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Contract No. DE-AC36-08GO28308

Conference Paper

NREL/CP-5400-74209 

April 2020 

Multi-Scale Thermal Analysis for 

Design of SiC-Based Medium Voltage 

Motor Drive

Preprint

J. Emily Cousineau,

1 Kevin Bennion,1 Karun Potty,2 He Li,2

Risha Na,2 Longya Xu,2 and Jin Wang2

1 National Renewable Energy Laboratory

2 The Ohio State University

Presented at ASME 2019 International Technical Conference and Exhibition 

on Packaging and Integration of Electronic and Photonic Microsystems

(IPACK2019) 

Anaheim, California

October 7–9, 2019
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Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

Conference Paper

NREL/CP-5400-74209 

April 2020

National Renewable Energy Laboratory

15013 Denver West Parkway

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303-275-3000 • www.nrel.gov

Multi-Scale Thermal Analysis for

Design of SiC-Based Medium Voltage 

Motor Drive

Preprint

J. Emily Cousineau,1 Kevin Bennion,1 Karun Potty,2 He Li,2

Risha Na,2 Longya Xu,2 and Jin Wang2

1 National Renewable Energy Laboratory

2 The Ohio State University

Suggested Citation

Cousineau, J. Emily, Kevin Bennion, Karun Potty, He Li, Risha Na, Longya Xu, and Jin Wang. 

2020. Multi-Scale Thermal Analysis for Design of SiC-Based Medium Voltage 

Motor Drive: Preprint. Golden, CO: National Renewable Energy Laboratory. NREL/CP5400-74209. https://www.nrel.gov/docs/fy20osti/74209.pdf
NOTICE

This work was authored in part by the National Renewable Energy Laboratory, operated by Alliance for Sustainable 

Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. Funding was 

provided by the U.S. Department of Energy Advanced Manufacturing Office. The views expressed herein do not 

necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the publisher, 

by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, 

irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for 

U.S. Government purposes.

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MULTI-SCALE THERMAL ANALYSIS FOR DESIGN OF SIC-BASED MEDIUM VOLTAGE MOTOR 

DRIVE

J. Emily Cousineau1, Kevin Bennion

National Renewable Energy Laboratory

Golden, Colorado 80401

Karun Potty, He Li, Risha Na, Longya Xu, 

Jin Wang

Department of Electrical and Computer Engineering, 

The Ohio State University

Columbus, Ohio 43210

ABSTRACT

This paper describes a multi-scale thermal analysis 

approach for the design of an air-cooled 1.7-kV SiC MOSFETbased medium-voltage variable-speed motor drive. The scope 

of the models and required efficient and flexible thermal models 

to be developed. Two modeling techniques are described that 

significantly reduced model run time and enabled more 

complex models to be run faster while retaining needed 

accuracy. The first technique uses the effectiveness-NTU 

method to extract convection boundary conditions from a CFD 

model that can be applied to a fast-running FEA model. The 

second is a porous media technique that enables system-level 

CFD simulations that incorporate effects from heat exchangers 

(e.g., pin fin heat sinks) that run in a fraction of the time 

required for fully resolved CFD simulations. The multi-scale 

approach to the thermal analysis enabled fast and accurate 

simulation for the converter design ranging from the die level 

up to the full system with 36 submodules. The modeling results 

were validated against experimental data from system tests 

performed by OSU.

