- Email: [email protected]
Fuzzy recognition processing of complex fault signals from the rotating electric circuit in synchronous generators
Electrical Power and Energy Systems 49 (2013) 354–358
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Fuzzy recognition processing of complex fault signals from the rotating electric circuit in synchronous generators Nian Liu a, Ying Liu b,⇑, Chi Xie c a
School of Electrical and Information Engineering, Sichuan University, Chengdu 610065, China School of Energy Science and Engineering, University of Electronic Science and Technology, Chengdu 611731, China c Department of Test and Control Engineering, Sichuan University, Chengdu 610065, China b
a r t i c l e
i n f o
Article history: Received 12 May 2011 Received in revised form 21 January 2013 Accepted 24 January 2013 Available online 6 March 2013 Keywords: Fuzzy recognition Complex electrical signal Circuit fault Brushless excitation
a b s t r a c t The brushless excitation system is widely used in synchronous generators in modern atomic power plants, although the excitation system is a very complicated rotating electric circuit, but because it has some outstanding advantages with being spark-free, higher reliability and little maintenance. When the rotating electric circuit of the brushless excitation system is out of work, in which some of the diodes have some fault conditions, some complex electrical signals will occur in the rotating electric circuit and the signal waveform is very complicated. This paper presents a fuzzy recognition method for the complex signals from the rotating electric circuit and builds the fuzzy diagnosis model. With the help of the method, the faults of the rotating electric circuit can be recognized. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The brushless excitation system is widely used in synchronous generators in atomic power plants [1], although the excitation system is a very complicated rotating electric circuit, but because it has some outstanding advantages with being spark-free, higher reliability and little maintenance [2,3]. When the rotating electric circuit of the brushless excitation system is out of work, in which some of the diodes have some fault conditions, some complex electrical signals will occur in the rotating electric circuit and the signal waveform is very complicated. In large synchronous generators, the great field current flows through the diodes of the rectifier circuit, and the diodes must undergo some opposing voltage occurring in the rectifier circuit. Hence, the power semiconductor diodes in the rotating electric circuit will be damaged occasionally. Because the rotating electric circuit in the large generator has the high revolution speed and the limitation of installed space, it is very difficult to directly detect faults of brushless rotating rectifier circuit [4,5]. The key to these questions is how to obtain the complex electrical signals, process these signals and recognize the faults of these complicated electric circuits effectively and correctly [6–9]. We can obtain the signal from a special exploring coil, which is taken place between the stator magnetic poles in AC exciter. The electrical signals have all a certain degree of complex deformation, ⇑ Corresponding author. Tel.: +86 28 85404597. E-mail address: [email protected] (Y. Liu). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.01.008
because there exists strong electromagnetic field around the stator magnetic poles in large synchronous generators. That is to say, the signals became illegible. It is difficult to process and recognize the complex signals from the rotating electric circuit. These large synchronous generators are all very important power points, which must be guaranteed to work safely for electrical power systems. Because the brushless excitation rectifier is located on the generator rotor, the contact-type method can be not used for monitoring the rotating electric circuit, and we must adopt the contactless monitoring method [10,11]. Of course, the fault in power generation system cannot be completely avoided, and different recognition methods for electrical power systems are currently studied by obtaining various fault features. However, these methods are computationally intensive, and they are not conducive to online monitoring [12–15]. In this paper, we present a recognition method for diagnosing faults in brushless excitation system of synchronous generators. The main idea of the work is based on the comparing location of investigated system in relation of predefined normal condition in the multidimensional feature space. Feature set is derived from electrical signal generated by special coil-probe, which can be located between poles of exciter system of generator. Electrical signal from the coil is represented by Fourier series and coefficients of the expansions are scaled on 1/100. Recognition technique is based on calculation distance measure in multidimensional space between normal and investigated conditions of exciter. It is demonstrated that the developed approach may recognize at least eight types of the system faults. In a word, the signals obtained from the
N. Liu et al. / Electrical Power and Energy Systems 49 (2013) 354–358
355
open-circuit for the rotating electric circuit, and the one bridge arm shorting means the one bridge arm to become short-circuit for the rotating electric circuit. 3. Obtaining the character of complex fault signal
Fig. 1. The main electric circuit of large brushless generator unit.
exploring coil between the stator magnetic poles in AC exciter can be preprocessed by the frequency analysis, then with the help of fuzzy recognition processing, the various faults of the rotating electric circuit can be detected.
