Quadrature Axis Research Articles

Asynchronous Performance Prediction of AC Permanent Magnet Motor

many permanent magnet synchronous motors are run up from standstill by a sudden connection with an ac supply. The cage windings in rotor slots produce induction motor torque to run up the rotor, but two torque dips are produced in the torque-slip curve of the permanent magnet motor; one is caused by the rotating permanent magnet, and the other by the magnetic and the electric asymmetry between the direct and quadrature axes. Therefore, the prediction of the asynchronous performance is very important, as motors cannot be run up, unless the minimum values of the torque dips exceed the load torques at the slips. In this paper, ``harmonic permeance coefficient'' is newly introduced, which is used to combine the finite element field solution with the calculation of air gap inductance, and equations for the calculation of asynchronous performance of permanent magnet motors are also expressed. The calculated value by these equations agreed well with the experimental results.

Rotor motion in the dynamic finite element analysis of rotating electrical machinery

In the analysis of rotating electrical machinery, the need often arises to analyze machines at different rotor positions. This may be for simple studies such as for obtaining the direct and quadrature axes reactances in a synchronous machine, or for a more complex time domain analysis, where the rotor assumes different positions with time. The obstacle to allowing the rotor to rotate, is that the integrity of the mesh is disturbed as the nodes of a finite element mesh cross edges. Indeed, in studies of electromechanical dynamics, a two-fold challenge is posed in first rotating the rotor and secondly in doing so to a position which may be revealed only as computation proceeds. This paper presents a novel method of rotating the mesh which is made adaptive through the application of the Delaunay criterion for optimality. The application of such adaptive rotating meshes in machine dynamics is then investigated. It is shown that the methodology of this paper paves the way to constructing general software models of rotating machines.

Analytical models for interior-type permanent magnet synchronous motors

Keen interest in the design of Permanent Magnet (P.M.) synchronous motors is being fuelled by continuing developments in permanent magnet material technology. The most recent of these developments has been in the introduction of Neodymium-Boron-Iron (N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</inf> BF <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> ) with residual flux density of 1.23 T and energy product (BH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</inf> ) of 320 kJ/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . However a continuing difficulty with the analysis of permanent magnet motors, irrespective of their magnet composition, is the prediction of the direct and quadrature axis reactances. This is particularly the case with motors having permanent magnets imbedded in the rotor iron below the cage winding. The purpose of this paper is to present equivalent circuit models for such interior-type P.M. motors and develop simple analytical expressions for the calculation of axis reactances. Computed reactances including saturation effects are presented along with experimental values for verification.

Iron saturation effects in PM AC motors

Iron saturation causes the lumped circuit parameters to vary with the point of operation. Experimental evidence shows that the field excitation voltage and the direct axis reactance are not affected significantly by the armature reaction. This can be attributed to the presence in the direct axis of the magnets whose thickness represents a large effective air gap. In the quadrature axis, instead, the contribution of the air gap to the reluctance is small. Therefore, the quadrature axis reactance depends strongly on both the quadrature and direct axis components of armature magnetomotive force. This suggests a simple, albeit approximate, approach for predicting the parameter variation with operating point. As a result, both the design and analysis of synchronous motors excited by permanent magnets (PM's) are facilitated.

Field Weakening in Buried Permanent Magnet AC Motor Drives

The usual uncoupled d - q model of salient pole synchronous machines (Park's model) may be insufficient for accurate modeling of buried magnet permanent magnet machines. The addition of a nonbilateral coupling between the direct and quadrature axis equivalent circuits is shown to improve the steady-state model greatly. The cross coupling reactance has important implications in improving operation in the constant horsepower mode. In particular, it is demonstrated that the cross coupling term acts to reduce the effective internal voltage so that some field weakening can be achieved. The results should be useful in permanent magnet machine design for variable speed drive applications.

Nonstationary Magnetic Fielddistribution in Yoke of DC Machines and its Particularities

ABSTRACT Eddy currents in the quadrature axis of O.C. machines, which arise in nonstationary conditions, affect the performance of the machine considerably. The nonlminated yoke of O.C. machine carry eddy currents, and the quadrature axis components of their M.M.F's are very important in analysing machine performance. For example the importance of these M.F.F. components in performance of the machine is evident from the fact that the normal commutation of machine may be severely disturbed due to their damping action on the magnetic field in the zone of commutation. But the yoke of D.C. machines due to its position in the magnetic circuit does not distribute its flux symmetrically in its radial section. This phenomenon, which is not considered in the publications, may perceptibly change the mathematical model, describing the effects of quadrature axis M.M.F. on the machine performance. But its mathematical consideration should be rational and easy in programming for computer analysis. In the present articl...