Keywords: Power Electronics, Thermal Modeling, Porous 

Media, Model Simplification, Effectiveness-NTU

NOMENCLATURE 

A area

C2 internal resistance factor

CFD computational fluid dynamics

CPU central processing unit

cp specific heat

FEA finite element analysis

h convective heat transfer coefficient

ṁ mass flow rate

MMC modular multilevel converter

MOSFET metal-oxide semiconductor field-effect 

transistor

NTU number of transfer units

p pressure

Q heat

SiC silicon carbide

T temperature

UA overall heat transfer coefficient

v velocity

Greek Symbols

1/α viscous resistance

Δn porous media characteristic thickness

ε effectiveness

μ fluid viscosity

ρ density

Subscripts

c,i coolant inlet

c,o coolant outlet

j-max junction maximum

lm log-mean

surf,av surface average

1. INTRODUCTION

Computer processing power and capability increases

continuously, and supercomputers even more so. With these 

increases come the ability to perform increasingly sophisticated 

simulations in less time. However, resources, budget, and time 

are still finite, and will be for the foreseeable future. This paper 

describes two useful techniques applied to the thermal analysis 

design of OSU’s 1 MVA 1.7-kV SiC MOSFET-based modular 

multilevel converter (MMC) for driving medium-voltage (i.e., 

1 kV–35 kV[1]) electric machines as shown in Figure 1.
2 

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Figure 1: Fully assembled medium-voltage drive converter

Details of the converter design, modeling analysis, and 

results are discussed in [2]. The tower is about 1.8 m tall. The 

drive consists of 36 submodules for three electrical phases. 

Each submodule is a self-contained unit consisting of an SiC 

power module with an air-cooled heat exchanger and capacitor. 

The middle shelf contains the arm inductors cooled by natural 

convection. The open rack design and reliance on air cooling 

and natural convection necessitated running the entire rack in 

simulation to determine, limit, and eliminate possible hot spots. 

For the air-cooled system, it was necessary to determine the 

overall airflow requirements, monitor air temperatures, and 

support ducting designs for airflow.

The thermal analysis of the system required studying the 

heat transfer characteristics from the semiconductor device out 

to the full system level of the complete tower. Using a single 

model of the full tower system to study the semiconductor 

module and device temperature profiles would be impractical. 

To support the thermal analysis and design, the analysis was 

performed at multiple scales from the chip level up to the full 

system.

Utilizing the multi-scale approach shown in Figure 2, the 

problem was divided into interrelated simulations. The 

modeling approach links a detailed device-scale FEA thermal 

model of the power module, detailed CFD model of the heat 

exchanger/fan subsystem, and the system-level full-tower CFD. 

This work highlights approaches to transfer results between the 

multiple simulation scales (Figure 1) and the objectives of each 

model scale.

The FEA model shown in Figure 2a is a fully resolved 

thermal model of the power module, including solder layers and 

attachments. The purpose of the FEA model is to determine the 

device or MOSFET junction temperatures at specific operating 

conditions for the converter. The boundary conditions for the 

model include the device heat loads, convective heat transfer 

coefficient (h), and ambient air temperature (T∞). The device 

heat loads were approximated as volumetric heat loads based 

on the converter operating conditions. Prior to selection of the 

heat exchanger and fan components, the FEA model was used 

to identity the initial performance requirements for the heat 

exchanger. Once a heat exchanger and fan were selected, the 

convective heat transfer coefficient and ambient temperature 

were transferred to the heat exchanger/fan CFD model (Figure

2b) and the full tower CFD model (Figure 2c)

The heat exchanger/fan model is a detailed CFD model of 

the heat exchanger and fan mounted to the power module. The 

objective of the heat exchanger CFD model is to estimate the 

convective heat transfer boundary condition (h) applied to the 

device-level FEA model. In addition, the heat exchanger CFD 

model provides inputs to the full-tower CFD model, including 

the heat exchanger pressure drop and the air temperature rise 

through the heat exchanger. The ambient temperature from the 

full-tower CFD model feeds into the heat exchanger/fan CFD 

model as highlighted in Figure 2b. The convective boundary 

condition (h) was estimated utilizing the effectiveness-NTU 

heat exchanger properties extracted from the fully resolved heat 

exchanger model (Figure 2b) and ambient temperature 

determined from the heat exchanger CFD model and full tower 

model (Figure 2c).

The full-tower CFD model (Figure 2c) focused on 

simulating the airflow through the entire system. The objective 

of the full-tower CFD model was to ensure uniform airflow and 

temperatures through the submodule assemblies. The model 

extracted the inlet air temperature to each of the submodules, 

which were used in the previously described module FEA 

thermal model and heat exchanger CFD model. The pressure 

drop calculated from the heat exchanger CFD model (Figure

2b) was used to construct an equivalent porous media region 

that was used to reduce computational requirements for the fulltower CFD model shown in Figure 2c. 

