Challenges in Electrical Insulation Materials and Thermal Management for Medium Voltage Power Cables for Envisaged Wide-Body All-Electric Aircraft

Abstract

All-electric aircraft (AEA) emergence is considered a promising initiative toward achieving net-zero aviation. Future wide-body AEA will require electric power systems (EPS) with high power density and minimal system mass. Power cables, a crucial element of the aircraft EPS, need to be designed to enhance the EPS's overall power density. At the cruising altitudes of wide-body AEA, the limited heat transfer by convection poses significant thermal challenges for the design of power cables. The challenges are further intensified when employing bipolar medium voltage direct current (MVDC) EPSs, typically consisting of two power cables, negative and positive poles, positioned adjacent. The cable's surface area influences both radiative and convective heat transfers. This book chapter deals with the design, fabrication, and testing of aircraft MVDC power cables. Multilayer multifunctional electrical insulation (MMEI) systems were recently introduced instead of single-layer insulation in the aforementioned cables, which are discussed. In addition to delineating coupled electrical, thermal, and computational fluid dynamic models to obtain thermal distribution and electric stress within the cable and using the model for optimal design of cable and duct geometries, all modeling details in COMSOL Multiphysics are also explained, resulting in this chapter book as a textbook and valuable reference.

1. Introduction

Moving towards net-zero emissions in transportation necessitates a comprehensive shift to all-electric solutions, including in aviation, where innovations are crucial. The UN’s Sustainable Development Goals aim for urgent action on climate change, targeting a 43% reduction in GHG emissions by 2030 and net zero by 2050 [1]. With transportation accounting for 29% of U.S. GHG emissions in 2021, including 8% from aviation, electrification is the most practical route to achieve net-zero emissions [2, 3]. The rapid advancement in battery technology and renewable energy integration, along with strong commitments from companies and governments, is greatly accelerating the adoption of electric vehicles (EVs), thereby reducing greenhouse gas emissions and fossil fuel dependency [4, 5]. The journey to net zero is more complex but equally crucial in aviation. The aviation sector, with a historical annual growth rate of 4–5%, presents a unique challenge, with over 80% of its greenhouse gas emissions originating from narrow and wide-body aircraft [6, 7]. Emerging technologies, such as electric and hybrid-electric aircraft, promise to decrease emissions, with several prototypes already demonstrating viable short-haul flights [8]. The International Air Transport Association (IATA) has set ambitious targets for net-zero aviation by 2050, emphasizing the need for sustainable aviation fuels (SAFs) alongside electrification to achieve these goals [9].

Although there have been considerable advancements in electric vehicles and other electrified transportation, the process of electrifying commercial wide-body airplanes is still in its initial phases. There are two main types of electrified aircraft: more electric aircraft (MEA) and all-electric aircraft (AEA). MEA uses conventional combustion propulsion systems but replaces pneumatic, hydraulic, and mechanical systems with electrical counterparts to enhance overall efficiency [10]. AEA, on the other hand, includes all the electrified systems of MEA and features an electrified propulsion system. Conventional aircraft’s electrified propulsion systems require a power density of 40 kVA/kg. Achieving this power density necessitates using EPS with high power density and low system mass [11, 12].

An aircraft’s EPS includes components like power electronic devices, electric machines, electrochemical energy units (EEUs), and multiple loads, all connected by power cables. These cables contribute significantly to the system’s total mass, accounting for more than 30% [10]. Optimizing the cable systems is crucial to creating EPS with high power density and low system mass. Operating at higher voltages can effectively reduce cable weight, but this introduces substantial challenges in designing appropriate cable insulation. The design of power cable systems requires accurate, current carrying capacity calculations, which can be challenging under complex environmental and geometric conditions. While analytical approaches per IEC 60287 are effective in homogeneous and simple scenarios, they struggle with heterogeneous environments, varied material thermal properties, and non-constant temperature limits. In such cases, numerical methods like the finite element method (FEM) are essential. FEM, as highlighted by standards such as IEC TR 62095, enables engineers to conduct detailed analyses of both electromagnetic and thermal behaviors within power cables. It enables precise temperature distribution and heat dissipation analysis, crucial for determining current ratings in different conditions [13, 14, 15].

This chapter of the book will explore the challenges related to insulation systems in aircraft cable systems. Section 2 delves into a detailed exploration of MEA and AEA EPS architecture. Section 3 covers the modeling and simulation of bipolar cable systems. Section 4 elaborates on the cable design modeling process using COMSOL Multiphysics software. Finally, Section 5 outlines the procedures for fabricating and testing cable insulation systems.

2. Overview of MEA and AEA electric power system (EPS) architecture

2.1 MEA EPS architecture (past to present)

The MEA concept in aircraft design focuses on substituting traditional pneumatic and hydraulic systems with electrical systems. Figure 1 shows the progression of electrical power capacity in commercial aircraft from the early 20th century to the present day. Starting with minimal power in the Wright Flyer, there’s a steady increase with models like the DC-3 and B707, followed by a significant escalation with the B737 in 1966. This growth continues with models like the B767, A320, B747–400, and A340, reaching 200–400 kVA capacities. The trend peaks with modern planes like the A380 and Boeing 787, which achieve impressive capacities, notably the 787 reaching 1000 kVA by 2010 [12]. These advancements reflect the industry’s shift towards MEA for improved efficiency, reduced weight, and better performance.

Figure 1.

Evolution of electrical power requirements: Gray represents short- to medium-range aircraft, and black represents medium- to long-range aircraft [12].

