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 leakage flux distributions in a salient-pole synchronous machine using finite elements

It is important to understand the relationship between iron core configurations and leakage flux distributions to get a better design of synchronous machines. This paper presents a method for calculating the steadyand transient-state leakage flux distributions in salient-pole synchronous machines. The method provides information on leakage flux distributions that cannot be obtained by terminal quantities. The method analyzes the leakage inductances that properly represent the corresponding leakage fluxes. They are calculated using the gap flux distributions by finite elements with magnetic saturation. The calculated leakage inductances of a synchronous machine under various loads are also shown and the relationship between the inductances and magnetic saturation is discussed.     

Performance analysis of wound-field synchronous alternators underload using finite elements

A method is described for evaluating the performance of wound-field synchronous alternators under load using finite elements. The space-time phasor relationships of quantities in the synchronous machines are used to coordinate the set of instantaneous phase currents in the armature and field current in the rotor, with the geometry and load condition. The method uses the fact that the sensitivity matrix of the power/voltage with respect to the armature/rotor currents is diagonally dominant. The weak coupling of the power/voltage attributes to the relevant current sources permits a disintegration of the computational loop into a weakly coupled dual loop, in which one loop tries to match the terminal power factor by systematically adjusting the armature currents while the other tries to match the terminal voltage by modifying the field current. The method is illustrated by examples of its application, and the results are given     

Standstill frequency response testing and modeling of salient-polesynchronous machines

Standstill frequency response (SSFR) testing and modeling of salient-pole synchronous machines are presented for two machines with integral and nonintegral numbers of stator slots per pole per phase. Frequency responses at different rotor positions have been investigated to explore the effects of rotor position in a machine with a fractional slot winding, as the electromagnetic fields and the armature magnetomotive forces do not precisely repeat every pole. The test results do not show any significant differences for various direct and quadrature axes rotor positions. The authors obtained a negative value of differential leakage inductance as theoretically postulated in the literature. The pertinent features of testing and modeling of salient-pole synchronous machines are described to point out the differences with SSFR testing of round rotor turbogenerators extensively published in the literature     

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     

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     

Measurement of the saturation characteristics in the quadrature axis of synchronous machines

For the accurate prediction of the performances of saturated synchronous machines, the saturation characteristics in both the direct and quadrature axes are needed. The d-axis saturation characteristic of a synchronous machine can be measured easily by the open-circuit test with the machine excited from its field winding. On the other hand, the q-axis saturation characteristic of a synchronous machine cannot be measured applying a similar easy, simple method and, as a result, these characteristics are usually not experimentally measured and are not available. In this paper, three possible experimental methods for determining the q-axis saturation characteristics of both cylindrical-rotor and salient-pole synchronous machines are presented. The merits and demerits of these experimental methods are discussed from the point of view of their complexity and their accuracy. Comparisons between the measured q-axis saturation characteristics obtained by these experimental methods are made for a cylindrical-rotor machine and two salient-pole machines. Moreover, the various sources of errors, which may affect the accuracy of determining the q-axis saturation characteristics by these methods, are investigated.     

Double winding, high-Voltage cable wound Generator: steady-State and fault analysis

This paper describes a detailed circuit representation of synchronous machines equipped with two similar or dissimilar armature windings. The equivalent circuit at steady state is presented. The self and mutual leakage inductances of the two sets of three-phase stator windings are evaluated by the finite element method as well as an analytical method. The simulation results from a steady-state analysis as well as a fault analysis are verified experimentally on the world's first high-voltage generator Powerformer installed in Porjus, Sweden, rated at 45 kV and 11 MVA.     

A finite element technique for calculating the magnet sizes andinductances of permanent magnet machines

A method for calculating the magnet size, and the direct and quadrature axis reactances of permanent magnet synchronous machines, using the finite-element method is presented. In this method the machine is modeled by its equivalent d-q representation of armature MMF and the appropriate reactances are calculated from the magnetic energy in the magnetic field. This is in contrast to the conventional approach of using an abc phase current model, solving the model and then converting the resulting quantities to respective d -q-o quantities. The method is applied to a permanent magnet motor design     

Comparison between analytical and numerical methods of calculatingtooth ripple losses in salient pole synchronous machines