In the coil-probe installed between two magnetic poles in the AC exciter, the alternating voltage will be induced by the armature magnetic flux of the AC exciter. Hence, the real-time signal of induced voltage wave obtained from the coil-probe includes some fault information for the rotating electric circuit of the rectifier, and it is very important to obtain the characteristics from the induced voltage wave of the coil-probe installed between two magnetic poles in the AC exciter. The symbol T is the period of the inducted electric signal wave e = E(t), after the expansion work in Fourier series,
EðtÞ ¼ A0 þ
1 X ðAk sinðkxtÞ þ Bk cosðkxtÞÞ
ð1Þ
k¼1
2. Sample processing of complex electrical signal A large generator unit in modern atomic power plant mainly consists of a large synchronous generator and a AC exciter; and the armature of AC exciter is linked with the rotating electric circuit of the rectifier, by which the field current can be supplied to the large generator. Hence, the rotating electric circuit is a very important key part linking the large generator and the exciter together, as shown in Fig. 1. The method to obtain the fault signal is to take place a special exploring coil between the stator magnetic poles in AC exciter. The fault signal of rotating electric circuit in synchronous generator is gained from the exploring coil, for example, as shown in Fig. 2. Fig. 2 is the stator section picture of 6 kW AC exciter used for a 360 kW generator with brushless rotating rectifier system in the laboratory, and in the coil-probe installed between two main magnetic poles, real-time voltage signals induced by the armature magnetic flux under the operation condition of the rotating electric circuit of the rectifier can be obtained, which are shown in Fig. 3. The coil-probe must be cut by the electromagnetic field, which is generated by armature current flowing in armature winding of AC exciter. In the operation of the large generator unit, three phase currents flowing over the exciter armature winding, can change with the fault type of rotating electric circuit, and these faults of rotating electric circuit are included in one bridge arm breaking, one bridge arm shorting, two bridge arms breaking, and two bridge arms shorting in the rotating electric circuit of large generator unit. The one bridge arm breaking means the one bridge arm to become
where x = 2pf = 2p/T. At the same time, we have
Ek ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Bk A2k þ B2k uk ¼ arctg Ak
ð2Þ
and
EðtÞ ¼ A0 þ
1 X Ek sinðkxt þ uk Þ
ð3Þ
k¼1
Because the numerical integration can be applied to this formula above, we have
8 N1 X > > 1 > Eðt i Þ > A0 ¼ N1 > > > i¼1 > > > < N1 X 2 Ak ¼ N1 Eðt i Þ sinðkxti Þ > > i¼1 > > > > N1 > X > >B ¼ 2 > Eðti Þ cosðkxt i Þ : k N1
ð4Þ
i¼1
where, N is the sampling number of signals in one cycle. When the ADC0809 is adopted for A/D transaction, the A/D transaction rate is 100 ls/time. So we can decide the sampling interval h, which is
h¼
T > 100 ls N1
ð5Þ
With the help of the frequency analysis, all kinds of different harmonic waves with different amplitude value can be decomposed from the complex signals for the rotating electric circuit,
Fig. 2. The stator section picture of 6 kW AC exciter used for a 360 kW generator.
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N. Liu et al. / Electrical Power and Energy Systems 49 (2013) 354–358 Table 1 Initial data obtained by the digital analyzer for the signal from the coil-probe. Sample model vector
The value of each harmonic wave of stator signals E(t)
P1 P2 P3 P4 P5
10.27 56.82 71.80 64.36 81.86
Fundamental Second Third Fourth Fifth Sixth wave harmonic harmonic harmonic harmonic harmonic 3.206 63.91 38.91 42.76 16.23
3.613 25.44 35.41 37.71 16.86
2.082 11.52 23.99 12.56 20.98
13.50 17.61 16.19 8.41 18.39
55.12 12.01 7.54 2.76 8.24
(a) Normal condition. analyzer for the complex signal from the coil-probe is shown in Table 1. In Table 1, some fault conditions for the rectifying bridge arm of rotating electric circuit can be defined as following: P1—normal operation of bridge arm P2—breaking fault of phase B + bridge arm P3—breaking fault of phase A and B+ bridge arms P4—shorting fault of phase B+ bridge arm P5—shorting fault of phase A and B+ bridge arms
(b) Fault of one bridge arm breaking.
