Experience with computer-aided graphical ... - Semantic Scholar

IEEE Transactions on Energy Conversion, Vol. 10, No. 3, September 1995

407

Experience with Computer-Aided Graphical Analysis of SuddenShort-circuit Oscillograms of Large Synchronous Machines I. XAMWA , MEMBER M. PILOTE, MEMBER Hydro-Que'bec Montrial, Que'bec, Canada

P. VZAROUGE,MEMBER Universite'Lava1 (LEEPCI) Que'bec, Que'bec, Canada

ABSTRACT - In a companion paper [l], computer programs are proposed for automating the analysis of sudden-short-circuit oscillograms in ahordance with present IEC and IEEE standards. In this paper, we will further illustrate the capabilities of computeraided graphical methods with a view to their incorporation into modern testing practices. Using synthetic short-circuit data obtained from an exact solution of the network equations of known machines, it is first shown that use of the proposed software leads to satisfactory parameters in a number of realistic situations, including those where sub-subtransient effects are present. When faced with real data, it is shown that pre-filtering, without phase distortion, is often necessary and some useful tools are suggested for carrying this out A thorough investigation of the automatic graphical method applied to three machines, differing widely in design, suggests that the new software is robust enough to be used on a regular basis, either in the field or in the design office. Using the Takeda & Adkins K-factor, derived graphically from the field current oscillogram, even a full second-order network is possible, matching the underlying phenomena, as seen from both the rotor and stator.

1. INTRODUCTION Recently, we have Seen an increasing interest in standstill testing, in both time [2] and frequency domain [3-4]. However, although this type of test is quite easy to implement with present-day technology, it is usually, of necessity, conducted with the machine operating under non-standard conditions (e.g. running with the magnetization current at levels different from those specified for the rated air-gap voltage). For this reason, the analysis of standstill test data usually yields models requiring further adjustments to correct for the overly low magnetizing currents that tend to occur during test. Bissig er al. [2] and Canay [3] relied on the AC component of the fieldcurrent during a sudden-short-circuit test to enhance the capability of the standstill-based transfer functions to predict dynamic phenomena, such as out-of-step operation subsequent to a close-up fault. Based again on short-circuit results, some quite unexpected and innovative ways of improving synchronous-machine models by including operational effects and leakage saturation have been reported in [5]. Even after the emergence of proven standstill procedures, a niche will still exist for other tests such as the shortcircuit test to help describe the normal operational behavior of the machine better. In an early comparison of models derived independently from standstill frequency response (SSFR) and shortcircuit tests on the same S W M W machine [6], it was reported that the latter was superior in predicting dynamic phenomena, which suggests that adjustment of the SSFR-based model using short-circuit data could be beneficial, at least in the case of some turbine-generators. The adjustment could also be carried out using on-line frequency responses or small signal responses recorded during transient disturbances [7].

B. MPANDA-MAB W E M.CRAPPE Faculte' Polytechnique Mons, Belgium

R. WIHFOUDZ GEC-Alsthom Electrome'canique Tracy, Que'bec, Canada

Yet, if one had to suggest the best single test to effectively complement standstill tests, this probably would be the sudden shortcircuit test, which still is the basis of the IEC and IEEE standards used for contract purposes at Hydro-Qu6bec [8,9] where it is applied for commissioning and retrofitting all facilities of 10 M W and upwards. Even in a foreseeable future, when finite-element methods have developed to such an extent that certain tests can be avoided, it seems reasonable to envisage calculations beiig performed in two different ways, using SSFR and short-circuit simulations, which complement each other. Since the beginning of the eighties, a number of powerful methods have b n devised to improve the information extracted from shortcircuit oscillograms [10,11] but they all are computationally intensive and generally require some minimal system identification skills on the part of the operator. By contrast, the graphical procedure described in the IEC and the IEEE standards require virtually no background in identification but a heavy reliance on hand calculations and graphics of a somewhat obsolete nature, considering modem data acquisition and computing possibilities. We therefore developed the appropriate software using standard personal computers and workstations, as described in [l]. In the present paper, following an assessment of the potential accuracy, we will apply the afore-mentioned tools to basic data obtained from commissioning tests on a number of large Canadian and European machines.

