Measurement of Synchronous Machine Parameters by a Modified Frequency Response Method - Part I: Theory

De Mello and Hannett [1] have theoretically proposed a method for determining the operational inductances Ld(j2w), Lq(j2w) of a synchronous machine at low values of generator speeds. Eitelberg and Harley [2] extended these ideas to obtain the inductances and time constants from the Ld(j2w), Lq(j2w) curves by a numerical procedure which allows one to attach different levels of importance to either the magnitude or phase fitting of the operational inductance expressions to the computed curves. The first part of this two-part paper extends these ideas [1-2] by proposing an improved MODIFIED data-processing method which uses a Fourier analysis of the open-phase voltage and short-circuit current to compute the operational inductances Ld(j2w), Lq(j2w) and avoids integration of the d,q axes flux linkages; providing that the fundamental and the third harmonic present in the recorded waveforms are considered. The second part [3] of this paper applies the improved MODIFIED data-processing method to a 3 kVA, 220 V microalternator.     

Measurement of Synchronous Machine Parameters by a Modified Frequency Response Method - Part II: Measured Results

De Mello and Hannett [1] have proposed a theoretical method for determining the operational inductances of a synchronous machine at low values of generator speeds. Eitelberg and Harley [2] extended these ideas to obtain the inductances and time constants from the Ld(j2w), Lq(j2w) curves by a numerical curve fitting procedure. Part I [3] of this paper broadens these ideas [1-2] by proposing an improved MODIFIED data-processing method which avoids the tedious integration of the d,q axes flux linkages [1]. Part II continues by performing a line-to-line short-circuit test on a 3 kVA, 220 V microalternator at different speeds covering the range which is of interest to subsynchronous resonance (SSR) studies [4]. Measured results illustrate the practical feasibility of this proposed frequency response method [1-3]. Practical problems associated with this test are also mentioned.     

Cell resistances of poly(2,5-benzimidazole)-based high temperature polymer membrane fuel cell membrane electrode assemblies: Time dependence and influence of operating parameters

Time-dependent measurements of cell impedance of a HT-PEFC based on ABPBI were performed at constant frequencies close to the high-frequency (h.f.) intercept of the corresponding Nyquist plots with the real axis. The h.f. impedances approximate the ohmic resistance of the cell and they decrease, when current (140 mA cm⁻²) is switched on. Steady-state values are attained after 10 min. Vice versa, when current is switched off (OCV), the h.f. impedances instantaneously increase but reach steady-state values only after about 1 h. These values rise with increasing gas flow rates. The results are discussed in terms of hydration/dehydration processes, changing the equilibrium between orthophosphoric and pyrophosphoric acid and thus the conductivity of the electrolyte as well as the mobility of molecules and charge carriers. Impedance spectra were recorded after each time-dependent measurement under OCV conditions. The fit of these impedance data based on an equivalent circuit revealed ohmic resistances corrected by h.f. inductances and low frequency impedances associated with the cathode oxygen exchange reaction. The charge transfer resistances deduced from the low frequency impedances strongly depend on both air and hydrogen flow rates.     

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     

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     

Identification of synchronous machine linear parameters fromstandstill step voltage input data

This paper presents the results of a time-domain identification procedure to estimate the linear parameters of a 15 kVA salient-pole synchronous machine at standstill. A step voltage input test is performed, and the parameters of the time constant models and equivalent circuit models are estimated. The maximum likelihood algorithm is used for the estimation, and the best-fit model is selected from a set of increasing order models. The initialization values for the parameters to be estimated are determined from the operational inductances derived directly from the measured time domain data. The simulated equivalent circuit model response is validated against the measured standstill time domain and frequency domain data. In addition, simulation of the model response to an on-line small disturbance test is compared to the measured dynamic response     

Synchronous Machine Modelling by Standstill Frequency Response Tests

The synchronous machine is modelled in terms of operational impedances derived from standstill frequency response measurements. A curve-fitting procedure in the complex plane yields all the parameters including the armature resistance without having to pre-process the data or make other measurements. The validity of the model is demonstrated for a micro-alternator by comparing the sudden short-circuit current predicted by the model with that obtained experimentally. Frequency response data obtained at different current levels are used to show that a useful model can be derived from tests at low per-unit current.     

Finite element calculation of double-cage rotor equivalent circuitparameters

This paper describes the use of a saturable single slot finite element model to determine the resistances and reactances of a double-cage rotor, allowing for the MMF balancing effect of the stator currents. The method is verified by comparing the impedances calculated for an unsaturated rotor with rectangular bars with their analytically determined counterparts. The model requires the user to specify both rotor frequency and current per slot. The effect of magnetic saturation is examined, and it is demonstrated that care must be taken in the choice of current at low frequencies, to avoid conditions of excessive saturation, leading to unrealistic values for inductances     

Characterising the d-axis machine model of a turbogenerator usingfinite 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     

A systematic method for the determination of the parameters ofsynchronous machines from the results of frequency response tests

