a thyristor controlled regulating transformer
DESCRIPTION
State Space Approach of modelling the regulating TransformerTRANSCRIPT
A THYRISTOR-CONTROLLED
A
presented for
ING TRANSFORMER
Doctor of Philosophy in Electrical Engineering
in the
University of
Christchurch, New Zealand.
RGM* DUKE B Sc., BGE. ( ), M.E.
1979
One goes to school not for knowledge so much as for
arts and habits: for the habit of attention, for the art
of expression; for the habit of submitting to censure and
refutation, for the art of indicating assent or dissent in
graduated terms; for the habit of regarding minute points
of accuracy, for the art of assuming at a moment's notice
a new intellectual posture, of ent~ring into another
person's thoughts quickly; for taste, for dissemination,
for mental soberness; above all, for self-knowledge.
William Johnson, Eton Master, 1867
TABLE OF
List of Illustrations
List
Glossary
Abstract
Acknowledgements
CHAPTER 1: INTRODUCTION
CHAPTER 2: THE PROPOSED CIRCUIT
2.1 In-Phase Boosting and Bucking
2.1.1 Operation of the Voltage Booster
2.'.2 Operation the Voltage Bucker
ii
ii
xv xvi
xxiv xxv
1
5
5
6
8
2.2 Proposed Quadrature Boosting and Bucking 11
2.3 Thyristor Gate Pulse Requirements 26
2.3.1 Gate Pulse Requirements for Booster Circuit
2.3.2 Gate Pulse Requirements Bucker Circuit
2.4 Use a Three-Phase Three-Winding
CHAPTER 3 THE
3.1 Gate
3 1 1
3 1.2
3.1.2.1
3 1.2.2
3 1 2.3
UNIT
led Thyristors
Booster
Operation
26
27
27
29
30
1
31
33
36
3 2
CHAPTER 4 THE MATHEMATICAL MODEL
4.1 Component Representation
4.1.1 The A.C. System
4.1.2 Thyristors
4.1.3 Transformers
4.1.4 Transmission
4.2 Method Analysis
4.3 Electric Network Relationships
4.3.1 Node Segregation
4.3.2 Branch Equations
4.3.2.1 Resistive Branches
4.3.2.2 Inductive Branches
i i
48
49
49
50
52
54
55
56
57
58
58
4.3.3 Voltage and Current Relationships 59
4.3.4 State-Space Formulation 61
4.4 Solution of Electric Network Equations 62
4.4.1 Implicit Integration of the State Vector
4.4.2 Change of State Variab Integration
4 5 Disconti
CHAPTER 5: THE COMPUTER PROG&~MME
5. 1 Data Input Equations
Network
5.1 1 Input
5.1 1.1 Data
5 1.1 2 Control Data
5 1.1.3 In Data
62
63
63
65
67
67
68
68
69
5 1.2
5.1 2.1
5.1.2.2
5.2 Modification
Renurnbering
Network
5.2.1 Determination of Variables for Thyristor Model
5.2.1.1 Determination of Thyristor Currents
5.2.1.2 Thyristor Turn OFF
5.2.1.3 Thyristor Turn ON
5.2.2 Topological Changes
s
5.3 Determination Integration Step-Length
5.4 Solution the Network Equations
5.5 Output
CHAPTER 6: DIGITAL MODEL PERFORMANCE
6.1 Initial Conditions
6.2 Validation of Harmonic Analysis
6.3 Validation of Transformer Model
6.3.1 Measurement Transformer Parameters
6.3.2 Dynamic Simulation B 25 kVA Trans
6.3.2.1
6.3.2.2
6.3.2.3
6 3.3 ion
CHAPTER 7: VOLTAGE REGULATION
Connection
7.1 of Existing Tap-Changing
70
70
72
72
74
75
77
79
83
86
86
89
91
97
101
101
'103
'10 I!,
107
107
112;
'114
7 2
7.2 1
7.2.1.1 Load
Fixed-Tap Changer
7.2.1.2 Harmonic Content
7.2.2 Voltage Bucking
7.2.2.1 Load voltage Regulation
7.2.2.2 Harmonic Content
7.3 Computer Simulation A c Alternative
v
'j 16
118
120
121
'128
131
133
to the Transformer On-Load Tap-Changer 137
7.4 Discussion 139
7.4.1 A Combined Voltage Boosting and Bucking Unit 1
CHAPTER 8: POWER TRANSFER ' CONTROL 143
8.1 Quadrature Boosting with Thyristor-Controlled Voltage Regulator 144
8.1.2 Case (a) - Mode (i) Operation 147
8.1.2.1 Harmonic Content 151
8.1.2.2 Fundamental Voltage Vari 155
8.1.3 Case (b) - Mode (iii) Operation 156
8 1.3.1 Harmonic Content
9.1.3.2 Fundamental
8.1.4 Trans
8 2
8.3 ion
CHAPTER 9: TRANSIENT STABILITY IMPROVEMENT
9.1
9.2 lizing Quadrature Vol
1
1
16
'164
168
1
173
173
'177
9 3
9.2 1 tem Damping Improvement
9 3" 1 Two ity
90301 1 Trans
179
18
18
Improvement 183
9.301.2 System Damping Improvement 184
9.4 Conclusions 186
CHAPTER 10: CONCLUSIONS 187
REFERENCES 192
APPENDICES
1 : G.E.C.R. FIRING CIRCUIT 195
2: G.E.C.R. FIRING CIRCUIT CALIBRATION 196
3: CONVENTIONAL PULSE TRANSFORMER '199
4: "MICRONE" PULSE TRANSFORMER 200
5: TRANSFORMER PARAMETERS 201
AS.1 8 25 kVA Transformer 201
AS.2 Series Transformer 202
6: MATHEMATICAL MODEL - INCLUDING CAPACITORS 203
A6.1
A602
A6 3
A6 5
A6 6
Network Relationships
Node Segregation
CUrrent
State~
Solut of Network Equations
.601 Implic the
.6.2
.6 3 Change State s
20
204
205
20
20B
211
211
214
215
i
7: LINEAR INTERPOLATION 216
8: FOURIER 218
9: THE RESPONSE OF A CURRENT TRANSFORMER TO FREQUENCIES OTHER THAN 50 Hz 219
A9.1 Harmonic Frequency Error 219
.2 Transformation Accuracy a Compo Waveform 224
10: VOLTAGE HARMONICS ON THE 400 V SUPPLY BUSBAR 226
11: A STATIC ALTERNATIVE TO THE TRANSFORMER ON-LOAD TAP-CHANGER 231
12: D.C. MOTOR-DRIVEN SINE WAVE ALTERNATOR SET 237
13: THYRISTOR-CONTROLLED QUADRATURE BOOSTING 238
14: TRANSIENT STABILITY STUDY SYSTEM PARAMETERS 244
1.1
2.1
2.2
2.3
2 4
2.5
2.6
2.7
2.8
2.9
2.10
2. 11
2.12
2.13
2.14
2.15
2.16
3.1
3 2
3.3
3 4
3.5
3 6
LIST OF ILLUSTRATIONS
Simple Thyristor~Control
Basic Voltage Booster
Theoretical Waveforms ~ Voltage Boost
Theoretical Waveforms - In-Phase Voltage Buck
Basic Quadrature Voltage Booster
Theoretical Waveforms - Mode (i)
Theoretical Waveforms - Mode (ii)
Theoretical Waveforms - Mode (iii)
Theoretical Waveforms - Mode (iv)
Theoretical Waveforms - Mode (v)
Theoretical Waveforms - Mode (vi)
Theoretical Waveforms - Mode (vii)
Theoretical Waveforms - Mode (vi
Mode (i) Operation with Lagging Quadrature Voltage
Mode (v) Operation with Lagging Quadrature Voltage
In-Phase Voltage Booster
Quadrature Booster
Booster Operation Logic
Booster Logic
Bucker Operation Logic
IIMicrone li e Transformer Output
ii
2
6
7
10
1 1
13
14
15
16
17
18
19
20
22
23
28
28
30
32
34
35
37
38
F
3~7(a) The Thyri Voltage Regulator - Front View
3.7(b) The Thyristor-Controlled Voltage Regulator Rear View
3.8 Boost/Buck Switch Connections
3.9
4. 1
4,2
4.3
4.4
4.5
4.6
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
6 1
6.2
6.3
6.4
6 5
6.6
6.7
6 8
Firing Ang Delay Against Helipot Reading
Simple A.C. System Representation
Alternative A.C. System Representation
Three-Wind Transformer
Per Transmission Line Representation
Resist Branch
Inductive Branch
General Flow Diagram
Control of Thyristor Switching
Two Back-to-Back Thyristor Switches
Determination of istor Currents
Determination Thyristor Turn OFF
Effect of Changing KYl
Integration Step-Length Determination
Solution of Network Equations
Single Line Diagram of Case (a) Circuit
Case (a) Initial Condit
Case (b) Initial Conditions
In~Phase Voltage Booster
Thyristor Switching Initial Conditions
Test Waveform
i Spectrum of Test Waveform
Spectrum Test Waveform
40
41
43
44
50
50
52
55
58
59
66
73
74
76
78
84
85
87
91
93
94
95
96
98
100
100
6 9
6.10
6. 11
6.12
6.13
6.14
6.15
7. 1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7. 11
7.12
7.13
7.14
Two-Winding Trans
Star/Delta/Star Voltages
Star/Delta/Star Currents
Node
Star/Delta/Delta Voltages
Winding
Proposed On-Load Fixed-Tap Variable Voltage Changer
Oscillograms of Typical Supply and Load Voltages and Currents
Oscillograms of Typical Voltage VT and Transformer Currents
Oscillogram of Typical Load Voltage
Load Voltage Variation
(a) Voltage Regulation (per cent)
(b) Phase Shift Fundamental (degrees)
Supply Voltage (VS ) Spectrum (0.4 V/em)
Supply Current (IS) Spectrum (0.1 A/cm)
Load Voltage (VL
) Spectrum (2.0 V/cm)
Load Current (IL) Spectrum (0.1 A/em)
Voltage Across
Maximum
Winding of (V
T) (4 0 V/cm)
Winding (0.4 A/cm)
Content at Supply
Maximum Harmonic content at Load Busbar
Maximum Harmonic Content Terti Winding Current
7 15" Supply Vol (VS ) Spectrum (0.4 V/cm)
101
105
106
108
109
110
111
116
119
119
120
12 'I
122
122
'122
123
'12
"123
124
125
126
126
7.16
7 17
7.18
7.19
7.20
7.21
7 22
(0 1 A/cm)
Typical Supply
Oscillograms and Current
Typical
Oscillograms Typical Voltage VT and Transformer Currents
Oscillograrns of Typical Three~Phase Load Voltages
Load Voltage Variation
(a) Voltage' regulation (per cent)
(b) Phase Shift of Fundamental (degrees)
Line-to-Line Supply Voltage (VS
) Spectrum (0.4 V/cm)
127
129
129
130
131
132
133
7.23 Line Supply Current Spectrum (0.08 A/cm) 133
7.24 Delta Winding Current ( Spectrum (0.08 A/cm) 134
7.25
7.26
7.27
7.28
7.29
7.30
7 31
7.32
7.33
8. 1
8.2
8 3
Load Voltage (VL) Spectrum (2.0 V/cm)
Load.Current (IL) Spectrum (0.08 A/cm)
Voltage Across Secondary Winding of Series Transformer (VT ) Spectrum (4.0 V/cm)
Current in Tertiary Winding of Transformer T1 (IT) Spectrum (0 16 A/cm)
Maximum Harmonic Content at Supply Busbar
Maximum Harmonic Content at Load Busbar
Maximum Content Supply Load Currents
Comb Boosting Bucking Unit
Voltage Bucking with Combined Unit
Single-Line Diagram of a Transmission System with Thyristor-Controlled Quadrature Boosting
(a) Vector Relationships
Case (b) Vector Relationships
134
134
135
135
136
136
'I 8
140
142
145
146
8 4
8 5
8.6
8.7
8.8
8.9
8.10
8 11
8.12
8.13
8.14
8.15
8.16
8.17
8.18
8. 19
8.20
B. 1
8.22
8.23
8.24
8 25
8.26"
Typical Series Trans Voltage and Currents
Oscillogram of Typical Booster Vol
Oscillograms Typical Three-Phase Booster Busbar Voltages
Supply Voltage (VM) Spectrum (0.8 V/cm)
Supply (IM
) Spectrum (0.04 A/cm)
Booster Busbar Voltage (VL
) Spectrum (2.0 V/cm)
Transmission Line Current (IL) Spectrum (0.016 A/cm)
Alternator Voltage (VG) Spectrum (O 2 V/cm)
Alternator Current (IG
) Spectrum (0.016 A/cm)
Maximum Harmonic Content at Supply
Maximum Harmonic Content at Booster Busbar
Maximum Harmonic Content at Alternator Busbar
Booster Busbar Voltage Magnitude Variation
Phase Angle Difference (8) Variation
Oscillograms of Typical Volt and Line Current
Oscillograms of Typical Voltage Currents
Booster Va
Supply Voltage (VM
) (0.0 V/cm)
Supply (IM
) (0 04 A/cm)
Booster (VL
) (2.0 V/em)
sion Line Current (IL
) (0.016 A/em)
148
149
150
150
151
152
15
152
153
153
15
154
154
155
156
157
158
'15
"'5
160
160
160
161
8 27
8 28
8
8 30
8.31
8.32
8.33
8.34
8.35
8.36
8.37
9.1
9.2
9.3
9.4
9.5
9.6
10. 1
1
.2
.3
• 1
A7.1
• 1
.2
(V G) {O 2 V/cm}
Current (IG
) (0 016 A/cm)
Maximum Harmonic at Supply
Maximum at Booster Busbar
Maximum Harmonic Content at
Booster Voltage Magnitude Variation
Phase Angle Di (9) Variation
Mode (i) Active Power Trans Variation
Mode (i ) Active Power Trans Variation
Reactive Power Transfer Variation
(a) Mode (i) Operation
(b) Mode (iii) Operation
Combined Quadrature Booster/Bucker
Quadrature Voltage Injection Circuit
Quadrature Voltage Injection
Power-Angle Curve Showing Improvement in Swing Stability with 20° Quadrature Boosting
Power-Angle Curve Showing the Maximum Possible Improvement in First Swing Stability with 20° Quadrature Bucking and Boosting
Power-Angle Curve Showing Method of Damping Improvement
Swing Curves Booster/Bucker Setting Angle
Four Quadrant ing Trans
of Start
Start ses
control
Rat Error Test C
2 1 Error Test Full Current
ii
161
162
162
162
163
163
16 Lj,
165
166
167
171
174
176
178
179
181
185
19 '1
'19
197
198
205
216
220
222
A9.3
.4
A905
A906
.7
A 1001
A10.2
A10.3
A10.4
A10.5
A10.6
A10.7
A10.8
2 1 Error Test ~ 50% 1 Load Current
10 1 Ratio Error Test Full
Error Test - 50% Full
(a) 100 Hz IIChopped" Current Waveform
(b) Compos Current Waveform
Transformation Accuracy Results
Typic 3rd Harmonic Voltage Var
Typical 4 Harmonic Voltage Variation
Typical 5th Harmonic Voltage Variation
Typical 6th Harmonic Voltage Variation
Typical Harmonic Voltage Variation
Typical 8th Harmonic Voltage Variation
Typical 9th Harmonic Voltage Variation
Current
Typical 11 Harmonic Vol Variation
A10.9 Typical 13th Harmonic Voltage Variation
A10.10 Typical 17th Harmonic Voltage Variation
A10.11 Typical 19th Harmonic Voltage Variation
Page
222
223
223
225
225
225
227
227
227
228
228
228
228
229
229
229
229
Table
2 1
5. 1
5.2
5.3
5.4
5.5
5.6
5.7
6.1
6.2
6.3
6.4
8. 1
9.1
A5.1
A5.2
A10.1
LIST
Quadrature Voltage Operational Modes
Connection Matrix
Composite Connection
Modified Connection Matrix I
Modified Connection Matrix II
Modified Connection Matrix III
7 and 9 ON
KYI - 7 ON
Square Wave Coordinates
Star/Star/Star rms Voltages and Currents
Star/Delta/Star rms Voltages and Currents
Star/Delta/Delta rIDS Terminal Voltages
Quadrature Voltages and Thyristor Switches Necessary to Operate the Combined Quadrature Booster/Bucker
Fault Clearing Times
8.25 kVA Transformer Impedance Parameters
Transformer Impedance Parameters
and 400 V
xv
25
71
79
80
81
81
82
82
99
104
107
110
172
184
201
20
230
abbreviations
given belowe
A
a.c.
Aal
b n
B aa
c
C
Ccc
C n
cos
cos
C aa,
D
d co
d/dt
e
1
, the
this have the meanings
ampere
alternating current
ampere centimetre
audio frequency
auxiliary inductance matrix
Fourier
auxil alpha node
icient
inductance
discrete Four coefficient
auxiliary alpha node matr
number of capacitive
capacitance
branch capacitance matrix
rms value of each Four
cosine
cosine
auxiliary
nodes
matr
prior
of
a thyristor
rate change with re
in a network
component
to time
source of ectromotive force
vector e.m.f sources
e m.f
f(
G
g( }
G.E.C.R.
G a.r
h
HC
HR
HV
h.v.d.c.
Hz
I
IAK
I.E.E.
I.E.E.E.
j
km
logical tion of
pules to a
: functional notation
General Electric Company
Division
Recti
auxiliary alpha node ~ res tance matrix
integration step-length
maximum integration step-length
during commutation
maximum integration length
variable integration step-length
high voltage direct current
hertz
current
logical representation of thyristor
anode-cathode current
: vector of capacitor currents
Institution of Electri Engineers
vector
vector
vector
j2 = -1
ki
s
of and
res
currents
currents
thyristor currents
(10 3 hertz)
(10 3 metre)
kV
kVA
kWs/kVA
1
L
m
M
rnA
mm
ms
MVA
MVAr
MW
,n
ns
p
p
. .
ii
of
and inductive
(10;) volt)
lovo (10 3
kilowatt-second per kilovolt-ampere
number induc branches in a network
inductance
branch inductance matrix
auxiliary inductance matrix of gamma nodes
over-relaxation factor
logical representation of pulse
output from monostable
milliampere (10- 3 ampere)
mutual inductance between branches i and j
auxiliary inductance matrix
millimetre (10- 3 metre)
auxiliary res matrix
millisecond (10- 3 second)
megavolt-ampere (10 6 vo ampere)
megavolt-ampere reactive (10 6 volt-ampere
a
istance matrix
of ent state
a thyristor
power
P f.
p.u.
Q
Q
r
R
rms
s
s
sin
t
T
-1 tan
Th
TIL
TR
·TTL
u
v
VA
unit
vector
number of stive a network
resistance
inductive branch resistance matrix
auxiliary inductive branch resistance
matrix
root mean square
revolutions minute
: branch resistance matrix
auxiliary resistance matrix of nodes
second
back-to-back thyristor switch
sine
time
transformer
inverse tangent
thyristor
ion line
transistor
istor
volt or voltage
of tor
anode-cathode vo
VAr
V/cm
w
X
X
y
Z
cc
:
volt
vo
vector vo
vector of node vo
vector
\l'latt
reactance
vol
a thyr tor
across inductive
s across resistive
xx
matrix of capacitive branch susceptances
matrix of inductive branch reactances
number of thyristor branches in a network
impedance
nodes connected to at
capacitive branch
tone
nodes connected to at least one resistive
branch, but with no capacitive branch
connections
nodes connected only to inductive b
constant terms in implicit integration
state vectors
to at one
f of a thyristor
: rotor
rotating
to synchronous
between
p
T
o
%
< «)
1
F
time
microsecond (1
3 1416
6 )
by
quadrature booster/bucker
algebraic sum
monostable output pulse ,length
phase angle difference between voltage and
current (i.e. power cos<j»
phase relationship of each. Fourier
component
state vector coefficient matrix
inductor flux
vector inductor fluxes
angular frequency
ohm
square root
degree
cent
approximately to
s than (or equal to)
y
y
NOT F
symbols
1
..
source
ammeter
resistor
capacitor
inductor
earth
diode
thyristor
Zener diode
npn transistor
series transformer with windings
wound in opposition to each other
current trans
star transi- ......... m'oV' connection
connection
two-winding
three-winding transformer
three-phase four-winding transformer
voltage comparator
non=inverting buffer
inverter
two input NAND gate
monostable (output pulse length T)
ABSTRACT
on the the ating
1
ef both magnitude and phase shi control
is proposed. Two back-to-back thyristor switches per
phase are required, and device provides fast
continuously variable voltage magnitude and phase
control at the expense of some waveform distortion.
A dynamic simulation computer programme, which is
on state-space approach, is developed.
A three-phase control unit, to control the thyristor
switchings on each phase, is described and the theoretical
waveforms are veri by both experimental tests and
digital computer Consideration is so given to
the harmonic content produced.
Applications of the proposed thyristor-controlled
regulating transformer to the problems of voltage
regulation, power trans control and improvement in the
ent stabi of systems are also
presented.
I am to my supervisor,
J. Arril enthus and
guidance throughout this project.
I wish to thank New Zealand Electricity
their financial as granting of study
to enable this project to be completed. The Christchurch
Draughting Section of New Zealand icity
are so thanked
of the many il
their diligence in the preparation
in s thesis.
The cooperation Mr J. 1, D the
xxv
Recti Division, General Electric Company, Great Britain,
in the provision various of hardware is ly
acknowledged.
During s project many hours have been in
building hardware and computing. I wish therefore to
thank the technical staff of the Department of Electri
Engineering and the Computer Centre of the ity
Canterbury for invaluable help expertise
Last, but most certainly not Q I wish to
express my to stine. Her as a
mother to Leanne
a wi
Timothy
been
·her
imable.
1
CHAPTER 1
INTRODUCTION
In the advancement of power electronics component
technology development of the thyristor must rank
as one of the more important technolog achievements.
improved quality the silicon has enabled the diameter
of the thyristor element to be increased, ting in
higher current ratings. Coupled with an improved reverse
blocking capab ity, this made it possib to increase
the power handling thyristors These
advancements in thyristor technology have made the
possibility of high-power thyristors a reality, and
individual thyristors with power ratings in the MVA range
are commercially availab
During the 1960's thyristors had been developed to
such an extent that they could replace mercury-arc valves
in some industrial applications, their application to
h.v.d c. transmission systems was considered when extens
to the Gotland h.v.d.c. link were mooted Thyristors were
in the extension in 1970 and their
iority over arc valves (Martens son 1975)
Since 1970 thyr s have led in most h.v d.c.
(Martens son 1975) and the ined in the
se s , in to
appl ion thyr to many other s of
are of use
in a network and
(1971), Sundberg (1976) Schwei
(1978) are but of terns 0
The simplest form of a thyristo I voltage
ator employs a r back-to-back thyristors
connected in with a load (Fig 1.1) By varying
phase-angle delayed gate pulses to the thyristors and firing
them symmetrically with to zero crossings the
supply voltage (Vs ) the load voltage (VL) can varied,
depending on the load power , from zero to full load
voltage VS. Although a wide range vol control is
possible, the thyristors must be to both full load
voltage and current, and the harmonic stortion of
load voltage is most severe.
t
" 1 1 s istor~Control Vo
The of harmonic stortion is
overcome ign a thyristor
(Marshall 1974) wh uses thyristor switches
to tappings. The trans th
primary connected to supply has a ser of
in ser with or bypas
by to the
output vol a non-
voltage is by
The provision of a I trans th a
large number of secondary windings for voltage control
together with four thyristors secondary winding, each
to I load current, would prove to be uneconomic
for many applications.
A recent publication (Arrillaga 1976) a
single-phase thyristor-controlled regulating transformer
for voltage boosting. on the principle
of the regulating transformer booster (Westinghouse 1964),
this device boosts the load voltage by means two phase-
controlled back-to-back thyristor , providing fast
and continuously variable voltage boost at the expense of
some waveform distortion. With this device the regulating
transformer is only handling a small proportion of the
transmitted power, and the four thyristors need not
rated full load vol and current
The work described in this study involves
singl led
trans , as by (1976) ,
s
both
the use of a phase displaced
a
regulation,
voltage to
e and
From
a
This was to
e
are
control
the
the
of
back thyristor switches so a assessment of
the ity of proposed system could made
Complementing 1 assessment the
3
proposed circuit, a computer programme based on state~space
techniques has so been written. The mathematical model
used the development of the computer programme is
presented in Chapter 4. Chapters 5 and 6 deal with the
actual programme, discussing operation and per
An evaluation, both by laboratory measurement
computer simulation, of the use the proposed as
a means voltage regulation is ented in Chapter 7.
Using a quadrature regulating tage, the ability the
proposed circuit to provide power transfer control in
transmission circuits investigated and discussed in
Chapter 8. The fast-acting nature the proposed c
is exploited in 9, where the injection
voltage is to control the transient stability of power
Finally a ion ts
during
are 10.
4
CHAPTER 2
Presented in this chapter a full description
the operation the proposed circuit, both as an in-phase
and quadrature voltage and an and
quadrature voltage bucker. Theoretical waveforms are
also presented along with the firing requirements for
each thyristor.
2 • 1 PROPOSED
The schematic diagram of Fig. 2.1 shows one
phase of a thyristor-controlled in-phase vol
interconnecting two systems represented by their respective
voltages VQ and VR• Shunt transformer T1 provides the
in-phase voltage (VS ) each phase and series transformer
T2 the controlled boosting voltage.
S1 and S2 are two back-to-back thyristor swi
The second thyristor switch (S2) to the
winding 51 is
I in to
current, causing
1 sing
and endangering the insulation
winding.
Reversing the sense the secondary winding the
ser trans converts vol
of Fig. 2 1 into an
5
Th1 Th4
Fig. 2.1 Bas In-Phase Voltage Booster
2. 1 • 1
The operation of the in-phase voltage booster
(Fig. 2.1) can be with r to the
theoretical waveforms of Fig. 2.2. These waveforms
correspond to a lagging power factor (~) and if the
thyristor switch S1 is triggered without delay (i e. at
the zero crossings of the current waveform) a constant
sinusoidal voltage added to the voltage VQ and
with it.
The s €1 £2 (meas
zero
in S1 and S2
tor of S1 can
at any the range ~ < £1 < 180°.
Simi ly, the appropr thyristor 82 can be
tr at-any time within the range 0° < £2 < ~.
6
I
1
Th2
Th3 Th4
• 2 2
¢.J • I
i7T----'
wt
wt
wt
wt
wt
se Boost
Hence
both
manner.
At
current (I) , when VQ
forward-bias and
provision a
ing can the
8 1 8 2 the
1
is istors 3 and 4 are
ed
pulse to thyristor 3
ly.
11
turn ON, thus short-circuiting the secondary winding of
T20 VT , the voltage across the secondary winding of T2 , is
now equal
thyristor 3.
where Vf is the forward voltage drop
With thyristor 3 conducting V8 positive,
thyristor 1 is forward-biased and a pulse to
thyristor 1 will turn it ON. VT
now , reverse-
biasing and turning OFF thyr 3. When Vs is ive,
thyristor 3 is again Hence the
thyristor 3 will turn it ON and a commutation from
thyristor 1 to thyristor 3 will take place, turning
thyristor 1 OFF.
Operation during the second hal Ie
current is
polarities
to the t, but with
and with the
1 voltage
st.or
one complete are . 2.2
102
As t . 2. 1
can when sens
of T2 is revers The
t
of
voltage
wave • 2. 3 •
The
be triggered at any
a lagging power
to
within the
switch 8 1 can
° e 0 < £1 < <P,
and the appropriate thyristor of switch 82
can be
triggered at any time within the range <p < £2 < 180°.
Therefore the ing of switches 8 1 and S2 can control
the voltage bucking
At the beginning of the positive half-cycle of
line current with thyristor 2 conducting, the voltage VT
is Vs + Vf which forward-biases thyristor 4. Firing
thyristor 4 reduces VT
to +Vfl reverse~biasing thyristor 2
and forcing it to turn OFF. When Vs changes polarity
thyristor 2 is again forward-biased. The provision of a
gate pulse to thyristor 2 will therefore turn it ON and
a commutation from thyristor 4 to thyristor 2 will take
place, turning thyristor 4 OFF.