II. FURTHER ASSESSMENTOF THE GRAPHICAL METHOD

The companion paper [l] presents evidence that the graphical method performs satisfactorily, provided the oscillograms satisfy the simplified closed-form equation of the short-circuit and the time scale decoupling windows are chosen appropriately. We noticed that the method works quite well with a certain level of second-harmonic content in the signal but a more stringent and challenging test for validating the graphical method is the following: what performance should be expected when analyzing general oscillograms simulated exactly, without adopting the six simplifying hypotheses stated in [l]? To investigate this point, we considered three fundamentally different machines whose equivalent circuits are given in Appendix D.The first and third machine loosely mimic the second- and third-order models of the Rockport turbine-generator [4] derived from SSFR test data, while the second is a fictitious machine with random parameters. Note that all machines possess some level of subtransient saliency. Their short-circuit signal responses were computed exactly as in [IO]. Results of the graphical analysis of these oscillograms are given in Table 1. The same four windowing alternatives described in [l] have been retained for comparison. We recall that N1 denotes the duration of subtransient effects in cycles, while N2 and N3 represent the assumed starting and ending cycles of the transient effects. In the case of the first model, the graphical analysis introduces serious errors in T d , whatever the windowing scheme, while the armature time95 WM 059-6 EC A paper recommended and approved by t h e IEEE E l e c t r i c Machinery Committee of t h e constant is almost always estimated correctly. The best setup seems, IEEE Power Engineering S o c i e t y f o r p r e s e n t a t i o n a t overall, to be the one with the longest number of cycles for the t h e 1995 IEEE/PES Winter Meeting, January 29, t o transient window (N3=180), providing a r d value significantly more February 2, 1995, New York, NY. Manuscript submitted accurate than even the IEC setting. With the second model, the November 23, 1993; made a v a i l a b l e f o r p r i n t i n g graphical method provides more consistent results, especially using December 19, 1994. the IEC setting, but the subtransient time constant is very inaccurate, 0885-8969E)5/$04.00 0 1995 IEEE

408 being out by more than 12%, even with the best choice of windows. The explanation is easily found: as shown in [l], the subtransient saliency (x" -x'd)/!"d of more than 80% for this machine induces a sufficiently 8igh second-harmonic content to preclude any satisfactory estimate of T d by computer-based graphical means. Table 1: Graphical analysis of noise-free short-circuit oscillograms simulated without approximations from network models in appendix D. Initial angle=-1 1.5'. Sampling: 5 kHz. In parentheses:percent error.

back into the normal rectifier mode. This hidden behavior invalidated the whole test and the questionable data was simply discarded in the analysis required to assess the manufacturer's contract. Other cases, more difficult to explain, are illustrated in Fig. 1. After a smooth start, the phase current in (a) became heavily distorted, whereas the field current in (b) seemed very noisy at the beginning and also later in the test. In both cases, the observed behavior raises doubts about the usefulness of the basic data.

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The last model includes sub-subtransient effects, in an aim to assess how such effects, extensively documented for turbinegenerators [2-41 and even a very large hydrogenerator [14], may degrade the accuracy of the graphical method. Admittedly, with the very short but realistic value of T"hfor machine 3, sub-subtransient effects may vanish so quickly that they will not be observed on the envelope data. Yet interesting results were obtained, especially using the window set (d) and the IEC scheme. This suggests that, even for machines with an eddy current induced small time constant T"'& the graphical method will most probably provide accurate mean values of the parameters best describing subtransient, transient and armature effects. However, if the additional time constant happens to be greater than the second-order subtransient and/or transient time constants, as seems to occur in some SSFR-based models with four rotor windings [4], the graphical method is bound to fail, even if implemented on a computer, since the former would radically violate the underlying time-scale decoupling scheme.

III. DATASCREENING AND SIGNAL ENHANCEMENT Prior to use in computer analysis progmms, field data should first be visually screened for early detection of pitfalls, which could invalidate the data. At Hydro-Qutbec for instance, a recent testing practice is to monitor systematically the field voltage during a shortcircuit to ensure that the excitation remain constant as required by current short-circuit analysis methods. This has tumed out to be extremely beneficial for data screening: in one test at 100% rated voltage, it was found that nine cycles after phase shorting, the field voltage switched into inverter mode for nine more cycles and then

SBC

Fig. 1: Examples of suspect raw data. In lb, shortsifwit occurs at 2s.

