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Dynamic and Static Eccentricity Fault Diagnosis in Salient-pole Synchronous Generator using Time Stepping Finite Elements Method Hossien Ehya and Jawad Faiz Center of Excellence on Applied Electromagnetic Systems, School of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, Iran. In this paper, a novel approach is presented to detect dynamic and static eccentricity in a salient pole synchronous generator (SPSG). An efficient index is introduced based on developed force using time series data mining (TDSM) method. This index can be utilized to predict fault and its degree. Force signal in an SPSG with different eccentricity faults are computed, and impact of eccentricity fault degree on the proposed index is inspected. Three-dimensional finite element method is employed to simulate the faulty SPSG having different eccentricity fault degrees Index Terms— Synchronous generator, static eccentricity fault, dynamic eccentricity fault, index.
I. INTRODUCTION
E
CCENTRICITY and short-circuit faults are taken into account as common faults in synchronous generator. These faults can cause irreparable damages to the generator. Therefore, diagnosing the fault and its type at initial stages of its occurrence is essential in order to prevent its extension. Short circuit fault occurs mainly due to insulation failure of windings and it begins when the winding temperature rises beyond its permissible range. In the last decade different techniques based on various signals have been proposed in electrical machines. Some of these techniques are based on the time signals; however, salient pole synchronous generator (SPSG) has non-uniform air gap and these signals cannot be useful for fault detection. A method based on magneto-motive force (mmf) generation along the slot has been used in [1] to diagnose the short circuit fault. In this case, the generated mmf along slot is lower than that of the healthy (H) generator and index is based on the comparison of these two mmf. A flux probe in the slot opening measures the mmfs. It is noted that fault has very low impact on the time signals [1, 2]. Although short circuit fault is very import in SPSG, more than 50% of the faults are caused by eccentricity [3]. So, the main purpose of this paper is investigating eccentricity fault. One of major impacts of eccentricity fault is generating unbalanced magnetic pull (UMP) in SPSG. Harmonic components of stator and rotor inductances caused by dynamic eccentricity (DE) fault in an SPSG have been paid attention in [4] in which saliency of rotor poles and its saturation have been taken into consideration using winding function method. Maxwell stress tensor can be used in FEM in order to estimate the UMP in an SPSG [5], and determined the impact of the static eccentricity (SE) fault degree and excitation upon the UMP value. Also the UMP in synchronous generator has been estimated considering the effect of dampers and parallel windings [6-8]. Eccentricity fault causes the increase and decrease of the air gap in Manuscript received March 5, 2014. Corresponding author: Jawad Faiz (e-mail:
[email protected]). Color versions of of the figures in this paper are available online at: http://ieeexplore.ieee.org. Digital Object identifier…..
different parts. By increasing the air gap length the inductance decreases and flux passes through the lower reluctance path. All windings are connected to each others, so a large current passes through the windings observing a larger air gap and this reduces the electromagnetic force. Damping factor and its impacts on the force reduction caused by eccentricity fault has been considered taking into account balancing current. This balancing current changes the force direction at the minimum air gap. Although many papers have been so far published to scrutinize the eccentricity fault in synchronous generators; appropriate indices based on force signal have not been introduced for fault diagnosis in an SPSG. This paper introduces a proper index to detect eccentricity fault, recognize its type and determine its degree. Also the impact of the load on this index is proposed. 2. SIGNAL PROCESSING Geometrical, physical and magnetic characteristics of the synchronous generator are the origins of magnetic field harmonics in synchronous generator. Eccentricity fault leads to asymmetry of the air gap magnetic field; on the other hand, rotor and stator fundamental components and harmonics caused by fault influences the air gap magnetic field. The air gap magnetic field is as follows: Bnormal
B
n
1,3,5,...
Sin nt
n 2,4,6,...
