Presence Of Magnetic Saturation Research Articles

Hybrid Continuous-Discrete State Observer for Induction Machine in Presence of Magnetic Saturation

AbstractThis paper addresses the problem of state observation of induction motors facing large flux and speed variations. In these conditions, state observation (and control) cannot be properly performed without accounting for the nonlinear nature of the motor magnetic circuit. A key feature of this study is that the state observer design is based on an experimentally validated continuous-time nonlinear model taking into account the saturation nature of a commercial induction motor of 7.5 KW. A continuous-time nonlinear state observer is thus obtained, using the high gain design technique, and is shown to be convergent when applied to the (continuous-time) system model. The point is that, in modern control applications, continuous-time systems are only observed through sampled output signal measurements. Then, one classical solution consists in constructing a discrete-time approximation of the (continuous-time) observer. This solution is somewhat computationally burdensome and does not preserve the convergence properties of the original continuous observer. Here, a different solution is developed according to the hybrid continuous-discrete (HCD) estimation principle. The obtained HCD observer is formally shown to preserve a quite satisfactory estimation accuracy when applied to the (continuous-time) system model. This theoretical result is confirmed by simulation, considering an operational protocol involving large speed and flux variations making the motor operate both in the linear on nonlinear parts of its magnetic characteristic.

多極集中巻埋込磁石モータの構造最適化設計に関する検討

Interior Permanent Magnet Synchronous Motors (IPMSM) have been found in many applications because of their high-power density and high-efficiency. The existence of a complex magnetic circuit, however, makes the design of this machine quite complicated. Although FEM is commonly used in the IPMSM design, one of disadvantages is long CPU times.This paper presents a simple non-linear magnetic analysis for a multi-pole IPMSM as a preliminary design tool of FEM. The proposed analysis consists of the geometric-flux-tube-based equivalent-magnetic-circuit model. The model includes saturable permeances taking into account the local magnetic saturation in the core. As a result, the proposed analysis is capable of calculating the flux distribution and the torque characteristics in the presence of magnetic saturation. The effectiveness of the proposed analysis is verified by comparing with FEM in terms of the analytical accuracy and the computation time for two IPMSMs with different specifications. After verification, the proposed analysis-based optimum design is examined, by which the minimization of motor volume is realized while satisfying the necessary maximum torque for target applications.

Dynamic Modeling, Experimental Characterization, and Verification for SRM Operation With Simultaneous Two-Phase Excitation

Dynamic modeling of switched reluctance motors (SRMs) is usually done on a per-phase basis. However, in most applications, SRMs are used with simultaneous excitation of more than one phase. Thus, a model accounting for mutual coupling in the presence of magnetic saturation is needed to predict and optimize their performance in terms of efficiency and torque ripple. This paper presents a dynamic two-phase excitation model of the SRM. Motor symmetry is used to reduce the amount of flux linkage data needed for the model. An experimental procedure to obtain the flux linkage data is described. Measured flux linkage data for the 8/6 SRM are also included. Details of the simulation model and comparison with experimental waveforms along with their implications for performance prediction are presented

Simple Nonlinear Magnetic Analysis for Permanent-Magnet Motors

This paper presents a simple nonlinear magnetic analysis for a surface-mounted permanent-magnet synchronous motor as an assistant design tool of finite-element analysis (FEA). The equivalent magnetic circuit of the motor used in the proposed analysis is composed of the saturable permeance tips in the stator teeth for considering the local magnetic saturation. As a result, the proposed analysis is capable of calculating the flux distribution and the torque characteristics in the presence of magnetic saturation. The effectiveness of the proposed analysis is verified by comparing with three-dimensional (3-D) FEA in terms of the analytical accuracy. The computation time is greatly reduced as short as 1.5 s while the 3-D FEA requires as much as 32 min for the same evaluation.

Rigorous definition of the transformation ratio in the presence of magnetic saturation and leakages

This paper proposes a new method for modelling multi-winding devices with non-linear magnetic core. This method is founded on rigorous theoretical bases. It is successfully applied to the study of a voltage transformer for 245 kV network.

Nonlinear differential-geometric techniques for control of a series DC motor

The problem of controlling a series DC motor using only current measurements is considered. It is shown that both speed and load-torque may be estimated from the current measurements. Two nonlinear feedback laws are considered based on feedback linearization and input-output linearization, respectively. Both of these control laws require knowledge of the speed and load-torque. The speed/torque estimation scheme and the control schemes are valid in the presence of magnetic saturation in the field circuit and when high-speed field-weakening is employed. By neglecting the armature inductance, the estimation is accomplished using nonlinear state-space and output-space transformations to construct an observer with linear error-dynamics whose rate of convergence may be arbitrarily specified. (Such an observer could provide reliability to existing systems in the event of a speed sensor failure.) The feedback-linearization controller involves a nontrivial state-space transformation allowing control of the full state trajectory. An input-output linearization controller with stable internal dynamics is also explicitly constructed. Finally, simulations are given to demonstrate the algorithms. >

EFFECT OF SATURATION THIRD HARMONIC ON THE PERFORMANCE OF SQUIRREL-CAGE INDUCTION MACHINES

ABSTRACT This paper contributes to the understanding of the behavior of the saturation third harmonic and how energy is converted from fundamental to third harmonic form in a squirrel-cage induction machine in me presence of magnetic saturation. It is shown that the power transferred via the third harmonic airgap flux is accounted for by a change in the magnitude and phase-shift in the fundamental airgap flux. A procedure is proposed to link the rotor third harmonic circuit quantities to a set of equivalent fundamental component circuit quantities which leads to a modified equivalent circuit for the induction machine.

