ispectru of Stator Phase Current for Faut Detection of Induction Motor Juggrapong Treetrong, Jyoti K. Sinha* Schoo of Mechanica, Aerospace and Civi Engineering, The University of Manchester, Seckvie Street, P.O ox 88, M6 1QD, UK Fengshou Gu, Andrew a Schoo of Coputing and Engineering The University of Huddersfied, Queensgate, Huddersfied HD1 3DH, UK Abstract The nuber of research studies have shown that the faut in the stator or rotor generay show sideband frequencies around the ains frequency (5Hz) and it higher haronics in the spectru of the Motor Current Signature Anaysis (MCSA). However in the present experienta studies such observations have not been identified, but any faut either in the stator or the rotor ay distort the sinusoida response of the otor speed and the ain frequency so the MCSA response ay contain nuber of haronics of the otor speed and the ains frequency. Hence the use of the higher order spectru (HOS), naey the bisepctru of the MCSA has been proposed here because it reates both apitude and phase of nuber of haronics in a signa. It has been observed that it not ony detects the eary faut but aso indicate the severity of the faut to soe extent. *Corresponding author Eai: Jyoti.Sinha@anchester.ac.uk
1.. Introduction Induction otors are the ost widey used otors aong different eectric otors because of their high eve of reiabiity, efficiency and safety. However, these otors are often exposed to hostie environents during operation which eads to eary deterioration eading to the otor faiure. It has aso been observed that 3-4% of a recorded fauts are generay reated to the stator or arature fauts caused due to the shorting of stator phase winding and 5-1% faut reated to the rotor (broken bar and/or end ring faut) [1]. Hence the condition onitoring technique has generay been used to detect the faut at the eary stage so that the reedia action can be done in uch panned way to reduce the achine downtie and to aintain the overa pant safety. Motor Current Signature Anaysis (MCSA) is one of the ost spread procedures for heath onitoring of the otor since decades. One of the ain reasons for using this ethod is that the other ethods require invasive access to the otor and they aso need extra equipent/sensors for easuring the required signas. The research has been progressed in ainy two directions using the stator phase current and votage signas the detection of fauts [1-12] and the quantification of the fauts by the otor paraeters estiation [13-18]. First one is iportant for the quick heath assessent on routine basis, however the ater one usefu to know the extent of the fauts so that reedia action can be done quicky. There are nuber of the research studies that have used the spectru of the stator phase current signa for stator faut [8-12] and the rotor faut [2-7], often based on the presence of the side band frequency (reated to the sip frequency) and its haronics around the power suppy frequency or/and its haronics. However in the present experients, the side bands were not ceary seen for both rotor and stator fauts in their spectra with frequency resoution of 1.25Hz when using the otor stator phase current signas, hence the use of the Higher Order Spectru (HOS) [19-2] has been appied on the stator phase current signa instead of the spectru. It is because the any faut in the otor expected to generate haronic coponents of the otor RPM and the ains frequency in the otor current signa so the reation between different haronic coponents in the signa has been expoited using the HOS, naey the bispectru, which has been observed to be usefu in detection and identification of the rotor and stator fauts. The paper discusses the concept of the bispectru and the presents the bispectru