Figure 2: The three primary models used in analysis and their 

interrelationships. The arrows denote properties that were 

obtained from each model as inputs to the other models. (a) 

Device-scale FEA model. (b) Heat exchanger CFD model. (c) 

Full-tower CFD model.

The benefits of the technique are clear. The quartersymmetry heat exchanger shown in Figure 2b consisted of 

5.2 million elements and took about 16 CPU-hours to solve. 

The FEA model shown in Figure 2a could only take advantage 

of one symmetry plane; thus, if a fully resolved model of the 

heat exchanger was used, it would require doubling the number 

of required control volumes and hence time to solve. However, 

extracting a convection coefficient from the quarter symmetry 

and applying it to the FEA in lieu of a fully resolved model 

resulted in a model that gave the same results, but with 

substantially reduced computation time. On the other end, using 
3 

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a porous media simplification in place of the pin-fin heat 

exchanger facilitated running full-scale CFD simulations of the 

MMC tower. The scope of the simulation domain in the full 

MMC tower model was such that it would not have been 

possible to run within the time constraints of the project without 

using the porous media simplification. 

This paper highlights the techniques used for linking the 

models. Two model simplifications, effectiveness-NTU and 

porous media, will be described. Both simplifications provide 

substantial resource and time savings with minimal sacrifice in 

accuracy when applied appropriately. The procedure for each 

model simplification will be shown in detail, as well as the 

results and limitations of each approach.

2. APPROACH

This paper highlights the approach to analytically link the 

different model scales to efficiently model the system from the 

device level to the full tower. Figure 3 summarizes the different 

simulation scales and highlights what is transferred between the 

modeling scales. The effectiveness-NTU method links the 

device and power module FEA model to the heat exchanger 

CFD. The porous media model links the heat exchanger CFD 

to the submodule and full-tower CFD. Each of these methods is 

described in more detail below.

Figure 3 shows the different simulation scales used in the 

project. In addition to the simulation scales highlighted in 

Figure 2, an additional “debugging” simulation scale 

(Submodule CFD in Figure 3) was added to minimize the 

number of times the full system model needed to be computed. 

Figure 3: Simulation scales and relationships utilized in 

MMC analysis.

2.1 Effectiveness-NTU Technique

The effectiveness-NTU method was chosen to represent 

the characteristic convective heat transfer coefficient of the heat 

exchanger. The approach was chosen because it captures the 

effect of the fluid properties and flow rate within the heat 

exchanger as highlighted by Moffat [3]. The approach 

described below outlines a method of extracting the effective 

convective heat transfer coefficient from a CFD model using 

the effectiveness-NTU approach. The benefit of the approach is 

it allows the performance and the heat exchanger to be modeled 

within the FEA thermal model with a convective heat transfer 

boundary condition.

A schematic of the effectiveness-NTU technique is shown 

in Figure 4. Note that the heat exchanger’s heat spreader is 

included in both the FEA and CFD models. The technique takes 

advantage of the physical purpose of the heat spreader to 

average the heat flow from the baseplate into the heat exchanger 

fins. 

The first step in extracting an effective convective heat 

transfer coefficient from the heat exchanger CFD model was to 

extract the average heat flux. For simple setups where all of the 

heat generated by the package is dissipated by a single heat 

spreader, this calculation is trivial (total heat divided by total 

contact area between the module base plate and heat spreader). 

If multiple heat spreaders are used, an initial FEA may be 

required to obtain the appropriate heat fluxes for each heat 

exchanger.

Extraction of the convection coefficient is an analytical 

process outlined in the literature [3], [4]. The process is stepped 

through below for convenience to the reader. The calculation 

begins with obtaining the differences in temperatures between 

the surface of the heat spreader, and inlet and outlet 

temperatures (ΔT) as shown in Equation 1.

Figure 4: Schematic of effectiveness-NTU technique.