A typical commercial airplane utilizes a 115-V AC voltage at 400 Hz, supplied by a generator connected to the main engine, to maintain a constant frequency. Air circulation fans, avionics, lights, and galley equipment are the main uses of electric power in that constant voltage and constant frequency architecture [16, 17, 18]. The conventional aircraft also has a 28-V DC bus, derived from the 115-V AC via transformer rectifier units (TRUs), which is further reduced within line replaceable units (LRUs) for lower voltage requirements such as 5 V and 3.3 V, used for integrated circuits and microprocessors [19].

Aircraft electrical systems employ multiple busses for redundancy, interconnected by tiebreakers, with switches managing generators, loads, and busses. The modern trend in aircraft, like the Boeing 787 and Airbus A380, replaces traditional constant voltage constant frequency (CVCF) systems with constant voltage variable frequency (CVVF) systems [19]. These maintain regulated voltage (115 or 230 VAC) while varying frequency (350–800 Hz) based on engine speed. Figure 2 illustrates the CVVF bus power system utilized in MEA.

Figure 2.

CVVF bus power system utilized in MEA [19].

The Airbus A380 integrates advanced “more electric” technology, including four variable-frequency electrical generators delivering 150 kVA each, enhancing power reliability and efficiency. This system supports the aircraft’s extensive electrical needs with flexibility in power output. The aircraft’s hydraulic systems have been upgraded with electrical systems 1 and 2, replacing traditional hydraulics with electrical backup hydraulic actuators (EBHA) and electro-hydrostatic actuators (EHA) [20, 21, 22]. These actuators combine electrical and hydraulic power for lighter weight and increased redundancy in flight controls, ensuring operational reliability even under hydraulic system failures. Airbus’s adoption of EHAs marks a significant advancement in aviation technology, demonstrating a move towards more efficient and reliable aircraft systems.

The Boeing 787 Dreamliner employs a four-channel variable frequency starter generator (VFSG) system featuring two 250 kVA VFSGs on each main engine. This innovative electrical system replaces traditional pneumatic systems, delivering enhanced efficiency and weight savings by eliminating heavy bleed air components. The VFSG simplifies auxiliary power unit (APU) design, operating as a shaft power-only machine and improving compatibility with ground support infrastructure. The VFSG is a six-pole, brushless, three-phase, alternating current synchronous machine housed in aluminum and driven directly from the main engine gearbox. It has a nominal rating of 235 volts alternating current (VAC), 250 kVA, three phases, and an output frequency of 360–800 Hz [23, 24, 25]. This design ensures more efficient power distribution and use, with approximately 20 miles (32 km) less wiring than the 767. Additionally, the 787’s electrical system allows for autonomous engine start without external power, and backup sources, including main and APU batteries, ensure continued operation in case of power failure. These advancements ensure better fuel efficiency, lower maintenance costs, and compliance with safety regulations, positioning the 787 as a cutting-edge aircraft in modern aviation.

2.2 Concept design of AEA

Researchers have developed a range of innovative aircraft concepts intending to make electric flight a reality for commercial transport. To support this initiative, NASA and its industry collaborators have undertaken design studies to assess the potential decrease in fuel consumption and emissions and investigate the technological prerequisites for different configurations across a range of sizes, markets, and time periods.

NASA’s SUbsonic Single Aft eNgine (SUSAN) Electrofan is an advanced hybrid-electric aircraft designed to cut emissions by 50% within the next few decades, aiming to net-zero emissions. It can carry 180 passengers with a 750-mile economic range, utilizing a 20 MW Electrified Aircraft Propulsion (EAP) system and advanced propulsion airframe integration (PAI) for improved aerodynamic efficiency. SUSAN incorporates technologies like the 1.4 MW High-Efficiency Megawatt Motor (HEMM) and the High-Efficiency Electrified Aircraft Thermal Research (HEATheR) power converter, aiming to revolutionize sustainable aviation while operating within existing airport infrastructures [26].

The STARC-ABL, developed by NASA, is an innovative electric aircraft concept that utilizes Boundary Layer Ingestion (BLI) to enhance aerodynamics and minimize drag. The turboelectric propulsion system of this aircraft incorporates under-wing turbofan engines that serve as generators for a rear motor. This design is intended to reduce fuel consumption. Featuring a 2–3 MW power system with the HEMM, STARC-ABL aims to showcase substantial advancements in electric propulsion for cleaner and more efficient air travel solutions [27].

The NASA N3-X features a hybrid wing body design with turboelectric distributed propulsion (TeDP), employing lightweight superconducting electric motors and generators. Sixteen distributed fans manage boundary layer airflow for improved aerodynamic efficiency and reduced noise, significantly lowering fuel consumption and emissions. This technology enables quieter operations and facilitates the use of smaller airports, marking a significant step towards sustainable and efficient commercial aviation [28].

Empirical Systems Aerospace’s (ESAero) ECO-150 concept employs a turboelectric setup with distributed electric propulsion, utilizing two large turboshaft generators to power electric ducted fans integrated into the wing surfaces. This split-wing configuration enhances aerodynamic efficiency and reduces noise through embedded propulsors. The design targets improved fuel efficiency, emissions reduction, and noise mitigation in alignment with NASA’s N + 2 goals for advanced aircraft technologies [29].