During the second half-cycle of line current
the operation of the voltage bucker is similar to the
first, but with all voltage polarities reversed and
the thyristor pair
conducting. switching s and the
ON are in Fig 2.3.
Th1
Th2
Ttl 3
Th4
2.3 Waveforms
10
In-Phase
1
2 2
F one e
a booster
interconnecting two by voltages
VQ and VR respectively. The vo each
is provided by shunt transformer T 1 , the
T2 provides the controlled quadrature
boosting voltage. S1 and S2 are two back~to-back thyristor
switches, and the quadrature voltage represented by
• 2.4 Bas
The
same as
described in
voltage can
I
•
Th4
Th2 Th3
Vol Booster
quadrature voltage booster is
voltage booster, which has been
2.1.1. The quadrature
or lag the
and depending on the phase f
em voltage VQ
((jl) between
'12
components of VQ I I a of
di modes of are e.
modes (i) and (ii) a
voltage and ~, lying in the ° ° o ~ ~ < 90 I
is lagging and leading s 5 and 2.6 show
the respective waveforms modes (i) and ) . Using a lagging quadrature voltage, when ~ in the range
90° < ~ < 180°, th " "t f F' 2 4 t" ~ . e ClrCUl 0 19. . opera es 1n
(iii) and (iv) ~ lagging and leading respectively.
Figs 2.7 and 2.8 show the respective theoretical wave
for modes (iii) and (iv).
The quadrature voltage booster shown in Fig. 2.4 is
converted into a quadrature voltage bucker by reversing the
sense of the secondary winding of the ser trans
Quadrature voltage bucker operation is the same as e
in-phase voltage bucker which was discussed in Section 2.1.2.
As with the quadrature voltage booster, the
quadrature voltage bucker can also operate in a number of
different modes. Modes (v) and (vi) have a leading
quadrature voltage and ~, which lies the range
lagging and leading tively. F 2.9
and 2 10 show theoretical waveforms modes
(v) (vi). When ~ 1 the
voltage
and the operational ~ lagging and ng are
(vii) and (viii). The
for modes (vii) i) are shown Figs 2 11 and 2 12
respective
1
I wt
wt
. 2.5 Theoreti Waveforms ~ (i)
I
.26 Waveforms Mode (ii)
'15
.27 Waveforms ~ ( iii)
1
wt
wt
wt
I wt
wt
2 8 Wave - Mode (iv)
I
.29 Waveforms (v)
'18
wt
wt
wt
I wt
wt
• 2.10 Mode (vi)
V T
I
VR
I I I I I I i
s11
Fig~ 2.11
1
wt
wt
wt
wt
wt
s1 S1 I
Waveforms Mode (vii)
20
wt
wt
wt
I wt
Fig 2.12 Waveforms ~- Mode ( ii)
21
Bes of discussed in
s is sible to the quadra-ture
vol booster or rcuit a number
modes. For , if for mode (i) a lagging
voltage used than a leading voltage
the theoretical waveforms of Fig. 2.13 are obtained.
appropriate thyristor of switch 8 2 , required to terminate
the voltage boosting period, reverse-biased until the
zero crossing of the line current (I) cannot conduct
until that instant. But even then the conducting thyristor
switch 8 1 , being still forward-biased, will continue
conducting and the switching of 8 2 will immediately short-
circuit the secondary winding transformer T 1 " To
overcome this problem a delay (A) could be built into the
control system to allow 8 1 to switch OFF and recover fully
before ing of 8 2 . This delay, however, would cause
a temporary open-circuit, with large overvoltages, across
the secondary winding of T2 and is not considered a
practical proposition.
In some cases, the resultant waveform VR is ident 1
with that obtained from one of the eight modes already
discussed. For example, if a lagging rather than a leading
quadrature vol is
resultant
mode (v)
identical with that
ion the
mode (i). F . 2.14 shows mode (v) operation with a lagging
voltage, and a comparison of
shows the resultant similarity in VR.
2.5 and 2.14
:2
'--., wt
I ~"H----~--~----+-. wt
Fig. :2 13 Mode (i) Operation with Lagging
Voltage
2
I
Fig. 2014 Mode (v) Operation wi'th Lagging
Voltage
24
Us modes of
in s and summarised in
2.1 it sible to phase r
or The fi ng
angle Ie for control the
thyristor switches S1 and are also listed in Table 2.1.
It can be seen from th Table that if ~ is leading or
1 ng by 90° the firing ranges of 8 1 and 8 2 are either
reduced to 0° or over 180°.
If ~ should be ther leading or lagging by 90°,
then neither the quadrature booster nor the quadrature
bucker will operate as described in Sections 2.1.1 and 2 1.2
ively. This is because the line current is now
either in-phase or 1800 out of phase with the quadrature
voltage and the thyristors of switches 8 1 and 8 2 , which are
not forward-biased at the appropriate times, cannot switch
in their correct sequence. There are two alternative
solutions to this problem: ther switch 8 1 or switch S2
can triggered without delay at the zero crossings of the
current waveform. If switch 8 1 is triggered without delay,
then depending on a boosting or bucking circuit i
being used, a constant sinusoidal voltage will be
to or tem voltage VQI i
maximum phase the fundamental of When
triggered thout del the voltage VR will not be
any magnitude change or phase shi
Table 2.J. Quadrature Voltage Booster/Bucker Operational Modes
Phase Angle Difference Range of Firing I of between V S and I Angle for Switch for Switch
Mode Circuit Voltage (<P) 81
(i) booster leading lag 90° + <p < E < 1800 00 < E < + <p
00 < $ < 900 1- - 2 -
booster leading lead 900
-$ < E < 1800 < C' < 900 _ $
00 ..2. $ < 90
0 1- - ~2
(iii) I booster lag 90° - (180° - $) < E < 1800 I 0° < < 90
0 ° 900
<$'::' 1800 1- - 1::2 - (180 -
( booster lead + (180° - ¢) < E1 ,2.1800
00
< < 900 + (180° .:.. cb)
900
< ¢ ..:: 180° _ E2
(v) bucker leading 0° <
lag $ <90
0 00
< - 1::1 < 90° + $ 900 + $ < 1::2 ..::
-lead
I
bucker I 0° < < 90° -¢ 900
- $ < E < 1800
00
,2. $ < 900 _ El 2-
(vii) bucker 90° < ¢ ..::
00
< < _ El 90° - (1800 - ¢) 90
0 - (180
0 - ¢)< E < 18 2-
(viii) bucker lead .::. El < 900
+ (1800
- <1» + (1800
- < E2 ..2. 180° 90° < $ ,2. 180° I I
26
2 3 THYRISTOR
For successful the ter or
c (both and ) v
study must when a pulse must be
provided for thyristor and also the at which a.
gate pulse must not provided. These times, the
provision or non-provision of pulses, can be
ascertained from theoretical waveforms discussed in
previous sections of this chapter.
In Section 2.3.1 any to a "booster c
to both in-phase and quadrature boosting. Likewise v
in Section 2.3.2 any reference to a "bucker circuit" re
to both in-phase and quadrature bucking.
2.3. 1
The gate pulses con)crolling the ing of the
thyristors of switch S1 are phase~controlled with
to voltage VS. Logic, derived from the circuit voltage and
current waveforms, is used to provide the gate pulses for
the thyristors of switch S2 and a careful examination the
theoretical waveforms (Figs 2.2, 2.5, 2.6, 2 7 and 2 8) is
necessary to
conduct over
positive 1
vol
the correct log Thyristor 3 must
sting va
current (I) the applicat
thyristor 1. Condit are again
thyristor 3 to conduct during the
(V ) S
of the
of
negative voltage Vs line current, and the
of 3 occur at any time after Va goes '"
negative and the 1 current goes i ve. 'rlhe
conduction s for stor 4 are similar to,
but of thyristor' 3"
2.3 2
For the pulses
firing of the thyristors 8 2 are
controlled with to vol V The 8
pulses
thyristors switch 8 1 are provided by logic
derived from the circuit voltage and current waveforms.
ing to the theoretical waveforms of Figs 2.3~ 2.9
2 10, 2.11 and 2.12, thyristor 2 must conduct over the
period of positive voltage Vs and itive 1 current I
the ing of thyristor 4. Thyristor 2 may again
be provided with gate pulses at
negative and before I goes negative.
time Vs goes
conduction
requirements for thyristor 1 are similar to, but di
180 0 , those of thyristor 2.
2.4 USE OF A TRANSFORMER
If the connection between two systems (VQ and VR
)
made via a power transformer, the shunt transformer T'I
Fig. 2 1 can be dispensed with required reduced
voltage obtained from a iary winding. F . 2.15
a s diagram of a where the e
to neutral tert vo are wi,th the
vol VQ and Thyristor control produces the wave~
27
• 2.2, upon revers the sense
of secondary winding of T2 the wave illus in
. 2.3 can (i e. the circuit can act as
an vo or bucker). In 1
manner, quadrature vol boosting and bucking can be
8 1
Fig. 2.15 In-Phase Voltage Booster
accomplished by making use of the interrelationships
between the voltages on star and delta connected wind
of a three-phase transformer. One possible set of
transformer connections illustrated in the quadrature
voltage booster of Fig. 2.16, where the line~to~l
tertiary voltages will be in quadrature with the line to
neutral voltages of the star connected primary and s
windings.
I
. 2.16 Quadrature Voltage Booster
8
3
THE CONTROL UNIT
A three-phase control unit, thyri
vol regulator, was built to produce direct the
firing pules to the appropriate thyristors. The product
of ing pulses, together with the assoc
circuitry, is discussed in this chapter. This control
was built so that a laboratory assessment of the
of the operation
made.
the proposed system (Chapter 2)
3.1 GATE PULSE DERIVAT
To ensure the successful firing of a thyristor the
gate should be provided with a high frequency train of
pulses with rising edges. If the first pulse of the
train does not initiate conduction then more pulses are
applied to the thyristor until conduction is in
The gate pulses for the phase~angle 1
thyristors, swi S1 (Section 2 • .1 )
and S2 for 2 p .2) f are
commercial pulse circuit. Any thyristor wh
is not cant led, switch S2 for
operation (Section 2.3.1) and
(Section 2.3.2), must conduct whenever
controll not conduct. The firing pulses -thea
are ived from the ci current and vol
2
()
are as log control
3. 1 Q 1
The e control of a b
of thyristors two high
one each thyristor. These two must be
the re
A pulse train ring circuit (RIS54) produced by
the General ic Company ,,- Recti Division (G E.C R.)
(Appendix 1) is used to provide pules This
circuit provides two outputs, separated by 180°, of
100 ~s pulses with a r time of 500 ns. A of
controllability between 15° and 165° is achieved with a
control signal of ±5 V d.c., and calibration of firing
circuit is ibed in Appendix 2. To ec ly
the firing circuit from thyristors, each ing circuit
output is connected to the appropriate thyristor of the
phase-angle controlled pair via a pulse transformer
(Appendix 3) as shown in Fig. 3.1.
Firing Circui-t Output
1N4148
1N4148
39R Thyristor
,----Q Gate
Thyristor -------------------------------0 Cathode
Pulse Transformer
Fig 3 1 Interconnection Between Fir
Thyristor
it
3 L
Re ing to
current waveforms VS ' VT
waveforms are
2.1 and 2.4,
I are
contro
the c
and
in the
istors. All
by transformers,
the current waveform being across a non~
resistor. The waveforms are then fed into type "710"
voltage comparators which give a TTL compatible output.
3.1.2.1 It
possible to have one set of logic which will control
thyristor switch S2 both in-phase and quadrature
31
boosting. Referring to Figs 2.2, 2.5, 2.6, 2.7 and 2.8, it
can be seen that are two distinc·t conduction periods
per cycle each thyristor of switch S2" During each
these four separate conduction periods there are di nct
relationships between the waveforms Vsr VT and I. In
Fig. 3.2 the waveforms VS ' VT and I are reproduced from
Fig. 2.5. These waveforms are used by way of example and
any of the other four sets could have been used.
From the logical representations of the waveforms
Vs and VT in Fig. 3.2, it can be seen that one of the
conduction periods for each
defined by the
respectively. To
thyristor 3, the log
waveform I is to
of length T. The logical
identify conduction
thyristors 3 and 4 can be
·V'r and
conduction
ion of the current
fol:'
a monostable, producing pulse
sion M30r used to
iod of thyristor 3
u the second conduction period of stor 4
by logical express
I
I
I
M4 I
Vs + M3 I
V V + M401 s T
30
3
ion Logic
stors 3 4
are by logical (3. 1)
and (3 2) ly
VS0VT + M3"r (3. 1 )
·V T + Mq, I (3.2)
The circuits used to produce the log expres
( 3 . 1) and ( 3 . 2 ) thyristors switch S2 are shown
in Fig. 3.3. The outputs of TTL logic circuit give
a logic level '1' when the particular thyristor it serves
must conduct, and a logic level '0' at all other times.
3.1.2.2 One logic
circuit is used to control thyristor switch S1 for both
in-phase and quadrature voltage bucking. Each thyristor
of switch 8 1 two conduction periods per cycle (see
3
Figs 2.3, 2.9, 2.10, 2.11 and 2.12). To i1 how the
logic controlling switch 8 1 is derived u the waveforms 'VT
and r from Fig. 2.9 are reproduced in Fig. 3.4. From the
logical representations of waveforms Vs and r in Fig. 3 4,
it can be seen that one of the conduction periods for each
of the thyristors 1 and 2 can be defined by the log 1
sions VS·I and vS"r respectively. Each of these
conduction shown ing into the region where
thyristors 3 and 4 are ing. Thyristors 1 2 are
at time a commutation from tch 8 1
to take place turning thyristors 1 tch S2 will
2 OFF. To de the second iod conduction
thyr tor 1, the logical representation of the current wave-. I tr a monos I producing pulse M, length T"
V T
. 3.3 Booster Logic
To Thyristor
3
I
I
t11 I---"=--!:---+----"-
M10 r
M· I 2
Vs I + M1"I
Fig 3.4 Operation Logic
35
36
The used to
conduction 1. In a simi manner, the
conduction thyristor 2 by
s I conduction
thyristors 1 and 2 are y fined by 1
ions (3.3) and (3 4) respectively.
or + M, I (3.3)
VS'I + M20I (3.4)
The circuits to the logic expressions (3.3) and
(3.4) for the thyristors of switch S1 are shown in Fig. 3.5,
3.1.2.3 The
TTL logic output from the circuits illustrated in 3.3
and 3.5 does not offer sufficient power to a thyristor,
and a high frequency pulse train is more desirable than a
ring pulse. For these reasons a known as
a "Microne" pulse transformer (Appendix 4) is used as an
output stage from the TTL logic circuits.
Using the circuit shown in Fig. 3.6, the TTL logic
output is converted into a 12 kHz pulse train. The
trans TR1 and amplifies the TTL logic pu e
and the "Microne" pulse transformer, which s on a
di
only the
input
Although the "Microne"
trans it not af
the thyristor the
se trans
, outputs a 12 kHz pulse
1 TTL
is
pulse,
as a pulse
electrical isolation between
There
(Appendix 3)
a
to
connect the II output to the thyristor.
v S o-----l1
I
I
* 3 * 5
V "I S
v . I S
M" I L.
Bucker Operation
- - - -V ·I+M·I
S 1
c s
To tor
1
To istor 2
Non-Inverting Buffer
390R
TR1 PN3643
F ,,3.., 6
1K
2K2
15R
100
1---1-00 + INPUT
+15 V
0.001
ov
C
OUTPUT
C1 1
+ 0--+---1 ov "HICRONE" Trans
former 1N4148
"Microne Pulse Transformer
Cathode
Gate 39R
3.2 ~T~HE~~~~~~~~~~~V~O~L~T~A~G~E~~~~~
A unit, istor~controlled
regulator shown in 3.7(a) and (b), has been
built to control switching two
of thyristors per phase. The unit is to
in conjunction with an 8.25 J<:VA th
transformer (Appendix A5.1) and
three~·winding
series transformers
(Appendix A5.2), where the tertiary voltage used
to control the secondary voltage of the 8.25 kVA
transformer. Typical per phase connections for the
three-phase transformer, series transformers and control
unit are shown in Figs 2.15 and 2.16.
The three-phase control unit shown in Fig. 3.7(a)
consists of three identical single-phase control units.
The operation of anyone of these units is completely
independent of the other two, and the following
description the unit only to each single-phase
unit.
The thyristors in each back-to-back pair, 8 1 and
8 2 , are rated at 25 A rms and are type 10RC60A manufactured
by International Recti Both thyristors of each
back-to-back are mounted on p but cally i
, a s of heatsink and s
with the two pulse transformers, mounted on ilVero ll
In all e components, with the exception of
the G.E.C.R. firing
voltage transr~rmg
ts, power supply and reference
, are mounted on "Verol! and are
easily removed from the rear of the cabinet.
• • .. •
Fig. 3. 7 (a)
• f 1
•
THfR'STOR CONTIlOl.l£O VOl. IAGE flfGUl.ATOR
. , -
• • • • .. •
-_. ,-
• • • • ..
The Thyristor-Controlled Volta ge Regulator - Fr o n t Vi ew
.,
• •
..
+= o
Fig . 3.7 (b ) The Thyristor-Contro lle d Vo ltage Re gulator - Re a r View
There
terminals for
of Figs 2.15 and 2 16
va r
a 38 V or 66 V
norma used as
e-angle
switch (Section 3.1.1) 38 V or 66 V input vo
transformed into a 200 V rms centre tapped
directly to theG.E.C.R. firing
The pairs terminals lab
tor
are
the input terminals for the corresponding waveforms, which
are isolated from the main by transformers and used
to determine the logic for firing the log control
thyristors (Section 3.1.2). These three inputs, together
with the +14 V, +5 V and -5 V power supplies for the
integrated circuitry are routed to the mode swi which is
a four position eight pole switch. In each control unit,
provision has been made up to four logic to be
ng of the accommodated. These logic boards control the
appropriate logic controlled thyristor tch, and each of
the four mode switch positions corresponds to one of these
logic boards. As each position of the mode tch
, the input waveforms Vs VT and and the log
power suppl s are routed to the appropriate logic
For
.us
ent
mode 1
the mode
(see Figs
4
(Fig. 3.6) . The
only two mode
voltage booster I and
are
ion. The remaining two poles on
route the two outputs logic board
3.5 for the log of 1 and
to two IIMicrone li output
length (T) each rnonos~cable
(Figs 3.3 and 305) by a the resistance
component the e timing c
Timing components to a
T from 1.5 to 15 ms.
The a two e
switch which switches the and
controlled firing pulses between thyr switches 8 1
S2" Fig. 3 8 is a diagram showing
to boost/buck switch, connection shown is
duplicated again to cater both the positive and negat
fi!ing pulse connections to the pulse transformer .
To Th 40---------_8
To Th
To Th 20---------.
To Th 1 0--------_.
... ------0 To Th '1
_-----oFrom "Microne" Output 1
... -----oTo Th 2
From "Microne" '1>=------0 Ou t put 2
_-----oTo Th 3
From G"E"C"R" """'-----0 Output 2
e---------QTo Tb 4
From G.E.C.R. -,---------0 Output 1 I
BOOST: BUCK
F .8 Boost/Buck Switch Connect
The del which production the
phase~angle firing pulses 1 and 2) is
adj via the multiturn helipot, and an ind
the f ing angle (in is given on the meter
mounted on the control unit. Use multi turn ,hel
allows fine adjustments to be made to the ang
of the phase-angle controlled thyristor switch. Fig. 309
is a graph showing the firing angle delay plotted t
helipot readingi where a reading of 10 corresponds to
ad. c. level of -5 V and a reading of 0 corresponds to a
d. c. level of +5 V.
Firing Angle Delay
(degrees)
.39
180
160
Firing Angle
Helipot Reading
t
ay
ly, cons was
the operation vol c
the booster. The turn OFF of the
thyristor tch 8 1 triggered the conduction
icularly
ng
the
alternate thyristor ng in the tert
of the three-phase transformer being
the conducting thyristor of switch 8 1 turns OFF the
alternate thyristor forward-bia and any rapid change
of this forward anode to cathode voltage can produce a
transient gate current (Ramshaw 1973) resulting in the
alternate thyristor turning ON. To overcome this problem
and lower the rapid changes in voltage across the thyr tors,
both snubbers and
circuit.
reactors were introduced into the
Each snubber consists of a series resistive~
capacitive network connected across each
thyristor pair. This technique for lowering the rapid
changes in voltage across the thyristors relies on the
integrating ability of the capacitor.
The low tertiary winding leakage reactance, as
measured by standard short-circuit tests, of the
transformer results in very short commutation times
consequent rapid in vol across thyristor
The addition a reactor, bet,ween the
thyristor the commutation times and
thereby the rapid voltage changes.
In the following discussion of protection, any
devices re
Internal
to are those shown Figs 2.1 and 2.4.
which cause the maloperation of the
switching sequences must cleared by open~
two
circuiting the winding T1 and
circuiting the winding of -the es trans
T 2 " Shorting the secondary winding of T2 avoids
magnetising current, which cause s
and endanger insulation.
Any internal faults causing the simultaneous
conduction of both thyristor switches and consequent short~
circuiting of the transformer winding T1 require the
provision of fast-acting Water were used
thyr tor protection in the thyristor-controlled voltage
regulator and they were placed between switch S1 and
transformer T1 on each phase.
Fai of a thyr normally results in a short-
circuit across the device. If such a lure occurred in
either of the thyristors of switch S1' then the fast~acting
fuse would IIblow" as soon as the appropriate istor
switch S2' causing the winding of T1 to be short-circuited,
was fired. Assuming the proposed circuit was operating in
46
a booster mode, the logic (Section 3.1.2.1) would ensure
that only the thyristors of switch S2 were fired, leaving
the transformer winding T1 open-circuited. Should a failure
of one of thyristors of switch S1 occur ng
as a voltage ,upon fault (Le"
the "blowing'! the fuse) . the S2 must
be triggered at the current waveform (I) zero crossings,
ircuiting the secondary winding of the ser s
transformer T2 Provision of this type of protection not
inherent the it log 3 • 1 • 2 • 2 ) and
1 protection logic is neces a I sca
device (n.b. this was not considered a necessary
of project).
A
ts a II
bucking operation,
e
sa
the thyristors
bot,h
as soon as ,the
switch
"blows" the winding T1 is open~circuited and
the secondary winding of T2 short-circui by the
iled thyristor.
Provision
was not considered
protection against external faults
for the thyristor-controlled
voltage regulator described in this chapter. However a
full scale device would require th type of protection.
L! 7
Upon the detection an external fault the thyristor switch
8 1 can immediately be blocked, leaving the switch 8 2 to
withstand the fault current (i.e. only the thyristors of
switch 8 2 need be rated to withstand the fault level on the
secondary side of the transformer) .
CHAPTER 4
THE
The mathematical model developed in is
ifically formulated to cater for res tance, inductance
and thyristor circuit elements only. Built up from these
three circuit ements, a mathematical model is defined for
each of the relevant system components.
Limitations are imposed on the way in which these
tem components may be interconnected This is done to
increase computing efficiency and does not severely re
the representation of system configurations.
In the analysis diakoptical tearing techniques are
applied to the various elements and sub~networks. This
enables that portion of the network affected by topology
changes, due to thyristor switchings, to be isolated
the remainder of the system.
A state-space approach used in the analysis of
the system equations, thus allowing a unified treatment
elements. The both and non-l
state
integration.
To
are solved by numer
tem components such as filters to be
modelled, a more complex mathematical model which includes
as well as res , inductive and thyristor
c ements, is developed in Appendix 6. This
mathernat model included because the computer
48
4
, to discus in 5, has
to include these ements. The
programme has been written in this way so l:hat can
in the analysis conf other than
those discussed in this study.
4 • 1 COMPONENT
The system components are:
1. The a.c. system~ the individual components of the a.c.
system may not be of particular importance, but
overall combined effects are.
2. Thyristors; the bistable action of each individual
thyristor must be represented to enable an accurate
simulation thyristor switching.
3. Transformers; the transformer model must accurately
represent fects such as phase shifts and neutral
earthing which are inherent in the various three~phase
transformer connections.
4. Transmission lines; transmission lines are normally
operated under balanced conditions and a " "
representation is therefore quite adequate.
4. 1 • 1
Normally an a.e power tern to
low-order harmonic is of an inductive nature.
The simple equivalent circuit of Fig 4.1, where the source
impedance Z = R + jWLs ' can there be used to s s
accurately an a.c. at sing frequency.
e
Fig 4.1 Simple A.C. System
However is 0 to ent a
over a range frequencies. g. 4.2 illustrates an
alternative equivalent circuit which has been proposed by
Bowles (1970) and maintains an almost constant impedance
angle for low~order harmonics. For the equiva
of Fig. 4.2, Rs and are chosen to give the
source impedance Zs' and Ra is determined by the
impedance angle at fundamental frequency.
Fig 4.2
4. 1 2
R a
lU
stors
The thyristor
e
A C,
L /2 s
entation
s a basic bistable
state cannot be deduced in every case
sent values of voltage and current at
and
o
s
some is known
A simple digital model of a istor must lude
table
(1973) have ed a
model which th and employs a
minimum of input functions, whose values are usual
required other purposes within the digital simulation 0
The state of each thyr is determined at the beginning
of every integration s , and the current through the
thyristor is then calculated assuming this part
state throughout the complete integration step. The value
this current then used to indicate the state
thyristor for the next integration
The thyristor model
information:
the following
anode to cathode voltage (VAK ) , at logic
for a forward-biased device and logic 1
a reverse-biased device.
1 "1 v
'0' for
anode to cathode current (IAK ), at logic level '1'
when the current is than holding current
and logic level '0 1 when it is less than
holding current.
the thyristor ing state (D) immed
to the ; at logic '1 i
the ON at logic level '0' when the
OFF.
of (G) is indicated by
logic level '1' and the by logic level 0'0
51
5
The ent state (P) of the thyristor thus
given by the lowing sion
P
4.1.3
The traditional transformer equivalent c t
(Say 1958) is not suitable a 1 dynamic
analysis, because dif transformer connections 0
different impedances to components of current and
the phase shifts inherent in the different connections
need to be represented.
A single~phase three-winding can
represented by three magnetically coupled coils as shown
by Fig. 4.3.
I1 M12 12
I R1 R2 t L2 V2
I V 1 L1
R3 I3
L3 V3
I
Fig. 4 3 Three~Winding Transformer
Using an impedance formulation, the relationships
between terminal va and winding currents are given
by the lowing equation:
Since trans
Z11 Z12 Z13
Z21 2 Z23
Z31 Z32 Z33
s are not
(l~ 1)
relative motion with respect to each other or to any
other magnetically coupled ci I the impedance matr
must be symmetrical about the diagonal (Le. Z12 ::;; Z21 p
Z13 ::;; Z31 and Z23 ::;; Z32). The matrix equation (4.1) can
therefore be rewritten in the following form:
d +
o
o (4.2)
The single-phase transformer model depicted by
matrix equation (4.2) produces a magnetising current which
based on the assumption linear core magnet ation.
It is possible to cater for non-linearities in the core
magnetisation (i.e. saturation) provided the relationship
between the equivalent circuit and the magnetising
characteristic established. However, the introduction
of former non~
a 1
throughout.
beyond
core
scope of this
is assumed
In , three-phase three-winding transformers
can by 1 9 x 9 impedance matrices.
There is however a
concerning
not to
cal di iculty in obtaining data
e mutuals, because manufacturers have
such Even when s
was ava , it was found to be
imposs to model
9 x 9 impedance matrix.
the
This was
of inductance
as a full
formulation
(see
equation (4.15)), and the tight coupled windings
an ill-conditioned (Conte 1965) inductance matrix which was
impracticable to invert Consequently all three-phase
transformers are as being three independent
single-phase trans (i.e. there are no interphase
coupling terms the impedance matrix). This is an
accurate representation for transformer banks of single
phase units and reduces the equations to three independent
sets, one representing each phase.
To implement this coupled circuit model of the
transformer, accurate determination of the self and mutual
impedances
impedances
required (the determination of e
discussed in detail in Section 6.3.1).
When these impedances have been obtained, any effects such
as phase shi and neutral earthing are automati ly
catered for by the terminal connections.
