International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com ( ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 4, April 2015)
Consulting Services, Buenos Aires - Argentina
Abstract
—
This paper presents a methodology for accurate and short-timed detection of the presence of subsynchronous oscillations in generators in series compensated systems.
This is done based on available information from:
1) The generator shaft system, such as the generator’s mechanical oscillation frequencies (which are known from calculation and / or measurement), and
2) The stator currents registered data
The proposed objective is achieved using a Butterworthlike filter with a response type that gives a flat characteristic in the frequency band of interest and very steep flanks at both edges of the band and performs the detection of sub synchronous oscillations accurately and fast.
In order to effectively complete it, accurate and short timed phenomenon detection will be necessary, so a
Butterworth-like special filter is presented as the solution for it.
An analysis within an Argentinean series compensated system is used as an application example, in which a contingency is simulated.
II.
A PPLICATION A NALYSIS
The following example was extracted from bibliography
[1]
Keywords
–
Butterworth-like Filters, Detection
Methodology, Generator Protection, Mechanical Natural
Frequencies, Stator Currents, Subsynchronous Oscillations
I.
I NTRODUCTION
In case of an eventuality in a series compensated system, subsynchronous frequencies can lead to mechanical stresses in the generator shaft systems.
The reason this happens is that the generator shaft system, is a flexible set of coupled masses and, taking the mass spring model, mechanical oscillation frequencies will take place.
It has n-1 oscillatory modes or frequencies, being “n” the number of coupled masses that make the shaft system.
That way, if an external torque is applied with an equal or a similar frequency than one of the shaft system oscillatory modes, it can be damaged.
These external torques are created due to the presence of currents with subsynchronous components upon the generator, and occur in series compensated systems under contingency events.
If these current components have a complementary frequency (in relation to the synchronous -network- frequency 50 c/s) equal o similar to the oscillatory modes of the shaft system, torques in those oscillatory modes will be generated and therefore, could damage the generator shaft system
Due to this reason, a real time stator current analysis would be of help, so as to trigger the shaft system protection.
Figure 1: Geographic diagram of the network studied
This geographic diagram shows partially an interconnected network in the southern region of
Argentina, and the Bahía Blanca thermal power plant built with 2 steam turbine generators of 310 MW each, it is located in an intermediate point where transmission lines with series compensation converge
For carrying out the studies, is used the following schematic representation. In detail are shown the steam turbine generators
Figure 2: Schematic representation of the network studied
1

International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 4, April 2015)
III.
M ODELING
For the modeling, the ATP program (Alternative
Transients Program) was used, with a detailed representation of the network shown. It is of vital importance modeling the steam turbine generators. So the same machine model described in the bibliography [1] was used, with the parameters shown in Figure 3.
A three phase fault (simulated at t = 200 ms) at the end of a transmission line, that converges to Bahía Blanca
(where the thermal power plant with the 2 steam turbine generator is located) occurs in a lapse of 80 ms. At this moment is produced the opening on both ends of that line, what leads to make an analysis of the stress of the torque affecting the generator shaft system
This presentation will describe the analysis of this scenario.
The following oscillogram, figure 4, will present the torques in the different shaft sections, described here as
TOR (i) where the shaft torque number [i], is the torque on the shaft section connecting masses [i] and [i+1].
Figure 3: Parameters of the steam turbine generator
As described before, the number of mechanical oscillation modes or frequencies is n-1, being n the number of coupled masses that make the shaft system (in this case n=5), 4 mechanical oscillation frequencies will result in this example.
According to the bibliography [1] for these machines, the following mechanical oscillation frequencies are present. (see Table I)
TABLE I
M ECHANICAL O SCILLATION F REQUENCIES [ C / S ] f m1
14.0 f m2
20.8 f m3
34.8 f m4
59.8
For this analysis, only the subsynchronous frequencies are relevant (i.e. f m1
, f m2
, and f m3
, [14.0, 20.8 and 34.8] c/s). This leads to the complementary electrical frequencies
(in relation to the synchronous -network- frequency 50 c/s), they become f e1
, f e2
, and f e3
, [36.0, 29.2, and 15.2] c/s. them could affect the generator shaft systems.
An eventuality is assumed that stresses the generator shaft systems considerably. In this analysis the following contingency is taken as an example.
2
Figure 4: Torques in the different shaft sections
2
This oscillogram shows that the torques that stresses the nd
and the 3 rd
shaft sections are greater.
By performing an analysis on those torques, a predominant frequency of 34,8 c/s is depicted, as so f m3
,
34,8 c/s. This result matches the results in the above mentioned bibliography, and its complementary electrical frequency (in relation to the synchronous –network- frequency 50 c/s) is f e3
, of 15,2 c/s.
IV.
P HENOMENON D ETECTION
As said before, in case of subsynchronous oscillation (in its oscillatory frequencies) great enough to affect the generator shaft system, a contingency detection plan (in the shortest time possible) is of vital importance, so as to protect it from irreparable damage.

