High-Fidelity Liquid-cooling Thermal Modeling of a WBG-based Bidirectional DC-DC Converter for Electric Drivetrains

Abstract

The advent of Wide-Bandgap (WBG) semiconductors, e.g., Silicon Carbide (SiC) and Gallium Nitride (GaN), power electronics E-drive converters are projected to obtain an increase in power density as ~2x
for SiC devices and ~4x for GaN devices, which demand detailed thermal modeling and analysis of power semiconductors and cooling systems. This paper has proposed high-fidelity (HiFi) modeling of
bidirectional DC-DC converter coupled with liquid cooling system providing detailed information with higher accuracy and less complexity to determine performance during conceptual modeling in electric vehicle drivetrain with minimum testing and development effort.

Full text

High-Fidelity Liquid-cooling Thermal Modeling of a WBG-based
Bidirectional DC-DC Converter for Electric Drivetrains
Sajib Chakraborty1,2, Sudhanshu Goel3, Iosu Aizpuru4, Mikel Mazuela4, Roberto Klink3, and
Omar Hegazy1,2*
1Vrije Universiteit Brussel (VUB), ETEC Department & MOBI Research Group, Pleinlaan
2,1050 Brussels, Belgium;
2Flanders Make, 3001 Heverlee, Belgium
3DENSO AUTOMOTIVE Deutschland GmbH
4Mondragon Unibertsitatea, Electronics and Computing Department, Loramendi, 4;20500
Arrasate-Mondragón (Spain)
Acknowledgments
This project (HiFi-Elements) has received funding from the European Union’s Horizon
2020 research and innovation program under Grant Agreement no. 769935. We also
acknowledge Flanders make for the support to our research group.
Keywords
«High-Fidelity », «Thermal modeling», «WBG », «Bidirectional », «DC-DC converter», «E-
drivetrain».
Abstract
The advent of Wide-Bandgap (WBG) semiconductors, e.g., Silicon Carbide (SiC) and Gallium Nitride
(GaN), power electronics E-drive converters are projected to obtain an increase in power density as ~2x
for SiC devices and ~4x for GaN devices, which demand detailed thermal modeling and analysis of
power semiconductors and cooling systems. This paper has proposed high-fidelity (HiFi) modeling of
bidirectional DC-DC converter coupled with liquid cooling system providing detailed information with
higher accuracy and less complexity to determine performance during conceptual modeling in electric
vehicle drivetrain with minimum testing and development effort.
Introduction
In electric drivetrains, a bidirectional DC-DC converter (BDC) is used as a booster between the electric
motor (EM) and battery. During the motor mode, the BDC is used to boost the low unregulated battery
voltage to a highly regulated DC link voltage level, while in braking, the battery is recharged using the
buck mode of BDC and EM runs as a high voltage generator [1]–[3]. Despite their many benefits, a DC-
DC converter adds input current ripples, losses, weight and costs. Many types of research are conducted
in order to mitigate these issues; for example, the ripples and losses problem can be overcome using
interleaving techniques and by embedding WBGs semiconductors. There is also the issue of weight and
power density in the power electronic converter, which directly depends on the cooling system. In order
to mitigate this, proper thermal behavior of the module needs to be estimated. Current research focuses
on thermal modeling in the context of lifetime and reliability analysis; in fact, Design for Reliability
(DfR) was familiarized in power electronics to achieve reliability and durability benchmarks [4]-[5]. To
achieve these targets with DfR, a proper and accurate analysis of the thermal domain is essential.

