Term-paper presentation for the 9th Semester for my M.Tech Thesis

1. DETECTION OF POWER LINE DISTURBANCES
USING DSP TECHNIQUES
A Presentation by
KASHISH VERMA
Exam Roll No. 510615017
Guided by: Prof. Debjani Ganguly
DEPARTMENT OF ELECTRICAL ENGINEERING
INDIAN INSTITUTE OF ENGINEERING SCIENCE AND TECHNOLOGY, SHIBPUR
Howrah-711103, West Bengal, India
December, 2019
1

2. 2
RECAP
Simulink Model for The Test case

3. 3
Current and Voltage Waveforms
across the load
(a) Normal Operating Conditions
(b) Test Case

4. 4
DSP Techniques used and their Drawbacks:
 Prony Analysis: It is computationally expensive because solving a nonlinear least
squares problem is necessary. Besides, it is sensitive to noise.
 FFT Analysis: The estimation accuracy of FFT requires a very low computational effort
for stationary signals where properties do not change with time. For non-stationary
signals, these methods can’t track the signal’s dynamic change and suffer from spectral
leakage.
 SVD Analysis: It is more mathematically complicated than FFT, this limits SVD from
working in online systems, even though it improves the harmonic frequency estimation.
We’d also be using DSP Algorithms such as MUSIC and ESPIRIT because they have
high spatial resolution, are able to detect multiple sources and if the measurements match
our predictions (about nature of the spectrum), we get a more accurate representation of
the spectrum.

5. ROTOR DYNAMICS & THE SWING EQUATION
Swing equation for a synchronous generator :
J = Ta = Tm – Te
A modified version of which is
= Pa = Pm – Pe
Incorporating the incremental rotor angle variations in the swing equation, we get
+ δΔ = 0
The solutions of this equation represent sinusoidal oscillations, provided the synchronizing power
coefficient Sp is positive. The frequency of the undamped oscillations is given by
fn =
d2θm
dt2
d2δ
dt2
2H
ωs
d2δΔ
dt2
ωsSp
2H
1
2π
ωsSp
2H
√ 5

6. TRANSMISSION SYSTEM MODELLING IN SIMULINK
Variable Frequency Model
Mathematical representation of the oscillating system frequency:
foscillating = ffundamental + fΔ(t)
fΔ(t) = (Δfmax). cos (2п fnt)
function y = fcn(u,v,t)
y = u*sin(2*pi*(50+v)*t);
where v = 1.5*sin(4*pi*t)
Fig. 1: Simulink Function Generator Block 6

7. Fig. 2: Output Waveform
for the function generator
(Simulation time = 1
second)
Fig. 3: Output Waveform for
the function generator
(Simulation time = 0.5
seconds)
7

8. Triangle Function Generator
The following Simulink Block is designed to output a Triangular wave with amplitude 25 and
frequency 10 kHz.
Fig. 5: Simulink Block for Triangle Function Generator
Fig. 4: Output waveform for
the sample function
generator, i.e. when
v = 5*sin(4*pi*t)
8

9. Sinusoidal Pulse Width Modulation (SPWM)
Fig. 6: Generation of Gating Pulses
9

10. Fig. 7: Triggering of The 3-Phase IGBT Inverter
Fig. 8: SPWM Output
for our Model
10

11. Advantages of SPWM
 Low power consumption.
 High energy efficiency up to 90%.
 High power handling capability.
 No temperature variation and ageing caused drifting or degradation in linearity.
 Easy to implement and control.
 Compatible with today’s digital microprocessors.
Disadvantages of SPWM
 Attenuation of the desired fundamental component of the waveform.
 Drastically increased switching frequencies that leads to greater stress on associated
switching devices and therefore derating of those devices.
 Generation of high-frequency harmonic components.
11

12. The Equivalent Simulink Model
Fig. 9: Diagram of the Overall Model
• Here, Inverter-1 employs variable frequency triggering, whereas Inverter-2 employs constant frequency
triggering. 12

13. Simulation and Results
Generated Waveforms
Fig. 10: Transmission Line Current
for Inverter-1
(a) Time of Simulation = 2
Seconds
(b) Time of Simulation = 0.5
seconds
13

14. Fig. 11: Transmission Line
Voltage for Inverter-1
(a) Time of Simulation = 2
Seconds
(b) Time of Simulation = 0.5
seconds
14

