Estimation of time varying Power Quality Indices using Adaptive Signal Processing Techniques

Acknowledgement

I would like to thank

• My supervisors for providing time and guidance whenever needed • Phd student Karthik Thirumala for his insightful suggestions• Institute for providing various licensed softwares and websites to access journals

and conference paper• Colleagues for making a competitive ambience

Motivation• Industries and end consumers are tending to use automated devices which uses control

interface, low power loss equipments, appliances with small size etc.

• These additional features requires extensive use of sophisticated power electronic components

• Increased use of converters,variable speed drives,push buttons,capacitor banks,circuit breaker etc results in distorted power signal

• Load variation also leads to voltage level and frequency variations

• Incidents like industry shutdown are happening frequently because of disturbances in power supply

Mitigation of disturbances

The unsolicited disturbances can be abated to lower extent using following equipments

a) Active Filters – For compensating harmonics

b) Dynamic Voltage Restorer(DVR) – For sag/swell compensation

c) Capacitor bank with pre-insertion resistor, arrestors – For transient mitigation

[1] Fernandez, P.C.; Esmeraldo, P.C.V.; Carvalho, F.M.S.; Camara, A.S.B.; Bronzeado, H.S.; Vaisman, R., "Mitigation of power system switching transients to improve power quality," in Harmonics and Quality of Power Proceedings, 1998. Proceedings. 8th International Conference On , vol.2, no., pp.988-993 vol.2, 14-18 Oct 1998

[2] Pakharia, Anita, and Manoj Gupta. "Dynamic voltage restorer for compensation of voltage sag and swell: a literature review." International Journal of Advances in Engineering & Technology 4.1 (2012): 347-355.

Where to place these mitigation equipments

• Mitigation equipments should be placed only at those places which are highly suspicious to have frequent disturbances

• Such lines can be identified from data collected by analysis of voltage and current signal for long duration of time(month,year)

[3] IEEE standard 1159-2009, IEEE Recommended Practice for Monitoring Electric Power Quality, 2009.

Methods available for signal analysis

[4] Math H. Bollen and Irene Gu Signal Processing of Power Quality Disturbances Volume 30 of IEEE Press Series on Power Engineering

Short Time Fourier Transform - 1970

Hilbert Huang Transform - 1998

Gabor Transform - 1946

Q1 Q2 Q3

Discrete Wavelet Transform – 1980s

Wavelet Packet Transform

Kalman Filter

Wigner Ville Distribution - 1980

S-Transform - 1996

Empirical Wavelet Transform - 2013

S-Transform

[5] M. Biswal, P. K. Dash, Estimation of time-varying power quality indices with an adaptive window-based fast generalised S-transform, IET Sci. Meas. & Tech. 6 (4) (2012) 189-197. [6] M. Biswal, and P. K. Dash, Detection and characterization of multiple power quality disturbances with a fast S-transform and decision tree based classifier, Digital Signal Processing 23 (4) (2013) 1071-1083.

2 2( , ) ( ) | | exp( ( ) )exp( 2 )x

S t f x f t f j f d

22( , ) { ( )exp( 2 )}*exp( )x

S t f x t ft t f

2 2 2( , ) { ( )exp( / )}x

S t f iFFT X f f

Limitation of S-Transform

Empirical Wavelet Transform

[7] K. Thirumala, A. Umarikar, T. Jain, Estimation of Single-Phase and Three-Phase Power-Quality Indices Using Empirical Wavelet Transform, IEEE Trans. Power Del. 30 (1) (2015) 445-454.[8] J. Gilles, Empirical wavelet transform, IEEE Trans. Signal Process. 61 (16) (2013) 3999-4010.

FFT• FFT of signal

Maxima

• Design filter according to boundaries

Boundaries

• Detecting maxima in FT of signal using amplitude threshold and frequency separation

Filter Design

• Boundaries for wavelet filters by detecting point of minima bw consecutive frequencies

Fourier spectrum segmentation

Filter Design

( )

( ) cos , , ( ) ( )

1

1 1 1 1

1 if 1

if 1 12

0 otherwise

1

1 1 1

1 1

1 12

1 12

i i

i i i

i

i i i

1 if ( ) ( )

cos , , if ( ) ( )( )

si n , , if ( ) ( )

0 otherwise

The parameter γ ensures minimal overlap between the two consecutive transition areas and its selection is based on the boundaries estimated

[9] J. Gilles, Empirical wavelet transform, IEEE Trans. Signal Process. 61 (16) (2013) 3999-4010.