International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 4, April 2015)
Accessible parameters to analyze it are the stator currents, upon which we can register the complementary frequencies (in relation to the synchronous -network- frequency 50 c/s) to the mechanical oscillation frequencies.
A filter is used that will provide an accurate and shorttimed detection of the presence of those frequencies.
In this case a first order RLC filter or its digital equivalent is of little use, due to its low selectivity and their high detection times.
That is the reason we use a band pass filter that utilizes the concept of a Butterworth filter.
Such a filter will have a response in function of the frequency with a flat characteristic in the frequency band of interest and very steep flanks at both edges of that band.
With an appropriate design of this filter, by defining the width of the band pass, and by choosing the filter order that defines the slope of the sides of the band pass, a correct and short-timed detection of the frequencies that might stress the machine can be achieved.
As described before, for this application example, the main oscillation of the shaft system is a mechanical oscillation frequency of 34.8 c/s.
So for our analysis of the stator current registry, it must detect the complementary frequency component (in relation to the synchronous -network- frequency 50 c/s). This will result in 15.2 c/s, which will indicate a mechanical stress on the shaft system.
And whose frequency response, according to the order N used for the filter, approach a perfect ideal low-pass filter as shown below, in figure 5.
Figure 5: Frequency Response of Ideal Low Pass Filter
So for the case of N = 1, 2, 3. Poles displayed below
N = 1 N = 3
S
S
1
2
= e j(3*π/4)
= e j(5*π/4)
S
S
1
2
= e
= e j(7*π/12) j(9*π/12)
N = 2 S
S
1
= e j(5*π/8)
S
S
S
2
3
4
= e j(7*π/8)
= e j(9*π/8)
= e j(11*π/8)
3
= e j(11*π/12)
S
4
= e j(13*π/12)
S
S
5
6
= e
= e j(15*π/12) j(17*π/12)
The figure 6 shows an example of the positioning of the poles in the case that N = 2 and k = 1, 2, 3, 4
V.
D EVELOPMENT OF B UTTERWORTH -L IKE F ILTER
A band pass Butterworth-like filter development is analyzed to show its performance in providing a timely detection of the presence of subsynchronous oscillations that may affect the shaft system.
To begin the process, it is initially analyzed the case of the Butterworth filter in its basic conception, for which we turn to the literature [2] and whose development is shown below.
Figure 6: Positioning of the Poles in the Case N = 2
A.
Butterworth Filter Concepts:
This filter is a low pass filter with poles arranged in a semi circumference, in the left side of s plane and has no zeros.
It has N pole pairs, located at the following positions of the plane s
S k
= e j(2k-1+2N)π/4N
k = 1, 2 …., 2N
Where N is the number of pole pairs, which are uniformly distributed on the unit circumference in the left side of s plane
This filter frequency response results in:
F(s) = 1/ [(s – s
1
)*(s – s
2
)*(s – s
3
)*(s – s
4
)]
As a methodology for developing of the filter, proceed as follows.
For each N

1, 2, 3, there are N pole pairs, and in each case we use the pairs that are symmetrical to the horizontal axis.
So, for N = 1 (with only one pole pair) its filter frequency response will be:
3

International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 4, April 2015)
F
1
(s) = 1/ [(s – s
1
)*(s – s
2
)] = 1/(s
2
+ 1.4142 s + 1)
In this case, the Butterworth function of order N = 1 results in:
As N grows, the Butterworth filter looks like the ideal low pass filter. Also included in this diagram is the frequency response of a conventional low pass filter, which has a transfer function

