Fault Diagnosis in Induction motor using Wavelet Packet Decomposition of Stator Current signal : Fault Diagnosis in Induction motor using Wavelet Packet Decomposition of Stator Current signal Jaganatha Pandian.B
Basic Idea : Basic Idea Fault Diagnosis in Induction Motor
Perform Motor Current Signature Analysis
Wavelet Packet Decomposition
Isolate the Fault reflecting Nodes
Find the Energy level of nodes to find Fault Depth
Model of the motor used for Validating the proposal
Modified Winding Functional Approach
Faults Considered : Faults Considered Broken Rotor Bar
Stator inter turn Short circuit
Mixed Eccentricity
Rotor Breakage : Rotor Breakage Occurs in
Rotor Bar
Rotor End Ring
Effect
The Broken piece moves along the Air-gap
Disrupt the surface of Stator Winding
Sudden Failure
Stator inter turn Short circuit : Stator inter turn Short circuit Failure of turn to turn insulation
Effects
Damages the adjacent coil
Reduction in no of coil - Reduces Phase MMF
Current through Shorted turn – Opposing MMF
Eccentricity : Eccentricity Unequal Air-gap between Stator and Rotor
Effects
Unbalanced Magnetic Pull
or
Unbalanced Radial Force
Rubbing between Stator and Rotor
Types
Static, Dynamic and Mixed
Static Eccentricity : Static Eccentricity Center of the rotor is fixed with the center of rotation
Position of minimal radial air -gap length is fixed in space. Healthy
Dynamic Eccentricity : Dynamic Eccentricity Center of the rotor is not at the center of rotation
Position of the minimum air gap rotates with the rotor
Mixed Air-Gap Eccentricity : Mixed Air-Gap Eccentricity Mix of static and dynamic eccentricity conditions
Rotor revolves around a point between stator and rotor
Fault Detection Techniques : Fault Detection Techniques Temperature monitoring
EMF Monitoring
Particle analysis
Vibration measurement
Model based approach
Motor Current Signature Analysis (MCSA)
Motor Current Signature Analysis (MCSA) : Motor Current Signature Analysis (MCSA) Stator current consists of various motor harmonics that corresponds to various faulty conditions.
Method of analyzing stator signal for the presence of such harmonics is called MCSA.
Techniques
FFT
STFT
WT
WPD
Fast Fourier Transform : Fast Fourier Transform Tells how much of each frequency exists in a signal
Limitation of FFT : Limitation of FFT The Time and Frequency Information can not be Seen at the Same Time
This limits the application of FFT when the signal is Non-stationary.
SFORT TIME FOURIER TRANSFORM (STFT) : SFORT TIME FOURIER TRANSFORM (STFT) Analyze only a small section of the signal at a time -- a technique called Windowing the Signal.
The Segment of Signal is Assumed Stationary
Limitations of STFT : Limitations of STFT Unchanged Window
Dilemma of Resolution
Narrow window -> poor frequency resolution
Wide window -> poor time resolution
Wavelet Transform (WT) : Wavelet Transform (WT) Similar to STFT: signal is multiplied with a function, but, Width of the Window is Changed as the Transform is Computed for Every Spectral Components
Split Up the Signal into a Bunch of Signals
Representing the Same Signal, but all Corresponding to Different Frequency Bands
Provides What Frequency Bands Exists at What Time Intervals
Slide 17: Step 1: The wavelet is placed at the beginning of the signal, and set s=1 (the most compressed wavelet);
Step 2: The wavelet function at scale “1” is multiplied by the signal, and integrated over all times; then multiplied by ;
Step 3: Shift the wavelet to t= , and get the transform value at t= and s=1;
Step 4: Repeat the procedure until the wavelet reaches the end of the signal;
Step 5: Scale s is increased by a sufficiently small value, the above procedure is repeated for all s;
Step 6: Each computation for a given s fills the single row of the time-scale plane;
Step 7: CWT is obtained if all s are calculated.
Signal Decomposition using WT : Signal Decomposition using WT The decomposition of the signal into different frequency bands is simply obtained by successive high-pass and low-pass filtering of the time domain signal. WT can be used to Decompose the signal to the depth of interest.
CA – Approximation coefficients
CD – Detail coefficients
Limitation of WT in Signal Decomposition : Limitation of WT in Signal Decomposition Wavelet transformation analyses only the ‘approximation portion’ of sub samples of each decomposed level, but not the ‘detail portion’.
The detail portion of sub- samples in those levels may also carry some critical information about motor health conditions.
For this reason we go for Wavelet Packet Decomposition, where both portions are considered in signal analysis.
Wavelet Packet Decomposition (WPD) : Wavelet Packet Decomposition (WPD) Only difference it makes with WT is that it splits Detail coefficients also in each level of decomposition.
WPD analysis after the final level of decomposition gives number of packets. Each packet corresponds to specific Frequency Band. By monitoring the Energy level of each packet we can identify the presence of that specific band of frequency components in the signal under study.
Harmonics affected by Fault : Harmonics affected by Fault Mixed eccentricity,
fecc = f ± k f r , k = 1,2,3,…
where f r is the rotational frequency of motor.
Rotor asymmetry
fbrb = 1 ± 2k s f , k = 1,2,3,...
where s is the slip of the induction motor.
Stator winding asymmetry
fst = f .[k (1 - s) / p ± n], k = 1,2,3…., n = 1,3,5… ,
p- no of pole pair in motor, f – fundamental supply frequency.
