Preface xi
Acknowledgments xiii
1 Definitions:Methods of Calculations 1
1.1 Time Behavior of the Short-Circuit Current 2
1.2 Short-Circuit Path in the Positive-Sequence System 3
1.3 Classification of Short-Circuit Types 5
1.4 Methods of Short-Circuit Calculation 7
1.4.1 Superposition Method 7
1.4.2 Equivalent Voltage Source 10
1.4.3 Transient Calculation 11
1.4.4 Calculating with Reference Variables 12
1.4.4.1 The Per-Unit Analysis 12
1.4.4.2 The %/MVA Method 14
1.4.5 Examples 14
1.4.5.1 Characteristics of the Short-Circuit Current 14
1.4.5.2 Calculation of Switching Processes 14
1.4.5.3 Calculation with pu System 14
1.4.5.4 Calculation with pu Magnitudes 16
1.4.5.5 Calculation with pu System for an Industrial System 17
1.4.5.6 Calculation with MVA System 19
2 Fault Current Analysis 23
3 The Significance of IEC 60909-0 29
4 Supply Networks 33
4.1 Calculation Variables for Supply Networks 34
4.2 Lines Supplied from a Single Source 35
4.3 Radial Networks 35
4.4 Ring Networks 35
4.5 Meshed Networks 37
5 Network Types for the Calculation of Short-Circuit Currents 39
5.1 Low-Voltage Network Types 39
5.2 Medium-Voltage Network Types 39
5.3 High-Voltage Network Types 44
6 Systems up to 1 kV 47
6.1 TN Systems 48
6.1.1 Description of the System is Carried Out by Two Letters 48
6.2 Calculation of Fault Currents 49
6.2.1 System Power Supplied from Generators: 50
6.3 TT systems 52
6.3.1 Description of the System 52
6.4 IT Systems 53
6.4.1 Description of the System 53
6.5 Transformation of the Network Types Described to Equivalent Circuit Diagrams 54
6.6 Examples 56
6.6.1 Example 1: Automatic Disconnection for a TN System 56
6.6.1.1 Calculation for a Receptacle 56
6.6.1.2 For the Heater 56
6.6.2 Example 2: Automatic Disconnection for a TT System 57
7 Neutral Point Treatment in Three-Phase Networks 59
7.1 Networks with Isolated Free Neutral Point 63
7.2 Networks with Grounding Compensation 64
7.3 Networks with Low-Impedance Neutral Point Treatment 66
7.4 Examples 69
7.4.1 Neutral Grounding 69
8 Impedances of Three-Phase Operational Equipment 71
8.1 Network Feed-Ins, Primary Service Feeder 71
8.2 Synchronous Machines 73
8.2.1 a.c. Component 78
8.2.2 d.c. Component 78
8.2.3 Peak Value 78
8.3 Transformers 80
8.3.1 Short-Circuit Current on the Secondary Side 81
8.3.2 Voltage-Regulating Transformers 83
8.4 Cables and Overhead Lines 85
8.5 Short-Circuit Current-Limiting Choke Coils 96
8.6 Asynchronous Machines 97
8.7 Consideration of Capacitors and Nonrotating Loads 98
8.8 Static Converters 98
8.9 Wind Turbines 99
8.9.1 Wind Power Plant with AG 100
8.9.2 Wind Power Plant with a Doubly Fed Asynchronous Generator 101
8.9.3 Wind Power with Full Converter 101
8.10 Short-Circuit Calculation on Ship and Offshore Installations 102
8.11 Examples 104
8.11.1 Example 1: Calculate the Impedance 104
8.11.2 Example 2: Calculation of a Transformer 104
8.11.3 Example 3: Calculation of a Cable 105
8.11.4 Example 4: Calculation of a Generator 105
8.11.5 Example 5: Calculation of a Motor 106
8.11.6 Example 6: Calculation of an LV motor 106
8.11.7 Example 7: Design and Calculation of aWind Farm 106
8.11.7.1 Description of theWind Farm 106
8.11.7.2 Calculations of Impedances 111
8.11.7.3 Backup Protection and Protection Equipment 116
8.11.7.4 Thermal Stress of Cables 118
8.11.7.5 Neutral Point Connection 119
8.11.7.6 Neutral Point Transformer (NPT) 119
8.11.7.7 Network with Current-Limiting Resistor 120
8.11.7.8 Compensated Network 124
8.11.7.9 Insulated Network 125
8.11.7.10 Grounding System 125
9 Impedance Corrections 127
9.1 Correction Factor KG for Generators 128
9.2 Correction Factor KKW for Power Plant Block 129
9.3 Correction Factor KT for Transformers with Two and Three Windings 130
10 Power SystemAnalysis 133
10.1 The Method of Symmetrical Components 136