H(s) = 1/(s+1)
F(s) = F
1
(s)
B.
Butterworth-like Band Pass Filters
For N = 2, it is breaks down into two functions , each with a pole pair symmetrical to the horizontal axis.
F
F
1
(s) = 1/ [(s – s
1
)*(s – s
4
)] = 1/(s
2
+ 0.7654 s + 1)
2
(s) = 1/ [(s – s
2
)*(s – s
3
)] = 1/(s
2
+ 1.8478 s + 1)
Therefore, the Butterworth function of order N = 2 results in:
It is in our interest use of filters with a frequency response with a flat characteristic in the frequency band of interest and very steep flanks at both edges of that band
To accomplish it, we utilized what was previously described for low pass Butterworth filters and added the frequency transformation, as explained in the bibliography
[2]. Figure 8 shows its transcription.
F(s) = F
1
(s) * F
2
(s)
The same procedure is used for N = 3, so the
Butterworth function of order N = 3 results in:
F
F
F
1
(s) = 1/ [(s – s
1
)*(s – s
6
)] = 1/(s
2
+ 0.5176 s + 1)
2
(s) = 1/ [(s – s
2
)*(s – s
5
)] = 1/(s
2
+ 1.4142 s + 1)
3
(s) = 1/ [(s – s
3
)*(s – s
4
)] = 1/(s
2
+ 1.9319 s + 1)
And Butterworth function of order N = 3 becomes
F(s) = F
1
(s) * F
2
(s) * F
3
(s)
It is noted that in the event of N pole pairs, can decompose Butterworth function, in N functions of a pole pair each, and the result is the product of these functions.
The Butterworth function can then be diagramed in the
TACS subroutine of the ATP as these N functions, being the output of one the input of the other.
Described below , in figure 7 is the frequency response for the Butterworth filter depending on the N order it adopts.
Figure 8 Frequency Transformations
To create a band pass filter using a low pass filter as its basis, the elements S of the H(s) -the low pass filter function- must be replaced according to the formula:
S = (1/w)*[(s
2
+w
0
2
)/s)]
Here: w = (w c2
- w c1
) band width filter [rad/s] w c1
and w c2
[rad/s]

are the angular frequencies where the response is -3 dB from the maximum. w
0

central angular frequency of band pass filter [rad/s] =
 w c 1
w c 2

Figure 7: Frequency Response for the Butterworth Filter Depending on the N Order
This way a band pass filter is created H
T
(s), with a particular central angular frequency w
0
and a specific bandwidth (BW) w [rad/s] = (w c2
- w c1
)
Based on the defined Butterworth filters and proceeding in a systematic way from above, we will have.
For N = 1:
The reference low pass Butterworth filter function is:
F
1
(s) = 1 / (s
2
+ 1.4142 s + 1)
4

International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 4, April 2015)
By converting the function [1 / (s
2
+ 1.4142 s +1)], from low pass to band pass as explained before, the result is:
H
T
(s) = F
T1
(s) * F
T2
(s)* F
T3
(s)
H
T
(s)

F
T1
(s) = w
2 s
2
/ [s
4
+ 1.4142ws
3
+ (2w
0
2
+w
2
)s
2
+ 1.4142ww
0
2 s + w
0
4
]
In the particular case of the conventional low pass filter with a transfer function H(s) = 1 / (s+1), by applying the concept of the frequency transformation leads to:
By using the referenced conversion, the following function is depicted for the band pass filter: This function represents a band pass Butterworth-like filter of order 1, as described before, has a central angular frequency of : w
0
[rad/s] =
 w c 1
w c 2

