A.M. El-Serafi

Experimental study of the saturation and the cross-magnetizing phenomenon in saturated synchronous machines

The cross-magnetizing effect in both the d- and q-axis in a small salient-pole machine was measured. Two simple equations describing the cross-magnetizing effect in both axis directions are derived. An accurate saturation representation that includes the effect of both the machine-saturated reactances and the cross-magnetizing phenomena is also given. In addition to this, the modified phasor diagram and power/load angle relationship are obtained. The results of the machine output power obtained by this technique show a good agreement with those obtained from test. The saturation effect in changing the power/load angle curves is seen to be noticeably large and depends mainly upon the cross-magnetizing effect. >

Determination of the parameters representing the cross-magnetizing effect in saturated synchronous machines

This paper introduces the concept of the cross-magnetizing phenomenon in saturated synchronous machines (the magnetic coupling between the direct and quadrature-axis). The parameters which represent this cross-magnetizing effect are defined and techniques for determining these parameters are proposed. In these techniques, there is no need for an auxiliary winding in the q-axis of the machine and, thus, they can be applied to conventional synchronous machines. Experimental results which verify the accuracy of these techniques are presented. >

Saturated synchronous reactances of synchronous machines

The authors present a model for the d and q-axis synchronous reactances in which the effects of both the d- and q-axis saturation factors and the cross-magnetizing phenomenon are included. The variations of the d- and q-axis mutual reactances versus the d- and q-axis ampere-turns are also shown. The results obtained by using this model were found to be in good agreement with those measured experimentally. These results show also that the saturation effects on the d- and q-axis mutual reactances could be large and its effect on the q-axis reactance could be larger than that on the d-axis reactance. The results demonstrate that the effect of the cross-magnetizing phenomenon could be appreciable and its negligence or improper representation could lead to inaccurate values for the machine reactances. >

Methods for determining the q-axis saturation characteristics of salient-pole synchronous machines from the measured d-axis characteristics

In the analysis of the steady-state performances of saturated synchronous machines using the classical two-axis (d- and q-axis) frame model, the accurate calculation of the machine performances depends to a large extent on their saturation conditions. However, the effect of saturation depends not only on the saturation level in the axis of the resultant machine ampere-turns (intermediate-axis) but also on the phase angle between the resultant ampere-turns and the resultant magnetic flux. This work presents four analytical methods for determining the intermediate-axis saturation characteristics of salient-pole synchronous machines from the measured d-axis saturation characteristics. The accuracies of these four methods have been verified by comparing the measured field currents and load angles of two laboratory salient-pole synchronous machines of different designs with those calculated using an innovated approach which uses the intermediate-axis saturation characteristics directly in the modeling of the saturated synchronous machines. Moreover, the calculated intermediate-axis saturation characteristics have been compared with the measurable ones in the case of one of these machines.

Digital simulation of an AC/DC system in direct-phase quantities

This paper describes a mathematical model for the simulation of an AC/DC system using direct-phase quantities. This system consists of an AC/DC converter station connected to a synchronous generator at its terminals as well as to an infinite bus-bar through a short transmission line. The proposed model in direct-phase quantities enables the study of the effects of the generated harmonics of the DC transmission on AC systems in general and on the behavior of synchronous machines in particular. The paper describes also a numerical solution using a digital computer for the mathematical model of this AC/DC system. The usefulness and versatility of the computer program are demonstrated by applying it to different AC/DC system configurations. The paper gives results of some studies concerning the effects of the generated harmonics on the behavior of synchronous machines with or without filters in the system.

A 'three transfer functions' approach for the standstill frequency response test of synchronous machines

A three transfer functions approach for the standstill frequency response (SSFR) test of synchronous machines is proposed. Network theory is employed for the explanation of the three-function approach. The three-function and two-function approaches, as well as the one-function approach, are compared. The verification of the approach is obtained through simulations and an application to an SSFR test on a 3 kVA laboratory microalternator. The accuracy of the determined d-axis model parameters, particularly of the rotor circuits, is improved by the use of the suggested third transfer function (L/sub afo/(s)) together with the two transfer functions (L/sub d/(s) and G(s)). This requires that the measurements of the three transfer functions be taken in the SSFR test and be involved in the d-axis model fitting instead of the common practice involving only L/sub d/(s) and G(s). >

Effect of saturation on the steady-state stability of a synchronous machine connected to an infinite bus system

A synchronous machine model that includes the effect of the saturated reactances the cross-magnetizing phenomenon is presented. This model is used to study the steady-state stability of a synchronous machine connected to an infinite bus system. These studies show that the effect of saturation is noticeably large and depends mainly on the cross-magnetizing effect. The results obtained by this model are found to be in good agreement with those obtained from the experimental results. >

Effect of synchronous generator regulation on the subsynchronous resonance phenomenon in power systems

Since the potential consequences of the subsynchronous resonance phenomenon were encountered in 1970, concern has escalated among those electric utilities which rely upon series compensation to seek reliable methods for determining the existing power systems subsynchronous stability margins. In the several publications available on this subject, no attempt has been made to represent the synchronous machine governing and excitation control systems in the mathematical models devised, particularly when the torsional dynamics of the shaft are considered. It is the main objective of this paper to present a rigorous mathematical technique for the evaluation of the subsynchronous resonance stability limits of regulated synchronous machines connected through series compensated transmission systems. The results of a digital simulation of the suggested mathematical technique is also presented. The investigations presented show that properly designed electrohydraulic governors can improve considerably the subsynchronous resonance stability limits. On the other hand, practical voltage regulators seem to be unable to achieve such an improvement.

Application of the Finite-Element Method for the Determination of the Parameters Representing the Cross-Magnetizing in Saturated Synchronous Machines

It has been recognized that the cross-magnetizing phenomenon of saturated synchronous machines plays an important role in their analysis using the two-axis frame models. In this paper, the finite-element method (FEM) is applied to determine from 2-D static electromagnetic field solutions the parameters representing this phenomenon. A specially designed synchronous machine that can be excited from both its direct and quadrature axes is used in this study in order that the parameters representing the cross-magnetizing effect could be measured experimentally and, thus, the accuracy of the numerical solution can be verified. The effects of some of the factors that may affect the accuracy of the FEM analysis have also been investigated. The results of these studies have shown that the calculated parameters representing the cross-magnetizing phenomenon using the FEM are consistent with the measured values.

Analysis of the Dual-Excited Synchronous Machine

This paper presents a generalized analysis for the dual-excited synchronous machine, in which, on the contrary of previous work, the two field windings are not necessary located on the rotor axes, and may not have the same number of turns or the same inclination angle to the physical axis of the pole structure. In deriving the general equation of the machine, no approximations are introduced other than those required for deriving Parks transformation, and so the analysis provides a more exact representation for this machine. Also a new per-unit system is applied, as the conventional one would introduce errors if the saliency is to be taken into consideration. The external connection is considered in a general form so as to allow for studying the machine performance when it is connected to an infinite-bus through a general transmission system. The small displacement model is derived and arranged in a form suitable for investigating dynamic stability problems. The model provides a good tool for studying the effect of using numerous schemes of excitation regulation on the dynamic behaviour of the machine.