Standstill Frequency Response Research Articles

Estimation of a global synchronous machine model using a multiple-input multiple-output estimator

In this paper, the measurement results of a series of standstill frequency-response (SSFR) tests, performed at different magnetization levels, are discussed. For each data set, an individual d-axis model is estimated, which allows seeing the variation of the different parameters as a function of saturation. A global estimator is presented which uses the different data sets to estimate one global model, including the field-to-armature turns ratio. The global estimator is based on an impedance matrix representation of the synchronous machine. This global estimator assumes that only the d-axis main inductance is saturation dependent. The individual estimated models justify this assumption. Finally, the relative additional error of the global estimated d-axis equivalent circuit with the individual estimated ones is studied. The measurement results discussed in this paper are obtained on a four-pole 130-kVA synchronous machine.

Estimation of a Global Synchronous Machine Model Using a Multiple-Input Multiple-Output Estimator

In this paper the measurement results of a series of standstill frequency response (SSFR) tests, performed at different magnetization levels, are discussed. For each data set an individual d-axis model is estimated, which allows the variation of the different parameters to be seen as a function of saturation. A global estimator is presented that uses the different data sets to estimate one global model, including the field-toarmature turns ratio. The global estimator is based on an impedance matrix representation of the synchronous machine. This global estimator assumes that only the d-axis main inductance is saturation dependent. The individual estimated models justify this assumption. Finally, the relative additional error of the global estimated d-axis equivalent circuit with the individual estimated ones is studied. The measurement results discussed in this paper are obtained on a four-pole 130 kVA synchronous machine.

Synchronous machine parameters from frequency-response finite-element simulations and genetic algorithms

This paper presents a novel way to obtain parameters of synchronous-machine equivalent circuits from standstill frequency response data using a hybrid genetic algorithm. The genetic algorithm is capable of finding a global minimum within a search interval of the fitness function used to match the equivalent circuit and the measured machine transfer functions, notwithstanding the initial guess of the identification process. Therefore, methods such as the maximum likelihood estimation technique, could be substantially enhanced. Results obtained in the identification procedure show that good matching can be obtained with either negative or positive leakage inductance values. These results cast some light on the possible physical meaning that circuit parameters may have. Finite-element modeling is used here to determine the transfer functions of a turbine generator. This approach is consistent with the general aim of obviating the requirement of field testing.

Synchronous Machine Parameters from Frequency-Response Finite-Element Simulations and Genetic Algorithms

This paper presents a novel way to obtain parameters of synchronous machine equivalent circuits from standstill frequency response data using a hybrid genetic algorithm. The genetic algorithm is capable of finding a global minimum within a search interval of the fitness function used to match the equivalent circuit and the measured machine transfer functions, notwithstanding the initial guess of the identification process. Therefore, methods such as the maximum likelihood estimation technique could be substantially enhanced. Results obtained in the identification procedure show that good matching can be obtained with either negative or positive leakage inductance values. These results cast some light on the possible physical meaning that circuit parameters may have. Finite-element modeling is used here to determine the transfer functions of a turbine generator. This approach is consistent with the general aim of obviating the requirement of field testing.

Influence of saturation on estimated synchronous machine parameters in standstill frequency response tests

In this paper the measurement results of a series of standstill frequency response tests, performed at different magnetization levels, are discussed. For each data set an individual model is estimated, which allows the variation of the different parameters to be seen as a function of the saturation. Further, an estimator is presented which uses the different data sets to estimate one global model, including the field to armature turns ratio. Finally the expected error level of a more traditional saturated synchronous machine model is studied.

Experience with standstill frequency response (SSFR) testing and analysis of salient pole synchronous machines

Standstill frequency response (SSFR) testing and analysis of salient pole synchronous generators and motors performed by the members of the Working Group are summarized. The papers presented in a panel session at the 1997 Winter Power Meeting are condensed into this paper for the benefit of future researchers. The pertinent features of SSFR testing and analysis of salient pole machines are described to point out the differences from those of round rotor turbogenerators extensively published in the literature.

Noniterative synchronous machine parameter identification from frequency response tests

In this paper, a method to identify synchronous machine parameters from standstill frequency response tests is presented. It is common practice to use iterative techniques first to match a set of time constants with the measured response, and then to solve a set of nonlinear equations to obtain the equivalent circuit parameters. However, there is a difficulty of specifying an initial parameter estimate before any iterations can commence. This problem is overcome by the method presented here, which is able to approximate machine parameters straightforwardly and without the need of iterating. It was found that the transfer functions produced by the calculated parameters very closely resemble the measured frequency responses. Should refinements of the solution become necessary, the obtained parameters will still serve as an excellent initial estimate for standard curve fitting procedures.

Standstill frequency-response methods and salient-pole synchronous machines

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/sub q//L/sub 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.