H
T
(s) = (w*s)/ (s
2
+w*s+ w
0
2
)
This equation results in a transfer function of a conventional band pass filter, where w
0
= 2π*F
C
,
F
C is central angular frequency of band pass filter [c/s] and w = 2π*ΔF with ΔF = bandwidth (BW) [c/s] with a bandwidth (BW) w = (w c2
- w c1
) , where w c1
and w c2 are the angular frequencies where the response is -3 dB from the maximum
Using this method, we can then convert the Butterworth filters of higher N order, so we have the following results:
For N = 2: The low pass Butterworth reference functions for this filter are:
VI.
A PPLICATION I N S UBSYNCHRONOUS O SCILLATIONS
F
F
1
(s) = 1 / (s
2
+ 0.7654 s + 1)
2
(s) = 1 / (s
2
+ 1.8478 s + 1)
By making the conversion to band pass we get to:
F w
T1
2
(s) = s
2
/ [s
4
+ 0.7654ws
3
+ (2w
0
2
+w
2
)s
2
+ 0.7654ww
0
2 s + w
0
4
]
F w
T2
2
(s) = s
2
/ [s
4
+ 1.8478ws
3
+ (2w
0
2
+w
2
)s
2
+ 1.8478ww
0
2 s + w
0
4
]
By using these functions to get to an order 2 band pass
Butterworth-like filter results in:
H
T
(s) = F
T1
(s) * F
T2
(s)
As seen in the previous application example, it is of interest to detect the predominant mode of oscillations of the shaft, resulting in 34.8 c/s.
In order to do it in the stator current register, we need to evaluate the complementary frequency component (in relation to the synchronous -network- frequency 50 c/s),
15.2 c/s
The following chart, figure 9, shows the band pass
Butterworth-like filter frequency responses proposed to the detection of the frequency we look for (15.2 c/s).
As a test example we use a bandwidth (BW) of 12 c/s, here defined as: ΔF = (F c2
- F c1
), F c2
and F c1
, are the frequencies where the response is -3 dB from the maximum
Also included in this chart, is the frequency response of a conventional band pass filter with equal central frequency and bandwidth (BW) of a Butterworth-like filter.
For N = 3: For this case, the low pass Butterworth functions for this filter are:
F
F
F
1
(s) = 1/(s
2
+ 0.5176 s + 1)
2
(s) = 1/(s
2
+ 1.4142 s + 1)
3
(s) = 1/(s
2
+ 1.9319 s + 1)
This leads to:
F w
T1
2
(s) = s
2
/ [s
4
+ 0.5176ws
3
+ (2w
0
2
+w
2
)s
2
+ 0.5176ww
0
2 s + w
0
4
]
F w
T2
2
(s) = s
2
/ [s
4
+ 1.4142ws
3
+ (2w
0
2
+w
2
)s
2
+ 1.4142ww
0
2 s + w
0
4
]
F w
T3
2
(s) = s
2
/ [s
4
+ 1.9319ws
3
+ (2w
0
2
+w
2
)s
2
+ 1.9319ww
0
2 s + w
0
4
]
And by using them to get to the order 3 band pass
Butterworth-like filter, the result comes to:
Figure 9: Band Pass Butterworth-like Filter Frequency Responses
5

International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 4, April 2015)
From this chart we can observe that the Butterworth-like filters show a flat characteristic in the frequency band of interest and very steep flanks at both edges of that band, unlike the conventional band pass filter, therefore, should be considered as a filter with better selectivity options.
Besides, as the order N ascends in the Butterworth-like filters, its characteristics in its bandwidth (BW) gets flatter, and the flanks at both edges get steeper, which makes the filter more selective.
As expected, it is also noticeable how the curves intercept each other at both edges of the bandwidth (BW), in which are the frequencies where the response is -3 dB from the maximum.
F c1

10.3 c/s and F c2

22.3 c/s, so (F c2
- F c1
) = 12 c/s and F c
= 10 .
3 * 22 .
3 = 15.2 c/s. As previously defined.
Going to the contingency before described, in which a three phase fault (simulated at t = 200 ms) at the end of a transmission line, that converges to Bahía Blanca (where the thermal power plant with the 2 steam turbine generator is located) occurs in a lapse of 80 ms. At this moment is produced the opening on both ends of that line.
It is investigated, using the above mentioned filters, their behavior to detect the subsynchronous oscillations phenomenon, to draw to a conclusion.
Below, figure 10 shows the stator currents register in the
3 phases.
Starting at 200 ms, a strong increase resulting from a short circuit, and after the opening of the line in t = 280 ms, the presence of the subsynchronous frequencies is observed.
In figure 11, it is shown torques in the different shaft sections:
There is a sharp rise in the magnitude of these torques at t = 280 ms, consistent with the presence of subsynchronous currents
That is the reason the time t = 280 ms is taken as the base evaluation time for filter analysis.
Figure 10: Stator Currents Register in the 3 Phases.
Figure 11: Torques in the Different Shaft Sections
VII.
F ILTERS A SSESSMENT
For the filtering process, proceeds to apply filters to each phase stator current, for the analysis, we need to determine the root sum of squares of these.
6

