Thermal Consideration and Design for a 200-kW SiC-Based High-Density Three-Phase Inverter in More Electric Aircraft

As advances in semiconductor, dielectric, and magnetic materials enhance the power density of power conversion systems, the emphasis on efficient cooling solutions becomes paramount. Effective thermal management is vital as it directly influences the power density and reliability of power inverters. This is especially crucial for high-altitude motor drives, given the challenges posed by reduced air density. This article provides a design process of thermal management for high-density high-power inverters. Thermal models for different scenarios are derived, and the hotspot temperature can be estimated under different cooling conditions. To demonstrate the proposed design process, a 200-kW three-level T-type propulsion inverter designed for an altitude of 7620 m (25 000 ft) is used to present the thermal designs. Several thermal mitigation techniques are also introduced. A critical finding is the potential for stagnating air spaces to produce localized hotspots in areas such as the busbar, gate-driver boards, and terminals. Historically, these hotspots have been overlooked, yet they can significantly degrade overall thermal performance and system reliability. To address the thermal issue of hotspots caused by stagnating air space, several solutions are proposed. Of these, the localized forced cooling air duct (AD) solution is selected in this work. By optimizing both internal and external airflows, the hotspot temperature in the stagnating air space is reduced by 37% using the designed AD without oversizing the overall cooling system. Moreover, based on full-power experimental thermal tests, we demonstrate that the inverter’s hotspot temperature within a sealed enclosure can be kept below 130 °C in an environment of 75 °C and at an altitude of 7620 m. The culmination of our research validates the efficacy of the proposed design process.

Abstract-As advances in semiconductor, dielectric, and magnetic materials enhance the power density of power conversion systems, the emphasis on efficient cooling solutions becomes paramount.Effective thermal management is vital as it directly influences the power density and reliability of power inverters.This is especially crucial for high-altitude motor drives, given the challenges posed by reduced air density.This article provides a design process of thermal management for high-density highpower inverters.Thermal models for different scenarios are derived, and the hotspot temperature can be estimated under different cooling conditions.To demonstrate the proposed design process, a 200-kW three-level T-type propulsion inverter designed for an altitude of 7620 m (25 000 ft) is used to present the thermal designs.Several thermal mitigation techniques are also introduced.A critical finding is the potential for stagnating air spaces to produce localized hotspots in areas such as the busbar, gate-driver boards, and terminals.Historically, these hotspots have been overlooked, yet they can significantly degrade overall thermal performance and system reliability.To address the thermal issue of hotspots caused by stagnating air space, several solutions are proposed.Of these, the localized forced cooling air duct (AD) solution is selected in this work.By optimizing both internal and external airflows, the hotspot temperature in the stagnating air space is reduced by 37% using the designed AD without oversizing the overall cooling system.Moreover, based on full-power experimental thermal tests, we demonstrate that the inverter's hotspot temperature within a sealed enclosure can be kept below 130 • C in an environment of 75 • C and at an altitude of 7620 m.The culmination of our research validates the efficacy of the proposed design process.
Index Terms-High density, high power, more electric aircraft (MEA), propulsion inverters, thermal management.

I. INTRODUCTION
H YBRID and full electric propulsions have emerged as leading contenders for reducing exhaust emissions [1].Power electronic drives that spin the motor-fan propulsor need to deliver high efficiency and high power density.Siliconcarbide (SiC) power devices provide a promising performance to achieve these targets compared to conventional silicon (Si) devices [2], [3], [4], [5].Combined with multilevel inverter topology, the propulsion drive features low switching loss and low electromagnetic interference (EMI) noise [6], [7].However, as power electronics become more compact, thermal challenges arise due to elevated heat flux.These thermal issues can lead to system failures, such as component cracks, solder joint fatigue, and wire liftoffs [8], [9].In high altitudes, the harsh environment worsens the thermal conditions because of the decreased air density [10], [11], [12], [13].
Efficient thermal management aims to keep all hotspot temperatures within safe limits in power inverters.To cool power devices, single-phase cooling using coolants of air or water mixtures is the most popular.However, in traction or propulsion systems, the inverters are often housed in sealed enclosures for safety reasons, which makes it challenging for conventional air cooling to meet the cooling requirements [14], [15], [16], [17], [18].The cooling capability of conventional forced air cooling is usually lower than 50 W/cm 2 [19], [20] and is insufficient to meet cooling demand for high-power devices especially when the total loss exceeds 1500 W [21].To address the cooling demand of higher power dissipation, microchannel liquid cooling (MLC), which has a cooling capability higher than 100 W/cm 2 , has become a widely adopted solution in power inverters due to its industry maturity, low weight, and low cost [15].Researchers have conducted studies to optimize the thermal performance of MLC [22], [23], [24], [25], [26], [27], [28], [29].The results indicate that the cooling capacity of MLC is significantly influenced by factors such as channel geometry, fluid characteristics, and coolant path configuration [30], [31], [32], [33].
The cooling capability of the system can be enhanced by using a coolant with higher thermal conductivity, such as a metal liquid coolant.This approach has been shown to reduce the temperature rise by 38% [34].In addition, recent studies have demonstrated the benefits of reduced pump power consumption compared to water-based pumps [35].The combination of metal liquid coolant and MLC has been demonstrated to achieve cooling capacities greater than 1000 W/cm 2 [36].Another advanced single-phase cooling technique, jet impingement liquid cooling, can offer cooling capability ranging from 200 to 1000 W/cm 2 [37].The cooling capacity of this method is largely impacted by nozzle design [23], [38], [39], [40], [41], [42].Although jet impingement has been utilized in some applications [43], [44], [45], it is not commonly adopted in electric vehicles (EVs) or high-altitude more electric aircraft (MEA) due to its higher pressure drop and complex structure [23].The risk of coolant leakage between the device and the cooling chamber also renders it unsuitable for high-altitude MEA applications.
Two-phase cooling technologies, such as vapor chambers, offer cooling capabilities beyond 1000 W/cm 2 .The technique leverages the fluid phase change transition and exhibits higher heat transfer efficiency and excellent heat spreading performance, making it ideal for applications with limited space constraints [46], [47], [48], [49].The vapor chamber can also be utilized as a substitute for traditional copper baseplate of MLC to reduce thermal resistance and improve temperature distribution.A study [50] demonstrated that the maximum temperature can be reduced by 26% and temperature distribution improved.Furthermore, an ultrathin vapor chamber with a thickness of 0.4 mm has been found to possess thermal conductivity 30 times greater than that of a pure copper baseplate [51].
Recently, researchers have focused on eliminating the thermal interface material (TIM) layer by integrating the cooling device into the device package or housing [52], [53].Studies [54] and [55] have demonstrated that incorporating MLC into an aluminum nitride (AlN)-layer in the direct bond copper (DBC) layer reduces thermal resistance by 80%.This concept has also been utilized in some EVs for power devices [56].The MLC has also been embedded in a printed circuit board (PCB) to cool chips [57].A vapor chamber baseplate with a DBC substrate integrated into power modules was presented in [58], resulting in a 40% improvement in total loop thermal resistance.Double-side cooling has been demonstrated for a 10-kV SiC MOSFET module [59], [60], achieving a cooling capability higher than 250 W/cm 2 .A comprehensive comparison of single-side cooling for different PCB technologies for power dies embedded in a PCB was recently published in [61], and double-side cooling for embedded die PCBs was also shown to result in a 57% reduction in junction-to-case thermal resistance compared to TO-247 devices [62].
Effective cooling of components beyond power devices is also a focus of research to mitigate localized hotspots.A thermal model for PCB-winding-based transformers is proposed and shows accuracy [63].In [64], an air-cooling duct is designed to cool planar transformer windings.By optimizing the cooling airflow, the peak winding temperature is reduced by 8%, and the power consumption is four times smaller than that without airflow optimization.Similarly, Ruan et al. [65] utilized forced air cooling for the PCB-winding of transformers, reducing hotspot temperatures by 40%.
The combination of forced air and phase change heat pipe has also been applied to cool transformer, as described in [66] and [67].A liquid cooling chamber was designed for 50-kW filters in high-altitude applications in [68].This approach was also utilized to cool EMI filters, as shown in [69].
Though cooling has been done for individual components in high-density power electronics inverters, a systematical thermal design process is missing in the literature.This article aims to provide a design process for thermal management.After all, optimal electrical design can only be achieved by having good thermal performance.The outline of this article is given as follows.In Section II, comprehensive thermal modeling, high-altitude impact, and proposed thermal design process are introduced.Section III presents the demonstrated 200-kW three-level (3-L) T-type inverter with its specifications.Thermal mitigation strategies and design for localized heat sources are also shown.Following the design workflow, the cooling design for SiC power modules is conducted in Section IV.Then, Section V discusses the thermal impact of stagnating air space and the proposed air-cooling duct solution with airflow optimization.All thermal designs are verified by experimental results shown in Section VI.Finally, Section VII draws the main conclusions.