Characterising the d-axis machine model of a turbogenerator using finite elements

An analysis of a long established fundamental assumption is presented. The assumption that superposition is valid in frequency response derived models is shown to be wrong, because eddy current losses in the solid rotor cannot be superimposed in the machine direct-axis. This implies that network theory is not valid in characterising the d-axis machine model. A machine model structure with one damper winding in the d-axis is derived from finite element analysis. Unequal mutual inductances in the machine d-axis are determined and hence the so-called differential leakage inductances are found and they are frequency dependent. The study is made on a 150 MVA turbine generator by simulating the standstill frequency response test with finite elements.

Identification of synchronous machine parameters using a multiple input 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.

Standstill frequency response testing and modeling of salient-pole synchronous 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.

Data translation and order reduction for turbine-generator models used in network studies

This paper develops suitable procedures for translating high-order networks into conventional stability constants. The approach is computer-oriented and imposes no restriction on the number of equivalent damper windings per axis. Optimum order reduction is used to demonstrate that second-order networks have a bandwidth limited to between 1 and 5 Hz while third-order models may extend this bandwidth beyond 100 Hz. The latter are therefore mandatory for subsynchronous resonance and harmonic studies. In the course of this investigation, the need for a precise definition of the so-called stability constants arises and it is concluded that only a second-order standstill frequency response (SSFR)-based model yields constants that are consistent with the latest, short-circuit test bound, IEEE standard definitions.

Finite element analysis of the skin-effect in damper bars of a synchronous machine

The skin-effect in the damper bars of a synchronous machine is analysed by a finite element simulation using SSFR (standstill frequency response test) data. In order to consider this effect in synchronous machine modelling, sub-subtransient parameters are introduced.

Estimation of synchronous machine parameters from multisine stand-still frequency response test data

This paper is dealing with high power broadband signals (multisines) applied in Stand-Still Frequency Response (SSFR) technique for the measuring and modelling of electrical machine characteristics. The powerful excitation signals used are periodic functions with controllable amplitude spectrum. Their are obtained using a thyristor rectifier as an amplifier. Therefore, the excitation signal (multisine waveform) is superimposed on a DC current. The effects of the DC component and of the excitation signal (multisine amplitude) on estimated parameter values are discussed. The aim of the topic is to show that, even in noise corrupted environment, the multisine (msine) signals applied to SSFR test can deliver coherent synchronous machine parameters, using the frequency domain Gaussian Maximum Likelihood Estimator (MLE) method for identification.

Third order turboalternator electrical stability models with applications 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. >

Estimation of Induction Machine Parameters from Standstill Time-Domain Data

This paper presents a step-by-step approach to identifying the parameters of an induction machine from standstill time-domain test data. A step voltage disturbance is applied across the stator terminals while the machine is in the standstill condition, and the resulting stator voltage and current responses are measured. The initialization of the transfer function model parameters is achieved by the Laplace transformation of the recorded time-response data, and the maximum likelihood (ML) method is used for both the transfer function and the equivalent-circuit-model parameter estimation. Based on the identified models, simulation studies are performed and compared to the measured standstill time-domain response, the standstill frequency response (SSFR), and the free-acceleration response to validate the identified models.

A time-stepped finite-element simulation of a symmetrical short-circuit in a synchronous machine

The of this work is to propose and apply the principle of superposition for the numerical simulation of a symmetrical short-circuit in an unloaded synchronous machine. For this purpose a linear, two-dimensional, time-stepped Finite-Element Method coupled with electric circuits is used which permits one to take into account the rotor movement and the end-winding impedances. Computed values of subtransient, transient and steady-state reactances, as well as, subtransient and transient time-constraints on D-axis are compared with those obtained by the short-circuit test and the Standstill Frequency Response (SSFR) test simulation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Identification of high-order synchronous generator models from SSFR test 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Advance calculation of the characteristic quantities of synchronous machines and comparison with measured values

A method is presented for the advance calculation of the characteristic quantities of synchronous machines. The method is based on the determination of the frequency response xd(js), xq(js) from primary equivalent circuits with an approximate consideration of the solid rotor part in accordance with the machine geometry. The procedure is explained using a turbogenerator as a practical example. The characteristic values are determined for the standard model with two rotor circuits in each axis and are compared with the results of the short circuit and standstill frequency response tests.

Three-transfer-function approach for building phenomenological models of synchronous machines

The established practice of using only two transfer functions when modelling the d-axis of a synchronous machine at rest is physically questionable since it leads, from the network theory point of view, to ambiguous equivalent circuit realisations. The paper provides analytical and experimental evidence for the claim that a triple transfer function (3TF) parameterisation is the only one general enough to cope with both stator and rotor voltage perturbations, thus broadening the range of physical phenomena the model can account for. It is proposed that the third transfer function can be conveniently chosen from three closely related impedance operators, only two of which are classical. Using standstill frequency response test data from the Ontario Hydro's Lambton generator, it is shown that, for a given number of damper windings (3, 5, or 6), at least one equivalent circuit exists capable of accurately modelling the stator input inductance Ld(s) and the short-circuit stator to rotor transfer function sG(s), but failing dramatically to fit the third transfer function, i.e. the stator to field transfer inductance with field open Lafo(s). Only the 3TF approach consistently leads to equivalent circuits with definite phenomenological significance, thus enhancing the understanding of machine behaviour as affected by damper-cage design and excitation system.