Digital Signal Processing in Power System Protection and Control

333 Pages·2011·3.44 MB·English

by  Waldemar Rebizant

Signals and Communication Technology
For furthervolumes:
http://www.springer.com/series/4748

Waldemar Rebizant Janusz Szafran
•
Andrzej Wiszniewski
Digital Signal Processing
in Power System Protection
and Control
123
Prof.Waldemar Rebizant Prof.AndrzejWiszniewski
Wroclaw University ofTechnology Wroclaw University ofTechnology
Wybrzeze Wyspianskiego27 Wybrzeze Wyspianskiego27
50-370 Wroclaw 50-370 Wroclaw
Poland Poland
e-mail: [email protected] e-mail: [email protected]
Prof.JanuszSzafran
Wroclaw University ofTechnology
Wybrzeze Wyspianskiego27
50-370 Wroclaw
Poland
e-mail: [email protected]
ISSN 1860-4862
ISBN 978-0-85729-801-0 e-ISBN978-0-85729-802-7
DOI 10.1007/978-0-85729-802-7
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Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Abnormal States in Power Systems and Criteria
for Their Recognition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Faults and Abnormal Phenomena in Power Networks. . . . . . . 4
2.3 Criteria Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Requirements for Protective Devices. . . . . . . . . . . . . . . . . . . 7
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Hardware and Functional Development of Protection
Devices and Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1 Protection Generations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Functional Blocks of a Digital Protection Device. . . . . . . . . . 17
3.2.1 Analog Antialiasing Filtering. . . . . . . . . . . . . . . . . . 17
3.2.2 Sampling Process and A/D Conversion. . . . . . . . . . . 19
3.2.3 Digital Signal Processing. . . . . . . . . . . . . . . . . . . . . 23
3.3 Hierarchical Structure of Protection and Control . . . . . . . . . . 24
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Fundamentals of System Analysis and Synthesis . . . . . . . . . . . . . 29
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Fourier Series. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3 Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4 Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.5 Z Transform for Sampled Data Signals and Systems. . . . . . . . 38
4.6 Fourier Transform of Sampled Data . . . . . . . . . . . . . . . . . . . 41
4.7 Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.8 Description of Discrete Dynamic Systems in Time
and Frequency Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
v
vi Contents
4.8.1 Description of Discrete Systems in Time Domain . . . 45
4.8.2 Discrete System Description in Frequency Domain. . . 48
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5 Infinite Impulse Response Filters. . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1 IIR Filter Fundamentals. . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2 Synthesis of IIR Filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2.1 Application of Bilinear Transformation. . . . . . . . . . . 55
5.2.2 Application of Impulse Response
Invariance Method . . . . . . . . . . . . . . . . . . . . . . . . . 60
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6 Finite Impulse Response Filters. . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.1 Finite Impulse Response Filter Fundamentals. . . . . . . . . . . . . 65
6.2 Analysis of Standard FIR Filters . . . . . . . . . . . . . . . . . . . . . 67
6.2.1 Filters with Walsh Windows . . . . . . . . . . . . . . . . . . 67
6.2.2 Filters with Sine and Cosine Windows . . . . . . . . . . . 75
6.3 Synthesis of FIR Filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.3.1 Application of Complex Fourier Series. . . . . . . . . . . 82
6.3.2 Application of Fast Fourier Transform . . . . . . . . . . . 87
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7 Correction of Errors Introduced by Instrument Transformers. . . 97
7.1 Correction of Voltage Transformers Performance. . . . . . . . . . 97
7.2 Correction of Current Transformer Errors . . . . . . . . . . . . . . . 98
7.2.1 Formulation of the Problem. . . . . . . . . . . . . . . . . . . 98
7.2.2 Detection of the Unsaturated Fragment
of the Waveshape. . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.2.3 Correction of the Secondary Current. . . . . . . . . . . . . 102
7.2.4 Other Methods of CT Saturation Detection
and Secondary Current Reconstruction . . . . . . . . . . . 106
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
8 Measurement Algorithms for Digital Protection. . . . . . . . . . . . . . 109
8.1 Fundamentals of Digital Measurements. . . . . . . . . . . . . . . . . 109
8.1.1 Digital Signal Conditioning. . . . . . . . . . . . . . . . . . . 110
8.1.2 Averaging Measurement Methods. . . . . . . . . . . . . . . 122
8.1.3 Measurement with Use of Orthogonal
Components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
8.2 Measurement of Protection Criterion Values . . . . . . . . . . . . . 130
8.2.1 Measurement of Magnitude of Voltage or Current . . . 131