II. THERMAL MODELING AND THERMAL DESIGN PROCESS
Before establishing the design process of thermal management, a proper thermal model should be built to understand heat transfer.In all cases, the heat source temperature T hs in power inverters can be impacted by factors listed as follows: 1) heat source; 2) heat transfer form; 3) heat transfer path; 4) ambient environment or cooling condition.In a thermal system, the heat flux dissipated from a heat source will always seek a path to transfer to the lowest temperature.This temperature is usually determined by the ambient environment or cooling conditions.Multiple paths may exist for heat dissipation, and each path may involve various forms of heat transfer, such as conduction between solids, convection between solid and fluid, and radiation between surfaces.The specific form and path of heat transfer vary depending on the situation.However, all cases can be described by using a thermal resistance R th network.

A. Modeling of Thermal Path With Passive Cooling
Fig. 1 illustrates the simplest thermal structure, wherein a heat source with passive cooling is located inside a sealed enclosure.For the purpose of analysis, the heat source can be assumed to have a rectangular body.T enc,int and T enc,ext denote the temperatures of the internal and external sides of the enclosure, respectively.To model this structure, the generated heat q is transferred from T hs to the ambient temperature T amb through events in categories of the following: 1) T hs to heat source surface T hs,surf by conduction; 2) T hs,surf to internal air T air,int by convection; 3) T air,int to T amb by heat exchange; 4) T hs,surf to T enc,int and T enc,ext to T amb through radiation.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The first event involves sole conduction through the heat source body, which may consist of various conduction paths such as die bonding, lead frame, device package, PCB, and thermal via.The conduction thermal resistance R th,cond can be expressed as where L cond , k cond , and A cond are the thickness, thermal conductivity, and area of the solid, respectively.In the second event, the heat is transferred by convection, as shown in the dashed arrow in Fig. 1.By defining the T air,int as the average bulk temperature of internal air, the convective thermal resistance R th,conv can be written as where h conv is the convective heat transfer coefficient where A conv is the convection area, k air is the conductivity of the air, and L c is the characteristic length which is defined as where P is the perimeter of the object's surface.Nu in (3) is the Nusselt number.For the case of natural convection, the correlation of Nu is impacted by the directions of convection.
By assuming that all six surfaces of the heat source are flat surfaces, the empirical Nu for top, bottom, and vertical surfaces can be derived as [70], [71] N u top = 0.54(GrPr) 1/4 10 4 < GrPr < 10 7 0.15(GrPr) 1/3 10 7 < GrPr < 10 11 (5) N u bot = 0.27(GrPr) 1/4 10 5 < GrPr < 10 11 (6) 1 + (0.492/Pr) 1 + (0.492/P r) 9/16 4/6 GrPr ⩽ 10 9 (7) where Gr is the Grashof number that describes the ratio between buoyancy to viscous forces acting on air and Pr is the Prandtl number that defines the ratio of momentum diffusivity and thermal diffusivity.It is clear that Nu top is the highest due to the nature of fluid mechanics, leading to a higher h conv at the top surface compared to bottom and vertical surfaces.Gr and Pr in ( 5)-( 7) can be expressed as where g is the gravitational acceleration, β is the thermal expansion coefficient, and ν is the kinematic viscosity.C ρ is the specific heat, µ is the dynamic viscosity, and ρ is the fluid density.
The mechanism of the third event can be understood through the analogy of a heat exchanger, in which two fluids are separated by a solid that facilitates heat exchange between them.The solid can be assumed to be a flat, clean, and unfinned surface composed of a single material.Therefore, the R th components in the third event consist of two R th,conv 's in series with one R th,cond in the middle of them.In addition, the third event is in series with the first and second events.
For the final event, heat can also be transferred through radiation without any interaction with air.Unlike conduction and convection, radiation does not require a medium and is most efficient in a vacuum.Radiation can also occur between two bodies separated by a medium at a temperature colder than both bodies.Therefore, an additional path for radiation appears between two surfaces and is in parallel with the previous events.Assuming that the heat source within the enclosure is one enclosed system, with radiation q rad,int , while the enclosure surrounded by external isothermal ambient is another enclosed system with q rad,ext , the equations can be written by obeying Kirchhoff's law where σ is Stefan-Boltzmann's constant, ε is the emissivity of the material based on its radiative property, and F is the view factor which depends on the geometry.For the second enclosed system, since the area of ambient air A amb can be Fig. 2. Thermal structure and corresponding R th network when the forced or active cooling method is adopted for the heat source.
assumed to be infinite, and F enc,ext−amb equals 1, then ( 11) can be simplified as It is observed that the radiation transfer is positively related to temperature, while the temperature dependence of convective h conv is usually weak.The radiative thermal resistance R th,rad is Finally, by combining (1)-( 13), the corresponding R th network for Fig. 1 can be depicted.The model is valid when assumptions are made as follows.
1) The system reaches a steady state.
2) The surfaces are isothermal.
3) The surfaces are gray bodies (emissivity = absorptivity), opaque (transmissivity = 0), and diffuse.4) The radiation is uniform on each surface.The model in Fig. 1 illustrates the mechanism of heat transfer from the heat source to the ambient.The steady state T hs requires an iterative process for results to converge, which can be easily implemented in computing software, such as MATLAB.