15. Fig. 12: Load Current Waveform
(a) Time of Simulation = 2
Seconds
(b) Time of Simulation = 0.5
Seconds
15

16. Fig. 13: Voltage across the load
(a) Time of Simulation = 2
Seconds
(b) Time of Simulation = 0.5
Seconds
16

17. Comparison between the Test case and normal operating
condition waveforms:
Fig. 14: (a) Both Inverters at different frequencies (Test Condition)
(b) Both Inverters at same (constant 50 Hz) frequency
17

18. Frequency Response for The Test Case (FFT)
Fig. 15: FFT Analysis through the In-Built Simulink Block
18

19. Ia Ib Ic
Frequency
(Hz)
Amplitude
(FFT)
Amplitude
(Prony)
Frequency
(Hz)
Amplitude
(FFT)
Amplitude
(Prony)
Frequency
(Hz)
Amplitude
(FFT)
Amplitude
(Prony)
0 0.4327 0.222 0 0.252 2.917 0 0.18 3.49
2.5 0.7736 0.4784 2.5 0.452 0.123 2.5 0.324 0.204
5 0.613 0.651 5 0.36 0.035 5 0.261 0.225
7.5 0.4853 1.3903 7.5 0.289 0.129 7.5 0.212 0.646
10 0.39 2.5659 10 0.24 0.336 10 0.179 1.12
12.5 0.3377 0.7856 12.5 2.078 1.091 12.5 0.159 0.295
Ia Ib Ic
Frequency
(Hz)
Amplitude
(FFT)
Amplitude
(Prony)
Frequency
(Hz)
Amplitude
(FFT)
Amplitude
(Prony)
Frequency
(Hz)
Amplitude
(FFT)
Amplitude
(Prony)
0 0.35 1.02 0 0.179 0.129 0 0.17 3.046
2 0.65 0.163 2 0.333 0.714 2 0.317 0.828
4 0.54 0.383 4 0.279 0.431 4 0.266 1.24
6 0.44 0.438 6 0.228 0.224 6 0.217 0.556
8 0.37 0.42 8 0.189 0.270 8 0.18 0.884
10 0.31 1.003 10 0.160 0.102 10 0.152 0.776
Frequency Estimates & their Magnitudes (FFT Analysis vs. Prony Analysis)
Table 1: Comparison between Prony Analysis and FFT Analysis (Sampling Window: 10 ms)
Table 2: Comparison between Prony Analysis and FFT Analysis (Sampling Window: 20 ms)19

20. Frequency Estimates obtained through MUSIC and ESPIRIT Algorithms
Sl. No.
Frequency estimates from
MUSIC Algorithm (Hz)
Frequency estimates
from ESPIRIT Algorithm
(Hz)
1 0 0
2 0.578571939 -0.37321
3 -0.578571939 0.37321
4 1.157508431 -0.9645
5 -1.157508431 0.9645
6 4.934802201 -1.18078
7 -4.934802201 1.18078
8 4.382832398 -1.4951
9 -4.382832398 1.495097
10 2.251339973 -2.18089
11 -2.251339973 2.180893
12 1.705913185 -2.60515
13 -1.705913185 2.60515
14 2.787244682 -3.17851
15 -2.787244682 3.17851
16 3.813788834 -3.46796
17 -3.813788834 3.46796
18 3.322110376 -4.63649
19 -3.322110376 4.63649
20 0 -4.9348
Table 3: An Independent set of Data for Frequency Estimates
obtained through both of these Algorithms
20

21. METHODS OF DIGITAL SIGNAL PROCESSING
Some Basic Terminologies:
 AR (Auto regressive) model: The autoregressive model specifies that the output variable
depends linearly on its own previous values and on a stochastic term (a variable whose
value depends on outcomes of a random phenomenon).
The AR(p) model is defined as
Xt = c + 𝑖=1
𝑝
𝜑i Xt-i + εt
 MA (Moving Average) Model: The moving-average model specifies that the output
variable depends linearly on the current and various past values of a stochastic (imperfectly
predictable) term.
The MA(q) model is defined as
Xt = μ + εt + 𝑖=1
𝑝
𝜃iεt-i
 An ARMA Model combines these two. Given a time series of data Xt , the ARMA model is
a tool for understanding and, perhaps, predicting future values in this series. The AR part
involves regressing the variable on its own lagged (i.e., past) values. The MA part involves
modelling the error term as a linear combination of error terms occurring at various times in
the past.
21

22. Multiple Signal Classification (MUSIC)
22
Steps to Calculate Spectral Peaks:
I. Define A Harmonic Signal for a power system, x(n).
II. Convert this signal into a complex frequency signal, x(n).
III. Write a Covariance Function of x(n).
IV. Write a P*P array covariance matrix, R. According to the hypothesis condition and the
properties of the Toeplitz matrix, we can get rank (R) = M, where M is the order of the
harmonic.
V. Eigen-decomposition of the covariance matrix R will contain the signal-space and noise-
subspace eigenvectors.
VI. Steering Vector is obtained.
VII. Based on the orthogonal characteristics of the noise subspace and steering vector, we obtain
the pseudo power Spectrum PMUSIC. The harmonic frequencies can be estimated from this
power Spectrum.
MATLAB Code is given in Appendix – 1.

