INTRODUCTION
Induction in the pipeline due to AC interference is a phenomenon that should be taken into account for planning and mitigating purposes. To evaluate the electric currents and voltages produced in the pipeline due to proximity of high voltage power lines, Transmission Line Theory (TLl) is often applied and a number of software packages using TLl has been developed.
In this paper the analytical approach to the problem of the AC induction in an infinitely long mUltilayered cylinder representing the pipeline has been used to evaluate effects of the different electromagnetic parameters of the pipeline and surrounding medium. Also, approximate formulas for pipeline steel impedances and coating admittances used in industrial software have been compared with the exact formulas and the results of the comparison are presented.
Understanding the impact of the external electromagnetic environment on pipelines is important for practical considerations and from a theoretical point of view, Theoretically, it is one of the applications of the general electromagnetic theory to the particular case, while in practice the general electromagnetic theory normally is replaced by application of the transmission line theory. One of the major limitations of the transmission line theory is the necessity to use approximations for the expressions of the impedances. In general, the impedance is the ratio of the electric field of some origin to the current in the conductor. Thus, if there is a need to calculate the electric current in a conductor (pipeline) produced (induced) by the known external electromagnetic source (power line), the impedance is what needs to be evaluated. Also, if there is a need to calculate the electric current produced in one conductor by the electric current in the other conductor, the term ~impedance" is used in this case as well. There are many types of impedances: self-impedance, mutual impedance, external impedance, internal impedance. Chapters in classic books, dedicated to the applications of the Transmission Line (originally telegraph line) Theory by Schelkunoff1 Sunde 2 etc. give expressions for the impedances. With regard to the power line-pipeline interference the works of Dawalibi and Southey3, and Taflove and Dabkowski4 can be listed as samples of the wide use of the transmission line technique and, inevitably, expressions for the impedances.
In this paper general Maxwell's equations are used to derive the expressions fully describing the electromagnetic response of a pipeline to an incident electromagnetic field. We show how the approach can be set up to include an arbitrary number of layers in the pipeline. This then lets us easily model the electromagnetic environment in and around a pipeline that includes a hollow (gas or oil filled) conducting cylinder with an insulating coating, in contrast to earlier studies that sometimes only considered solid pipes or neglected the pipeline coating. The full expressions are used to calculate the electric and magnetic fields in any layer of the pipe and in the surrounding medium. This allows determination of the electric current produced in the pipeline steel, potential drop through the coating.