resuts of the experienta cases of the induction otor with the heathy, stator winding short-circuits (stator faut) and broken rotor bars (rotor faut) conditions. 2.. Higher Order Spectra (HOS) The n rd order oent function of a signa, x (t) is defined as, R τ, τ, τ,..., τ ) = E[ x( t) x( t τ ) x( t τ ) x( t τ )... x( t τ )], xxxx... x ( 1 2 3 n 1 2 3 n where E[.] denotes the expectation operator, and τ as deay. The Power Spectra Density (PSD) is defined as the Fourier Transforation (FT) of a 2 nd order oent function of Equation (1), and is coputed as (1) * PSD, S ( f ) = E[ X( f ) X ( f )], k = 1, 2, 3,, N (2) xx k k k * where S f ) is the PSD, X f ) and X ( ) are the DFT and its copex conjugate at frequency xx ( k k ( k f k f for the tie series x (t). N is the nuber of the frequency points. E[.] denotes the ean operator here. Let us assue that the tie doain signa, x (t), of the tie ength equas to t. This tie signa has been divided into n nuber of segents with soe overap and each segent contains 2N nuber of data points with saping frequency, f s Hz. If X r ( f k ) is the FT of the rth segent, x r (t), at the frequency, f k, then the averaged or ean PSD can be coputed as where f s f k = ( k 1) df, df = 2N n * X r ( f k ) X r ( f k ) r= S xx ( f x ) = 1 n, (3) The PSD gives ony the content of different frequencies and their apitudes in a signa. However, the HOS ispectru and Trispectru provide insights into non-inear couping between frequencies (as it invoves both apitudes and phases) of a signa copared to the traditiona PSD. For exape, the ispectru is the doube FT of a 3 rd order oent of a tie signa [19-2] that invoves two frequencies coponents (both
apitudes and phases) of the signa together with a frequency coponent suation of first two frequencies, and is atheaticay expressed as + + j2π ( f1τ 1+ f2τ 2 ) xxx = R xxx ( τ 1, τ 2 ) e dτ 1dτ 2, (4) where R τ, τ ) = E[ x( t) x( t τ ) x( t )] is the 3 rd order oent, and the xxx( 1 2 1 τ 2 ispectru is coputed by the signa DFT as * ispectru, ( f, f ) = E[ X( f ) X( f ) X ( f + f )], f + f f N (5) n * X r ( f ) X r ( f ) X r ( f + f ) r= ( f, f ) = 1 n (6) The ispectru is copex and interpreted as easuring the aount of couping between the frequencies at f, f, and f + f, and is described by quadratic phase couping. It has been assued that if the frequencies, f and f are the p th and q th haronics of the otor RPM then the coponent of the bispectru, f, f ) has been represented as pq for better understanding. ( 3.. Experient Study The scheatic of the test rig is shown Figure 1. The test rig consists of an induction otor (4kW, 14RPM) with oad ce with a faciity to coect the 3-phase current data directy to the PC at the user define saping frequency. The experients were conducted for these 3 different conditions Heathy, Stator Faut and Rotor Fauts at different oad conditions. The data were coected at the saping frequency of 128 sapes/s. The stator faut was siuated by the short circuits - 5 turn shot circuit, 1 turn short circuit and 15 turn short circuit whereas the rotor faut by the broken rotor bars. Tabe 1 gives the eve of fauts in the stator and the rotor [18].
Tabe 1 The eve of fauts in the stator and the rotor 1% Load Rs xs Rr xr x Heathy 1.5766.917.9577.8795 4.879 5 Turn Short.914.6554.9934.837 4.2341 1 Turn Short.564.4944.9671.8297 4.1754 15 Turn Short.346.2896.9473.8534 4.233 roken ars 1.55.9257 1.373 1.2678 4.3 Unit: Oh (Ω) Figure 1 Scheatic of the test rig 4.. Data Anaysis A typica current pot for the heathy otor operating at 1% oad is shown in Figure 2. The rated current for the otor is cose to 1 Apere. The apitude spectra and the bispectra have aso been estiated for a the experienta data. The frequency resoution was kept 1.25Hz with 9% overap and nuber of average 82 for a the signa processing. The coputation tie using the Pentiu-IV PC for both the spectru and bispectru was ess than 3s which is definitey quick process for the heath onitoring purpose. Few typica pots for the apitude spectra and the bispectra at fu oad condition are shown in Figures 3-8.
