ASPECTS OF IDENTIFICATION OF EQUIVALENT CIRCUIT PARAMETERS OF LARGE SYNCHRONOUS GENERATORS BY SSFR-TESTS

     Michael Freese, Meinolf Klocke
     University of Dortmund, Institute of Electrical Drives and Mechatronics, Prof. Dr.-Ing. Dr.-Ing. Stefan Kulig Emil-Figge-Str. 70, 44227 Dortmund, Germany, e-mail: michael.freese@uni-dortmund.de

     Abstract. A Standstill Frequency Response Test (SSFR) at a synchronous machine is an alternative method for determining its dynamic performance. Therefor three measurements at a stopped machine have to be done. Four voltage, current and frequency depending values represent the frequency response function of the machine. This function is reproduced over the equivalent circuits by Park. A calculation program creates sets of parameters, the quality of which is tested. The preliminary best sets are determined and new set generations are build up by them over an evolutionary algorithm. This paper shows an exemplary application of the SSFR method and its advantages but also some problematic aspects.

     I. INTRODUCTION A preferably exact prediction of the dynamic performance of a synchronous machine is the basis of a safe grid operation. Therefor characteristic machine values have to be determined. The examination of a three-pole sudden short circuit is a standard method for determining the equivalent circuit parameters by Park (see figures 1 and 2). Whereas this method is preferably applied in the test bay by the manufacturer, such experiments can hardly be conducted with generators already installed in power plants. In this case the aforementioned characteristic parameters should also be identifiable by other testing methods like the standstill frequency response test according to [1] as described below. The required measurements of this method can be done relatively easy at a stopped machine and do not produce risk to the machine because the currents are not as high as those caused by a sudden short circuit. The results of the measurements have to be formatted and transformed. The resulting data build up the frequency response function of the machine and the target function for a calculation program as well. This calculation program with its evolutionary algorithm for determining the best parameter set will be explained below, too.

     II. STANDSTILL FREQUENCY RESPONSE TEST A standstill frequency response test is done at a stopped machine as the name reveals. This is one of the significant advantages in comparison to the method of a sudden short circuit. Just two rotor positions - mostly set by hydraulic help -are needed to do three measurements and to get four significant values. A low-frequency, dual-channel spectrum analyzer is used to measure the magnitudes and phase-angles of two signals in the frequency range 0.001 Hz to 1 kHz. Furthermore an oscillator and a power amplifier are required. The three measurements to be done are explained in the following. A. Measurement 1 With the first rotor position the main flux should go at right angle to the q-axis. That means a minimum value of voltage ought to be measured at the open rotor winding when injecting a sinusoidal current into the stator circuit.

     This measurement provides the first of the four frequency response significant values, which is the quadrature-axis operational impedance Zq calculated as:

     B. Measurement 2 The direction of the main flux can be aligned to the d-axis just by changing the electrical connections as shown in figure 4. The result is a maximum value of voltage induced in the rotor winding.

     The quotient of the stator current and the rotor voltage multiplied by 1 / v 2 and the transmission ratio uf (between stator and rotor values) results in the armature-to-field transfer impedance Zdf:

     These values enable the calculation of the direct-axis operational impedance Zd and the current transfer function Tfd, where the transmission ratio has to be considered again:

     III. IDENTIFICATION OF THE EQUIVALENT CIRCUIT PARAMETERS A. Considerations, assumptions and reference values In order to determine a set of equivalent circuit parameters, that reflect the measured frequency response function and by that the performance of the machine under investigation, some considerations and assumptions have to be done as well as reference values have to be consulted. As one example here, the stator dc resistance Ra can be appraised: Therefor the curve of the direct-axis opertional impedance Zd (see figure 6) of one exclusive machine has to be extrapolated to zero point, because at a frequency of 0 Hz Zd complies with Ra.