3. Model and design of bipolar cable systems

As a crucial component of the aircraft EPS, power cables offer significant potential for reducing the overall system mass through improvements. Medium voltage (MV) power cables operating within the range of several kilovolts meet high power density requirements. However, increasing voltage necessitates thicker insulation, resulting in significant weight gain. Designing power cables for aircraft applications presents various challenges, including surface charge management, arc and arc tracking prevention, partial discharge (PD) mitigation, and efficient thermal management [12]. Thus, lightweight MV cables resistant to PD and arcs are crucial for electrified propulsion systems. In bipolar cable configuration, these challenges are much more critical. Achieving lightweight MV cables suitable for aircraft systems involves two approaches: redesigning the cable insulation system to enhance performance and reliability under aviation’s challenging conditions and modifying the cable’s shape to improve heat dissipation capabilities. These efforts aim to create lightweight MVDC power cables that meet the critical requirements of aircraft applications.

3.1 Challenges associated with designing aircraft cable systems

Arc tracking is a critical failure mode in electrical cable systems, characterized by forming a conductive path along the surface of insulating materials, leading to carbonization and eventual electrical breakdown. This phenomenon is particularly concerning in high-voltage environments, where the risks of arcing are elevated due to higher voltage levels, increased dv/dt (rate of voltage change), higher power densities, and reduced wire distances. The chemical composition of the insulation is a key factor in determining its susceptibility to tracking, with PDs being the main cause [30]. Arc tracking in aircraft cables can be classified into two main categories based on the environmental conditions and mechanisms involved: wet arc tracking and dry arc tracking. Wet arc tracking occurs when moisture or fluids create a conductive path between exposed wires or to the aircraft structure, leading to short circuits and carbonization. This is common in humid or fluid-exposed environments. Dry arc tracking results from insulation degradation due to aging, UV radiation, abrasion, and poor installation, causing localized heating and erosion [31].

PDs are localized electrical discharges that partially bridge the insulation between conductors. They pose a critical concern in aircraft electrical systems, especially during rapid ascents and descents when lower air pressures and increased moisture condensation exacerbate their occurrence. Lower air pressure enhances both the magnitude and frequency of PDs while reducing the partial discharge inception voltage (PDIV), particularly at higher operating voltages. Furthermore, higher voltage frequencies further decrease PDIV, increasing the likelihood of PDs [32, 33]. To manage PDs effectively, aircraft systems can utilize screened cables or incorporate corona-barrier materials in unscreened cables [34]. Corona-barrier materials significantly enhance the system’s resistance to PDs, prolonging the time to failure compared to conventional insulation materials. While they do not eliminate PD-induced failures, they notably delay the onset of failure, thereby improving system reliability. Addressing PD challenges in aircraft electrical systems involves developing insulation systems with screened cables or integrating corona-barrier materials, which effectively mitigate PD effects and enhance the durability and performance of cable systems.

Surface discharges in polymer insulation occur when the electric field at the insulator surface becomes strong enough to ionize surrounding air, resulting in PDs. This typically arises from air gaps or dry bands on the insulator surface, often due to hydrophobicity loss, contaminants, or moisture presence. When the voltage gradient surpasses a critical level, it triggers surface discharges, generating localized heating that can carbonize the polymer material, forming conductive tracks. These carbonized paths progressively reduce surface resistance, exacerbating material degradation. Continuous surface discharges lead to erosion and deeper carbonization, eventually creating conductive pathways that may bridge electrodes, causing complete insulation failure and compromising equipment integrity. Effective management of these phenomena is crucial in maintaining the reliability and safety of high-voltage systems, necessitating careful material selection and environmental control measures.

Thermal management is the most important among the challenges faced in aircraft systems, particularly due to limited convection at low air pressures encountered during wide-body aircraft cruising altitudes, such as 12.2 km, where air pressure is around 18.8 kPa. This reduced convection significantly impacts heat transfer, necessitating careful consideration. Compared to conditions at atmospheric pressure, the maximum permissible current through cables decreases under these circumstances [35, 36]. Moreover, the distribution of electric fields in DC cables is influenced by temperature, which affects conductivity. Understanding the cable’s temperature profile is crucial for managing electric field distribution across the insulation. Temperature differentials also influence conductivity gradients within the insulation, contributing to space charge accumulation. Accumulated space charge can alter electric field distributions, potentially leading to dielectric failure and degradation [37]. Polymeric insulation materials are particularly susceptible, as they tend to accumulate space charge more readily beyond their electric field thresholds. To ensure the safe and reliable long-term operation of DC cables in aircraft, it’s essential to maintain electric fields below critical thresholds. This necessitates meticulous temperature management throughout the cable’s length to design for high safety margins and dependable service life in airborne applications.

3.2 Multilayer multifunctional electrical insulation (MMEI) system

The design of aircraft cables has addressed the above-mentioned challenges by creating MMEI systems. When developing these insulation systems, the key focus is on selecting dielectric materials that offer both high thermal conductivity and dielectric strength. Plastics and polymers, such as aromatic polyimides like Kapton®, are prone to arc tracking due to carbonization under electrical stress. In contrast, aliphatic fluoropolymers exhibit greater resistance to carbon deposits from heat degradation, making them more capable of withstanding wet arc tracking. Additionally, it has been shown that enhancing polyimide insulation like Kapton® with thin fluoropolymer coatings such as PTFE (Teflon®) can further improve its resistance to wet arc tracking [38].

Research indicates that insulation systems with increased ratios of polyimide demonstrate higher breakdown voltages. Multi-layer configurations incorporating more than three layers of polyimide and fluoropolymer significantly enhance dielectric strength compared to simpler three-layer systems like TKT and Teflon® PFA/Kapton®/Teflon® PFA [39, 40]. In [41], numerous MMEI designs for aviation cables, including T-MMEI, SC-T-MMEI, ARC-SC-MMEI, PD-T-MMEI, and ARC-PD-T-MMEI, were proposed and examined. Figure 3 shows the different MMEI designs.