The application of analytical and numerical methods to an electromagnetic problem requiring an accurate representation of saturation is examined. The problem considered is that of tooth-ripple losses in salient-pole synchronous machines for the situation where the pole pitch is much greater than the armature slot pitch so that the applied DC field can be taken as uniform. To calculate these losses, several analytical methods have been developed over a period of many years. Two such methods, one devised by Oberretl (1972) and a modified version of the considerably older one-dimensional approach of Gibbs (1947), are compared with results obtained from the finite-element and finite-difference methods. Using a time-stepping finite-difference calculation, the influence of moving boundaries and the imposed DC field are taken into account for the first time in this tooth-ripple calculation. A saturation factor is defined that allows the designer to calculate the tooth-ripple losses of solid salient-pole synchronous machines for a wide range of machine size taking magnetic saturation into account. To verify the theory, the results are compared with measurements on a small model. These measurements were done using a torque meter placed between the model and a DC drive motor and were cross-checked by the Poynting vector method. Rules and limits are given for the use of the analytical methods     

Hydropower Development in Southwestern China

A simple expression is derived to obtain the direct axis synchronous reactance (x/sub d/) of synchronous machines from operating conditions. This method is suitable for obtaining this parameter where original data are lost and no other information is accessible.     

An algebraic approach for identifying operating point dependentparameters of synchronous machines using orthogonal series expansions

This paper presents a method for identifying armature and field parameters of synchronous machines from digital fault recorder (DFR) data. The method uses operational properties of orthogonal series expansions such as the Hartley, Walsh and Fourier series to transform a set of differential equations into linear algebraic equations. The algebraic formulation and use of operational calculus reduce the problem of identifying parameters to the manipulation of matrices that may be easily performed in such computational packages as Matlab. The variation of machine parameters with operating point is considered     

Simulation Studies of the Transients of Squirrel-Cage Induction Motors

A new simulation approach is proposed in consideration of a saturation and a deep bar effect for the study of transients of three-phase squirrel-cage type induction motors. The mathematical model of an induction motor is expressed by the six differential equations of three-phase instantaneous voltage and current. The torque of an electric equation is related to the motion equations of motor and driven machine in the mathematical model. The values of reactance of stator and rotor are changed by the saturation of core caused by starting current. Also both the values of reactance and resistance of rotor bar are varied by the deep bar effect in the rotor core during starting. The calculation method of circuit constant that adds the influence of saturation and deep bar effect is proposed in this paper. The circuit constant of simulation model in consideration of saturation and the deep bar effect are decided by these computation methods in accordance with the conditions of rotation speed and current. If the large current flows, the leakage reactance of the stator and the rotor decreases by saturation. Moreover, the resistance of the rotor gradually decreases when the rotational speed rises from stop to synchronous speed, and the leakage reactance increases gradually. The calculated values were compared with the observed values of the examination machine of 1100 kW4P and an excellent agreement was obtained demonstrating the accuracy of the proposed simulation. Consequently, it is shown that the saturation and the deep bar effect are the essential factors to perform the accurate simulations of the induction motor. After checking the validity of the proposed approach, the simulation of the grounding faults was performed. In this study, all the simulation programs have been developed in the Matlab/Simulink environment.     

Field Computation for an Axial Flux Permanent-Magnet Synchronous Generator

An analytical method to determine the no-load and armature reaction magnetic fields of a single-sided, axial flux permanent-magnet synchronous generator without armature core is presented. Laplace's equation is solved in the rectangular coordinate system to give the scalar magnetic potentials, using a Fourier series method. For computation of the armature reaction field, a multi-current-sheet model is employed in order to account for the distributed nature of armature conductors in the axial direction. Finite element analysis and experimental results on a prototype machine are presented for verifying the accuracy of the proposed method.      

A dynamic on-line parameter identification and full-scale systemexperimental verification for large synchronous machines

An on-line parameter identification and full-scale experimental verification for large synchronous machines (>50 MVA) is presented in this paper. A step change of excitation is imposed to a generator when the machine is in normal operation. The transient voltages, currents and the power angle are recorded. Based on the large disturbance equations and using the measured power angle as an observation argument in an identification algorithm, the synchronous machine electrical parameters (x_d, x_d', x_d", T_do', T_do", x_q, x_q", T_qo") and mechanical parameters (H,D) are obtained. In addition, the system parameters (equivalent infinite bus voltage V_bus and line reactance x_e) are identified as well. The proposed method has been repetitively applied to turbogenerators and hydrogenerators with capacities up to 300 MVA. In particular, a field test has been conducted on a system with a capacity of 15000 MVA. The experimental results from all of the full-scale tests are consistent and the effectiveness of the proposed on-line identification method is verified. The plant experiences indicate that by adopting the identified parameters, the stability margin of the generator can be improved by up to 5%, resulting in 30-50 MVA more power generation     