23. 23
Pros Cons
Unlike DFT, it is able to estimate frequencies
with accuracy higher than one sample because
its estimation function can be evaluated for
any frequency, not just those of DFT bias.
It requires no. of components to be known in
advance.
MUSIC is preferred over other methods when
the no. of components is known in advance,
because it exploits the knowledge of this no.
to ignore the noise in its final report.
MUSIC assumes coexistent sources to be
uncorrelated.
MUSIC requires high computational cost (for
searching over parameter space).
It requires matrix decomposition, which is a
huge computational burden and thus isn’t
suitable for real-time application.
Bias and sensitivity in parameter estimates
(primarily because they use an incorrect
model AR instead of ARMA).

24. 24
Estimation of Signal Parameters via Rotational Invariance Technique (ESPIRIT)
Steps to Calculate Spectral Peaks:
I. Consider a vector of observations of x[n], i.e. x of order N.
II. Now we partition this vector as follows:
A2 = First (N-1) rows of x; and
A1 = Last (N-1) rows of x
III. Let R be the covariance matrix for the given system. The eigenvalue decomposition of R (using
State Value Decomposition) gives us the U, E and V* matrices.
IV. For eigenvalues greater than the variance of noise, we separate orthonormal eigenvectors from U
corresponding to these eigenvalues. This gives us a matrix S, defined as S = first N columns of
the U Matrix.
V. Again, we partition this vector as S1 and S2, same as that in Step II. To accommodate the
rotational info, we define a matrix F such that S1 = A1 F. This gives us S2 = S1 P. The P matrix
contains rotational information with respect to frequency contents such that the rotation on the
first set of orthonormal eigenvectors yield the second set.
VI. Solving S2 = S1 P, we get the frequency estimates as P = (S1 * S1)-1 S1 * S2.
MATLAB Code is given in APPENDIX – 2.

25. 25
POWER LINE DISTURBANCES & RELAYING
 Numerical Distance relays : Based on numerical (digital) devices e.g. microprocessors,
microcontrollers, digital signal processors (DSPs) etc.
 As the microprocessor requires computationally simple and fast algorithm in order to
perform the relaying functions, not all methods are suitable for microprocessor
implementation.
Mann – Morrison Algorithm
I. The Mann Morrison Algorithm works on a three sample window.
II. The voltage and current waveforms are assumed to be pure sinusoids and are defined
as v & i respectively.
III. Their first derivative v’and i’can be approximated by the difference between the two
samples on either side of the central sample point k.
IV. The peak magnitude (modulus) and phase angle (argument) of the voltage and current
signals are found in terms of v,v’ and i, i’at an arbitrary sampling instant k.
V. The phase difference φ between voltage and current is calculated.
VI. The line impedance from the relay location to the fault point is calculated.

26. 26
LabView Model for Mann-Morrison Technique
Fig. 16: LabView Model

27. 27
Pros Cons
This algorithm has a fast response due
to a three sample window.
It does not recognise the possible
existence of an exponentially decaying
dc offset or of higher harmonics in the
incoming signal.
The accuracy of this method is not
good since it assumes voltage and
current waveforms to be sinusoidal.

28. 28
Other Possibilities in Detection of Power Line Disturbances
1. Short duration fault clearance using Prony Method : Correct results are obtained if the
dominant mode is close to ±5% from the fundamental mode.
2. Moving Window Prony Method : A modification in the traditional Prony Method, which
can take advantage of the calculation result in the previous step without calculating from
scratch when a new sampling point comes.
 Moving Window method eliminates the time-consuming pseudo inverse, which constrains
prony in an area of off-line application. It works through economic SVD.
Pros Cons
Feasible for detection of oscillations
and online tracking.
Not all modes are tracked (Low rank
Modification method is used).
Effective rank is assumed to be
constant during Updating and
Downdating.
Further precautions should be taken
for Adaptive Rank detection, Restart
Strategy and error Analysis.