8.2.2 Measurement of Power . . . . . . . . . . . . . . . . . . . . . . 135
8.2.3 Measurement of Impedance and Its Components . . . . 139
8.2.4 Phase and Phase Shift Measurement. . . . . . . . . . . . . 149
Contents vii
8.2.5 Measurement of Frequency . . . . . . . . . . . . . . . . . . . 152
8.2.6 Filtering of Symmetrical Components. . . . . . . . . . . . 161
8.3 Summary, Conclusions and Recommendations. . . . . . . . . . . . 164
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
9 Characteristics of Measurement of Criterion Values
and Adaptive Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
9.1 Dynamics of the Measurement Process. . . . . . . . . . . . . . . . . 169
9.2 Dynamical Correction of Measurement of Criterion Values. . . 176
9.3 Frequency Characteristics of Measurement Algorithms. . . . . . 180
9.4 Adaptive Frequency Insensitive Estimators . . . . . . . . . . . . . . 190
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
10 Decision Making in Protective Relays . . . . . . . . . . . . . . . . . . . . . 199
10.1 Deterministic Decision Making . . . . . . . . . . . . . . . . . . . . . . 200
10.2 Statistical Hypotheses Testing . . . . . . . . . . . . . . . . . . . . . . . 203
10.3 Decision Making with Multiple Criteria . . . . . . . . . . . . . . . . 209
10.4 Adaptive Decision Schemes. . . . . . . . . . . . . . . . . . . . . . . . . 213
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
11 Elements of Fuzzy Logic in Protective Relays . . . . . . . . . . . . . . . 219
11.1 Fuzzy Sets and Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . 219
11.2 Boolean Versus Fuzzy Logic. . . . . . . . . . . . . . . . . . . . . . . . 228
11.3 Fuzzy Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
11.4 Fuzzy Logic Applications for Protection and Control . . . . . . . 237
11.4.1 Example of Fuzzy Logic Application
for Distance Protection . . . . . . . . . . . . . . . . . . . . . . 238
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
12 Application of Artificial Neural Networks . . . . . . . . . . . . . . . . . . 245
12.1 Neuron Models and Neural Network Structures . . . . . . . . . . . 246
12.2 ANN Design and Training Issues. . . . . . . . . . . . . . . . . . . . . 253
12.3 ANN Applications for Power System Protection . . . . . . . . . . 258
12.3.1 Example of ANN Application for CT Saturation
Detection and Compensation . . . . . . . . . . . . . . . . . . 259
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
13 Genetic and Evolutionary Algorithms for PSP. . . . . . . . . . . . . . . 271
13.1 Basics of Evolution and Genetics for Technical Problems. . . . 272
13.1.1 Selection Versions . . . . . . . . . . . . . . . . . . . . . . . . . 274
13.1.2 Emerging of the Next Generation. . . . . . . . . . . . . . . 276
13.2 Application Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
13.2.1 Optimization of the ANN Structure . . . . . . . . . . . . . 278
viii Contents
13.2.2 Optimal Selection of the Generator AVR Settings . . . 285
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
14 Expert Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
14.1 Components of an Expert System. . . . . . . . . . . . . . . . . . . . . 294
14.2 Knowledge Processing Methods. . . . . . . . . . . . . . . . . . . . . . 296
14.3 Designing of an Expert System . . . . . . . . . . . . . . . . . . . . . . 297
14.4 Expert System Applications. . . . . . . . . . . . . . . . . . . . . . . . . 299
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
15 Artificial Intelligence: Summary and Hybrid Schemes. . . . . . . . . 303
15.1 Comparison, Advantages and Disadvantages
of AI Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
15.2 Hybrid Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
15.2.1 Fused Hybrid Schemes . . . . . . . . . . . . . . . . . . . . . . 305
15.2.2 Cooperative Hybrid Schemes. . . . . . . . . . . . . . . . . . 308
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Symbols and Abbreviations
Symbols
a Complex rotation operator (by 2p/3)
a , a Coefficients of the orthogonal filters F , F with
c s c s
sine, cosine windows
a , b Constant factors in a difference equation
k k
nominator and denominator
a(k), b(k) Filter equation coefficients
a , b , a Coefficients of the Fourier series
n n 0
A Signal magnitude
A, A Fuzzy set and its complement
A(z), A(jX) Z and Fourier transfer functions of the sine
s s
window filter
A (z), A (jX) Z and Fourier transfer functions of the cosine
c c
window filter
A, B Probabilistic thresholds (SPRT test)
A, B, C Coefficients of the filter design procedure with
bilinear transformation
A , s Residuum values and poles of the transfer func-
k k
tion partial expansion
B Flux density value leading to CT saturation
s
B Maximal expected flux density level in the CT
max
core
c Coefficients of the complex Fourier series
n
C Capacitance
d A/D converter range resolution
d (n), d (n), d (n), d (n) Filter coefficients in transient state
CC SS SC CS
df/dt Rate offrequency change
D Range of possible values of the decision random
X
variable X
e(t), e(n) Error signal, continuous and discrete
ix