This paper deals with the analysis of the frequency responses of the d and q axis impedances of synchronous machines. Numerical curve-fitting techniques have normally been used to find the best set of time constants to fit the frequency response data, but limitations or constraints are introduced with these techniques. The process to be described here is based on characteristic features of the equivalent circuits which overcome the need to make the assumptions inherent in a numerical approach. The extraction process is demonstrated using an equivalent circuit chosen to produce a frequency response similar to that for the direct axis of a production machine. This enables the intrinsic advantages of the proposed process for extraction of the time constants to be demonstrated which then leads directly to a unique set of equivalent circuit parameters     

Maximum likelihood estimation of synchronous machine parametersfrom standstill time response data

This paper presents a systematic approach for identification of a three-phase salient-pole synchronous machine rated at 5 kVA from standstill time-domain data. Machine time constant models and the equivalent circuit models are identified and their parameters are estimated. The initialization of the estimated parameters is achieved by the Laplace transformation of the recorded standstill time-response data and the derivation of the well-known operational inductances. The estimation is performed using the Maximum Likelihood algorithm. Based on the best estimated equivalent circuit models, simulation studies using the measured on-line dynamic responses are performed to validate the identified machine models     

On the K + P Problem for a Three-Level Quantum System: Optimality Implies Resonance

We apply techniques of subriemannian geometry on Lie groups to laser-induced population transfer in a three-level quantum system. The aim is to induce transitions by two laser pulses, of arbitrary shape and frequency, minimizing the pulse energy. We prove that the Hamiltonian system given by the Pontryagin maximum principle is completely integrable, since this problem can be stated as a k p problem on a simple Lie group. Optimal trajectories and controls are exhausted. The main result is that optimal controls correspond to lasers that are in resonance.     

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 the Double Output Induction Generator Using Direct Three-phase Model Part I - Commutation Angle Analysis

This paper investigates the overlap angle of the bridge rectifier for the variable speed constant frequency double output induction generator VSCF-DOIG that has a dc-link converter in its rotor circuit. A direct three-phase model for the VSCF-DOIG during the commutation and interlude intervals is set forth. This model takes into consideration the machine resistances, mutual inductances and machine electric transients. Using this model, the overlap angle for different slip values was found.     

Transient Analysis of Partial Armature Short Circuit in an Electronically Commutated Permanent Magnet Motor System using an Integrated Nonlinear Magnetic Field-Network Model

The simulation of the dynamic performance characteristics of an electronically commutated brushless dc machine system with radially oriented permanent magnets, which is experiencing a partial short in one of its phases, is reported in this paper. The newly introduced integrated field network (IFN) method was used throughout this work. The IFN method, which is detailed in a companion paper, is based on simultaneously solving the dynamic equations of the machine system network, using machine winding parameters (inductances and emfs) which are determined from numerical solutions of the nonlinear magnetic field prevailing in the machine cores for the corresponding winding currents. These field solutions and corresponding machine parameters are updated at every time step of the solution of the dynamic equations. The results presented here document effects of the shorting of a portion of an armature phase winding on the dynamic performance of a 15 hp (11.2 kw), 120 volts samarium-cobalt permanent magnet brushless dc motor. A comparison of the current, inductance, enf, torque and power time profiles of the motor system with and without partial armature winding failure (short) is given here. These studies are of importance in motor system security and redundancy considerations. The dramatic change of the values of machine parameters upon occurrence of the partial short circuits demonstrate that conventional solution methods would have left much to be desired.     

IGSPICE simulation of induction machines with saturable inductances

A novel approach to the dynamic analysis of induction machines with saturable inductances is presented. The machine dynamics are represented by a set of nonlinear time-varying differential equations. The machine parameters (i.e. saturable inductances) are modeled by closed-form nonlinear functions. The equations which define the machine operation are modeled by d and q equivalent circuits. The equivalent circuits are simulated using the IGSPICE software package     

Short-circuit test based maximum likelihood estimation of stabilitymodel of large generators

This paper presents a time-domain statistical identification method for synchronous-machine linear parameters from the standard line-to-line short-circuit test. The measurements are recorded on a 13.75-MVA hydrogenerator at Hydro-Quebec's Rapide-des-Quinze generating station. A complete mathematical model for synchronous machine asymmetrical test analysis is proposed. An efficient algorithm is built to accurately calculate the standard equivalent circuit from time-constants and operational inductances. The maximum likelihood estimator derived from the generalized least-squares method is then used for parameter identification. Validation of the estimated model response against the measured running-time domain data confirms the effectiveness of the proposed estimation technique     

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     

Online Synchronous Machine Parameter Extraction From Small-Signal Injection Techniques

This paper proposes using a novel line-to-line voltage perturbation as a technique for online measurement of synchronous machine parameters. The perturbation is created by a chopper circuit connected between two phases of the machine. Using this method, it is possible to obtain the full set of four complex small-signal impedances of the synchronous machine $d$– $q$ model over a wide frequency range. Typically, two chopper switching frequencies are needed to obtain one data point. However, it is shown herein that, due to the symmetry of the machine equations, only one chopper switching frequency is needed to obtain the information. A 3.7-kW machine system is simulated, and then constructed for validation of the impedance measurement technique. A genetic algorithm is then used to obtain IEEE standard model parameters from the $d$ –$q$ impedances. The resulting parameters are shown to be similar to those obtained by a series of tests involving synchronous reactance measurements and a standstill frequency response.