29. 29
3. An Improved Least Square Error Algorithm for Digital Relaying
 This algorithm is used with the goal of estimating the magnitude and phase of both
fundamental and harmonic elements of the fault current signal.
 The decaying dc component is one of the major reasons which causes mal operation,
especially in distance relays.
 This method described below accurately estimates the decaying dc component and
eliminates it by subtracting the dc value from fault current signal after one cycle from the
fault instant.
 The biggest advantage this method has over conventional algorithms is its less
computational burden and its accuracy. This method takes only one cycle plus one additional
sample to estimate the phasors.

30. 30
Fault Detection during Power Swings
 The Prony method: Current waveform components are calculated using Prony method. If the
decaying dc amplitude is among the two first biggest amplitudes for three successive
windows, three-phase fault is said to have happened and the relay should be unblocked.
 Wavelet transform: Based on the presence of high frequency signal components created at the
inception of the fault. The implementation needs high frequency sampling.
 An adaptive neuro-fuzzy inference systems (ANFIS) based method: A huge number of
training patterns required.
 For unsymmetrical faults, negative and zero sequence components are observed, which do not
exist during the stable power swing.
 For Single Phase, unsymmetrical faults, a method based on the monitoring of the voltage
phase angle at the relay location is proposed to discriminate fault from power swing.
 Magnitude of the swing-center voltage (SCV) is used to distinguish faults from power swing,
the drawback being that it is difficult to set the threshold, especially when a fault arc is
considered.

31. 31
FUTURE SCOPE OF WORK
 Detection of Power system faults during Power Swing: For methods
involving DSP (such as Moving Window Prony and Wavelet
Transform), we will be implementing appropriate Hardware for the test
case and verify the efficiency of the aforementioned algorithms.
 Effect of presence of harmonics and decaying dc components on
Traditional fault analysis: Moving window Prony method and an
improved Least Square Error Algorithm can be tested by generating a
controllable decaying dc component and thereby eliminating it.

32. 32
REFERENCES
[1] John J. Grainger, William D. Stevenson, Jr., Power System Analysis, ISBN 0-07-113338-0, International Edition
1994, p695-707
[2] Central Electricity Regulatory Commission New Delhi, GRID SECURITY – NEED FOR TIGHTENING OF
FREQUENCY BAND & OTHER MEASURES, CERC STAFF PAPER March 2011
[2] ShahrokhValaee, Peter Kabal, An Information Theoretic Approach to Source
Enumeration in Array Signal Processing, IEEE Transactions on Signal Processing, Vol. 52, No. 5, May 2004
[3] L.A. Trujillo Guajardo, Prony filter vs conventional filters for distance protection relays: An evaluation, Electric
Power Systems Research 137 (2016) 163–174
[4] Xiangwen Sun and Ligong Sun, Harmonic Frequency Estimation Based on Modified-MUSIC Algorithm in Power
System, The Open Electrical & Electronic Engineering Journal, 2015, 9, 38-42
[5] Hamilton, James D. (James Douglas), 1954- (1994). Time series analysis. Princeton, N.J.: Princeton University
Press. ISBN 0691042896. OCLC 28257560.
[6] Faraz Zafar Khan, R. Nagaraja and H. P. Khincha, Improved Fault Location Computation using Prony Analysis for
Short Duration Fault,
[9] Saeed Lotfifard, Jawad Faiz and Mladen Kezunovic, Detection of Symmetrical Faults by Distance Relays During
Power Swings, IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 1, JANUARY 2010
[10] Babak Jafarpisheh, Seyed M. Madani, An Improved Least Square Error Algorithm for Digital Relaying,
Conference Paper · January 2016
[11] Faraz Zafar Khan, R. Nagaraja and H. P. Khincha, Improved Fault Location Computation using Prony Analysis for
Short Duration Fault
[12] IEEE Std C37.114-2004, “IEEE Guide for Determining Fault Location on AC Transmission and Distribution
Lines", 2005