Figure 3.

Different MMEI designs [41].

These designs utilized varying combinations of polyamides and fluoropolymer films to address specific challenges. Kapton® MT+ was chosen for its superior thermal conductivity and high dielectric strength among polyimide options [42]. However, Kapton® MT+ remains susceptible to arc tracking, mitigated using Teflon® PFA as a protective coating [43]. Additionally, Kapton® CRC, known for its corona-resistant properties [44], was incorporated into some designs to enhance corona-barrier functionality. Here is a concise overview of various MMEI systems used in aviation cables [41]:

• T-MMEI: Optimized for thermal performance, featuring a 12-mil wrapped layer comprising Teflon® PFA (0.5 mil film) and Kapton® MT+ (1.5 mil film). Here, 1 mil equals 0.0254 mm.

• SC-T-MMEI: Combines thermal optimization and screening with a 5-mil copper layer, 2 mil Teflon® PFA (0.5 mil film) layer, and Kapton® MT+ (1.5 mil film) outer layer.

• ARC-SC-T-MMEI: Includes additional arc prevention mechanisms, featuring a 5-mil copper layer and a 4 mil Teflon® PFA jacket.

• PD-T-MMEI: Designed for corona-barrier and thermal optimization, with a 4.5 mil wrapped layer of Teflon® PFA (0.5 mil film) and Kapton® CRC (1 mil film) in the outer layer.

• ARC-PD-T-MMEI: Combines arc prevention, corona-barrier, and thermal optimization with a 6-mil wrapped layer of Teflon® PFA (2 mil film) and Kapton® CRC (1 mil film).

3.3 Increasing the heat transfer capacity by changing the shape of the cable systems

The shape of a cable significantly affects its maximum current carrying capacity due to variations in radiative and convective heat transfer, both of which depend on the cable’s surface area [45, 46, 47]. Radiative heat transfer increases with surface area expansion, while convective heat transfer response can vary—increasing, decreasing, or remaining constant—due to numerous influencing factors that may not correlate directly with surface area growth. The radiative heat transfer $Q_{\mathit{ij}}$ between two surfaces $i$ and $j$ can be expressed as:

$$Q_{\mathit{ij}}={\mathrm{ℇ}}_i\sigma A_i{F}_{\mathit{ij}}\left(T_i^4-T_j^4\right)$$E1

where ${\mathrm{ℇ}}_i$ is the emissivity of the surface, $\sigma$ is the Stefan-Boltzmann constant, $A_i$ is the surface area of object $i$, $F_{\mathit{ij}}$ is the view factor, $T_i$ is the absolute temperature object $i$, and $T_j$ is the absolute temperature of the object $j$.

Cuboid and rectangular shapes provide a larger surface area while maintaining the same cross-sectional area and mass compared to cylindrical cables. This increase in surface area enhances the maximum current capacity of a cable due to improved radiative and convective heat transfers. This principle is also applicable to bipolar cable systems. In studies comparing different bipolar cable systems of the same weight and size, such as cylindrical, cuboid, and rectangular shapes, it was found that changing the cable shape to a rectangular form increased the maximum current capacity by approximately 8.3% compared to cylindrical systems and 5.6% compared to cuboid systems [47]. To avoid the issue of theoretically infinite electric fields at the sharp edges of rectangular and cuboid cables, a rounded corner design is implemented. Figure 4 illustrates the geometry of cylindrical, cuboid, and rectangular cable systems with ARC-SC-T-MMEI insulation systems.

Figure 4.

Geometrical arrangement of three types of cable.

The orientation of a surface significantly influences radiative heat transfer. When bipolar cables are placed near each other, the orientation and distance between them impact radiative heat transfer by affecting the view factor. The view factor determines the portion of radiation emitted by one surface that is received by another and varies with shape, influencing the overall radiative heat transfer between objects. The view factor $F_{\mathit{ij}}$ represents the proportion of radiation emitted from surface $i$ that is intercepted by surface $j$ can be expressed as

$${\mathrm{F}}_{\mathrm{ij}}=\frac{1}{{\mathrm{A}}_{\mathrm{j}}}{\int }_{{\mathrm{A}}_{\mathrm{i}}}{\int }_{{\mathrm{A}}_{\mathrm{j}}}\frac{cos{\mathrm{\theta }}_{\mathrm{i}}cos{\mathrm{\theta }}_{\mathrm{j}}}{\mathrm{\pi }{\mathrm{R}}^2}\mathrm{d}{\mathrm{A}}_{\mathrm{i}}\mathrm{d}{\mathrm{A}}_{\mathrm{j}}$$E2

where, $A_i$ and $A_j$ are the surface area of objects $i$ and $j$, elemental areas on each surface, $d{A}_i$ and $d{A}_j$, are connected by a line of length $R$, which forms the polar angles ${\theta }_i$ and ${\theta }_j$, respectively, with the surface normal $n_i$ and $n_j$. The analysis of the view factor is crucial in designing bipolar cables. By examining the view factor, engineers or researchers can better understand the radiative heat transfer characteristics between different surfaces of the cable, which is essential for optimizing thermal performance and ensuring the reliability and efficiency of the cable system.

3.4 Coupled electro-thermal model

To attain a high-power-density and low-system-mass EPS for aircraft, cables must support higher currents within existing dimensions or reduce size and mass while maintaining same ampacity. Pursuing the latter, thermal analysis becomes vital in designing cables for optimal heat transfer.

