Coupled finite-element/state-space modeling of turbogenerators inthe abc frame of reference-the no-load case

This first of two companion papers centers on applying a coupled finite-element/state-space technique to the determination of self and mutual winding inductances of a 733 MVA turbogenerator and computing its open-circuit characteristic, in the natural abc frame of reference. In this method, the apparent self and mutual inductance profiles of the armature and field windings, expressed as functions of rotor position angle, are computed from a series of magnetic field solutions performed at uniformly-distributed samples of rotor positions covering the entire 360° electrical cycle, using the energy perturbation method. These inductances, which are obtained at no-load for three different excitation levels, include the full effect of space harmonics introduced by the magnetic circuit geometry, winding layouts and magnetic circuit saturation. The abc-frame/finite-element computed open-circuit characteristic is in excellent agreement with the test results. This computed no-load set of parameters forms the initial data for simulation of the full-load performance given in the companion paper, including the full impact of space harmonics and saturation on the flux linkage, current and voltage waveforms, and other performance parameters     

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 load on winding inductances of permanent magnetgenerators with multiple damping circuits using energy perturbation

A computer-aided method for determining the impact of load on winding inductances and other machine parameters of permanent magnet generators with multiple damping circuits is presented. The method is general in nature so that it can be applied to detailed computer-aided design processes of permanent magnet generator systems. The method is based on use of the abc frame of reference for development of the necessary state equations     

Methodology development for estimation of armature circuit andfield winding parameters of large utility generators

This paper presents a methodology to estimate armature circuit and field winding parameters of large utility generators using the synthetic data obtained by the machine natural abc frame of reference simulation. First, a one-machine infinite bus system including the machine and its excitation system is simulated in abc frame of reference by using parameters provided by the machine manufacturer. A proper data set required for estimation is collected by perturbing the field side of the machine in small amounts, The recursive maximum likelihood (RML) estimation technique is employed for the identification of armature circuit parameters. Subsequently, based on the estimates of armature circuit parameters, the field winding and some damper parameters are estimated using an output error estimation (OEM) technique. For each estimation case, the estimation performance is also validated with noise corrupted measurements. Even in case of remarkable noise corruption, the agreement between estimated and actual parameters is quite satisfactory     

Finite-element calculation of leakage inductances of a saturated salient-pole synchronous machine with damper circuits

It is important to understand the relationship between leakage flux distributions and machine characteristics for better design of synchronous machines. This paper presents a calculation method for leakage inductances of saturated salient-pole machines with damper circuits. All leakage inductances are divided into the self-leakage, gap leakage, and winding-differential leakage inductances. The leakage inductances correspond directly to the leakage flux distributions in the machines. Cross-magnetizing inductances are also calculated. The method is applied to a 300-MVA class generator. The relationship between the winding distributions, flux distributions, saturation, and inductances is discussed. Weak magnetic influence of the damper circuits on the armature in the d-axis is quantitatively illustrated through values of the winding-differential leakage inductances. The cross-magnetizing inductances, except for the d-axis damper circuits, are relatively large. Variations of the armature self-leakage inductances with saturation are small, and variations of the field and damper self-leakage inductances are larger.     

Analysis of a concentrated winding induction machine for adjustablespeed drive applications. I. Motor analysis

The performance of multiphase machines designed for operation with static power converters is investigated. The winding distributions are intentionally rectangular to better accommodate the rectangular waveforms of solid-state inverters. Equations which define the transient as well as steady-state behavior, including the computation of all machine inductances, are derived. In deriving these equations the space harmonics are specifically included. Equations for calculation of terminal voltages and electromagnetic torque are modified to account for nonsinusoidal air-gap-flux distributions. A conventional three-phase induction motor including the effect of space harmonics is simulated     

Comprehensive salient-pole synchronous machine parametric designanalysis using time-step finite element-state space modeling techniques

This paper details the application of a time-stepping coupled finite element-state space (CFE-SS) model to predict a salient-pole synchronous generator's parameters and performance, including damper bar current profiles and bar losses as well as iron core (including pole face) losses, under various operating conditions. The CFE-SS modeling environment is based on the natural ABC flux linkage frame of reference, which is coupled to a time/rotor stepping FE magnetic field and machine winding inductance profile computation model. This allows one to rigorously include the synergism between the space harmonics generated by magnetic saturation and machine magnetic circuit as well as winding layout topologies, and the time harmonics generated by the nonsinusoidal phase currents, ripple rich field excitation and damper bar currents. The impact of such synergism between these space and time harmonics on damper bar current profiles and losses, iron core losses, various machine winding current, voltage and torque profiles/waveforms is studied here for a 10-pole, 44.9 kVA, 17,143 RPM, 1428.6 Hz, 82 V (L-N), wound-pole aircraft generator     

