Disciplinary area: ELECTROTECHNICS

HIGH-FREQUENCY CIRCUIT MODELLING FOR WOUND COMPONENTS

Research Team: U. Reggiani, G. Grandi, G. Sancineto, A. Massarini (Università di Modena e Reggio Emilia), M. K. Kazimierczuck (State Wright University, Dayton,USA)

Objectives: Development of lumped parameter models for predicting the frequency behavior of wound components used for filtering applications

Research topics

Calculation of stray capacitances of solenoid inductors

The research concerns the development of methods for analytical calculation of turn-to-turn and possible turn-to-shield (and/or to-conducting core) of coils. These methods are based on the prediction of the electric field line paths in the dielectric surrounding the turns or on the employ the capacitance per unit length of two infinitely long straight parallel conductors. The calculated and measured values were in good agreement.

Calculation of the overall inductance and optimal design of solenoid air-core inductors

An analytical expression of the overall inductance is derived from the formula that gives the mutual inductance between two circular coaxial turns by means of elliptic integrals. For single-layer inductors, an optimised design is also carried out. The optimization procedure aims to obtain a first self-resonant frequency well above the desired frequency range of operation and given values for the inductance and rated current. The winding length (i.e., inductor losses and weight) is the objective function that has to be minimized. The optimization procedure is formulated as a nonlinear programming problem.

Ferromagnetic core inductors: main inductance and core equivalent series resistance as functions of frequency

The expressions of these parameters as functions of frequency are obtained solving Maxwell’s equations for both a ferrite core and a laminated iron core one. For a ferrite core, a complex electric permittivity and a complex magnetic permeability as a function of frequency are introduced in the field equations. For a laminated iron core, possible air gaps are tare ken into account by defining an equivalent permeability of the magnetic circuit. The determination of the time-varying core magnetic flux density allows one to derive the voltage induced across the winding by the corresponding magnetic flux and consequently the core equivalent series resistance and main inductance. The calculated values were compared with the measured ones, obtaining a good agreement.

Laminated iron-core inductors: a model for time-domain 

A circuit model useful to simulate electromagnetic transient of laminated iron-core inductors is developed. The analysis can be performed by means of standard circuit-oriented simulation programs. The winding is modeled by series Foster circuits, and each sheet of the packet by a suitable lumped parameter magnetic circuit. Numerical results obtained by the overall model and experimental measurements were compared. The agreement is good in a wide range of frequency.

Comparison of the performance of different kinds of inductors

The models developed for different kinds of inductors allow one to investigate their high-frequency behavior. The comparison is carried out in terms of inductance, losses and quality factor as a function of frequency. This study can give useful guidelines for the choice of the most suitable winding and core for the considered application.

Application to AC motor windings 

In cooperation with Prof. D. Casadei of the Group “Electrical Machines and Drives”, the proposed high frequency models have been used to treat a single coil of a mush wound winding of an AC motor. The model is a three-terminal circuit the parameters of which are identified by the measures of the impedances among each pair of terminals for different frequencies. The model can be easily extended to multi-coil windings and three-phase windings.

Main publications

A. Massarini, M. K. Kazimierczuck, G. Grandi, “Lumped Parameter Models for Single- and Multiple-Layer Inductors” Proceedings IEEE Power Electronics Specialist Conference (PESC’96), Baveno (Italy), June 17-22, 1996, Vol. 2, pp. 295-301

G. Grandi, M. K. Kazimierczuck, A. Massarini, U. Reggiani “Optimal Design of Single-Layer Solenoid Air-Core Inductors for High Frequency Applications” (invited paper) Proceedings 40th Midwest Symposium on Circuits and Systems (MWSCAS ‘97), Sacramento CA (USA), August 3-6, 1997, pp. 358-361

G. Grandi, M. K. Kazimierczuck, A. Massarini, U. Reggiani “High-Frequency Small-Signal Model of Ferrite Core Inductors” IEEE Trans. on Magnetics, Vol. 35, No. 5, September 1999, pp.4185-4191

G. Grandi, M. K. Kazimierczuck, A. Massarini, U. Reggiani “Stray Capacitance of Single-Layer Solenoid Air-Core Inductors” IEEE Trans. on Industry Applications,Vol. 35, No. 5. September/October 1999, pp. 1162-1168

U. Reggiani, G. Grandi, G. Sancineto, M. K. Kazimierczuck, A. Massarini “High-Frequency Behavior of Laminated Iron-Core Inductors for Filtering Applications” Proceedings of Fifteenth Annual IEEE Applied Power Electronics Conference and Exposition (APEC 2000), New Orleans (USA), February 6-10, 2000, Vol. 2, pp. 654-660

U. Reggiani, G. Grandi, G. Sancineto, G. Serra “Comparison Between Air-Core and Laminated Iron-Core Inductors in Filtering Applications for Switching Converters” Proccedings VII IEEE International Power Electronics Congress (CIEP 2000), Acapulco, Mexico, October 15-19, 2000, pp. 9-14

G. Grandi, A. Massarini, U. Reggiani, G. Sancineto “Laminated Iron-Core Inductor Model for Time-Domain Analysis” in Proceedings 4^th IEEE Power Electronics and Drive Systems Conference (PEDS 2001), October 22–25, 2001, Bali, 2001, Vol. 2, pp. 680-686

G. Grandi, D. Casadei, U. Reggiani, “Equivalent Circuit of Mush Wound AC Windings for High Frequency Analysis” Proceedings IEEE International Symposium on Industrial Electronics (ISIE’97), Guimaraes (Portugal), July 7-11, 1997, Vol. 1, pp. SS201-SS206

G. Grandi, D. Casadei, A. Massarini “High Frequency Lumped Parameter Model for AC Motor Winding” Proceedings European Conference on Power Electronics and Applications, (EPE’97), Throndhein (Norway), September 8-10,1997

G. Grandi, U. Reggiani, C. Rossi, G. Sancineto “High-Frequency Behavior of Three-Phase Induction Motor Windings” Proceedings 4^th International Symposium ElectroMotion (EM 2001), Bologna (Italy) June 19-20, 2001,Vol. 2, pp. 493-497