10.2 Fundamentals of Symmetrical Components 137
10.2.1 Derivation of the Transformation Equations 139
10.3 General Description of the Calculation Method 140
10.4 Impedances of Symmetrical Components 142
11 Calculation of Short-Circuit Currents 147
11.1 Three-Phase Short Circuits 147
11.2 Two-Phase Short Circuits with Contact to Ground 148
11.3 Two-Phase Short CircuitWithout Contact to Ground 149
11.4 Single-Phase Short Circuits to Ground 150
11.5 Peak Short-Circuit Current, ip 153
11.6 Symmetrical Breaking Current, Ia 155
11.7 Steady-State Short-Circuit Current, Ik 157
12 Motors in Electrical Networks 161
12.1 Short Circuits at the Terminals of Asynchronous Motors 161
12.2 Motor Groups Supplied from Transformers with TwoWindings 163
12.3 Motor Groups Supplied from Transformers with Different Nominal Voltages 163
13 Mechanical and Thermal Short-Circuit Strength 167
13.1 Mechanical Short-Circuit Current Strength 167
13.2 Thermal Short-Circuit Current Strength 173
13.3 Limitation of Short-Circuit Currents 176
13.4 Examples for Thermal Stress 176
13.4.1 Feeder of a Transformer 176
13.4.2 Mechanical Short-Circuit Strength 178
14 Calculations for Short-Circuit Strength 185
14.1 Short-Circuit Strength for Medium-Voltage Switchgear 185
14.2 Short-Circuit Strength for Low-Voltage Switchgear 186
15 Equipment for Overcurrent Protection 189
16 Short-Circuit Currents in DC Systems 199
16.1 Resistances of Line Sections 201
16.2 Current Converters 202
16.3 Batteries 203
16.4 Capacitors 204
16.5 Direct Current Motors 205
17 Power Flow Analysis 207
17.1 Systems of Linear Equations 208
17.2 Determinants 209
17.3 Network Matrices 212
17.3.1 Admittance Matrix 212
17.3.2 Impedance Matrix 213
17.3.3 Hybrid Matrix 213
17.3.4 Calculation of Node Voltages and Line Currents at Predetermined Load Currents 214
17.3.5 Calculation of Node Voltages at Predetermined Node Power 215
17.3.6 Calculation of Power Flow 215
17.3.6.1 Type of Nodes 216
17.3.6.2 Type of Loads and Complex Power 216
17.3.7 Linear Load Flow Equations 218
17.3.8 Load Flow Calculation by Newton-Raphson 219
17.3.9 Current Iteration 223
17.3.9.1 Jacobian Method 223
17.3.10 Gauss-Seidel Method 224
17.3.11 Newton-Raphson Method 224
17.3.12 Power Flow Analysis in Low-Voltage Power Systems 226
17.3.13 Equivalent Circuits for Power Flow Calculations 227
17.3.14 Examples 228
17.3.14.1 Calculation of Reactive Power 228
17.3.14.2 Application of Newton Method 228
17.3.14.3 Linear Equations 229
17.3.14.4 Application of Cramer's Rule 229
17.3.14.5 Power Flow Calculation with NEPLAN 230
18 Examples: Calculation of Short-Circuit Currents 233
18.1 Example 1: Radial Network 233
18.2 Example 2: Proof of Protective Measures 235
18.3 Example 3: Connection Box to Service Panel 237
18.4 Example 4: Transformers in Parallel 238
18.5 Example 5: Connection of a Motor 240
18.6 Example 6: Calculation for a Load Circuit 241
18.7 Example 7: Calculation for an Industrial System 243
18.8 Example 8: Calculation ofThree-Pole Short-Circuit Current and Peak Short-Circuit Current 244
18.9 Example 9: Meshed Network 246
18.10 Example 10: Supply to a Factory 249
18.11 Example 11: Calculation with Impedance Corrections 250
18.12 Example 12: Connection of a TransformerThrough an External Network and a Generator 253
18.13 Example 13: Motors in Parallel and their Contributions to the Short-Circuit Current 255
18.14 Example 14: Proof of the Stability of Low-Voltage Systems 257
18.15 Example 15: Proof of the Stability of Medium-Voltage and High-Voltage Systems 259
18.16 Example 16: Calculation for Short-Circuit Currents with Impedance Corrections 269
Bibliography 273
Standards 277
Explanations of Symbols 281
Symbols and Indices 283
Indices 286
Secondary Symbols, Upper Right, Left 287
American Cable Assembly (AWG) 287
Index 289