Bn Sin nt
(1)
where the even harmonics related to the mmf ripples and odd harmonics to the fundamental harmonics of the magnetic flux density. The air gap magnetic field can be used to analyze the generator performance and monitor its conditions. Magnetic field harmonics also lead to the harmonics on other quantities such as induced voltage, force, load current, air gap torque. However, considerable variations cannot be visualized in the time signals except force signal. Interaction between the magnetic field harmonics and harmonics caused by eccentricity fault generates UMP. To estimate this force, the square of the air gap magnetic field in
2
(a) Fig. 1. 3D FE model of synchronous generator
circumference direction is evaluated as follows (Fig. 1):
UMP
2
0
B( , t ) 2 .Cos( ).L d 2 0
(2)
According to (2), magnetic field consists of a number of harmonics. UMP causes a destructive effect leading to stress on the generator. This stress exerts more shock on the bearing which affects the generator performance and shortens its life span. One method for reducing this force is the use of parallel windings and dampers. On contrary to the slight change of time signals of voltage, current and torque in an SPSG, the time signal of the force changes significantly as such that SE fault varies the appearance of the time signal (Fig. 2b). In addition, SE fault displaces the mean value of the force time signal in an SPSG. Mean value of the force in no-load healthy generator is 0.087 N (Fig. 2a) which rises to 0.505 N in the case of SE fault (Fig. 2b). DE fault also increases this force to 7.8 N (Fig. 2c). As seen the mean force in the case of DE fault is very larger than that of the SE fault. It means that the SE fault generates uniform stable pull, while DE has no such effect, and high frequency harmonic components is more excited in the DE fault. Force in full-load healthy motor is 1.8 N along horizontal axis. SE fault at full-load increases the force to 2.5 N while this force is 47.6 N in DE fault (Fig. 3). The reason for increasing this force, even in healthy case, is the interactions between the stator field and excitation winding field. So, impact of the DE fault at full-load is very larger than that of the no-load case. It means that fault must be quickly diagnosed in order to prevent serious damage such as rubbing rotor and stator and destructing core and windings. The result indicates that eccentricity fault causes the increase of the forces exerted on the generator. In the no-load case the trend of the forces increase and its stress has linear relation with the eccentricity degree while this is not so for on load case. On the other hand, distinction of the force waveforms in the SE fault is the existence of the dominant twice synchronous frequency. However, this frequency also exists in DE fault but the amplitudes at high frequencies are rather higher than that frequency (twice supply frequency) and this is not observable. Based on the obtained waveform from the force signal in the faulty generator, the type of the SE or DE fault can be recognized. 3. INTRODUCING NOVEL INDEX A. Force Analysis using TDE Method
(b)
(c) Fig.2. Force exerted on no-load generator under (a) healthy, (b) 30% SE and (c) 30% DE along horizontal axes.
(a)
(b) Fig. 3. Force exerted on full-load generator in (a) 30% SE and (b) 30% DE faults
Based on the above-mentioned results, eccentricity fault disturbs the force signal. One of the competent methods for analyzing systems under chaos is TDE (Time Delay Embedding) method. Here, the TDE method is employed to elicit efficacious criterion functions from the force signal produced by the three-dimensional (3D) time stepping finite
3 TABLE 1 EVALUATED RADIUS OF GYRATION FOR DIFFERENT STATIC AND DYNAMIC ECCENTRICITY FAULT R___ No load Full load
___H___ 21.71 48.89
10%SE 21.65 14.65
30%SE 16.31 12.66
10%DE 0.76 2.1
30%DE 0.31 1.27
kth point in the phase-space is as follows: d(k)2=(x(k)-C0)2+(x(k-l)-Cl)2 (b)
(a)
(c) Fig. 4. Gyration radius of: (a) Healthy (b) 30% SE and (c) 30% DE
elements method (TSFEM). Based on dynamic systems theory, the TDE method reveals hidden patterns in time series data [9]. In this paper, time series data is time domain force profile. The TDE method is used to transform the force profile into reconstructed state-spaces called phase-spaces. The following nominated force time series: F={F(k), k=1…..,M}
(3)
