Iec and iec figure vector diagram and time course

Power and Energy Series 51

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List of figures	xiii

List of tables xxiii

1.3 Maximal and minimal short-circuit currents 3

1.4 Norms and standards 4

2.3.1 Transformation matrix 14

2.3.2 Interpretation of the system of symmetrical

2.4 Equivalent circuit diagram for short-circuits 24

2.5 Series and parallel connection 27

2.8 Examples 34

2.8.1 Vector diagram and system of symmetrical

viii				37
	2.8.2

3	2.8.3		Conversion of impedances (�; %/MVA; p.u.)	40
	2.8.4		Impedances in %/MVA-system based on	40
	2.8.4		Impedances in %/MVA-system based on	41

	2.8.5		Representation of a line in the RYB-system and in the
	2.8.5		Representation of a line in the RYB-system and in the	42
				42
				45
4	3.1			45
	3.2	Equipment in a.c. systems		45
	3.2.1		General	45
	3.2.2			46
	3.3			50
	3.3.1			50
	3.3.2			58
	3.4	Examples for calculation		63
	3.4.1		a.c. equipment	63
	3.4.2			64
				64
5				67
	4.1			67
	4.2	Methods of calculation		68
	4.3	Calculation of parameters of short-circuit currents		70
	4.3.1			70
	4.3.2			70
	4.3.2			72
				72
	4.4			84
	4.5	Minimal short-circuit currents		85
	4.6	Examples		86
	4.6.1			86
	4.6.2			87
	4.6.3			88
	4.6.4			89
	4.6.5		Influence of impedance correction factors on	89
	4.6.5		Influence of impedance correction factors on	91
	short-circuit currents
	4.6.6
	4.6.6			94


				97
	5.1	General		97
	5.2	Power system with low-impedance earthing		98
	5.3			102
	5.4			105

6	Contents			ix
	5.5
	5.5.1		General	108
	5.5.2			112
	5.5.3			115
	5.6			116
				116
	5.7	Examples		119
	5.7.1		Increase of displacement voltage for systems with	119
				119
	5.7.2

	5.7.3		Design of an earthing resistor connected to an artificial	124
	neutral			124
	5.7.4
	5.7.5
	residual current
	5.7.6		Voltages at neutral of a unit transformer

7	6.1			131
	6.2	Types of faults
	6.3
	6.4			132
	6.4.1		Impedances
	6.4.2
	6.4.3			134
	6.5	Minimal short-circuit currents
	6.6
				139
	7.1	General
	7.2
	7.2.1			139
	7.2.2		current I′′k	139
	7.2.2		current I′′k
	7.2.3
	7.2.4		Symmetrical short-circuit breaking current Ib and	143
				143
	7.3
	7.3.1			143
	7.3.2		Short-circuit inside a switchyard
	7.3.3
	7.4			146
	7.4.1		Double earth-fault in a 20-kV-system
	7.4.2

x				151
8	Factors for the calculation of short-circuit currents			151
9	8.1			151
				152
		Impedance correction factors		154
	8.4			156
				158
		Factor λ for steady-state short-circuit current		160
	8.7			160
	8.7			162
				162
				165
10		General		165
	9.2			169
				170
		Short-circuit currents from rectifiers		172
	9.5			172
	9.5			174
				174
				178
	9.7	Example		182
	9.7.1			182
	9.7.1			184

	9.7.2
	9.7.2			185

	9.7.3		Calculation of the correction factors and corrected
	9.7.3		Calculation of the correction factors and corrected	190
	parameters			190
	9.7.4			191
	9.7.5			193
				195
	10.1			195
	10.2	a.c. systems		195
	10.2.1		Thermal effects and thermal short-circuit strength	195
	10.2.2			201
				201
	10.3			209
	10.3.1			209
	10.3.2		Mechanical short-circuit strength of rigid	212
	conductors			212
	10.3.3			215
	10.4			216
	10.4.1			216
	10.4.2			217
	10.5	Calculation examples (d.c. system)		218
	10.5.1		Thermal effect	218
	10.5.2			220