B. Modeling of Thermal Path With Active Cooling
If the cooling solutions, such as forced air or liquid cooling, are adopted to cool components with high heat flux, the thermal scenario is described in Fig. 2. The heat source inside the enclosure is attached to the cooling device, such as a heat sink or cold plate.The cooling path aims to bring heat to the ambient or external system.To model the structure, the mechanism is summarized as in the following events: 1) T hs to T hs,surf through conduction; 2) T hs,surf to T cool,surf1 to T cool,surf2 through spreading and conduction;  I. 3) T cool,surf2 to T cool,out through convection; 4) temperature rise between inlet T cool,in and outlet T cool,out .
Similarly, the first event involves conduction from T hs to T hs,surf .In the second event, heat spreads from T hs,surf to T cool,surf1 due to area mismatch, followed by conduction from T cool,surf1 to T cool,surf2 , which contacts the cooling path.If the cooling device area is designed to be the same or similar to the heat source area, the spreading thermal resistance R th,spre can be negligible [72].In the third event, the general expression is given in (2).The value of h conv varies depending on the cooling techniques and requires empirical study.For the final event, R th,calo can be expressed as [73] where ṁ is the mass flow rate and R th,calo is usually a much smaller fraction of the total R th .Based on the above equations, the R th network is illustrated in Fig. 2 with assumptions.
1) The natural convection and radiation from the heat source to the ambient are neglected since they are much larger than the branch of the active cooling path.
2) The fluid temperature is considered the average bulk temperature of the fluid.

C. High-Altitude Impact
In high-altitude applications, the harsh environment causes deterioration of convective R th,conv due to the decreased air density.Table I lists the parameters of air at both sea level and 7620 m (25 000 ft) in 75 • C ambient.Fig. 3 further shows the comparisons of calculated R th,conv at different altitudes with different natural convective areas A conv .Due to air's lower ρ and higher ν, Gr and Pr are influenced, and R th,conv at 7620 m Fig. 4. Proposed design process of thermal management.becomes higher than that at sea level.Fig. 3 also suggests that the thermal path is mainly determined by R th,conv,top and R th,conv,bot in which R th,conv,ver can be neglected.

D. Design Process of Thermal Management
Fig. 4 presents a design process of thermal management.First, the heat sources and ambient environment of the inverter should be identified.Once q from the heat source is obtained, a decision must be made to use either natural convection (with passive cooling) or forced convection (with active cooling) based on the volume density (VD) and weight density (WD) of the two cases.Based on the power dissipation of the object, a cooling method with sufficient cooling capacity can be preliminarily selected.T hs can be estimated by using models presented in Figs. 1 and 2. If q cannot be further decreased, the loop R th should be minimized by modifying geometry parameters or adopting more advanced cooling.Once T hs meets the targeted temperature T hs,max , the VD and WD of both cases can be calculated and compared to make a final decision based on the application's requirement.In addition, if the cooling method is used to cool multiple heat sources, the cooling path can be arranged in either series or parallel configurations.The design stage should also consider electrical performances, and the process can be optimized utilizing finite element analysis (FEA) or computational fluid dynamics (CFD) simulations.It is crucial to identify any stagnating air space in the designed structure.As power inverters become more compact, the trapping heat in stagnating air space can cause hotspots in surrounding components.Section V presents the impact of stagnating air space and proposed solutions.To demonstrate the design process, thermal designs and mitigation strategies are presented for a 200-kW high-density 3-L T-type SiC-based propulsion inverter.