4. Fuzzy recognition of complex faults for the rotating electric circuit In operation of large generator unit, the faults of the rotating electric circuit are mainly included in one bridge arm breaking, one bridge arm shorting, two bridge arms breaking and two bridge arms shorting. The collection of the operating conditions for the rotating electric circuit can be expressed as universe of discourse U.
U ¼ fP1 P2 P3 P n g
(c) Fault of one bridge arm shorting.
ð6Þ
In which, n can be determined by the fault condition for rotating electric circuit, for example, if n = 5, so each element of the discourse U can be defined as in Table 1, P1—normal operation of bridge arm P2—breaking fault of phase B + bridge arm P3—breaking fault of phase A and B+ bridge arms P4—shorting fault of phase B+ bridge arm P5—shorting fault of phase A and B+ bridge arms P6—breaking fault of phase A+ and A bridge arms P7—shorting fault of phase A, B+ and C bridge arm P8—breakinging fault of phase A, B+and C bridge arms
(d) Fault of two bridge arms breaking.
When the element Pi in universe of discourse U has r characteristic values, Pi can be expressed as a vector
Pi ¼ ðxi1 ; xi2 ; xi3 ; . . . ; xir Þ 2 Rr
(e) Fault of two bridge arms shorting. Fig. 3. The real-time voltage signals obtained from the coil-probe.
such as the induced voltage wave of the coil-probe. For a 6 kW AC exciter used for a 360 kW generator with brushless rotating rectifier system in the laboratory, the initial data obtained by the digital
ð7Þ
Every vector may be called as a mode. The element of every model includes some characteristic values, which indicate the operating condition information of rotating electric circuit. When the voltage signal E(t) of the coil-probe is preprocessed by the frequency analysis, the relative value of each harmonic wave amplitude value can be gained as a fault information characteristic value. In this way, Pi (i = 1, 2, 3, 4, 5) will construct a set of fuzzy sample model group, such as the fuzzy pattern recognition sample of a 360 kW synchronous generator with brushless excitation system shown in Table 2. For a 6 kW AC exciter used for a 360 kW generator with brushless rotating rectifier system in the laboratory, the fuzzy pattern recognition sample group can be calculated and obtained from the initial data obtained by the digital analyzer for the complex fault signal shown in Table 1.
N. Liu et al. / Electrical Power and Energy Systems 49 (2013) 354–358
H3 (P3, Px) = 0.93 H4 (P4, Px) = 1.00 H5 (P5, Px) = 0.83
Table 2 Fuzzy mode identification sample collection group for complex fault signals. Sample model vector
The relative value of each harmonic wave of stator signals E(t)
P1 P2 P3 P4 P5
0.10 0.57 0.72 0.64 0.82
Fundamental Second Third Fourth Fifth Sixth wave harmonic harmonic harmonic harmonic harmonic 0.03 0.64 0.39 0.43 0.16
0.04 0.25 0.35 0.38 0.17
0.02 0.12 0.24 0.13 0.21
0.14 0.18 0.16 0.08 0.18
0.55 0.12 0.08 0.03 0.08
ð8Þ
In order to diagnose the vector Px belongs to which kind of fuzzy collection group fP 1 P 2 P3 P n g correctly, the comparison of every Hi(Px, Pi) adjoin degree in the mapping universe is very necessary. The two fuzzy collection groups with the biggest adjoin degree can be determined as a kind of fault condition for the rotating electric circuit.