Although a complete test may be invalidated for not fulfiing the hypotheses required in the subsequent software analysis, a more frequent situation is one where a high noise level corrupts the records of an otherwise satisfactory test. Unfortunately, recordings in power environments tend to be very noisy, suffering most notably from high harmonic and electromagnetic interference (c.f. [16] for examples of raw noisy data) and in such cases, signal enhancement is necessary prior to analysis. This was achieved in [7] by passing the raw signals through a Butterworth filter with a 100-Hz cut-off frequency. Phase distortion was avoided by forwadbackward filtering, with the starting and ending transients minimized by matching initial conditions. In the Hydro-Qukbec software described in [I] and used in [8], finite impulse response (FIR) filtering served a similar purpose. Unfortunately, linear filters tend to distort the waveform of signals such as oscillogram envelopes because they smooth out signal edges and since this may cause serious problems in the graphical analysis of the filtered envelopes, we took another route by experimenting with a class of nonlinear filters known as median filters, which can enhance a signal without smoothing its edges [15].

409 Median filtering is performed as follows: (1)For each output point to be generated, a window of contiguous data is selected - this could be 5 adjacent time samples in an oscillogram. (2) The data is sorted so that the order is from highest signal value to lowest value in order. (3) the central value of the sort (i.e., element number 3 in a sort of 5 values) is selected as the median of the data set. (4) The median value of the set is used as the filter output. This simple procedure is very effective for suppressing impulses in the signal when a proper number of samples is used in the sliding window. However, more specialized median Fiters can be designed to selectively preserve sharp or sinusoidal changes in the signal while suppressing spikes. The idea is to predict the signal x(n) at a given discrete time n, by taking the statistical median of several predictors of the actual signal x(n), based on its k nearest forward and backward neighbors in a sliding window. These are level or ramp predictors, which can be efficiently implemented using FIR subfiters as outlined in Appendix A. (a) RAW

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signal, while strongly reducing the spike. Equation (A3) with a running window of length N=5 was used in this case. A second example, assessing the effectiveness of median filters in enhancing envelope data strongly corrupted by impulsive noise, is shown in Fig. 3. This time, the filtering equation (A2) was used, with N=5. Clearly, the resulting median filter smoothed out the spike without any apparent deformation of the underlying envelope, which could then be used with a greater degree of confidence in the subsequent analysis.

IV. SALIENT-POLE-MACHINE CASESTUDIES To assess the effectiveness of our software in real-life analyses, we were lucky to have different sets of oscillograms recorded on two salient-pole machines differing greatly in size and purpose. The first series of oscillograms pertain to the Dorsey condenser unit #8, which was analyzed in various ways in [IO], using a multi-response estimation method. Based on different windowing strategies, the graphically oriented analysis software was successively applied at 25%, 50% and 75% of the rated voltage; the results are summarized in Table 2. For comparison, the last column includes optimally estimated parameters of the closed-form analytic model taken directly from [IO] (parameter vector OIn). It is perhaps worth noting that the open-circuit transient time constants of the graphically based models are only indicative, since, for simplicity, they were calculated from the wellknown approximate formula (T'h= XdTd / x'd) instead of the exact roots of the second-order polynomial in Appendix C. Table 2: Oscillograms recorded on a 361-MVA synchronous condenser. Sampling rate: 5 kHz. Normal: 25%; underlined: 50%; bold: 75%.

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As a first example, we considered the problem of removing the spike in Fig. 2a, while preserving the rated-frequency ripple in the field-current response. This is particularly important, since the ripple amplitude is an important factor in most schemes for improving network models [3,4] using short-circuit prediction techniques. As illustrated in Fig. 2(b), the median filter preserves the sinusoidal

Table 2 indicates that all the windowing schemes provided reasonably self-consistent estimates, although, when focusing on the IEC setting which with the ad hoc setting #2 proved the most accurate in simulations, we realized that, except for the transient reactance, the graphical method does not lead to exactly the same parameters as the maximum-likelihood method. Nevertheless, the parameters from the two methods are close enough to hope the final results from the graphical method may still be satisfactory. The illustrations in the appendix in [I] support this affirmation. The graphical goodness-of-fit criterion suggests that the overall behavior of the graphically based model for the 25% rated-voltage test is acceptable. Yet the question remains, why do continuous wave and graphical methods show, at least in this case, such high discrepancies between the characteristic quantities? This point already arose in [IO], where it was observed that only the x d values from these two sources were close. Even integrating more sophisticated windowing schemes into the graphical method does not clear up these differences entirely.