Hence, to achieve accurate thermal analysis, the instantaneous losses profile of the BDC is calculated
with respect to the standard New European Driving Cycle (NEDC), which includes device losses
(switching losses and conduction losses) and passive components losses (ESR losses, air-gap losses and
core losses). Losses calculations are based on CAS120M12BM2 SiC MOSFET module datasheet values
providing by the CREE while ensuring less complexity along with high accuracy. Afterward, a liquid-
cooling system (SKiiP1814GB17E4 mounted on the fluid cooler NHC) is characterized for the
bidirectional DC-DC converter with full detailed function of flow rate, glycol concentration and fluid
temperature for water-glycol mixtures, which considers instantaneous power losses of the converter,
coolant flow rate and coolant inlet temperature as inputs. The proposed multi-physics modeling can be
directly embedded in E-drivetrain Hardware-in-Loop (HiL) testbeds for system characterization and
component validation. Therefore, the proposed HiFi model is informative and useful at the conceptual
design stage in the automotive industries to estimate the thermal behavior of the power electronics
components coupled with the cooling module, which will reduce testing and development effort can be
directed to reduce time-to-market. The flow diagram of the HiFi modeling technique is illustrated in
Fig.1.
Fig. 1. Flow diagram of HiFi modeling technique of a Bidirectional DC-DC converter.
Modeling of Instantaneous Power losses Profile
Power device loss distribution
The losses produced in power semiconductors comprise the conduction and switching losses. On the
one hand, the conduction losses are only produced during the on-state of a given semiconductor
(MOSFET, IGBT, diode, etc.) and result in the product of the voltage drop and the current through the
device, as shown in Equation (2). Although this voltage drop depends on different variables, the
conducted current and the junction temperature (Tj) are the more commonly considered factors, as
shown in Equation (1). On the other hand, switching losses are produced during the turn-on and turn-
off transitions of the semiconductors, due to the non-ideal voltage and current transitions, which produce
an eventual coexistence of voltage and current. Although the transitions depend on many different
variables (current, voltage, temperature, a driver circuit, etc.), manufacturers usually provide the energy
losses depending on the conducted current, the switched voltage and the junction temperature (Tj),
Equation (3). Therefore, as shown in Equation (4), the switching losses are modeled as the sum of the
energy losses produced for an ON and OFF switching transitions, each of them distributed along a single
I
Electrical Domain
Data Sheet Selection of WBG Semiconductor and L,C
Conduction
(VDS, IDS)
Switching
(Esw,on, Esw,off)
Thermal
(IDS,Tj[0C])
Electro-Thermal Domain
Features
• Material
(WBG, L,C)
Measurement
• Looses (W)
• Junction
Temperature (K)
Frequency(Hz)
Amp.
(normalize)
LPF
Thermal Domain
V
High_Fidelity design of Converter
with Heatsink (P_lossTotal, TH, TJ)
Ploss_T1
Temp_JUN
Ploss_Tn

Ploss_D1
Ploss_Dn

step-size-pulse (Ts) [6]. These power losses could easily be coupled to the thermal models of the
semiconductors and the resulting temperatures could be fed back again to complete the electro-thermal
coupling, being able to achieve a high degree of accuracy with a reduced computational cost. The
instantaneous voltage, current, power losses and junction temperature waveforms are depicted in Fig. 2.
 
(1)
  
(2)
  
(3)
     


(4)
Fig. 2. Instantaneous voltage, current, power losses and junction temperature waveforms.
The analysis of I, V, Tj power loss dependencies in an electric vehicle drivetrain is especially interesting
due to:
• Output current: Main contributor to semiconductor losses. Varying condition in a very different
acceleration and deceleration values. High current value variation in electric vehicle drive
patterns.
• DC link voltage: Contributes to switching losses and is especially important due to DC link
variation in battery power applications. The battery voltage could have a variation of more than
60% depending on the lithium chemistry applied.
• Junction temperature: Discontinuous power working principle (accelerations and decelerations)
and environmental temperature dependencies (summer-winter; day-night) meets mandatory to
consider Tj dependency for semiconductor losses.
Loss distribution in passive components
The inductor losses consist of core loss , conduction loss  and air-gap loss . And
the capacitor losses comprise the ESR loss of capacitor. As shown in Equation (6), the conduction loss
 is dependent on the internal resistance of Litz wire winding . The core loss  as in
Equation (7) are produced from the flux density ripple , which is proportional to the inductor current
ripple . The core losses are estimated based on the charts given by the manufacturer (METGLAS,
Inc., CC core). High-frequency gap loss  in nanocrystalline cores [7] can be computed as in
Equation (8). In addition, the ESR losses of DC link capacitor can be calculated as Equation (9). The

instantaneous current response is considered during the losses’ calculation of passive components.
Therefore, the temperature stresses in the passive components can be identified easily. The instantaneous
power losses waveform in passive components is depicted in Fig. 3.
     