Analysis of torques in large steam turbine driven inductiongenerator shafts following disturbances on the system supply

The paper first summarises the advantages of steam turbine-driven induction generators over conventional generators such as low cost, less maintenance, rugged and brushless rotors (squirrel cage type, no need for synchronisation, etc.), together with problems concerning excitation (VAr compensation at loads etc). A mathematical model of the induction generator simulated in direct-phase quantities where saturation of the magnetising reactances is simulated and saturation of stator and rotor leakage reactances is ignored is developed and employed for detailed simulation of the machine. Discrete-mass models of the machine shaft where both steam and electrical viscous damping is simulated are employed in comparing transient shaft torsional response evaluated by time domain simulation and frequency domain analysis following incidence and clearance of severe system faults. The paper then investigates torsional response following incidence and clearance of severe supply system disturbances, when the rotor is stationary and when running at close to synchronous speed unexcited, and following malsynchronisation when excited by a controlled VAr source, together with torsional response following bolted stator-terminal short-circuits at full-load and no-load following switching in of the induction generator onto the system supply. It examines precision of predicting torque in turbine-generator shafts by frequency domain analysis not analyzed for induction generators in the literature heretofore following incidence and clearance of worst-case disturbances on the supply. Effect of steam and electrical damping on maximum shaft torques predicted by frequency domain analysis is also illustrated. The results illustrate there is no tendency for shaft torques to become more onerous as the fault clearing time is increased as is the case for shaft torques in large synchronous machines. Three large two-pole machines of rating of up to a few hundred MWs are analysed     

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.     

Two-Step Method for Identification of Nonlinear Model of Induction Machine

A two-step method is applied for parameter identification of a saturated electromechanical model of an induction machine (IM). The k-factor cross saturation technique is used to account for iron saturation. Balanced and unbalanced short-circuits armature current waveforms of this machine are less sensitive to variations in the mechanical parameters. Conversely, any change in these parameters has a strong impact on the start-up test. Accordingly, in the proposed estimation method, the online double-line-to-neutral short-circuit test is performed to estimate the electrical parameters of the machine and the results obtained are then used to compute the mechanical parameters from the starting test. The good agreement of the estimated results with actual data attests to the effectiveness and suitability of the proposed algorithm in computing the electromechanical parameters of these machines.     

Coupled finite-element/state-space modeling of turbogenerators inthe abc frame of reference-the short-circuit and load cases includingsaturated parameters

In this paper, a coupled finite-element/state space modeling technique is applied in the determination of the steady-state parameters of a 733 MVA turbogenerator in the abc frame of reference. In this modeling environment, the forward rotor stepping-finite element procedure described in a companion paper is used to obtain the various machine self and mutual inductances under short-circuit and load conditions. A fourth-order state-space model of the armature and field winding flux linkages in the abc frame of reference is then used to obtain the next set of flux linkages and forcing function currents for the finite-element model. In this process, one iterates between the finite-element and state-space techniques until the terminal conditions converge to specified values. This method is applied to the determination of the short-circuit, and reduced- and rated-voltage load characteristics, and the corresponding machine inductances. The spatial harmonics of these inductances are analyzed via Fourier analysis to reveal the impact of machine geometry and stator-to-rotor relative motion, winding layout, magnetic saturation, and other effects. In the full-load infinite-bus case, it is found that, while the three-phase terminal voltages are pure sinusoidal waveforms, the steady-state armature phase currents are nonsinusoidal and contain a substantial amount of odd harmonics which cannot be obtained using the traditional two-axis analysis     

Force density limits in low-speed PM machines due to temperature and reactance

This paper discusses two of the mechanisms that limit the attainable force density in slotted low-speed permanent-magnet (PM) electric machines. Most of the interest is focused on the force density limits imposed by heating of the windings and by stator reactance. The study is based on analytical models for the force and reactance calculations and a lumped parameter thermal model. It is found that in a machine with an indirectly cooled stator, it is difficult to achieve a force density greater than 100 kN/m/sup 2/ due to temperature limits. A high force density is achieved by using deep slots, which lead to high reactance. The high reactance severely increases the converter kilovolt-ampere requirement and total system cost. It is also shown that the cost caused by the high reactance will also limit the force density reached. In machines with one slot per pole per phase, the reactance limited the useful slot depth to approximately 200 mm. However, in machines having a greater number of slots per pole per phase the reactance becomes no longer an important limiting factor for the slot depth and force density.