∆TT1 = TTssssssss,aaaa − TTcc,oo ; ∆TT2 = TTssssssss,aaaa − TTcc,ii (1)

where Tsurf,av is the area average surface temperature of the 

plane where the heat spreader meets the fins, including the 

surface temperature and the cross-section through the fins. Tc,o 

and Tc,i are the mass flow average temperatures of the coolant 

at the outlet and inlet, respectively. Overall heat transfer 

coefficient (UA) uses the log-mean temperature difference as 

calculated in Equation 2.

∆TTllll = (∆TT1 − ∆TT2)

LLLLLLee(∆TT1⁄∆TT2) (2) 

Next, the UA is obtained in Equation 3.

UUUU = QQ⁄∆TTllll (3) 
4 

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where Q is total heat through the control surface. In our 

experience, 1/UA tends to overestimate the convection 

coefficient when using Tc,i, so the NTU refinement is used as 

shown in Equation 4.

NN = UUUU⁄mṁ ccpp (4) 

where ṁ is the mass flow through the system, and cp is the mass 

flow average specific heat of the fluid volume. Typically, a heat 

exchanger will have a high enough flow rate that the specific 

heat does not change significantly as it passes through the heat 

exchanger. If the specific heat changes substantially (such as a 

phase change), this technique will not be valid. Finally, the 

effectiveness ε is calculated as shown in Equation 5.

εε = 1 − ee−NNNNNN (5) 

The convection coefficient (h) is calculated in Equation 6 and 

applied to the FEA model as shown in Figure 4.

h = εεmṁ ccpp⁄ (6) 

where A is the contact area between the module baseplate and 

heat exchanger spreader.

2.2 Porous Media Approximation

It is often impractical to geometrically model every detail 

of a component in a computational model; therefore, 

simplifications are used. For example, electric machines have 

multiple composite components (e.g., windings, lamination 

stacks). For an FEA thermal model, modeling each individual 

wire within a winding or each sheet of metal within a lamination 

stack would be extremely time consuming. Instead these 

composite components are modeled with representative thermal 

properties that treat the component as a continuum to reach a 

solution [5]. There is also an analogue of the composite material 

for fluid flow in CFD called porous media. Instead of resolving 

the flow field through intricate passages and fins of a heat 

exchanger, a zone with effective pressure losses can be 

substituted to simplify the model while still retaining the intent. 

The porous media model requires two inputs: viscous resistance 

and internal resistance factors. While there are multiple 

methods to calculate these factors, this paper will cover a simple 

method that uses pressure and velocity data from the fully 

resolved model [6]. 

The first step is to obtain a quadratic equation relating 

pressure drop (Δp) to velocity (v) as shown in Equation 7. In 

this case, the air velocity range was used to represent the air 

velocities obtained in the heat exchanger-level CFD. Simulated 

data are not subject to noise or measurement uncertainty, so 

only a minimum number of points are needed to obtain the 

coefficients for Equation 7. If these were actual experimental 

data, it would be advisable to obtain at least three times as many 

data points. If the data do not follow the quadratic curve in 

Equation 7, it may be an indication that the porous media 

approximation is unsuitable for the system. Note that the 

coefficient C is calculated in Equation 7. Physically, C should 

be zero; however, it was found that forcing the curve fit through 

the origin produced less agreement between the fully resolved 

and porous media models than a curve that is allowed to offset. 

Figure 5: Pressure drop versus velocity plots for cross-fin (top) 

and inline flow (bottom). The flow direction relative to the fins 

is shown at the right of each plot.

Because the pressure drop is different for flow across the fins 

as compared to flow in-line with the fins, it was necessary to 

run simulations for both flow directions of the cross-fin flow 

shown in Figure 5. The resulting porous zone was orthotropic.

∆pp = vv2 + BB + CC (7) 

From Equation 7, the viscous resistance (1/α) and the internal 

resistance factor (C2) can be obtained using the relationships 

shown in Equations 8 and 9.

1⁄αα = BB⁄(μμ ∙ ∆nn) (8) 

where B is the coefficient from Equation 7, μ is the viscosity, 

and Δn is the thickness of the porous media region in line with 

the flow.

CC2 = 2 ⁄(ρρ ∙ ∆nn) (9) 

where A is the coefficient from Equation 7, and ρ is the density 

of the fluid.