A. Demonstrated 3-L T-Type Inverter
Table II summarizes the specifications of the demonstrated 3-L T-type inverter, and Fig. 5 shows the single-phase circuit and overview of the designed inverter assembly.The inverter is required to operate to a thermal steady state at the full-load condition at high altitude, i.e., V dc range of 500-1000 V and i o of 300 Arms at 7620 m.In accordance with the design process illustrated in Fig. 4, the heat sources in the demonstrated inverter can be identified as busbars, power devices, dc-link capacitors, and dc and ac EMI filters.The inverter adopts PCB-busbar technology for laminated busbar to control the e-field for insulation.The losses in the PCB busbars are generated when conducting currents such as dc current I dc , capacitor current i C , device current i S , and output current i o between nodes.For a worst case scenario in thermal design, the maximum current values should be used in calculations.The copper trace resistance R PCB can be easily calculated using available standards [74], [75].The power devices in the inverter contribute to dissipated loss mainly from switching and conduction losses.The losses incurred in different switching positions depend on the adopted PWM scheme, switching status, and operating conditions [76].In this work, the inverter employs the conventional modulation of 3-L SPWM.Figs. 6 and 7 illustrate the normalized switching loss and current distributions in different switching positions over one line cycle, obtained from the circuit-level simulations.The results show that the generated losses are significantly affected by the power factor ϕ and the modulation index (MI).In particular, switching position S 1 /S 4 generates more switching loss at high ϕ, and conducting currents between S 1 /S 4 and S 2 /S 3 become more balanced at high MI.The dc-link capacitor bank is designed to handle the switching current and limit the voltage ripple across the capacitor bank under all operating conditions.The capacitor loss P C is generated when capacitor current i C with switching ripples flows through the capacitor bank [77].The losses of both dc and ac filters are mainly determined by conduction losses when currents conduct in the filter windings.The maximum currents in dc and ac filter windings are I dc and i o , respectively.In addition, the total core loss can be estimated by the improved Generalized Steinmetz Equation (iGSE) [78].Table III summarizes all critical currents and dissipated losses in the inverter based on specifications in Table II.By conducting systematic optimization [79], a total of six 1200-V SiC MOSFET modules from GE shown in Fig. 8 are selected as power devices.The values in Table III will be used for temperature estimation and thermal design.

B. Thermal Mitigation Techniques and Design Workflow
The initial geometry for a thermal design is usually determined by the electrical components.The next step is to identify  thermal paths and forms, with the aim of reducing thermal resistance R th along the heat transfer path.In a system with passive cooling, such as the one shown in Fig. 1, heat is mainly transferred through R th,cond and R th,conv , while R th,rad becomes more significant only in a vacuum environment.To mitigate R th,cond in (1), the thickness L cond can be reduced, or k cond and A cond can be increased.To reduce R th,conv in (2), h conv and the area A conv can be increased.As presented in (5), natural convection is most intense at the top surface, so it is desirable to place heat sources facing upward to achieve a higher h conv .
Conduction is much more effective than convection for heat transfer efficiency.If heat is difficult to dissipate by natural convection alone, an additional conduction path, such as using TIM to fill the air gap, can help reduce the total loop R th .If the forced cooling technique is adopted, Fig. 2 explains the improvements between different cooling solutions.The forced air-cooling method can significantly increase h conv by improving Nu in (3).Different approaches, such as optimizing fin efficiency for MLC, jet impingement, two-phase cooling, and immersion cooling, seek to improve either h conv or A conv to reduce R th,conv .Using a heat spreader like a heat pipe or vapor chamber can further reduce R th,cond , R th,spre , and R th,conv due to the wick's high spreading performance and the fluid's two-phase transition nature [46].For the double-side cooling method, the cooling area is basically doubled [60], [61].
To decide whether to adopt passive or active cooling methods for heat sources, power densities should be compared.Taking the PCB busbars as an example, the ambient temperature is set to 75 • C. Since the footprint area of PCB busbars is preliminarily determined by electrical components, the losses from all PCB busbars can be easily calculated with the current values in Table III.When passive cooling is adopted, the generated heat of the PCB busbars is dissipated through natural convection, and T hs can be estimated using the model in Fig. 1.To keep the temperature within T hs,max , the heavy copper PCB technology is adopted, and the copper thickness is increased to minimize the electrical resistance.
On the other hand, if active cooling is adopted to cool PCB busbars, T hs can be calculated using the model in Fig. 2. Because of the low heat flux, the forced air-cooling solution is selected to compare the power densities with the case with passive cooling.If T hs,max is set to a lower value, the sizes of the heat sink and required fans are increased to achieve a lower loop R th .The total volume and weight can be estimated based on the documented data from off-the-shelf products.
Fig. 9 shows the comparisons of VD and WD between the two cases.When T hs,max is set to a specific value, the case with passive cooling always has higher VD than the case using forced air cooling.Furthermore, when T hs,max is set to be higher than 87 • C, the case with passive cooling also has higher WD than the case with active cooling.By increasing the copper thickness of busbars, T hs can be kept within T hs,max without mounting bulky heatsink and fans.The workflow can be applied to other heat sources.For power devices with high heat flux, if passive cooling is adopted, the resulting power densities to keep T hs within T hs,max are extremely low.Therefore, active cooling solutions should be adopted to cool power devices.PCB technology.Fig. 10 illustrates temperature comparisons obtained using different copper thicknesses while conducting a current of 300 A. The results indicated that the 2-oz copper is inadequate to withstand the harsh environment at high altitudes.By using 20-oz copper, the temperature could be lowered to below 130 • C for a footprint area larger than approximately 275 cm 2 .

C. Thermal Design for Localized Heat Sources
The dc busbar has three main potential layers, namely, p, n, and o potentials that are responsible for conducting high currents.Each potential layer is manufactured with a copper thickness of 0.8 mm to ensure optimal thermal and current density performance.In addition, the edge plating technique is utilized to ensure that the board is in direct contact with the enclosure, providing an additional conduction path.The dc-link capacitors are positioned below the dc busbar and are also in contact with the bottom of the enclosure.As a result, the enclosure served as a large heatsink for the dc busbar and capacitors, and the surface of the PCB is exposed to the top direction, thereby accelerating natural convection based on (5).
The dc EMI filter features a three-turn winding with an integrated DM-CM core structure, as shown in the bottom left of Fig. 5(b).To handle the dc current I dc of 285 A, two layers of 2-mm-thick copper and a current density of 3.4 A/mm 2 are selected for PCB-based windings.The winding turns are connected by copper interconnects, which are firmly fixated by four M5 screws to provide sufficient A cond and reduce the air gap between parts.Moreover, the dc integrated core is positioned naturally on the bottom plate of the enclosure, serving as both a grounding connection and a conduction path for heat dissipation.The ac busbars that conduct i o of 300 Arms have a copper thickness of 3 mm.They are separated from other PCBs to improve heat dissipation by exposing themselves to the air without FR4 material layers.The ac EMI filter shown in the bottom right of Fig. 5(b) features a single-turn winding structure realized by using heavy copper PCB with two 2-mm-thick copper layers.The ac CM core is designed to have a large contacting area A cond with the PCB.For more detailed design optimization of the dc and ac filters, please refer to [80], [81], [82], and [83].
Fig. 11 depicts customized screws and spacers that are utilized to connect the boards.Copper is used as the material for these customized parts due to its higher k cond compared to the steel alloy of off-the-shelf parts.The copper parts provide lower conducting resistance and reduce R th,cond by improving k cond and A cond from a wider screw head and body    radius.Fig. 12 shows the FEA simulations that are performed to validate the thermal designs when boards are conducting currents at an ambient of 75 • C and an altitude of 7620 m.All boards are well controlled below 130 • C by following the design process.

