Standstill Frequency Response Research Articles

Estimation of Synchronous Machine Parameters by Stand Still Frequency Responses Testing

This paper presents a general method based on the standstill frequency response (SSFR) tests cited in IEEE Std 115-A. The used methodology consists of determining the frequency response of the measured values of the direct axis and quadrature operational inductances. Subsequently, we identify the different models of transfer functions, which are functions of time constants, using curve-fitting techniques. Then considering the time constants as inputs and the parameters of the equivalent circuits of the synchronous machine as outputs. We can identify all the parameters of different topologies of the models, using the numerical Newton Raphson method. The approach used is inexpensive, accurate, and reliable.

Solid-Rotor Induction Motor Modeling Based on Circuit Model Utilizing Fractional-Order Derivatives

This paper presents the Park model of a solid-rotor induction motor. In this model, the dynamic state of the motor is described by integer and noninteger order differential equations. The skin effect in the solid rotor was represented by resistance and inductance with lumped constants, and the fractional inductance was dependent on the frequency of the eddy current induced in the rotor. The parameters of the equivalent circuit were determined by the standstill frequency response test with the stationary machine on the basis of the finite element method analysis of the electromagnetic field. A simulation of the dynamic states of the induction motor with a solid rotor was carried out based on the calculated parameters. The simulation was carried out using a program written in the Matlab environment. The simulations show that the electromagnetic moment during the motor start-up is about 2 times greater than the initial torque in the steady state. On the other hand, the maximum value of the stator current during the start-up is about 1.5 times greater than the effective value of the inrush current in the steady state. A good agreement was obtained between the results calculated from the distribution of the magnetic field by the finite element method and the results obtained on the basis of the equivalent circuit and, in the case of the electromagnetic torque, with the results obtained from the transient state during motor reversal.

Parameters Identification of Synchronous Machine Based on Particale Swarm Optimization

This paper, deals with a meta-heuristic method, the Particle Swarm Optimization (PSO), for operational parameters identification of synchronous machine. The considered method consists of minimizing quadratic criterion that represents the difference between simulated model at standstill frequency response output and those computed from the model to be identified. The obtained results by simulation show that the method based on particle swarm optimization is efficient in terms of convergence speed and gives optimal solution.

Standstill Frequency Response Test and Validation of a Large Hydrogenerator

This paper intends to contribute to the revision process of the IEEE Standard 115 by demonstrating the applicability of the standstill frequency response (SSFR) test on large salient pole hydrogenerators. The presented SSFR tests are carried out on a 55.6-MVA salient pole machine with laminated rotor, non-continuous damper windings, and a nonintegral slot number. The IEEE-115 SSFR test procedure is applied with special care to rotor positioning as well as accurate data acquisition in the low-frequency range. The maximum likelihood estimation method is utilized for machine parameter identification from the SSFR tests. Obtained parameters are compared with design values in addition to the ones obtained using traditional “sudden no-load three-phase short-circuit,” Dalton–Cameron and “open stator d-axis transient time constant” methods. The accuracy of parameters is also confirmed by comparing the measured three-phase short-circuit current waveforms with the ones obtained by simulating the SSFR-based machine models in an electromagnetic transient -type software. Unlike previous SSFR test cases on large salient pole hydrogenerators, accurate results are obtained.

A Novel Inertia Identification Method and Its Application in PI Controllers of PMSM Drives

A novel method for inertia determination of a permanent magnet synchronous machine (PMSM) drive is proposed and analyzed, which employs a sinusoidal perturbation torque with a dc offset to drive the PMSM, and the amplitudes of reference sinusoidal torque and sinusoidal speed response are used to compute the system inertia. Compared with other methods, it is robust and fast to obtain the accurate quantity of the inertia. First, the inverter measures the resistances and inductances of a PMSM through a static voltage vector and stand-still frequency response experiments. The parameters are adopted to design the current proportion and integral controller and make both dq-axes currents to perform the first-order response. Second, the results of constant torque experiment employing the current controller are applied to get the friction coefficient and no-load torque. Third, a sinusoidal torque with a dc offset is applied and the response performs a sinusoidal speed with a constant offset. All the above experimental results and other preinstalled parameters are employed to get the system inertia, and the accuracy is verified by another experiment. As compensation for a position signal from a hall sensor, a corresponding method is also proposed to compute the sinusoidal speed response amplitude, which is the key in the procedure.