A complete model characterization of brushless DC motors

The authors address the modeling problem associated with brushless DC motors (BLDCMs) with nonuniform air gaps that operate in a range where magnetic saturation may exist. The mathematical model includes the effects of reluctance variations as well as magnetic saturation to guarantee proper modeling of the system. An experimental procedure is developed and implemented in a laboratory environment to identify the electromagnetic characteristics of a BLDCM in the presence of magnetic saturation. It is demonstrated that the modeling problem associated with the class of BLDCMs can be formulated in terms of mathematically modeling a set of multidimensional surfaces corresponding to the electromagnetic torque function and the flux linkages associated with the motor phase windings. The accuracy of the mathematical model constructed by the developed method is checked against experimental measurements. >

Selection of Flux Level in Field-Oriented Induction Machine Controllers with Consideration of Magnetic Saturation Effects

The magnitude of rotor flux is a primary design and application variable for field-oriented induction machine controllers. Optimization of a nonsaturating machine controller for peak torque/A will lead to operation at the peak of the constant current torque-versus-slip curve. It is shown how flux level selection for both standard and high efficiency motors is altered by including saturation characteristics. Theoretical and experimental approaches for calculation of flux-producing current in the presence of magnetic saturation are presented. The theoretical method includes a straightforward two-parameter saturation model, which is demonstrated to possess characteristics very close to experimental data. This approach contributes substantial insight to saturated machine analysis while retaining relative simplicity as a design tool. The experimental approaches developed are straightforward and general.

Nonlinear three dimensional field computation methods in laminated iron cores under saturated conditions

Two methods of accounting for magnetic saturation in nonlinear three dimensional magnetic field problems using finite elements, are given. The magnetic field formulation used here is based on the curl curl approach which was detailed in earlier papers. The three dimensional finite element method is used once in conjunction with the Newton Raphson technique and once with a Gaussian method to obtain solutions of such fields in the presence of magnetic saturation in laminated cores. The laminated iron core of an example transformer is represented by three composite reluctivities to account for the anisotropy of the core. The saturated values of these composite reluctivities are obtained by curve fitting the magnetization characteristics of composite materials using cubic spline polynomials in conjunction with special treatment of the highly saturated core regions. For comparison purposes, solutions obtained using the Newton-Raphson and the Gaussian methods of inclusion of saturation, are obtained for the same problems in the presence of same degrees of saturation. Very good agreement between calculated and measured data for the chosen problem is achieved. Comparison between convergence and implementation characteristics of the two methods used here are given.

Shaft currents in electric machines

This paper describes the causes of, and remedies for, the existence of “shaft currents” or “bearing currents” which sometimes flow across the rubbing surfaces of the bearings of electric machinery, thereby gradually damaging the shaft and bearings. Up to the present time the only cause of shaft currents that has attracted any particular attention has been the use of sectionalized stators, and the published discussions have been chiefly confined to synchronous alternators. Fleischman <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> and others have shown that sectionalizing causes shaft currents for the reason that the extra reluctance of the joints causes an unequal division of the flux between the clockwise and counter-clockwise paths in the yoke, thus giving a resultant flux linking the shaft. Applying the same method of reasoning used in the case of sectionalizing to the general case of any machine with segmental punchings, the following facts are shown: 1. A principal cause of shaft currents in revolving electric machines is the use of poles and segments in certain ratios. 2. The frequency of the shaft current due to joints in the stator yoke is an odd multiple of the frequency of the stator flux, the frequency of the shaft currents due to rotor joints is an odd multiple of the rotor frequency, and these frequency multiples are determined by the ratios of poles to segments. 3. Machines with 4, 8, 16, 24, 32, etc., poles are especially likely to have shaft currents, and machines with 6, 10, 14, 22, etc., poles are relatively immune. 4. By the proper choice of the number of segments for use with any machine, or by the use of segments with offset dovetails, or both, shaft currents can be effectively eliminated in most cases. The possibilities of shaft currents being caused by homopolar action as the result of magnetic flux flowing in the shaft, or by other means, are discussed, and it is concluded that such causes are seldom important. A possible useful application for the theory of shaft currents in the design of a high-current transformer is mentioned, and the possibility of obtaining multiple frequencies from a stationary transformer in this way is shown to be dependent upon the presence of magnetic saturation. A table of combinations of poles and segments that will cause shaft currents is given, and a bibliography of the subject is appended.