Hmax ðPi ; Px Þ ¼ max fH1 ðP x ; P 1 Þ; H2 ðPx ; P2 Þ; . . . ; Hn ðPx ; Pn Þg
ð9Þ
So the vector Px of the synchronous generator can be diagnosed as the fault condition of the vector Pi. As some examples for the fuzzy pattern recognition, we have done a lot of test in the 360 kW synchronous generator with brushless excitation system in the laboratory. For the fuzzy pattern recognition sample of shown in Table 2, two examples for the fuzzy pattern recognition are given as following now. When the synchronous generator with brushless excitation system in the laboratory works in normal condition, the characteristic vector Px of the sampling voltage signals E(t) from the coil-probe is obtained,
Px ¼ ð0:06; 0:04; 0:03; 0:08; 0:43Þ So, the adjoin degree for the fuzzy pattern recognition can be calculated as following: H1 H2 H3 H4 H5
(P1, (P2, (P3, (P4, (P5,
and we have the biggest adjoin degree for the fuzzy pattern recognition,
Hmax ðP4 ; Px Þ ¼ maxf0:62; 0:88; 0:93; 1:00; 0:83g ¼ 1:00
In the practice, the fuzzy identification sample collection can be stored in the computer memory [16–18]. When user need to monitor the synchronous generator on line, the adjoin degree calculation is necessary between the characteristic vector P x ðP x 2 FðUÞÞ of the sampling voltage signals E(t) and the vector Pi of the fault sampling group. The adjoin degree is introduced, r 1X Hi ðPx ; Pi Þ ¼ 1 jPx ðxj Þ P i ðxj Þj r j¼1
357
Px) = 0.43 Px) = 0.12 Px) = 0.08 Px) = 0.08 Px) = 0.08
and we have the biggest adjoin degree for the fuzzy pattern recognition,
Hmax ðP1 ; Px Þ ¼ maxf0:43; 0:12; 0:08; 0:08; 0:08g ¼ 0:43 Therefore, we can correctly predicate that the synchronous generator with brushless excitation system in the laboratory is working in normal condition. On the other hand, when we obtain the characteristic vector Px of the sampling voltage signals E(t) from the coil-probe,
Px ¼ ð0:64; 0:43; 0:38; 0:08; 0:03Þ Then, the adjoin degree for the fuzzy pattern recognition can be calculated as following: H1 (P1, Px) = 0.62 H2 (P2, Px) = 0.88
Therefore, with the help of the fuzzy recognition processing for the complex fault signal from the rotating electric circuit and the fuzzy pattern recognition model, the fault of the rotating electric circuit can be recognized quickly and correctly. We can correctly predicate the fault condition for the rectifying bridge arm of rotating electric circuit, which is shorting fault of phase B+ bridge arm. 5. Conclusions We analyze the complex fault signals from the rotating electric circuit in synchronous generators used in nuclear power plants, and we build the new fuzzy recognition model which can process the fault signals. The problem about detecting fast and correctly various fault types of the brushless rotating rectifier system used in synchronous generators in modern atomic power plants have been solved better in this paper. As a fault recognition example for a tested 360 kW generator unit with brushless rotating rectifier system, the test recognition results verify that the fuzzy pattern recognition method has high accuracy of identification, high reliability and high testability for synchronous generators. In the paper, we recognize the essential importance of monitoring the safe operation of large brushless generators used in nuclear power plants using the fast fuzzy pattern recognition method. The main contributions of the paper compared to previous works are that a kind of coil probe is firstly designed to be placed between the magnetic poles of the AC exciter for the complex signal; using the time–frequency method, we can extract very fast the fault characteristic quantities from the complex signal; the fuzzy identification method is firstly used to recognize the rectifier circuit fault inside synchronous generators. Acknowledgments This work was supported by Dongfang Electric Machine Company in China for a 360 kW generator with brushless rotating rectifier system in the laboratory. We greatly thank also the support of Electric Machine Laboratory, School of Electrical Engineering and Information, Sichuan University, China. References [1] Orear J. Fundamental physics. New York: Jonn Wiley & Sons, Inc.; 1967. [2] Babak A, Amir RH, Gevorg GB. Reliability considerations for parallel performance of semiconductor switches in high-power switching power supplies. IEEE Trans Ind Electron 2009;56(6):2133–9. [3] Electric Machinery Company Inc., Product manual of brushless excitation system.
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[11] Karthikeyan J, Sekaran RD. Current control of brushless dc motor based on a common dc signal for space operated vehicles. Int J Electr Power Energy Syst 2011;33(10):1721–7. [12] Zhang YG, Wang ZP, Zhang JF, Ma J. Fault localization in electrical power systems: a pattern recognition approach. Int J Electr Power Energy Syst 2011;33(3):791–8. [13] Suja S, Jerome J. Pattern recognition of power signal disturbances using S transform and TT transform. Int J Electr Power Energy Syst 2010;32(1):37–53. [14] Hoseynabadi HA, Oraee H, Tavner PJ. Failure modes and effects analysis (FMEA) for wind turbines. Int J Electr Power Energy Syst 2010;32(7):743–834.
