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This paper discusses general methods of modelling magnetic saturation in steady-state, two-axis (d & q) frame models of dual stator induction generators (DSIG). In particular, the important role of the magnetic coupling between the d-q axes (cross-magnetizing phenomenon) is demonstrated, with and without cross-saturation. For that purpose, two distinct models of DSIGs, with and without cross-saturation, are specified. These two models are verified by an application that is sensitive to the presence of cross-saturation, to prove the validity of these final methods and the equivalence between all developed models. Advantages of some of the models over the existing ones and their applicability are discussed. In addition, an alternative is given to evaluate all saturation factors (static and dynamic) by just calculating the static magnetizing inductance which is simply the magnitude of the ratio of the magnetizing flux to the current. The comparison between the simulation results of the proposed model with experimental results gives a good correspondence, especially at startup.

This paper presents the modeling of saturated dual stator induction generator (DSIG) for analysis of its transient and dynamic behavior for stand-alone operation. In the analytical model, the e®ect of common mutual leakage reactance between the two three-phase winding sets and the cross saturation have been considered. For this purpose, a detailed description of a procedure to introduce magnetic saturation in found models is presented. Paper also discusses the possibility of DSIG for supplying two individual loads by presenting the results of analytical and experimental study of transient behavior under various operating conditions. Use of such models leads to more accurate predictions in industrial drives, especially wind driven power generation systems. This is veri¯ed by experimental lab tests.

Purpose – When magnetic saturation in ac machines is evolved, the theory of main flux saturation in d-q axes remains the best. Because of its simplicity, it is the most used in either motoring or generating mode for synchronous or asynchronous machines. Although, it is considered as a global way of introducing the iron saturation, compared to other methods, today, its fidelity has no contest in predicting complex ac machine operations. For this purpose, the aims of this paper consists of modeling these machines whatever the state-space variables values are taking into account the magnetic saturation. Two unified procedures are proposed. The first one deals with a common approach to establishing a complete and detailed model synthesis in d-q axes. The second also presents a unified approach to introducing magnetic saturation of the iron core in the characteristic equations. The analysis takes the salient pole synchronous machine as a general case of study. Then the approaches are extended to undamped and smooth air gap synchronous machines as well as induction machines. The paper aims to discuss these issues. Design/methodology/approach – The present paper, which is a first part of a work under study dealing with a unified method to derive multiple models of saturated ac machines, is intended to the description of an alternative method and its application for induction and synchronous machines. It mainly consists of the following parts: first, after writing the stator and rotor space vector d-q equations, the number of possible models is immediately discussed. By considering the currents and fluxes as state-space variables, 14 models are obtained for AC induction machine (IM and SM). They are classified into three families, current (three), flux (three) and mixed models (eight). Second, in order to easily introduce the magnetic saturation in the 14 developed models, a method is presented. It consists of just elaborating the model with the winding currents as state variables, then deriving all the other models from it. Third, to emphasize the influence of the presence of magnetic saturation, in each model, each inductance along the d and q axes is written with a fundamental expression which exists with or without saturation and an additional one due purely to saturation. Hence the additional terms can be studied and quantified in an easy way or simply removed when linear case is assumed. Fourth, adopting such strategy to write the different coefficients of the models had led to the definition of common saturation factors. In turn, the definition of common saturation factors had allowed the definition of different groups of models within each family. Fifth, an alternative to evaluate the static and dynamic saturation coefficients is also proposed. It is shown that by proper fitting of the experimental magnetizing curve, all saturation coefficients can be written only in terms of which is simply the magnitudes ratio of the magnetizing flux and current. Sixth, although the theory of the main flux saturation is now admitted, an investigation was carried out on a self-excited induction generator and the build-up of voltage and current phases of a standalone alternator, to prove the equivalence between the all developed models. Findings – The number of models based on the state-space variables choice, of a saturated ac machine, is reviewed. A simple method consisting of elaborating just the winding currents model, with magnetic saturation and deriving all the other models from it, is presented. In this study special interest was particularly focussed on either novel models or existing models cited in the literature but cannot be obtained by other approaches. In all cases, if the differential equations of the machine are formulated in terms of a set of variables other than the winding currents, a noticeable reduction in the size of equations may be obtained and consequently less time computing. The approach seems to be able to derive any possible model whatever the state-space variables and the type of the ac machine and hence can be classified as a general approach. Practical implications – The experiments of synchronous and induction machine transients prove the validity of the method. Originality/value – By suitable choice of state-space characteristic vectors among the fluxes and the currents, a synthesis of AC machine models in d-q axes is established. To introduce magnetic saturation in each model, an approach-based uniquely on the elaboration of the winding currents model is exposed and applied. In addition, the analysis gives a detailed classification of all found models taking into account the state variables nature as well as the cross-coupling coefficient considered as a saturation factor. The study is completed with a simple alternative to evaluate all saturation factors by just calculating the static magnetizing inductance.

Recently, the self-excited induction generators (SEIG) have been widely employed to operate as wind-turbine generators of an isolated power system. This paper proposes a simple method for the steady-state performance characteristics of a SEIG. Unlike the previous method, the proposed method avoids the tedious and erroneous manual work of segregating the real and imaginary components of the complex equation of the model. In this method, the model is formulated in a simple way and then solved using a numerical MATLAB function "fzero". The effectiveness of this method has been confirmed by comparing on a 0.8-kW induction generator the computed results obtained by the proposed method to those obtained by classical methods.