Main flux saturation modelling in double-cage and deep-barinduction machines

The available models of saturated double-cage and deep-bar induction machines are the current state-space model and the flux state-space model, where state-space variables are selected either as stator current and currents of both rotor cages, or stator flux linkage and flux linkages of both rotor cages. This paper presents a number of models of saturated double-cage (deep-bar) induction machines where alternative sets of state-spate variables are selected. The method of main flux saturation modelling relies on recently introduced concept of `generalised flux space vector', which has originally been developed for modelling of saturated single-cage induction machines. The procedure and the novel models are verified by experimental study and simulation of self-excitation process in a double-cage induction generator     

Modelling of magnetic saturation in smooth air-gap synchronousmachines

Main flux saturation in d-q axis representation of synchronous machines is at present modelled by selecting either all the winding currents or all the winding flux linkages as state-space variables. However, these two available models are just a tiny portion of the complete set of models that can be obtained by selecting other combinations of state-space variables. This paper presents a general procedure for main flux saturation modelling in smooth air-gap synchronous machines, that is applicable for most selections of state-space variables. The method relies on the concept of `generalised flux' and `generalised inductance', that has been successfully applied in modelling of saturated single-cage and double-cage induction machines. The concept is extended to saturation modelling in smooth air-gap synchronous machines. A number of models, that result from the application of the method for different selections of state-space variables, are presented in detail     

Saturation modelling in d-q axis models of salient pole synchronousmachines

Presently available transient d-q axis models of saturated salient pole synchronous machines are derived by selecting either all the winding currents or all the winding flux linkages as state-space variables. This paper presents a number of novel models where state-space variables are selected in various different ways. The idea originates in the `generalised flux' and `generalised inductance' concept, which has recently been successfully developed and applied in the derivation of numerous models of saturated smooth air-gap AC machines. The concept is here extended to salient pole synchronous machines. Saturation itself is accounted for by means of a single saturation factor approach and conversion of an anisotropic to an isotropic machine is executed in the usual way. The new models, presented in the paper, yield the same accuracy as the existing models that are based on single saturation factor approach. This statement is confirmed by a simulation study and a sample of simulation results is included. However, a number of new models are considerably simpler than the existing ones, and thus more convenient for application in simulations     

Impact of dynamic cross-saturation on accuracy of saturatedsynchronous machine models

Cross-saturation effect in synchronous machines has been a subject of considerable attention. Inclusion of the cross-saturation in the machine model has two consequences. The first one, called here “steady-state cross-saturation”, consists of dependence of the steady-state d-q axis magnetizing inductances on the currents in both axes. The second one, termed here “dynamic cross-saturation”, is the existence of nonzero elements in the system matrix, that describe cross coupling between d- and q-axis. Dynamic cross-saturation appears in all the saturated machine models, regardless of the selected set of state-space variables, with the exception of the winding flux linkage state-space model. The aim of this paper is to compare behavior of various models when dynamic cross-saturation is neglected. It is shown that the impact of dynamic cross-saturation on accuracy depends on the selected set of state-space variables. In the majority of cases omission of dynamic cross-saturation leads to very inaccurate results. However, it is found that for one particular class of models, omission of dynamic cross-saturation has practically no impact on accuracy. These models therefore fully describe the complete saturation effect by means of only continuous variation of the d-q axis magnetizing inductances     

Impact of cross-saturation on accuracy of saturated inductionmachine models

Cross-saturation in smooth air-gap AC machines has been a subject of controversy in the 1980s. The discussions were based on the model of a saturated AC machine with d-q axis winding currents acting as state-space variables. The recently introduced concept of generalised flux and generalised inductance has enabled the derivation of a series of models of saturated smooth air-gap AC machines for various selections of state-space variables. All the models, except for the winding flux model, contain explicit terms that describe cross-saturation. The aim of this paper is to compare behaviour of various models when cross-saturation is neglected. Two transients of a single-cage induction machine are analysed: motor starting with increased voltage; and induction generator self-excitation. Some experimental results are included. It is shown that the impact of cross-saturation on accuracy depends on the type of the model. All the models that ask for a time derivative of the generalised inductance yield poor results if cross-saturation is neglected. However, the models that require a time derivative of the inverse of the generalised inductance are basically unaffected. Thus these models can be simplified without any loss of accuracy     

A Refined Method of Deriving Reduced Order Models of Induction Machines

A refined method of deriving non-linear, reduced order models of induction machines is presented and evaluated. This method differs from the classical method of neglecting stator transients (p? terms) in that only the fast components of the stator flux linkages are neglected when solving for the slower rotor variables. The accuracy of the refined model is assessed by comparing its transient characteristics with those of a detailed model and the standard reduced order model obtain by neglecting the stator transients. It is shown that the refined model more closely approximates the lower frequency characteristics of the induction machine following both large and small disturbances than the standard reduced order model.     