Motivation to Adaptive Frequency Threshold Sag signal with high spectral leakage

Interharmonics with 10,50,80,100,120,150,250,350Hz frequencies

Frequency separation threshold = 15 samples Frequency separation threshold= 25 samples

Generalized EWT

• A particular default value for frequency threshold can not be used for detecting exact frequency components of signal in every case

• Frequency threshold can be made adaptive using time domain information of signal

rmsX [ (1), (2),......, ( )]rms rms rmsX X X n2

( 1) 1

1( ) ( )nS

rmsi n S

X n x iS

( ,2) ( ,2) 1 resdF quot NS rem NS f

Where NS is total number of sign changeand fres is frequency resolution in Fourier domain

Calculation of signal variation

Flicker signal Rms per cycle

Swell signal

Interharmonics signal

Flow chart for signal analysis using GEWT

Compute the rms vector (Xrms) and the signal variation (SV)

dF = 25 Hz

Find the number of sign changes (NS)

If NS < 3

dF eq. (8)

Windowed signal

YesNo

Identify the significant frequencies from the Fourier spectrum X(ω) utilizing the specified thresholds

Compute the filter boundaries for each frequency component

Construct an empirical wavelet filter bank based on the boundaries computed as given in (1) and (2)

Inverse FFT of the filtered coefficients will give the time varying individual frequency components

IMF 1 IMF NIMF i. . . . . .

Power Quality Indices

• PQ Indices are mathematical expression used for quantitative analysis of any signal

• iRMS

• Instantaneous Frequency Variation

• Instantaneous Normalized Distortion Energy Index

2

1

1( ) ( , )2

N

rmsi

X n IA i n

1

1

( , )

( , )

N

ii

N

i

IA i n fiFV

IA i n

2[{ ( , )} ]2

2[{ ( , )} ]1

kA n fiiiNDEI

kA n fii

[10] Y. J. Shin, E. J. Powers, M. Grady, Ari Arapostathis, Power quality indices for transient disturbances, IEEE Trans. Power Del. 21 (1) (2006) 253-261.

Cont..

• Instantaneous Total Harmonic Distortion

• Instantaneous K-Factor

• Instantaneous Form Factor

21

2

1

[{ ( , )} ]

( , )

k

hA n hf

iTHDA n f

2

1

1

{( ) ( , )}

( , )

k

Ni ii

k

ii

A n fiK

A n f

50

iNi

f

1

2 ( , )n

ii

iRMSiFFA n f

[11] M. Biswal, P. K. Dash, Estimation of time-varying power quality indices with an adaptive window-based fast generalised S-transform, IET Sci. Meas. & Tech. 6 (4) (2012) 189-197. [12] Naik, Chirag, and Pratim Kundu. "New Power Quality indices based on S-transform for non-stationary signals." In Power and Energy (PECon), 2012 IEEE International Conference on, pp. 677-682. IEEE, 2012.

Results and Discussion

Signal analysis using GEWT and Fast S Transform

Sag signal Swell signal

Cont….

Harmonics and Interharmonics

Cont..

Transient signal

Cont..

Flicker signal

Conclusion

From the comparison between FST and GEWT in terms of various PQ indices we can say GEWT detects disturbance start time,end time,duration of existence and its content more accurately hence it is better than FST

Research Paper

• K. Thirumala, Shantanu, T. Jain and A. C. Umarikar, “Visualizing Time Varying Power Quality Indices using Generalized Empirical Wavelet Transform,” Electr. Pow. Syst. Res., (in communication).

References1. R. C. Dugan, M. F. McGranaghan and et al, Electrical Power Systems Quality, McGraw-Hill

Education, New York, USA, 2012.2. S. L. Hahn, Hilbert transforms in Signal Processing, Artech House, London, 1996.3. J. Gilles, G. Tran, S. Osher, 2d Empirical Transforms. Wavelets, ridgelets, and curvelets revisited,

SIAM J. Imaging Sci., 7 (1) (2014), 157–186.4. Stockwell, R.G., Mansinha, L., Lowe, R.P.: ‘Localization of the complex spectrum: the S-

transform’, IEEE Trans. Signal Process.,1996, 44, (4), pp. 998–10015. Wang, Yanwei, and Jeff Orchard. "Fast discrete orthonormal Stockwell transform." SIAM Journal

on Scientific Computing 31, no. 5 (2009): 4000-4012.6. S.K. Jain, S.N. Singh, Harmonics estimation in emerging power systems: key issues and

challenges, Electr. Power Syst. Res. 81 (9) (2011) 1754–1766.7. T. Yamada, High-Accuracy Estimations of Frequency, Amplitude, and Phase With a Modified DFT

for Asynchronous Sampling, IEEE Trans. Inst. Meas. 62 (6) (2013) 1428-1435.8. M. Islam, H. A. Mohammadpour, A. Ghaderi, C. W. Brice, Y. J. Shin, Time-Frequency-Based

Instantaneous Power Components for Transient Disturbances According to IEEE Standard 1459, IEEE Trans. Power Del. 30 (3) (2015) 1288-1297.

Thank you