IV. COOLING DESIGN FOR POWER DEVICES
In high-altitude environments, the reduced air density makes it difficult to cool power devices with high heat flux using natural convection or conventional air-cooling methods.To maintain a safe junction temperature T j within T j,max , an aluminum-based liquid cooling MLC is selected due to its low weight, low cost, and high cooling capability.

A. Design and Optimization of Liquid-Cooling MLC
The MLC is designed based on the highest loss of 198 W from each switching position with an additional thermal margin.The cooling conditions are listed in Table IV.By using the derived model in Fig. 2, the thermal requirement of the MLC can be derived.Fig. 13 shows the physical structure of the MLC.The concept is to increase A conv by fabricating microlevel fins on the fin plate to reduce overall R th,conv [22].Using MLC, L c and increased A conv can be expressed as where N is the number of fins and η fin is the fin's efficiency [84].Nu can be written by correlation studied in [85] N u = 0.00805 where Re is the Reynolds number that describes the fluid characteristics.In addition to the thermal performance, the pressure drop P between the inlet and outlet coolants is also important since it determines the required external pumping power P pump where f is the Fanning friction factor [84] and u cha is the coolant velocity in a single channel.The MLC with lower P helps in reducing the weight of the external pump since the size of the pump is usually positively related to its rating power.The design process of the MLC is illustrated in Fig. 14.The idea is to shrink the fin height h c to reduce the weight of the MLC while still meeting all requirements [30].Once the initial conditions are identified, the performance and weight can be calculated depending on geometry parameters.

B. Comparisons of Cooling Path Configurations
To effectively cool multiple power devices using MLC, it is necessary to compare the performance of different cooling path configurations, such as series and parallel configurations, following the design process [31].Thus, the MLC optimization is separately conducted for both configurations, and their performances are further compared through CFD simulations.The designed MLCs for both configurations, namely, MLC-Series and MLC-Parallel, are shown in Fig. 15, with loose part samples illustrating the internal fin structure.Fig. 15(a) and (b) shows the base plates of both designs, with the power modules on MLC-Series cooled by the total amount of mass flow rate ṁ, while ṁ in MLC-Parallel is separated into six paralleled branches.The effect of design optimization is revealed in Fig. 15(c) and (d).Here, minimizing h c eliminates additional volume on the back side of the MLCs.The MLC-Series and MLC-Parallel weigh 671 and 810 g, respectively.Fig. 15(e) and (f) compares the corresponding fin plates of both versions, with the MLC-Series having fewer fins than MLC-Parallel, due to the characteristic of large P caused by a long distance L in (19).Installing more fins would increase u cha due to a narrower channel and eventually exceed P max .Conversely, the MLC-Parallel has a larger P margin, allowing more fins to be manufactured.
To compare the thermal performances, the CFD simulation results using Star-CCM+ are shown in Fig. 15(g) and (h).Each module is assigned to dissipate 300 W (total 1800 W), while T cool,in and ṁ are set to be 75 • C and 0.25 kg/s, respectively.The modules are not included in the CFD simulations to show the surface temperature of the MLCs.The results show that the highest surface temperature of MLC-Series is 87 • C, which is lower than 89 • C of MLC-Parallel, but only at the top right corner where no coolant path is present.If only focusing on the fin plate locations where the modules are mounted, the MLC-Parallel has a temperature of only 78 • C, which is 3 • C lower than the 81 • C of the MLC-Series, indicating that the former has a better dissipation efficiency for power modules than the latter.Fig. 15(i) and (j) further shows that P of the MLC-Parallel is several times lower than that of the MLC-Series, implying that using an MLC-Parallel would result in a lighter external pump.Although MLC-Parallel is slightly heavier than MLC-Series, when considering a footprint area of 360 cm 2 , it is at least 40% lighter than most off-the-shelf cold plates on the market.Therefore, the MLC-Parallel is chosen as the final design due to its better efficiency and P performances.

V. THERMAL ISSUE OF STAGNATING AIR SPACE
While the individually designed parts meet the thermal requirements, the high-density inverter is still prone to stagnating air spaces after assembly.As shown in the design process in Fig. 4, the next step is to avoid or mitigate the impact caused by stagnating air space.It is most desirable to eliminate it at the beginning of the design stage and, however, is also hard to anticipate the impact at the time.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

A. Thermal Impact of the Stagnating Air Space
The negative impact of stagnating air space on thermal performance is demonstrated by the inverter structure in Fig. 5(b).The side view of the board configuration is shown in Fig. 16(a).To optimize the commutation loops, the p, o, and n potential layers are embedded in the gate driver board.These layers, along with decoupling MLCCs, work together with the ac busbars to form loops [86], [87].However, as indicated by the red dashed box, a stagnating air space is formed, which is trapped by the dc busbar, dc-link capacitors, gate driver boards, and ac busbars.Furthermore, both sides of the air tunnel are blocked by the enclosure.Fig. 16(b) highlights the stagnating air space, and the corresponding CFD simulation result is shown in Fig. 16(c) with thermal conditions listed in Table V.Heat is generated when currents conduct through MLCC vias on gate driver boards and ac busbars, which leads to an undesirable high temperature of around 180 • C on the left-hand side of the driver boards.Although the ac busbars on the right are exposed to ambient air, the temperature still reaches almost 150 • C. It is clear that the stagnating air space has a detrimental effect on thermal performance and is created due to the combination of optimal electric performance and high-density nature.