Theory and analysis of three-phase series-connected parametricmotors

This paper presents the steady-state performance of a three phase wound-rotor parametric motor. This type of motor can be practically realized by connection of stator and rotor phases of a conventional wound-rotor induction machine. The analysis is based on the d-q axes model, from which a phasor diagram is presented. The analysis is extended to include the magnetic saturation effect. Comparison between theoretical and experimental results showed a satisfactory agreement proving the validity of the mathematical model as well as magnetic saturation effect representation. Also the motor stability is investigated     

An improved model for saturated salient pole synchronous motors

An improved model for the transient analysis of saturated salient pole synchronous motors is presented. With the aid of saturation factors obtained by test or with finite elements, Park's equations for a synchronous machine are modified to independently account for the saturation of the magnetizing flux linkages in the region of the stator teeth and rotor pole face as well as saturation of the total flux linking the stator core. The model is used to calculate the starting performance for a direct online start as well as the transient performance during a load change. The model shows improvement over more traditional models, indicating that representation of both main flux and core saturation are important for synchronous machine analysis     

Application of Floquet's theory to the analysis of series-connectedwound-rotor self-excited synchronous generator

In this paper, Floquet's theory for solving differential equations with periodically varying coefficients has been utilized in evaluating the steady state performance of a three phase wound rotor series-connected self-excited synchronous generator SCSESG. This type of generator is practically realized by the series connection of stator and rotor windings of a conventional wound-rotor induction machine. Self excitation may occur when a suitable capacitor bank is connected across the machine terminals. The analysis gives the same results that are obtained when the d-q transformation model is utilized. Application of Floquet's theory has the advantage of reducing the mathematical manipulation needed. The results are checked experimentally. Saturation effects on each axis inductance as well as iron losses show satisfactory agreement. The generator acts as a hypothetical salient pole machine operating at half the rotor electrical angular frequency and is independent of load conditions provided that the prime mover speed is kept constant     

Direct active and reactive power control of DFIG for wind energy generation

This paper presents a new direct power control (DPC) strategy for a doubly fed induction generator (DFIG)-based wind energy generation system. The strategy is based on the direct control of stator active and reactive power by selecting appropriate voltage vectors on the rotor side. It is found that the initial rotor flux has no impact on the changes of the stator active and reactive power. The proposed method only utilizes the estimated stator flux so as to remove the difficulties associated with rotor flux estimation. The principles of this method are described in detail in this paper. The only machine parameter required by the proposed DPC method is the stator resistance whose impact on the system performance is found to be negligible. Simulation results on a 2 MW DFIG system are provided to demonstrate the effectiveness and robustness of the proposed control strategy during variations of active and reactive power, rotor speed, machine parameters, and converter dc link voltage.     

An induction machine model for predicting inverter-machineinteraction

The conventional qd induction motor model typically used in drive simulations is very inaccurate in predicting machine performance, except perhaps for the fundamental component of the current and the average torque near rated operating conditions. Predictions of current and torque ripple are often in error by a factor of two to five. This work sets forth an induction machine model specifically designed for use with inverter models to study machine-inverter interaction. Key features include stator and rotor leakage saturation as a function of current and magnetizing flux, distributed effects in the rotor circuits, and a highly computationally efficient implementation. The model is considerably more accurate than the traditional qd model, particularly in its ability to predict switching frequency phenomena. The predictions of the proposed model are compared with those of the standard qd model and to experimental measurements on a 37 W induction motor drive     

Real-Time Speed and Flux Adaptive Control of Induction Motors Using Unknown Time-Varying Rotor Resistance and Load Torque

In this paper, an algorithm for direct speed and flux adaptive control of induction motors using unknown time-varying rotor resistance and load torque is described and validated with experimental results. This method is based on the variable structure theories and is potentially useful for adjusting online the induction motor controller unknown parameters (load torque and rotor resistance). The presented nonlinear compensator provides voltage inputs on the basis of rotor speed and stator current measurements, and generates estimates for both the unknown parameters and the nonmeasurable state variables (rotor flux and derivatives of the stator current and voltage) that converge to the corresponding true values. Experiments show that the proposed method achieved very good tracking performance within a wide range of the operation of the induction motor (with online variation of the rotor resistance: up to (87%). This high tracking performance of the rotor resistance variation demonstrates that the proposed adaptive control is beneficial for motor efficiency. The proposed algorithm also presented high decoupling performance and very interesting robustness properties with respect to the variation of the stator resistance (up to 100%), measurement noise, modeling errors, discretization effects, and parameter uncertainties (e.g., inaccuracies on motor inductance values). The other interesting feature of the proposed method is that it is simple and easily implementable in real time. Comparative results have shown that the proposed adaptive control decouples speed and flux tracking while standard field-oriented control does not.      

Modeling of Induction Machines Using a Voltage-Behind-Reactance Formulation

Over the past several years, there has been renewed interest in modeling electrical machines using phase (abc) variables. This paper considers modeling induction machines using phase variables in a voltage-behind-reactance (VBR) formulation. Specifically, three VBR models are proposed wherein the rotor electrical subsystem is modeled using flux linkages as state variables expressed in the qd reference frame. The stator electrical dynamics are represented in abc phase coordinates that enable direct interface of the machine model to an external network. Such a direct interface is advantageous when the machine is fed from a power electronic converter and/or when the modeling is carried out using circuit-based simulators. Computer studies of an induction machine demonstrate that the proposed VBR models achieve a 740% improvement in computational efficiency as compared with the traditional coupled-circuit phase-domain model.     