[15] Safty SE, Zonkoly AE. Applying wavelet entropy principle in fault classification. Int J Electr Power Energy Syst 2009;31(7):604–7. [16] Louise S, Kevin B. Achieving generalized object recognition through reasoning about association of function to structure. IEEE Trans Pattern Anal Mach Intell 2000;13(10):1097–104. [17] Miranda V, Saraiva JT. Fuzzy modeling of power system optimal load flow. IEEE Trans Power Syst 1992;7(1):843–9. [18] Bald JF, Pilsworth BW. Dynamic programming for fuzzy system with fuzzy environment. J Math Anal Appl 1982;85(1):21–3.
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Fuzzy recognition processing of complex fault signals from the rotating electric circuit in synchronous generators Nian Liu a, Ying Liu b,⇑, Chi Xie c a
School of Electrical and Information Engineering, Sichuan University, Chengdu 610065, China School of Energy Science and Engineering, University of Electronic Science and Technology, Chengdu 611731, China c Department of Test and Control Engineering, Sichuan University, Chengdu 610065, China b
a r t i c l e
i n f o
Article history: Received 12 May 2011 Received in revised form 21 January 2013 Accepted 24 January 2013 Available online 6 March 2013 Keywords: Fuzzy recognition Complex electrical signal Circuit fault Brushless excitation
a b s t r a c t The brushless excitation system is widely used in synchronous generators in modern atomic power plants, although the excitation system is a very complicated rotating electric circuit, but because it has some outstanding advantages with being spark-free, higher reliability and little maintenance. When the rotating electric circuit of the brushless excitation system is out of work, in which some of the diodes have some fault conditions, some complex electrical signals will occur in the rotating electric circuit and the signal waveform is very complicated. This paper presents a fuzzy recognition method for the complex signals from the rotating electric circuit and builds the fuzzy diagnosis model. With the help of the method, the faults of the rotating electric circuit can be recognized. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The brushless excitation system is widely used in synchronous generators in atomic power plants [1], although the excitation system is a very complicated rotating electric circuit, but because it has some outstanding advantages with being spark-free, higher reliability and little maintenance [2,3]. When the rotating electric circuit of the brushless excitation system is out of work, in which some of the diodes have some fault conditions, some complex electrical signals will occur in the rotating electric circuit and the signal waveform is very complicated. In large synchronous generators, the great field current flows through the diodes of the rectifier circuit, and the diodes must undergo some opposing voltage occurring in the rectifier circuit. Hence, the power semiconductor diodes in the rotating electric circuit will be damaged occasionally. Because the rotating electric circuit in the large generator has the high revolution speed and the limitation of installed space, it is very difficult to directly detect faults of brushless rotating rectifier circuit [4,5]. The key to these questions is how to obtain the complex electrical signals, process these signals and recognize the faults of these complicated electric circuits effectively and correctly [6–9]. We can obtain the signal from a special exploring coil, which is taken place between the stator magnetic poles in AC exciter. The electrical signals have all a certain degree of complex deformation, ⇑ Corresponding author. Tel.: +86 28 85404597. E-mail address: [email protected] (Y. Liu). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.01.008
because there exists strong electromagnetic field around the stator magnetic poles in large synchronous generators. That is to say, the signals became illegible. It is difficult to process and recognize the complex signals from the rotating electric circuit. These large synchronous generators are all very important power points, which must be guaranteed to work safely for electrical power systems. Because the brushless excitation rectifier is located on the generator rotor, the contact-type method can be not used for monitoring the rotating electric circuit, and we must adopt the contactless monitoring method [10,11]. Of course, the fault in power generation system cannot be completely avoided, and different recognition methods for electrical power systems are currently studied by obtaining various fault features. However, these methods are computationally intensive, and they are not conducive to online monitoring [12–15]. In this paper, we present a recognition method for diagnosing faults in brushless excitation system of synchronous generators. The main idea of the work is based on the comparing location of investigated system in relation of predefined normal condition in the multidimensional feature space. Feature set is derived from electrical signal generated by special coil-probe, which can be located between poles of exciter system of generator. Electrical signal from the coil is represented by Fourier series and coefficients of the expansions are scaled on 1/100. Recognition technique is based on calculation distance measure in multidimensional space between normal and investigated conditions of exciter. It is demonstrated that the developed approach may recognize at least eight types of the system faults. In a word, the signals obtained from the
N. Liu et al. / Electrical Power and Energy Systems 49 (2013) 354–358
355
open-circuit for the rotating electric circuit, and the one bridge arm shorting means the one bridge arm to become short-circuit for the rotating electric circuit. 3. Obtaining the character of complex fault signal
Fig. 1. The main electric circuit of large brushless generator unit.