B. Proposed Solutions for the Stagnating Air Space
To mitigate the impact of stagnating air space in a sealed enclosure, several solutions are proposed as follows.
1) Modify or Redesign the Inverter Structure: This solution involves eliminating existing stagnating air space or hotspots by modifying or redesigning the inverter structure.While suitable for early stage design processes, achieving the original optimal electrical performance may not be possible, and the redesign process can be time-consuming and costly.2) Introduce Additional Cooling Methods: This solution involves installing additional heatsinks or cold plates to cool the high-temperature regions.It is a cost-effective and time-efficient solution that allows for maintaining the original optimal electrical performance.However, it may increase the weight of the inverter due to additional parts, and the required power of fans, external heat exchangers, or pumps may further increase external system weight.3) Introduce Circulating Air to Harmonize the Temperature Distribution in Sealed Enclosure: This solution involves introducing circulating air to eliminate the stagnating air spaces by using an internal cooling air duct (AD).
The circulating air stream can be created by using an internal fan or from external air sources.It requires minimal cost and time, and original optimal electrical performance can also be maintained.Moreover, the fan and AD add little weight to the inverter system.However, fan-generated acoustic noise and AD's optimal airflow require additional design efforts.The most appropriate solution for eliminating stagnating air space depends on the specifics of each case.In this study, the method of introducing circulating air by utilizing an internal fan and cooling AD is chosen due to its low cost, short design time, and ability to maintain optimal electrical performance with minimal drawbacks such as increased noise and weight.

C. Location of Fan and AD
Fans provide blowing air, while the AD aims to guide the cooling flow to the hotspots.When space is not a constraint, the conventional rectangular AD (AD-REC) is a good option due to its simple and designless structure.However, in most cases, the remaining space inside the sealed enclosure is limited, and the AD-REC cannot fit.To overcome this dilemma, an alternative solution is proposed in Fig. 17, which highlights the stagnating air space with fans installed on both internal sides of the enclosure.This solution requires designed AD to guide the air through two 90 • turns and provide consistent airflow to the stagnating air space.Fig. 18(a) shows the conceptual original AD (AD-O) without airflow optimization.The AD-O serves as a design benchmark and is optimized through the next two steps.

D. Internal Airflow Optimization: Vanes Design
The purpose of the fan is to provide the necessary power to overcome the head loss h L experienced by the air as it flows through the path including AD.The relationship can be simplified from the extended Bernoulli equation and expressed as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.where γ is the specific weight of the fluid, and p f,o and p f,i are the pressure of the outlet and inlet of the fan, respectively.Equation ( 21) is valid by assuming that the inlet and outlet ports of the fan have the same flow velocity and height level.It also suggests that the pressure drop P is positively related to h L .The required fan power P fan can be expressed as a function of AD's cross section area A AD,o and velocity V AD,o From ( 22), if P fan and A AD,o is fixed, an AD with a smaller P(or h L ) can result in higher V AD,o .Since h conv is positively related to the flow velocity, an AD with higher V AD,o provides better cooling.By using AD-O in Fig. 18(a), the calculated h L is around 2.2 [84].
Fig. 18(b) shows the modified AD with optimized internal vanes (AD-IV) to optimize internal airflow.The AD-IV is proposed to reduce h L for better cooling performance.Internal vanes are installed inside the AD-IV at the locations of two sharp turns.The vane structure is shown in Fig. 19, and the geometry parameters are defined as The comprehensive analysis of vane parameters is studied in [88] and [89].In this work, α and β are selected as 1 and 0.25, respectively.With the aid of the internal guided vanes, the calculated h L of AD-IV is around 0.4, which is 5.5 times lower than 2.2 of AD-O.The impact of internal airflow optimization can be observed from CFD simulations, as shown in Fig. 20(a) and (b), where airflow comparisons are presented at the outlet ports of AD-O and AD-IV, respectively.Line probes are placed to measure airflow velocity along horizontal distances.Using the same fan and having the same outlet area A AD,o , it is evident that the AD-IV has much more evenly distributed airflow at the outlet port than the AD-O.The outlet air velocity of AD-O is extremely uneven and accumulates at the bottom of the duct.In contrast, the airflow for the AD-IV, as shown in Fig. 20(b), presents a much better distribution as the air velocity is evenly distributed around 12.5 m/s.The AD-IV efficiently guides the airflow from fan to hotspots even with sharp turns.Furthermore, the cooling performances of AD-O and AD-IV are compared in Fig. 21, using the same conditions in Table V.Both top and side views are shown for airflow and thermal comparisons.Compared with the original case in Fig. 16(c), using AD-O improves the highest temperature from the original 180 • C to 145 • C.However, the design is not satisfactory because the blowing air is unevenly distributed, and consequently, the airflow is unable to cover all hotspots on the gate driver boards.Moreover, the middle phase gate driver board experiences a 10 • C higher temperature than the other two phases.On the contrary, using AD-IV not only reduces the highest temperature to 130 • C but also results in much better temperature distribution among the three phases.Since AD-IV has a lower h L than AD-O, a higher average V AD at the outlet of AD-IV can be expected, which aids the convective heat transfer efficiency.

E. External Airflow Optimization: Air Blocks Design
The thermal robustness can be further enhanced by optimizing external airflow.In Fig. 21(b), although AD-IV successfully addresses the issue of stagnating air space, some air leaks through certain areas and goes unused.This results in reduced cooling efficiency.To mitigate this issue, an air block is added to the AD-IV, namely, AD-IVB, as shown in Fig. 22(a).
Comparing the performance in Fig. 22(b) with the case using AD-IV in Fig. 21(b), the airflow in Fig. 22(b) penetrates the stagnating air space more efficiently with minimum leaking air.The highest temperature is further reduced to approximately 125 • C. The final designed AD-IVB is 3-D printed using resin, as shown in Fig. 23.Each AD-IVB has a volume of 45 cm 3 and weighs 59 g.The weight is increased to 179 g if the fan and screws are included.The printed AD-IVB can be even lighter by using other materials.The designed AD-IVB proves to be a suitable solution for cases that have limited space to eliminate the stagnating air space.In this way, the optimal electrical performance and inverter structure can remain unchanged.

