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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