*

The computer-aided analyses in [8] were among the first performed systematically using the new Hydro-Quebec software. The results of the most successful tests are shown in Table 3. along with some new results using alternative windowing schemes. The most notable discrepancies are in the transient time constants. It was a continuous wave validation attempt as in [lo] using the initial model in [8], which directed our attention to the important problem of timescale decoupling through a proper choice of windows. For the 60% voltage test, Table 3 shows differences of over 50% between the transient time constants of the IEC scheme (T'd = 1.64s) and the HydrO-@&C tests (T'd = 1.14s) ! Table 3: Oscillograms recorded on a 182-MVA hydrogenerator. Normal: 25%. underlined: 40%; bold: 60%.

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Fig. 5: Effect of a non-simultaneous breaker closure Manic 5 test at 60% rated voltage.-Phase a; ----Phase b; -.-.-.-Phase c. -30

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Fig. 4 Assessing graphical models of the 187-MVA generator from a 60% voltage test. -Initial model [a]; --IEC Model (Table 3); x test.

The second salient-pole machine was hydrogenerator unit #58 recently retrofitted at Hydro-Qukbec's Manic 5 power plant. Although the test report covers all the major acceptance tests in StdllS, a large section is devoted to an analysis of the sudden-short-circuit oscillogram tests at 255,4096,608and 100% rated voltage, with the aim of comparing the field test characteristic quantities at rated current and rated voltage with contract requirements. For completeness, we have included in appendix E, the main characteristics of current transducers used for the short-circuit tests.

A question then springs to mind : how do these two models compare with the original data? Figure 4 helps provide an answer to this question. Initially, both models behave similarly. Then, as time elapses, the initial model damps out more quickly than the test envelope, while the IEC model follows the test data quite closely on all phases, up to two seconds and beyond. Using too short a window in the graphical method ( N 3 0 0 ) thus leads to inaccurate values of Y d in the case of machines such as the present one, with long settling times. The same plots demonstrate that the IEC model provides no improvement in fitting the initial section of the envelopes, despite its good behavior in the transient regime. However, considering the high level of second harmonics (see[ 11, Fig. l), the failure of the graphical method comes as no great surprise, whatever the windowing scheme.

411 The level of harmonics is related not only to the subtransient saliency typical of hydrogenerators, but also to a non simultaneous shorting of the three phases during the test [17]. In fact, a closer data screening revealed that while phases b and c shorted almost simultaneously, phase a was lagging by 0.1 cycle (Fig. 5). This pitfall, related to the breaker, should be a serious concem in test planning, since it leads to the violation of one essential recommendation of Std.115, which we feel necessary for the graphically based analysis to be applicable.

v. TURBINE-GENERATOR CASE STUDY This is the same 361-MVA machine previously studied by Crappe er al. [ 113. Two sets of oscillograms recorded at the same pretest voltage of 10% were available for analysis. Since a visual screening of the data showed a considerable level of noise (transient hunting, spikes, etc.), median filters were used to increase the signalto-noise ratio. Figure 6 shows a sample of the enhanced signals, while Table 4 contains the dynamic quantities obtained based again on several typical windowing schemes. With the Std.115 windows set, the graphical analysis failed to provide meaningful time constants in a few cases, such as when the polynomial fitting unexpectedly produces a positive value of the slope in the log-line representation. However, these failures were not inherent in the graphical method itself but was traced back to excess noise in the underlying oscillogram (Fig. 3). Although very noisy (c.f. Figs. 2 and 7), field data was available for this machine and we attempted to derive a complete second-order d-axis network, suitable for both armature and rotor dynamics. This problem was first tackled by Takeda and Adkins [12] who introduced the so-called K-factor, which basically characterizes the initial subtransient DC component of the field current. It can be determined through a simple process of time-scale decoupling applied to the field oscillogram data in Fig. 7. The DC component is the half-sum of the upper and,lower envelope data and can be decomposed using the twin time-scale hypothesis described in Appendix B. Once the initial currents have been determined, the K-factor is computed from Takeda and Adkins' definition. The amplitude of the fieldcurrent symmetrical component, introduced by Canay, follows from equation (B2) but may also be obtained directly by a graphical analysis of the half-difference of the envelopes in Fig. 7. Interestingly enough, besides the K-factor, a fieldcurrent analysis also yields an alternative set of parameters x h , T'd, T"d, and T,, which Can be used as a consistency check. Table 4 OsciNOgrams recorded on a 361-MVA-Tuhinegenerator. Sampling :2 kHz. Normal: 1Ph; bold: 70% (second trial). IECa

