The research of the dependence of the short circuit location on the magnitude of the phase shift

With increasing electrification of aircraft increases the load on the power supply systems [1]. The main disadvantage of electromechanical and non-contact automaton network protection is the inability to determine the type and location of failure. The total length of the wires on a modern passenger aircraft can take values of a hundred kilometers or more, for example, the modern Airbus A380-800 has a total length of wires of about 470 km [2]. Therefore, in the event of a failure in the power supply lines (for example, a short circuit), determining their types and location is a very laborious process. The paper considers the case of a phase short circuit.

Based on the results of the simulation carried out in Matlab, it should be concluded that at the time of a phase short circuit in the section of the power supply line with zero resistance (at the terminals of the distribution device) the voltage signals of the shorted wires coincide in phase and value.

In the case of a short circuit with a certain value of the resistance of the wires (not at the terminals), the voltage signals of the shorted wires at the time of the phase short circuit have a phase shift less than 120 degrees. Thus, the magnitude of the phase shift between the voltage signals of the shorted phases depends on the magnitude of the resistance of the wire section after which a phase short circuit occurs [3, 4].

From the above conclusion it follows that the diagnostic sign of a phase short circuit is the phase shift between the voltage signals of the shorted wires [3, 4]. Consequently, having information about the magnitude of the phase shift, it can be argued about the place of occurrence of a failure (in this case, a phase short circuit).

During simulation, we define the relationship between the length of the wire and the magnitude of the phase shift between the voltage signals of the shorted wires. Conventionally, we choose the current consumed by the load I = 1.5 A. Then, the cross section of single-core copper wire is S = 0.2 mm² [3]. The length of the wire is 10 m. We calculate the impedance of a single-conductor copper wire, with given geometrical characteristics, using formula 1.

,                                                                                                               (1)

where: ρ – the resistivity of copper;

l – the length of the conductor;

S – the conductor cross section.

Then, according to formula 1, the impedance of the wire is R = 0.85 Ohm. The graph of cable resistance versus its length is a linear increasing function.

During the simulation, the dependence of the phase shift on the resistance of the wire section was determined. We will conduct simulations for some values of resistance obtained in the course of calculations. The plot of the phase shift of the voltage signal from the resistance of the cable section is approximately a linear function.

The dependence of the magnitude of the phase shift on the length of the wire section is approximately linear function. To simplify the algorithm for determining the location of failure according to the proposed approach, we approximate the graph of a linear straight line.

The plot of the approximating straight line is described by the following expression:

Then, knowing the magnitude of the phase shift, it is possible, approximately, to determine the place of occurrence of a phase short circuit:

where: l – the length of the wire section;

φ – the magnitude of the phase shift.

The use of the linear approximation method is associated with the appearance of a methodological error. The average deviation of the approximating straight line from experimentally determined values is 1.95 degrees. Since the entire range of phase shift values, for the considered case, is 93.3 degrees, the accuracy of calculations, using the linear approximation method, is 1.8%, which is acceptable [1, 3].