exploring coil between the stator magnetic poles in AC exciter can be preprocessed by the frequency analysis, then with the help of fuzzy recognition processing, the various faults of the rotating electric circuit can be detected.
In the coil-probe installed between two magnetic poles in the AC exciter, the alternating voltage will be induced by the armature magnetic flux of the AC exciter. Hence, the real-time signal of induced voltage wave obtained from the coil-probe includes some fault information for the rotating electric circuit of the rectifier, and it is very important to obtain the characteristics from the induced voltage wave of the coil-probe installed between two magnetic poles in the AC exciter. The symbol T is the period of the inducted electric signal wave e = E(t), after the expansion work in Fourier series,
EðtÞ ¼ A0 þ
1 X ðAk sinðkxtÞ þ Bk cosðkxtÞÞ
ð1Þ
k¼1
2. Sample processing of complex electrical signal A large generator unit in modern atomic power plant mainly consists of a large synchronous generator and a AC exciter; and the armature of AC exciter is linked with the rotating electric circuit of the rectifier, by which the field current can be supplied to the large generator. Hence, the rotating electric circuit is a very important key part linking the large generator and the exciter together, as shown in Fig. 1. The method to obtain the fault signal is to take place a special exploring coil between the stator magnetic poles in AC exciter. The fault signal of rotating electric circuit in synchronous generator is gained from the exploring coil, for example, as shown in Fig. 2. Fig. 2 is the stator section picture of 6 kW AC exciter used for a 360 kW generator with brushless rotating rectifier system in the laboratory, and in the coil-probe installed between two main magnetic poles, real-time voltage signals induced by the armature magnetic flux under the operation condition of the rotating electric circuit of the rectifier can be obtained, which are shown in Fig. 3. The coil-probe must be cut by the electromagnetic field, which is generated by armature current flowing in armature winding of AC exciter. In the operation of the large generator unit, three phase currents flowing over the exciter armature winding, can change with the fault type of rotating electric circuit, and these faults of rotating electric circuit are included in one bridge arm breaking, one bridge arm shorting, two bridge arms breaking, and two bridge arms shorting in the rotating electric circuit of large generator unit. The one bridge arm breaking means the one bridge arm to become
where x = 2pf = 2p/T. At the same time, we have
Ek ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Bk A2k þ B2k uk ¼ arctg Ak
ð2Þ
and
EðtÞ ¼ A0 þ
1 X Ek sinðkxt þ uk Þ
ð3Þ
k¼1
Because the numerical integration can be applied to this formula above, we have
8 N1 X > > 1 > Eðt i Þ > A0 ¼ N1 > > > i¼1 > > > < N1 X 2 Ak ¼ N1 Eðt i Þ sinðkxti Þ > > i¼1 > > > > N1 > X > >B ¼ 2 > Eðti Þ cosðkxt i Þ : k N1
ð4Þ
i¼1
where, N is the sampling number of signals in one cycle. When the ADC0809 is adopted for A/D transaction, the A/D transaction rate is 100 ls/time. So we can decide the sampling interval h, which is
h¼
T > 100 ls N1
ð5Þ
With the help of the frequency analysis, all kinds of different harmonic waves with different amplitude value can be decomposed from the complex signals for the rotating electric circuit,
Fig. 2. The stator section picture of 6 kW AC exciter used for a 360 kW generator.