11				xi
11
12	11.1	General		225
	11.2
	11.2.1
	11.2.2		Measures in installations and switchgear
	11.2.2		Measures in installations and switchgear	232
	arrangement			232
	11.2.3		Measures concerning equipment
	11.3
	11.3.1			240
	11.3.2		Radial system
	11.3.3
	11.3.4			241
	Special problems related to short-circuit currents
13	12.1
	12.1.1			245
	12.1.2		Calculation of impedances for inductive	245
	12.1.2		Calculation of impedances for inductive	247
	interference			247
	12.1.3
	12.1.4		Characteristic impedance of the pipeline
	12.1.5			254
	12.2	Considerations on earthing
	12.2.1
	12.2.2			257
	12.2.3		Soil conditions
	12.2.4
	12.2.5			261
	12.3	Examples
	12.3.1		Interference of pipeline from 400-kV-line
	12.3.2
	Data of equipment			267
	13.1
	13.1.1
	13.1.2		Transformers	267
	13.1.3
	13.1.4
	13.1.5		Cables	276
	13.1.6
	13.1.7
	13.2	d.c. equipment		281
	13.2.1
	13.2.2
	13.2.3		Batteries	283

	Importance of short-circuit currents and definition of tasks as	2
		2
Figure 2.1	Vector diagram and time course of a.c. voltage	12
		12

	(positive-sequence component)	14
	Vector diagram of current, voltage and power of a three-phase	14

a.c. system represented by the positive-sequence component. (a) Consumer vector system and (b) generator vector

		15
		15
	a.c. line	16
	Vector diagram of voltages in RYB-system and in the	16

		18
		18

positive-sequence component, zero- and negative-sequence

Figure 2.7		19
Figure 2.7		19

	components are NIL	19
	Measurement of impedance in the system of symmetrical	19

		21
		21

transformer (YNd). Diagram indicates winding arrangement of the transformer: (a) measuring at star-connected winding

Figure 2.10		22
		22
		22

Figure 2.11 Measurement of zero-sequence impedance of a three-winding transformer (YNyn + d). Diagram indicates winding arrangement of the transformer 23 Figure 2.12 General scheme for the calculation of short-circuit currents in three-phase a.c. systems using the system of symmetrical

Figure 2.13	components	25
Figure 2.13		25
Figure 2.14		25
Figure 2.14		25
Figure 2.15		26
Figure 2.15	Equations for impedance analysis in power systems	30
Figure 2.16	Equivalent circuit diagram of a power system with different	34
Figure 2.16
Figure 2.17

Figure 2.18		38
Figure 2.18	Simplified equivalent circuit diagram in RYB-components	41
Figure 2.19	Equivalent circuit diagram in the system of symmetrical	42
Figure 2.19		42
Figure 2.20	Equivalent circuit diagram of an overhead line of infinitesimal	43
Figure 2.20
Figure 2.21	Equivalent circuit diagram of an overhead line of infinitesimal

Figure 4.1		43
Figure 4.1	Types of short-circuits and short-circuit currents.	43

(a) Three-phase short-circuit, (b) double-phase short-circuit without earth/ground connection, (c) double-phase
short-circuit with earth/ground connection and

Figure 4.2		68
Figure 4.2		68

Figure 4.3	(b) far-from-generator short-circuit (according to Figure 1 of	69
	current, ip – peak short-circuit current, Ik – steady-state
	short-circuit current and A – initial value of the aperiodic

Figure 4.4	List of figures	xv
Figure 4.4		xv

types of short-circuit and different impedance ratios Z1/Z0 and Z2/Z1. Phase angle of Z0, Z1 and Z2 assumed to be identical. Parameter r: ratio of asymmetrical short-circuit