4. 1 .4 sion Lines
Transmission are normally operated with
Although lines are not
equilaterally, and may not be , the
ssymmetry is slight, and phases can be
considered to be balanced. The importance of stributed
and current with the
1 I but for short lines (say less
than 80 km long) the total susceptance is
55
lly so may be (stevenson 1962).
di
, a ssion can as
a simple, lumped, constant impedance, because
no di , as as measurements at the ends the
line are concerned, whether the parameters are lumped or
uniformly distributed. The lumped parameter per phase
representation of a transmission line is illustrated in
Fig. 4.4.
v s
R
Fig. 4.4 Per Phase Transmission Line Representation
Where V and V are the voltages at the sending and s r
receiving ends of the line respectively, I the line
current and the line impedance Z = R + jwL. Therefore
the transmission line model can be represented by the
following equation:
4.2 IS
The most
=: V + IZ r
approach the solu·tion of
containing non-linear elements
1 1977 ) This
treatment both 1
non-l circuit elements.
Linear
currents are
variables
s are assumed, so
to winding
The currents and
winding
which are
purely
56
are
are non-state and asso
. resistors
voltages
currents can be obtained from the state variab (winding
fluxes). The following two determine the
branch currents and node voltages of a network containing
inductive and resistive elements:
1. Topological constraints; the way
are interconnected.
which the branches
2. Algebraic constraints; ic electric network laws
such as Ohm's Law and Kirchhoff's Laws.
So long as both of these sets of constraints are fied
is theoretically possible to solve the equations
irrespective of the method solution.
4.3 ELECTRIC
It is assumed that the network has n nodes
interconnecting r stive, 1 inductive and y thyristor
branches. The following assumptions are also made
concerning the interconnection of these s:
1 res
2. are no
inductive
and sources
3. Thyristor
to the
restr
u
m. f
s are
or
on
which may
to the
r resi tors.
the connection of
include resistances
s must connected ther di
point or to an
57
4. e.m.f sources are defined as in
the direction current
4 3.1
It computationally to use branch
formulation and subdivide the nodes to the type
of branches connected to them.
a nodes connected to at least one res tive branch
y nodes - connected only to inductive branches.
o nodes - connected to at least one thyristor branch.
Since the topological changes are mainly caused by
thyristor switchings it
which are a special type
convenient to def the 15 nodes,
y node. A conducting thyristor
is as a short-circuit, thus converting two 6 nodes
into a y node and a non-conducting thyristor is as
an open-circuit, converting two 0 nodes two y nodes
Although the 0 nodes do not figure in the formulation they
are useful to identify which nodes are fected by thyristor
switchings during the dynamic simulation.
h I · 1 t' T d KT th T e topo og1ca rna r1ces Krn an In are e
node incidence
branches respectively.
s is
T K.. = +1; if 1J
~1; if
:= 0; if
It is convenient to
as
j
j
j
of resistive and inductive
these
end anch i 0
receiving end of branch i.
not to branch i.
the topolog 1
to node types as
KT [ KT rn r(3
KT In [ KiB
and from the definition of y
4.3.2
4.3.2 1
KT ] ry
KT ] ly
KT ry 0
Fig. 4.5 Resistive Branch
For each individual resistor
relationship applies:
== V. 1.
V. J
:; V I •
1.J
58
lowing
When all r resistive branches and n nodes are considered,
the following matrix equation can be written:
"" V n (LL 3)
is the branch resistance matr
Ir is the vector res currents, and
V is n vector node
4.3.2 2
j
g. 4.6 Inductive Branch
For each individual inductive branch the lowing
relationship applies:
:::: e
and since Lb Ib :::: Wb , where $b is the winding flux
= e
When 1 1 inductive branches and n nodes are cons
the following rna equation can be written~
(4.4) .
the vector of inductor fluxes,
El is the vector e.rn.f. sources in
inductive branches,
the inductive branch resistance
vector inductor currents.
4.3.3
In of current sources, Kirchhoffis
current gives:
o (IL 5)
From which
(4.5)
K Y
o
o
In to obtain an for the vol
vector of e (Ve), equation (4.3) is first
partitioned form.
60
( 4. 7)
Premultiplying this equation by KSr' noting that K~y = 0
and using equation (4.6) leads to the following express
:: K
I or Vs
:::: -R(:H3 KSI II ( 4 • 8)
where -1 :::: K -1 KT RSS R
Sr rr ri3
Similarly, an sian can be obta for
voltage vector of y nodes (V ) as follows y
Premultiplying equation (4. LI) K yl 11°
pa ianing
sian
Using (4 7) noting o
(i.e are cons to unchanging with ) v
Vy -L, K T III) (lL ) yy y KU~V8
where -1 Lyy
-1 T KYlLllKlY
Defining the ancil VI as
VI El T
II (4.10) ::::: + Kll3 Vs - Rll
Equation (4 .9) can now be sed more simply as
Vy -1 (4.'11) ;;:::: -LyyKYlLllVl
4.3.4
Using the flux linkages (~ll) as state variables
and node subdivision described in Section 4.3.1, the rate of
change the state variable (equation (4.4») can now be
expres as follows:
(L~.1 )
Using equation (4.9) to eliminate Vy
CUll KT L K
iJ [El + SV B = T
Iy yy yl l~
where U a unit matrix 1 0
Using (4 8) to iminate Va
d(~ MIl [El = R~lIlJ UI,~13)
where MIl
Finally equation (4.13) in
-1 and remembering that II = Lll~ll
4.4 SOLUTION OF
Because of the thyristor switchings v the topology
6
undergoing repeated changes and the network must
therefore be solved by a "single-step" method, which is
starting. This necessary because "multi- Ii
methods require information from previous and are
normally started by a "single-step" procedure. The
frequency of occurrence of switching discontinuities means
that a "multi-step" method would barely get started before
another discontinuity occurred and the "single-step"
procedure was recalled to start the s again.
4.4 1
state vector di
the lowing
f(~) =
Then using the zoidal (Darn 1972), the state
vector ~ at the of an integration s h
given by:
lJ!t+h Wt + h
(f (Wt) + f(W t +h ) "'" '2
ituting (4.14)
Wt +h := Wt + h[ I '2 -M1lRl Ml
1 lW t +h + Ml + lEt+~]
Rearranging and defining
=
the following expression results
(4.15)
Within each integration step length h the
hand side of equation (4.15) considered constant
therefore lJ!t+h is determined directly, without the need for
any iterative process.
4.4.2
The actual values of flux linkages (lJ!11) are in
general small quantities in the systems being modelled
The. numerical accuracy the integration process is
improved by using WlJ!ll as the state variable, i.e.
-1 II = Xll(wlJ!ll)' where 1 WLll"
4 5 DETECTION INUITIES
The cause abrupt in t.he
vol and must in to
the ate topological changes.
The thyri turn ON is predictable since its ing
instants are decided by control system In is case
the integration s length can adjusted so that the
fi
The
re
by 1
any
a s
ng instant r to the zero eros
vol , this can be
ion (Appendix 7) without the
in the s
An accurate turn OFF can only at
expense of slowing down the computation. Sufficient
for
accuracy normally achieved by detecting the turn OFF
after it occurs and then using 1 interpolation to
determine the actual turn OFF instant. The turn OFF
thus obtained is then used to interpolate for 1 the
variables.
65
CHAPTER 5
THE COMPUTER
A general flow diagram of the computer programme
which has been developed for the study of power system
circuits involving thyristor shown in Fig. 5.1.
The programme has been written according to the mathemati
formulation discussed in Appendix 6 (i.e. capacitive
branches can be included). Inclusion the capacitive
branches makes the programme more general in application
(e.g. harmonic lters can be modelled) and it can
be used for the study of circuits other than those
investigated in this project
Examination Fig. 5.1 shows that the programme
can broken down into five basic processes:
(i) Data input and the formation of network equations.
(ii) Modification of the network equations whenever
thyristor switching occurs.
(iii) Determination of the length of the next
integration
(iv)
. (v) Output.
Each of these five ses cons
subprogrammes. The subdivision
a number of
ses in this
be deve~oped and
allowed the various subprograoones to
lity to the
independently, adding a
programme.
INPUT DATA AND FORM NETWORK EQUATIONS
MODIFY NETWORK EQUATIONS
DETERMINE NEXT INTEGRATION STEP-LENGTH
SOLVE NETWORK EQ1UA']~IONS I
NO
PRODUCE OUTPUT
STOP
Fig. 5.1 Flow Diagram
66
The only
resist
(a) The
t
on
any
and thyristor
branch element types must
use of programrne
t involving
ements are:
the various
A6. 1) •
67
(b) When thyristor branches are included the logic section
of ·the programme, which controls the switching, must
be amended each new situation. For this project,
the logic is designed to switch blocks of four
thyristors (i.e. two back-to-back pairs of thyristors) .
The programme can cater for up to a total of
50 branches and 50 nodes. There is so provision for up
to three independent
input data.
5. 1
nodes to be specified in the
A dynamic simulation study of a power system
configuration, involving a.c. system busbars, three-phase
transformers, transmission 1 and thyristor switches,
can involve a considerable quantity of input data. This
allows the programme to form the required network
equations, control the integration length control the
switching any I and to output
information from the simulation Initi
conditions, which include the states any thyristors, must
also included input
5. 1 • 1
The
broad
input data can
as lows:
into
list information abou·t each
individual
Control used to
Initi itions ~ from this 1
branch currents and node are
5.1.1 . 1 Branch ----------------- A separate input
is required each branch the network The
contained on each card includes the branch number, the
sending and end node numbers the speci
current direction in that branch, the rms value of any
sinusoidal voltage source, and the impedance of the branch
(capacitance in farads, resistance ohms, inductance
henries, and thyristors have zero impedance) A second set
of cards contain the mutual inductances and branch numbers
between which they are fective. Each mutual inductance
has either a positive or negative sign depending on the way
in which the two branches have been wound.
The branch list data cards are input in the
following order:
5.1.1.2
capacitive branches
res ive branches
inductive branches
thyristor branches
mutual i
Data: The ...;..,,;;.-'---------~
rst control
integration s length and simulation
card
the study, both
switching inc
in mill
the integration
When thyristor
length is
considered to be maximum permissible s length. 'l'his
the programme the i ty, under
68
certain cond
length. An over
must also be
equations is
included) •
, to sown
if
(i.e if capacitor
69
simultaneous
are
The next two control data need only be included
thyristors are The rst of e has
information on the thyristor holding current and the ring
angles of the thyristors, while the second card has a 1 t
of the node voltages which are used asa re
firing of the thyristors.
for the
The remaining control are us to specify the
output of information required from the programme. Up to
a total of nine output variables (node voltages, vo s
across branches and branch currents) may be specified.
5.1.1.3
conditions data includes not only the capacitor node
voltages (Va) and inductor currents (II) but also the state
of thyristor (i.e. whether the thyristor ON or OFF)
and their respective firing angles (in radians) up to the
f zero crossing the reference voltage
To obtain the init 1 condi data Va
f, log control statement is the programme
to cause the , which can then
be us all simulation runs with the same
network. Initial conditions, how they are obtained, and
the on the ts the simulation are d sed
in il in 6.
70
5. L 2
Immediately has been
in, a subroutine through 1
and nodes. Once the node renumbering
complete the connection s
in the solution (either equation (4.15) or equation (A6.30))
are formed. Together with these matr and tial
conditions data, the state variab s ($11 and Qaa) are
calculated and the dynamic simulation is ready to begin.
5.1.2.1 N~o~d~e~~~~~~ When the branch list
data input to programme, the nodes can be numbered
in any order. A node renumbering subroutine identif
and renumbers the nodes in
a nodes
B nodes
y nodes
o nodes
following order:
reference nodes
This makes subsequent identification of any part
node type a relatively simple and eliminates the
for sorting during later ing
If thyristor in branch 1 s
from the
When the being reformed
each thyristor switching only the 0 (a et:. of y
examined. ly this involves only a
s to a minimum.
cus on the reformation star
switching ed in
5.1.2.2 cases
ity obvious the
can compacted without an undue amount of It
no 1 is compacting es. Some
matrices, which only terms (e g. l'
and C ), are easily stored as vectors. cc
connection , which are
stored as two vectors in the following way
zero elements of a connection matrix are
ly se, are
Since
± 1 ,
first vector used to store the column number together
with the respective plus or minus sign. The second vector
used to store information about the number of non~zero
elements in each row. In this vector the di
each pair of successive entries indicates number of
non-zero elements of each new row. When a icular row
has no non-zero the previous address is
The element corresponds to a fictitious extra non~zero
entry in the original connection matrix indicating the end
of the final row.
As an example, assume the connection
Table 5.1.
Number ~
1 2 3 4 5 6
1 1 1 1
2 1 1
3 1 1
Number 4
5 1 1
6 1 -1 1
Tab 5.1 connection
Th connection can two vectors
(KON and IR) as
KON
IR
5.2 MOD
Whenever thyristor are included in a
network, their switching causes changes in the topology.
Subsequently these topological changes
the network equations.
The control of thyristor switching and
changes in topology and network equations are
from one subprogramme. The flow diagram of Fig. 5.2
outlines the process performed by this section of the
programme. This flow diagram is subdivided
processes as follows:
four
(a) Determination of the variables for the thyristor
model from the previous integration step.
(b) Interpolation for reference voltage zero crossing
and the production of thyristor pulses.
out
(c) Determination
(d) Topological
state of 1 i tors.
ion
which t
5.2.1
7
1
This deals with the determination four
logical , VAK
, D and G) which are u ed
ionship (Section 4.1.2) ining the stab
I START I
DETERMINE VARIABLES FOR THYRISTOR MODEL
INTERPOLATE FOR REFERENCE VOLTAGE ZERO CROSSINGS AND PRODUCE GATE PULSES
FOR THYRISTORS
DETERMINE STATE OF THYRISTORS
'II
ANY TOPOLOGICAL
CHANGES?
YES \'
NO ""
MAKE APPROPRIATE TOPOLOGICAL AND NETWORK EQUATION CHANGES
I I I I
Fig 5.2 Thyristor
73
Be
r act
known
the
D,
determined which thyri
state
computat
currents and
tor can be
have
st:or, i
it must
OFF the
previous integration step. Once this turn OFF time
calculated, and VAK
can found (VAK zero for a
conducting thyristor) and a decis can be made regarding
74
the production gate pulses (G). The present state (P) of
each thyristor can now be determined using the logi
sion P = VAK0GoD + lAKD
5.2.1.1 Two
back~to-back thyristor switches are normal us in each
, in the present work, and F . 5.3 shows two such
switches and their associ
Th1
Th2
Th3 ThL~
.53 Two Thyristor Switches
this conf ig-uration,
istor (Iy > is calculated from the vector
currents (II) according to the flow
4. The following notation is
diagram and for the explanation
individual thyristor currents:
(x) ~ current flowing in thyristor x
1 currents flowing
in inductors connected to node 0 n
stor 1 or 2 The currents flowing in
be calculated by applying
node 0 1 •
ff's current law to
i.e. x 1, 2
Similarly, if no commutation ace, currents
flowing in either thyristor 3 or 4 can
Kirchhoff's current law to node °2 "
by applying
When a commutation
place, the currents in
using equation (5.1),
include the current f
i e
flowing
the
5.2 1.2
currents
(x)
x = 3, 4 (5.2)
thyristor switches is taking
1 or 2 are calculated
equation (5.2) is modified to
in e thyristor 1 or 2.
(x=2) "'" 0 for x := 3, 4 (5 3)
Once the currents
1 thyristor have been calcul
turned OFF during the previous
by comparing their
holding current (S
tantaneous
51.12).
NO
CALCULATE Iy (I) OR (2) USING EQUATION (S.l)
NO
NO
CALCULATE ry(3) OR Iy(4) i
USING EQUATION (5.3)
CALCULATE ry(3) OR Iy(4) USING EQUATION (5.2)
STOP
Fig. 5.4 Thyristor Currents
76
An accurate turn OFF time can only
slowing
is normal by
a occurs and improving
interpolation (Appendix 7). The
determination of thyristor turn OFF
diagram of Fig. 5.5.
at the
Suffi
turn OFF
the
shown by flow
When a number of thyristors are involved, as
for a three-phase study, one or more thyristors may have
turned OFF during the previous integration step. This
necessitates determining the earliest turn OFF time. The
turn OFF or earliest turn OFF time (if more than one
thyristor has turned OFF) then us to interpolate
77
all the other variables (node voltages and branch currents)
5.2.1.3 Thyristor turn ON is
predictable s the production of gate pulses is ded
by the control system. In this case the integration step~
length can be adjusted so that the firing instant coincides
with the beginning of a step. The firing instant related
to the zero crossing of the reference voltage, and this
point can be determined by linear interpolation
(Appendix 7) without the need for any change in
step- From the time at which the
zero cross occurs the spec
delay of thyristors (Section 5.1.1.2)
e determined and
At the beginning of integration s I the
firing ang
iest to
stors are
If this
to determine
cular f ng
DETERMINE ANODE-CATHODE CURRENTS OF THYRISTORS
HAS MORE THAN
ONE THYRISTOR
DETERMINE THYRISTOR TURN OFF TIME
INTERPOLATE FOR ALL OTHER VARIABLES AT TURN OFF TIME
YES
DETERMINE EARLIEST THYRISTOR TURN OFF
TIME
Fig. 5.5 of Thyristor Turn OFF
78
7
angle (£) is within some rance of actual angle (wt)
the c istor model (
4. L 2) , set at 11'
i , s are produced if
1 20 (max step-length) < wt < £ + 1 (max. s length)
5.2.2
Any changes in topology, caused by thyristor
switching, affect only a portion of ynode-induct
branch connection matrix Kyl . Because of the way in which
the network analysis and problem formulation have been
carried out these changes in KYI are effected relatively
simply.
At the beginning of each dynamic simulation study
the programme forms a composite connection matrix. This
matrix is bui up inductor and thyristor branch-node
, and an example of such a matrix is given in Tab 5.2.
Inductor Branches Thyris-cor 1 2 3 4 5 6 7 8 9
y nodes l 1 +1 +1 -1
2 +1 "~ 1
0 nodes l 3 1 1 +1 1
4 +1 1 +1 "lVI ~1
Re 5 +1 -1 ~'I +1
5.2 Composite Connection Matr
As dynamic simul the programme
es ishes which thyristors are ON whi are OFF.
with this the
is ch in following manner. For all stors
which are OFF, any in the composite
are So if it is that
.6 and S are OFF thyristors 7 9 are ON, the
compo connection matrix changed to that shown in
Table 5 3.
Node Numbers
1
2
3
4
5
I 1
+1
1
Table 5.3
Branch Numbers
2 3 4 5 6 7 S
+1 -1
+1 -1
-1 -1
+1 +1
+1 -1
Modified Connection Matrix I
Next the programme examines the connections of
remaining thyristor branches of the modi
matr Table 5.3 and combines any rows which are
by a tor Th is pos
a conducting as a
4.3.1) For , rows with node
4 and 5 in Table 5.3 are added and
in row 4 so that modi matrix is
transformed into matrix 'l'able 5 4.
80
9
1
+1
Node Numbers
1
1 +1
2
3 1
4
5
Table 5.4
2
+1
1
Numbers
3 4 5 6 7 8 9
~1
+1 1
-1
+1 ~'l +1 +1
Modified Connection Matrix II
Rows 3 and 4, of Table 5.4, can also be added together and
placed
Node Numbers
By
at
row 3 (see Table 5.5).
Branch Numbers
1 2 3 4 5 6 7 8
1 +1 +1 -1
2 +1 1
3 -1 -1 +1 -1 +1
4
5
Table 5.5 Modified Connection Matrix III
a which rows have
and the
the 0 can be found from Vy during the
of the network
In example, node 5 was orig lly
g s to a
conducting thyristor now trans row 3
Table 5.5, then node 3 now node.
9
as
of
81
82
row 3 KYl is as shown in 5,6
are now two y
Inductor Branch Numbers
1 2 3 4 5
1 +1 +1 ~1
y nodes 2 +1 1
Table 5.6 7 and 9 ON
If it had been assumed that only thyristor 7 was ON,
then rows 3 and 4 are combined and row 5, as the
node, is deleted. This transforms the original composite
connection matrix (Table 5.2) into the KYl matrix of
Table 5.7, where there are now three Y nodes.
Inductor Branch Numbers
1 2 3 4 5
1 +1 +1 -1
Y nodes 2 +1 -1
3 -1 -1 +1
Table 5.7
, the as stor
switching e, ing to determine each
new K 1 Y
of the composite
and
unchang!;3d.
only takes place on a subsection
matr by the <5 s
the majority of original
Any
formulation
flow
5.3
ly
These
of
to
are
. 5.6.
stor
in the
to the
Whenever the network under study conta only
capacitive, resistive or inductive branches (or any
combination of two or more e branch types) the
integration step-length is set in the input control data
(Section 5.1.1.2). Under conditions the integration
length remains unchanged throughout the study.
83
When thyristor branches are included in the network,
the programme should be able to alter integration step~
length, within some specified limits (Section 5.1 1.2).
This facility that the ing thyristors occurs,
as closely as possible, at the beginning of an integration
step. Fig. 5.7 shows -the method used to determine the
integration step-length. The following symbols are defined
and used in the flow diagram:
e:: thyristor firing
wt actual angle
HR maximum
HV length < HR
HC maximum commutation length
A maximum commutation length (HC) def
ion times, stems studied, are
than 0.05 milliseconds in some cases)
START
FORM NEW CONNECTION MATRIX
KYI
-1 Lyy '"
Mll "'"
,~
FORM NEW MATRICES
KYI -1 T
Ln Kl y
T ull K1y Lyy l<Yl
IN EQUATION .(A6,30)
RECALCULATE
MATRIX ill
CONSTANT r1
STOP
-1
Fig. 5.6 Changing KYl
START
SCAN FIRING ANGLES OF ALL THYRISTORS AND SELECT EARLIEST FIRING ANGLE (£)
YES
STEP-LENGTH =: HR
Fig. 5.7
STEP-LENGTH = HV
WHERE HV ;: £ - wt.
STOP
5
srrEP~ LENGTH He
Determinat
The He "" 5 Q v.lhich ensures
number s occur during
a truer entat the tern is
5.4 SOLUTION OF THE
Once the ial conditions (W t , Qt and have
been established, integration length (h)
hence Et +h determined, then the matrix equation (A6.30)
can be solved the new state variab Wt+h and Qt+h.
Using these new state variables, the non-state variables
can calculated in the shown in Fig. 5.8.
The way in whi the thyristor currents ( ) are
calculated from the inductor currents (II) is discus
in Section 5.2.1.1, and the vector of voltages at 0
(V8 ) found from the vector of vditages at y nodes (Vy ).
Any thyristor switching in changes in topology
which are mirrored in changes to the Kyl connection ma'trix
(Section 5.2.2). If these changes to Kyl are recorded at
each switching instant the vector Vo can easily be found
from Vy ' s
short-circuit
a conducting thyristor modelled as a
4.3.1).
5.,5 OUTPUT
Only those les which are i ed the
control 5 {.1.2) are by the
programme, and all are automatically dis
they are no Normally each tenth
output, the only deviation from is
86
7
START
,II
CALCUr~TE STATE VARIABLES
1J!t+h AND Qt+h
FROM EQUATION (A6.30)
'\ 1I
== Xli (w1J!t+h)
,
-1 V =: Xcc (wQt+h) a
+ Va == -Raa {K
e1 + KS R-1V )
r rr r
t -1 T
I == R (V + K eVe) r rr r r
t T T
VI ::: ~I + KlaVa +KIBVa - Rll II
t -1
Vy "" -LyyKylLllvl
t AND Va CALCULATED FROM
AND Vy RESPECTIVELY
,II
5.8 Solution Network Equat
88
stor occurs then at
of switching are output.
A wh
conducting, thyristor ang
also output automatically at a thyristor
switching is detected. This is a relatively and
simple method checking the thyristor switching
sequences are correct.
The discrete information obtained from the dynamic
simulation can be used to obtain the harmonic content and
phase relationships the voltage and current waveforms
Since the time steps used the dynamic solution are not
generally equally , linear interpolation (Appendix 7)
is used to obtain the approximate data at regular So
This data is then processed by the Fast Fourier Trans
(Cochran 1967) and discrete Fourier c and
b n (Appendix 8) are computed. The Fast Four r Trans
is an efficient method for computing the discrete Fourier
coefficients and takes advantage of the fact that the
calculation these coefficients can be ed out
iteratively, ing in considerab savings in bo·th
storage and computing time. The rms values (C ) n
re (¢n) each component of the compos
are by the following re
ively:
Cn "'" (S.Li)
, ¢ n tan 1 ( J an
(5.5)
89
CHAPTER 6
DIGITAL
The computer programme discussed in Chapter 5 was
written in Fortran IV and implemented using Burroughs
B6700 digital computer at the University Canterbury
Computer Centre. 7 9 kilowords of core storage were
required for the programme. Total array storage,
including the output and plotting subroutines, required
another 61 kilowords core.
In order to cater for the harmonic voltages and
currents generated by proposed circuit an integration
step-length of a few degrees of fundamental
(50 Hz) should be used. Experience shown
(Campos-Barros 1976) that a sampling rate which
at least 6 integrations per cycle, at the highest frequency
of interest, is necessary for good results Assuming th'::it
the highest frequency is the 20th harmonic
(1 kHz), a s length of o s than 167 ~s (3 of
fundamental) is necessary.
Because the c length e
facility (Section 5.3) in programme the
t system configuration, vary
considerably di speci thyristor swi
ing The computer simulated transformer on'~load
v which in Section 7.3,
an to il th
Th
The
so
time neces
inc 12
the maximum
some of
and 21 di
ion
as 0.12 ms (2 16° fundamental) and
length
simulation
topological 42 ms of real time. Owing to the
changes (30 switching per 50 Hz cycle for a
of
three~phase system), the solution proceeds with a
maximum integration length of 0.12 ms and execution
90
times were within the range 485 to 627 seconds. The
simulation of a typical three-phase system is thus expensive
as as computer time is concerned. No doubt considerable
savings could be made by compacting I s and keeping
array processing to a minimum. This was considered to
beyond the scope of this project, which was concerned with
using the programme as an investigative tool
optimising its operation
than
Obtaining satisfactory initial conditions for a
particular system configuration involves a large proportion
of computer time. Eliminating the mismatch which exists
between the sinusoidal waveforms initially assumed and the
actual distorted waveforms, to obtain good initial condi
data, is di 6.10
The lity to
s waveforms (Section 5.5) 0
6 2 the idity, using a square wave
test waveform, of is harmonic analys process.
The of trans , the
ty the mathemati transformer model (Sec·tion
4.1 3) and its ability to with
9
trans connect are discussed on 6 3.
6.1 INITIAL
To ini condi
and state of each thyristor)
(inductor currents
computer studies
d cus in Chapters 7, 8 and 9, the thyristors are rst
removed from the circuit and the secondary winding of
series transformer is short-circuited (i.e. steady state
sinusoidal waveforms are rst assumed). Two cases,
wh will illustrate some of the problems associated with
attaining good steady state sinusoidal init
are described.
conditions,
Case (a) - In-phase voltage boosting, where the
voltage of an 8.25 kVA 400/200/66V three-phase
transformer (Appendix A5.1) contro the secondary
voltage via a 25/38 V series transformer (Appendix
A5.2). The circuit is illustrated in g. 6.1,
T1 and T2 are the three-phase and series transformers
respectively the load, represented by voltage VL
and current IL v a series impedance 7.8 SI with
power 0.9.
Fig. 6.1 Sing Line Diagram of Case (a)
Case (b) - boosting, where the
main trans is 450 MVA,
are given in 14
and c is illustrated 9.1.
each simulation to the steady
state sinusoidal initial conditions begins, 1 branch
currents are assumed to be zero and voltage generator
is sconnected from circuit. The instant the
simulation starts the voltage generators are connected to
circuit, and currents begin to flow in each branch.
Figs 6.2 and 6.3 are examp of two initial condition
computer runs done cases (a) and (b) respectively.