(5)
  

(6)
  󰇛

󰇜
 

(7)
  


(8)
  

(9)
Fig. 3. Instantaneous power losses waveforms in passive components.
Thermal Modeling Methodology
Electro-thermal model of the switch module
The electro-thermal model of the HV DC-DC converter permits to couple the electrical output voltage
equation with the thermal circuit. The model structure is defined in Fig. 4.
This electro-thermal coupling permits to:
• Power losses modeling: Obtain a power loss dependency in the electrical switching pattern and
the junction temperature as presented in the previous subchapter.
• Output voltage modeling: The output voltage of the converter is modeled as Tj dependent. This
modeling technique permits to obtain an exact output voltage for harsh temperature
environments, and it is especially interesting in order to simulate short circuit behavior and very
tight output voltage converters.
    󰇛󰇜   󰇛󰇜
(10)
The Mid-Point Voltage VMP classically defined as 0 V or VDC depending on the switching pattern, is
redefined as an equation with current and junction temperature dependencies. This dependency is not
taken into account in most of the available electrical simulators.

Fig. 4. Electro-thermal model used for the DC-DC converter modeling. Simplified model overview for
a single semiconductor model.
Dynamic thermal modeling
The principle of dynamic thermal modeling is based on a combination of temperature dependent loss
models of power electronic devices (Switch and Diodes) and dynamic thermal models of the junction to
heatsink and heatsink to ambient behavior [8]. The device losses model describes the instantaneous
power dissipation at a given junction temperature whereas the thermal model determines the temperature
gradients across device chip, package and heatsinks as a result of power losses being injected by the
device in the thermal network. The thermal models ultimately calculate the junction temperatures used
by power losses profile. The dynamic thermal model can be represented by the following equations [9]:
    
(11)
 󰇛󰇜
(12)
 󰇛󰇜
(13)
 󰇛󰇜
(14)
Tjn is the junction temperature, ΔTSA is heatsink to the ambient temperature drop, ΔTCS is common case
to the heatsink temperature drop, ΔTJC is junction to the case temperature drop, Zth(sa) is heatsink thermal
impedance, Zth(CS) is thermal grease impedance used as case to heatsink impedance, Zth(JC) is junction to
case thermal impedance and Pn is the power losses of nth MOSFET or diode in the converter. In
continuation with the power losses modeling described in the previous section, the next sub-section
describes the modeling of the thermal module.
Thermal modeling of the switch module
Thermal equivalent models are obtained using electrical analogies to thermal parameters. The total
power losses correspond to the current source, temperature levels are represented as voltage sources and
the thermal impedances are represented as nth order RC elements as shown in Fig. 5. Foster network
parameters mentioned in vendor data sheets are used to model the thermal equivalent network at the
device level. Generally, the 4th-6th order RC network is used to represent the junction to heatsink
behavior. In this paper, [10] is used as a reference where the junction to heatsink behavior is
characterized by a 5th order network. The junction to case thermal transfer function is as follows:
󰇛󰇜󰇛󰇜  

 

 

 

   

 
(15)
Switching losses
Conduction losses
Datasheet
parameters Specialized
tests
Thermal Model
Ploss
Output voltage eq
Vout=f(Tj,I)
Tj
DPT
etc
I
2D
3D
V
Switching pattern
Datasheet
parameters
THERMAL MODEL
ELECTRICAL MODEL