where k is the time index, M is the number of observations, a two-dimensional (2D phase space is generated by plotting F(k100) on the x-y plane and F(k) on the ordinate. Then, ΔF= F(k)-F(k-1) is calculated by applying the TDE process to the time series of the torque profile. Fig. 4 illustrates the phasespace of the force first difference time series (FFDTS) for the healthy and faulty motor. According to Fig. 4, variations rate of the FFDTS in the faulty cases is less than that of the healthy case which was justified in the previous part. It is seen that for 30% SE fault, the radius of the FFDTS is smaller than that of the healthy case. The extension of the DE fault decreases this radius noticeably. B. Radius of Gyration Radius of Gyration around the center of mass of the points in the phase-space mass is proposed as an efficient index for eccentricity fault detection. The radius of gyration R is computed as follows [9]:
R
N k 1 l
(5)
d (k ) 2
where x(k) is the time series observations at time index k1 C0 and C1 are centers of mass for their respective dimensions. It is noticeable that d(k) is the distance of the kth phase-space “point” from the center of mass of the phase-space “points”. Table 1 shows the evaluated R for SE and DE faults under no load and full load condition. According to Table 1, the eccentricity fault decreases the radius of Gyration which can be utilized as a proper criterion to detect the fault; therefore, this radius is employed to determine the eccentricity fault degree. Fig. 4 shows trend of decreasing of Gyration radius by increasing the fault degree under no load condition. This index can easily diagnose the type of eccentricity fault as such that the rate variations of R in no-load and DE fault is very larger than that of the SE fault. For fault detection, the force signal is used where R is also obtained using variation of rate of force profile. It is noted that the load affects the force and fault diagnosis by this index depends on the load range from no load to the full-load. So, according to Table 1, R not only depends on fault and its type but also affects by the load supplied by the generator. It means that on-load fault diagnosis by R is more reliable. However, when R is under influence of some conditions such as on load and non-linear load, the use of precise strategy for reliable fault diagnosis is essential. To overcome this, the procedure introduced in this paper is addressing R value at the same loads. Fig. 5 shows the harmonic components of the force in the synchronous generator in healthy, 30% SE and DE faults. In Table 2 sideband components in force signal of an SPSG with DE and SE faults have been compared; these faults cause the increase of the generator vibrations. A 10% and 30% SE fault in the generator increases considerably the frequency components compared to the healthy case. According to Table 2, higher degree of the eccentricity fault causes the increase of the amplitude of sidebands. A 10% eccentricity fault changes 75 Hz and 125 Hz sideband components from -46 dB and -43 TABLE 2 COMPARISON OF SIDEBAND COMPONENTS IN FORCE SIGNAL OF A SALIENTPOLE GENERATOR DUE TO (a) SE (b) DE FAULT (IN dB) Freq. H 10% 30%
25 -25 -42 -16
50 -59 -73 -53
75 -48 -39 -14
25 0 -16 -16
50 -76 -52 -53
75 -46 -23 -14
100 -49 -48 -32
125 -37 -31 -19
150 -56 -60 -49
175 -33 -24 -14
200 -70 -59 -37
225 -31 -21 -8
250 -58 -56 -49
(a)
(4)
N l where l is the time lag of the phase-space, M is the number of observations and d(k), distance between the center of mass and
Freq. H 10% 30%
(b)
100 -61 -32 -32
125 -43 -22 -19
150 -77 -49 -49
175 -36 -12 -14
200 -68 -39 -37
225 -38 -8 -8
250 -77 -49 -49
4 ACKNOWLEDGEMENT The authors thank the Iran National Elites Foundation (INEF) for partial support of the project. REFERENCES [1].
[2].
[3].
[4].
[5].
[6].
[7]. Fig. 5. Force frequency of force in a no-load SPSG: (a) healthy, (b) 30% SE fault and (c) 30% DE fault.
dB in the healthy case to -23 dB and -22 dB in the faulty case respectively. The main reason for significant change in the time signal of vibrations in SE fault is the presence of the twice of supply harmonic as such that for 10% SE, this side band increases from -63 dB to -22 dB. 4. CONCLUSION The radius of Gyration was utilized as a proper index for precise eccentricity fault diagnosis in salient pole synchronous generators. It was presented that increase of the eccentricity degree decrease the radius of Gyration which was used to determine eccentricity degree. Proposed index was extracted from the force processing by TSDM. Using TSDM helps to analyze evaluated time-variant signals without utilizing their spectra. Type of eccentricity fault could be distinguished using the force time signal.
[8].
[9].
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