Once the above procedure was applied to develop the 

porous media parameters specific to the pin fin heat sink, it was 

necessary to correctly determine the heat transfer from the solid 

zone to the fluid zone. For this it was necessary to calculate the 

porosity. For this model, the porosity was determined to be 0.96 

using a simple Newton-Raphson iterative process to find the 

porosity value that resulted in the same temperature rise of the 

fluid as the fully resolved pin fin model.

Finally, the porosity parameter (in ANSYS Fluent) was 

used to tune the thermal performance of the porous media heat 

exchanger.
5 

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3. RESULTS & DISCUSSION

The effectiveness-NTU and porous media methods 

provided significant time saving benefits compared to the fully 

resolved models, with only a modest reduction in fidelity. The 

reduction in model fidelity was far outweighed by the 

throughput and responsiveness of the simplified models. The 

effectiveness-NTU technique resulted in a tremendously faster 

solution speed than the fully resolved heat exchanger model. 

Key results, such as maximum junction temperature, matched 

the fully resolved model exactly. The porous media 

approximation resulted in a 90% reduction in run-time and 

memory usage for the model, with only a modest reduction in 

accuracy.

To validate the model, a negative temperature coefficient 

(NTC) thermistor was included in the FEA device model 

analogous to the NTC on the physical power module. The 

temperature measurement of the NTC was 110°C, and the FEA 

computed value for the same location was 106°C. The 4°C 

difference between model and experiment was considered 

acceptable given the temperature limit of 125°C. 

3.1 Effectiveness-NTU Technique Results

As mentioned above, the device FEA model using a 

convection coefficient calculated using the effectiveness-NTU 

technique gave identical results to the fully resolved CFD heat 

exchanger model, which are shown in Figure 6. The notable 

difference was the time to reach the solution. The fully resolved 

model took 16 CPU-hours to solve, amounting to about 15 

minutes to obtain a solution on a 64-core system. However, a 

solution could be obtained from the device FEA model in just 

under 3 seconds on a standard workstation. This resulted in a 

significant amount of flexibility and design space exploration 

that would not have been possible with a fully resolved model. 

It also enabled transient simulations to be run which would not 

have been possible to achieve within the budget and time 

constraints of the project using the fully resolved model.

Figure 6: Comparison of surface temperature of plate heater 

mounted on heat exchanger. Left: Fully resolved CFD model. 

Right: FEA model with effective convection coefficient. 

The intrinsic limitation of the device FEA model was that

it could not predict temperature rise in the fluid or evaluate 

different fluid flow rates, which require running the fully 

resolved CFD heat exchanger model and recalculating the 

convection coefficient, as necessary. Another limitation would 

be if the temperature distribution in the heat exchanger varied 

significantly enough to result in variation in local heat transfer 

coefficients. If the fluid flow rate was so slow that the properties 

could change significantly as the fluid moved through the heat 

exchanger, the technique may not be valid. General 

quantification of when the effectiveness-NTU simplification 

breaks down is beyond the scope of this paper. It is always a 

good practice to verify simplifications against high-fidelity 

data. 

3.2 Porous Media Results

The differences in key parameters are shown in Table 1. 

Average refers to mass flow average. Fan velocity is the 

average velocity through the fan zone. ΔP is the average 

pressure drop from the inlet to the fan boundary. ΔT ave is the 

average temperature rise through the porous zone. ΔT max is 

the maximum temperature rise through the porous zone, which 

was matched to the fully resolved model by adjusting the 

porosity parameter in ANSYS Fluent. 

Table 1: Comparison of critical parameters between the 

fully resolved model and porous media model.

Fan Velocity ΔP

ΔT 

average

ΔT 

max

Model (m/s) (Pa) (°C) (°C)

Fully Resolved 3.18 47.52 0.68 2.10

Porous Media 3.61 47.96 0.70 2.10

Difference 13.5% 0.9% 1.8% 0.0%

With the exception of the average velocity through the fan 

boundary, the critical parameters were within 2% of the fully 

resolved model. The porous media model differed from the 

fully resolved model by 13.5% for the average velocity through 

the fan zone. A notion as to why this occurred is shown in 

Figure 7.