356
N. Liu et al. / Electrical Power and Energy Systems 49 (2013) 354–358 Table 1 Initial data obtained by the digital analyzer for the signal from the coil-probe. Sample model vector
The value of each harmonic wave of stator signals E(t)
P1 P2 P3 P4 P5
10.27 56.82 71.80 64.36 81.86
Fundamental Second Third Fourth Fifth Sixth wave harmonic harmonic harmonic harmonic harmonic 3.206 63.91 38.91 42.76 16.23
3.613 25.44 35.41 37.71 16.86
2.082 11.52 23.99 12.56 20.98
13.50 17.61 16.19 8.41 18.39
55.12 12.01 7.54 2.76 8.24
(a) Normal condition. analyzer for the complex signal from the coil-probe is shown in Table 1. In Table 1, some fault conditions for the rectifying bridge arm of rotating electric circuit can be defined as following: P1—normal operation of bridge arm P2—breaking fault of phase B + bridge arm P3—breaking fault of phase A and B+ bridge arms P4—shorting fault of phase B+ bridge arm P5—shorting fault of phase A and B+ bridge arms
(b) Fault of one bridge arm breaking.
4. Fuzzy recognition of complex faults for the rotating electric circuit In operation of large generator unit, the faults of the rotating electric circuit are mainly included in one bridge arm breaking, one bridge arm shorting, two bridge arms breaking and two bridge arms shorting. The collection of the operating conditions for the rotating electric circuit can be expressed as universe of discourse U.
U ¼ fP1 P2 P3 P n g
(c) Fault of one bridge arm shorting.
ð6Þ
In which, n can be determined by the fault condition for rotating electric circuit, for example, if n = 5, so each element of the discourse U can be defined as in Table 1, P1—normal operation of bridge arm P2—breaking fault of phase B + bridge arm P3—breaking fault of phase A and B+ bridge arms P4—shorting fault of phase B+ bridge arm P5—shorting fault of phase A and B+ bridge arms P6—breaking fault of phase A+ and A bridge arms P7—shorting fault of phase A, B+ and C bridge arm P8—breakinging fault of phase A, B+and C bridge arms
(d) Fault of two bridge arms breaking.
When the element Pi in universe of discourse U has r characteristic values, Pi can be expressed as a vector
Pi ¼ ðxi1 ; xi2 ; xi3 ; . . . ; xir Þ 2 Rr
(e) Fault of two bridge arms shorting. Fig. 3. The real-time voltage signals obtained from the coil-probe.
such as the induced voltage wave of the coil-probe. For a 6 kW AC exciter used for a 360 kW generator with brushless rotating rectifier system in the laboratory, the initial data obtained by the digital
ð7Þ
Every vector may be called as a mode. The element of every model includes some characteristic values, which indicate the operating condition information of rotating electric circuit. When the voltage signal E(t) of the coil-probe is preprocessed by the frequency analysis, the relative value of each harmonic wave amplitude value can be gained as a fault information characteristic value. In this way, Pi (i = 1, 2, 3, 4, 5) will construct a set of fuzzy sample model group, such as the fuzzy pattern recognition sample of a 360 kW synchronous generator with brushless excitation system shown in Table 2. For a 6 kW AC exciter used for a 360 kW generator with brushless rotating rectifier system in the laboratory, the fuzzy pattern recognition sample group can be calculated and obtained from the initial data obtained by the digital analyzer for the complex fault signal shown in Table 1.
N. Liu et al. / Electrical Power and Energy Systems 49 (2013) 354–358
H3 (P3, Px) = 0.93 H4 (P4, Px) = 1.00 H5 (P5, Px) = 0.83
Table 2 Fuzzy mode identification sample collection group for complex fault signals. Sample model vector
The relative value of each harmonic wave of stator signals E(t)
P1 P2 P3 P4 P5
0.10 0.57 0.72 0.64 0.82
Fundamental Second Third Fourth Fifth Sixth wave harmonic harmonic harmonic harmonic harmonic 0.03 0.64 0.39 0.43 0.16
0.04 0.25 0.35 0.38 0.17
0.02 0.12 0.24 0.13 0.21
0.14 0.18 0.16 0.08 0.18
0.55 0.12 0.08 0.03 0.08
ð8Þ
In order to diagnose the vector Px belongs to which kind of fuzzy collection group fP 1 P 2 P3 P n g correctly, the comparison of every Hi(Px, Pi) adjoin degree in the mapping universe is very necessary. The two fuzzy collection groups with the biggest adjoin degree can be determined as a kind of fault condition for the rotating electric circuit.