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where it is seen that the subtransient time constant is not consistent with the value from the armature oscillograms (Table 4). The question, then, is whether the second-order hypothesis holds in this case. Possibly the small time constant obtained by fitting the field current actually represents a certain level of sub-subtransient activity m o ~ observable in the field current than in the armature currents. Despite these concerns, the resulting K-factor may still be useful as an initial procedure for building a second-order network aiming at predicting both the armature and field oscillograms. la

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However, applying the procedure in Appendix B to the data in Fig. 7 led to somewhat confusing results. For instance, with the windows defiied by N1=3, N2=6 and N3=58, we obtained

Ti = 0.929; Ti = 0 . 0 0 4 7 ; A i h (0) = 0.17; A i h ( 0) = 0.18;K = 4.51

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The network topology assumed for this purpose is based on Fig. 8 and its parameters, derived using the exact procedure of Salvatore and Savin0 [13] (c.f. Appendix C), are shown in Table 5, assuming the manufacturer's unsaturated value of x d [111.

412 Also included is a typical equal-mutual circuit which reproduces (s) exactly without taking the field current response (or the Kfactor) into account. It was computed using the most recent Canay formulas [4]. Effective utilization of the K-factor information led to a damper winding time constant Tld = 0.0079 which, when introduced in the formulas of Appendix C, resulted, as is usual in turbinegenerators, in a positive differential mutual.

Xd

la

The characteristic data of the two networks in Table 5 were computed and found identical to the original set given in bold in Table 4, thus confirming the correctness of the procedure in Appendix C, as well as Canay's scheme in [4]. As a final overall check, we computed the short-circuit oscillograms predicted for a 10%-voltage test and compared their envelopes to test data. Envelopes rather than continuous waves were chosen for comparison, because, with no good q-axis network available, the two-axis simulation could hardly achieve the proper Tu value shown in Table 4, which of course is needed to properly reproduce DC and AC components of the armature and field currents, respectively. Figure 9 c o n f m s the good performance of the K-factor-based network of Table 5, especially in predicting the symmetrical component of the armature currents. Also, despite the severe inconsistencies noted following its graphical analysis, the fieldcurrent DC component is approximated reasonably well in the initial and transient regions by the K-factor-based network, although some discrepancies still remain near the subtransient peak. Interestingly enough, the standard network, without any adjustment, performed equally well as regards the armature response, but failed in predicting the initial field-current response. Table 5:Exact network from characteristic quantities with K=4.51. Italics: Canay circuit for an exact matching of xds) only (xu=.249).

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VI. CONCLUSION In analysing sudden-short-circuit oscillograms by graphical

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Fig. 9 Assessing second-order d-axis networks - 10% voltage test on a 361-MVA-Turbine. -Test;

--

K-factor adjusted ;o Unadjusted.

means, the major practical difficulty encountered was the high noise levels which corrupt digital recordings taken in power plants much more frequently than initially thought. Median filters selectively tuned to remove spikes from envelope or continuous wave data, while still preserving basic sharp or sinusoidal shapes, were shown to be effective in enhancing the signal-to-noise ratio up to acceptable values prior to analysis. The first actual application dealt with a 360-MVA synchronous condenser, where we observed that the graphically based characteristic constants were somewhat different from those derived using the maximum-likelihood method [lo]. In the second study, a detailed analysis of test data from a 187-MVA hydrogenerator illustrated the detrimental influence of the windowing scheme currently recommended in the Std.115 on the accuracy of certain parameters when the machine displays sustained transient effects with T'd values out by more than 50%. This case also highlighted the fact that neglect of the second-harmonic component, whether generated by an unaccounted subtransient saliency or a non simultaneous closure of the test breaker, can lead to unsatisfactory subtransient quantities. The final case study dealt with a 361-MVA turbine generator. Besides armature oscillograms, field data was also analyzed by graphical means and the resulting K-factor used to derive an initial second-order model, targeting both rotor and armature dynamics. Good correlation was obtained with actual measured envelopes, at least with respect to the classical network with no adjustments. We thus recommend that a K-factor adjustment scheme, as presented here, should be used whenever possible with, of cowse a proviso, regarding the questionable quality of many fieldcurrent recordings.