Heat is transferred from the core conductor to the cable surface exclusively through conduction. Within the cable, the heat equation describing this transfer from the inner conductor to the outer jacket can be described as

$$\rho C_p\frac{\partial T}{\partial t}+\nabla .\left(-k\nabla T\right)=Q_s$$E3

where $\rho$ is the density (kg.m⁻³), $k$ is thermal conductivity (W.(K.m)⁻¹), $C_P$ is the specific heat capacity at the constant pressure (J.(kg.K)⁻¹), and $T$ is the temperature (K). $Q_s$ stands for the rate of heat generation per unit volume within the material, where it should be transferred from the cable surface via radiative and convective transfers, as can be described as

$${\mathrm{Q}}_{\mathrm{s}}={\mathrm{Q}}_{\mathrm{r}}+{\mathrm{Q}}_{\mathrm{c}}$$E4

where, $Q_r$ denotes the radiative heat transfer (W.m⁻³) and $Q_c$ signifies the convective heat transfer (W.m⁻³). Reducing the cross-sectional area and mass of cables while maintaining a specific ampacity leads to an increase in $Q_s$ due to the increased resistivity of the core conductor resulting from decreased cross-sectional area. Consequently, to counterbalance this rise in total heat loss, adjustments must be made to enhance radiative and convective heat transfers. The heat generated due to Joule losses $Q$ and the relationship between $Q_s$ and $Q$ can be described as follows:

$$Q_s=Q/V$$E5

$$Q=I^{2}R$$E6

where $V$ represents the volume of the material (m³), $I$ denotes the conductor current (A) and $R$ denotes the resistance (Ω). The resistance of the conductor varies with temperature according to the following expression for linear resistivity (${\rho }_e$):

$${\rho }_e={\rho }_0(1+\alpha \left(T_C-T_{\mathit{ref}}\right)$$E7

where $\alpha$ is the resistivity temperature coefficient (K⁻¹), $T_{\mathit{ref}}$ represents the reference temperature (K), $T_C$ is the conductor temperature (K), and ${\rho }_0$ denotes the electric resistivity (Ω.m) at the reference temperature.

The temperature of the cable is significantly influenced by natural heat convection. The heat equation in the air domain can be described as follows [48]:

$$\rho C_p\frac{\partial T}{\partial t}+\rho C_{p}u.\nabla T+\nabla .\left(-k\nabla T\right)=Q+q+\tau :\nabla u+\frac{-T}{\rho }\frac{\partial \rho }{\partial t}\left(\frac{\partial P}{\partial t}+u.\nabla P\right)$$E8

where $\rho$ is the air density (kg.m⁻³), $u$ is the air velocity vector (m.s⁻¹), $C_p$ is the heat capacity at the constant pressure of the air (J.(kg.K)⁻¹), $k$ is the thermal conductivity of the air (W.(K.m)⁻¹), $\tau$ is the viscous tensor (Pa), $P$ is the pressure (Pa), $q$ is the heat flux (W.m⁻³) and $T$ is the temperature (K). The operator “:” represents the double dot product. The velocity field of the fluid (in this case, air) can be determined by solving the momentum equation and the equation of continuity. These equations are expressed as:

$$\rho \frac{\partial u}{\partial t}+\rho \left(u.\nabla \right)u=\nabla .\left(-P{I}_I+\tau \right)+\left(\rho -{\rho }_{\mathit{ref}}\right)g$$E9

$$\frac{\partial \rho }{\partial t}+\nabla .\left(\mathit{\rho u}\right)=0$$E10

where ${\rho }_{\mathit{ref}}$ is the reference density (kg.m⁻³), and $g$ is the acceleration of gravity (m.s⁻²). The electric field distribution can be calculated using

$$E=-\nabla V$$E11

$${\mathrm{J}}_{\mathrm{e}}=\mathrm{\sigma E}$$E12

where $\sigma$ is the conductivity (S.m⁻¹), $J_e$ is the current density (A.m⁻²), and $V$ is the voltage (V). Furthermore, the determination of the steady-state space charge density can be achieved by:

$$\mathit{\sigma E}.\nabla \left(\frac{{\epsilon }_e}{\sigma }\right)={\rho }_e$$E13

where ${\rho }_e$ is the space charge density, and ${\epsilon }_e$ is the permittivity.

The analysis and discussion in [49, 50] focuses on different types of bipolar cable configurations, including conventional cylindrical, cuboid, rectangular, and coaxial. The study specifically examines the behavior of a ± 5 kV, 1 kA power cable under a low pressure of 18.8 kPa. Figure 5 illustrates the 2D geometries of four different bipolar cable systems used for modeling and simulations. These systems employ the previously discussed ARC-SC-T-MMEI configuration for insulation. For simulating heat radiation, the bipolar cable system is enclosed within a duct, represented as the ambient surface in Figure 5.

Figure 5.

Geometry of the four types of bipolar cable systems [50].

Figure 6 illustrates the weight per unit length and cross-sectional area of the different bipolar cable systems [50]. From the results, it can be shown that the rectangular bipolar cable demonstrates a more efficient weight and cross-sectional area compared to the other three bipolar cable systems. For cylindrical, cuboid, and rectangular bipolar cables, the distance of two inches between the cables results in the lowest weight per unit length and cross-sectional area. At S = 2 inches, rectangular bipolar cables have a weight per unit length of 1.3548 kg/m, making them about 9% and 11.5% lighter than cuboid and cylindrical bipolar cables, respectively, and 26% lighter than coaxial bipolar cables. These findings are consistent with the cross-sectional area measurements, where rectangular bipolar cables at S = 2 inches also have the smallest cross-sectional area compared to the other cable types. This is due to the increased radiative and convective heat transfers of the cables, which result from the greater distance between them. Figure 7 illustrates the radiative and convective heat fluxes for various types of bipolar cable systems.