Synchronous machines with contrarotating armatures: steady-state behaviour

A synchronous machine can be constructed with two armatures and one field. If the armatures contrarotate, the armature-reaction flux in the quadrature axis, ideally, is eliminated. The machine therefore operates with a high saliency ratio. The voltage regulation for a unity power-factor load is then only affected by winding resistance and leakage reactance. This unique feature allows the machine to have a peak power capability several times that of conventional machines of the same size. Two contrarotating machines have been designed and tested. One of the arrangements has steady-state behaviour approaching the expected ideal behaviour. The test machine built has three rotatable machine elements which allows the examination of a number of operating modes.

Experimental Study of the Effect of Saturation on the Steady State Operation of a Salient Pole Microalternator

ABSTRACT The direct and quadrature axis inductances of a salient pole micro alternator have been measured by low frequency, standstill tests. Existence of a strong cross saturation between the two axes has been shown. The application of the results to the P, Q curve of the microalternator for given supply voltage and field current has shown the importance of saturation and cross saturation on the maximum value of P. The choice of a value of the unsaturated leakage reactance of the machine appears as a difficult problem.

Superconducting Generator Modeling by Iterative T-Network Equivalent Circuits for Investigation of Transient Performance

Novel iterative T-network equivalent circuits are derived for the direct and quadrature axes of a generator with superconducting field winding and stator air-gap winding. They enable the treatment of the complex skin effect phenomena in a multi-shell damper system for any non- periodical time variation as well as of the mutual inductive couplings of the various rotor damper cylinders and the field and statorwindings. Consisting of linear RL networks, similar to the equivalent circuits of conventional generators, they can be included in existing computer programs for power system and machine dynamics. In this way an efficient tool is obtained to analyze the transient performance of a superconducting generator in the power system, including the torsional behavior, flux density distribution in the superconducting field winding and design optimization of the damper system.

Determination of Saturated Values of Rotating Machinery Incremental and Apparent Inductances by an Energy Perturbation Method

Energy and winding current perturbations form the basis of a method for calculation of the saturated apparent and incremental inductances of rotating machinery as functions of rotor position and machine winding excitation currents. The method is totally general and utilizes numerical field calculation techniques in obtaining stored energy in the magnetic circuits of such machines. Thus, it can be applied to a wide class of machinery with practically any cross-sectional contours and number of windings. It can be used at any given set of excitations (any loads). This method was applied to the calculation of the apparent and incremental inductances of a 15 hp samarium cobalt permanent magnet synchronous machine. The necessary-numerical field soluitions were obtained by finite elements at both rated and no load conditions. The calculated inductances, at various rotor positions, were compared with those obtained during laboratory measurements and the agreement between calculated and measured values was consistently very good. The advantage of this method over the more traditional calculations of only the direct and quadrature axes inductances (or reactances, including transient and subtransient components) is that the entire n > n matrix of incremental inductances that truely govern the dynamic performance of an n winding machine can be determined regardless of the validity of a rotating d-q-o frame of reference.

Torque of solid salient pole machine by finite element method

This paper presents a method of deriving the average torque of solid salient pole machine by finite element method (FEM).1 In this calculation, the effect of the armature resistance is included. The harmonic torque associated with the Görge effect (the dip in the torque curve at half rated speed) need to be examined as that can affect the torque close to half speed. The direct axis impedance and the quadrature axis impedance of rotor side at asynchronous operation of solid salient pole machine are obtained by a Poynting vector calculation.2 But by the average torque calculation in the literature (2), armature resistance was neglected. The method presented in this paper has been applied to analyze a 4-pole, 3-kVA, 220-volt, 50-Hz solid pole machine. The computed result shows good agreement with the test data. As the impedance is obtained from the flux distribution by FEM, the torque obtained is more accurate than the conventional method.

