Standstill frequency-response methods and salient-pole synchronousmachines

Standstill frequency-response (SSFR) literature to date has primarily focused on turbo-alternators, which have a double-cylindrical topology. Synchronous machines driven by hydraulic turbines or internal combustion engines are salient-pole machines whose electrical constants are somewhat different due to construction differences: (1) the salient-pole topology produces a ratio of L_q/L_d of approximately 0.5 as opposed to unity for cylindrical-rotor machines; (2) the salient poles are constructed of steel-sheet stampings rather than forged steel; (3) salient-pole field windings are concentric whereas those of cylindrical rotor machines are distributed; (4) salient-pole generators often have amortisseur windings embedded in the pole faces; and (5) fractional slot/pole/phase (SPPP) stator windings are commonly employed in salient-pole machines whereas turbo-alternators are more apt to be limited to integral SPPP windings. These differences alter time constants, inductances, and transfer functions. This paper provides needed information for the modeling of salient-pole machines for use in simulation studies using a theoretical approach     

A standstill frequency response method for large salient pole synchronous machines

In this article, a Standstill Frequency Response Test (SSFR) is proposed, with the aim of determining the direct and quadrature axis operational impedances for salient pole synchronous machines. The method is applied with the rotor at standstill in a given arbitrary position, thus avoiding the difficulties in rotor mechanical alignment and rendering it suitable for large salient pole synchronous machines of hydroelectric power plants.     

Investigation and Simulation of Fields in Large Salient-Pole Synchronous Machines With Skewed Stator Slots

This paper presents the results of an investigative study performed on a large salient-pole synchronous machine with skewed stator slots. The study was carried out to aid the understanding of the phenomena related to electromagnetic field distribution, rotor damper currents and pole face iron losses in machines with skewed stator slots and an armature winding design with a fractional number of stator slots per pole. A hydrogenerator was specially instrumented to measure the variation of magnetic fields along the axial length of the machine and the induced currents in the damper bars on the rotor poles. A computational model has been developed to predict the air-gap flux density, damper currents and rotor iron losses. Measured results are compared with those predicted by simulation.     

On equivalent circuit modeling for synchronous machines

This paper presents alternative equivalent circuits for modeling the steady state frequency response (SSFR) data measured for turboalternator synchronous machines. These models provide direct representation of the frequency-dependent skin-effect properties of the dampers and rotor iron. The parameters are determined by matching the measured data to the model frequency response using standard optimization methods. The accuracy of matching is comparable to that of conventional third-order d-q models but the required number of parameters is reduced     

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     

Third order turboalternator electrical stability models withapplications to subsynchronous resonance studies

This paper deals primarily with the application of standstill frequency response (SSFR) models to subsynchronous resonance (SSR) studies involving large turbogenerators. It has been already recognized that models derived from SSFR testing intrinsically define the so-called subsubtransient frequency domain as well as the transient and subtransient domains. The application of a variety of SSFR models has been described previously only for one machine. Another turbogenerator possessing markedly different damping characteristics is compared with the one referred to above. Comparisons are also made with an IEEE “Benchmark” model. Comments regarding the damping performance of each of these three machines in the SSR range are discussed as well as the effect of rotor and field on stator differential leakage fluxes. Proposals are made for consideration by the IEEE Power System Engineering and Electric Machinery Committees involved in benchmark SSR stability programs or in related generator modeling standards     

Identification of high-order synchronous generator models from SSFRtest data

This paper presents a direct maximum-likelihood estimation procedure to identify the synchronous machine models based on the standstill frequency response (SSFR) test data. The method presented in this study is the first and only algorithm utilizing all available SSFR test data under both shorted and open field circuit conditions to establish a unique equivalent circuit model by maximizing the conditional probability density function of the error residuals. The method is applied to the modeling of two well-known generators, namely the Rockport and Nanticoke generators, using the measured SSFR test data. The results of the study show that by incorporating both the open and short-circuit SSFR data in the modeling process, the SSFR characteristics of the two generators can be accurately represented by the established high order synchronous models up to 1 kHz. The identified synchronous machine model consists of five amortisseur windings on each axis. In addition, an eddy-current effect impedance is included in the d-axis model for representing the increased influence of rotor eddy current under the open-circuit test condition     

Methods for determining the intermediate-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.     