A new induction motor drive based on the flux vector acceleration method

A novel control strategy for the induction motor drive, based on the field acceleration method, is presented. The torque is controlled through variations of the stator flux angular velocity. The stator flux is controlled by using a feedforward control scheme, with the stator flux reference vector adjusted so as to obtain the fixed rotor flux amplitude. The applied controller assures a fast torque response, low torque ripple in the steady state, and drive operation with a constant switching frequency. The algorithm includes the improved stator and rotor flux estimation that guarantees the stable drive operation in all operating conditions, even at low speeds. The experimental tests verify the performance of the proposed algorithm, proving that good behavior of the drive is achieved in the transient and steady-state operating conditions.     

Pattern recognition-a technique for induction machines rotor brokenbar detection

A pattern recognition technique based on Bayes minimum error classifier is developed to detect broken rotor bar faults in induction motors at the steady state. The proposed algorithm uses only stator currents as input without the need for any other variables. Initially, rotor speed is estimated from the stator currents, then appropriate features are extracted. The produced feature vector is normalized and fed to the trained classifier to see if the motor is healthy or has broken bar faults. Only the number of poles and rotor slots are needed as pre-knowledge information. A theoretical approach together with experimental results derived from a 3 hp AC induction motor show the strength of the proposed method. In order to cover many different motor load conditions, data are obtained from 10% to 130% of the rated load for both a healthy induction motor and an induction motor with a rotor having 4 broken bars     

Machine modeling and universal controller for vector-controlled induction motor drives

Developments of machine model and a universal controller for vector-controlled induction motor drives are presented in this paper. The machine representations associated with vector-control methods referring to various frames, including stator, rotor, and air-gap flux frames, can be derived simply by selecting different state variables; thereby clearly identifying the relationship between machine modeling and vector control. Moreover, a universal vector controller for induction motor drives fed by a voltage-controlled voltage source inverter is presented. It is shown in this paper that various vector controllers, including rotor flux-oriented controller, stator flux-oriented controller and air-gap flux-oriented controller, can be realized by simply changing few parameters. It is demonstrated by experimental results that the developed universal vector controller for various vector-control approaches can be implemented using the same hardware with a minor change to software associated with parameters; and thereby confirming the theoretical analysis.     

Modelling of synchronous machines for dynamic studies withdifferent mutual couplings between direct axis windings

Synchronous machine models commonly utilized for transient performance calculations normally disregard such effects as induction of currents on slot walls and rotor surfaces during canceling or blocking of field current and the difference of mutual coupling between direct axis windings. It is shown how such different couplings can easily be incorporated into the synchronous machine conventional modeling and how the characteristic reactance to be used in this representation can be determined through the reactive power rejection test with zero active power. The air gap flux saturation representation, when considered together with the inclusion of the effect of the difference of mutual couplings between direct axis windings, is also discussed     

A Field Reconstruction Technique for Efficient Modeling of the Fields and Forces Within Induction Machines

Traditional analysis and design of induction machines have been largely based upon lumped-parameter models. An alternative tool used for field-based evaluations of an induction machine is the finite-element method. Although useful, its computational complexity limits its use as a design tool. In this paper, a field reconstruction (FR) method for induction machine simulation is introduced. The FR method utilizes a small number of finite-element evaluations to establish basis functions of normal and tangential flux densities. The basis functions are then used to estimate the magnetic field under arbitrary stator excitation. Using such a tool, evaluation of fields and forces produced by a machine under alternative excitation strategies can be explored efficiently. Moreover, alternative field-based derivation of stator/rotor excitation control can be explored.      

Modelling adequacy of the doubly fed induction generator for small-signal stability studies in power systems

The dynamics of the doubly fed induction generator (DFIG) with a closed-loop control is analysed. The analysis provides explanations of the impact of the closed-loop control on the DFIG dynamics and relevant modelling requirements for power system stability studies. The discussion considers generic PI controllers for the regulation of rotor speed, reactive power and pitch angle. It is shown that for the closed-loop-controlled DFIG, a simplified model, whereby both stator and rotor dynamics are neglected, is adequate. In such model, stator and rotor variables are algebraic, that is, they change instantaneously and the modelled dynamics are those of the controllers and mechanical parts. The observations and conclusions are obtained from eigenvalue, participation factor and time-domain analysis.     

Induction machine field orientation along airgap and stator flux

Airgap and stator flux field orientation control (FOC) methods are discussed as an alternative to the familiar rotor flux orientation approach. The principal motivation is the relative accessibility of the two alternative fluxes. Motor flux models are developed in a unified manner, and it is shown that inherent coupling between flux and torque exists in the stator and airgap models. Two decoupling methods are presented. Simulation results are given for an airgap oriented control; the performance approaches that of a rotor flux oriented drive