The Fields and Parameters of Interior Type AC Permanent Magnet Machines

This paper begins with a survey of the first principles of permanent magnet machines and then proceeds to find the air gap fields caused by the magnets and armature currents. From these fields, the three most important parameters are derived: namely, the direct and quadrature axes inductances Ld and Lq and the open-circuit voltage Eo

Field computation of subtransient damper impedances for use in optimal generator design

Damper resistances and reactances at sub-transient frequencies in large generators are computed rapidly from standard design data in a program written for repeated use in optimal design. Two non-linear, two-dimensional field problems in complex algebra, one for each of the direct and quadrature axes, are set up and solved in five to eight seconds on an IBM 4341 digital computer. Local negative sequence losses can be computed in a further three to five seconds. A diakoptic treatment, the modelling of singularities and the use of surface impedances give the method its economy. Comparisons with another method and with measurements suggest an accuracy within ten per cent.

IDENTIFICATION OF TURBOGENERATOR MODELS FROM FREQUENCY RESPONSE TESTS

ABSTRACT In recent years, growing attention has been paid to frequency response techniques for identifying turbogenerator models. A large amount of experimental results provided by frequency response tests carried out on a 107 MVA turbogenerator, is shown in this paper. The direct and quadrature axis transfer functions of the generator are experimentally identified over a frequency range up to 100 Hz; specifically, experimental results obtained from measurements at standstill and with rotating generator are carefully compared in order to investigate rotation effects. Additionally, low order models for use in stability studies are considered; proper parameters are identified by optimal fitting of test data and compared with design values

Development of Detailed Turbogenerator Equivalent Circuits from Standstill Frequency Response Measurements

A novel technique for deriving direct and quadrature axis equivalent circuit models of turbogenerators from standstill frequency response measurements is proposed. This technique differs from that proposed by previous investigators, and results in better representation of rotor body effects, particularly in the d-axis. This new method is applied to results of measurements on three large turbogenerators of similar rating but different rotor construction.

Comparative study of saturation methods in synchronous machine models

The paper investigates the use of various mathematical models to represent saturation in a synchronous machine. For the first time special attention is given to quadrature axis saturation. Calculated transient-response results are compared in order to find an accurate and computationally economical method of allowing for saturation.

EFFECT OF UNEQUAL MUTUAL COUPLINGS OF SYNCHRONOUS MACHINE ON ITS DYNAMIC RESPONSE

Abstract In the conventional models derived for the synchronous machine, it is assumed that all the mutual couplings on each of the direct and quadrature axes are equal. This assumption is satisfactory for calculation of the armature quantities, but it is insufficient in calculating the field circuit quantities. Hence, an extra mutual inductance is considered between the field and the damper winding. The model parameters are derived and the effect of the extra mutual inductance is obtained on the eigenvalues of the short-circuit model and the model of a synchronous machine connected to an infinite-bus.

SINGLE-PHASE INDUCTION MOTOR WITH ASYMMETRICAL STATOR

ABSTRACT This paper describes a single-phase single-winding induction motor which is self-starting without the use of a shading winding. Starting torque is produced by a combination of several stator asymmetries: an airgap under the main pole which is-tapered down in the direction of rotation, poles without windings in the quadrature axis with solid iron flux bridges to the lagging sides of the main poles, and yoke sections which are larger on the leading than on the lagging sides of the main poles. A qualitative explanation of the action of these asymmetries is presented using equivalent circuits.

Characterization of a Closed-Loop Controlled Current-Fed Reluctance Machine Taking into Account Saturation

A current-fed inverter-reluctance motor drive controlled in a closed-loop is described. A method of characterization is presented which takes the saturation into account in direct and quadrature axes. An experimental method is described which is able to determine direct and quadrature inductances with influence of the magnetomotive force (MMF) in one axis upon the flux in the other axis. The model is then used for the investigation of the electromechanical characteristics of the converter-machine system. Calculated results are compared with experimental results.

Generalized transient analysis of induction motors

Using state-space vectors, general transient statevariable equations for induction motors are derived. The equations hold for symmetrical and asymmetrical induction motors and for machines with thyristor connections in the stator and rotor phases. All parameters are expressed in terms of the actual physical phase coordinates. General transient time constants and transient inductances for the direct and quadrature axes of both stator and rotor of the asymmetrical machine are being introduced in literature for the first time.