Damper Currents Simulation of Large Hydro-Generator Using the Combination of FEM and Coupled Circuits Models

A high-order model is required for an accurate simulation of the synchronous alternator spatial harmonic content. However, some hydro-generators have fractional slot per pole per phase windings, and carrying transient simulations of these machines with finite-element software often leads to unacceptable computation time. This paper details a large alternator modeling method that provides an excellent compromise between accuracy and speed. It is a combination of magnetostatic finite element method and coupled circuits model. The paper details the construction of this model and explains the procedures to identify several model parameters from experimental data as the standstill frequency response and open and short circuit tests. The effectiveness of this modeling method is validated by the study of a large 109-MVA hydrogenerator having an instrumented rotor pole. We compare transient and steady-state simulation waveforms of the damper bar currents during sudden two- and three-phase short-circuit to the experimental measures.

Induction motor inter-turn fault modeling and simulation using SSFR test for diagnosis purpose

This paper presents a new idea to establish a simplified model of the short-circuit turns (SCT), in the stator winding of the squirrel-cage induction motor (IM) using standstill frequency response test (SSFR). This method may offer more precision in parameters estimation independent of variations in motor or load operating conditions since it is at standstill test. However, high-performance field-oriented control, or diagnosis purpose of the IM requires accurate knowledge of the electrical parameters. Furthermore, we propose to model the IM by a multiple cage equivalent circuit (EC) that enables us to take into account the deep bar effect with accuracy.The specific advantage of the proposed method that we can create a true SCT at several levels using fault simulator in order to estimate the EC model parameters in each case of fault severity, with a low probability of risk to the machine being tested, and a relatively modest expense.At the first time the healthy machine is identified and experimentally validated, then the models have been successfully used to study the transient and steady-state behavior of the IM with SCT fault, which a practically oriented scientific value.

Development and application of a standstill parameter identification technique for the synchronous generator

This work presents the development of an offline standstill estimation technique, where the synchronous machine is locked at an arbitrary (but known) angle and is excited over a short period of time. The proposed time domain method requires few seconds of captured data in contrast to the well-known standard Standstill Frequency Response (SSFR) technique that could take more than 6h to conduct. This is based on nonlinear least squares estimation and algebraic elimination theory. The resulting algorithm is non-iterative where the data is used to construct polynomials that are solved for a finite number of roots which determine the electrical parameter values. Experimental results are presented showing the efficacy of the technique in furnishing the parameters of a salient pole synchronous machine.

Half-Order Modeling of Saturated Synchronous Machine

Non-integer-order systems are used to model diffusion in conductive parts of electrical machines as they lead to more compact knowledge models and also to improve their precision. In this paper, a linear half-order impedance model of a ferromagnetic sheet deduced from the diffusion of magnetic field is briefly introduced. Then, from physical considerations and finite-element simulation, the nonlinear half-order impedance model of a ferromagnetic sheet is proposed, taking into account both saturation and diffusion effects. Next, it has been proved that this model can be successfully included in the equivalent circuits of a synchronous machine (SM), taking into account eddy currents in massive parts of the rotor or damper bars and of small-signal saturation. The new SM equivalent circuit is validated by stand-still frequency response tests performed on the solid salient-pole SM of 125 kVA for variable field excitation conditions. An example of the SM transfer function computation in relation to different magnetization levels indicates the usefulness of this modeling approach for robust control issues.