Development of a neural network based saturation model forsynchronous generator analysis

This paper presents a new approach to model synchronous generator saturation based on a feedforward artificial neural network (ANN) model. The machine loading conditions, excitation levels and rotor positions are all included in the modeling process. The nonlinear saturation characteristics of a three-phase salient-pole synchronous machine rated at 5 kVA and 240 V is studied using the ANN model. An appropriate selection of input/output pattern for the ANN model training based on an error back-propagation scheme is developed using the on-line small-disturbance responses and the well-known maximum-likelihood estimation algorithm. The developed ANN model is implemented in the generator dynamic transient stability study requiring only small computational alteration in saturation model representation     

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     

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.     

Use of a permeance model to predict force harmonic components and damper winding effects in salient-pole synchronous machines

This paper presents a combined finite-element and analytical modeling technique for the prediction of force-density harmonics in salient-pole synchronous machines. The model calculates the induced currents in the damper winding cage and includes their effect on force-density components in the solution. Use of a combined analytical and finite-element approach considerably reduces simulation times compared to full time-stepping finite-element solutions, while including the effects of design changes on air-gap force harmonics. Results of the model predictions are presented together with measured data from two different machines.     

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

For the accurate analysis of salient-pole synchronous machines using the two-axis frame models, the direct- (d-) and quadrature-axis (q-axis) saturation characteristics are needed. Usually, the d-axis saturation characteristics can be obtained easily by the conventional open-circuit test with the machines excited from their field winding. On the other hand, the q-axis saturation characteristics of synchronous machines cannot be measured applying simple, conventional methods, and thus, they are usually not available. In this paper, four different methods for calculating the q-axis saturation characteristics of salient-pole synchronous machines from the measured d-axis saturation characteristics are explored. In these methods, the q-axis saturation characteristics can be calculated from the readily available test data, namely the d-axis saturation characteristics and the d- and q-axis unsaturated magnetizing reactances. Finally, a comparison between these methods is made.     

A `three transfer functions' approach for the standstill frequencyresponse 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 _afo(s)) together with the two transfer functions ( L_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_d(s) and G(s)     

Maximum Permissible Slip for Synchronizing Salient-Pole Synchronous Motors

The paper presents a method for determining the maximum permissible slip for synchronization of a salient-pole synchronous motor using machine, load and system parameters. An exact differential equation of motion of the salient-pole rotor during the synchronizing period is derived and then solved by means of a digital computer program using a fourth-order Runge-Kutta method. The synchronizing criterion involves two factors: the displacement angle must decrease, and this angle must not exceed 540 electrical degrees. Curves showing the relationship between load torque and maximum permissible slip with load inertia as a parameter are shown for a given motor. These results are compared with test data on the actual machine.     

Reluctance distribution modelling of saturated salient polesynchronous machines

This model was developed in response to the demand for fast, simple, and reasonably accurate methods for modelling heavily saturated synchronous machines. This paper outlines the development and performance of a new air gap flux density model for saturated salient pole synchronous machines. The model has four main components and its performance is demonstrated by comparing its computed flux density distribution and rotor torque with measured results for static conditions. The model gives reasonable results considering its simplicity     

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     

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.     

A general model of synchronous machine for its steady-stateperformance analysis

A general model for analyzing a salient-pole machine as well as a nonsalient-pole machine under steady-state conditions is developed. The classical two-reaction theory method is replaced by the present method to analyze synchronous machines with salient-rotors. The method presented is applied to a 6.25 kVA test machine with a salient-rotor and is found to give accurate results     

Identification of synchronous machine parameters using a multipleinput multiple output approach

This paper presents an alternative method for the identification of the d-axis parameters of a synchronous machine. The first part of the paper describes a multiple input multiple output (MIMO) broadband excitation and measurement method which is more time efficient than the standard standstill frequency response (SSFR) method. The second part describes a MIMO frequency domain identification procedure which estimates the d-axis parameters in 3 steps. The proposed identification procedure is self starting. It does not require starting values or other prior information. The measurement method and the identification procedure are tested on a 20 kVA salient pole synchronous machine