Contents
1
1.1
1.2
Symbols and indices
10
General
Kinds of short circuit
Definitions according to VDE 0102
13
13
14
2
2.1
2.2
2.2.1
2.2.1.1
2.2.1.2
2.2.2
2.3
Short-circuit currents, magnitude, and time variation
Introduction
Short circuit with constant voltage (remote from generator)
Single-phase system
Without load
Withload
Three-phase system
Short circuit in operation with synchronous generators (short
circuit close to generator)
;.
2.3.1
Terminal short circuit in no-load operation
2.3.1.1 The effect of disconnection times
2.3.2
Reactances during the short-circuit period
2.3.3
Terminal short circuit in on-load operation
2.3.4 " Synchronous generator and network impedance
2.3.5
Time constants
2.4
Short circuit in an interconnected system
2.5
Short-circuit characteristics of motor loads
2.5.1
Synchronous motors and synchronous capacitors
2.5.2
Asynchronous motors
2.5.3
Example
2.6
Summary
3
3.1
3.1.1
3.1.2
3.2
3.2.1
3.2.2
3.2.3
Determination of short-circuit currents
Symmetrical components
The method
Positive-, negative- and zero-sequence impedance
Calculation of initial a.c. short-circuit current with and without
reference to system loading
Method taking account of system loading
Method neglecting system loading
Summary
http://d-nb.info/860122646
17
17
18
18
18
23
25
29
29
33
35
37
40
40
42
44
44
44
44
46
48
48
48
51
53
54
55
56
4
4.1
4.2
4.3
4.4
4.5
4.6
4.6.1
4.6.2
4.6.3
Particular short-circuit conditions
57
Three-pole short circuit
58
Two-pole short circuit without earth fault
60
Two-pole short circuit with earth fault
63
Single-pole short circuit to earth
71
Double earth fault
77
Comparison of short-circuit conditions with various neutral
connections
83
Systems with isolated neutral
83
Systems with earth leakage compensation
85
Systems with low-impedance neutral earthing
86
5
5.1
5.1.1
5.1.2
5.1.3
5.1.4
5.1.4.1
5.1.4.2
5.1.5 ,
5.1.6
5.1.7
5.1.8
5.1.9
5.2
5.2.1
5.2.2
5.2.2.1
5.2.2.2
5.2.2.3
Calculation of plant and system impedances
Plant impedances
System infeed
Synchronous machines
Asynchronous motors
Transformers
Positive-sequence impedance
Zero-sequence impedance
Short circuit current-limiting inductors
Series capacitors
Busbars in switching installations
Cables
Overhead lines
System short-circuit impedances
Meshed systems with multiple infeeds
Systems with different voltage levels
Calculation with absolute impedance values
Calculation with dimensionless impedance values
Consideration of transformer voltage ratios
6
6.2
6.3
Calculation of short-circuit currents according to the recommendations of VDE 0102 Part 1/11.71 and Part 2/11.75
Calculation of initial a.c. short-circuit currents using the equivalent
voltage source
Calculation of short circuit currents / s , /„, and Ik
General factors in calculation
7
7.1
7.2
7.3
Examples of the calculation of short-circuit currents
Example 1
Example 2
Example 3
6.1
88
88
88
89
90
91
91
93
98
98
100
100
100
103
103
106
106
107
107
109
109
112
113
115
115
118
122
8
8.2
8.2.1
8.2.2
8.2.3
8.2.4
8.2.5
Factors according to VDE 0102 and characteristic values for 50 Hz
three-phase equipment
Factors from VDE 0102 Parts 1 and 2 for the determination of
J s , J a , and Jk
Characteristic values for three-phase 50 Hz equipment
Characteristic values for three-phase synchronous generators
Characteristic values for oil-immersed transformers
Characteristic values for busbars in switching installations
Characteristic values for cables
Characteristic values for overhead lines
131
133
134
136
139
139
149
9
9.1
9.2
9.3
9.4
9.5
Calculation of overhead line impedances
Positive-sequence impedance Z\
Effective capacitance C'b
Earth capacitance C'E
Zero-sequence impedance Z'o
Symbols
154
154
154
155
155
157
10
Calculation of short-circuit currents by means of digital computers
159
Appendix: Symbols, terms and definitions
164
Index
165
8.1
131