󰇛󰇜
󰇛󰇜󰇛󰇜(s)
(16)
Where r1-5 and 1-5 are parameters of 5th order foster network.
Thermal modeling of the heat sink
There are primarily two approaches to electro-thermal modeling of heatsink behavior. The first is an
analytical approach using the data from vendor data sheets where the thermal impedance is represented
as 2nd-4th order foster network. However, these impedance values are defined for specific values of
coolant temperature and liquid flow rate. For accurate modeling of thermal behavior, the effect of
coolant temperature and liquid flow rate on thermal impedance must be considered using data available
from data sheets. In this paper, a 2nd order model of the heatsink is considered along with the
dependencies on coolant temperature and liquid flow rate [11]. The second approach is an experimental
approach where the dynamic thermal behavior of the heatsink is determined by feeding a constant power
loss in the cooling network and measuring the temperature behavior of the coolant in and outlet. The
thermal impedance can be derived by the ratio of the temperature difference with respect to the applied
power losses. The order and magnitudes of foster network parameters can be extracted using curve
fitting on the obtained data.
Results and discussion
The bidirectional DC-DC converter losses are measured using the load current profile of the NEDC
driving cycle. Based on the measured losses, the thermal behavior of the converter is obtained. A Foster
network is used as shown in Fig. 5, where the RC network values are taken from the datasheet to
determine the junction temperature and the heatsink temperature under different coolant flow rate
4L/min and coolant temperature of 450C for 50% water and 50% glycol (Glysantin G48 by BASF). The
thermal behavior of the proposed liquid-cooling system is realized to be satisfactory under the NEDC
driving cycle for E-drivetrains.
Fig. 5. Power losses and thermal profile of the Bidirectional DC-DC converter regarding the HiFi
thermal modeling.
TJ_S
TJ_D
Rthjc_S1
Rthjc_D1
Rthjc_S5
Rthjc_D5
Cthjc_S1
TH
Tcoolant
Rth,SA
Cth,SA
Thermal model 3-ph HV DC/DC
MOSFET Module Heatsink
Electrical domain (W)
Thermal Domain(OC)
1-ph
2-ph
3-ph
Rth,TIM
gTX
Vd Id
PLoss Pcond
Pswon Pswoff
T [s]
Cthjc_S5 Cthjc_D5
Cthjc_D1

The pressure drops of the cold plates regarding to the different flow rates are depicted in Fig. 6, when
the amount of flow rate increases by a factor of 2 and the pressure drops increase by a factor of 0.78.
Fig. 7 shows the MOSFET temperature effect at various driving conditions, quantified by different load
currents; it can be seen that for a load increases by a factor of 2, junction temperature increased on
average by 5%. At full load 50kW, the junction temperature is about 1190C at switching frequency of
60kHz, coolant flow rate of 4L/min and coolant temperature of 450C, which is significantly lower than
the upper-temperature limit of SiC technology (~1500C). Moreover, in rash driving condition with 100
kW load, the junction temperature is 1440C, which is also slightly lower than the upper limit of the
switch. The frequency effect on junction temperature at full load condition is illustrated in Fig. 8; it is
seen that the junction temperature at 60kHz is well below than the maximum tolerance limit. To verify
the DC-DC converter’s thermal modeling for E-drivetrains, NEDC driving cycle and rash-case driving
scenario are taken into consideration.
Moreover, Si MOSFETs have poor performance with respect to SiC devices at high switching
frequencies where their on-resistance (RDSon) increases by a factor of 3 over temperature increase of
1200 C as illustrated in Fig 7, which triggers thermal instability and derating of the converter during peak
power operation. However, the SiC technology ensures low RDSon at high temperatures allowing a huge
size reduction in the cooling system, which optimizes the power density (kW/l) and minimizes the cost
and expands the reliability of the bidirectional DC-DC converter in E-drivetrains.
Fig. 6. Pressure drop measurement of the DC/DC
converter’s cold plate at a different flow rate.
Fig. 7. Junction temperature measurement of the
DC/DC converter at different load current.
Fig. 8. Switching frequency effect on junction
temperature of the DC/DC converter at fixed load
power.
Fig. 9. On-resistance comparison over junction
Temperature of Si and SiC.
0
2
4
6
8
10
12
14
510 15 20
Pressure drop (kPa)
Flow rate (L/min)
0
20
40
60
80
100
120
140
10 60 110 160
Junction Temperature (0C)
Load current (A)
0
20
40
60
80
100
120
140
525 45 65
Junction Temperature (0C)
Switching frequency (kHz)

Conclusion and future work
The HiFi modeling technique proposed in this paper can accurately estimate the electro-thermal
behavior of DC-DC converter in electric vehicle drivetrains, which targets to reduce development and
testing effort of EV-industries. The calculation of the losses is accurate as of the loss data provided by
the manufacturers after the experimental validation. The proposed modeling technique is easy to be
implemented, enable an accurate estimation of the cooling characteristics of the converter system in the
E-drivetrain system.
The electro-thermal behavior will be further investigated with different driving profiles (i.e WLTP,
HWFET, NYCC) in the future work to observe their impact of temperature on the performance and
reliability.
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