VII. ACKNOWLEDGMENT The authors are indebted to GEC-Alsthom ~ktrvm&anique Ltd of Tracy (Canada) for having gracefully released the Dorsey test data for further analysis and publication. The help of B. Paiement of Service Essais et Etudes Techniques (Hydro-QuBbec) and G. Desrochers of

413 Service Robotique, lnformatique et ttalonnage (IREQ) in, respectively, collecting Manic 5 test data and translating them from the proprietary Sman database into a more usable form, was greatly appreciated. Lastly, we acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada.

VIII. REFERENCE [l] I. Kamwa. H. Carle, M. Pilote, P. Viarouge, B. Mpanda Mabwe, M. Crappe, "Computer Software to Automate the Graphical Analysis of Sudden-Short-circuit Oscillograms of Large Synchronous Machines," Companion paper submitted to /E€€ Trans. on EC . [2] I. Kamwa, P. Viarouge, J. Dickinson, "Identification of Generalised Models of Synchronous Machines from time-Domain Tests," Proc. /E€C, 138(6), ~p.485-498,Nov. 1991. [3] H. Bissig, K. Reichert, T.S. Kulig, "Modelling and Identification of Synchronous Machines, a New Approach with an Extended Frequency Range," /E€€ Trans., EC-8(2), pp.263-271, June 1993. [SI I.M. Canay, "Determination of Model Parameters of Machines from the Reactance Operators xd(p), xq(p)," Ibid., pp.272-279. IS] D.W. Auckland, S.M.L. Kabir, R. Shuttleworth, "Generator Model for Power System Studies," Proc. I€€ C, 137, pp.333-390, Nov. 1990. [SI R. Diggle, J.L. Dineley, "Generator Works Testing: Sudden-ShortCircuit or Standstill Variable-Frequency-Response Method," Proc. I€€ C, 128(4), pp.177-182, July 1981. [g J.C. Wang, H.D. Chiang, C.T. Huang, Y.T. Chen, C.L. Chang, C.Y Chiou, "On-line Measurement-based Model Parameter Estimation for Synchronous Generators: Solution Algorithm and Numerical Studies," /E€€ Trans., EG8(2), June 1994. [a] B. Paiement, Centrale Manic 5 R&quipement: essais de reception sur alfemafeur groupe no 58. Hydro-Quebec Report no EMC-92052, Essais et Expertises Techniques, Montreal, Canada, 1992. [9] V.Q. Do, A.O. Barry, H. Nakra, L. Vaughan, Modhle numerique en temps r6el dun groupe turbine-alfernateur hydraulique, I REQ Technical Report No 92-303C, Varennes, Canada, December 1992. [lo] I.Kamwa, P. Viarouge, R. Mahfoudi, "Phenomenological Models of Large Synchronous Machines from Short-circuit Tests During Commissioning - A ClassicaVModern Approach," /E€€ Trans., EG9(1), pp.85-97. March 1994. [ll] M. Crappe, M. Delhaye, M. Naciri, A. Crispin, Ph. Lorent, L. Soenen. "Experimental Determination of Large Turbo-Generator Dynamic Parameters by Computer Aided Analysis," CIGRE-84, paper 38-10. [12] Y. Takeda. B. Adkins. "Determination of Synchronous-Machine Parameters Allowing for Unequal Mutual Inductances," Proc. /€€, 121(12), pp. 1501-1504, Dec. 1974. Discussion: Proc. /€E, 123(5), pp.429-432, May 1976. [13] L. Salvatore, M. Savino, "Exact Relationships Between Parameters and Test Data for Models of Synchronous Machines," €/ectric Machine & Power Systems, 8. pp.169-184, 1983. [14] V.S. Borushko, V.I. Bryzgalov, LA. Glebov,G.V. Karpov, L.G. Mamikoniants, V.M. Nadtochy, V.V.Romanov, G.N.Ter-Gazarian, "Resultats d'essais d'un alternateur hydraulique de 590 MVA & la centrale hydro-electrique Krasnoyarskaya," CIGRE-74, paper 11-04. [15] J. NeejBnri, A. VBrri. S.Fotopoulos, Y. Neuvo, "Weighted FMH Filters," Signal Processing, 31, pp.181-190, 1993. [16] P.A. Rusche, I.R. Willis, E.L. Denning, G.J. Block, Confirmation of Test Methods for Synchronous Machine Dynamic Performance Models, EPRl report EL-5736, Aug 1988. [17] S. Sriharan, S.E.M. De Oliveira, "Analysis of Synchronous Generator Sequential Short-Circuit,'' Proc. /€E, 124(6), pp.549-553, June 1977.