Hmax ðPi ; Px Þ ¼ max fH1 ðP x ; P 1 Þ; H2 ðPx ; P2 Þ; . . . ; Hn ðPx ; Pn Þg
ð9Þ
So the vector Px of the synchronous generator can be diagnosed as the fault condition of the vector Pi. As some examples for the fuzzy pattern recognition, we have done a lot of test in the 360 kW synchronous generator with brushless excitation system in the laboratory. For the fuzzy pattern recognition sample of shown in Table 2, two examples for the fuzzy pattern recognition are given as following now. When the synchronous generator with brushless excitation system in the laboratory works in normal condition, the characteristic vector Px of the sampling voltage signals E(t) from the coil-probe is obtained,
Px ¼ ð0:06; 0:04; 0:03; 0:08; 0:43Þ So, the adjoin degree for the fuzzy pattern recognition can be calculated as following: H1 H2 H3 H4 H5
(P1, (P2, (P3, (P4, (P5,
and we have the biggest adjoin degree for the fuzzy pattern recognition,
Hmax ðP4 ; Px Þ ¼ maxf0:62; 0:88; 0:93; 1:00; 0:83g ¼ 1:00
In the practice, the fuzzy identification sample collection can be stored in the computer memory [16–18]. When user need to monitor the synchronous generator on line, the adjoin degree calculation is necessary between the characteristic vector P x ðP x 2 FðUÞÞ of the sampling voltage signals E(t) and the vector Pi of the fault sampling group. The adjoin degree is introduced, r 1X Hi ðPx ; Pi Þ ¼ 1 jPx ðxj Þ P i ðxj Þj r j¼1
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Px) = 0.43 Px) = 0.12 Px) = 0.08 Px) = 0.08 Px) = 0.08
and we have the biggest adjoin degree for the fuzzy pattern recognition,
Hmax ðP1 ; Px Þ ¼ maxf0:43; 0:12; 0:08; 0:08; 0:08g ¼ 0:43 Therefore, we can correctly predicate that the synchronous generator with brushless excitation system in the laboratory is working in normal condition. On the other hand, when we obtain the characteristic vector Px of the sampling voltage signals E(t) from the coil-probe,
Px ¼ ð0:64; 0:43; 0:38; 0:08; 0:03Þ Then, the adjoin degree for the fuzzy pattern recognition can be calculated as following: H1 (P1, Px) = 0.62 H2 (P2, Px) = 0.88
Therefore, with the help of the fuzzy recognition processing for the complex fault signal from the rotating electric circuit and the fuzzy pattern recognition model, the fault of the rotating electric circuit can be recognized quickly and correctly. We can correctly predicate the fault condition for the rectifying bridge arm of rotating electric circuit, which is shorting fault of phase B+ bridge arm. 5. Conclusions We analyze the complex fault signals from the rotating electric circuit in synchronous generators used in nuclear power plants, and we build the new fuzzy recognition model which can process the fault signals. The problem about detecting fast and correctly various fault types of the brushless rotating rectifier system used in synchronous generators in modern atomic power plants have been solved better in this paper. As a fault recognition example for a tested 360 kW generator unit with brushless rotating rectifier system, the test recognition results verify that the fuzzy pattern recognition method has high accuracy of identification, high reliability and high testability for synchronous generators. In the paper, we recognize the essential importance of monitoring the safe operation of large brushless generators used in nuclear power plants using the fast fuzzy pattern recognition method. The main contributions of the paper compared to previous works are that a kind of coil probe is firstly designed to be placed between the magnetic poles of the AC exciter for the complex signal; using the time–frequency method, we can extract very fast the fault characteristic quantities from the complex signal; the fuzzy identification method is firstly used to recognize the rectifier circuit fault inside synchronous generators. Acknowledgments This work was supported by Dongfang Electric Machine Company in China for a 360 kW generator with brushless rotating rectifier system in the laboratory. We greatly thank also the support of Electric Machine Laboratory, School of Electrical Engineering and Information, Sichuan University, China. References [1] Orear J. Fundamental physics. New York: Jonn Wiley & Sons, Inc.; 1967. [2] Babak A, Amir RH, Gevorg GB. Reliability considerations for parallel performance of semiconductor switches in high-power switching power supplies. IEEE Trans Ind Electron 2009;56(6):2133–9. [3] Electric Machinery Company Inc., Product manual of brushless excitation system.
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