Figure 6.

Weight per unit length and cross-sectional area of the four types of cable systems [50].

Figure 7.

Radiative and convective heat fluxes of four types of cable systems [50].

According to Figure 7, the radiative heat flux for cuboid and cylindrical bipolar cables is approximately equal when S = 0 inches, measuring 304 W/m. This value is 9.5% higher than that of coaxial cables, but 21.7% lower than rectangular bipolar cables. As the distance increases, rectangular bipolar cables, despite their smaller cross-sectional area, show increased radiative heat transfer due to a varying view factor. At S = 2 inches, their radiative heat flux is 414.97 W/m, 18.5% and 24.2% higher than cuboid and cylindrical systems, respectively. For convective heat flux, at S = 0 inches, cylindrical, cuboid, and rectangular bipolar cables have lower values due to reduced convection when cables touch. As distance increases, convective heat transfer improves for all systems due to exposure on all sides. Cylindrical and cuboid systems show a slight decrease in convective transfer beyond 0.5 inches, while rectangular cables reach maximum convective transfer at S = 1.5 inches. For a comprehensive analysis, refer to the study mentioned in [50].

4. Modeling detail in COMSOL multiphysics

4.1 Simulation approach

Power cables are subjected to simultaneous electrical, thermal, and mechanical stresses depending on the applied voltage and current flow. In recent years, the FEM has become crucial for designing reliable insulation systems. FEM simulations enable engineers to analyze insulation materials under various conditions, offering valuable insights into their durability. By accurately modeling complex geometries and material properties, FEM helps create insulation that withstands extreme temperatures, pressures, and environmental challenges, improving overall reliability and performance.

To achieve EPS for aircraft with high power density and low system mass, cable design must focus on either increasing the maximum permissible current without enlarging their cross-sectional area and mass or maintaining the necessary ampacity while reducing the cross-sectional area and mass. In this section, for cable design, the latter approach will be discussed. A comprehensive coupled FEM model is developed using COMSOL Multiphysics software to analyze the temperature and electric field distributions along the MVDC bipolar cable. This model incorporates different modules such as laminar flow, magnetic fields, heat transfer, surface-to-surface radiation, and electric currents. The three modes of heat transfer—radiation, convection, and conduction—are considered during the modeling process.

Three different EPS architectures were introduced and studied in [51] for a wide-body AEA. A maximum ampacity of 1000 A was required for connecting EEUs to busbars. As a result, the bipolar cable was designed and optimized in this work to carry 1000 A of current with the poles’ voltages being +5 kV and −5 kV, respectively. The overall size of the cable was optimized for all bipolar cable systems at 1000 A of current to achieve the maximum permissible temperature of 260°C using COMSOL Multiphysics software. After optimization for 260°C, the cross-sectional area and weight per unit length of the cables were evaluated using the Results branch of the COMSOL Multiphysics model tree.

4.2 Cable geometry and simulation settings

Figure 8 illustrates the geometry of the bipolar cylindrical cable systems. To accurately model the three modes of heat transfer under low-pressure conditions, the cables are placed within a duct, which serves as the ambient surface. The duct, made of aluminum alloy, has a square-shaped domain with each side (L) measuring 1 meter in length and a thickness of 1 mm. The emissivity of the aluminum surface varies based on factors such as alloy composition, temperature, oxidation, and surface roughness. For this study, the aluminum alloy is roughly polished, with an emissivity of 0.18, making it suitable as an ambient surface material. The outer surface of the duct is maintained at a constant temperature of 40°C, reflecting typical conditions at the cruising altitude of a wide-body aircraft. The internal pressure inside the duct is considered to be 18.8 kPa. In Figure 8, “S” represents the separation between the negative and positive poles, crucial for optimizing the design of future wide-body airplane bipolar cables. Additionally, it is crucial to maintain a sufficient gap between the cables and the sides of the duct to ensure that any potential cable failure does not compromise the safety of the aircraft or its systems. Throughout all simulations conducted in this study, the poles are positioned 1 inch above the duct floor, following the guidelines recommended in [52]. In this bipolar cable system analysis, the previously discussed ARC-SC-T-MMEI insulation system is used, which has a 6.5-mil wrapped layer of Kapton® MT+ and Teflon® PFA. As a screened layer 5 mil copper layer and as a jacket 4 mil Teflon® PFA is used. The zoomed view of this insulation system is shown on the right side of Figure 8. The material properties used for this simulation are shown in Table 1.

Figure 8.

The geometry of the bipolar cylindrical cable systems in COMSOL.

Material	Density (kg.m^−3)	Dielectric constant	Thermal conductivity (W.m^−1.K^−1)	Dielectric strength (V.m^−1)
Copper	8960	—	400	—
Kapton® MT+	1420	4.2	0.75	208.5 × 10^6
Teflon® PFA	2150	2	0.195	256 × 10^6
Kapton® CRC	1550	3.4	0.2	256 × 10^6
Aluminum 1350	2705	—	238	—

Table 1.

Materials properties used in analyzed cables [41, 42, 43, 44].

