. 20. Comparison between simulation and experimental temperature rise of the case at

0

0

inductance load variation

10

20

30

40

**T[ºC]**

50

60

70

firing angle variation

10

20

30

**T[ºC]**

40

50

60

T means the temperature of element [ºC];

j – current density [A/m2];

σ – electrical conductivity [1/Ωm];

ρ – material density [kg/m3];

c – specific heat [J/kgºC];

λ – thermal conductivity [W/mºC].

The left term of before equation (it exists only in the device conductor elements), denotes the heating power from the current flow. It is in balance with the heat stored by temporal change of temperature, and the power removed from the element by thermal conduction. For the steady state temperature calculation, the heat storage term is zero, and the equation (19) becomes,

$$\left[\iiint \frac{\dot{j}^2}{\sigma}dV = -\iiint div(\mathcal{A} \cdot \operatorname{grad} T)dV\right] \tag{20}$$

Taking one's stand on the above thermal equations, first of all a 3D model for a power thyristor has been developed using a specific software, the Pro-ENGINEER, an integrated thermal design tool for all type of accurate thermal analysis on devices.

It has been considered an application which includes a bidirectional bridge equiped with power thyristors type AT505, with the average direct current of 430A and an internal resistance of 0.68m. The current which flows through the converter branches is about 315A. This value allows computing the power loss for each tyristor, which results in 67.47W. The material properties of every component part of the thyristor are described in the Table 2 and the 3D thermal models of the thyristor with its main component parts and together with its heatsinks for both sides cooling are shown in Fig. 22, respectively, Fig. 23.

Thermal Analysis of Power Semiconductor Converters 147

The thermal model of the power semiconductor has been obtained by including all the piece part that is directly involved in the thermal exchange phenomenon, which is: anode copper pole, molybdenum disc, silicon chip, cathode copper pole, Fig. 22. The device ceramic enclosure has not been included in the model since the total heat flowing trough it is by far less important than the heat flowing through the copper poles. All the mechanical details which are not important for the heat transfer within the thyristor and from the thyristor to the external environment (e.g. the centering hole on the poles) have been suppressed.

 (kg/m3) 8900 2330 10220 2700 c (J/kgºC) 387 702 255 900 (W/mºC) 385 124 138 200

The heat load has been applied on the active surface of the silicon of power semiconductor. It is a uniform spatial distribution on this surface. The ambient temperature was about 25ºC. From experimental tests it was computed the convection coefficient value, kt = 14.24W/m2ºC for this type of heatsinks for thyristor cooling. Hence, it was considered the convection condition like boundary condition for the outer boundaries such as heatsinks. The convection coefficient has been applied on surfaces of heatsinks with a uniform spatial variation and a bulk temperature of 25ºC. The mesh of this 3D power semiconductor thermal model has been done using tetrahedron solids element types with the following allowable angle limits (degrees): maximum edge: 175; minimum edge: 5; maximum face: 175; minimum face: 5. The maximum aspect ratio was 30 and the maximum edge turn (degrees): 95. Also, the geometry tolerance had the following values: minimum edge length: 0.0001; minimum surface dimension: 0.0001; minimum cusp angle: 0.86; merge tolerance: 0.0001. The single pass adaptive convergence method to solve the thermal steady-state

Then, it has been made some steady-state thermal simulations for the power semiconductor. For all thermal simulations a 3D finite elements Pro-MECHANICA software has been used. The temperature distribution of the tyristor which uses double cooling, both on anode and cathode, is shown in the pictures below, Fig. 24 and Fig. 25. The maximum temperature for the power semiconductor is on the silicon area and is about 70.49ºC and the minimum of

Further on, the thermal transient simulations have been done in order to compute the

From thermal transient simulations we obtain the maximum temperature time variation and the minimum temperature time variation. From the difference between maximum temperature time variation and ambient temperature divided to total thermal load it gets the thermal transient impedance. Dividing the thermal transient impedance to the thermal resistance, the normalised thermal transient impedance can be obtained. This is a thermal quantity which reflects the power semiconductor thermal behaviour during transient

To understand and to optimize the operating mechanisms of power semiconductor converters, the thermal behaviour of the power device itself and their application is of major interest. Having the opportunity to simulate the thermal processes at the power

transient thermal impedance for power thyristor. The result is shown in Fig. 26.

Copper Silicon Molybdenum Aluminium

Parameter Material

Table 2. Material Data and Coefficients at 20ºC

simulation has been used.

conditions.

47.97ºC is on the heatsink surfaces.

