International Journal of Aerospace Engineering

Volume 2016 (2016), Article ID 7430293, 11 pages

http://dx.doi.org/10.1155/2016/7430293

## Study on Impedance Characteristics of Aircraft Cables

^{1}Department of Electrical Engineering, Northwestern Polytechnical University, Xi’an 710072, China^{2}State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China^{3}China Aero-Polytechnology Establishment, Beijing 100028, China

Received 28 July 2015; Accepted 10 March 2016

Academic Editor: Christopher J. Damaren

Copyright © 2016 Weilin Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Voltage decrease and power loss in distribution lines of aircraft electric power system are harmful to the normal operation of electrical equipment and may even threaten the safety of aircraft. This study investigates how the gap distance (the distance between aircraft cables and aircraft skin) and voltage frequency (variable frequency power supply will be adopted for next generation aircraft) will affect the impedance of aircraft cables. To be more precise, the forming mechanism of cable resistance and inductance is illustrated in detail and their changing trends with frequency and gap distance are analyzed with the help of electromagnetic theoretical analysis. An aircraft cable simulation model is built with Maxwell 2D and the simulation results are consistent with the conclusions drawn from the theoretical analysis. The changing trends of the four core parameters of interest are analyzed: resistance, inductance, reactance, and impedance. The research results can be used as reference for the applications in Variable Speed Variable Frequency (VSVF) aircraft electric power system.

#### 1. Introduction

VSVF (Variable Speed Variable Frequency) system is now under consideration for modern aircraft electric power system in order to replace CSCF (Constant Speed Constant Frequency) system, due to the fact that it is simpler and more energy-efficient and has higher power density **[1]. However, the use of VSVF system also proposes new challenges, such as the voltage decrease and power loss caused by aircraft cable impedance.

An aircraft cable can be represented with series connected resistor and inductor when alternating current flows through it. The cable’s resistance and inductance will not keep constant but vary due to various factors, among which the gap distance and the voltage frequency matter the most.

Nowadays in China, data of aircraft cable impedance and current-carrying capacity used is still determined by HB5795-82 released in 1982 **[2]. However, the data obtained at 400 Hz at that time is not so accurate due to the poor equipment and backward measurement method. Moreover, this industrial standard needs to be expanded as the voltage frequency in VSVF system is variable.

Literatures can be found, which analyze or calculate the resistance and inductance of a straight conductor. References **[3, 4] present calculation of total inductance of a straight conductor with direct current (DC) using the Biot-Savart law. Reference **[5] proposes a method to calculate the AC resistance of a straight cable but the inductance is neglected. Experimental study of skin effect which is closely related to voltage frequency is displayed in **[6]. The experimental result correctly reflects the change trend of cable resistance and inductance with frequency variation but it lacks theoretical analysis. In a nutshell, problems still exist in the following aspects.(1)Most papers calculate cable resistance and inductance only concerning the condition when DC flows through the conductor **[3, 4]. Other articles study this issue under AC condition, but the conclusion is not satisfactory.(2)Reference **[7] analyzes this problem using a finite element magnetic field analysis program but does not solve the issues completely. In addition, it is necessary to popularize the method with which problems can be studied by building simulation models because it is more convenient to change parameters and view the current density and flux density which are not easy to achieve in practical experiments.(3)None of the references above studies how the external electromagnetic environment will influence the resistance and inductance of transmission lines. For example, the aircraft skin has great impact on aircraft cable impedance. More attention should be paid in this area.

Thus, it becomes necessary to further study the impedance characteristic of aircraft cables.

Great efforts have been done in this paper. The impedance characteristic of an aircraft cable, when AC flows through it, consists of four relations: resistance versus frequency, inductance versus frequency, resistance versus gap distance (the distance between aircraft cables and aircraft skin), and inductance versus gap distance. Change trends of cable resistance and inductance with frequency and gap distance are analyzed based on electromagnetic theory. Some derivations based on fundamental theory are used. An aircraft cable simulation model is built using Maxwell 2D, a product of ANSYS Corporation. Simulation results are provided in both electromagnetic field graphs and data reports. Consistent conclusions are drawn from the two analytical approaches above. In this study, the voltage frequency varies within the range of 360 Hz to 800 Hz. According to HB5795-82, the gap distance ranges from (the cable’s radius) to 110 mm. The gap distance is measured from the center of the cable to the surface of the aircraft skin, which means the cable clings to the aircraft skin when the gap distance equals the cable’s radius .

#### 2. Analysis Based on Electromagnetic Theory

##### 2.1. Resistance Analysis

It is well known that a cable’s AC resistance is larger than its DC resistance. This is due to three reasons: skin effect, proximity effect, and external electromagnetic environment **[8]. Proximity effect is a phenomenon that a conductor carrying a high-frequency current induces copper loss in an adjacent conductor **[9]. This means at least two wires are required when referring to proximity effect. As to single cable studied in this paper, proximity effect does not exist.

Skin effect is the phenomenon that AC tends to flow mainly at the surface of a conductor which is different from distributing uniformly throughout the cross section of the conductor in the case of DC, as shown in Figure 1. Higher frequency will lead to smaller skin depth. The skin effect will reduce the effective cross-sectional area of the cables and increase the resistance **[10]. It should be noted that the AC current density at the center of the cable may not necessarily be zero. In fact, the current density at the surface of the cable is only a little larger than that at the center since voltage frequency used in VSVF system is only several hundred hertz.