The three waveforms plotted in each of Figs 6.2 and 6.3
are the three 50 Hz secondary winding currents of main
three-phase transformers. Fig. 6.2 shows that steady state
sinusoidal initial conditions are in ss than half
a 50 Hz cycle. The waveforms Fig. 6.3, on the other
hand, show quite clearly that even 5 cycles of
simulation time, steady state sinusoidal initial conditions
have not been reached. It may therefore necess to
2
extend the initial conditions simulation run beyond 5 cycles
and up to 20 cycles or so. Wi a t,
involving a number of branches, this can
ive and computer time consuming s. The cost
steady state initial conditions can be reduced by
starting the simulation using a ively long ion
length as the waveforms approach
state conditions.
· 6.2 Case (a) Conditions
-~. -
F . 6.3 Case (b) Initial Condit
Once ste
have been e
state
into the circuit as shown
idal initial conditions
can reintroduced
Fig. 6.4.
Fig. 6.4 In-Phase Voltage Booster
The transformer and load parameters this circuit are
the same as those quoted for case (a) earlier in this
section. Now the simulation restarted from the
sinusoidal initial conditions already established,
and the sinusoidal currents flowing in the secondary
windings of the s determine
which thyristor of switch
conducting at the beg inn
initial cond ions input
thyristors fied as
each be
the simulation. In the
(Section 5.1.1 3) these
ing ON and all others OFF.
The simulation is then re with only the thyristors
of switch S2 conducting until a zero crossing the
5
voltage is and then appropriate
thyristor of switch 8 1 can conducting
specif fir delay. This s is illustrated
F 0 6.5, where
three-phase load voltage
(c) are the
wave
(d), (e) and (f) are the voltages across the secondary
windings of the series transformers (VT ) Once one of
the thyristors of switch 8 1 has started conducting, the
switching sequence on that phase proceeds as predicted
by the theoretical waveforms of Chapter 2.
(a)
(b)
(c)
(d) 1-------'
(e) 10------,
(f) 10--------.,
o 10 40
Fig 6.5 Switching Initial Condit
9
As each istor switching occurs, the
programme outputs which
which thyr s are ON and so prints the
firing angle of The distorted
waveforms from this run are considered to
as initial conditions further dynamic studies, on
the same system, when the d.c. component each
waveform, as calculated by the Fast Four Transform
(Section 6.2) drops to s than 0.1% the
fundamental.
Obtaining a set of realistic initial steady
state waveforms for circuits involving thyristors can
thus be every expensive in terms of computing time.
As far as can be ascertained, no formal study has been
made of the problem of obtaining initial conditions
data non-linear state-space computer analyses.
Such a study may be able to determine a much more
ficient method than the empirical methods ently
used and thereby make considerable savings in the
computing time neces
conditions
6.2
for attaining good initial
IS
To veri the validity of mathematical
the accuracy numerical solution
of the harmonic analys of waveforms as discus ed
Section 5.5, a study which can ver ied by
means is
97
9
A wave 't'11ith a fundamental
50 Hz, as shown . 6.6, was as test
Volts ,~
+100
o .. 0 10 20 Time (rns)
-100
Fig. 6.6 Test Waveform
To simulate the output from a dynamic simulation,
where discrete unequally t s are usual, an
case only e coord are
Table 6.1 shows these eight , and the
programme used 1 interpolation (Appendix 7) to obtain
neces The interpolation
produces 128 ly time-spaced points
over a single cyc This "equal interval data" was then
by the Fast Fourier Transform (Cochran 1967) to
the discrete coeff a n
b 0
n
(5.4) and (5 5) were to ca
rms
each harmonic.
(C ) n
Table 6.1
The rms
phase
Time (ms) Volts
0.0 0.0
O. 1 +100.0
9.9 +100.0
10.0 o 0
10. 1 -100.0
19.9
20.0 0.0
20.1 +100.0
Square Wave Coord
of harmonic were then expressed
99
as a percentage of fundamental rms Figs 6.7 and
6.8 show the percentages of each harmonic present and their
phase relationships respectively. Notice that because
the half-wave symmetry no even harmonics are present. The
Four ser expans contains only terms because
the is an function and us the
fundamental rms (90.014V) by programme,
the input waveform can be sed
as:
4~0 (sin wt + t s 1 1
3wt + ~ sin 5wt + , sin 7wt + ..• )
This Fourier ion a square wave. with the
phase re are by Kuo ( 1 966) .
Fig. 6.7
F . 6.8
Amplitude Spectrum WaVefOrIll
Phase Spectrum of Test Waveform o o
6.3 VALIDATION
The validity
model (Section 4.1 3) is
transformer
when the
programme the which correctly
the behaviour the s phys transformer
var three-phase trans connections
To achieve this a suitable method of measuring the
transformer and formulating the mathematical
model is necessary. The measurement of transformer
parameters is discussed Section 6.3.1.
Using impedance parameters the 8.25 kVA
transformer (Appendix AS.1), a number of dynamic
simulations are in this section. Various
three-phase transformer connections are used, enabling
a comparison between the physical transformer and
mathematical model to be made. Discrepanc in the
results comparisons can indicate ser errors
in modelling or, alternatively, give a measure of the
numerical accuracy of the digital solution.
6.3.1 Parameters
Consider a coupled circuit model (Section 4.1 3)
a two-winding trans as in 6 . 9 .
. 6.9 Two-Winding Transformer
101
'102
Analyt two~winding trans can be
by the (6 1) (Section 4 1 3)
( 6 • 1 )
To determine the self and mutual inductances
in (6.1) to required ion is beyond the
of practical inductance measurements. For this
reason short-circuit s 'are standard means of obtaining
reliable figures for leakage inductance in power
trans Assuming that the resistance of the windings
is negl in comparison with the reactance. The
impedance matrix equation (6.1) for the two~winding
transformer can be as:
where Z1 ~ jwL 1
Z2 ~ jWL2
Z12 jWM12
To determine Z 1 f full tage is to winding 1
and winding 2 these
conditions
and L1 can be L2 i determined in a
similar- manner. To determine Z12' voltage ied to
winding 1 increased 1 full rated flows
'103
c winding 2. Under conditions:
(602)
so that Z12 :::
To determine all the
multi-winding
measurement is
::: reactance)
determined
and mutual inductances of a
transformer, the open~circuit
each winding and
the short-circuit measurement is repeated for each and
every pair of windings.
These "standard" open and short-circuit tests
presuppose sinusoidal conditions in both the voltage and
current waveforms. Chen (1962) showed, using search coils,
that the assumption sinusoidal conditions is indeed
invalid. He also shows that the transformer parameters
can be more precisely determined using the 1
method, but because the practical fficult of
inserting search coils this method was not used.
For the reason already discussed in Section 4.1 3,
three-phase transformers are modelled as three independent
single-phase units. In Appendix 5 the per phase impedance
parameters are given
in various dynamic s
are ca
6 3.2
two trans which are
These impedance
the re II open
resistance measurements using a
Transformer
Using transformer impedance paramet"ers of
Table .1 and the dynamic simula programme discus
104
in 5 transTnrmiP connections
are investigated
di tri':tTIsformer
are In each case winding is
connected to a star 0.9 p f. load
the ary winding is open-circuited.
8Q impedance
three sets
of dynamic simulation results are compared with I
measurements on the transformer.
6.3.2.1 Fig. 6.10
shows clearly that primary, secondary and tertiary
terminal vol are all in phase. The rms terminal
voltages and transformer winding currents as calculated
by the computer programme and measured
are given in Table 6.2.
the laboratory
Calculated Measured
ry terminal vol 230 V 230 V
Primary winding current 7.69 A 7.66 A
Secondary terminal voltage 115.5V 11S.7V
Secondary winding current 14.4 A 14.6 A
Tertiary terminal voltage 36.0 V 38,6 V
Table 6 2 rms Vo and Currents
The primary winding currents, as
lated the computer programme, are shown Fig. 6.11.
A Fourier analysis of two waveforms, formed by th e
secondary computer programme (Section 5.5),
winding current is the primary
that
a ing current by 3
-
-160
o
Fig. 6.10
Primary Terminal
__ ~_, __ ~ __ --Secondary Terminal Voltage
Star/Star/Star Volt
Tertiary Terminal Voltage
(MI lSE:cor-os )
s o
Current
Current
5
o
-10
- 5
-20
o TIME
Fig, 6, 11 Currents c
se
currents, was
on
pr
-107
and
measurement out
e
ft
the primary
shown by Fig 6.12
wi
1 voltag'es is
to
early
A son Figs 6.10 and 6.12
shows reduction the secondary terminal vol f by a
1/13, to delta winding. The rms
voltages and currents, bot.h calculated measured, are
given Table 6.3.
Primary terminal age 230 V 230 V
Primary winding current 2 61 A 2.69 A
terminal vol 67.6 V 67.5 V
Secondary load current 8.30 A 8.59 A
Secondary winding current 4,58 A 4.90 A
terminal voltage 36.3 V 39.7 V
Table 6.3 Star/Delta/Star rms Voltages and Currents
The phase relationship pr wi
current, s
current shown
ing current
6. 13 "
Connection: At the
l
beg of each dynamic simulation a re
in es.ch of ci
e node mus't
is
electr s but magnetically coupled to
In ns 6.3.2.1 and 603 2.2 a ent
60
-320
o
F . 6.12
_____ -- primary Terminal Voltage
Secondary Terminal Voltage
Star/Delta/Star voltages
Tertiary Termina Voltage
LLlSEC'O'OS) 40
16
12
8
4
o
-4
-8
--12
--16
o
Fig. 6.13
, .... _--- Secondary Load Current
~~ ____ ~-Secondary Winding Current
20 Tlt'E (MILLJS£CCX'iJS)
Star/Delta/Star Currents o '-0
'j 10
node was (i e.
delta
star point)
in
winding a
shed by
circuit. For
voltages can
must be
calculated
to
connection as shown in Fig. 6. 1.4. These
which have a high impedance compared to that
transformer , have ly no ef
voltages and around delta winding.
so that
This is
resistors,
the
on the
•• ~ __ ~r--Reference node
• 6. 14 Re Node ta Winding
primary and winding currents, both
calculated and measured, are the same as those for
Star/Delta/Star connection discus in Section 6.3.2.2
Fig. 6.15 shows the relationship of the
secondary tertiary terminal vo and their rms
values are given in 6.4.
Calculated Measured
Primary 230 V 230 V
Secondary 67.6 V 67.
20.9 V 23.0 V
6.4 ta/Delta rms Terminal Voltages
Primary Terminal Voltage
.-..
o
-00
20 )
. 6. 15 1 Voltages
6 3.3
Transformer , as calculated from
open and circuit tests and measurements
(Section 6.3.1), give a ently accurate mathematical
representation of the the purpose this
investigation Phase and magnitude of terminal
voltages are automatically by the various three~
phase transformer connections and modelling three-phase
transformers as three single~phase units does not
significantly effect the accuracy of representation
1 1
CHAPTER 7
VOLTAGE REGULATION
Most electricity supply authorities are committed to
provide their customers with a supply which maintained
within certain limits both frequency and voltage.
Frequency control taken care of at the generating source,
but the voltage control presents a much more complex problem
and not only involves control and correction at the
generating source but points along the transmission
and distribution system. To maintain the correct system
voltages on industrial and domestic supplies, it is now
commonplace to provide means of on-load vol variat on
the main transmission and base-load substation transformers.
In general, a tap-changer provided on a transformer for
maintaining a edetermined outgoing voltage where the
incoming voltage is subject to variation. There are many
industrial applications where variable voltage requ
for manufacturing ses and typical instances where
transformer on-load tap-changers are used, are arc es,
electrolytic chemic manufacturing esc
A tap-changing techniques is
section this chapter. The
section es the proposed
on-load variable voltage changer (Section 2.1),
obtained the atory using an 8 25 kVA
transformer (Appendix A5.1). The voltage this
'114
conjunction with
in Section 3.2, is used to
In Section 703 results of a
the output a 30 MVA di
unit discussed
voltage.
simulation p where
transformer is
controlled by two back~to-back thyristor switches per phase
is discussed. s chapter concludes an evaluation of
the proposed on-load fixed-tap variable voltage changer as
an alternative to sting on-load
7.1 RESUME OF EXISTING TAP-CHANGING
In the
found it neces
days, if the trans designer
to provide means of changing the
transformer ratio then this was done with a number of bolted
links. When the transformer ratio was to be the
tedious business of undQing nuts and changing over
became a necessity. problem with this method
control was the need to interrupt the supply wh
voltage
the
transformer ratio was changed. Therefore a system
involving the use of 0 load switches was produced that
11 gave continuity of lye
This off-load switch system used two trans
windings in parallel, each winding capable of
the load current for a 1 and each tap
was provided with its own 0 switch and ,t
When a tap was required one of the
1
was opened and the assoc off-load switch was
moved. Once the correct ion was achieved the
breaker was re-closed.
The in~roduction of the centre point reactor of
115
I f t the on- u was 'the
In many countries the
seems to
major developments over
on- (Stigant 1973) 9
Tap-changing a conventional type on-
changer is accompanied by arcing at contacts. Various
methods been employed to reduce
however, some contact eros and
to a minimum,
contamination must
11 place. Roberts and Ashman (1969) suggest a
changer which combines thyristors and mechanical switches in
such a way that the thyristors relieve the switch contacts
of current making and breaking duty, and mechanical
switches relieve the thyristors of any fault currents and
overvoltages when
A number of
tap-changer is not being operated.
prop6sals concerning thyristor
assisted tap-changers have been put forward over recent
years. Examples these are given by OiKelly Musgrave
(1973a). The quest to eliminate contact wear and oil
pollution has led to the development of tap-changers
with vacuum interrupters {Fohrhaltz 1967}, the vacuum
interrupters are used in of thyristors the
The
ternative
changing the
and can only
on~
only
are still
of swi in 1 the
systems discussed means that
rat is s 11 relatively slow
be changed propos
tap voltage changer has a number of
The thyr tor
in proportion to the maximum pe
tches
116
regulation i no for multiple
the is only limi by
intervals thyr s.
The proposed on~load variable volta
changer is illustrated by the single line agram of
F • 7.1. Transformer T1 an 8.25 kVA three~phase
three-winding transformer (Appendix A5.1), and the series
transformer T2 (Appendix A5.2) has a ratio of 25/38 vo
The load, represented by voltage VL
and current
a power of 0.9 and IL is 50% of full load current
when no voltage boosting or bucking taking (i. e,
thyristors of switch 52 are switching at the zero
crossings of the current waveform). Vs and IS represent
the supply voltage and current respectively The vo
across the secondary winding (i.e. 38 V winding) the
series transformer T2 is VT ' and is the current flowing
in one arm of the star connected tertiary winding of T1
Fig. 7 1 On-Load
Voltage Changer
Variable
All 1
and phase angle are
A F. Power
measurements vol tage I current:
using a" ssey"
ey 1977). This
-, "I '7
des to measure the voltage, current, power
angle of selected audio frequency signals of up to 2.5 kHz
in a power supply network. The instrument a s
differential voltage input (maximum input voltage swi
125 V rms / 250 V rms) and the current input (maximum input
current switched 1 Arms / 5 Arms) uses a current trans
which effectively isolates the instrument from the system
current transformers. To monitor current, a 1n res tor is
connected in series with a corresponding system current
transformer secondary as a safety precaution to prevent
accidental open=circuiting of the system current transformer
secondary.
The ratios of the system current transformers in
the laboratory are quoted for a frequency of 50 Hz. S
the thyristor switchings of the proposed on~load fixed~
variable voltage changer introduce harmonics which are
mUltiples of 50 Hz fundament power frequency, a
on the frequency response of a system current transformer
was performed. These frequency response tests are cr
in in Appendix 9 The these tests to
conc s i no detectable waveform
distortion through tem current transformer and that
the primary harmonic current, for frequencies up to 2 kHz,
in the secondary winding in with
"I "18
7 2.1
The is shown in
Fig 7.1. If S £ 1 and e: 2 ent
firing of
re , the thyr of S, can
be at any time with the range cos- 1 0.9 < £1 ~ 165°.
The upper limit 1650
is fixed by the controlling
production of gate pulses (Section 3.1.1) to switch S1'
The appropriate thyristor switch S2 can be fired at any
° -1 time within the 0 < £2 < cos 0.9. Within these
two sets limits on the delays £1 and £2 the following
control strategy is adopted:
~ 1 0 9 165° cos . < £1 <
E 2 :: 15°
(i.e. £1 is varied while £2 is kept constant at 15°).
All oscillograms of typical voltage and current
waveforms illustrate a particular case when the firings
f th ' . h d dId by 90° o yr1stor SW1tc es S1 an S2 are e aye
respectively. The oscillograms shown in Fig. 7.2(a) f (b) f
(c) and (d) show the supply voltage (VS), the supply current
), the load voltage (VL
), and the load current
respectively. . 7.3(a), (b) and (c) are oscil
of the across the winding of the es
current the winding
the series the current in terti
wind T1 (IT) respectively.
The vol waveform 0 F . 7.2(c)
not c show 1 the inuities, Fig. 7.4
another oscillogram of load voltage where thyr tor
are clearly visible
(a)
(b)
(e)
(d)
Fig. 7.2 Oscillograms Typical Supply
and Load Voltages and Currents
(a)
(b)
(e)
Fig. 7.3 Oscillograms of Typical Voltage VT Currents
1 0
Fig. 7.4 Oscillogram of Typical Load Voltage
In particular oscillograms 7.3(a) 7.4 the
predicted waveforms VT and VR Fig. 2.2
7.2.1.1 Although it
not immediately obvious from oscillogram 7.4, the
fundamental component of the load voltage (VL
) has been
boosted by 6%. The percentage regulation of the fundamental
component of the load voltage as a function of the f ing
angle 81 (while 8 2 is kept constant at 15°) is il
in Fig 7 5(a). This graph shows that a stepless vo
variation, with percentage +14,,5%
3%, lee
Point on wave control boost has
a small the fundamental components of
voltage at terminals of trans T'I
and load The ation phase ft, as a
tion of the fi angle e: 1 ' is plotted in Fig. 7 5 (b)
1 in range +2.8° to -0. Between A
the
B 0 7 Sg 13 by '1 0
voltage y 9%0
the major vo
occurs over a 1 e fto
16
2
o
-2
. _j~oP =
A
(b)
( a) -4b-__ ~ __ ~ __ ~ __ ~ __ ~b-__ b-__ ~ __ ~ __ ~
o 20 40 60 80 100 120 140 160 180 Firing Angle (:'1 (degrees)
Fig. 7.5 Load Voltage Var
(a) Voltage Regulation (per cent)
(b)
7 • :2 • 1 :2 gs 7. 6 to 70 '11
1 current
ly. ~['hese
This
content each of these
when thyristor 1
by 90° and 15° re ly
121
2
3 5 7 9 11 13 15 17 19
076 Supply Voltage (VS
)
3 5 7 9 11 13 15 17 19
Fig. 7.7 Supply Current ( Spectrum (001 A/ern)
3 5 7 9 11 13 15 17 19
7.8 Volt (VL
) Spectrum (2.0 V/cm)
3 5 7 9 11 13 15 17 19
Fig. 7.9 Load Current ( ) Spectrum (0.1 A/cm)
3 5 7 9 11 13 15 17 19
Fig. 7.10 Across Secondary Winding of
Trans (VT
) Spectrum (4.0 V/cm)
3 5 7 9 11 13 15 17 19
7 11 Current Tertiary Winding '1'rans
T1 (IT) Spectrum (0.4 A/em)
of and current vary the
fi £1 £2" harmon content
the vo and current load
vol and current are in s
and 7 13 respectively. harmonic is
as a respective fundamental
and each current harmonic is expressed as a
the current of the respective trans
(Appendix .1).
5%
4%
3%
2%
1%
3
voltage Current
Fig. 7.12 Maximum Harmonic Content at
point on wave
acts as a source
voltage booster
plus harmonic voltage
']. '1
of
Fig. 7 13
the
that
levels
predominant vo
5th and 7c,h are
harmon C :LS
so signi
leve current are 1 ted by the load
I
as shown F
7%
6%
5%
4%
3%
2%
3
'7 1 '7. 130
7 11 15 19
Voltage
3 7 11 15 19
Current
<C'
'"
Fig. 7. 1 3 Maximum Harmonic Content at Load Busbar
A comparison the harmonic content of e
"
and load currents, 7 7 7.9 Figs 7.12 and 7.1 ,
shows a larger harmonic content on supply side.
is caused by harmonic current from
The maximum harmon content 0 the
winding current sed as
of winding current) is shown in
• 7.14. It can be seen the oscil of ter ary
winding current ( '7.3(c)) that the nature of
waveform indicates presence of relatively high
harmonic current s.
Fig. 7.14
14%
12%
10%
8%
6%
4%
2%
I I I ! J 3 7 11 15 19
Maximum Harmon
Winding Current
Content of
'1 6
ary
If the thyristors of at the
zero crossings the current waveform and the thyristors
of switch 8 2 are not ng fired at en all wave
both current and voltage, are sinusoidal. Under these
switching conditions, Figs 7.15 and 7.16 show typical
voltage and current spectra.
3 S 7 9 11 13 15 17 19
7. 15 Supply voltage (Vs ) (0.4 V /crn)
'127
3 5 7 11
Fig. 7.16 Supply Current ( (0.1 l\jcm)
A compar Figs 7.7 and 7.16 shows c
harmonic content of the supply current, which is due to
the operation of thyristor switches 51 and 52" The supply
voltage spectra, Figs 7.6 and 7 15, show that the operation
both thyristor switches does not nece ly result in
an in the level individual harmonic.
This situation arises out of the nature of the 400 V system
harmonics (Appendix 10)" 50me system voltage harmonics can
exhibit relat ly large magnitude ons over very
short periods of time (see Figs A10.1 to A10.11) and
therefore two spectra, recorded at the same point in the
circuit at different times, may be quite different. When
the maximum supply voltage harmonics (Fig. 7.12) and supp
voltage spectrum (Fig. 7.6), with both thyristor swi
operating, are compared to table
A10.1)
typ 1 and pea.k
harmonic
majority of
lis
the
and 13th harmonics)
at supply
s ( can be seen t
harmonic magni are Ie than the
do
by
harmonic magnitudes which do
ofT ab 1 e A 1 0 . 1 ( L e . 5 th 17th 1 1 t h
so by a maximum of 0.25%. It can
that voltage harmonics generated
thyristor do no
s ficantly increase those vol harmonics
7.2.2
To act as an voltage , the sense
one winding on es trans T2 (Fig 7.1) must
be reversed. In addition to this change, the
transformer is connected delta/star/star (Appendix A5.1)
to show the fect of winding on the triplen
harmonics. Vs and IS now represent line-to-line
supply voltage and supply current
and I D (IS/I3) is the current flowing in the delta
connected primary windings of T10
ly,
If the angular intervals £1 and £2 again represent
delays in the firing of thyristor switches S1 and S2
1 8
e
respectively, the forward-biased thyristor switch 8 1 can
o 1 now f at any time within the range 0 < £1< cos 0.9.
The appropriate thyristor switch S2 can be red at
t . . h' th 1 0 9 1 65 0 • Th ~me w~t ~n e range cos . < £2 < e lowing
control strategy is used:
::
The s thyristor S 1 and 52 are
100
900 re I asciI
thi 7.17(a),
(b) (0) show the I line supply vol (V S)
the I supply current the current the
winding of T1 ) . vol (VL
) and current
are il Figs 7.18(a) and (b)
(a)
(b)
(c)
Fig. 7.17
(a)
(b)
o 7. 18
Oscillograms of Typical Supply Voltage
and Currents
Oscillograms of Typical Load Voltage
1 9
7 • 1 9 (a), (b) (c) are 1
vol across winding
transformer (VT), the current in
the s
secondary winding
winding of '1'1 of T2 the current in
respectively.
(a)
(b)
(c)
Fig. 7.19 Oscillograms of Typical Voltage VT
and Trans .... "''rITlIO Currents
In , the wave
of • 2. are ly by oscil
7 1 B (a) and 7 1 9 (a) . 7 20 is an
1 0
os llogram of a typical set
waveforms, c ly showing
load voltage
thyristor switching on each
phase.
Fig. 7.20
7.2'.2.1
regulation
Oscillograms of Typical Three~Phase
Load Voltages
The rcentage
fundamental component the load
voltage as a function of e firing angle £2 (while £1
kept constant at 10°) is illustrated in Fig. 7.21 (a).
Completely stepless voltage variation is possible, with
percentage regulation between -3% and -23%.
A small phase shift between the fundamental
components of the voltage at the secondary s of
transformer T1 and has been introduced
on wave contra buck. The
shift, as a tion the
plotted in Fig 7.21 (b) and I o
in the range -0.5 to
_4.8° As with
can seen
between A
of
boost
o a small (1 )
(Section 7. 2 • 1 • 1 ) u
change,
B of Fig. 7.21, vol regulation
12% is possible.
131
132
Firing Angle E2 (degrees)
o 20 40 60 80 100 120 140 160 180
-2 (b)
.... A B '" .... ",,"" ,\, ... ( I '"",,- ,,pi> • • _._-<ifJIII' I
-4
I • o I I . • I I 0 , !
-6
-8
-10
-12
-14
-16
-18
-20
-22 (a)
-24
. 7.21 Vol
(a) Regulation (per cent)
(b) Shi of Fundamental (
7.2 2.2 and
current c
are i s 7.22 to 7,28 These harmonic
il content for a
case when thyristor
90° respectively.
are delayed
3 5
Fig. 7.22
7 9 11 13 15 17 19
Line-to-Line Supp Voltage (VS )
Spectrum (0.4 V/cm)
3 5 7 9 11 13 15 17 19
'133
7.23 Supply Current ( (0.08 A/cm)
'I 4
3 5 7 9 11 13 15 17 19
Fig. 7.24 Delta Winding Current ( Spectrum (0.08 A/cm)
3 5 7 9 11 13 15 17 19
Fig. 7.25 Load Voltage (VL) Spectrum (2.0 V/cm)
3 5 7 9 11 13 15 17 19
. 7.26 (0.08 A/crn)
Fig. 7.27
Fig. 7.28
3 5 7 9 11 13 15 17 19
voltage Across Secondary Winding
Tran (VT) Spectrum (4.0 V/cm)
3 5 7 9 11 13 15 17 19
Current in Tertiary Winding of Trans
(IT) Spectrum (0.16 A/cm)
'j 5
The maximum harmonic the vo
current: current
are il 7.29 7.30
harmonic as a of -the
component, and current harmon
e ra for at
circuit. The currents 0 the
~I '36
re ) are Append A5 ') rated
current
2%
1%
3 7 11 15 19 Line-to~Line voltage (Vs )
4%
3%
2%
1%
3 15 19 3 7 15 19 Line Current ( ) Delta Current (1 D)
Fig. 7.29 Maximum Harmonic Content at Supply Busbar
10%
8%
6%
4%
2%
3 7 3 7 11 15 19
Voltage (VL
) Current (IL
)
Fig. 7 30 Maximum
'137
of current
contents, Fig 7629,
of 1 tr
supply current. As with the va
(Sect 7.2.1.2), harmonic current inj
tertiary winding results in a harmonic content
the primary wind current than in load current"
This illustrated by the respective graphs 7.29
and 7.30. Fig. 7.30 shows that the predominant load
vol harmonic the 3rd. Significant levels of 5th
7th load voltage harmonic are also present.
7.3 COMPUTER S IVE TO
THE
The essence of this section is embodied
entitled "A Stat Alternative to the Trans
a paper
On~Load
Tap-Changer". This paper was accepted for n
at the I.E.E.E. Power Engineering Socie Summer Meeting
in 1979 and for full publication in the Trans ons on
Power Apparatus and Systems, and is
11.
in
The bulk
development
4 5 and a
computer simulation
var e voltage
Typical voltage
simul
the paper i concerned with
discus
proposed on~
a 30 MVA
tap
tribution
1.2 MVA
current
1, are
transformers,
computer
a
1
The maximum content and current
at the and load
11), as s are also
scus content of current
waveforms are in this they
are now current -to
conform with ts presented Sections 7.201,2 and
7.2.2.2. The ta connected primary winding and
load currents are 300 A and 1300 A respectively and
rated supply 1 current is (primary winding current).