Figure 7: Comparison of critical parameters between the fully 

resolved model (top) and porous zone model (bottom).

The porous zone accurately replicates the pressure and 

temperature fields through the heat exchanger. The velocity 

field was not accurately captured because the porous media 

approximation only models the pressure drop through the heat 

exchanger. In the fully resolved model, the geometry causes 

constrictions through which the flow must pass, resulting in 

higher localized velocities, boundary effects, and changes in 

direction as the air flows past the obstacles. No such obstacles 

exist in the porous zone. This is an important limitation of the 

porous media model. It cannot replicate the flow field through 

the zone. Fortunately, resolving the velocity field through the 
6 

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heat exchangers was not necessary in the full system model, 

only the fluid temperature rise and pressure drops through the 

heat exchangers were needed. 

Accepting the 2% reduction in accuracy of pressure drop 

and temperature rise in the porous media model reduced the run 

time of the full system model dramatically. While a version of 

the full system model containing fully resolved heat exchangers 

was not run, it was estimated based on the number of control 

volumes saved by using the porous media model that the run 

time was reduced by 83%. This translated into a time savings 

of 108,000 CPU-hours on hardware available at the time of the 

project (2017). Put another way, on a 128-core system a fully 

resolved full-system model would have taken six weeks to 

complete and required prodigious quantities of physical 

memory, while the full system model using the porous media 

model only took about seven days to run.

Figure 8: Left, the simulation revealed an air flow issue that 

was corrected easily with a baffle (right). The left image only 

has a few submodules included to reduce time requirements, 

while the right image is representative of a final run including 

all submodules used as a final check of the system.

The full system model was able to identify issues with 

airflow for the system. For example, in Figure 8 it was 

identified that heat coming off an inductor on the fourth shelf 

would create a plume that ended up being pulled into a module 

on the top shelf, raising its temperature by several degrees. By 

installing a simple baffle on the front of the shelf above the 

inductor bank the issue was resolved. Utilizing the porous 

media simplification enabled the full system model to be run 

multiple times, allowing identification and correction of flow 

issues prior to turning on the MMC tower experimental setup, 

and potentially saving the expense of having to identify the 

problem and, in the worst-case, replacing a failed module. The 

issue would have been difficult to detect in the actual test setup 

due to safety requirements (no one was allowed in the room 

while operating) and would have only showed up as a hot-spot 

that would have resulted in project delays to identify and 

resolve.

4. CONCLUSION

This paper outlines two methods for simplifying 

computational models to significantly reduce run time and 

resource requirements, while obtaining reliable and accurate 

results. The effectiveness-NTU method is used to generate 

boundary conditions for a detailed, fast-running FEA model 

from a fully resolved CFD model. The effectiveness-NTU 

method allows engineers to simultaneously take advantage of 

the fidelity of CFD simulation and the speed of FEA simulation, 

reducing the time requirements for analyzing “what-if” 

scenarios and design changes. The porous media method 

enables analysis of flow fields around heat exchangers without 

the additional computational expense of geometrically 

modeling the heat exchanger itself, facilitating system-level 

simulation. By performing system-level simulations it was 

possible to evaluate the entire design and check solutions to 

potential problems before running the experimental setup, 

reducing risk of failed parts and improving safety.

ACKNOWLEDGMENTS 

This work was authored in part by the National Renewable 

Energy Laboratory, operated by Alliance for Sustainable 

Energy, LLC, for the U.S. Department of Energy (DOE) under 

Contract No. DE-AC36-08GO28308. Funding was provided by

the U.S. Department of Energy Advanced Manufacturing 

Office. The views expressed in the article do not necessarily 

represent the views of the DOE or the U.S. Government. The 

U.S. Government retains and the publisher, by accepting the 

article for publication, acknowledges that the U.S. Government 

retains a nonexclusive, paid-up, irrevocable, worldwide license 

to publish or reproduce the published form of this work, or 

allow others to do so, for U.S. Government purposes. 

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[2] H. Li et al., “Hardware Design of A 1.7 Kv Sic MOSFET 

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