Fig. 22. Thermal model of the thyristor (1 – cathode copper pole; 2 – silicon chip; 3 – molybdenum disc; 4 – anode copper)

Fig. 23. Thermal model of the assembly thyristor - heatsinks

**1** 

Fig. 22. Thermal model of the thyristor (1 – cathode copper pole; 2 – silicon chip;

3 – molybdenum disc; 4 – anode copper)

**2** 

**3** 

**4** 

Fig. 23. Thermal model of the assembly thyristor - heatsinks

The thermal model of the power semiconductor has been obtained by including all the piece part that is directly involved in the thermal exchange phenomenon, which is: anode copper pole, molybdenum disc, silicon chip, cathode copper pole, Fig. 22. The device ceramic enclosure has not been included in the model since the total heat flowing trough it is by far less important than the heat flowing through the copper poles. All the mechanical details which are not important for the heat transfer within the thyristor and from the thyristor to the external environment (e.g. the centering hole on the poles) have been suppressed.


Table 2. Material Data and Coefficients at 20ºC

The heat load has been applied on the active surface of the silicon of power semiconductor. It is a uniform spatial distribution on this surface. The ambient temperature was about 25ºC. From experimental tests it was computed the convection coefficient value, kt = 14.24W/m2ºC for this type of heatsinks for thyristor cooling. Hence, it was considered the convection condition like boundary condition for the outer boundaries such as heatsinks. The convection coefficient has been applied on surfaces of heatsinks with a uniform spatial variation and a bulk temperature of 25ºC. The mesh of this 3D power semiconductor thermal model has been done using tetrahedron solids element types with the following allowable angle limits (degrees): maximum edge: 175; minimum edge: 5; maximum face: 175; minimum face: 5. The maximum aspect ratio was 30 and the maximum edge turn (degrees): 95. Also, the geometry tolerance had the following values: minimum edge length: 0.0001; minimum surface dimension: 0.0001; minimum cusp angle: 0.86; merge tolerance: 0.0001. The single pass adaptive convergence method to solve the thermal steady-state simulation has been used.

Then, it has been made some steady-state thermal simulations for the power semiconductor. For all thermal simulations a 3D finite elements Pro-MECHANICA software has been used. The temperature distribution of the tyristor which uses double cooling, both on anode and cathode, is shown in the pictures below, Fig. 24 and Fig. 25. The maximum temperature for the power semiconductor is on the silicon area and is about 70.49ºC and the minimum of 47.97ºC is on the heatsink surfaces.

Further on, the thermal transient simulations have been done in order to compute the transient thermal impedance for power thyristor. The result is shown in Fig. 26.

From thermal transient simulations we obtain the maximum temperature time variation and the minimum temperature time variation. From the difference between maximum temperature time variation and ambient temperature divided to total thermal load it gets the thermal transient impedance. Dividing the thermal transient impedance to the thermal resistance, the normalised thermal transient impedance can be obtained. This is a thermal quantity which reflects the power semiconductor thermal behaviour during transient conditions.

To understand and to optimize the operating mechanisms of power semiconductor converters, the thermal behaviour of the power device itself and their application is of major interest. Having the opportunity to simulate the thermal processes at the power

Thermal Analysis of Power Semiconductor Converters 149

1E-06 0,00001 0,0001 0,001 0,01 0,1 1 10 100 1000 10000 100000 1000000 **t [s]**

semiconductor junction dependent on the power device design enables new features for the optimization of power semiconductor converters. This has a great impact to the

From all previous thermal modelling, simulation and experimental tests, the following conclusions about transient thermal evolution of power semiconductor devices can be

the shape of input power and temperatures evolution depend on load type, its value

increasing of load inductance value leads to decrease of input power and temperature

in the case of steady state thermal conditions, the temperature variation is not so

at big values of firing angle it can be noticed a decrease of input power values and

 because of very complex thermal phenomenon the analysis of power semiconductor device thermal field can be done using a specific 3D finite element method software; therefore, the temperature values anywhere inside or on the power semiconductor

 using the 3D simulation software there is the possibility to improve the power semiconductor converters design and also to get new solutions for a better thermal

Extending the model with thermal models for the specific applications enables the user of power semiconductors to choose the right ratings and to evaluate critical load cycles and to identify potential overload capacities for a dynamic grid loading. It was shown that the described thermal network simulation has a high potential for a variety of different

there is a good correlation between simulation results and experimental tests;

assembly can be computed both for steady-state or transient conditions;

and firing angle in the case of power semicontrolled rectifiers;

important at big values of load inductance and firing angle;

0

**4. Conclusion** 

values;

applications:

development support;

temperatures;

outlined:

Fig. 26. Transient thermal impedance of the thyristor

development and test costs of new power converters.

behaviour of power semiconductor devices.

0,1

0,2

0,3

0,4

**Zth [°C/W]**

0,5

0,6

0,7

Fig. 24. Temperature distribution through the thyristor mounted between heatsinks at 50% cross section, yz plane

Fig. 25. Temperature distribution through the thyristor mounted between heatsinks at 50% cross section, xz plane

Fig. 26. Transient thermal impedance of the thyristor

semiconductor junction dependent on the power device design enables new features for the optimization of power semiconductor converters. This has a great impact to the development and test costs of new power converters.