Figure 4.5	current to three-phase short-circuit current	74
Figure 4.5		74
Figure 4.6		75
Figure 4.6		75
Figure 4.7		77
Figure 4.7	Factor κ for the calculation of peak short-circuit current	78
Figure 4.8	Equivalent circuit diagram for three-phase short-circuit	78
Figure 4.8		78
Figure 4.9		79
Figure 4.9		79
Figure 4.10	Factor μ for calculation of symmetrical short-circuit breaking	81
Figure 4.10		81
Figure 4.11	Factors λmax and λmin for turbine generators (Figure 17 of DIN	83
Figure 4.11	EN 60909.0 (VDE 0102)). (a) Series one and (b) series two	83
Figure 4.12	Factors λmax and λmin for salient-pole generators (Figure 18 of	83
	DIN EN 60909.0 (VDE 0102) 1988). (a) Series one and (b)

Figure 4.13		86
Figure 4.13		86
Figure 4.14		87
Figure 4.14	short-circuit location	87
Figure 4.15	Equivalent circuit diagram of a 110-kV-system with	88
Figure 4.15		88
Figure 4.16		89
Figure 4.17		90
Figure 4.18		91
Figure 4.18		91
Figure 4.19	High-voltage system configuration for the auxiliary supply of	95
Figure 4.19	a power station
Figure 5.1	Equivalent circuit diagram of a single-phase short-circuit

Figure 5.2		100
Figure 5.2		100
Figure 5.3		101
Figure 5.3		103
Figure 5.4	Earth-fault factor δ depending on X0/X1 for different ratios	104
Figure 5.4	R0/X0 and R1/X1 = 0.01 Earth-fault factor δ and ratio I′′k1/I ′′k3depending on X0/X1	104
Figure 5.5		104

xvi List of figures

Figure 5.7		105
Figure 5.7		105
Figure 5.8		106
Figure 5.8	Vector diagram of voltages, power system with isolated	106
Figure 5.9	neutral. (a) Prior to fault and (b) during earth-fault	107
Figure 5.9	Time course of phase-to-earth voltages, displacement voltage	107

Figure 5.10		108
Figure 5.10		108

Figure 5.11	diagram in the system of symmetrical components	109
Figure 5.11	Current limits according to VDE 0228 part 2:12.87 of	109
Figure 5.12		111
Figure 5.12		111

Figure 5.13		112
Figure 5.13	Polar plot of the displacement voltage in a power system with	112
Figure 5.14	resonance earthing	114
Figure 5.14	Voltages and residual current in the case of an earth-fault;	114
Figure 5.15		115
Figure 5.15		115
Figure 5.16		117
Figure 5.16		117

Figure 5.17	of the Petersen-coil	118
Figure 5.17	Transformation of voltage in the zero-sequence component of	118

transformers in the case of single-phase faults. (a) Equivalent circuit diagram in RYB-system and (b) equivalent circuit

Figure 5.18		119
Figure 5.18	Alternate earthing of transformer neutrals by Petersen-coils.	119

Figure 5.19		121
Figure 5.19	Fault current in the MV-system in the case of a short-circuit in	121
Figure 5.20		121
Figure 5.20	Resonance curve (displacement voltage) for different detuning	121
Figure 5.21	factors in a 20-kV-system for different conditions	122
Figure 5.21	Voltages in a 20-kV-system with resonance earthing for	122

Figure 5.22	List of figures
Figure 5.22	Equivalent circuit diagram of a 20-kV-system with resonance
Figure 5.23		125
Figure 5.23		125
Figure 5.24	short-circuit location	126
Figure 5.24	Equivalent diagram in the zero-sequence component for fault	126
Figure 6.1	location F	128
Figure 6.1		135
Figure 7.1		144
Figure 7.1		144
Figure 7.2	Equivalent circuit diagram with short-circuit at overhead-line	146
Figure 7.2		146
Figure 7.3	Equivalent circuit diagram of a 20-kV-system	147
Figure 7.4	Equivalent circuit diagram of a 110-kV-system with	148
Figure 7.4		148
Figure 8.1		152
Figure 8.1		152
Figure 8.2		153
Figure 8.2	correction factor using %/MVA- or p.u.-system
Figure 8.3	Generator directly connected to the power system.