A. System Setup and Full-Power Pump-Back Tests
To conduct the thermal test at full power, two inverters are assembled and arranged in a pump-back configuration, as shown in Fig. 24(a).Both Inverter 1 and Inverter 2 have identical designs.The enclosure for Inverter 1 is opened to the ambient environment to allow for easy monitoring of all hotspots' temperatures, while Inverter 2 is sealed to validate the final thermal design.The edges are sealed with Kapton tape, which creates a worst case scenario due to its low thermal conductivity.Considering safety for thermal tests, all power cables, inverters, and components are arranged carefully to prevent contact with each other.Fig. 24(b) provides a closer view of Inverter 1.The dc busbar is disconnected to reveal the stagnating air space beneath it.Table VI details the testing parameters for the full-power thermal test, while the tested full-power waveforms are presented in Fig. 25.All thermal tests last at least 20 min with V dc around 700 V and i o of 300 Arms to reach a thermal steady state.

B. Validation of Designed MLC
To evaluate the performance of the MLCs, power resistors of similar size to the power modules are used in preliminary tests.The fin and base plates of the tested MLCs are soldered Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.together by the manufacturer to ensure a leakage-free system.ṁ is controlled by the external heat exchanger and chiller, and is monitored by the flowmeter.Figs. 26 and 27 show the comparisons of R th,MLC and P performances of MLC-Series and MLC-Parallel, respectively.In both Figs.26 and 27, the CFD simulation results well correspond to the mathematical predictions for both R th,MLC and P. In Fig. 26(a), compared to the model results, the experimental R th,MLC has an overall error of less than 30% and is always higher than the results obtained from the mathematical model.The experimental P in Fig. 26(b) is also 0.05 bar higher than the results from both model and CFD simulations.This error may be caused by the reading error from measurement.On the other hand, in Fig. 27(a), the experimental R th,MLC of MLC-Parallel is always higher than mathematical results with a maximum error of around 28.5%.However, as shown in Fig. 27(b), differences of P are discovered between model and experimental results.The experimental P is larger than both the model and CFD simulations.It is suspected that this difference is caused by the fabrication defects of the fin plate.Fig. 28 shows the loose part sample of the fin plate of MLC-Parallel.The deformation of fins and small particles on the fin plate may block the channel and result in higher P. It is found that the optimized performance of MLC-Parallel requires the effort of fine manufacturing.Since the channels of MLC-Series are much wider than those of MLC-Parallel, no major defects are observed, so the experimental results match with the model and CFD simulations with small errors.Despite that, the measured maximum P of MLC-Parallel is always lower than 0.37 bar, which is three times lower than that of the MLC-Series.As a result, the MLC-Parallel is a Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.more attractive design.Since the 30 • C EGW 50/50 has lower thermal conductivity and higher viscosity than the 75 • C one [90], both R th,MLC and P performances are expected to be better when 75 • C EGW 50/50 is adopted as coolant.

C. Junction Temperature Measurements
The junction temperature T j is measured by the temperature detector of the power module.The thermal grease TIM with thermal conductivity of 3 W/m•K is applied between modules and MLC-Parallel.All switching positions in Inverter 1 are measured, and the results are summarized in Fig. 29.By using the designed MLC-Parallel, the maximum measured T j is around 67 • C at full power when ṁ is at 0.25 kg/s.Fig. 29 also reveals that the temperature distribution is mainly determined by the loss difference among switching positions in the 3L T-type inverter instead of the configuration of paralleling coolant paths.The small temperature difference  among modules may be caused by the fin plate difference.The TIM may also have an impact on temperature distribution if the applied thickness is uneven for different modules.

D. Thermal Performance of Localized Heat Sources
Two ADs in Fig. 24(b) are first removed from the inverter to understand the thermal performances of localized heat sources.The temperatures of all heat sources are measured by using K-type thermocouples U1186A with multimeters.A comparison of the two setups is shown in Table VII by using Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.off-the-shelf and customized parts.The measured temperatures using designed heavy copper PCBs and customized parts are much alleviated compared to the case using off-the-shelf   By replacing parts, the maximum hotspot temperature rise is improved by 34.4%.The highest temperatures can be observed on ac busbar screws and MLCC vias on gate driver boards that are located in the stagnating air space.These locations are highlighted in Fig. 30.It is undesirable to have a temperature of 101 • C on the gate driver boards when tests are conducted at a room temperature of 25 • C. To verify the proposed circulating air AD solution for stagnating air space, the following tests will focus on those hotspot locations shown in Fig. 30.

E. Air Ducts' Validations for Stagnating Air Space
The ADs are later installed in an inverter to improve the hotspot temperatures in the stagnating air space.The fan used in this work is GFB0412ES-E from Delta Electronics.Fig. 31 shows the temperature improvements by using different versions of ADs.By introducing circulating air using AD-O, the temperatures of ac busbar screws and MLCC vias drop Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.significantly from 95 • C to 74 • C and 101 • C to a decent 52 • C, respectively.The result in Fig. 31 also suggests the necessity of optimizing the cooling airflow.Due to a smaller h L , the AD-IV with internal vanes helps decrease temperatures by around 10 • C compared to the case using AD-O.With optimization of both internal and external airflows using AD-IVB, another 5 • C temperature drop is achieved.Fig. 32 shows the photted thermal images of Inverter 1 using AD-IVB.The heat is observed concentrating in the location of the stagnating air space.The highest temperature of 59.8 • C is only located on the bottom of the middle phase ac busbar.The measured temperature profile validates the thermal designs and proposed solutions for the stagnating air space.

F. Sealed Enclosure Thermal Test
The thermal design is further tested by using Inverter 2 with a sealed enclosure.Only the temperatures of ac busbar screws are measured since they present the highest temperature in thermal tests and images.Compared to the opened enclosure case, the measured hotspot temperature rise increases approximately 19% in the sealed enclosure from temperature 59.8 • C to 66.4 • C. The enclosure temperature also rises to 31.5 • C since the heat is dissipated to the through the enclosure.