Parameter calculation of a turbogenerator during an open-circuit transient excitation

A time-domain parameter calculation of a turbogenerator state-space model is presented. The finite-element (FE) method has been used to simulate a two-dimensional (2-D) nonlinear transient condition of the turbogenerator. An open-circuit transient excitation of the machine in closed-loop conditions (excitation system and unloaded synchronous generator) was reproduced to extract flux linkages, power losses, and eddy currents produced within the generator, which allowed the computation of the parameters of an electrical circuit. An electrical circuit structure with one d-axis damper winding is proposed. New parameter behavior profiles were found for the fictitious damper winding, and the saturation effects on the field winding reactance were determined. FE commercial software is employed during the research as a validation tool. It is found that the simulated time-domain response of the lumped model closely follows the time-stepping FE model. The research was carried out for a large turbine generator of 150 MVA, 13.8 kV, 50 Hz, and two poles.     

A novel method for modeling dynamic air-gap eccentricity insynchronous machines based on modified winding function theory

This paper presents the modeling of synchronous machines under eccentric rotors. The winding function theory accounting for all space harmonics and presented by earlier researchers has been modified to adopt a nonsymmetric air-gap for the calculation of machine winding inductances. The effect of dynamic air-gap eccentricity on the inductances of a salient-pole synchronous machine using the modified winding function approach (MWFA) has been discussed. The coupled magnetic circuits approach has been used for simulating the machine behavior under healthy and eccentric rotor conditions. The simulation results are in close agreement with the experimental results     

Analysis and Detection of Short Circuits in Fractional Horsepower Commutator Machines

An improved mathematical model for transient simulations of commutator machines is presented in this paper. This model can simulate and predict the line current harmonics during healthy and faulty operation conditions. A lumped parameter model that considers every single coil in the stator and rotor as a separate electrical and magnetic circuit is proposed. Self and mutual inductances of the coils are estimated by means of the winding function approach (WFA), accounting for the most relevant space harmonics in the machine air gap. The commutation is modeled by using the real brush width and assuming that the brush-commutator contact resistance is a function uniquely of their contact area, which depends on the armature position. Short circuits between adjacent commutator bars are investigated. It is shown that the model achieves good accuracy, reproducing fairly well the armature current ripple for healthy and faulty operation of the machine.     

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.     

Integrated Nonlinear Magnetic Field-Network Simulation of an Electronically Commutated Permanent Magnet Motor System under Normal Operation

An integrated magnetic field-network computer-aided method is presented, and is verified here by applying it in the determination of the performance of an electronically commutated permanent magnet motor system, and comparing the results with test results at rated operating conditions. Test results were found to be in very good agreement with numerical simulation data. At the core of this method are the instantaneous calculation of the magnetic field distribution within the machine, using the finite element method, and the determination of the winding inductances from these field solutions with the aid of an energy perturbation technique. The armature induced emfs are also obtained from these field solutions. These winding parameters, which are load dependent, are used in a nonlinear time domain network model of first order differential equations governing the dynamic performance of the motor to solve for the instantaneous phase currents. These new currents are then used at every time instant to determine the corresponding machine winding parameters, and the above process is repeated at successive time instants until the complete analysis period is covered. Though the validity of this method of analysis is verified in this paper by applying it to a 15 hp (11.2kw), 120 volt electronically commutated brushless dc motor system operating under normal and balanced conditions, the real utility of the method lies in its ability to analyze these motor systems under unbalanced partial or total component failure (fault) in the windings and associated conditioners. This type of application is given in a companion paper.     

Analytical prediction of eddy-current loss in modular tubular permanent-magnet machines

The paper describes an analytical technique for predicting the eddy-current loss in the moving armature of a tubular permanent magnet machine. This loss component is usually neglected in conventional tubular permanent magnet machines since high-order time harmonics in the stator current waveform and space harmonics in the winding magnetomotive force (MMF) distribution are generally considered to be insignificant. However, a relatively new topology of tubular permanent magnet machine, sometimes referred to as "modular", has emerged in which the fundamental component of the stator MMF has fewer poles than that of the permanent-magnet armature, the thrust force being developed by the interaction between a higher order MMF harmonic and the permanent magnet field. Thus, the presence of lower and higher order space harmonics in the winding MMF distribution of a modular machine may gives rise to a significant eddy-current loss in the moving-magnet armature. An analytical model is developed to predict the eddy currents which are induced in the magnets, as well as in any electrically conducting supporting tube which may be employed, and to quantify the effectiveness of axially segmenting the magnets in reducing the eddy-current loss. The validity of the developed model, which is also applicable to conventional designs of tubular permanent-magnet machine, is verified by time-stepped transient finite-element analysis (FEA).     