Standstill frequency response test analyzer by using Excel Macros for educational purposes

AbstractAccurate knowledge characteristics of a synchronous generator are very essential to have an idea of its operation conditions. In the presented paper generator standstill frequency response tests is used as an approach to derive dynamic models and equivalent circuits descriptive of machine behavior for dynamic studies by using Excel Macros. The method is described and applied to a case study. The extraction process for obtaining the parameters is demonstrated. Evaluation of the method with 20 senior under graduate students and 20 junior power system engineers is very positive in terms of their developing confidence in and understanding of this test and deriving the dynamic model. © 2010 Wiley Periodicals, Inc. Comput Appl Eng Educ 20: 474–483, 2012

Standstill Frequency Response Test on a Synchronous Machine Extended With Damper Bar Measurements

Standstill frequency response (SSFR) test data from a salient-pole synchronous machine with reconfigurable damper winding are presented. In addition to the regular measurements, the damper bar currents are measured and used to obtain the stator-to-damper transfer functions. The test is performed three times with physically different damper winding configurations. An extension to the standard SSFR test analysis scheme is suggested, where the stator-to-damper transfer functions are included. The validity of the identified models is substantiated by comparison of the simulated and measured machine response to a drive torque step disturbance. It is found that the damper winding measurements can be incorporated in the analysis scheme to isolate the effect of the damper circuits. However, for a machine of the type studied, also the standard SSFR test procedure yields models that are accurate enough for power system studies.

Numerical pulse test for synchronous machines

PurposeThe purpose of this paper is to propose the numerical pulse test for the parameter estimation of the synchronous machine models.Design/methodology/approachIn order to generate data for the parameter estimation, the numerical pulse test was utilized. This test was implemented within the two‐dimensional finite element analysis (FEA). From the test data, the parameters of the equivalent circuit model were estimated. The differential evolution algorithm was used to minimize the cost function.FindingsThe equivalent circuit model with the estimated values of the parameters matches well with the data generated by the FEA. Thus, the equivalent circuit model with the parameters estimated represents the behavior of the machine accurately.Originality/valuePreviously, the numerical pulse test for synchronous machines has not been introduced. The numerical pulse test takes the real operation point of the machine into account. In the test, phenomena like the changing permeability distribution and the eddy‐currents in the damper bars (windings) are considered unlike in the standardized standstill frequency response test.

Generation of Multisinusoidal Test Signals for the Identification of Synchronous-Machine Parameters by Using a Voltage-Source Inverter

With the standstill frequency-response (SSFR) test, accurate electrical-machine models can be identified. However, it can be a time-consuming method, particularly in case the machine has to be identified at low frequencies. To shorten the required time for identification, in this paper, the response on a broadband signal is measured, resulting in a multisine SSFR test. To generate the broadband signal, a high-power linear amplifier can be applied as a waveform generator. As this signal generator is not commonly available in the field, the application of a voltage-source inverter (VSI) is discussed. The multisine SSFR test with a VSI allows swift evaluation of the influence of frequency, saturation, and cross saturation on the q-and d-axis parameters with a signal generator that is often already available to control the machine. Extensive measurements are performed on several permanent-magnet synchronous machines and the method can be extended to synchronous machines with rotor-field winding. By applying a switching converter instead of a linear amplifier, it can be expected that the identification results are affected by the switching actions. Therefore, multisine SSFR tests with either a VSI or a high-power linear amplifier as well as conventional tests as described in the IEEE standard are performed, and the results are compared.

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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> 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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> 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.

Semi-analytical method for determining d-axis synchronous generator parameters using the DC step voltage test

The DC step voltage experiment is an alternative and non-destructive time-domain test to extract parameters from electrical machines that follows the standstill frequency response test procedure described in IEEE standard 115A. This work presents a new method for semi-analytically determining the characteristic parameters of the d-axis synchronous machine model. The test is carried out when the machine is at rest and the rotor&apos;s position is at d-axis; a DC-controlled power source is applied suddenly at two of the three terminals of the stator machine and the field circuit is short-circuited. Test measurements of d-axis stator voltage excitation and field and d-axis stator current responses were used. Both stator and field current patterns are simultaneously fitted to exponential functions which coefficients are analytically related to the d-axis characteristic parameters of the equivalent circuit. These characteristic parameters come from the conventional two transfer functions: direct-axis operational inductance Ld(s) and the armature to field transfer function sG(s). To validate the proposed methodology, test data is used in the d-axis parameter determination of a 7 kVA, 220 V, 60 Hz synchronous generator.