G. High-Altitude Thermal Test
The temperature rise at a high altitude of 7620 m is estimated based on thermal tests conducted in the lowpressure chamber, as shown in Fig. 33(a).The dc busbar, gate driver board, and ac busbar are placed in the low-pressure chamber with thermocouples mounted on them.A dc current of 200 A flows through the dc busbar, and the measured steady temperatures are recorded in Fig. 33(b).When the altitude increases from sea level to 7620 m, the temperature rise increases by around 40%.Since the ac busbar has no current conducting, the temperature rise is not obvious in this test.The error between the theoretical and measured temperature is around 6 • C, which may be caused by airflow difference between the chamber and the real environment [91].The dynamic viscosity µ the air density ρ would also Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
have an impact on natural convection and generate a slightly lower thermal resistance, which results in a lower measured temperature.
To summarize the testing results, the MLCs are first tested, and the accuracy of the mathematical model is validated by both CFD simulations and experimental results.The designed MLC-Parallel is proven to have good R th,MLC and superior P performances compared to MLC-Series.P of MLC-Parallel is always lower than 0.37 bar within the flow rate range from 0.05 to 0.25 kg/s.The power modules are later mounted on the MLC-Parallel, and the maximum T j is around 67 • C at full power condition when ṁ is at 0.25 kg/s.The temperatures of all localized heat sources are also measured by using thermocouples.By replacing the off-the-shelf mechanical parts with optimized copper parts, the hotspot temperature rise is reduced by 34% for ac screws.Moreover, the temperature rise is further reduced by 54% by introducing circulating air, which is intended to harmonize the temperature distribution within the enclosure.After the enclosure is sealed, a 19% temperaturerise increment is observed from the hotspot temperature.By using the pressure chamber to run thermal tests at the altitude of 7620 m, the temperature rise increases by around 40% compared to that at sea level.Combining all thermal results from the above tests, the maximum hotspot temperature within the sealed enclosure can be estimated as around 130 • C at the ambient temperature of 75 • C and an altitude of 7620 m.Also, the highest temperature only occurs on part of the ac busbar without damaging other electrical components.The experimental results verified the feasibility of the proposed systematic design flow of thermal management.

VII. CONCLUSION
In this article, a systematic design process of thermal management for a high-density high-power propulsion inverter is presented and demonstrated by a 200-kW 3-L T-type propulsion inverter.Based on the derived thermal models, cooling designs with high density and high efficiency are proposed.In addition, it is found that the stagnating air space created by the high-density structure of the inverter has a detrimental effect on thermal performance and can generate localized hotspots on electrical components.To address the thermal issue, localized AD and a small fan are used to mobilize the stagnated air in a sealed enclosure and harmonize the temperature distribution.By optimizing both internal and external airflows, the designed AD addresses the hotspots effectively without adding extra cooling weight and size.Moreover, the proposed AD solution eliminates the usage of oversized copper parts and terminals.The experimental full-power thermal tests validate the thermal design, showing that the highest temperature of the prototype in a sealed enclosure is around 130 • C at an ambient temperature of 75 • C and an altitude of 7620 m.

Fig. 1 .
Fig. 1.Thermal structure and thermal resistance network when a heat source within a sealed enclosure dissipates the heat via natural convection.

Fig. 3 .
Fig. 3. Calculated R th,conv for top, bottom, and vertical surfaces at an ambient of 75 • C and an altitude of 7620 m based on parameters in TableI.

Fig. 5 .
Fig. 5. (a) Single-phase circuit and (b) designed assembly of the demonstrated 200-kW 3-L T-type propulsion inverter with EMI filters.Critical conducting currents between connecting nodes of components are highlighted in the circuit diagram.For the convenience of displaying the inverter, power cables, some connectors, and spacers, as well as the top and side plates of the enclosure, are removed.

Fig. 9 .
Fig. 9. Comparisons of (a) VD and (b) WD for PCB busbar under conditions of passive cooling and active cooling.

Fig. 5 (
Fig.5(b) depicts the inverter assembly and the various components that are designed for the dc busbar, dc filter, ac filter, and ac busbars.To address the thermal issue of localized heat sources, T hs,max is set to 130 • C for all operating conditions.The designed boards utilize heavy copper

Fig. 10 .
Fig. 10.Estimated temperatures using different copper thicknesses for PCB busbar at an ambient of 75 • C and an altitude of 7620 m.

Fig. 17 .
Fig. 17.Proposed solution for eliminating stagnating air space to prevent enlarging the enclosure.

Fig. 18 .
Fig. 18.(a) AD-O and (b) improved AD-IV with internal guided vanes to reduce pressure drop caused by sharp bend turns.

Fig. 20 .
Fig. 20.Comparison of airflow distribution at the outlet port of (a) AD-O and (b) AD-IV.

Fig. 21 .
Fig. 21.Comparisons of airflow and cooling performance by using (a) AD-O and (b) AD-IV in CFD simulations.

Fig. 22 .
Fig. 22.(a) AD-IVB with air block to improve external airflow and (b) airflow and cooling performances.

Fig. 23 .
Fig. 23.AD-IVB is 3-D printed into two parts to show the internal vane design.

Fig. 28 .
Fig. 28.Fabrication defects of small particles and distorted channels in the loose part sample fin plate of MLC-Parallel.

Fig. 29 .
Fig. 29.Measured T j of power modules in different switching positions when using 30 • C EGW 50/50 as coolant with ṁ of 0.25 kg/s.

Fig. 30 .
Fig. 30.Two locations of hotspot temperature in stagnating air space.

Fig. 31 .
Fig. 31.Measured temperature of hotspots in stagnating air space by using different versions of AD.

Fig. 32 .
Fig. 32.Thermal images of the full-power thermal test after 20 min.

Fig. 33 .
Fig. 33.(a) Pressure chamber test setup and (b) measured temperatures.Due to the limited space, it is unable to place the entire inverter into the chamber.
Thermal Consideration and Design for a 200-kW SiC-Based High-Density Three-Phase Inverter in More Electric Aircraft Che-Wei Chang , Graduate Student Member, IEEE, Xingchen Zhao , Graduate Student Member, IEEE, Ripun Phukan , Member, IEEE, Rolando Burgos , Senior Member, IEEE, Simon Uicich , Pascal Asfaux , and Dong Dong , Senior Member, IEEE

TABLE I PARAMETERS
OF 75 • C AIR AT DIFFERENT ALTITUDES

TABLE II SPECIFICATIONS
OF 3-L T-TYPE INVERTER

TABLE III LOSS
DISSIPATION IN DEMONSTRATED 3-L T-TYPE INVERTER

TABLE V CONDITIONS
OF STAGNATING AIR SPACE IN SIMULATION

TABLE VI PARAMETERS
FOR FULL-POWER PUMP-BACK TEST