     Here a stator dc resistance of about 3.6 m? can be appraised. The data sheet of the machine declares a value of 3.6799 m?, so this valuation seems to be respectable. Furthermore existing parameter lists of several classes and sizes of machines show similar values at machines of similar power. This knowledge is an important basis for a reasonable result of the evolutionary algorithm described below. B. Evolutionary algorithm While the frequency response functions can be calculated over the equivalent circuit parameters, the calculation in the other direction is not possible. With the aid of a solution strategy and a calculation program, that realizes this strategy, it is possible to converge to a set of parameters that reflects the frequency response function best. The quantity of the potential parameter sets with the multiplicity of different parameters has to be limited. Therefore the considerations, suppositions and consulted reference values mentioned above help to reach a manageable mass of parameter sets. In the calculation program sixty starting compositions chosen by random but regarding user defined boundaries of parameter values are created. These compositions are mutated with random numbers. The new variations are tested by building up the frequency response of the respective parameters and comparing to the frequency response that is given by the measurements done at the machine. The appearing deviations at the performance of the magnitudes and phases of the four values Zd, Zdf, Tfd and Zq are weighted by a function that uprates differences at frequencies near zero and about 50 Hz. The square sum of all deviations is calculated and the composition of parameters with the lowest sum is set to the best. Its parameters and its frequency response are displayed along with that of the measured values for comparison. As long as a certain accuracy is not achieved the mutation will be repeated, each time with the 8 best compositions of parameters determined before that can be seen as parents producing further children. Only the best will accomplish and be the basis for a new generation. Worse compositions are not considered and will be deleted. By this evolutionary algorithm the compositions of parameters are getting better with each cycle. In the end of the evolutionary cycles the putative best equivalent circuit parameters are found. These parameters are unsaturated values, because the measurements at the machines are not conducted at rated values. III. RESULTS OF AN EXAMPLARY MACHINE INVESTIGATION Determining the equivalent circuit parameters of a synchronous machine accords with finding one composition of parameters that builds up a frequency response fitting to that of the machine best. The identified parameters do not have to correspond to those determined by other procedures as long as the electrical behaviour of the machine is reproduced equally. In the following the parameters that are determined by the SSFR-procedure for one exclusive machine are listed below in Table I. Also the frequency responses of the four basic values Zd, Zdf, Tfd and Zq are diagrammed in Figure 7 .

     In Figure 7 the dashed (red) curves show the frequency response determined on the results of the measurements at the machine while the solid (blue) lines represent the frequency response of the parameters identified by the SSFR procedure. The diagrammed curves show the typical frequency responses of a synchronous machine with a smooth-core rotor that can be reproduced by the evolutionary algorithm approximately.

     V. ASPECTS AND QUALITY OF THE SSFR TEST AND OF THE IMPLEMENTATION OF THE PARAMETER IDENTIFICATION A. Evaluation of the SSFR test The two significant advantages of the SSFR test in comparison to the sudden short circuit method are the absence of risk to the machine because of low measurands and the resting rotor that makes the measurements easier. However measurements done at a machine at standstill cannot consider any rotational effects. Non linear effects are not included in the investigation, too. The fundamental wave determined by a fourier analysis is solely considered while all harmonics are filtered. Furthermore the equivalent circuit by Park is defined for 50 Hz - the measurements run from 0.01 Hz to 1000 Hz, so a wide range of frequencies is referred to the model by Park that will certainly cause failings at the parameter determination. As prescribed in [1] the frequency range should contain the small frequencies to 0.001 Hz. Although the measuring setup is able to implement such low frequencies, the particular measurements would take more time and cause high temperatures thus exposing the windings to a considerable risk. Besides the constant temperature demanded through all measurements cannot be complied. So a minimum frequency of 0.01 Hz is chosen, lower frequencies are not considered. B. Evaluation of the parameter identification The functionality of the calculation program with its evolutionary algorithm has been confirmed at an exclusive machine. The frequency response functions calculated from the equivalent circuit parameters of the data sheet could be rebuild by the evolutionary algorithm almost congruently. The resulting values for each determined parameter fit to those of the given parameters. If the frequency response functions are not determined by the parameters of the data sheet but by the frequency response functions of the SSFR test, the deviations in the resulting parameters are distinctive, so not the calculation program but the measuring method causes the problems to represent the performance of the machine by the determined parameters Actual measurements carried out at a machine in service suffer from usual deviations and in particular from incompleteness concerning the extremely low frequency range. Thus, from the theoretical point of view the SSFR test as described in [1] and [2] is an easily understandable and comprehensive procedure for determining the equivalent circuit parameters of a synchronous generator. However, the transfer to practice is quite difficult. Technically uncompliant data are computed from actual measurements unless the search space for the circuit parameters is restricted in many ways based on the practical experience of a machine designer. Only such restrictions lead to reasonable parameter estimations. VI. CONCLUSION The equivalent circuit parameters by Park are required for specifying the characteristics of the machine in order to analyze the transient behaviour in the system of grid and turbogenerator. Here the measured frequency response functions are used to determine the d- and q-axis parameters according to the model by Park. For the optimization of the parameters an evolutionary algorithm that is currently seen as the most effective method is used. The research shows that the method can be applied successfully only if realistic starting values are chosen and the search space is constrained in a reasonable manner. For two pole turbo generators these values and wise restrictions can be set up because of a multiplicity of reference machine data. For generators with a higher number of pole pairs not enough reference data can be reverted to, so that the determination of parameters of those machines implicates more difficulties. An approach to enhance the results of the SSFR test method could be the consideration of the non linearities in the system.

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