Fig. 7.31 shows the maximum harmonic content of both the
supply and load currents A comparison of the supply 1
and currents shows quite ly the
delta winding on the. primary side of the main
transformer eliminating
6%
5%
4% :-
3%
2%
1%
I 35791113 Supply Line
I I 35791113
Delta
• 7. 3 1 Maximum
Load Currents
harmonics.
t I I 35791113
Load
of
of
7 4 DISCUSSION
The proposed on~
changer has been shown to be a
to on-
vo
of
continuous vol control which can is
only limited by the level of harmonic content
by the appropr choice the transformer
Under reasonably balanced power flow conditions v
most of the 3rd and triplen harmonics can
by trans delta connections. If the
eliminated
Is of the
harmonics, other than triplen harmonics, are considered
unacceptable, some filtering plant may be necessary.
The relatively high levels of harmonic current flowing
the tertiary winding the three-phase transformer (see
Fig. 7.14) will mean that the designer of a 11 scale unit
must pay partie attention to the problems 0 transformer
winding overheating and increased iron s.
7.4.1
For the on-load fixed-tap variable voltage
discussed in Section 7 2, is necessa to reverse
the sense of one of the trans windings to
accommodate both and bucking modes of
If the
transformer
winding 5e
to se and
voltages, with re
winding a third
to the secondary
thyristor switch
without the
Fig. 7.32
boosting and bucking are
to connections.
single-line diagram of such a un
s e
v s
F ~ 7.32 Comi':;!ined Boo and
o
The switches are
by 8 1 , S2 and S3 and tert
by +VB ~VB
of this unit as a voltage
requires the use of S1
The thyristor switching sequence is the same as
ibed in Section 2.1.1, and the resultant load voltage
waveform is identical with waveform VR of Fig. 2.2.
Voltage bucker operation requires the use of thyristor
switches S2 and S3 conjunction with anti-phase
tertiary voltage -VB" The thyristor switching lows
same pattern as was described in Section 2.1.2 and
a set theoretical waveforms are shown in Fig 7.33.
A comparison the waveforms VR in Fig. 2.3 and VL in
Fig. 7.33 shows that these are indeed identic
A unit, such as that illustrated in Fig. 7.32,
would combine the boosting and bucking voltage regulation
prof which Figs 7.5(a) and 7.21 (a) are typical
examples) into a single range of continuous voltage
controllabil There , at the of some
waveform stortion I phase shift, voltage ranges
simi to those normal provided by
can
-v B
VL I wt I I I I I I 8 2
8 2
Fig 7 33 Voltage Bucking with Combined Unit
"14
CHAPTER (I
POvmR TRANSFER CONTROL
The flow of power over a transmission I
connecting two power systems, or two parts of the same
system, is inflexibly tied to the power frequency ang~e
difference between the busbar voltages at either end of
the interconnecting line (Elgerd 1971).
System planning requirements normally decide
the nominal power rating of a particular interconnection,
and transient-stability considerations restrict the
maximum steady state power frequency voltage angle
difference to relatively low values (of the order of 30°).
These constraints are checked by load-flow stud and
often, as a result of such studies, quadrature booster
transformers are added to produce a phase shift and thus
satisfy the specified power limits.
Phase shift is normally achieved by means of
phase shunt with windings to
add a fixed quadrature voltage to each phase (Westinghouse
1964) e of voltage boosting level
achieved by the provision of a of transformer
which are by on-load tap-changing equipment.
Using
only
on-load equipment the quadrature voltage can
changed d , and control (i.e.
the pI;'ovision a taps) can only be
at considerable
'14
/144
of providing
between two
the power flow
operating the
s with the use of the proposed
circuit (Section 2.2) as a means
ft and controlling the power flow
c
Section 8.1 discusses
, in the laboratory, by
in modes (i) and (iii)
Typical vol e current as well as their
harmonic content are In Section 8.2 the results
of a computer simulated led quadrature
booster are discussed. The concludes with a
discussion of the use propo quadrature booster/
bucker circuit as a means of controlling the power flow
between two interconnected
8. 1 BOOSTING WITH THE THYRISTOR-CONTROLLED
VOLTAGE REGULATOR
The single-line diagram of "8.1 shows a
transmission line (T/L), with 0.2 + j33.0 ohms
per phase, interconnecting two power s
by their terminal voltages and currents VM, IM and
Transformer T1 is an 8.25 kVA three~phase three-wind
transformer with voltage rating 400/200/66 V (Append AS.1),
T2 (Appendix A5.2) has a of
2 transformer T3 has a voltage rat of 200/230V
represented by VM and IM is the main 400V
A ine wave motor-alternator set (Appendix 12) is
power system and it is represented by terminal
VG current I G" IL represents the transmiss
1 current, and the voltage at the booster bus bar is
e
Fig. 8.1 Single-Line Diagram of a Transmiss System
Quadrature
The vol t.age across the winding (i De. 66 V
winding) of ser trans T2 i VT , and IT
the current flowing in one arm the star
winding T1 8 the power
phase angle d between voltages at -the
represented by VL and VGo
Two cases are to show that power flow,
e
control
direction, between busbars VL and VG can be
by the proposed quadrature booster.
Case (a)
The busbar voltage VL
leads the busbar voltage VG
by an angle 8 and the alternator is operating as an
overexcited synchronous motor. The
VL , VG, IL and 1G are illustrated in
(Fig. 8.2). Since IL lagging
tionships between
vector diagram
the quadrature boosting at busbar VL
is of the mode (i)
type (Fig. 2.5).
8.2 (a) Vector Relat
146
s
Case (b)
vol vo by an
angle e and the is as an overexc
synchronous Fig. 8.3 il tes the
relationships between VL , VG' IL and s e the
transmission line current IL is lagging the busbar
voltage VL and 90° < ~ ~ 180°, the quadrature boosting at
busbar is of the mode (iii) type (Fig. 2.7),
Fig. 8.3 Case (b) Vector Relationships
'147
For both cases, the direction of pos power flow;
which was measured at the booster busbar (VL), was as
to from VL to VG
" All laboratory measurements of
voltage, current, ang and power (both and
) were using a "Plessey" Select A.F. Power
Analyser { sey 1977} 0
8. 1 2
ing to . 8.1, S1 and 8 2 are two
tor switches with angular iring de c 1 and £2
respec'tively." The ed thyristor of tcll S1
90o
+¢< 0
can be at any time within the £1 ~ 165
"148
angle
can at t
illustrate a particular case when fir of thyristor
s S1 S2 are by 148 0 36 0 respectively.
Figs 8.4 (a), (b) , (c) (d) show the supply e (VM
)
booster busbar voltage (VL
), sion I
the voltage (VG
) respect
(a)
(b)
(0)
8.4
Figs 8.5 (a), (b)
across
(c) are oscil
winding
of vol
ser
the current (IT) owing one arm of the star connected
winding of transformer T1
, current
winding of the t.rans
(a)
(b)
(c)
Fig. 8.5 Oscillograms of Typical Series Trans
Voltage and Transformer Currents
A o oscil
8.5(a) with
8.6 c
Fig. 2.5
ly shows the
busbar voltage,
vol s are illus
8.4(b) and ()
retical waveforms
their val ity.
scontinuities in the
se booster
in F . 8.7.
the
Fig. 8.6 Oscillogram of Typical Booster Busbar Vol
. 8.7 Osc of Typical Three-Phase
Busbar Voltages
50
8 1.2.1
typical harmonic
These
harmonic content of each
thyristor switches S1
Variation
re ts in a change in
8.8 to 8.13
VM
, 1M
, VL
, f VG 1G
the
wave when the f
S2 are by 130 0 and
the firing angles £1 and £2
harmonic voltage and current
s. The maximum harmonic content the voltage and
current waveforms at the supply, booster and alternator
busbars is illustrated in Figs 8.14, 8.15 and 8.16
respectively. Voltages are expressed as a percentage of
the respective fundamental component, and currents are
as a percentage of the current for that
151
ings
36°
particular part of system. (1M and IL are respectively
expressed as a percentage of the rated current of the
primary and secondary windings of T 1 (Appendix AS. 1 )
and IG is as a percentage of the rated current
of the voltage alternator (Appendix 12).)
3 5 7 91113 17 19
.88 Supply Vol
1 2
3 5 7 9 11 13 15 17 19
Fig 8.9 Supply Current (1M) Spectrum (0.04 A/em)
3 5 7 9 11 13 15 17 19
Fig. 8. 10 Booster Busbar Voltage (VL
) Spectrum (2.0 V/cm)
3 5 7 9 13 17
Fig~ 8 11 Transmission Line Current
Spectrum (0.016 A/cm)
Fig. 8.12
Fig. 8.13
3%
2%
1%
3
Fig. 8 14
'15
7 9 11 13 15 17 19
Alternator Voltage (VG) Spectrum (0.2 V!cm)
3 5 7 9 13 17
Alternator Current (IG) Spectrum (0.016 A/em)
7 11 15 19 Voltage (V
M)
3 7 11 Current
19
Maximum Harmonic Content at Supply Busbar
7%
6%
5%
4%
3%
2% l-
i-
I I i I
1%
3 7 11 15 19 3 7 11 15 Voltage (VL) Current (IL)
Fig. 8.15 Maximum Harmonic Content at Booster Busbar
3%
2%
1%
3 7 11 Voltage (V )
G
3 7 11 15 19
154
Fig. 8.16 Maximum Harmonic Content at Alternator Busbar
A comparison
(Figs 8.9 and 8.13 re
harmonic current on the
than those on
current inj
Comparing the maximum vo
supply and nator current
that the 1 s
s are lly higher
tor side. This is caused by
from the tertiary winding of T1~
harmonic content at the supply
(Fig 8.14) with the peak harmonic voltage levels
measured on the 400V supply (Table Al0.1), shows that only
155
the 5th harmonic vo I peak
the voltage harmonics at -the supply
not to signi e
harmonic voltage 1 s a
8.1.2.2 The
stor-controlled quadrature booster of Fig. 8.1 causes
voltage magnitude variations as well as phase shift of the
fundamental voltage component at the booster bus bar (VL ).
The voltage magnitude ations are plotted in Fig. 8.17
and these indicate a magnitude variation from 2.6% at
o 0 £1 = 165 to +2.6% at £1 = 120 .
+4%
+3%
+2%
+1%
0%
-1%
-2%
-.3%
100 120 140 160 180
Firing angle £1 (degrees)
Fig. 8.17 Booster Busbar Voltage Magnitude Variation
156
variat the voltage Ie dif (e)
the al"ternator is shown
Fig. 8.18 angle change 3.5 0 has been achieved
using the
38
36 phase angle
difference 34
e (degrees) 32
30
Fig 8.18
outlined in
100 140 Firing angle £1 (degrees)
Phase Ang Di (8) Var
The forward-biased thyristor of switch 8 1 can be
fired at any time within the range 90°
where ~ is the power frequency phase angle dif e
between VL and IL' when IL ate
thyristor switch 8 can be at any thin the
lowing
strategy is the tigation of mode (iii)
ting:
900 - ( 1800 - ~) < e: 1 < 1650
£2 15 0
(i. e. £1 is var wh e £2 is kept constant at "1 ) .
All typical
a
8 1 and 8 2
The supply vol
the ssion I
current
case when the
are delayed 1lt
(VM
) , the
current
'157
I
of thyristor
ively.
voltage (VL
) f
the ternator
voltage (VG) are shown in Figs 8.19(a}, (b), (c) (d)
respectively.
(a)
(b)
(c)
(d)
Fig. 8 e 19 Oscillograms of Typical Busbar Voltages
and Line Current
Figs 8.20 (a), (b) and (c) are 0 llograms the vo
across the ing of ser s trans rmer
current ( IT) flowing in the winding
(VT
)
T 1 ' the current in the s winding
s T2 ly. The
di ies in the booster busbar vol are c ly
shown typical three-phase booster bus bar
va are'illustrated in 8 22.
8
(a)
(b)
(c)
Fig. 8.20 Oscillograms of Typical S s Trans
Voltage and Transformer Currents
F . 8.21 llogram of Typical Booster Busbar
Fig. 8.22 Oscillograms of Typical Three-Phase
Booster Busbar Voltages
The validity of the predicted theoretical waveforms VR,
I and VT of Fig. 2.7 is confirmed by the oscillograms
8.19(b) and (c) and 8.20(a) respectively.
8.1.3.1 Harmonic Content: Typical harmonic spectra
Figs 8.23
to 8.28 respectively. These harmonic spectra illustrate a
particular case when firings of thyristor switches S,
and 8 2 are delayed by 1100
and 150
respectively. The
maximum harmonic Is of the voltage and current wave
at supply, are
illustrated in 8 , 8.30 and 8 31 tively
maximum harmonic vol and currents are expressed
as of the same bases described in
Section 8.1.2 1.
160
3 5 7 11 13
Fig. 8.23 Supply Vol (VM) Spectrum (0.8 V/cm)
3 5 7 9 11 13 15 17 19
Fig. 8.24 Supply Current (1M) Spectrum (0.04 A/cm)
3 5 7 9 11 13 15 17 19
Fig 8 25 Booster Voltage (VL
) Spectrum (2.0 v/cm)
3 5
Fig. 8.26
3 5
. 8.27
7 9 11 13 15 17 19
Transmission Line Current
Spectrum (0.016 A/cm)
7 9 11 13 15 17
Voltage (VG
) Spectrum (0.2 V/cm)
16 ")
'162
3 5 7 9 11 13 15
Fig. 8.28 Alternator Current (IG) Spectrum (0.016 A/em)
2%
1%
3 7 11 15 19 3 7 11 15 19 Voltage (VM) Current ( I
M)
Fig. 8.29 Maximum Harmonic Content at Supply Busbar
7%
6%
5%
4% i'"
3%
2% l-
F
I I 1 -1 3 7 11 15. 19 3 7 11 15 19
Voltage (VL
) Current (IL
)
. 8.30 Maximum Harmonic Content at Booster Busbar
16
3%
2%
1%
3 7 11 i5 19 3 7 11 15 19
Fig. 8 31 Maximum Harmonic Content at Alternator Busbar
Compar the maximum voltage harmonic levels
at supply (Fig. 8.29) with peak harmonic
voltage s recorded on the 400 V supply (Table A 10.1) ,
shows that none of the harmonic levels of • 8.29
the corresponding listed values. It can therefore
concluded that the voltage harmonics at the supply
busbar do not have any significant effect upon the of
voltage harmonics already present.
8.1.3.2 The
voltage magnitude variations of fundamental component
of the booster busbar voltage (VL
) are shown in Fig. 8.32.
-4%
100 120 140 Firing angle £1 (degrees)
Fig. 8 32 Booster Magnitude Variation
164
The
on with the Fig. 8.17 for
mode (i)
a var
been
of Section B.1.3.
48
46 phase angle
difference 44
e (degrees) 42
Fig. 8.33
8.1.4
to only 17L • 8 33
in phase di ( e)
us mode (iii) control strategy
100 120 140 160 180 Firing angle E1 (degrees)
Phase Angle Difference (6) Variation
All fundamental frequency power flow measurements
.both act v were out at the ter
by VL in Fig 8 1) measurement
fundamental cJ> and cJ> is
between VL
and , is possible
with the II A F. Power Analyser (Plessey
1977). From thes measurements (P) and reactive (Q)
are using the following
165
Q == inti>
The flows phase
modes (i) i) (cases (a) (b) ly) are
shown in Figs 8.34 and 8.35 ly. . 8.34 shows
an active power flow from 200 W to 232W (Le.
an increase of 16%) and Fig 8.35 shows a change in active
power from 242 W to -293 W (i. e. a var ion of 17%).
Active power
p
(W/phase)
Fig. 8.34
260
240
220
200
100 120 140 160 180
Firing angle £1 (degrees)
Mode (i) Active Power Tran er
-220
Active power
p
(W/phase) -260
-280
-300
100 120 140 160 Firing angle E1 (degrees)
Fig. 8.35 Mode (iii) Active Power Trans
'166
180
Variation
The reactive power flows for both modes of operation
are shown in Fig. 8.36. Mode (i) operation gives an almost
flat Q profile (a change of approximately 6%), while mode
(iii) operation produces a slightly ing a
negative direction) flow of Q as E1 changes from 1650 to
1100 (a total change of 19%). in the
react power can in the following
manner.
Let of reactive (QGL) from
VG to ,the busbar VL
be described
by ( 1971)
o
-40
Reactive power
Q
(VAr/phase) -80
(a. )
-120
(b)
-160
100 120 140 160 180
Fig. 8.36
Firing angle £, (degrees)
Reactive Power Transfer Variation
(a) Mode (i) Operation
(b) Mode (iii) Operation
where X is the system reactance between busbars VL and VG
of Fig. 8 1 (the resistance term being neglected) and e
is the phase between vo
For , as £, changes from 1650
to
'120°, the at ter r by
5% (see F 17) • increase in vol
magnitUde is 0 by a e in cos8
(see Fig 8 18) over same iod, resulting
1 change in the term vLcosS of equa.tion (8.1) Thus
1 Ie change in QGL' and " "reactive power
'168
f Ie of • 8. (a) For mode (iii)
, both magnitude of VL cosB
(see B 32 and 8.33) as E1 from 1650
to 110°.
Re ing to equat (8.1), can be seen that
re an over
and this is confirmed by g. 8.36 (b) .
Assuming a choice of thyristor switch
firing control strategy and operation in mode (vii)
(Fig. 2 11) rather than mode (iii) for case (b) 1 the
voltage variation, of the fundamental component of VL would
show an increase in magnitude as the phase angle difference
8 increased. This combination of increasing voltage
magnitude of VL with increasing phase angle dif ence e
would result in a "flat" reactive power flow profile
similar to that of Fig. 8.36(a).
8.2 COMPUTER SIMULATION - THYRISTOR-CONTROLLED
QUADRATURE BOOSTING
Using a 6.6 MVA (per phase) 33/6.6/2.4 kV
(phase-to-phase) three-phase transformer and 1.1 MVA
0.76/1.38 kV s transl"'""..-m,Q , a computer simulation
with the propos thyris ture booster
(Section 2.2) was out to gauge the proposed
's abi f between two
resu this simulation are included in
a which has been publ ation in the
I.E.E. Proceedings in June 1979 and reproduced in
13.
A description of propo rcuit's
'16
in mode (i) is given, 1 and
experimental are so The mathematical
model developed in 4 of
computer scussed in Chapter 5 are also
Two di control es the of thyristor
switches S1 and S2 are used and consequent on
harmonic production, voltage magnitude and phase shift at
the booster busbar (busbar Vs in Fig. 3, Appendix 13) and
active and pO'Vler flows are discussed. The results
of computer simulation show is possible to
implement a continuous variation of phase shift and thus
achieve very fast power transfer control.
8.3
The results of Sections 8.1 and 8.2 demonstrate that
it possible to achieve power trans control. The
variation of the firing delays of thyristor switches S1 and
S2 gives se to different control strategies, and the
maximum phase shift obtainable is only limited by the ratio
of the transformer (T 2 in g. 8.1)
causing , the operation of the
proposed circuit the voltage magnitUde at
c
to
harmonic tortion. The
8.1.3 show the
harmonic levels of less than 1.1%
voltage at the supply (VM
) and alternator
in 8.1.4 that it is
the active flow in either
'170
by us the
(i.e. modes (i) i» . a combined
quadrature would allow the
act power flow to or
of power flow
Such a unit is illustrated
tert winding of the three-phase transformer
to provide both leading (+V Q) and lagging. (-V Q)
quadrature voltages, with respect to the secondary winding
vol The addition of a third back-to-back thyristor
switch makes it possible to control the phase shift of
VL without the need to change transformer connections
(i.e. there is now no need to reverse the sense of one
winding of the series transformer).
For the experimental system illustrated in
Fig. 8.1, and using the combined quadrature booster/bucker
of Fig. 8.37, it is possible to increase and ase the
active power flow in either direction by using operating
modes (i), (iii), (v) and (vii). Table 8.1 1 the
quadrature voltages and thyristor switches neces
for each mode of operation with the combined quadrature
booster/bucker. If the
pI i
8.37 (i.e. at
I
booster/bucker had
by trans
the
T in 3
ssion
direction could have
using operational modes ( ), ( ), (vi)
and (viii)
· 8.37 Combined Quadrature Booster/Bucker
Tab 8.1
Necessary to
Booster/Bucker
Quadrature
Mode Voltage
(i) +VQ
(ii) +VQ
,
(iii) ~V Q
(iv) -v Q
(v) ~V Q
(vi) -V Q
(vii) +VQ
(viii) +VQ
1
and Thyristor 8wi
the Comb Quadrature
Thyristor 8witches
8 1 ' 8 3
8 1 ' 8 3
8 2 , 8 3
8 2 , 8 3
82 , 8 3
8 2 , 8 3
s 1 ' 83
S1 ' 8 3
17
CHAPTER 9
TRANS
The poss lity of transient stability improvement
by shi insertion has been considered by O· ly
and Musgrave (1973b). Their phase-shifting equipment
involved the insertion of auxiliary transformer windings
in discrete steps by on line tap-change control, and
although the benefits of continuous quadrature voltage
injection were also scussed, no practical solution was
offered for implementation.
In this chapter the combined quadrature booster!
bucker, which was proposed in Section 8 3, is us to
achieve a range continuous phase-shift voltage control
at the generator end of a transmission line connecting it
to a large power system. Various quadrature voltage
injection control strategies and their on tern
damping during the transient period are considered. All
of the results presented are based on computer s
of the proposed vo injection
9 •. 1 VOLTAGE
The diagram of Fig. 9.1 shows one
of proposed quadrature booster/bucker unit connecting
a generator to power stem, via transmission lines
T/L 1 and The generator, quadrature voltage inj
power stem are by
voltages VG, VB primary and
windings
the
(T 1) are
es transformer
windi of
so that
(rr ) 2 are
lagging (-VQ) quadrature voltages may be obtained
8 3 are back-to-back thyristor switches.
Fig. 9. 1 Quadrature Voltage Injection Circuit
When the phase angle dif (eI» between the
vol (VB) and current (I) components 1
.the 0 0 < '" 90° 'I' < . g use lagging
17Ll
e
and
quadrature two ternative operating modes
(i e. s (i) and (v) ly) Mode (i) operation
2 2), which involves use of tor
with a leading quadrature voltage,
simply re to as quadrature ting throughout this
175
e, mode (v) 2.2), which
involves use s 8 2
simply
8 3 toge·ther
with a lagging quadrature voltage, to as
bucking.
Using the dynamic computer programme in
Chapter 5, the behaviour of three single~phase 150 MVA
generator transformers coupled with 30 MVA series
transformers acting as the quadrature voltage injectors
was investigated. The relevant parameters for this study
are given in Appendix 14.
Within the limitations set on the ranges of the
firing angles £1' £2 and £3 (Table 2.1) of thyristor
switches 8 1 , 8 2 and 8 3 respectively, many different firing
control strategies are possible. For this study the
following strategies are used:
Quadrature boost -
Thyristor switches 8 1 and 8 3 are fired symmetrically
with respect to the zero crossings of the leading
quadrature voltage (i.e. £3 = 180° - £1) and when
minimum £1 has been reached £3
from (180° £1) to (90° + ¢)
Quadrature buck ~
Thyristor 8 2
further increased
symmetrical
with to the zero crossings of the lagging
( . '180°) d h 1.e. £2 - £3 an w en
minimum £3 has been £2 is further increased
from {180°
Figure 9.2 shows the percentage regulation the
fundamental component plotted phase shift for
'176
The sign convention is
used the if the frequency
component of VB is
shi as
positive. line AC and Be show the ts
obtai for quadrature boosting bucldng
ively. The percentage regulation VB 1 within
the limits +5%
-10
Fig. 9.2
The
for a phase ft ± 10 o
Percentage Voltage Regulation
+6%
-6%
o Phase shift (degrees)
Quadrature Vol Inj
on wave
'inject produces
£1' £2 and £3' and
harmonic voltage VB are:
harmonic 7 1%
harmonic 4.0%
7th harmonic 2.8%
9th harmonic 2 1%
A
+10
stics
es th
maximum leve
177
, which are culated by
Fast Four 505), are
as a fundamental component at
However, is injection
the quadrature unit only during the period
of any power stem disturbance. When there no
quadrature voltage injection (i e when thyristor switch
S3 is switching at the current zero crossings) or
is full quadrature voltage injection (i.e. when either
thyristor switch S, or S2 is switching at the current zero
crossings), harmonics are not produced by the quadrature
booster/bucker unit.
The response the quadrature booster/bucker unit
is very t, as it achieved by varying the firing angles
of the thyristor switches in the phases. The controls
implement a new setting immediately the thyristor
switches in each phase respond at the appropriate instant
every half cycle. One phase will totally reflect the new
o setting in 60 or , depending on the instant of
change of control setting. On average, three
will have responded in 1500 of the tern frequency
9.2 ZING EFFECT OF INJECTION
By power= curve is
shi to a.nd quadrature booster/bucker unit
any intermediate angle cha s between
the no-boosting and ting curves
Without boosting e maximum power
occurs at approximately 90°, while with full
178
quadrature boosting it occurs at approximately 900 + P,
p the ft by the quadrature
booster/bucker unit. By suitable control, is s
to keep the power to a maximum when the angle
between 90° and 90° + p, as shown in Fig 9.3. Thus rst
swing stability is improved because the area on the power~
angle curve between transmitted and generated power is
increased.
Fig. 9.3 has been simplified for clarity by assuming
that the network prior to and after the fault is identical,
that there is zero power transfer during the fault and that
° fault clearance occurs before the power-angle reaches 90 .
NO
CONTROLLED BOOSTING
Power BOOSTING E---I
I, I Fault I Removal I I I I
/ Maximum
swing I I I
No Boosting
I
90 Angle (degrees)
FULL BOOSTING
Maximum Iswing,with
Boostlng
Power Input
Fig 9.3 . Power-Angle Curve Showing Improvement in st
Swing Stability with 20° Quadrature Boosting
lity improvement can be achieved by
negative quadrature vol inj (bucking). The
bucking can on inception so that full
bucking immediately the is removed.
The maximum possible both quadrature boosting
and bucking is shown in Fig. 9 4. This improvement
smaller in practice than would appear from Fig. 9,4,
because during the period in which the system is faulted,
the bucking will have little or no effect.
Power
. 9.4
9.2 1
Once
FULL <E<f.-----I BUCKING
CONTROLLED
90
FULL BOOSTING
Power Input
e (degrees)
Power~Angle Curve Showing the Maximum Pass t Swing i1 20°
Quadrature Bucking and Boosting
ility has been achieved l then
further control of the quadrature booster/bucker
unit can be
179
180
In the damping, and di
system would osci
ing point the areas
the ion and trans curves would be
Instead, rst maximum angle
excursion, it is desirable to reduce the decelerating area.
This can be achieved by reversing the controls so for
power-angles greater than 90°, there is quadrature bucking
and for power-angles s than 90° there quadrature
boosting.
It possible to change from full quadrature
boosting to full quadrature bucking immediately after the
maximum swing has been reached. However the power-angle
cannot change instantaneously, and as a result the power
would be lowered considerably. In the scheme
shown in Fig. 9.5 full boosting implemented
h th I t to 90°. w en e power-ang e :re urns The problem with this
scheme is that there is a possibility of the loss of
stability if the maximum swing angle is close to the
stability limit. Thus the quadrature voltage injection
must be modified in a controlled manner to ensure that
does not occur. Various means of achieving th are
'Damping Mode A
At maximum swing o than 90 ), the quadrature
vol inj is immediately modified so the power
than the input power This ensures
that occur.
Damping Mode B:
Full boosting over the whole of
swing
At maximum boosting can
immediately be changed to bucking to
reduce the next accelerating period. s is illustrated
graphically
Power
• 9 5
Fig. 9.5.