International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 4, April 2015)
An evaluation will be done for the conventional band pass filters and band pass Butterworth-like filters of order
N = 2, in both cases with a bandwidth (BW), 6 c/s and
12 c/s.
Below, the transfer functions of the filters are described.
1] Band Pass Conventional Filter
H
T
(s) = (w*s) / (s
2
+w*s+w
0
2
) where w
0
is 2*π*F
C
, F
C is the central frequency of the bandwidth (BW) and w is
2*π*ΔF with ΔF = Bandwidth (BW)
Therefore
A] F
C
= 15.2 c/s and Bandwidth (BW) 6 c/s
H
T
(s) = (37.7*s) / (s
2
+37.7*s+ 9121)
B] F
C
= 15.2 c/s and Bandwidth (BW) 12 c/s
H
T
(s) = (75.4*s) / (s
2
+75.4*s+ 9121)
2] Band Pass Butterworth-like Filter to:
With order N = 2, as exposed before, the equation comes
F w
T1
2
(s) = s
2
/ [s
4
+ 0.7654ws
3
+ (2w
0
2
+w
2
)s
2
+ 0.7654ww
0
2 s + w
0
4
]
F w
T2
2
(s) = s
2
/ [s
4
+ 1.8478ws
3
+ (2w
0
2
+w
2
)s
2
+ 1.8478ww
0
2 s + w
0
4
]
H
T
(s) = F
T1
(s) * F
T2
(s)
And as defined: w
0
is 2*π*F
C
, F
C
is the central frequency of the bandwidth (BW) and w is 2*π*ΔF with
ΔF = Bandwidth (BW)
Therefore:
F
C
= 15.2 c/s - bandwidths (BW) 6 c/s and 12 c/s
We reach to the following coefficients for the numerator and denominator for the transfer functions.
F
T1
(s) Function bandwidth (BW) = 6 c/s
F
T2
(s) Function bandwidth (BW) = 12 c/s
A# and B# are the coefficients of the terms of S
#
in numerators and denominators respectively in the F
T1
(s) and
F
T2
(s) functions.
Figure 12 shows the input data file of function H
T
(s) to
TACS subroutine.
For the Butterworth-like filter of order N = 2, with an
F
C
= 15.2 c/s and ΔF = 6 c/s.
Besides, the product function H
T
(s) = F
T1
(s) * F
T2
(s), is generated from the output of F
T2
(s), whose input is the output of F
T1
(s)
C BAND PASS FILTER - FUNCTION 1 BUTTERWORTH N = 2
C REF. FREQ. 15.2 C/S WITH BANDWIDTH = 6.00 C/S
C
4IMA0 +IMA 1.
0.0 0.0 1421.22
83.194E6 263.19E3 19.663E3 28.85 1.0
C
4IMB0 +IMB 1.
0.0 0.0 1421.22
83.194E6 263.19E3 19.663E3 28.85 1.0
C
4IMC0 +IMC 1.
0.0 0.0 1421.22
83.194E6 263.19E3 19.663E3 28.85 1.0
C ******************************************************
C BAND PASS FILTER - FUNCTION 2 BUTTERWORTH N = 2
C REF. FREQ. 15.2 C/S WITH BANDWIDTH = 6.00 C/S
C
4IMA1 +IMA0 1.
0.0 0.0 1421.22
83.194E6 635.38E3 19.663E3 69.66 1.0
C
4IMB1 +IMB0 1.
0.0 0.0 1421.22
83.194E6 635.38E3 19.663E3 69.66 1.0
C
4IMC1 +IMC0 1.
0.0 0.0 1421.22
83.194E6 635.38E3 19.663E3 69.66 1.0
Fig. 12: Band Pass Butterworth-like Filter - Data Entry to TACS
Subroutine
VIII.
S UBSYNCHRONOUS F REQUENCIES D ETECTION
The contingency previously described is created in the system, and the stator current is registered to detect the subsynchronous frequencies that may affect the shaft system.
7