Wavelet used : Wavelet used Discrete Mayer Wavelet
least leakage with lateral Nodes in frequency domain
Depth of decomposition - 10
WFA Modeling of Induction Motor : WFA Modeling of Induction Motor Replace rotor by n identical loops
Calculate Inductances of ‘n’ rotor bars and ‘m’ stator bars using
MMF, Permeance, Air-Gap function
From the Inductance Stator Current can be estimated
Modeling Equations : Modeling Equations mutual inductance between any coils i and j
θrm Angular position of the rotor
Φ is a particular position along stator inner surface,
g-1(θr,Φ) is termed the inverse gap function
l is the length of the stack
r is the average radius of the air-gap.
ni(θr,Φ) is the winding distribution of winding I
Nj(θr,Φ) is the winding function of winding j.
Modeling Equations – cont. : Modeling Equations – cont. Air gap Function
g = g0[1 - δs cos θ - δd cos(ωmt-θ)]
δs, δd are degrees of static and dynamic eccentricities
Voltage & Current Equations
Impact of Faults in Model : Impact of Faults in Model Eccentricity
Air-gap function affected
Stator Winding Shortage
current flow through the shorted turns
new term introduced in Flux linkage matrix and stator phase equations
Broken Rotor
Modeling Result : Modeling Result Stator Current With 25% Eccentricity 10% Winding Shortage With 2 Rotor Bars broken
Frequency Band coverage per Node : Frequency Band coverage per Node At the depth of 10 in WPD, each Node covers a frequency band of,
fs – sampling frequency, here 10000 Hz
j – depth of decomposition, here 10
The band coverage here is 4.8828 Hz per Packet.
Packet Signal25% Eccentricity : Packet Signal25% Eccentricity Node [10, 3] Node [10, 26] Healthy Faulty
Packet Signal10% Winding Shortage : Packet Signal10% Winding Shortage Node [10, 6] Node [10, 12] Healthy Faulty
Packet SignalNode [10,9], with Broken Rotor : Packet SignalNode [10,9], with Broken Rotor Healthy 2 bars broken 5 bars broken
Energy of Packets : Energy of Packets The energy of Node (i) in Depth (j) is given by, where N is number of coefficients in each Node in depth J.
N = D2-j,
D is Length of original signal (or) Total number of samples in original signal
Energy of Nodes under Faulty Conditions : Energy of Nodes under Faulty Conditions
Conclution : Conclution Can detect faults present together or alone, by monitoring Energy level of Decomposed Packet Signals
Wavelet analysis is effective on Non-stationary real time signal analysis.
On-line condition monitoring Application : On-line condition monitoring Application
References : References Al-Nuaim, N.A. and H.A. Toliyat, “A Novel Method for modeling Dynamic Air-Gap Eccentricity in Synchronous Machine Based on Modified Winding Function Theory,” IEEE Transactions on Energy Conversion, 13, 156-162 (1998)
Nandi,S., R. Bharadwaj and H.Toliyat, “Performance Analysis of a Three Phase Induction Motor Under Mixed Eccentricity Condition,” IEEE Transactions on Energy Conversion, 17, 392-399 (2002)
J. Faiz, B.M. Ebrahimi, “ Mixed Fault Diagnosis In Three-Phase Squirrel-Cage Induction Motor Using Analysis Of Air-Gap Magnetic Field,” Progress In Electromagnetics Research, PIER 64, 239–255, 2006.
W.T. Thomson, R.J. Gilmore, “Motor Current Signature Analysis to Detect Faults in Induction Motor Drives-Fundamentals, Data Interpretation, and Industrial Case Histories”, Proceedings of the Thirty-Second Turbomachinery Symposium, 2003, page(s): 145-156.
Randy R.Schoen, Brian K.Lin, Thomas G.Habetlar, Jay H.Schlag and Samir Farag, “An Unsupervised, On-Line System For Induction Motor Fault Detection Using Stator Current Monitoring,” IEEE Transaction on Industry Applications, vol.31, No 6, 1280-1286, 1995.
H.Douglas, P.Pillay, A.Ziarani, “Detection Of Broken Rotor Bars In Induction Motors Using Wavelet Analysis”, IEEE Transaction on Industry Applications, 2003.
References : References H.Douglas, P.Pillay, “The Impact of Wavelet Selection on Transient Motor Current Signature Analysis”, IEEE Transaction on Industry Applications, 2005.
Arezki Menacer, Hamid Benakcha, “Stator Current Analysis of Incipient Fault into Asynchronous motor rotor bars using Fast Fourier Transform”, Journal of Electrical Engineering, Vol. 55, No. 5-6, 122-130, 2004.
Lorand SZABO, Jeno Barna DOBAI, Karoly Agoston BIRO’ “Discrete Wavelet Transform Based Rotor Faults Detection Method for Induction Machines”, Intelligent Systems at the Service of Mankind, vol. 2., Ubooks, Augsburg (Germany), 2005, pp. 63-74.
Stephane G. Mallat, “A Theory For Multiresolution Signal Decomposition: The Wavelet Representation”, IEEE Transactions On Pattern Analysis And Machine Intelligence. Vol., No. 7. 674 - 693, 1989.
Williom T. Thomson, Ronald J. Gilmore, “ Motor Current Sig nature Analysis to Detect Faults in Induction Motor Drives – Fundamentals, Data Interpretation, and Industrial Case Histories”, Proceedings of the Thirty Second Turbo Machinery Symposium, 2003, 145 – 156.
Slide 38: T H A N K Y O U