A Methodology for Remote Sensing Inter-Turn Fault Events in Power System Air-Core Reactors, via Simulation of Magneto Quasi-Static Fields in 2D FDTD

Abstract

We present a numerical methodology to estimate the transient fault currents and to simulate the remote sensing of transient fault information embedded in the magnetic field emissions caused by interturn shorts in 60 Hz air-core reactors, thru a magneto quasi-static (MQS) field approximation in the method of Finite-Difference Time-Domain (FDTD) in 2-dimensional (2D) space. The MQS 2D FDTD fields of reactor in normal operation are scaled by correlation against an equivalent circuit model that is derived from application of basic physics principles to parameters of the 3D air-core reactor. The proposed multi-scale quasi-static modeling methodology, based on the reduced c modification, provides fine-feature access down to the single-wire level and can efficiently estimate the transient fault fields and currents due to turn-to-turn short in a reactor with core height in several meters, core diameter in meters, wire diameter in millimeters, and number of turns in the thousands, at 60 Hz; this is accomplished by using computational resources of a typical laptop computer within seconds or minutes, as opposed to days that would be otherwise required without the reduced c modification.

A Parametric Integral Formulation to Approximate the Magneto Quasi-Static Fields of 3D Cylindrical Solenoids with Helical Winding

“…The author is grateful to the anonymous reviewers of IEEE Transactions on Magnetics for their thorough review and invaluable feedback that resulted in marked elevation in the quality of this manuscript. Also, the author acknowledges Dr. Hangtian Lei, Dr. Brian Johnson, and Dr. Joseph Law at the University of Idaho, and Dr. Normann Fischer at the Schweitzer Engineering Laboratories, for discussions around modeling and characterization of inter-winding shorts in aircore reactors through participation in, and financial support of, the research grant cited in [7] that provided the initial motivation for this work.…”

A Parametric Integral Formulation to Approximate the Magneto Quasi-Static Fields of 3-D Cylindrical Solenoids With Helical Winding

“…An accurate and complete analytical model of the magneto quasi-static (MQS) fields of solenoids is indispensable, given the long history of solenoids in a wide range of electrical applications; for example, magnets [1] and omni-directional electromagnets [2], permeameters [3], current sensors [4], magnetic heads for digital recording [5], displacement transducers [6], power system reactors [7], power regulation for in-package micro-electronics [8], through-the-wall MQS coupling [9]- [11], and magnetic induction [12], etc.…”

“…Other works in the literature pertaining to modeling solenoids, include: (i) the work by [17] studies the pitch effect of helical coils, using finite elements software, (ii) the work by [7] proposes a computational model based on the method of finite-difference time-domain (FDTD) for solving the MQS fields of air-core solenoids in 2D space, (iii) the work by [18] develops a field mapping method, based on the scalar magnetic potential, to obtain the z-component of the magnetic field inside air-core solenoids, (iv) the work by [19] proposes an analytical model of the modulated double helical coils, by relying on the infinite thin sheet current approximation, valid for long and tightly-wound windings, and (v) the work by [20] studies the effects of high frequency in sparse-wound solenoids.…”

“…The aforementioned formulations lack in one, or more, of the following ways: (i) they may not be analytical models, instead they rely on computational (finite elements [17] or finite difference [7]) methods that may not offer direct insights into the asymptotic (limiting) effects of geometric and material variables for general solenoids, and their computational nature often implies that conclusions may be confined to the specific solenoid configurations being simulated. Additionally, the simulations are dependent on finite computational resources (memory and processor) and may often experience non-convergence for solenoids of increasing complexity, due to the disparately scaled and quasi-static nature of the problem [7], (ii) they may be two-dimensional approximations of the three-dimensional solenoid and may not include all three orthogonal field components [7], [18], (iii) some analytical models may rely on approximations that are valid only for certain configurations (e.g., infinitely long solenoids [16] and tightly wound windings with an infinitesimal wire pitch [16], [19], circularly symmetric loops [13], certain core material [18], etc. ), or they may be valid only in certain regions (e.g., only inside [18] or only outside the solenoid volume, only along the solenoid's axes, or only in the far-field, etc).…”

“…Our parametric integral formulation of the helical contour facilitates inclusion of spatial irregularities in coils at the individual wire winding level; a feature with numerous potential applications where granular access to position of the individual wires is needed, e.g., modeling inter-turn shorted coils [7]. Furthermore, the field computation time increases approximately with order O(log(N T )) and O(N L ), where N T is the number of wire turns per winding layer, and N L is the number of winding layers.…”