International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 4, April 2015)
Thus, the case is analyzed to use the conventional band pass filter and the Butterworth-like filter of order N = 2 for a F
C
de 15.2 c/s and a ΔF de 6 c/s and 12 c/s respectively, to compare results.
For the conventional band pass filter results are given in figure 13:
Figure 13: Oscillogram of the outputs from the conventional band pass filters of the stator currents .
Checking the conventional band pass filters output records (with ΔFs, 6 c/s and 12 c/s) applied to the stator currents, the results show elevated magnitudes prior to the subsynchronous oscillations [t = 280ms]. These magnitudes are comparable to the ones that show with the phenomenon presence in t > 280 ms. This happens because the filters do not block the synchronous -network- frequency [50 c/s] appropriately and, therefore, are not adequate for subsynchronous frequencies detection
For the band pass Butterworth-like filter of order N = 2 results are given in Figure 14:
Figure 14: Oscillogram of the outputs of the band pass Butterworth like filters (order N = 2) of the stator currents.
In the order N = 2 band pass Butterworth-like filters, it is noted that the magnitudes are relevant after the appearance of the subsynchronous components t > 280 ms
The same chart is copied below, in Figure 15, but with the curve ΔF = 6 c/s changed by a 1.35 factor, to contrast both curves and make a comparative analysis.
8
Figure 15: Similar to Figure 14, but with the curve ΔF = 6 c/s changed by a 1.35 factor

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From this chart we notice a greater selectivity in the bandwidth (BW) ΔF = 6 c/s filter than in the case of 12 c/s, what emerges from the ratios of the maximum magnitudes of both cases, with the magnitudes preceding the appearance of the subsynchronous frequencies
On the other hand, the bandwidth (BW) ΔF of 12 c/s shows a quicker response than the 6 c/s one.
The maximum in the 12 c/s is noticed in t = 400 ms. In the case of the 6 c/s, the maximum is noticed in t = 470 ms.
Referencing these values at t = 280 ms (that, according to what was expressed before, is the time in which the subsynchronous frequencies appear), the delay detection for both cases will be:
Bandwidth (BW)
ΔF = 6 c/s 
delay = 470 ms – 280 ms = 190 ms
ΔF = 12 c/s 
delay = 400 ms – 280 ms = 120 ms
In consequence, Butterworth-like filters will show a better selectivity in case the bandwidth (BW) is shortened, but this case will have a larger detection time.
This goal can be achieved based on the knowledge on mechanical oscillation frequencies, of shaft systems which are known from calculations and / or measurements together with the use of Butterworth-like filters. To that end, an analysis using the filters parameters, (order N and bandwidth -BW-) must be completed to effectively achieve a suitable design for a protection development.
REFERENCES
[1] J.A. Nizovoy - J.L. Alonso, A.C. Alvarez - L.M. Bouyssede.
SSR Studies in Argentina for the Bahía Blanca Generating Plant.
IPST 1997 - International Conference on Power Systems Transients.
Seattle, June 22 - 26, 1997
[2] Sundaram Seshu, Norman Balabanian. Linear Network Analysis
Copyright © 1959 by John Wiley & Sons, Inc.
[3] Linear Circuit Design Handbook, Chapter 8 - Analog Filters, edited by Hank Zumbahlen – 2007. Analog Devices, Inc.
[4] Alternative Transient Program (ATP) - Rule Book
[5] Hermann W. Dommel, Electro – Magnetic Transients Program
(EMTP) Theory Book - Second Edition
[6] K. Kabiri, H.W. Dommel, S. Henschel. - A Simplified System for
Subsynchronous Resonance Studies. - IPST 2001 – International
Conference on Power Systems Transients - Rio de Janeiro –
June 24 - 28, 2001
[7] Maciej Orman , Przemysław Balcerek , Michał Orkisz .
- New effective method of subsynchronous resonance detection - IPST 2011 -
International Conference on Power Systems Transients - Delft, the
Netherlands - June 14-17, 2011
IX.
C ONCLUSION
Based on what it has been shown in this paper it is concluded, that we can have an alternative for subsynchronous oscillations detection to protect generator shaft systems by using the real time stator currents records.
This detection must be performed in a timely and accurate manner to provide an effective generator shaft systems protection.
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