Early detection of short circuit between turns in stator winding of induction machines via multivariate statistics
S. Aouabdi H. Merabet
Welding and NDT research center (CSC) BP 64 Cheraga, Algeria Welding and NDT research center (CSC) BP 64 Cheraga, Algeria [email protected] [email protected]
Abstract – Online monitoring of induction machine health is of increased interest, as the industrial processes that depend on the machines becomes more complex and as performance to cost ration of monitoring technology.
Several efforts have been directed towards developing methods that use the conventional signal processing and pattern classification techniques. This paper focuses on fault diagnosis in induction machines operating under transient conditions. A new tool of anomaly detection based on multi-scale entropy MSE of Park vector approach and information theory combined with current trajectory mass center with principal component analysis (PCA) are proposed. The faults study in this paper is short circuit between turns in stator winding of induction machine. Simulation results show that the proposed method are able to detect short circuit between turns in stator winding of induction machine in the permanent period.
Keywords – Induction Machine, Fault Diagnosis, multi-scale entropy, Principal Component Analysis, Current trajectory mass center.
I. INTRODUCTION
Squirrel cage induction machine is one of the most widely used machines in the industry. Because of its simple structure and high reliability, it has been used for many purposes, such as pump, blower, fan, compressor, transportation, etc. Under normal operation conditions, the components of induction machine are subjected to thermal, mechanical and electrical stress. The stress is increased during transients, such as load and supply variations, and may cause mechanical and insulation failure of the induction machines. More advanced techniques of pattern classification have been used, such as signal spectral analysis, neural networks [1], these techniques have their respective shortcomings and advantages, this paper focuses on robust method for early detection of anomalies due to short circuit between turns in stator winding of induction machine, where an anomaly is defined as a deviation from the nominal expected behavior of machine dynamics.
Based on the observed anomalies, signal processing for fault detection. The methodology is primarily data driven. The idea is to first understand the mechanisms of fault and then apply these data driven techniques
cleverly to extract information that gives the indication of the health of the machine. Fig (1) shows the various steps involved. Anomaly detection is posed as a two-time-scale problem. The objective is to make inferences on occurrence of the evolving slow- time-scale faults based on changes in the observed statistics of the fast- time-scale process dynamic of the induction machine (short circuit between turns in stator winding of induction machine). Early detection of anomalies and pattern recongnition have motivated formulation of multivariate statistics (principal component analysis (PCA)) [2, 3]. The framework of the anomaly detection problem consists of the following two steps:
• Preprocessing of observed time series data using Park’s vector representation [4];
• Pattern Classification based on the pre- processed data sets (using multi-scale entropy, a current trajectory mass center and PCA decomposition).
Fig. 1. Overall implementation diagram.
Current signals
Induction Machine
Park vector (Isalpha, Isbeta) 3D view
(Phase A, Phase B and Phase C)
Current trajectory mass center
Anomaly Measure On-line Analysis
Multi-scale entropy
PCA approach
-20 -15 -10 -5 0 5 10 15 20
-10 -5 0 5 10 -20 -15 -10 -5 0 5 10 15 20
Ialpha (A) Phase A
Ibeta (A)
Igama (A)
15% turns 5% turns Healthy case
10% turns
II. ANALYSIS OF FAULT SIGNATURES
The information on short circuit between turns in stator winding of induction machine faults is not readily discernable from the line current, , and , especially true for small amounts of s. The park vector transformation [5] has been adopted to isolate and identify this fault signature.
Through the use of Park’s vector approach a two dimensional (2-D) representation can be used to describe three-phase induction motor phenomena. A suitable 2-D representation is based on the current Concordia vector; sometimes called Park’s vector.
The 3-phase stator current equations are reducible to a set of two appropriate variables in a 2-phase reference frame (called the α β reference frame).
= − − (1)
= − (2) Where and are the direct and quadrature axis currents respectively. These currents should ideally be
/2 radians out of phase.
In ideal conditions, three-phase currents lead to a Concordia vector with the following components[7]:
= (3)
= ( − /2) (4) In a parametric plot with t as the parameter, the direct and quadrature axis currents represent an ellipse.
² + ² = ² (5) Where is the supply phase current maximum value and is supply frequency.
The current Concordia vector is a circular pattern centered on the origin of the coordinates as shown in Fig.2. By analysing the currents in a 3D.