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IX. APPENDIXA: HYBRIDMEDIAN FILTERS The hybrid median FIR filter selects its output from three points:

r(n>= MED[xfwo(n),x(n),Xbwo(n)]

where subscripts 0 and 1 refer to ramp and level predictors respectively. Whilst both remove impulsive noise effectively, filters (A2)and (A3) attempt respectively, to preserve sharp and sinusoidal changes in the signal. The ramp detectors are predictive FIR subfilters described by the following transfer function:

H , ( z ) =CO-

1 -z-k 1-z-I

kz-& - ((1 -z-&) / ( 1 - Z - l ) + CI

1-z-

I

(A41

with co=fo and cr=f1 for the forward predictor and co=fo and c l = f l , for the backward predictor, where:

fo = ( 4 k + 2 ) / k ( k - l )

fi = - 6 / k ( k - 1 )

bo=-(2k+4)/k(k-1)

bl = 6 / k ( k - 1 )

Substituting c ~ 7 / kin the first term of (A4) yields the transfer function of the level predictor (averager).

x. APPENDIX B: THE K-FACTOR FROM FIELDCURRENT To determine the K-factor, the transient section of the DC component, i'Dc(t), between N2 and N3, is first fitted by an exponential, using standard polynomial-regression procedures:

logAib(t)=logim(t)=Ajt+B) Knowing A)and B' , estimates of the transient time-constant and the initial transient field lurrent are readily computed from equation (9c) in [l]. Hence, with current and reactancesexpressed in the standard x d p e r unit system, we obtain:

T i = - l / A j ;AijDc(0) = exp(Bj) ; x i = i f # d / c A i b c ( o ) + if01 Once the transient model is known its effect can be eliminated from the original data, leading to the subtransient DCcomponent:

Ai&(')

= i p c ( t ) -Ai&-(t)

= im(t) -exp(Ajt

+ fly)

which may also be modeled as a single exponential:

log Aih-t) = Azct + B& From the line-parametersA " and B'), the initial subtransient field): current is given by ( c.f. eq. 9c in

b]

with the same definition of the K-factor as in [12]. This special characteristic quantity can be related, either approximately [1,12] or exactly [13], to the winding timeconstant T l d Besides, it is also related to the amplitude of the alternative component, which has been used for a while by Canay (41 to enhance the capability of networks derived solely from xds), to predict field winding dynamics. From (9c) in [l], the of the field current symmetrical component is given by: amplitude

9-

Such an expression is only approximate, being based on the Finally, can be second-order closed-form solution derived in [l]. estimated in another way, along with T,, by applying the same procedure, given in [l] for the graphical analysis of the armature current DC component, to the half difference of the fieldcurrent envelopes, since the two signals have the same basic form.

9-

XI. APPENDIX C EXACT SECONDORDER NETWORK ('41)

where x(n) is the input signal, and x d n ) and xbwo(n) are respectively the outputs of the forward and backard averager. The MEDO operator yields the central value of its sorted arguments, as explained in section 111. With a running window of length N=2k+7, the forward and backward averagers respectively use the k data points before and after the center value x(n). With N=3 (or k=l), definition (Al) is also known as the standard median filter. More effective median filters, with more than two substructures, were introducedin [15]:

We assume the short-circuit analysis has provided the characteristic quantities (T'd,Td,xd,x"d,K)where K is the Takeda and Adkins Kfactor [12,13]. Also, the synchronous (Xd) and magnetizing ( x d ) reactances are assumed known. The initial step of the translation process consists in converting, without any approximations, the raw empirical parameter set into an alternate one ( T ' d , T d , T ' ~ , T ~ , T l d } , where Tld is the amortisseur winding timeconstant. The open circuit timeconstants needed are computed from a second-order equation:

414 HYDRO-QUEBEC :Non inductive shunts of 2 5 m 0.02%. Calibration performed by the National Research Council of Canada. Time response to a step voltage : c 4 p . POWER TESTS: 2s at 2OOkAcrest and 30s at 20kAcrest. Maximum variation in shunt resistanceafter tests: 0.055%. Maximum variation in time response after tests: < lps.