\ \
\ \ Power
Input \ 1\ \ \ I \
~Fault removal
90
e Curve
\ I \ \ \ \ \ ~ \ \ ~ \ \ 1\ \ \ I \ \ \ I \ \ \ I \ \ \
Angle (degrees)
Method of
Damping
state operating point
(no voltage i ection)
~2 maximum st forward swing angle
/;3 ~ minimum backswing angle
1;4 maximum second swing angle
1 8 '1
For the
full
booster/bucker unit
of the transient period
bucking may not be required
continuous
the quadrature
s to
182
the amount boosting or bucking accordingly. Because of
the di culty of calculating the correct amount of
voltage inj to reduce the transient to
zero, there will be an error and small swings will continue
(see . 9.5). To overcome th error problem, the
quadrature voltage injection can be gradually reduced to
zero a predetermined number of swings and no further
attempts made to control damping
9.3 COMPUTER
A multi-machine transient stability programme
(Arnold 1976) has been used to simulate the dynamic response
of the system. Neither the modelling nor the programming
techniques used in this transient stability programme are
considered a part of this project. The object of this
chapter is to show
booster/bucker unit to
ability of the proposed quadrature
in sIng a
trans
. has been used
purpose.
e, and the trans
ely as an inves
a lity programme
step-length 25 ms, the of the
booster/bucker unit to a new control setting is
assumed to immediate.
is
9.3.1
The , shown in Fig. 9.1,
18
the trans
with a
This
1
a
improvement
injection
coupled
through the quadrature voltage injection transformer and
bITO transmission lines to a power system. The
parameters of the system are given in Appendix 14. A
three-phase fault occurred on one transmission line close
to the transformer and was cleared by removing the line from
service. The system was deliberately made simple to ensure
that the effects of the quadrature booster/bucker unit were
not obscured.
9.3.1.1
Initi studies were performed with no quadrature voltage
injection to determine the normal response of the system to
the fault. By repeating the study with several different
fault removal times, in increments of 5 ms, it was found
that the system was stable with removal at 160 ms
but unstable at 165 ms.
From Fig. 9.2 it can seen that the vo
injection does not a quadrature
component, an component so The e
curve is not just to right or left
but has tude ed so. During boosting the
curve's magnitude is
magnitude is
boost~r/bucker
sed during bucking.
while
The ef
sting
bucking the curve's
the quadrature
thus reduced, but
Because of th change the
from bucking boosting
90° • It was
best at
that 105 0 was a
test case, and
fault clearing times are given Table 9.1
Table 9.1 Clearing Times
Buck/Boost Changeover Angle 1050
No vol injection 160 ms
Boost only 165 ms
Buck and boost 170 ms
9.3.1.2 Several of
the fault simulations describ Section 9.3.1.1 were
repeated for longer periods with quadrature voltage
injection control extended to improve stem damping,
results, which are shown Fig. 9.6, clearly
demonstrate the improvement possible. The amount of
quadrature voltage injection and time during which it
acts are shown Fig. 9.6.
Damping mode A reduced
amount, but it
near maximum
two
could
a
backswing by
to rema
for a long t In a
test case , this
u provided possibili
time scounted. On a
more pract system containing many machines
ion ine wi fferent periods
5e to ins lity.
'184
Angle (degrees)
20
o
-20
o
I
\ \ \ \ \ \ \
\/ , '(
\. /\ " . \. ----' "-
1.0
Mode A
Mode B
\ , ,
I ,
---, \ \ \ ,
\ I -_ '. i -- \'
I
\ ---~/~----~-=--~-~--~-~--=~~~~ ;
I
-'" ,_/' I I r--r--- -----: : . Quadrature-------L_~ ________ ~I~. Booster/Bucker Unit
Setting Angle
2.0 3.0 4.0 Time (s)
F • 9.6 Swing Curves Booster/Bucker Setting
mode B better lows
to e more f t
swing maximum.
than mode A to
Since this damping mode is more
s was It that th
was the most me'thod of damping
swing maximum.
F'or comparative purposes, a third swing curve
corresponding to the same system but operating with an
st
uncontrolled transformer shown in Fig 9.6. Aswould
be expected for a simple system th kind, the curve
shows the tern swinging with undamped oscillations.
9.4 CONCLUSIONS
installing a quadrature voltage injection
transformer at the generator end of a transmission line
connecting it to a large power system, maximum ang
to which the generator will swing
can be reduced.
a particular fault
Also by extending the control strategy, extra
damping can be introduced into the tern during
186
transient iod, thus reducing second and subs swings
as well as backswing. Damping strategy i complex,
requiring s b on gnals and
ly
Short
lowing a
harmonic inj will occur
sturbance, but no harmonic injection
during state when there no
voltage injection or even with 1 quadrature voltage
inj
187
CHAPTER 10
CONCLUSIONS
A tal computer programme, suitable the
analysis of the dynamic performance of power system circuits
involving thyristor switching, has been developed. It
includes mathemati modelling of the various system
components, with representation of the mutual effects
between inductive branches, which makes it possible to
model ef such as the phase shi inherent the
various three~phase transformer connections. The branch
and node equations are set-up by applying tearing techniques
to separate the various types of circuit elements and nodes.
Separation of the thyristor branch elements, which are
represented as ideal switches, from the remainder of the
system makes the frequent topological changes computationally
more efficient.
The difficulties involved in obtaining good initial
conditions data and the
each simulat
expensive to use. A
can be with
ively long execution times
run
tate solution il 1 76)
mathema al models, but the
f ility to general operating conditions requires
the use of the dynamic approach.
The range of voltage control lity which can be
achie~ed with the ed thyristor-controlled ng
188
trans may
Under
by the
anced
1 of content
the
trans
higher
fil
can
\\findings If the
harmonics are cons
plant may be necessary.
flow conditions
by
5th 17th and
Ie, some
The proposed stor~controlled regulating
former has shown to provide both positive and
negative amplitude regulation. Subject to some waveform
distortion and by appropriate choice of the series
transformer ratio any voltage range provided by sting
on-load tap~changers can achieved. Inevitably there is
some shi in the fundamental voltage component, but
most of the voltage regulation range can generally be
achieved with phase shifts of less than one degree.
It has also been demons that the phase ang
component of the power frequency voltage at a point of a
transmission line can be varied continuously by using
thyristor-controlled quadrature boosting bucking.
Again maximum phase shi
by the ratio of the ser
obtainable is only limited
transformer. This phase angle
variation provides a region of continuous power trans
control. the very nature the point on wave led
boost/buck, a as well as e
i introduced into the fundamental voltage component.
These changes in voltage magnitude are mirrored, some
big changes in react power cases, by unrealis
flow But by a su e of thyristor firing control
and mode of , a "flat" reactive
trans i can
active power trans
Reduction
will
injection at
a
connecting it to a large
18
e
maximum to whi a
faul't, by e vo
of line
system has
Various control s have also been shown to introduce
extra damping into the system during transient period,
ting in a reduction of second and subsequent swings.
The thyr switches the thyristor-controlled
regulating transformer only handle a small proportion of
the transmitted , the actual ratings for a
system being dependent on e series trans rmer
From a protection point of view, only the thyristors across
the secondary winding of the ser transformer need be
rated to withstand the fault level on that of the
series transformer. While it is possible to consider series
and parallel thyristor connections, the simplicity of the
single device switch is attractive and individual
thyristors with power ratings in the MVA range are
commercially lable.
In some indus·tr
S,
vo
ations, such as
tioh of
e
ed
Also
the small phase 8h component of
as with any magnitude change would not be
importance in rectifier ope There f as a
replacement on-load ther
tor or saturable reactor control the ed c t
of both voltage labil
If a winding four-windi
trans to and
ant e a n9' is
arranged to provide and ing ture
vol F with to secondary windi
then quadrant thyristor~controlled voltage tion
poss Ie. To maintain f lity individual
in~phase and quadrature vol control, it is necessary
to provide ther two windings on secondary side of
the s transformer or alternatively two series
transformers. One possible arrangement, where six
back-to-back thyristor are requi shown
in Fig. 10.1. T, the three-phase four-winding
transformer, and T2 series transformer.
represent in-phase and e ary vo
-v B
leading lagging quadrature voltages
of the quaternary winding, and 8, to 8 6 represent the
six thyristor switches.
The ary winding together with thyristor
switches 8" 8 2 and 8 3 operate as an e voltage
booster/bucker the quaternary winding
thyristor
voltage
operating
as that
o through 360 .
84 8 5 and 6 operate a
a s ce of
voltage vector produced by
in . 10. 1 can be
th
190
Fig.. 0 ~ 1 Four Transformer
ARNOLD C.P. (1976): "Solutions of the Multi~Machine Power
System Stability Problem". Thesis, Ph.D., University
of Manchester Institute
Great Britain.
Science and Technology,
ARRILLAGA J., BARRETT B. and VOVOS N.A. (1976):
"Thyristor-Controlled Regulating Transformer for
Variable Voltage Boosting". Proc. I.E.E., Vol. 123,
No. 10. pp.1005-1009.
ARRILLAGA J., AL-KHASHLI H.J. and CAMPOS-BARROS J.G.
(1977): "General Formulation for Dynamic Studies
in Power Systems Including Static Convertors".
Proc. I.E.E., Vol. 124, No. 11. pp. 1047-1052.
BEATTIE W.C. and MONTEITH W. (1973): "Digital Modelling
of a Thyristor". Froc. LE.E., Vol. 120, No.7.
pp.789-790
"192
BOWLES J. P. (1970): "AC System and Trans former Represent
ation for HV-DC Transmission Studies ll• I.E.E.E. Trans.,
Vol. PAS-89, No.7. pp.1603-1609.
CAMPOS-BARROS J.G. (1976): "Dynamic Modelling of
Synchronous Machines Connected to HVDC Transmission
Systems". Thesis, Ph.D., Victoria University of
Manchester, Great Britain.
CHEN W. Y. (1962): "An Investigation of Commutation
Problems In a Static Power Convertor" Thesis,
Ph D , University of Manchester, Great
COCHRAN W T et al. (1967): "What is the Fast Four
Transform"? Proc I.E E.E., Vol. 55, No. 10.
pp.1664~1674.
CONTE S.D and DE BOOR C. (1965): IlElementary Numerical
Analysis". 2nd ed. New York, McGraw-Hill Book
Company Inc. chap. 3.
DORN W S. and McCRACKEN D.O. (1972): "Numerical Methods
with Fortran IV Case Studies". New
& Sons, Inc. PPM 232~233.
ELGERD O. L (1971): "Electric Energy
An Introduction". New York,
Inc. chap. 3.
, John Wiley
11 Book Company
FOHRHALTZ H.A. (1967): "Load Tap Changing wi-th Vacuum
Interrupters". I.E.E.E. Trans, Vol. PAS-86, No.4.
pp. 422~428
19
FRANK H. and LANDSTROM B. (1971): "Power Factor Correction
with Thyristor-Controlled Capacitors". ASEA Journal,
Vol 44, No.6. pp. 180-184.
KUO F.F. (1966): "Network Analysis and Synthesis".
Tokyo, John Wiley & Sons, Inc. chap. 3.
MARSHALL P. and LLOYD S. (1974) "A 3-Phase A.C.
Thyristor Voltage Regulator". I.E.E. Conference
Publication, No. 110. pp. 198-202.
MARTENSSON H. and DANFORS P. (1975): "The Development of
HVDC Technology at ASEA". ASEA Journal, VoL 48,
No.3. pp. 51- 54 .
MEDEARIS K.G. (1974): "Numerical-Computer Methods for
Engineers and Physical Scientists". KMA Research,
Denver-Fort Collins, Colorado. pp. 122-124
O'KELLY D. and MUSGRAVE G. (1973a): "An Apprai
Transformer Tap-Changing Techniques". I.E.E.
Conference Publication, No. 123. pp. 112-117.
O! KELLY D and MUSGRAVE G. (,197 3b) "Improvement of
Power tem Transient 1
Insertion". Proc. I.E.E., Vol 120, No 2.
pp. 247 251.
PLESSEY (1977): " Instruction Manual".
A.F. Power Analyser -
Plessey (N.Z.) Ltd.
RAMSHAW R. (19 "Power Electronics". London,
Chapman- and Hall.
ft
ROBERTS M.E. and ASHMl1.N W.G (1969): "A Thyristor
Ass Mechanical
Publ
and The Appl
SAY M.G. (1958) liThe
Alternating Current
Pitman Publishing.
On~Load 'rap
, No 53,
, pt. 10
Machines".
p. 21.
Changer". I.E.E.
Power Thyristors
pp 185~192.
Des
3rd
of
London,
SCHWEICKARDT H. and ROMEGIALLI Go (1978): "The Static
VAR Source in EHV Transmission Systems and
Control". Brown Boveri Review, Vol. 65, No.9.
pp. 585-589.
STEVENSON W.D. (1962): "Elements of Power System Analysis".
2nd ed. Tokyo, McGraw-Hill Book Company Inc. p. 96.
STIGANT S.A. and FRANKLIN A.C. (1973): "The J & P
Transformer Book". 10th ed. London,
Newnes-Butterworths. chap. 12.
SUNDBERG,Y.(1976): "The Arc Furnace as a Load on the
Network". ASEA Journal, Vol. 49, No.4. pp. 7 87.
WESTINGHOUSE ELECTRIC CORPORATION (1964): "Electrical
Transmission and Distribution Reference Book'~.
4th ed. U.S.A., Westinghouse Electric Corporation.
chap. 5.
WRIGHT A. (1968): "Current Transformers: Their Transient
and Steady State Performance". London, Chapman and
Hall. p. 11.
195
P.PPENDIX -I
G.E CoR. FIRING CIRCUIT
The G.E.C R. f
ing pulses with a
ng circuit RIS54, produces 100 ~s
time of 500 ns for a phase-angle
controlled back-to-back pair of thyr The ends tops
on the production of firing pules are at 15° and 165°.
Therefore the actual phase-angle controlled ing pulses
are produced, from the two outputs which are separated by
180°, over a range of 150°.
The RIS54 f ing circuit cons
interconnected printed circuit boards:
of two
(a) Trigger unit PCO~555
(b) Output unit PCO~392
Power Supply: 50 HZ, 28 V rms, 300 rnA rms.
Reference Voltage: Single phase 200 V rms
centre tapped, 150 rnA rms.
Control Signal: ± 5 V de.
Pulse Ma'tch Within ±2° over the full
control rzmge"
APPENDIX 2
GoE.C.R. FIRING CIRCUIT
Although the G.E C.R. firing circuit two
sets of f ing pulses by 180°, the following
description of the calibration technique s to only
one of these sets of firing pulses. The manufacturers
claim that the two sets
tolerance 180° ± 2°.
firing pulses are within the
During the formation of the high pulse
trains, a "block ll pulse produced which marks the
beginning and of the high frequency pulse tra
To cal the c , this "block" pu (B)
is used in conjunction w voltage (VREF ).
196
A negative going pulse, coinciding with the beginning of
the reference voltage positive half-cycle, is used to start
an electronic timer and a negative going pulse, co iding
with the beginning of the production of firing pulses, is
used to stop the electronic timer. The Galbraith Counter-
Timer used not respond to any pulse at stop
pulse at start input, or any
the next reset is The c ts used pulses
to the tart the electronic
t are shown in A2.1 and r positions
are shown 6 A2.2.
19
>-~~~~=---~VREF
pulses)
8v
B
OV
ses)
4.7 V LAV47
Fig. A2,1 Production Start and Stop Pulses
• A20 2 Pos of Start Pulses
t 1
stop pulses is then converted
angle (£.) p assuming that the
the 50 Hz.
for the G C.R. f
in . A2 3
COS £.
+1.0
+008
+0.6
+0.4
-5 -4 -3 -2 -1 +2
-0.2
-0.4
-006
-008
-LO
• A2. Circuit
+3
198
the tart
f ·the
of
control
ts
+4
is shown
Control Signal
+5 (v doc.)
Characteri
APPENDIX 3
CONVENTIONAL PULSE
Core: Philips toroid, 3E1,
dimensions 36 x 23 x 15 ~n.
Winding: single core 10/0.010 remit wire
primary turns 24
secondary turns 24
Both primary and secondary windings
are wound together so that each
alternate turn is secondary.
The imary and secondary windings
are brought out at oppos S
of the core.
199
APPENDIX 4
liMICRONE" PULSE
The "Microne" pulse transformer, which
manufactured by GoE.CoR , has been spec ly designed
to supply isolated firing pulse for thyr in
demanding applications. It gives an output pulse of any
duration without saturating, and the time is always
than 1 ~So The frequency of the output pulse train
adjusted by connecting different timing components,
R1 and C1, across the COMP terminals (see Fig 3.6).
The integrated circuit type of construction the
"Microne" pulse transformer leads to a compact device
(33 x 33 x 25 rom), which is suitable printed
board mounting.
Maximum
Input vol tage ~ 17.5 V peak
Output voltage 10.5 V on open circuit
Output current - 0.4 A output
200
APPENDIX 5
PARAMETERS
In the
an 8.25 kVA
assessment of
three-winding transformer
trans are used. The voltage
ratings transformers are given
The impedance parameters these trans
calculated from results of open
current
this appendix.
, which are
ircuit tests
and Kelvin Bridge resistance measurements (Section 6.3.1) j
are also presented.
AS.1 8.25 kVA
The 8.25 kVA transformer a
phase unit th voltage 400/200/66 V
star connection, and 230/200/66 V
connection. This transformer has
delta/star/star
f secondary
winding current of 12A, 17.4A and 19.8A
per are
Table AS.1.
Table 1 8 25 kVA Trans Parameters
Secondary
185 + j353.8 j185.6
j18S.6 070 + j97 5
j57.76 j30 36
20
AS 2
Three trans s igned and
bui use as s s sting/bucking trans s
conjunction with
For flexibility, the imary s of the trans has
four windings, two 13 V two 25 V s
it poss Ie to primary
ranging from 13 V to 76 V, lable boosting and bucking.
The two windings (38 V and 28 V) f which are
to be compatible with voltages avai from
the 8.25 kVA three-phase transformer, are connected s
to give a vol 66 V. The primary and s
windings s tran are 16 A and 20 A
respectively.
The impedance parameters for one s transformer
are given in Table .2
Table A5.2 Transformer Impedance Parameters
13 Volt 25 Volt 25 Volt 13 Volt 38 Volt 28
13 Volt 0.011 j3.30 j3.30 j L 7'1 j4.78 j +j 1 .74
25 Vo j3 30 0.020
j6032 j .30 j 008 j +j6 7 0
25 Volt j3.30 j6.32 0.020 j3.30 j9008 j608 +j6 37
13 Volt j 1 71 j3.30 j3.30 0 01'1 j4 78 j3. +j 1 .74
-38 Volt j4.78 j9 08 '9 08 j4.78 0.027 j9.89 J 1+ '13.3
28 Volt j3.56 j6.S3 j6.83 j 56 j9.89
Be
6
rvlATHEMATICAL MODEL -~ INCLtTDINGCAPAC
the 1 inductors Q
itors
were
assumedG Sect
that the
charge.
s are to the·
two state are now wind flux
e Resistors are non~state variab sand
their
state
A6.1
Let the
ab
vo and currents can
n
c itive, r resistive, I inductive
branches. The ions concerning
the branches (Section 4.3) must be mod
following to accommodate
ob
stor
203
means
c
from
1. All capacitors are connected to the poin-t
2
The
or
Purely res is
or
with
a
itors.
ive
c
to
stor
thyristor is
in Section 4.3.
204
02 NODE
In
a node to and ni-tion
of S (Sect 4.3.1) to be ified. The
node types are:
eI. nodes to at least one capacitive branGh.
to at one resis
but no capacitive branch connections.
y nodes connected only to inductive
o nodes connected to at least one thyristor branch.
The introduction of 0 nodes i a convenient way
the nodes fected by topologi
changes. 0 nodes do not appear itly in the
formulat to low, but are a of y nodes (a more
detailed explanation the treatment of 0 is
in Section 4.3.1).
The topological matrices K~nl K~n and K~n are the
branch-node incidence matrices of capacitive, res
and inductive branches It is convenient to
tion e topological
according to types as
r KT rn [ KT rei.
~ [ KT la
20
From ion
of var A6 ¢ 'I ) G
o
A6.3
The both resist and inductive
branches, which were ived Sect LI. ,2 • 1 and 4 3. 2 • 2
respectively, st I apply to Rewr ing
these matrix equations~
For
When all c
the
r
d(l./J1I)/dt
ip
. 1
(v . .1
=
Capaci
and n s are cons
on can wr
(K'r V ) en n
(A6, 1 )
(A6 .2)
• 3)
i t:he vec1:or ctlrrent !l
V n
is
A6 4 VOLTAGE
In
current law 9
vector of
AND
current sources,
r = KnlIl
206
ffls
(A6. 4 )
To obtain s the voltage vectors (Va v V (3
Vy ) I equation (A6. 3) premult ied by K , nc a
for K I then made equation (A6o 4 ) on nc c
[K C KT ] d(V l/dt :::: - KnlIl nc cc en i n !
Noting that KI3C
(A6 05) in
K C KT ac cc c
0
0
Defining
Q is aa
Kyc
tioned
d
vector
Kyr o and
Va K +- KalIl ar
VI3 r + KI3 1
Vy KYlll
=
sUbstitution
(A6 5)
207
Then
d(Q )/dt ~ I + Ill) aa r (A6 .6)
K81.' ~
K81 I l
and III := 0
which
Ky 1 d (II ) / d t 0 (A6 08)
In to an expression for
vector of S (Vs) ,equation (A6o') st ltvritten
in partitioned form.
=
Premultiplying this by KSr' noting ::::: 0
and us equation (A6.7) to the lowing s
where
(A6o 2)
or R (K I + K R 1KT V ) - 88 81"1 8r rr ra a (A6 .9)
In a imil manner, an s can be
vector of y 1
Remembering
K Y
ion re
~11 = Ill' premult
itioning KT V the In n'
ng equa
110wing
208
~ 'I KYILll [Llld(I l ) + I (L11 ) Id .. tJ ~~
.~ 1 '1' rr KT V KYILll (E l + K V + f3V[3 -~ .. 1) la a ly y
the are cons to be unchanging with
time, using equation (A6 . 8) and
Vy -1 'II T
RIII I ) ~r.yyKYILll( + K V + KlSVe la a
(A6. 10)
where ~1
K " T
L "" lKly yy Y
Defining the ancillary variab V and Vl as: r
Vr :::: KT V (A6 • 11 ) ra a
VI EI + KT V T RIIII (A6, 12) =: + KISVS ~
la a
Equations (A6.1) I (A6.9) and (A6.10) can now be expressed
more simply as:
Ir 1 (V T (A6. '13) + Kr(3VS} r
V(3 = ~RS/3(KelIl + K (A6. '14) (3
Vy == -L K L- 1 VI (A6o 'I 5)
yy yl 11
A6.5 STATE=SPACE:
Us ,the (Qaa) ux s
(W ll ) as state , the rate change the
state var (equations (A6 .2) and A606)) can no,,! be
combined into a single matr equation
rate
(equation (A6.2) can now be
substituting for VI Vy
state
VI + K:r' V ly y
d($ll'
/ dt = [U11 - K~yLyyKYIL~;J ~1 + KiaVa + KiBVS
UII a unit L
Substituting V and V 8 v ning r
MIl UII T ~1
KlyLyyKYILl1
and rearranging
d(1/JII)/dt [El + KT V T = MIl (KlSRSSKr31 10:. 0:.
T 1 KT V l KII3 RI3I3 KS ro:. ex ~
Defining I
Rll + T
RII ::::: K113 R1313K131
and N1r T
KII3 RSSKS
equation (A6.16) can now be as
By substituting
)v 0:.
rate of
+ RII)I I
state (A6.6) can now be
as
209
(A6. 16)
• 1 7)
d(Q )/dt aex 1 1/J + I 11
'1 (V + KT V ) ] r rS f3
10
(~~6 'I 8)
r
Nlr T
KlSRSSKS
then NT 1
sRseKSl rl
Now equation (A6. 18) can
Defining
~, 1 and substituting CaaQaa
expressed as:
d(Q )/dt -A "" aa a
Since A al
then AT la
KT la
be tten as:
(A6. 19)
v g equation (A6.19) can be a
1 G I(T C- 1Q 1* - ar ra aa aa (A6 .20)
K N'Ii ar rl
N KT lr ra
(A6.21)
Us (A6.21) arid substituting C:~Qaa for Va'
equation (A6.17) can as:
(1\6.22 )
.20) (A6. 22)
a
+ (A6. 23)
A6.6 SOLUTION
Because of the switching of the thyristors, the
topology is undergoing repeated changes and network
equations must therefore be solved by a "single-
method, which is starting.
1\6.6.1
Expressing the state vector differential equations
in the following form:
d(ljJll}/dt f(1jJ Q)
d(Q )/dt g(ljJfQ) a. a.
Then using the (Dorn 1972), the state
vectors IjJ and Q at the an integration
length h are given by:
= (A6. 24)
Using
t/l t +h in terms
obtained as
t/l t +h
(A6.22) and (A6.24) an
state
lows:
Rearranging the previous equation and defining
=
leads to the following sion:
+ (
21
(A6.25)
ion
(A6.26)
An sian Qt+h in terms the state variables
Qt' t/lt and t/l t +h may
(A6. 25) •
obtained from equations (A6.20) and
Uaa is a unit of
h "2
()I, 0
equation and defining
B U + h G KT C 1 aa aa 2 ar ra aa
to following expression
+ t/lt+h)
(A6.27)
213
In .26) (A6.27) the terms involving
can considered to be constant s within
each integration length h. equations
(A6.26) and (A6.27) can more simply as:
= (A6 28)
B-1 h A L-1~, + f' - aa 2 al ll~t+h 2 (A6 29)
where f1 and f2 are defined as follows:
Defining
o
o
and rewriting equations (A6.28) and (A6.29) as a single
matrix equation
where U a unit matr
r 2
order (l + a) .
(A6 Q
Equation (A6.30) can be solved by standard technic
the solution simultaneous linear equations.
A6.6 2
The Gauss and Gaus can be
to by successive
approximations. e methods treat the the
order they are The method makes
po the application of a variety of schemes that may
speed the convergence the For the
solution of the simultaneous state equations (equation
(A6.30» the over-relaxation method (Medearis
1974) was chosen.
If the set of simultaneous equations
a 11 x 1 + a, + a 1 = c 1
a 21 x 1 + a 22x 2 + a 23x 3 = c 2
1x 1 + 2x 2 + a 3 = c 3
is considered, the Gauss-Seidel over-relaxation method
operates in the following manner.
The previous set of simultaneous equations can be
rearranged to give the following:
:=
these
1 (-
- a
1 + L:
k:=1
+ C 1
a more
+
and
14
215
If during a computer solution
'the various are denoted by the
solution, using most current
, can be
1 1 ::
i
as:
(- c. + .1
The two iterative approximations x:+1 and x: are therefore .1 .1
related through "correction terms", and the Gauss-Seidel
over-relaxation method involves multiplying ese
"correction terms" by a numerical coefficient m
(over-relaxation factor).
The computational form used given by:
r+1 x. .1
::::: r x. .1
m - a.-:- (-.1.1
where the value of m
+
in the range 1 < m < 2
The actual value of mused problem dependent and
the optimal value has to be determined experimentally
for each particular problem.
A6.6.3
To be cons with the change of state variable
(Section 4.4.2), the state
by wQ so aa
- we aa
Q is aa
216
APPENDIX 7
The fact that digital integration is based on the
a smooth curve by a of short approximation
straight 1 , justi the use of a linear interpolation
technique. If (t 1 ,y,) and (t2 'Y2) are the coordinates
two points obtained from a digital integration process,
where t2 - t, = h (the integration step-length). Then
the time to at which the y coordinate becomes zero can be
determined (see Fig. A7.1).
o 1
17
Us the a 1
given the fol
Once t been the of all o
other variables (x), at this time, can be found from
the lowing equation, which is so derived from the
general equation a straight line:
=
2Hl
APPENDIX 8
FOURIER
Any periodic function f(t) can be as
a Fourier (Kuo 1966) as follows:
00
f (t) ::: a + E ( (milt) + b sin(nwt») 0 n:::1 n
where a ::: ~ J: f(t)dt
0 (AS. 1)
2 JT f(t)cos(nwt)dt a :: if n
0
(AS.2)
bn 2 JT f(t)sin(nwt)dt ::: if
0
(AS. 3)
and T the period of f (t) .
When digital analys techniques are used for
analysing a continuous waveform, it is necessary to sample
the data at equally spaced time intervals (~T) in order to
produce a time ser of discrete samples. For the qth
sample the integral equations (AS.1), (AS.2) and (A8 3)
can the lowing
"" .1 l: f(q~T)~T T q
3.. E T q
f(q~T)cos[nw(q~T)]~T
= 3.. E f(q~T)sin[nw(q~T)]~T T q
are known as the
APPENDIX 9
THE RESPONSE OF
TO
The current transformer, manufactured by Smith
& Hobson Ltd., following nameplate
Ratio 100/50/25/10 1
Rating 7.5 VA
Class AL
Frequency 50 Hz
No. X-7110
The tests described th appendix were only
performed on the 25 and 10 - 1 ratios, because these were
the only two to be used experiments associated
with this report.