In equation (5) is known as the Parks vector modulus, which may be subjected to significant deviations as a result of the short circuit between turns in stator winding of induction machine
The short circuit between turns in stator winding is represented by positive sequence and negative sequence currents, and !; and ! and and ! The positive and negative sequence currents have maximum values of and !, respectively. Then, the three line currents are represented as follows:
= Cos ( + φ )+ !Cos ( +φ_) (6)
= Cos( + φ − 2 /3 )+ !Cos( +φ_- 4 /3) (7)
= Cos( + φ − 4 /3 )+ !Cos( +φ_-
2 /3) (8) Where φ and φ_ are phase angles of the positive and negative sequence currents, respectively. For an short circuit condition, the direct and quadrature axis currents are:
= Cos ( + φ )+ !Cos ( +φ_) (9)
= sin ( + φ )+ !sin( +φ_) (10)
² + ²= ( ² + !²) + 3( !cos (2 + φ + φ_) (11)
The analysis of turn- to-turn short circuit in stator winding of induction machine can be modelled using different models. Machine modelling under fault conditions is a key to predict its behaviour [6]. For a healthy machine the current pattern is a circle centered at the origine. For an induction machine working with a stator winding fault the current pattern assumes an elliptic pattern as shown in Fig.3.
Fig. 2. Stator current pattern for: a healthy case, a machine with stator winding faults :(Phase A, Phase B,
Phase C). 3D view.
Fig. 3. Current signals were recorded from induction machine in four conditions: Healthy case, 5% turns, 10%
turns and 15% turns of phase A. 3D view of measure and estimation of current signals.
Fig.10. Park’s vector plot of the last decomposition of the principal component analysis.
Fig.5. Five statistics over MSE of the signals showns in Fig. 3 depicted in Fig 4.
Fig.6. Five statistics over MSE of the Isalpha.
Fig.7. Five statistics over MSE of the Isbeta.
Fig. 5 give the MSE over 20 scales corresponding to the signals shown in Fig.3. From Fig .4, we can see that the MSE of healthy case hasn’t the largest entropy values over the most scales in comparison with [9], which means that the phase current signals with healthy case and with those with faulthy case are highly correlated. After extracting Mutli-scale entropy (MSE) as feature vectors, a multi-variate statistics will be used to acheive fault diagnosis as shown in Fig.5.
III. DEVELOPED ALGORITHM
For fault diagnosis of the short circuit between turns in stator winding the research follows these steps :
Max 1,5 Min 2,5 Mean 3,5 Geo-mean 4,5 std
0 0.002 0.004 0.006 0.008 0.01 0.012
Feautures
Feautures values
isalpha (A)
Healthy case 10% turns 15% turns 5% turns
Fig.4. MSE over 20 scales of the corresponding current signal Ialpha.
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
x 10-15 -1.5
-1 -0.5 0 0.5 1 1.5
2x 10-15
id (A)
iq (A)
Healthy phase A phase B phase C
-8 -6 -4 -2 0 2 4 6 8
x 10-16 -1
-0.5 0 0.5 1 1.5x 10-15
Id (A)
Iq (A)
sain 60% turns 100% turns 40% turns
0 2 4 6 8 10 12 14 16 18 20
0 0.005 0.01 0.015 0.02 0.025
Scale factor
Sample entropy
(Isalpha) (A)
Healthy case 5% turns 10% turns 15% turns
3.5 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 x 10-3
Feautures
Feautures values
isalpha (A)
Healthy case 10% turns 15% turns 5% turns
Fig.11. Park’s vector plot of the last decomposition of the principal component analysis.
0 200 400 600 800 1 000 1 200 1 400 1 600
0.2 0.25
Mean
0 200 400 600 800 1 000 1 200 1 400 1 600
0 0.1
0.2 std
0 200 400 600 800 1 000 1 200 1 400 1 600
0 0.5 1
Max
0 200 400 600 800 1 000 1 200 1 400 1 600
0.2 0.25
Geo-Mean
0 200 400 600 800 1 000 1 200 1 400 1 600
0 0.1 0.2
features
features values isbeta a phase A
Min
Healthy case 5% turns 10% turns 15% turns
0 200 400 600 800 1 000 1 200 1 400 1 600
0.2
0.25 mean
0 200 400 600 800 1 000 1 200 1 400 1 600
0 0.1 0.2
Std
0 200 400 600 800 1 000 1 200 1 400 1 600
0 0.5 1
Max
0 200 400 600 800 1 000 1 200 1 400 1 600
0.2
0.25 Geo-mean
0 200 400 600 800 1 000 1 200 1 400 1 600
0 0.1 0.2
features
features values isalpha a phase A
Min
Healthy case 5% turns 10% turns 15% turns
Fig.8. Five statistics over MSE of the norm signal (isalpha, isbeta) (phase A).