IlNNoCENT KAMWA

XIV. BIOGRAPHIES (S'83.M'88) has been with the HydroQuebec Re-

search institute, IREQ, since 1988. He is an associate professor of Electrical Engineering at Lava1 University in Quebec, Canada. His current interests involve the areas of system identification, synchronous-machine advancement, and control and real-time monitoring of electric power systems. Kamwa received his B.Eng. and Ph.D. Degrees in Electrical Engineering from Laval University in 1984 and 1988 respectively. He is a member of the IEEE Power Engineering and Control System societies. Kamwa is also a registered engineer in the Province of Quebec and was elected a member of the New York Academy of Sciences in 1992. MARCEL PlLOTE (M'65) received his B.Sc.Appl. and electrical engineering degrees in 1965 from h o l e Polytechnique de Montreal, Canada. Now working for Hydro-Qu&ec, his current interests are in field acceptance tests of new and upgraded synchronous machines and evaluation of solutions related to upgrading problems. He is a member of the IEEE Power Engineering Society and Synchronous Machinery Subcommittee. He is a registered professional engineer in the Province of Quebec. PHILIPPE VIAROUGE was born in Perigeux, France, in 1954. He received his Engineering and Doctor of Engineering degrees from the lnstitut National Polytechnique, Toulouse, France, in 1976 and 1979, respectively. Since 1979, he has been a professor with the Department of Electrical Engineering, Laval University, QuBbec. Canada, where he is conducting research in the Laboratoire d'Electrotechnique, d'Electronique de Puissance et de Commande lndustrielle (LEEPCI). His current interests include power electronics, AC drives, and the design and identificationof electrical machines.

XII. APPENDIX D: TURBINE-GENERATOR STUDY MODELS Normal :Rockport 2.1: 1talic:Fictitious :Bold: Rock~ort3.3 (see Fiu.6)

B. MPANDA-MABWE graduated as civil mining engineer in 1979 from the Facult6 Pdytechnique de Lubumbashi (Zaire). In 1983, he joined the Facult6 Polytechnique de Mons (Belgium) where he received his MSc. in 1985 and Ph.D. degrees in 1990. He is presently an R&D engineer at the same institution where his research interests are nonlinear powersystem phenomena and system identificationtechniques. MICHEL CRAPPEreceived his degrees in Civil Mining and Civil Electrotechnical Engineering in 1959 and 1962 respectively, from the Faculte Pdytechnique de Mons (Belgium), where he is now full professor in charge of the Electrotechnical Chair. Author and co-author of numerous scientific papers, his research areas include electrical machine development, variable-speed drives, and system identification concepts. Since 1982, he has also taught Electrical Machines in Ecole nationale supckieure dingenieurs de Valenciennes, France. He has been Chairman of the Scientific Committee of the Royal Belgian Electrical Engineering Society since 1985 and is currently a member of IMACS TC1 International Scientifc Committee. Prof. Crappe has been on the editorial board of the European Transactions on Elecrical Power €ngimering(ETEP) since its launching in 1991

X I k APPENDIXE: INFORMATIONON CURRENT TRANSDUCERS USED Current transducers used by Gec-Alsthom and Hydro-QuBbec are high-performance devices which do not saturate under DC excitation. They have been tested individually at the HydroQuebec High-Power Laboratory (IREQ). Their performance is summarized below. GECALSTHOM (Dorsey Condenser): Hall-effectbased transducers. Maximum of 1% error on r.m.s. value in the range 25 1Maximum of 5% error on crest value in the range 37 265 kA. Maximum phase-shift of 8O.

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REFAATMAHFOUM was bom in Carthage, Tunisia, on November 29, 1962. He received a Bachelor's degree in Electrical Engineering and a M.Sc.A. in Power Electronics from the University of Quebec in TroisRivieres (Canada), and a Ph.D. from Laval University (Quebec), respectively in 1985. 1987 and 1992. In 1989, he joined GEC-Alsthom h3rom6canique (Tracy, Quebec) as design engineer of hydraulic generators and has been involved in the development of technical tools for optimizing machine design. He is a registered Professional Engineer in the Province of Quebec. His fields of interest include research and design of electric machines, power electronics and DC drives.