1206 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 36, NO. 5, SEPTEMBER/OCTOBER 2000 Prediction of Magnetic Fields in Multiconductor Systems with Significant Harmonic Currents Marco Carrescia, Francesco Profumo, Senior Member, IEEE, and Michele Tartaglia Abstract—Electric and magnetic fields produced by transmis- sion systems have received strong interest both for biological ef- fects and for interference with electrical and electronic devices, measuring sets, computers, control systems, etc. A deeper atten- tion has been more recently devoted to magnetic fields which are difficult to screen and which can be significant when produced by transmission, but also by distribution and utilization systems. This paper proposes a simplified approach which seems to be useful in the case of lines set up by cables and, in particular, when more ca- bles are connected in parallel, considering currents affected by sig- nificant harmonics content. Complete simulation results for several selected cases to analyze the electromagnetic field under quasi-sta- tionary conditions in a multiconductor system are reported and discussed in detail, and the main results are summarized. It was found that the parallel connection of conductors can amplify or re- duce magnetic field amplitude with respect to the single conductor case and that this effect depends on the harmonics order. Index Terms—Harmonic current, magnetic fields prediction, power transmission lines. I. INTRODUCTION E LECTRIC and magnetic fields produced by transmission systems have received strong interest both for biological effects and for interference with electrical and electronic de- vices, measuring sets, computers, control systems, etc. A deeper attention has been more recently devoted to magnetic fields which are difficult to screen and which can be significant when produced by transmission, but also by distribution and utiliza- tion systems [1]. The interest in possible neoplastic effects and in interference with electric and electronic systems suggests analyzing with particular accuracy fields having low magnitude, too [2]. In this paper, the main interest is devoted to the accurate prediction of magnetic fields due to three-phase distribution multiconductor systems. Because of the frequent use of power electronics sys- tems, particular attention to effects produced by the currents har- monics content is required. A general procedure to analyze the electromagnetic field under a quasi-stationary hypothesis in a multiconductor system Paper ICPSD 99–38, presented at the 1999 Industry Applications Society An- nual Meeting, Phoenix, AZ, October 3–7, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Power Systems En- gineering Committee of the IEEE Industry Applications Society. Manuscript submitted for review October 8, 1999 and released for publication March 30, 2000. The authors are with the Dipartimento Ingegneria Elettrica Industriale, Po- litecnico di Torino, 24-10129 Turin, Italy (e-mail: profumo@polito.it; tarmich@ athena.polito.it). Publisher Item Identifier S 0093-9994(00)07623-4. has been proposed in [3]. Magnetic field computations by a finite-element formulation allow the determination of the magnetic field distribution within the conductors and in the neighbors. When sources are affected by significant harmonics content, it seems convenient to take advantage of linearity. As a consequence, one can solve the field problems at a certain fre- quency and at a certain time, calculate the impedances matrices at each frequency and, finally, be able to analyze the system under the desired conditions, by means of a circuit analysis [3]–[4]. This procedure is quite general, because it takes into consideration the eddy currents and the proximity effects, but it is also very expensive. As a consequence, this procedure seems convenient when one has to design a new system like a bus bar system, but it looks heavy, when one has to make predictions on magnetic fields produced by lines in electrical power systems, which can give rise to a lot of possible configurations. This paper proposes a simplified approach, which seems useful in the case of lines set up by cables and in particular when more cables are connected in parallel. If one neglects the eddy currents and the proximity effects, one can use well-known relations to evaluate the impedances matrices, at different frequencies. When the number of required predictions is high, the geometry of the conductors is relatively simple and the frequencies involved are lower than a few kilohertz, and this procedure seems to be satisfactory and convenient. The magnetic field computation can be performed by the numerical integration of the Biot and Savart relation, neglecting the Carson terms due to ground effects [5]. Moreover, if the end effects are neglected and only rectilinear conductors having cir- cular cross sections are considered, very simple computations give the resultant magnetic field. Magnetic fields generated by lines constituted by single-wire cables, having one or more conductors per phase, have been studied. The eddy currents and the proximity effects have been neglected, but the uniform current sharing in the phase subcon- ductors due to magnetic coupling has not been considered. Thus, the effects of the conductors configuration have been studied. The case of two conductors per phase has been analyzed, with the conductors lying on a plane or on two parallel planes. The possible configurations are also many in this simple case, and the preliminary evaluations allowed us to determine the situ- ations giving rise to the worst and to the best results. The fre- quency effects are considered with reference to a static converter (six-pulse rectifier), without neutral conductor, taking into ac- count the 5th, 7th, and 11th harmonics. The effects of the fre- quency on the magnetic field distribution are evaluated and dis- cussed. 0093–9994/00$10.00 © 2000 IEEE