A brushless, exciterless, single-phase, sinusoidal wave synchronousmachine having an auxiliary stator winding

Analytical and experimental studies of a brushless, exciterless, single-phase, sinusoidal-wave synchronous machine operating as a generator or a motor, derived from a three-phase machine, are reported. One phase armature winding of the three-phase machine is used as an auxiliary stator winding of the single-phase machine and is used to supply the exciting power for the other two-phase armature windings acting as the load winding of the single-phase machine. A 1.5 kW, 200 V, 60 Hz, four-pole synchronous machine was used the experiments. It is shown that the waveforms of the armature terminal voltage and the load current are nearly sinusoidal. The advantages of the single-phase machine as a portable generator or small-load motor are discussed     

Computation of load performance and other parameters of extra highspeed modified Lundell alternators from 3D-FE magnetic field solutions

A combined magnetic vector potential, magnetic scalar potential method of computation of 3-D magnetic fields by finite elements, in combination with state modeling in the abc frame of reference, is used for global 3-D magnetic field analysis and machine performance computation under rated load and overload condition in an example 14.3 kVA modified Lundell alternator. The results vividly demonstrate the 3-D nature of the magnetic field in such machines and show how this model can be used as an excellent tool for computation of flux density distributions, armature current and voltage waveform profiles, and harmonic contents, as well as for computation of torque profiles and ripples. Use of the model in gaining insight into locations of regions in the magnetic circuit with heavy degrees of saturation is demonstrated. Experimental results which correlate well with the simulations of the load case are given     

Mathematical and experimental method to obtain the inverse modeling of nonsinusoidal and saturated synchronous reluctance motors

This paper presents new inverse modeling for synchronous reluctance motor (SyRM). This modeling is valid when the inductances are sinusoidal or nonsinusoidal and even when the machine is saturated. This technique involves the generation of constant torque curves as a function of two-phase currents in the Concordia's reference frame when the rotor angle is fixed. We also introduce an experimental method to obtain directly the inverse modeling. This practical method takes into account the saturation of the motor. This technique allows the reduction of the low torque ripple in the case of nonsinusoidal inductances.     

Advanced fault diagnosis of a DC motor

This paper presents a model of the DCc motor with an eccentric rotor. The winding function theory shows the effect of eccentricity fault on the motor inductances and the simulation is done using a nonsymmetric air-gap function. A modified equation is presented to show the existence of rotor slot harmonics in the DC motor current. To detect the eccentricity fault, a pattern recognition technique is utilized. The proposed algorithm works at steady state and uses armature current as input. The rotor speed is needed in order to provide the appropriate feature for the classifier. Therefore, rotor speed is estimated from the armature current using the commutation harmonics. The experimental results obtained from a 1/3-hp shunt DC motor verifies the proposed method. In order to cover different motor conditions, data are collected at different shaft speeds for both a healthy dc motor and a dc motor with an unbalanced load which exhibits static eccentricity.     

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     

Lumped modelling of open-circuit turbogenerator operationalparameters

Solid-rotor turbine-generators have commonly been derived from the fitting of curves to terminal characteristics obtained by measurement or from finite element simulations. The paper presents a new method to represent the open-circuit operational inductances of a large turbogenerator of 150 MVA. The method differs from current estimation techniques because the lumped model and its parameters are determined simultaneously. It is based on a finite-element electromagnetic linear analysis of the solid-rotor machine cross section in the frequency domain. Network theory is used to characterise the quadrature-axis model where the problems of model structure and parameter determination are treated. A q-axis equivalent circuit with one damper winding and frequency dependent parameters is found. In addition, an analysis of the machine d-axis is presented. It is based in an electromagnetic study of the “black box” two-port network, where the open-circuit operational inductances are represented by frequency dependent parameters     

Harmonic compensation using a synchronous machine with resonantfield circuits

This paper deals with a harmonic compensation method using a synchronous machine with resonant field circuits. Harmonics have become one of the major problems in power systems and a lot of methods of harmonic suppression have been studied. The authors have proposed a new method of harmonic suppression using a synchronous machine excited with the 6th harmonic current. This paper shows that armature inductances for the 5th or 7th harmonics decrease when the field circuits are connected to capacitors resonating at the 6th harmonic. The variations of armature impedances are explained theoretically by Park's equations. The optimal capacitances are selected so as to resonate with field inductances for the short-circuited armature. The experiments to suppress the 5th and 7th harmonics using the synchronous machine are successful