Genetic Algorithm-Based Induction Machine Characterization Procedure With Application to Maximum Torque Per Amp Control

There has been considerable research in developing improved induction motor models. One recently developed model simultaneously includes magnetizing path saturation, leakage saturation, and a highly flexible transfer function approach to represent the rotor circuits. This alternate QD model (AQDM) is also computationally efficient in that it is noniterative at each time step. It is considerably more accurate than the classical QD model (CQDM). However, the suggested characterization procedure is complicated and time consuming. This paper proposes a new characterization procedure for the AQDM. The proposed procedure employs a genetic algorithm (GA) as an optimization engine to identify the parameters of the AQDM by simultaneously considering per-phase fundamental frequency impedance and stand-still frequency response (SSFR) impedance. The proposed approach is validated by comparison of current ripple predictions (to validate high-frequency model behavior) and by application to maximum torque per ampere control design (to validate fundamental frequency model behavior). The proposed procedure is significantly more straightforward than the other published method of obtaining AQDM parameters.

Frequency-dependent equivalent circuit for the representation of synchronous machines

A frequency-dependent equivalent circuit is developed to encapsulate the standstill frequency response (SSFR) of synchronous machines. A new method, which uses a hybrid genetic algorithm, is proposed to identify the circuit parameters. As a result the local minima problem associated with deterministic approaches is overcome. The equivalent circuit used has only one damper branch, but its capacity to reproduce the SSFR data is very good. This leads to a very simple representation of the machine, which can be readily used to compute transient conditions. In addition, the equivalent circuit can also be used to store the results of complex finite-element models, which are not readily available to power system engineers, providing a simple representation of the frequency response of the machine.

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.

A study of the variation of synchronous machine parameters due to saturation: a numerical approach

This paper shows the variation of the fundamental parameters of synchronous machine two-axis equivalent circuits due to magnetic saturation. The different magnetic states of the machine are obtained using finite-element magnetostatic solutions. This way the permeability patterns of the saturable parts of the machine can be stored and used in a specially designed finite-element program that outputs the standstill frequency response (SSFR) of the machine. A hybrid genetic algorithm, capable of finding global extrema is then applied to obtain the parameters of two equivalent circuit structures for the d-axis. The process is repeated for each magnetic state, so that the variation of parameters can be seen. The magnetic states of the machine are validated by comparing the measured open-circuit characteristic with the one calculated from the finite-element model. In order to validate the d-axis equivalent circuit parameters identified, they have been adopted in the simulation of a synchronous machine short-circuit and the results obtained have been compared to those calculated by a transient finite-element program.

Hybrid genetic algorithm for the identification of high-order synchronous machine two-axis equivalent circuits

A hybrid genetic algorithm is used to find high-order equivalent circuits (ECs) of synchronous machines using standstill frequency response (SSFR) data. The algorithm performs satisfactorily despite the great deal of local minima surrounding the optimal solution of high-order ECs. It gives circuit parameters that simultaneously fit the three independent transfer functions given by the d-axis two-port network of the synchronous machine. It is found that as the order of the EC is increased, the optimization index used in the identification procedure is enhanced in a clear fashion. This leads to a new way for determining the right number of rotor branches required to correctly reproduce the SSFR data. The q-axis network is also analyzed with the hybrid algorithm. The so-called Canay's inductances are included in this one-port network to test if the fitting properties of the q-axis EC can be improved. The SSFR data used in this work is generated by a finite element model of a turbine generator, but actual data can also be readily handled.