1 5 Current, A -5-1.5.1.15.2.25.3.35.4 Tie, s Figure 2 A typica current signa 1 1 Current Apitude, A 1 1-1 1-2 1-3 1-4 1-5 1 2 3 4 5 6 Frequency,Hz Figure 3 The spectru of the stator phase current for the heathy otor
Current Apitude, A 1 1-2 1-4 (a) 1 2 3 4 5 6 Frequency,Hz Current Apitude, A 1 1-2 1-4 (b) 1 2 3 4 5 6 Frequency,Hz Current Apitude, A 1 1-2 1-4 (c) 1 2 3 4 5 6 Frequency, Hz Figure 4 The spectra of stator phase current: (a) 5 turns short circuit, (b) 1 turns short circuit, and (c) 15 turns short circuit
Current Apitude, A 1 1-2 1-4 1 2 3 4 5 6 Frequency, Hz Figure 5 The spectru of the stator phase current for the broken rotor bars otor 3 Apitude, A 3 2.5 2 1.5 1.5 24 42 2 15 1 5 Frequency (f 5 1 15 Frequency (f 2 Figure 6 The bispectru of the stator phase current for the heathy otor
2.5 2 (a) Apitude, A 3 1.5 1.5 24 42 2 15 1 Frequency (f 5 5 1 15 Frequency (f 2 Apitude, A 3 2.5 2 1.5 1.5 26 24 42 62 (b) 2 15 1 Frequency (f 5 15 1 5 Frequency (f 2 2.5 Apitude, A 3 2 1.5 1.5 26 24 (c) 42 62 2 15 1 Frequency (f 5 5 1 15 Frequency (f 2 Figure 7 The bispectra of the stator phase current: (a) 5 Turns Short Circuit, (b) 1 Turns Short Circuit, and (c) 15 Turns Short Circuit
.35 Apitude, A 3.3.25.2.15.1 24 12 11 21 42.5 2 15 1 Frequency (f 5 5 1 15 Frequency (f 2 Figure 8 The bispectru of the stator phase current for the broken rotor bars otor 4.1. Discussion As can be seen fro Figures 3-5, it is difficut to identify the fauts based on the spectra with the frequency resoution of 1.25Hz of the current signas. A spectra aost ook identica. In a cases, achine RPM (1x coponent) and its higher haronics (2x, 3x, ) are present and no side band frequency at the ain frequency reated to the sip frequency has been seen to identify the faut as suggested in the earier studies. The apitude deoduation at a frequency for any signa reoves that frequency, but oduated frequencies can be ceary identified fro the deoduated signa. Hence here aso, the apitude deoduation at the ains frequency, 5Hz has been carried out for the phase current signas for the fauty rotor and stator conditions. The apitude spectra of a the deoduated signas have shown ony a singe peak at the RPM of the otor. A typica such spectru is shown in Figure 9 for the fauty rotor condition. Here again, the spectru is not showing any peaks other than achine RPM which indicates that the frequency reated to the sip frequency due to faut was not present in the current signa and so the identification just based on side-band was not possibe for the present experienta cases.
1-2 Apitude 1-3 1-4 1 2 3 4 5 Frequency, Hz Figure 9 The spectru of the apitude deoduated stator phase current at ains frequency for the broken rotor bars otor However, the bispectra of stator phase currents fro the 3 different otor conditions see to identify the fauts as can be seen in Figures 6-8. The peaks in the bispectra pots are indicated by 11, 12, 21 and so on. Here 11 eans the reation of 1x, 1x and 2x coponents, = ) the reation of 1x, 2x and 3x (1x+2x) coponents in a signa. 12 ( 21 In the bispectru, the ony significant peak has been seen for the heathy otor condition. However, the for the fauty stator cases the apitude of the bisepctru coponent,, decreases as the eve of the stator faut increases and the significant increase in the apitude of the bispectru coponent, 24 (= 42 ) copared to the heathy condition, neary 2.4 ties. Other peaks, 11, 12 ( = 21) and 26 ( = 62 ) observed to reain coparabe with the apitudes for the heathy condition (Figures 6-7). However, in case of the fauty rotor case the peak,, reduced significanty fro the heathy condition (neary.1 ties) and the fauty stator cases, but other peaks, 11, 12 ( = 21) increased significanty (neary 8-1 ties) copared to the heathy and the stator faut cases. These observations are aso suarized in Tabe 2. Hence the based on the observation, it can be concuded that the bispectru of the phase current signa can identify and distinguish the rotor faut and stator faut of the eectric otor. It has aso been observed that the apitude of the peaks can show the severity of the stator and the rotor fauts.