33. 33
[13] Babak Jafarpisheh, S. Mohammad Madani, Siamak Jafarpisheh, An Improved Least Square Error Algorithm for
Digital Relaying
[14] B. Su, X. Z. Dong, Z. Q. Bo, Y. Z. Sun, B. R. J. Caunce, D. Tholomier, and A. Apostolov, “Fast detector of
symmetrical fault during power swing for distance relay,” in Proc. Power Eng. Soc. General Meeting, San Francisco, CA,
Jun. 2005, vol. 2, pp. 1836–841.
[15] G. Benmouyal, D. Hou, and D. Tziouvaras, “Zero-setting power-swing blocking protection,” presented at the 31st
Annu. Western Protective Relay Conf., Spokane, WA, Oct. 2004.
[16] A. Mechraoui and D. W. P. Thomas,“A new blocking principle with phase and earth fault detection during fast power
swings for distance protection,” IEEE Trans. Power. Del., vol. 10, no. 3, pp. 1242–1248, Jul. 1995.
[17] A. Mechraoui and D. W. P. Thomas,“A new principle for high resistance earth fault detection during fast power
swings for distance protection,” IEEE Trans. Power. Del., vol. 12, no. 4, pp. 1452–1457, Oct. 1997.
[18] S. M. Brahma, “Distance relay with out-of-step blocking function using wavelet transform,” IEEE Trans. Power.
Del., vol. 22, no. 3, pp. 1360–1366, Jul. 2007.
[19] H. K. Zadeh and Z. Li, “A novel power swing blocking scheme using adaptive neuro-fuzzy inference system,”
Electric Power Syst. Res., vol. 78, pp. 1138–1146, 2008.
[20] H. K. Zadeh and Z. Li, “A novel power swing blocking scheme using adaptive neuro-fuzzy inference system,”
Electric Power Syst. Res., vol. 78, pp. 1138–1146, 2008.
[21] J. Faiz and S. Lotfi-Fard, “A novel wavelet-based algorithm for discrimination of internal faults from magnetizing
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[22] Julius Kusuma, Parametric Frequency Estimation: ESPIRIT and MUSIC, Article, June 2002
[23] N. Zhang and M. Kezunovic, “Transmission line boundary protection using wavelet transform and neural network,”
IEEE Trans. Power. Del., vol. 22, no. 2, pp. 859–869, Apr. 2007.

34. APPENDIX -1
MATLAB code for MUSIC
% w = music(y,n,m);
% y = the data vector
% n = the model order
% m = the order of the covariance matrix
% w = the frequency estimates
y=y(:);
n=length(y); % data length
m = % assign the order of correlation matrix
R = corrmtx(y,m,'covariance'); % correlation matrix
[U,D,V]=svd(R); % Getting the Eigen decomposition of R; we
use SVD because it sorts eigenvalues
G=U(:,m+1:n);
GG = G*G';
for j=-(m-1):(m-1) % coefficients of the polynomial
a(j+m) = sum( diag(GG,j) );
end
34

35. % finding the n roots of the a polynomial that are nearest and inside the unit
circle
ra=roots([a]);
rb=ra(abs(ra)<1);
% picking n roots that are closest to the unit circle
[dumm,I]=sort(abs(abs(rb)-1));
% [Y,I] = sort(___) shows the indices that each element of Y had, in the
original vector or matrix X.
w=angle(rb(I(1:n)));
f = w/2*pi;
35

36. 36
APPENDIX - 2
MATLAB code for ESPIRIT
% w = esprit(y,n,m);
% y = the data vector
% n = the model order
% m = the order of the covariance matrix
% w = the frequency estimates
y=y(:);
N=length(y); % data length
m = % assign the order of correlation matrix
R = corrmtx(y,m,'covariance'); % correlation matrix
% Geting the eigendecomposition of R; we use svd because it sorts eigenvalues
[U,D,V]=svd(R);
S=U(:,1:m+1);
phi = S(1:m-1,:)S(2:m,:); % assign vector phi
w=-angle(eig(phi));
f = w/2*pi;

37. 37
APPENDIX - 3
MATLAB Code for Prony Analysis
load('Data001.mat'); % load data
A = Data001;
T = 0.001; % sampling time
m = 300; % assign the values of m and n
n = 200;
for i= 1:n
for j = 1:m
B(j,i) = A(n-i+j);
end
end
% d matrix ranges from n+1 to N. Here N is the no. of Samples such that N =
m+n and N>2n
d = A(n+1:m+n);
a = pinv(B)*d; % pseudoinverse
z = roots([1;-a]);

38. 38
for i = 1:n
for j = 1:(m+n)
U(j,i) = power(z(i),j-1);
end
end
C = pinv(U)*A;
f = atan(imag(z)./real(z))*(1/(2*pi*T)); % frequency
sigma = log(abs(z))/T; % damping ratio
amplitude = 2*abs(C); % amplitude
phi = atan(imag(C)./real(C))*(180/pi); % phase angle

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THANK YOU!