A9.1 RATIO ERROR
The current transformer error tests 'Vlere
performed using a modi
which the
A9 1
two ammeter method (Wright 1968)
test shown in F
The winding the current is
have negligible impedance. To match 20 W
19
amplifier (Sanken"S1 1020G) harmonic current generator
c an an non-inductive resistive and t is
no 50 Hz current this t.
"Plessey" Selective A.F. Power Analyser
F' A901 Current Trans
o ~ 25 A
20 W Sanken Amplifier
Marconi Si9na1
Generator
50 Hz Current Generator
Selective A.F. Power Analyser
Error Test
o
Rather than
Power
The
an ammeter, a Ii
to measure
50 Hz
high in comparison to that
II ive A.F.
harmonic current
winding
current , and no harmonic current
to flow in the SO Hz current circuit. (When the SO Hz
current generator circuit is disconnected there is no
apparent change of the harmonic current in either the
primary or secondary current transformer windings.)
On the secondary side of the current transformer
the ammeter by a second "Plessey" Selective
A.F. Power Analyser.
221
the
The harmonic current input kept constant at 500 rnA
all tests, and two tests are described for each the
ratios under consideration. The rst with load 50 Hz
current and the second with 50% full load 50 Hz current.
Frequency measti.rements below 1 kHz are done at 120, 220,
420 and 820 Hz to avoid any possible interaction of the
harmonics present in the SO Hz current circuit and those
generated by the signal generator
tests are
measurement
within the
the
the turns
the harmonic error
5, where in A9 2 to
maximum error (±5%)
all the recorded points 1
±5% zero error, can concluded that
harmonic current, frequencies up to 2 kHz,
in the secondary winding in accordance with
The amount SO Hz does
Secondary
current
(rnA)
2 2
10
OL---~--~ __ ~ __ ~ __ ~~~ __ ~ __ -4--~--~--__ 2 4 6 8 1012 14 16 18 20
• A9.2
30
Secondary 20
current
(rnA)
10
.3
102 Hz
2 1 Error Test - Full Load Current
.."...-...,.,,-------.. .
2 4 6 8 10 12 14 16 18 20 102 Hz
2 1 Error Test ~ 50% 1 Current
Secondary
current
60 .
40
(mA) 20
Fig. A9.4
60
40
Secondary
current
(mA) 20
2 4 6 8 10 12
102 Hz
10-1 Ratio Error
- """"'" - -.- - -=> """""
22
14 16 18
- Full Load Current
o ~ __ ~ __ ~ __ ~ __ ~ __ -L __ ~ __ -L __ ~ __ ~ __ ~~ __
2 6 8 10 12 14 16 20
102 Hz
Fig A9 5 10-1 Error Test 50% Full Current
not significantly
current trans
.2 TRANSFORMATION
Two more ts, one for
224
of the
are where a 100 Hz fundamental frequency "chopped"
current waveform superimposed on a 50 Hz sinusoidal
current waveform For tests, the Marconi signal
generator by a General Radio R-C Oscil ,
type No.1210-C, and the Sanken 20W amplifier and an load
are replaced by a Radford 15W ampl and 16n load.
The rms harmonic current the "chopped li waveform
(Fig. A9.6(a» is kept constant at 750 rnA and
superimposed on a 50 Hz 50% full load sinusoidal current.
The harmonics generated resultant compos current
waveform (Fig. A9.6(b» are measured on either side of the
current The these measurements,
which are normalised to
are shown in F • A9.7.
fundamental (100 Hz) component,
There is no significant f in the ratios of
higher order harmonics to the fundamental component on
side of current can
current waveT~~mla
on to the of current trans with
no
................................. " ..
(a)
(b)
Fig. A9.6 (a)
(b)
1.0 F
0.8 r-
0.6 F
0.4 f-
0.2 I-
0.0 1 3
1.0
0.8 I=-
0.6
0.4
0.2 l-
0.0 1 3
. A9.7
5
5
100 Hz "Chopped" Current Waveform
Composite Current Waveform
Primary Harmonics
•• ~,. ... ~ •• * " ." • ~ • u Secondary Harmonics
Ratio 25 - 1
I I l I I I : I I :
7 9 11 13 15 17 19
102 Hz
Ratio 10 - 1
I I . I I : I ; I I :
7 9 11 13 15 17 19
10z Hz
2
226
APPENDIX 10
VOLTAGE HARMONICS ON THE 400V SUPPLY BUSBAR
In order to obtain a quantitative assessment of the
magnitude of the voltage harmonics present on the 400V
supply busbar to the Power Systems Laboratory, University
of Canterbury, a Selective A.F. Power Analyser, manufactured
by "PlesseylD, is used. This instrument enables a particular
harmonic frequency to be selected and monitoring of this
harmonic voltage, to the exclusion of all other harmonic
voltages, is then possible.
Figs A10.1 to A10.11 show typical variations of each
harmonic voltage level (fundamental frequency 50 Hz) over a
period of 25 minutes. The vertical scale for each trace is
0.4 V/cm or 0.174% of nominal fundamental voltage per cm.
Each harmonic voltage has a distinctive pattern of variation
and harmonics such as the 12th, for which there is no trace,
were on occasions present but could not be monitored
continuously over a 25 minute period because the instrument
could not lock on to the very low level harmonic signal.
The traces of Figs A10 1 to A10.11, which are a
representative sample, together with many other traces
obtained give an estimate of the typical and peak harmonic
voltage lev~ls. Table A10.1 lists these typical and peak
harmonic voltage levels.
Fig. A10.1
Fig. A10.2
Fig. A10.3
i , , 1,·-,::
·r·· ·1
Typical 3rd Harmonic Voltage Variation
I -1--'-.1- .
,:1 I
I. I -+
Typical 4th Harmonic Voltage Variation
I -, r' I ~
I
I i ~.
i' i
Typical 5th Harmonic Voltage Variation
227
22
. A10 4 Typical 6th Harmonic Vol
. i'-
Figo A10.5 Typical 7th Harmonic Voltage Variation
• A10.6 8th Harmonic Vol Variat
"[ " ,
0.7
Fig. A10.8
Fig. A10.9
Fig. A10.10
o 11
1 1
Typical 1
.. ! J •
•
Voltage Variation
.1
Variation
Typical 17th Harmonic Vol
I
i , .
·1
1 19th Harmonic Voltage Variation
229
2 0
0. 1 and Harmonic Voltage
Leve on 400 V Busbar
Peak Level
Harmonic (% of (% nominal
fundamental) fundamental)
3 0.70 1.70
4 0.26 0.52
5 0.61 0.65
6 0.17 0.30
7 0.35 0.37
8 0.09 0.17
9 0.04 0.07
11 0.09 0.10
13 0.04 0.07
17 0.17 0.22
19 0.09 0.13
2 1
11
A STATIC I>LTERNATIVE TO THE TRANSfOIlMli:R ON-LOAD TAP-CHANGER
J. Arrillaqa (Non-member) University of Canterbury, Christchurch, New Zealand.
Abstract - An alternative approach to the conventional on-load tap-change voltage control is described. The proposed solution involves the use of in-phase booster transformers and phase-angle controlled thyristor switching. Any specified range of continuous voltage variation can be achieved and the response is practically instantaneous. Computed and experimental results are presented,illustrating typical voltage and current Waveforms as well as their harmonic content.
INTRODUCTION
There are many disadvantages in the use of on-load tap-changing control, whereby the current is switched from tap to tap by mechanical means. Among these are its cost, the inertia of the moving parts which severely restrict the speed of response causing wide temporary voltage variations and the high level of maintenance caused by the mechanical switching due to eontacts And oil deterioration.
It is not suprising. therefore, that various attempts are being made to try and introduce static switching eoft~o} as part of the transformer tap-changer system.(l 2 However there seem to be enormous technical and economical problems in the integration of thyristor switching with the conventional on-load tap-changer principle. Perhaps .the main difficulty encountered is the ratings of the devices, which have to withstand full fault current and surge VOltage conditions; another major difficulty relates to the large number of thyristor switches required to provide reasonably stepped voltage controllability.
To OVercome the above problems, a new principle of transformer voltage ratio control is described in this paper, based on the use of point on wave controlled switching. The switching prinCiple itself is widely used in low power electronic circ'..lits and recently hag also been proposed for the continuous control of ~ regulating transformer booster().
BASIC CIRCUIT AND THEOR&TICAL WAVEfORMS
The single line diagram of Fig. 1 illustrates the basic circuit of the pfoposed alternative solution. It consists of a three-winding transformer (T
l) with the
t,ertiary winding feeding a boosting transformer (T ) throu~h a back-to-back thyristor switch (51" If t~e thyristor switch is triggered without delay (1 .... at the zero crossings of the current waveform) a constant voltage is added to the secondary voltage and in phase with it. If the triggering of switch 51 is delayed, a shortCircuiting switch (S~) is required to prevent an open circuit condition of ~the series boosting transformer~ Varying delays in the trig'lering of switches 51 and 52 will result in corresponding variations of the secondary
paper IEEE Tr,"Ansfol:F.lel:S Cor:.mittee of !:he IEEE !'c'.'lCr n~ir.g Society for presentation at !:he n:m PES SlJlTIIror 1Iceti1l'.J. VI.!.l1CO\.l\leC, Qritish Columbia, canada, July 15-20, 19"19. Manuscript submitted September S, 1978; !!lade available for printing April 26, 1979.
R. H. Duke (Student Hc~r) New Zealand Electricity, Christchurch, New Zealand.
Fig. 1. Proposed alternative to the transformer On-Load tap-changer.
voltage. The phenomena is better explained with reference
to the "idealisedw waveforms of Fiq~ 2 which use a power factor of 0.9, not untypical of power distribution systems~ The voltage and current waveforms of Fi9~ 2 refer to the positions indicated in Fig. 1. The angular intervals 0 and £ represent delays 1n the firing of thyristor switches $1 and 52 respectively.
The forward-biased thyristor of switch 51 can be triggered at any time within the range ¢<a<180o, where ~ is the pha~e angle difference between the voltage and current waveforms. Similarly, the appropriate thyristor of switch 52 can be triggered at any time within the range 0°<£<,. Hence the voltage boosting can be controlled by the triggering of both switches 51 and 52 a3d the effective boosting period can range from 0
0 to 180 •
EXPERIMENTAL VERIFICATION
Experimental verification of the theoretical waveforms described in the previous section was carried out using an 8.25 kVA, 400/200/66 Volt, three-phase transformer, 'with its tertiary winding connected for in~phase
boosting to a 750VA (per phase), 38/25 volt series transformer~ The transformer and thyristor switches were connected as showh in Fig. 1 to provide point ~n \-tnve boost control.
Fig. 3 shows a set of typical voltage and current waveforms for a particular case when the firings of the boostinq (51) and short-circuiting (52) pairs were d~layed by 80 and 10 dO'/rees respectivoly and the load power' factor was 0.9. The oscillogram" 3(.», (bl. (c) and (dl show the supply voltage (V), the load voltage IV), the voltago across the seconda~y windin9 of the serie~ trdnsformer IV ) and the load current (! , respectively. Tho similarityTof oscillogram" J(b) and ~(cl with'the theor~ etical waveforms V
L and V
T of Fig. 2 illustrate thG fea
sibi Uty of the proposed control sequence,.
ANALYTICAL MODEL
Voltage and current relationships
The discontinuities !ntroduc"d by point - on - wave controlled switching cannot be prespecified and the resultin,} waveforms require dynamic rather than steady state analysis.
With reference to the basic circuit of Fiq. 1, and
. " i e: I" I I I I I I i I
Fig. 2. Theoretical waveforms.
using the branch formulation, the followifi9 matrix equations can be written for the resistive and inductive branches ..
V !l
1;9 It current vectors
Vn - nodal voltage vector
E£ - ~.m.f.'vector of inductiv(jj branches
- resistive branches matrix
(2)
232
,:~.l....
~
Fig. 3. Oscillograms of typical voltage and current waveforms.
'. . ,
(b)
(C)
(d)
resistance matrix of the inductive branches
Ltt
- inductance matrix
T '1' and K and Kt are the resistive and inductive branch-node ICcidencenmatrices respectively; their elements are ±l depending on whether node n is at the sending or receiving end of the branch. Also, expressing Kirchhoff's current law in terms of these incidence matrix yields.
(3)
Node segregation
It is computationally efficient to subdivide the nodes accordinq to the type of branches connected to them ioto:
nodes with at least one resistive branch (6) nodes with only inductive branches (y)
Moreover, since the topological changes are mainly caused by thyristor switchinqs it is convenient to define a special type of y node. i.e.
nodes with thyristor branches (oj A conducting thyristor is treated as a short-circuit~ thus converting two 6-nodes into a ~-node and a non-con~ ductinq thyristor is treated as an open circuit. converting two a-nodes into two y-nodes. Although 6-nodes do not figure in the fonnulation they arc useful to identify which nodes are affected by thyristor svlitchinq during the dynamic simulation.
It is also convenient to partition the topological matrices according to node types as follows:
where, from the definition of ~ nodes, KT ~ 0 Rewritinq equation (l) in partitiQ~~d fom
From which
(4 .. )
(4b)
Finally rewrltin~lcquation (9) in matrix fogm and reme@(5) bering th"t I,3LUil'U
In order to obtain an expression for the voltage vector of B nodes (Val,equation (1) is fir~t written in partitioned form, i.e.
I r (K;II VB • K!'l V'l )
premultiplying this equation by KA ' noting that KT = 0 and using equation (4a) leads to t~e followin~ ex~lession,
(6)
where
!!:~larlY. an expression can be obtained for Vy am f011-
Premultiplying equation (2) by K 'L~l, remembering that ~tl ~ Ltt It and partitioning'll!n ~n the following express~on results
Ky! -1
LU (LU II ,,1 d
-4- 11 dt (LUI) m
-1 u:! +
T KT V - Il.U It' Kyl Lu KiS VB + ty y
Using equation (5) , noting that ..!!. (IoU) ~ 0, and rearr-anging: dt
Vy L -1
(Et
+ T (7) n Ky! Lu. KJ!.B Va - lin 1 1 )
wh"re
-1 -1 11.'1' L " \tLu yy ty
State sl:'!,ace formulation
Experience with dynamic analysis in a.c./d.c. transmission systems(4) has shown the advantages of usin9 the state space formulation. Using the flux linkages (~u) ,as the state variables and the node subdivision described in the last section. the rate of change of the state variables (equation (2)1 can now be expressed as follows.
(8)
Using equation (7) to eliminate Vy
is a unit matrix of order t
u~ing equation (6) to eliminate V /;l
(10)
Numerical solution
Because of the thyristor $witchings, the topology is undergoing repeated changes and the network equatlon~ must therefore be solved by a 'single-step' method,which is selfstarting.
Using an implicit integration routine, the state vector (~) at the end of each integration step of length h. can be expressed as follows;
(11)
where!
and substituting from equation (10)
Rearranging and making.
the following expression results
-1 h 1 -1 -1 h ~t+h g AU (UI'.C '2 MU RU LU) >lit + AU 2' MU (Et+Enh'
(12)
where,~t' Et ~nd Et
+h are considered constant within each ~ntegratlon s~ep. Finally, the flux linkages (~tt)
are small quantities in the system being modelled and the numerical accuracy is greatly improved by using (w'bu ) as the state variables, Le.
The stability of the numerical solution depends on the accuracy of the initial conditions. Approximate in~ itial conditions for a particular study cao"bQ obtained from the load flow solution in the absence of thyristor control (i~e. with the 'boosting' pair permanently open and the 'short-circuiting' pair permanently closed). However the load flow solution is expressed in terms of pure sinewa'ves, whereas the actual waveforms are disto4'''' ted. .115 a result of the waveform mismatch, the dynamic simulation under thyristor control requires a very long computer run to reach steady state conditions~
Oetection of discontinuities
Thyristor switching must be detected accurately in order to perform the approp' ote topological changes.
'l'he 'sta\:.<! of each thyristor is determined at th" beginning of every integration step and the current through the thyristor is then calculated assuming this
d dt(~U)
whe .....
1 ., "Uh: .. -RU (9) particular state throughout the complete integration
step. The value of this current is then used to indicate the state of the thyristors for the n .. "t integration interval.
"u ~ Uu -
and 1 RU Ilu. ..
itT L 11 YY
'I' • Kill !lll/J
ItY1
J
The following information is used to model th~
state of the thyristor. anode to cathode voltage (V.IIK) , which is at logic
level~ '1' or '0' depending on whether the device is
anode to cathode current IIAK ) which i~ at logic level~ 'I' or '0' depending on whether this current is greater or less than the holding current.
prior is at 'OFF'
operating state of the thyristor IC) immediately to the ,integration step under consideration which loqic level tIt or '0' when the device is 'ON' or
respectively. presence of gate pulses (G) is indicated by logical
level 'I' and absence by '0'. Thus the state (S) of the thyristor is given by the fol~ lowing logical relationship:
The thyristor turn ON is predictable since its firing instants are decided by the control system. In this case the integration step-length can be adjusted so that the firing instant coincides with the beginning of a step. The firing instant is related to the zero crossing of the reference voltage, this reference point can be determined by linear interpolation without the need for any change in the integration step-length.
An accurate turn OFF can only be predicted at the expense or slowing down the computation. Sufficient accuracy is normally achieved by detecting 'the turn OFF after it occurs and then improving it by linear interpolation. The turn OFF instant thus obtained is then used to interpolate for all the other variables.
CU~PUTED WAVEFORMS
A computer programme, based on the dynamic analysis described in the previous sections WqS used to investigate the behaviour of a three-phase three-winding )0 !!VA distribution transformer and a series boosting tra'nsformer as shown in Fig. I, the relevant parameters for the main and series transform""s are given in Append!x A.
Due to the frequent topological Changes caused by' the multiple switching, the solution required long comp~ utinq times~ Most of the time was spent in obtaininq realistic initial conditions, i.e. 90in9 from the sinus~ oidal waveforms initially assumed to the actual distorted waveforms. However, once a set of realistic initial steady state waveforms had becn Obtained, these could be uscd for all the subsequent dynamic cases on the same system.
Some of the results of a three-phase symmetrical study are plotted in Fig_ 4 and their similarity with the theoretical (Fig. 2) and experimental (Fig. 3) reSults is very apparent. These waveforms illustrate the effect of a 750 delay'in the firIng of the boosting pair sl and a 100 delay in the firing of the short-circuiting periods are clearly seen in curve (V
T) which represents
the tertiary side voltage across the ,series transforrner~ The fundamental component of the load side voltage
waveform (VL), although not immediately obvious from the
figure, has been boosted by G\, for these particular delay angles, with respect to the voltage at the secondary terminals of the main transformer. Small 'dips' are clearly visible in the load voltage waveform 89 a result of the c~nutations between the loading and short-circuiting thyristor5.
The percentage regulation of the fundamental component of the 10lld voltage as iii function of the firing angle a (while £ is kept constant at 10°) is illustrated in Fig. 5. The graph $hows a stepless voltage variation between +11\ and -3.4\.
There is ~ small phase shift between the fundarnent~l components of the voltage at the secondary terminals of the main transformer and the load voltage. The var1-atio~ of phase-shift with Q is also plotted in Fig. 5 and a maximum of +1.50 is observed.
Finally it should be noted that the eadiest firing instant for the boosting pair corresponds to an angle equal to the phase difference between the actual voltage
234
flnd current waveformm; this intervlll will, of course, vary with the power factor of the load.
Harmonic content
The disc .. ete information obtained irOOl the dynamic simulation can be used to obtain the harmonic content of the 'voltage and current waveforms. Sinee the time steps used for the dynamic solution are not equally spaced, linear interpolation is used to obtain the approximate data at regular intervals.
The Fast Fourier Transform (5) is then used to process this data and compute the discrete Fourier coefficients a and b. The rms values (C ) and phase relationships ~~ ) ofneach component of tHe composite WaVeforms are glOen by the following two relationships respectively.
C n 12
-1 -b
+n IIIJ tan ( an) n
Cycles
Fig. 4. Computed waveform ••
G
o (b)
(a)
o 40 80 120 1£>0 IBO
Firing angle « (degrees)
Fig- 5. Load voltage variation. (a) Voltage regulation (per cent) (h) Phase shift of fundamental (degrees)
The maximum h;rmonic content of the load voltage and current waveforms and the supply voltage and current waveforms are illustrated in Figs. 6 and 7 respectively. Each harmonic is expressed as a of the funda-mental cOllIponent of the waveform.
The point on wave control booster acts as a source of fundamental plus harmonic voltage. The harmonic levels of the load voltage vary with the firing angles and their maximum values are plotted in Fig. 6. Third halmonic is predominant, but the levels of 5th, 7th, 11th and 13th are also significant. The levals of harmonic current at the load are limited by the load impedance, thus reducing the increasing harmonic orders (Fig 6).
2
II, I I 35791113 35791113
Voltage Current
Fig. 6. Harmonic content at load bus.
As a result of the delta winding on the primary side of the main transformer, Fig. 7 contains no third or triplen harmonics. However there 1s a relatively high level of internal third harmonic current.circulation in the delta winding (up to 6\ for the case under consideration) $
A comparison of supply and load harmonic currents shows a larger content of 5th. 7th, 11th and 13th on the supply side. This is caused by the extra current injection from .the tertiary (point on wave controlled) winding.
!! 4
., ; 3 ., c 0 2 u (j .,. c 1
e tl) ;I;
S 1 911 13
Voltage Current
l"i9. 7. lIarmonic content at supply bu".
DISCUSSlm~
The range of voltage controllability which can be achieved with the proposed solution is only limited by the level of harmonic content produced. Onder reasonably
plen .. tlKlll<.>" .. "·,,
windings.
flow conditions, most of the lrd and tri-can be eliminated by transformer delta
If the levels ot the 5th, 7th, 11th or 13th harm-
235
onics are considered unacceptable, "om@ filtering plant may have to be add~d to th~ basic unit of Fig. 1.
The thyristor "witch"" need only be rated according to ·the maximum p~rcentage voltage requlation required,
While it is possible to consider series and parallel thyristor connections, the simplicity of the aingIe device switch is attractive. As an example of the field of application of the single device switch, consider the 30 MVA transformer taken as a basis for the computer studies. Assuming 8 150'MVA fault level on the 11 KV side and a voltage regulation of 10%, the shortcircuiting pair in each phase would have to cope with 10' of (1/3 x 150), i.e. 5 MVA for two or three cycles, which is within the range of present thyristor technolo-gy.
Moreover. under external fault conditions th~
pair 51 can be blocked, thus leaving the short-pair S2 to withstand the fault current. Int
ernal faults caUSing simultaneous conduction of the boasting and short circuiting pairs will require the provIsion of fast acting fuses between 51 and the transformer tertiary winding.
CONCLUSIONS
The static alternative based on point on wave cQntrolled voltage boost has been shown to be technically feasible. By appropriate choice of the boosting transformer ratio any voltage range provided by on-load tapchangers can be achieved subject to some waveform distortion and phase-shift. There is no need for mUltiple taps, each phase requiring four thyristors,and the speed of response is only limited hy the intervals between thyristor switchinqs.
The results of this preliminary investigation are sufficiently encouraging to justify the necessary reliability and economic studies prior to the design of a full scale unit.
ACKNOWLEDGE:MJ::NTS
The authors are grateful to Mr. P. W. Blakeley, General Manager of the New Zealand Electricity Department; and to the Department of Electrical Engineering and Computer Centre of the University of Canterbury for their help.
[1]
[2]
[3]
[4]
REFERENCES
Roberts, M. E. and Ashman, W. G.,"A Thyristor Assisted Mechanical On-load Tap-Changer", I.E.E. Conference Publication No.5) on Power Thyristors and their applications, pp. 185-192, May 1969. O'Kelly, O. and Musgrave G., NAn Appraisal of ~rran"" sformer Tap-Changing Techniques U
, I.E.E .. Conference publication No. 123, pp. 112-117, 197). Arrillaqa, J., Barrett, B*, and Vovos, N; A. I NThy_ ristor-Controlled RegUlating Transformer for variable Voltage Boosting", Proc. I.E.E., Vol. 123,NO. 10. pp. 1005-1009, 1976. Arrillaga, J., Campos Barros, J. G. and AI-Khashali H .. J., IIDynamic modelling of single generators connected to HVOC Convertors", I.E.E.E. PES July 1977, 1"77647-l.
[5] Cochran, W. T. et aI, "What is the Fast Fouri",r Transform?U, Proc~ I~E~E.E,.t Vol~ 55, No .. lOa pp~
1664-1674, 1907.
APPENDIX A: PARAMETERS FOR COMPUTER STUD~
Supply bus fault level Load power factor
Main Transformer -
480 MVA. 0.9
The main transformer consists of three phase units connected in delta/star/star.
Ratings. 10 MVA phase) 33/11/2.4 kV 1;9
9ing16-
(phMe-
ThG ~clt and mutual winding reactancU9, calculated in ohms par phase, from the manufactur@r s op~n circuit ~d short circuit tests, were as follows!
Prilll,,!:y Secondary Terth."y
Primary 60500 12900 2153
Secondary 12900 2760 587
Tertiary 215l S97 125
236
Series transformers ~ Three independent transtormer$ were used (with
their primary windings in series with tho resp~ctlvu phases of the loed).
Rating, 1.2 HVA. 0.76/1.39 kV Winding reactances:
by
D
The motor
e & Co.
following
APPENDIX 12
set, which was manufactured
, Hebburn-on-Tyne, England,
data.
D.C. Motor -
Compound wound No.83768
Volts 0 Amps 85 R P.M. 200/1800
Current Alternator -
No.83771
Continuous rating 10 kVA
29 Amps 200 R.P M. 1500
3 Periods 50 P F. 0.8
Volts 220 Amps 11
No.8 69
kVA
520 R P.M. 1500
3 50 P.F. 0 8
Volts 220 F ld Amps 9.5
7
238
APPENDIX 13
led Indexing Remu: 1PIu!SIi! conlrol, A.wef C",,,"".Il'o~i'I!"on"$I<·1II conll'V', Power mlllil/armen. ThyrizlOr OppliClltiOIl'
Abstract Wi!h reference 10 the cOllveniional quadrature booster transfomlcr. this paper describes a way of achieving continuous phase.mift control b,ued on point-onowave thyristor swiiching. TIu: proposed unit can provide continuous and practically instantaneous power-transfer control in transmission circuits. The theoretical waveforms are verified by experimental lests and computer sludies. Consider:uion is also given to the hamlOnic content produced.
1 Introductioll
The flow of power over II transmission line connecting two power systems, J)r two parts of the same system, is innexlbly lied to ahe power.angle difference between the voltages at the inteH;onnected busbm.
System-planning requirements normally decide tMI nominal power rating of II particular interconnection, and transient-lltability consider· lltions restrict the maximum steady·state phase difference to relatively low values (of the order or thirty degrees). nUlse constraints Ire checked by means of)oad·f1ew studies and often, ~s II result of such studies, quadrature booster transformers are added to produce phare ~hifl and. thus, satisfy Ihe specified power limiU.
Phase shift is normally achie\"d by means of 3-phase shunt transformers with series windings arranged to add II fixed quadrature voltage to each phase. Taps are often used to permit variation of the quadrature boosting level, and.(inc variation can only be achieved by the use of automatically controlled onload tap changing, which is eXp"flsh'e and requires considerable maintenance. ..
A recent publ.icationt has described II w3'1 ~f achieving continuous voltage-ma!,Ulitude variation by exercising thyristor-controlJed point. on·wave switching of a.n in-phase regulating transformer. The same principle is applied in this paper to !he quadrature booster trans· former. The paper describes mathemllticaJl)' and Ilxperimentally !he conditions under which it is possible to achieve continuous powertransfer control.
:2 Basic circuit and modes of operation
The schematic diagram of Fig. 1 mows one phase of ill
thYlistor-controlled quadratuJe booster connecting iwo systems represented by their respective voltages V", and Vs. Shunt transformer T I proVides the quadrature vOltage for each phase, and series traos. former T, the controlled boosting voltage.
