Quadrature-axis Synchronous Reactance Research Articles

Estimation of Quadrature Axis Synchronous Reactance Using the Constant Excitation Test

This paper introduces the constant excitation test to be applied in synchronous machines. The results obtained from this test allow the determination of the quadrature axis synchronous reactance of the salient pole synchronous machines. Despite standard present methods for its determination, the proposed method is suitable for large installed machines. The method basis is described and it is applied to several existent hydrogenerators. The calculated quadrature axis synchronous reactances are compared with the values supplied by the manufacturers, resulting in very good agreement. The appendix shows the quadrature axis location from the previous calculations results to obtain transient parameters from load rejection test.

Development of the Phasor Diagram and Equivalent Circuit for the Salient Pole Synchronous Machine

Phasor diagrams and equivalent circuits are widely used for analysis of AC electrical machines for a long time. Different variants of the phasor diagram for the salient pole synchronous machine are composed using the principle of two reactions. Variants of the equivalent circuit of such machines are known too. Traditional phasor diagram enables to calculate machine power only in separate way (from the phasors of external voltage and armature current). The developed phasor diagrams and equivalent circuit, in which the directaxis and quadrature-axis synchronous reactances and additional resistances with the components of armature current are used, are presented in the paper. They enable to calculate power of the considered machine in various ways and more successful to analyse them. Ill. 9, bibl. 3 (in English, summaries in English, Russian and Lithuanian).

Performance of a Three-Phase AC Generator With Inset NdFeB Permanent-Magnet Rotor

This paper presents the analysis and performance of a three-phase AC generator with an inset, neodymium-iron-boron (NdFeB) permanent-magnet (PM) rotor. Such a rotor construction gives rise to an inverse saliency effect (i.e., the direct-axis synchronous reactance is less than the quadrature-axis synchronous reactance). This feature results in an improvement in the voltage regulation characteristics when the generator supplies an isolated, unity-power-factor load. By solving the equations derived from the two-axis theory, it is found that there exists, in general, two values of load current at which zero voltage regulation is obtained. The relationship between armature resistance, inverse saliency ratio, and the operating speed to give zero voltage regulation is investigated. The finite-element method (FEM) is used for computing the pertinent generator parameters for performance evaluation, namely the no-load voltage and the synchronous reactances. Flux plots are presented to confirm the origin of inverse saliency in the inset PM rotor. The theoretical analysis is validated by experiments carried out on a 2.5-kVA prototype generator.

Estimation of parameters and performance of rare-earth permanent-magnet motors avoiding measurement of load angle

The paper describes a static test which, in conjunction with a no-load test, can be used to determine the parameters needed to apply the two-axis machine analysis to modern rare-earth permanent magnet synchronous motors. An iterative solution of the two-axis theory is presented which, together with the static test, avoids the use of the load angle. The solution includes the effect of core (iron) loss and allows for the estimation of current, power factor and efficiency for a motor running normally from inputs of terminal voltage and torque alone. The parameter values and machine performance predicted by the new methods are confirmed against test data obtained from a samarium-cobalt synchronous motor which has an asymmetrical buried magnet rotor. For this configuration, it is observed that saturation can cause significant variation in the permanent magnet excitation and the direct-axis synchronous reactance as well as the quadratureaxis synchronous reactance. When the variation of each of these parameters is included in the analysis, it is found that the two-axis theory gives a good representation of the motor performance in both the preferred and nonpreferred directions of rotation at a variety of voltages, frequencies and loads.

A simplified approach to determination of saturated synchronous reactances of large turbogenerators under load

This paper details the use of computerized magnetic field solutions, based on magnetic vector potential, to develop a simplified approach to the calculation of saturated values of steady state reactances of turbogenerators under various load conditions. When magnetic nonlinearity of the stator and rotor materials is taken into account, the turbogenerator reactances become dependent on the saturation conditions in the machine, which are a function of the operating conditions (terminal voltage, current and power factor). Quadrature axis synchronous reactances are reduced by as much as 40% from their classical unsaturated values under rated load. Torque angles deduced from the model at rated load are lower by as much as 20% than values obtained by standard methods. The method is applied to two typical 4-pole, 659 MVA and 2-pole, 733 MVA turbogenerators of the gas inner-coaled type. Supportive shop floor test results are provided.

Simulation for Design Purposes of Magnetic Fields in Turbogenerators with Asymmetrical and Symmetrical Rotors Part II - Model Calibration and Applications

This paper compares shop floor test results and results from simulation using the model presented in Part I. Also, it contains applications of rated load simulation. The results given are for two typical 4-pole and 2-pole turbo-generators. The 4-pole machine is equipped with an asymmetrically slotted rotor. The results show general agreement, within 2%, between theory and test. Some useful findings are obtained regarding the use of asymmetrically designed rotors. Asymmetry leads to lower flux densities in critically saturated parts of the rotor under full load. The effects of rotor asymmetry on excitation current, quadrature axis synchronous reactance and torque angle under rated full load condition are explored. The effect of saturation at full load on the values of quadrature axis reactance and torque angle is presented.

Derivation of the Basic Constants of Three-Phase Inductor Alternators in Terms of Winding Parameters

A mathematical analysis has been made to determine the constants of three-phase inductor alternators in terms of winding parameters. The flux distribution in the air gap on the basis of harmonic permeance distribution due to both stator and rotor slot openings has been found. Self- and mutual inductances of phase and field windings have been determined in terms of machine constants. Expressions for direct- and quadrature-axis synchronous reactances have been determined in terms of machine constants, as in the case of a salient-pole synchronous machine. An equivalent circuit has been established and performance has been calculated for a typical alternator of this type.

Variable-characteristic synchronous machines

The paper deals with the operation of a standard cylindrical-rotor synchronous machine with several novel forms of excitation control. It shows how, by using a nonlinear function of load-angle control, the machine can be made to develop characteristics normally associated with a salient-pole machine, and how a very wide range of the effective ratio of direct-axis to quadrature-axis synchronous reactances can be produced. Alternative control functions, designed to produce a machine with infinite stiffness, or with tangential forms of power/load-angle characteristics, are also described. Possible applications in large power systems, local generating plant and synchronous motor control are discussed.

An experimental effective value of the quadrature-axis synchronous reactance of a synchronous machine

The author carried out experimental tests upon two dissimilar salient-pole synchronous machines. Each machine was run as a synchronous motor on constant-voltage busbars. An examination of the results confirmed the inaccuracy which occurs in the predicted value of the load angle, σ when the quadrature-axis reactance is assumed constant.An original analysis of the experimental results is given whereby it is shown that the effective value of the quadrature-axis reactance can be expressed in the form