0 200 400 600 800 1,000 1,200 1,400 1,600
0.32 0.34 0.36 0.38
0.4 mean
0 200 400 600 800 1,000 1,200 1,400 1,600
0 0.2 0.4
Std
0 200 400 600 800 1,000 1,200 1,400 1,600
0 0.5 1 1.5
Max
0 200 400 600 800 1,000 1,200 1,400 1,600
0.2 0.3 0.4
Geo-mean
0 200 400 600 800 1,000 1,200 1,400 1,600
0.16 0.18 0.2 0.22 0.24
features features values norm (isalpha a isbeta a)
Min
15% turns 10% turns
5% turns Healthy case
0 200 400 600 800 1000 1200 1400 1600
0 0.5 1 1.5 2
SPE (1)
0 200 400 600 800 1000 1200 1400 1600
0 0.5 1 1.5
SPE (2)
0 200 400 600 800 1000 1200 1400 1600
0 0.5 1 1.5
SPE (3)
0 200 400 600 800 1000 1200 1400 1600
0 0.5 1 1.5
Data points
SPE (4)
Fig.9. SPE of : Healthy case, 5% turns, 10% turns and 15% turns of (phase A).
0 50 100 150 200 250 300 350 400 450 500
0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78
Training Error
Number of Epochs
Training Error
Fig.12. Checking data error
0 50 100 150 200 250 300 350
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
output Chkfuzout4 Chkfuzout2
Fig.13. the comparison of the output of fismat2 and fismat4 against the checking data Chkdatout.
IA, IB, and IC: are the three stator currents were recorded from of induction motor.
Application of The multi-scale entropy MSE algorithm latter is based on the application of SampEn for different scales of the same process instead of traditionally used regularity measure ApEn statistics.
Details on the Sampen algorithm can be found in many literatures [10,11]. SampEn measures the regularity in serial data. It provides a likelihood measure that two sequences of + consecutive data points within given tolerance , remain similar when one consecutive points is included. SampEn increases as , decrease, because the criterion for sequence matching becomes more stringent. Therefore, the determination of these two parameters is of importance.
In the MSE analysis, a coarse-grained time series is first constructed from the original time series -x , … , x0, … , x12. One constructed consecutive coarse-grained time series 3y(5)6 with scale factor τ(τ = 1,2, … N), according to the equation:
y:(τ)= 1/τ∑:τ x0
0<(:! )τ (12) Where τ represents the scale factor and 1 ≤ j ≤ N/τ
Test of missing value for the Indicators Ia,Ib and Ic.
Five statistics over the MSE are calculed mean (mi) Std (si), geo-mean (gmi) and max (mxi)
PCA model and evaluation of squared prediction error (SPE) by taking the square difference between the observed values and predicted values from the normal condition or reference model:
?@A = ∑ BCGD< DE− CDEF
Where CDE and CDE are measured and predicted values, respectively by the PCA model. Initially, a model was developed from a normal condition data set using k principal components and this data set was decomposed as :
H = I@J
Where T is score matrix and P is the loading matrix which are the PCA model parameters[7].
Norm of the indicators are calculated.
Used of the Multivariate statistics approach.
Used of the current trajectory mass center approach.
The fault detection and severity index computation based on the circumference radius and the distance between the far center longer of cluster Park’s vector and the origin and the distance between the mass center and the origin [8].
So different pattern will be obtained in the 3D, specifically a circle, the radius of the circle is related to the center longer of cluster between each other and the fault severity related with the far center longer of the 6 clusters. In this case the normalized fault severity index is:
si ≥ONPMN (15) Where: dcm denotes the distance between the mass center and the origine. If the fault increases, then si also increases.
Anfis continues to minimize the error against the training data all the way to the 500 th epoch.
IV. CONCLUSION
A new approach for the short circuit between turns in stator winding fault diagnosis in induction machine was presented. This approach is based on the application of the Park transform to the stator currents. A theoretical analysis of the three phase induction machine was also presented. This inspection was made for healthy and with a short circuit between turns in stator winding fault working conditions.
Multi-scale entropy (MSE) across 20 scales are extracted so as to account for the dynamic nonlinearity as well as the coupling and interaction effects between electromechanical parts. In order to reduce the number of the input to multivariate statistics approach five statistics over MSE are utilized which are maximum value minimum value, arithmetic mean value, geometric mean value and (13)
(14)
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standard deviation value. These five features are then presented multivariate statistics approach.
From this analysis the PCA approach and the mass center and the correspondent circle radius. This circle radius related with the center longer of the 6 clusters this last related with the fault severity.
Our study suggests that multivariate statistics based on PCA only is not a good tool to detect abnormalities in induction machine, but it can also be used as a helpful tool for fault detection in induction machine combined with other approach like MSE.
The SPE doesn’t only indicate fault conditions, but it also provides information about the location of the fault as well as its severity.
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