S, and Sa are two back·to-bllck phase-controllcd thyristor sw~c:hes; SI is !he boosting pair md 52 B short-circuiting switch, which is necessary to prevent In opcn-circuit condition of the series transformer during the nonboosting periods.
There are two basic operating modes, depending on whether the quadrature 'tohage V Q leads lmode (i)] or lags Imode (ii)1 the primary voltage V,..
Fh,.1 ThyriJJl@r'4:onlrolled qllfulrl1ll1Yi! booliell'
IIJIOI', llr:fJf ,,,.; ... d 14lh NOVf:mbri:f nntJ "nd I" ,.vI"d rom. HJlh 1!l1V •
mi. ;t .. mOf1!J b w/th the f),port"..", of EhCfrk;,,' Eng/".,rln9, IJnlv."tfyof C<tnte,twfJl. Chrl>l<hurth, N ... • ,gntlll>llr. Oil;'" i. wit/, Ih. Ne", Z«%nd Elect,lcllylH(J@!lm<fII. Chris/drurY, "
The operation of Ihe circuit in mode (i) em be belief described wi!h reference to the theoretical waveforms of Fig. 2. The~ wave· forms correspond to III CMe of lagging power factor I/J and with the. quadrature voltage leading the primary vohage by 90".
During the positive halfcycle oninc current I, when VI' is positive, the voltage V T lill.:roSS the secondary winding or the series transformet is negative. This voltage forward-biases !hyristor 3 lind reverse-blares thyristor 4. The provision of a S31e pulse to thyristor 3 will thererore tum on, thus short-circuiting the secondary winding of T1. "1' 1$ now equal to - "I. where V, is the forward voltage drop of thyristor 3.
fill. 2 VutoFietical waj'e{Q1I1U "'l'irh leading qUfJdroluff' .vIM,"
When h positive, thyriUor 1 is forwlrd bias.ed. Therefore, I 1l!~I\: puls.e applied to thyristor I will 111m II on, lind Y'if will become posit ive. l!kcause, thyristor 3 Is IIOW uovene biagd. Ii wiJIlllrl! off.
When il; negative, thyristor l b again forward biased. HI:II~. dle firing thyristor:3 will lum it on, and I commutation from th)'ristor I 10 thyristor 3 will like pl8ce, thus turninglbyristof I off.
The Ilperluion during the s.econd hlllfcycle is similar to the fint, but wilh all voltage polarities reversed lUId '''ilh the altelillite thyrislm of nch back·to-back pair conducting. •
Thus, for operation in mode (i), with lagging power factor, Ole efrective fange of the firing angle g ror S, is; 90" + 1/1 <!l < 180" ,lUId the range of firing angle Ii for 81 is O· < iii < 90" + 1$1. The firing angles o lind f Ire both measured wilh respect 10 the zero crossings of VQ •
If lagging quadrature boosting is us.ed (mode (ii»). i.e. If Q lags V", by qO·, the appropriate thyristor of switch Sa required to terminate the boosting period, will be rcvcne biased until the uro crossing of the line current and cannot conduct until that inuan!. But, even then. the conducting thyristor of switch S. , being still forward biased, will continue conduct' 19 lUId the ' .... itching of Sa will immediately short· drcuit the secondary ",inding of transformer T I. To overcome this problem, II dday could be buill into the control syste,,' to allow S I to switch off and rtco"cr fully before the firing of Sa. This delay. however. would cause III temporary open circuit, with large overvoltages, across the iccondary winding of T 1, and Is not considered II practical proposition. Operation under mode Oi) was thus discarded, illnd the rest of the paper deals-with operation in mode (i).
If the transmissiQfl line connecting the two systems contains power transformers III either end, Ihe ~hunl transformer of fig. I can be dispensed wilh, and the requirta reduced vollage obtained from II
tClliary winding. Fig. 3 illustrates one phase or :iI transmission line (between busbars V. and VII) with ~ 3-winding transformer at the sending end. In the absence of tftvristor switches. the phas.e-to-neulral lertiary voltages will be in quadrature with· the line vohages of the delta.(Oimecled windings. Thyristor control produces the waveforms illustrated ill Fig. 2.
fill. 3 One-phase ,epr;w:ntor;on 0/ IJ trarumiu;on sysrem w/rh thyristor-1I:0II"01/,,d quadrature boosf/fl/l
3 Mathematical model Owing to waveform distortion, the exact position of the
crossing poifl'b used as II reference for the switching instanls is not known in advance; moreover, point-on.w3ve switching is transient by nature, IlI1d the analysis of voltage and current waveforms requires a dynamic: model.2
Ii is computationally efficient 10 use the branch formuk\tion and subdivide the nodes according to thll Iype of branches connected 10 them i'll!o:
la) (J nodes connected III least to one !resistive branch (b)., nodes connected only 1.0 inductive branches (c) l; nodes wnneeled to thyristor branches (this is u spedallype of.,
node).
The introouction of I) nodes s.epllrales the nMes affected by continuOUs topological
Althoul!h IS nodes 1101 figure in the formulation, iJilry lire useful 10 idenaif), which nodes life affected by thyristor switching during the dyn!lfllic llimulalion.
A conduct ins thyristor b heated ~ II shorl circuit, thus converting two Ii nooes into II ., .!lode, IIIld a nonconducting thyristor Is treated IS lin opllin circuit, converting two li nooeJ> into 11'10 '1nooes. Using Ole 31101l1l cla!l>ificlition, thl!) following mllhix Ilqu<ltioo$ C3n be written for the Jesisliw <lnd ~du!:iJve !mmches III partitioned form;
(I)
+ (2)
II = cllrreni vecton nodal volt age vecton
= e .m.f. vector ofinduclive branches "" resistive branches matrill
239
'" fesistan~ matriK of the inductive lmillllchet = inductance matrix
resistive branch-lo·node incidence matriCt's for the 8 and 'Y nodes
K;~. K'f., = inductive branch·lo·node incidence matrices for Ihe tJ and '1 nodes
Two more mlltrix equations can be wrilten relating some of the abo" variables by using Kirchhoffs current law and remembering {10m the definitigrll of ",nodes that K;" = 0, i.e.
K!J,', = - KfJJl,
K.,I/, == I)
and also
3.1 State-llp,,"" lInalVlfh
(l)
(4)
(5)
By using Ihe flux linkages !/Ill as the state variables and Ole node subdivision described in Ole preceding Section, the rate of change of the state variables (eqn. 2) can now be expressed liI!i folloWll:
d 'II' ,. ;U(tJill) == £, + K,jl"p-RII/, + K,yV., (6)
The voltage vectors Vii lind V'I' appearing on the righi-hand side of eqn. 6 need 10 be expressed in terms of the current vectors l1li(\ their values calculated at every step of the dynamic solution.
An expression for the voltage vector of IJ nodes J-p can be defllled as follows:
(0) premultiply eqn. tl T'by (b) note that K'[., = 0 (c) substitute eqn. 3 in eqn. I
The resulting expression is
Vi! '" - R(J~Kt:II/,
where
RiJ "" KtlrRr-: K'Jp
(7)
Simnarly, an expression can be obtained for I/y as follows By premultiplyinC eqn. (, by K'r,I.,,1 • and remembering Ihal ';/1 '"
.1",,1,. 'he followiJlgexpression results:
K-"I;il[l.lI fUI)"l-/, ~(I'/I)] "" K.."Lil(l:', + KI~Vp + K,;VT -Rill,)
Using '''In. S, noting tilal d/dl(LII ) 0, alld re~rranging. we !let
V,l (EI + Ki~YtJ -Rill,) (a)
Referring back 10 the slale->&pace matrix tqn. 6 1I11d ming eqn. S If' eliminilite Vl1
.!.(I,bll) == IV" - KI~l.nK'I'ILiii liE, + KI~I~ -Rul,1 lit
where V" is <II unil matrix of ordell. lIy using '''l". 7 10 eliminate VGI
finillly, thllt II
eQn.9 In matrix form, lind II being remembered
[~(""I) ] '" i-MuRALiiil (i0)
The flumcrit:illlOlulion ohqn. 10 il disC:l!~d In Appendix 9J,l!lld ihe detection of the discontinuities pIQ(I'Icing topological changes il; descril:Hld in Appendix 9.'2.
Fig. 4 Computed walleform,
e Primary vohaa./(C b Vollase on the Hcondary I1de or tbe m::l.)n traodormef e Voltast' 8t the undinl end of trensmb:aiolA liM d i\eceivlnl-cn4 vottal_ It Qu.d,o'IJ,e """,ling voll ... ~ f Current on the "rlmarY .Ide bf the main eransfonner I. Cun«tlu on the leC'undary side of tb .. ma;n "$nJlormlff Ii CUNeo. on 1he st'cotlduy aide of the &.cries .,andormer" I Curten1 on the .ertiar), aidr of the main Il'IInsf08fPft
4 Camp'uter results
4.1 Wav.forml
The mathematiclll model described in Section .) hIs been pfogrammed for numerical solution III l!l digital computer. Owing to the frequent topological chanllH (30 switching instants per cycle for 13
3·phue system), the solution requires vllry small steps and, consC!· quenlly, much computing time.-A large proportion of the time is used in eliminllting the mismatch which cxists between the sinusoidal wive· forms initially assumed and the actual distorted waveforms. However, once l! lei of realistic initi~1 steady.state wneforms has been obtained. these can be llsed for subsequent dynamic c~s on the same system.
The leU system under consideration is illustrated in Fig. 3, and the relevant are given in Appendix 9.3.
wlivefonns. cakullted with contre! angles a'" I2S" and e , liITe illustrated in Fig. 4. Waveforms (11) lind (d) Ire the sinuwidlll \toluses It the terminal luubars 1',. l!lld "J\l. respectivel: (assumed to be connecled to very strong 5y:1tems). Wavefonlli (b) lind
fc) correspond 10 "'ohagn I:Hlfore v.,€ and lifter VB the series ifl!llS' fOlll'ler; the effect of ~omm!ltaliorl$ Is clearly visible in these W<lveforms. The boosting 1/ollllge IIr Icrms thl: Iccol\(bry winding or the series Ifl!lniformer ii illustrated by wlIIlleform (c). The f:ummt wave· forms 00 the primary; iecondary and tertiary ;ld!:1 of tbe 3.winillng lilliliformer are shown in waveforms (g) and (0, respectively. Md wlIVdoM1 (iii) illustrates the cUllenl on Mcondmry side of the Mnn tfl!llilfOl:imllf.
40
4.2 fourier l!:omponenb
The discrete inlomlalion obtained from the dynamic simu· lation cln be used 10 ohlain thl1 Fourier components of the vollage and cuneni wavefomll. Beclluse the rime step' used for the dyn~mlc !!olution Ire 1101 equaU ... sp:!ced. linear interpolation is \.'s~d 10 obtain the !!pproximate data :ill regular intervals.
The fasl Fourier uansforml is then used to process this data lUld compute the discrete Fourier cOI'fficienlS tin and lI". The r.m.s. ",alues C" and phase relationships 9" of ~ach component of the compo'lile waveforms are given. resp!:clively, by the following two relationmip>!:
C.,
4.2.1 Fundamental voitlltp
Quadrature boosting causes phase-shift and voHage-magnitude variations. The effed of firing·angle control on such parameten b now discussed with reference to the particubr system described in Section 4.1.
Two limiting cases will help to explain the effect of varying the firing angles or the boosting and short-circuiting thyristor pain; the results life iUustraled in Fig. 5.
Qse(fJ) Phase-angle control is exercised at the boosting pair (angle 0:), whercall the delay of Ihe short..circuiting pair" is kepi constant aI 5". The results Ire plotted between points A and B in Figs. 50 md Sb. These indicate II maximum phase shift of 4" with a voltage-magnitude Vlri
alion of3-6%. Qse(b} The boosting and short-circuiting thyristol1! lire fired symmetricillly with respect 10 the zero crossing; of the tertiary voltage (i.e. i! = 180" - a). The results. plotted between points A and C in FilP. Sa and 5b, show that Ihe maximum pha~e shift has increased 10 9"', whereas the voltage·magnitude change has.l .. c~..Jto 1-4%. A:J l!lfI
extension of Ihis case. and stalling from point C (i.e. when minimum 0: has been reached). further phase shifts can be achleved by delaying angle £ from 1800 -a) to (90· + 4». The results. plolted between points C and D in Figs. So and Sf). show Ihat the maximum phase shift can be extended from 9" \0 I!". and thai the voltage magnitude increases bY'0'7% al point D (this point requires continuous boosting operation, I.e. with switch S, permanently on and switch Sa penmmently off).
4.2.2 Harmonic content
The sendiog.end voltage on the line side or the series 113ns
former shows considerable dislortion (Fig. 4c). The harmonic con lent VlInes with the firing lI.IJgles 0 and t", and the maximum leveb (expressed IS II percentage (Jllh" fundamental voltage). calculated by the faSI fourier Iransrorm for Ihe lest eKample, art illustrated ill Fig. 6 for the Iwo cases discussed in Section It2.1.
elise (b) shows considerable increase in harmonic content oVllr case (/I). This is explained by the larger voltage jumps caused by the firing delays of the short-circuitiog Ihyrulon.
The only sourcc €I f triplen harmonics is the tertia!)' (clearly illustrated by the voltage and current waveforms Lt. fig>. and 4i). For the test exam!,I!:', the maximum levels of third· and ninlh· harmonic currents in Iht tertiary windings are 310 mil I roT.nu. , respec;li"ely. (or 39?( and I J% of the nominal fllndamental-componell\ filling).
No triplen hamlOnics 1m: present in the unding. or .<<,. .. 'In''..£:f,(I ~yst"ms as II result of the delta...:onnccled transformer winding:;. is. however. intern:!! circulalion of triplen harmonics in the deh; winding;. The maximum levels for the ca~ under consideration 1111:
3'3% Md 1% of third- lind llinth.IJarmonic Cllrrents, respectively, in the primary windings. The corresponding levels in the secoilduy windings IIrt 4·8% and 1-6'J:.
Other imporunl maltimum harmonic currents ill the Iti1iuy windinp :lIfe liS follows:
(11) 5ih - 23% (1/) 71h '6IJ. (c) 11th 9% (.I) 13th 8%
It must be poinled out, however, that the brger.IJarmoruc contents in the tertiary winding coincide with reduced conlent or fundllmen111l oompllilmt.
4.3 PmAmv trml'lafllf
'The complex power IIi the receivinll-end busbar is obtained from the expression S" VI, where V Bnd lare the Im.s. fundamentHI <l:omponenll obtained from the fourier analysis. The IIlctlve· IIJId luctivc.po"er Illlws per phue for the two cases (11) lind (b) discussed In Section 4.1.1 are illustrllted in fi~. 7& IIJId 7b.
44
44'
40
'" .. 31\ ... @
Hi
34
:112 ~-----Ji.
100 120 140 160 1110 g [Onlrol angle ... deg
3
2
:-
>'" 0
"" -1
-2
-3
100 120 140 160 11\0 t.J control anglli! B<. deg
fill.!lii FunJamen',,' polt: Is lor 1 (6th rated series tram/ormen
a PhUfNBnsie Incfelllse (deareH) Celie A: I~ne A .. R/Jncre8H for variable o. fiBed fl = S· Clue B: I~e A..cl..lncfl~au' for var1ablr Q. variohlte fl = (I ROC!» - Q) lin~ C-'fj
furlher Incruse for variahle (f hcyund Vltin' C = (900) ... 0) €I Volts." ma.",'tud. ('Il)
Casr A: Une A-8llncrgmse for vBllable Q. tiKed fl = SOD
emMB: line A.c o Ineresut' for variable a. vAriable «=(190° -1J) line C .. O. FUilher Increulll ror variable c b=vond poin. C == (90(l) ... @)
I}
;f. !i
c .. c II. <l ... .. 3
'" <!) , Ie @ g
I)
fl;.~ "/"JlimlAm yol'IJle-·harmon/e <:om.,,,, 411 I'll! FOR 1/6,,, ,,,,ed seri", ""'''/OrMerR . Cue II: Vwimbh CI. fiati'd ffl lie §'i!>
Cun B: V~bk fl.V@ltablceJ;;.::(lIMl!' """"€ill)
241
With rderence to fig. 7IJ, the power transfer can be increased by 20".f> for case (a) (line AIl) and by 25% for case (b) (line AC). If case (b) is extended b)' furlher delaying f. as described in Section 4.2.1t the power trllnsfer can be further increased up to a maximum of 3091-(line CD).
With reference to fig_ 7b, case IJ causes I 7% maximum variation of reactive power al the receiving end (line AB). The rI!3ctive'powl:r requirements of the transmission line increase substantially in case (1'.») 115 indicated by lines AC (65% variation) and line CD (135% variation).
s·o
4 5
0: B
;[ I.-I.
~ 4- 2 ., ~ <!)
11.-0 " .. ,. ] tI ..
0::1 3·6
100 120 140 160 1110
(j control angte "'-, deg
control angte <IJ(. €leg
100 120 IU) 160 11)0
II: -1·0 «
~~ ,.,
-1'4 ;[
~ .. -I-II ~
" " OJ -2': ,. I -:; -2-6 I " .. 0 1 b
-]. 0
Power·trom/er ~'ariorion receiving elld lor I/Illh ra,cd uries irQ",· formers
(jJ At.'liv4' pnw~i' (MlA' P"" phi~) CDEr A: line ,A·U. Im'rt'a.;.\' rur 'I:.lri;.&hIL' LII. liBltd (( = (' Csse 11: line A"(\ Incn:a.\>e fur v:ariahlt' 0:, v;tri:able tl == (160° - a) lind (>1»,
Furlher incn:Dlc for v.riahl~ If heyomJ point C = (90~ i- 0). D Reaclivc power (MVAN. Pie, phillie)
Co.n A: lin~ A·8. Increast! for variahle 0, fixed (I = '!t C\!I'Ulf' flJ: line A...c, Incrg,u4' for varliahle G. variBhle 4'':; (IHO!l'l ~ a) line (" .. D.
Fur.hlli' increase for variahle f heyond point c: = (900 -+ 0.)
4.4 Discussi@!'O
The results illustrated in Sections 4.1 to 43 demonstrate Ihllt it is possible 10 implement a continuous variation of phasacshif! and thus achieve lIel)' fasl power transfer conlrol. The relative variation @f the liring delays at the boosting and short-circuiting Ihyrislon givn rise to different control strategies. and ii is possible 10 operate al;my point within the shaded areas of figs. 5 and 1.
lFig. 1IJ illustrates that most of the real-power transfer .... riation can be achieved by using the control outlined in caSe Cal and Figs. 71'.» IIJId 6 indicate that both the variation of reacthe-power fequircment lind the harmonic content lire kept to a minimum using this control strategy.
for a modest increase of the power-transfer capability, case (b) increases consillcr~bl)' the h3l1nuni.: content. Moreover, in the tnt example under discussion this case I!ivl!s rise to consider:!ble variation in the reactive-power requirements of the line.
The extra power-transfer control possible outside the shaded mrn (line CD in Fig. 1) can only be achieved with unrealistically high Ineh of reactive JXlw.er. This result cannot be generalised, however. and may b<! quit~ different when Ihe linite short-circuit npacity of the rea:iving-end system b laken into consideration.
Fig.S OSt:ilIog'l1ffla of typical voltage (mil CU'Ti"" ..... velom"
41: Voltage on IJrimM}I !.ide or main transformer b Volta,*, oft nne side of "tin transformer t: "ottilIe &(TO!3 acc:ondary windi"l of "riEi lfaniformer d Line current
6 Experimentalllerification
An 8·2S kVA. 400/200/66 V. J-winding )·phase transformer. with its tertiary windinp connected to three 1S0VA (per phase) 66/25 V series transformers wa used to verify cxperimentlllly the thcoreticlll waveforms described in preceding Sections.
The transformers and thyristor switches were connected a shown in Fig. 3, and II set of typical voltage lind current waveform:nml shown in Fia. II. The waveforms illustrated in Fig. 8 were obtained with firing delays of 120· and 4S· for the boosting 11/ lind shortcircuiting € !hyriston, respectively.
Oscillograms So, b, t: and d show the primary voltage VI', the phase·shifted voltage VB. the voltage across the secondary winding of the series transformer I'T lIIId the line current I. respectively. In particular. the Similarity of oscillograms lib and c with the theoretical waveforms Va and 1fT of Fig. 2 iIIustrllte the feasibility of the proposed switching sequence.
6 Conclusions
It has been demonstraled that the phase Ingle of the power· frequency·voltage component of II transmission line can be varied continuously by using thyristor-controlled quadrature boosting. The maximum phase shift obtainable is only limited by the ratio of the quadrature booster transformer. Such variation, in tum, provides II
corresponding region of continuous power·transfer control. TIle speed of response is similar to that of the thyristor.controlled rectifier, II
properly which could be exploited to improve the transienl-!ltabilily limits of the interconnected systems.
Besides causing phase shift, quadrature booster controlliffects the voltage magnitude lind int roduces harmonic distortion. Regions of controllability lind the levels of active reactive power and harmonic content have been defined. The luger proportion of power control· lability hu been shown to produ~ \loltllge·hamlonic levels within 3% of the fundamental Yolillge.
7 . Acknowledgments
The lIUlhOB are grateful to P.W. Blakeley, General Mmager of New Zealand Electricity ~nd to the technical stafr of the Department of Electrical Engineering and Computer Centre of the University of OlJlterbul'}' (or their help.
R.,ferenC!!i,§
ARRIU.AGA. B., ."dVOVOS, KA.: "Thy.I.lo,-oonl.ollcd fel"!.'i,,, Ir.n.ro,,,,~, f"r ¥Qli.JIllI iIooJlins',lI'mf:. lEt:. 1916, fU, (lO).pI'. '005 -1009
2 AIUliLLAGA. J., AI.·KHASHAU. J.G.: 'Go"",.1 form"liu;"n ro, Ily .... ",\<: IlIslie "" .. "",tc ... ·.lbltl .• ~911, U4,Ul).I'P.
II ('(l('IlI'tAN, VI.T., <!!I" <d : 'Whot 10 the IEE£, 1961. 55, pp. 16~-1614 .
.Ii OORW. "'S., .nd McCRACKEN, D.D.: 'WumnigJ _1"<><1. ",illl "'etlian IV ClIO ..... d."'· Uobn WlMy" S""., Inc .. i9ll" 1'1'. nl-2U
~ SEAnn;. WI: •• and MONTfiTH. W.: 'Dj,j:ilolm<><l.II;"s I>r" tllyrilll",,', 1I'mf:.1££. 1913, no, (1J. PI'. 1119-1110
242
9 AppendixGs
1).1 Implicit integration .,f mi!'! stlilte ~eC,l)f
Becllus~ of the thyri5lor Iwilchinp. the topology Ii under~oing repeated ("h~ng"" IIml the network equillions must therefore be lIolved by II ',ingle·step· method, which is sdrsUrting.
Expressing the state·vector differential equation in the following form:
f(w)
then, by using the trapezoidal rule,4 the lillie \lector !/I lit the end of lin integration step of length h is given by
and. by substituting from eqn. 10, we get
ob,." = 1/1, + i t-Jlf"RM·ii' ~, - JIf"RMir' Ib,+"
+ Milt', + Mult,." l By rearranging, lind making
All "' V,,'" i M"R,',Lil
the following expression resuits:
!/I, + Ail i Mu(£, + £,u)
(U)
Within each integration slep. the values of 1/1" £, :and £,." are CO/1·
sideredconstant. finally, the flux linkages !/I" lire small quantities in the system being modelled, and the numerical accuracy is gready improved by using W!/lll as the stale variables,l.e. .
I, = xiNw\lll/)
The stability of the numerical soluHon depends on the accuracy or the initial conditions. Approximate initial conditions for II particular study can be obtained from the load-flow solution in the absence or thyristor conlrol (i.e. with switch S, permanently open and switch !OJ permanently closed). HowevfOr, the load-Ilow solution is expressed III terms of pure sinewaves, whereas the actual waveforms are distorted. As 1I result of the waveform mismatch, the dynamic simulation under thyristor control requires a very long computer run to reach steady. state conditions.
9.2 on/off detec:1ion of thyristor switching
Every thyristor switching elluses a topological change in the system. The state of each thy ristor is determined at t he beginning of every integration step, and the current through the thyristor b then calculated assuming this particular Uate throughout the complete inte. grlltion step. The ulue of this currenl is then used to indicate the state of the thyristors for the nut integration interval.
The thyristor mooelused requires the following information:
(o)anooe·lo..;alhode voltage "AIr; lilt level '&' for forward·biased device
fb) anOOe·to..:athode curreRI 1M!:: :lit level 'I' when larger than. the holding current.
(c) the thyristor operating state (C)immedialely before the Integratioll 5tep; at level 'j' when the devi~ is on
(d) presence of gate pulses (G) b indicated by logic level 'J '.
The sllte (S) of Ih. thyristor iI thus ginn by Ihe following Il'si~al expression: $
s= The thyrilltor turn on is predictable because Ib firing instllJlU are decided by the control 5yslem. In this case. the inlef!lation 5t~p length elln be adjusted so that the firing instant coincides "'"ith the bfl!inninl! or liteI" The iirinlt inSl:!!nt is related to the zero croililing of me referellC'll 'ifoILl£!e, Ihis referen~ point «:all be delermlned by linell1 inlerpolation without the need for lIny chan!!e in the intes.ation step length. .
An ~rate tum off clln only bI: predicted II the tllpenHl of glowing' down the tOOlllpulltion. Sufficient alccur;u:y U nomlllliy
llI.::hleved by detecling Ihe «urn orf liner II occur. ~nd Iheillnlproviilg Ii by linear Interpolation. The !lIlli/of( ioshn! thu. obtained b then u~d to interpolate (01 all tht olher variabl;:;s.
il):S Comptlillf Utldy p.illrlll'lMl1ln
The primary VI" Mel receiving end ".!it busban were both considered to be I.:onnecled 10 l,Yiilems. The ph~se·.'lmgle difference 8 belween the l!endinR receivinll"nd Vl\! bluban "'115 initiilly 32".
The main transformer consisted of three singlt·phil!e IInib coone.:· ud deltIlJdelta/.12r. willi the following cbarllclerisiits:
Ralin~: 6-6 MV '" (per phMe) 33/6<6/2-4 kV (phll!e 10 ph~).
Self and mutual winding reaclanceS (calculated in JI.. per ph~. from Ihe manufacturer's open-circult lind lilorl-circuil tests):
12900 :n60
24
:!i5l :lSi
The Ihree independent hoo.lillg Iransfonneq (with their primary windings in l!eries with lhe respective phues of the trllnsmisslon line) had the following characteristics:
Rating: H MVA.O·76/1·3BkV.
Winding reaclmcel:
Each phase of Ihe transmission line was represented by Ii HriU impedance orO·ISl + j2-ofl..
APPENDIX 14
TRANSIENT
Base MVA
Generator transient reactance
inertia constant
Large power system reactance
Transmission line res
reactance
Transformers:
PARAMETERS
450 MVA
0.2 p.u.
4.0 kWs/kVA
0.004 p.u.
0.05 p.u.
0.5 p.u.
244
The main
units connected
characteristics.
con of three single-phase
I with following
Ratings - 150 MVA, 15/110/11 kV (phase-to-phase)
From the equivalent c
0.02 p.u. 0.08 p.u.
15 kV '-----0 11 0 kV
11 kV
Assuming 1% , 1% losses and the equal divis
of 1 the windings the
{in ohms phase} were
24
Tertiary
Primary 0.015 + j150 j1100 j190
Secondary j1100 0.807 + j8067 j1396
Tertiary j190 j1396
The three transformers (with their
primary windings in phases of the
transmission line), had the
Rating - 30 MVA, 15/11 kV
Winding impedances (ohms
Pr
) :
Primary 0.003 + j30 j22
Secondary j22 0.002 + j16
For the transient stability ,
the quadrature booster/bucker unit was as a
es impedance of 0.01 + jO.1 p.u. The quadrature and
in-phase tap settings were varied by inj
each s of the transformer. The transformer
1 are shown in Fig. 9.2.
state operating condition the
to
(with
voltage Vs )
1.0 p.u.
20.30
450 MW
current at
11.67 MVAr lagging
of