Heat is generated within the core conductor due to joule losses, which then is transferred to the cable surface through conduction. Subsequently, this heat dissipates into the surrounding environment through convection and radiation. To accurately model this process, the study incorporates COMSOL’s heat transfer in solids and fluids, laminar flow, magnetic field, electric currents, and surface-to-surface radiation modules. In this analysis, the core conductors are modeled as solid single conductors to simulate heat generation. The magnetic field module in COMSOL is employed and coupled with the heat transfer module to automatically calculate conductor losses. These losses are determined using the electrical resistivity data provided by the magnetic field module. The heat transfer module then incorporates these losses as a heat source when solving the FEM model. This approach ensures a comprehensive simulation of heat transfer dynamics within the cable system, accounting for both electrical and thermal interactions.

The ‘coil’ node within the Magnetic Field module was utilized in this study, which is normally used to model coils, cables, and other conductors subject to a lumped excitation, such as externally applied current or voltage. Under the coil node as a conductor model, the ‘single conductor’ model is used. The electric resistivity of the conductor was calculated by the Magnetic Field module using inputs such as current, reference temperature, reference resistivity, and resistivity temperature coefficient. A standard formula available in Section 3, Eq. (7) was employed for this calculation. Figure 9 shows an illustration of two core conductors designated as heat sources within the Heat Transfer in Solids and Fluids module.

Figure 9.

Two core conductors were chosen as heat sources by the heat transfer in solids and fluids module.

The electric field distribution along the DC cables is influenced by conductivity, which is directly affected by temperature. Concerning the issue of DC conductivity in insulation materials, it is important to consider the non-linear nature of DC conductivity and its implications for electric field distribution. Due to the lack of conductivity data for Kapton® MT+ and Teflon® PFA, Kapton® MT+ was classified as a polyimide material, and Teflon® PFA as an ETFE material. The electrical conductivity of PI and ETFE has been determined by curve-fitting data from [53] using Eq. (14). Table 2 shows the parameters for calculating the DC conductivity of polymeric materials.

Parameter	$a$ (K)	$b$ (mm/kV)	${\sigma }_0$ (S/m)
ETFE	4061	0.03097	2.027e-10
Polyimide	3319	0.05558	1.677e-9

Table 2.

The parameters of the electrical conductivity [50].

$$\sigma \left(E,T\right)={\sigma }_0{e}^{\left(\frac{-a}{T}+\mathit{bE}\right)}$$E14

where $E$ is the electric field (V.m⁻¹), $a$ is the temperature coefficient, $b$ is the electric field coefficient, and $T$ is the temperature (K).

In screened cables, the screen is grounded. Conversely, for unscreened cables, the outer surface of the cable (the outer boundary of the outermost layer) is grounded. As the ARC-SC-T-MMEI configuration has a 5-mil copper screen layer, those are considered grounds for the simulation. Figure 10 shows the EC module’s ground setting for two cables.

Figure 10.

Ground (0 V) selection of two cables under EC module.

Figure 11 illustrates the meshing arrangement of bipolar cylindrical cables. The precision of computational simulations improves with an increased number of finite elements, as it allows for a more detailed and accurate representation of the model. In this arrangement, a finer mesh is applied to both cables, while a normal mesh is used for areas like the air and duct sides. The mesh consists of 196,123 vertices and 383,696 elements, including 377,992 triangles, 5704 quadrilaterals, and 59,294 edge elements. This process is managed automatically through adaptive mesh refinement techniques in the software. Adaptive mesh refinement dynamically adjusts the mesh density based on the solution’s needs, refining the mesh in regions with high gradients or complex features and coarsening it where less detail is necessary, optimizing both accuracy and computational efficiency.

Figure 11.

Meshing arrangements of bipolar cable systems.

The simulation incorporates both time-dependent and stationary studies to thoroughly analyze the system. A stationary study is utilized exclusively for the Electric Current module, while time-dependent studies are employed for the other four modules. The simulation runs for 30 hours to ensure it reaches a steady state. Figure 12 shows the temperature distribution of the bipolar cable systems.

Figure 12.

Temperature distribution of the bipolar cylindrical cables.

In bipolar cable systems, the overall diameter of the cable is carefully adjusted to ensure it can withstand a maximum permissible temperature of 260°C under a current load of 1000 A. To measure the density, the Surface Integration (∫∫) function located in the Integration submenu within the Derived Values section was utilized. The derived integration values are used to calculate integrated quantities for each solution in a dataset. The ht.rho function was employed within the expression for surface integration to accurately calculate the density of the chosen domain. For measuring the cross-sectional area, the Surface Measurement function within the Derived Values section was used, which evaluates the surface area over a set of domains in 2D. By using these two functions, the weight per unit length and cross-sectional area of the cables were directly calculated from the COMSOL Multiphysics software. Table 3 shows the optimized data for cylindrical bipolar cables for different distance between the cables. To simultaneously assess both the weight and dimensions of bipolar cables, a parameter $J$ is defined as:

Distance between the poles (inch)	Core conductor diameter (mm)	Cable diameter (mm)	Cross-sectional area (mm2)	Weight per unit length (kg.m^−1)	$J$ (g.mm)
0	19.18	19.97	626.25	1.7636	1104.46
0.5	17.97	18.76	552.65	1.5602	862.25
1	17.90	18.69	548.53	1.5488	849.56
1.5	17.81	18.60	543.26	1.5342	833.47
2	17.74	18.53	539.18	1.5320	821.17

Table 3.

Data for optimized cylindrical bipolar cable systems [49].

$$\mathrm{J}=\mathrm{m}.\mathrm{A}$$E15

where $m$ is the total cable’s mass per unit length (kg.m⁻¹) and $A$ is the overall cross-sectional area of the bipolar cable system (m²).