To confir the robustness of the proposed study, the tests were conducted for different oad eves of the otor. The observation ade in the bispectru at 1% otor oad for the heathy, the stator faut and the rotor faut cases was consistent with the different oad conditions. Figure 1 shows the typica cases for the rotor faut at no oad, 25% oad, 5% oad and 75% oad where it can be seen that the appearance of peaks in the bisepctra at different oads is consistent with the bispectru shown in Figure 8, hence ethod sees to be robust for the faut detection in the otor. Apitude, A 3.3.2.1 (a) Apitude, A 3.3.2.1 (b) 2 15 1 5 Frequency (f 5 2 15 1 Frequency (f 2 15 1 5 Frequency (f 5 2 15 1 Frequency (f Apitude, A 3.3.2.1 (c) Apitude, A 3.3.2.1 (d) 2 15 1 5 Frequency (f 2 15 1 5 Frequency (f 2 1 Frequency (f 5 2 15 1 Frequency (f Figure 1 The bispectra of the stator phase current for the broken rotor bars otor, (a) No Load, (b) 25% Load, (c) 5% Load, (d) 75% Load 5.. Concusions A ethod that can identify the faut in the otor at eary stage and aso capabe to distinguish the rotor faut and the stator faut is aways iportant so that the reedia action can be carried out quicky. Hence the use of the higher order spectra (HOS), naey the bispectru has been tested and appied to the phase current signa of the otor for this purpose. The bispectru is the too which reates both apitude and phase of nuber of haronics in a signa. The otor phase current signa in case of any faut expected to contain nuber of haronics coponents reated to the otor RPM and the
ains frequency. It is because any faut (either in the stator or the rotor) ay distort the sinusoida response of the otor phase current signa which resuts in nuber of haronics of the otor RPM and the ains frequency. This has aready been observed in the otor phase current spectra. ut the apitude spectra coud not abe to detect the rotor and the stator fauts for the induction otor used in the experients, however the bispectru of the otor phase current successfuy abe to detect the stator and the rotor faut and aso abe distinguish the stator and the rotor faut which is considered to be usefu inforation for fixing the probe quicky. Moreover, it has aso been pan to test the trispectru, other kind of the HOS, to observe possibiity of the further iproveent in the otor faut diagnosis. Tabe 2 Coparison of the bispectru coponents apitude for different faut conditions for the otor when operating at 1% oad Apitude (Cubic Apere, A 3 ) of ispectru Coponents 11 12 21 = 24 = 42 26 = 62 Heathy.25 2.7.2.8.18 Fauty Rotor..28.19.18.23 Fauty Stator (5 turn).24 2.6.18..15 Fauty Stator (1 turn).5 2.3.39.19.42 Fauty Stator (15 turn).3 2..23.17. 6.. References [1] Nandi, S., Toiyat, H.A., Li, X., Condition Monitoring and Faut Diagnosis of Eectrica Motors A Review, Energy Conversion, IEEE Transactions 2(4)(25) 719 729. [2] Schoen, R.R., Habeter, T.G., Effects of tie-varying oads on rotor faut detection in induction achines, Industry Appications, IEEE Transactions 31(4)(1995) 9 96. [3] eini, A., Fiippetti, F., Franceschini, G., Tassoni, C., Kian, G.., Quantitative evauation of induction otor broken bars by eans of eectrica signature anaysis, Industry Appications, IEEE Transactions 37(5) (21) 1248 1255.
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