The Electric Currents (EC) module was employed to analyze the insulation characteristics of the cables. The electric field distribution across the insulation in DC cables results from the combined effects of the current field and Poisson’s electric field. The EC module calculates the space charge density within the cables and incorporates the associated Poisson’s electric field into the current field. By solving the electrical conductivity expression, the EC module determines the electric field across the insulation, encompassing both the current and Poisson’s electric fields within its solution. Thus, the resultant electric field across the designed cables represents a comprehensive total electric field. Figure 13 shows the electric field distribution of the bipolar cylindrical cables. By using the “Cut Line 2D” feature (red line in Figure 13), the electric field distribution across the MMEI insulation is determined.

Figure 13.

Electric Field Distribution of bipolar cables.

5. Fabrication and testing

In previous discussions, the simulation and modeling procedures for bipolar MVDC power cables in wide-body AEA were explored. To ensure proper electrical insulation performance of these power cables, experimental testing, in addition to modeling and simulations, is required. The dielectric strength and time-to-failure of these designs must be validated through experimental evaluation. Specifically, comprehensive testing of power cables with MMEI configurations is essential for assessing their commercial viability. Consequently, samples of the designed MMEI structures need to be fabricated for testing.

The prototyping process of MMEI insulation, both as flat samples and MVDC power cables with MMEI configurations, is discussed here. The necessity of optimizing manufacturing conditions to ensure uniformity and eliminate defects is emphasized, aiming to produce high-quality samples for testing.

5.1 Compression molding process

The compression molding process is a crucial method for creating MMEI samples. Several factors, such as mold size, compression pressure, duration, and temperature, significantly influence this process. Careful attention to these techniques and optimization of these parameters is essential for enhancing the quality of the fabricated samples. The process can be outlined as follows:

1. Design and Fabrication of Molds: The initial step involves designing molds that match the specifications of the MMEI configurations. The mold size must accommodate the desired dimensions of the dielectric layers and the overall cable structure. For fabricating flat samples, high-precision A2 steel molds with lengths of 6 inches and widths of 1, 2, and 6 inches are used [54].

2. Layer Arrangement: The dielectric layers must be precisely arranged in the mold to ensure uniform distribution and proper adhesion during the molding process. The formation of voids depends on the arrangement of different polymeric layers. It has been shown that spiraling different dielectric layers in opposite directions improves the PD performance of the fabricated cable samples [55].

3. Optimization of Compression Molding Parameters:

   • Compression Pressure: Sufficient pressure must be applied during molding to bond the layers without introducing voids. For fabricating flat samples, high-temperature C3 Connor sealing clips are used. The quantity of clips for each mold size is modified to ensure uniform compression pressure and to prevent void formation in the manufactured MMEI system [54]. For fabricating MMEI cable samples, adjustable T-bolt hose clamps are used [55, 56, 57].

   • Duration: The molding duration should be sufficient for proper bonding of polymeric materials without causing degradation.

   • Temperature: The molding temperature must be optimized to ensure material flexibility and effective bonding without compromising dielectric properties. PD tests on different flat samples have been conducted to optimize the duration and temperature, with the best results achieved at 360°C and 40 minutes [54].

4. Quality Control: Post-molding, the samples should undergo rigorous quality control checks to identify and rectify any defects. This includes visual inspections, dielectric testing, and mechanical assessments.

By meticulously managing these steps and optimizing the compression molding parameters, high-quality MMEI samples can be produced for experimental testing. Figure 14 shows the fabricated flat MMEI samples and MMEI cable samples. This approach is crucial for validating the performance of MVDC power cables in AEA applications and ensuring their commercial viability.

Figure 14.

Fabricated samples for testing.

5.2 PD test setup and experimental procedure

The experimental setup for analyzing PD is depicted in Figure 15. The high-voltage DC source utilized in this study is the PHENIX Model 4100–10, which can generate an output voltage of up to 100 kV DC and measure leakage currents ranging from 0.01 to 20,000 μA DC. The OMICRON MPD 800, a state-of-the-art system for PD measurement and analysis, was employed. To detect PD signals, a coupling capacitor was used per the standards specified in IEC 60270 [58]. An HV resistor capable of withstanding voltages up to 100 kV was also employed to control the high current directed into the OMICRON MPD 800 device. As an electrode setup, a sphere-sphere electrode was used for measuring the PD signal [54]. This setup can be used as a reference for doing the PD test for the MVDC system.

Figure 15.

PD test setup.

6. Conclusion

Transitioning to AEA is a crucial step towards achieving net-zero GHG emissions in the transportation sector, particularly within aviation. The power cable, as a fundamental component of an aircraft’s EPS, plays a significant role in achieving a low system mass EPS. Given the limited heat convection at the cruising altitudes of wide-body AEA, thermal management of the power cable is one of the most critical challenges. The introduction of MMEI systems represents a significant advancement over traditional single-layer insulation, effectively addressing these thermal challenges. This book chapter provides a comprehensive overview of the design, fabrication, and testing processes for aircraft MVDC power cables, supported by detailed coupled electrical, thermal, and CFD models. These models, implemented in COMSOL, enable optimization of cable geometries and provide valuable insights and methodologies for developing efficient and reliable EPSs in AEA. This work serves as an essential reference for researchers and engineers and as an educational resource for understanding the complexities of power cable design in the context of electrified aviation.

Acknowledgments

This work was supported in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy, under Award DE-AR0001677.

Conflict of interest

The authors declare no conflict of interest.