Figure 8.4		154
Figure 8.4		155
Figure 8.5		155

short-circuit. (a) Circuit diagram, (b) simplified diagram of a single-fed three-phase short-circuit and (c) time course of

Figure 8.6	voltage with voltage angle ϕU	157
Figure 8.6		157
Figure 8.7		161
Figure 8.7		161

Figure 9.1	IEC 60909-1:1991.)	163
Figure 9.1	Equivalent circuit diagrams of equipment in d.c. auxiliary	163

Figure 9.2		166
Figure 9.2	Standard approximation function of the short-circuit current	166
Figure 9.3		167
Figure 9.3	Factor κC for the calculation of peak short-circuit current of	167
Figure 9.4		169
	Time-to-peak tpC for the calculation of short-circuit	169
	currents of capacitors (according to Figure 13 of	170
		170

Figure 9.5	Factor k1C for the calculation of rise-time constant (according	171
Figure 9.5		171
Figure 9.6		171
Figure 9.6	(according to Figure 15 of IEC 61660-1:1997)	171
Figure 9.7	Rise-time constant τ1B and time to peak tpB of short-circuit	172


Figure 9.8	Factor λD for the calculation of quasi steady-state short-circuit	173


Figure 9.9	Factor κD for the calculation of peak short-circuit currents of rectifiers. Factor: R∗= (RN/XN)(1 + 2RDBr/3RN) (according to Figure 8 of IEC 61660-1:1997)	173
Figure 9.10	Factor κM for the calculation of peak short-circuit current of	176


Figure 9.11		176
Figure 9.11		176
Figure 9.12	Factor k1M in the case of d.c. motors with independent	177
Figure 9.12	excitation and τMec ≥ 10 ∗ τF (according to Figure 18 of IEC 61660-1:1997)	177
Figure 9.13		177
Figure 9.13		177
Figure 9.14		178
Figure 9.14		178
Figure 9.15	Factor k4M in the case of d.c. motors with independent	178
Figure 9.15	excitation and τMec < 10 ∗ τF (according to Figure 21 of IEC 61660-1:1997)	178
Figure 9.16		180
Figure 9.17		180

Figure 9.18		181
Figure 9.18	Equivalent circuit diagram of the d.c. auxiliary installation	181
Figure 9.19	(220 V), e.g., of a power station	182
Figure 9.19		182
Figure 9.20		193
Figure 9.20		193

Figure 10.1	List of figures	xix
Figure 10.1	Factor n for the calculation of thermal short-time current	xix

(heat dissipation of a.c. component) (according to Figure 22 of

Figure 10.2		197
Figure 10.2		197

Figure 10.3		198
	Rated short-time current density of conductors. δ0 is the
	temperature at beginning of short-circuit and δ1 is the temperature at end of short-circuit. (a) ____: Copper;

Figure 10.4		199
Figure 10.4		199
Figure 10.5		200
Figure 10.5	Arrangement of parallel conductors	202
Figure 10.6	Correction factor k12 for the calculation of effective distance	203
Figure 10.6		203
Figure 10.7		205
Figure 10.7		205
Figure 10.8		205
Figure 10.8	(according to Figure 5 of IEC 60865-1:1993)	205
Figure 10.9	Factor VF for the calculation of bending stress (according to	207
Figure 10.9
Figure 10.10

Figure 10.11		208
Figure 10.11	Standard approximation function (a) and substitute rectangular	208

function (b) (according to Figure 4 of IEC 60660-2:1997). Not

Figure 10.12	to scale	210
Figure 10.12		210
Figure 10.13		214
Figure 10.13	Factor VF for the calculation of forces on supports (according	214
Figure 10.14		215
Figure 10.14		215
Figure 10.15	at 20◦C	216
Figure 10.15	Equivalent circuit diagram of a power system with	216
Figure 10.16		217
Figure 10.16		219
Figure 10.17		223
Figure 10.17		223
Figure 11.1	Selection of suitable voltage level for the connection of power	226
Figure 11.1	stations
Figure 11.2	Schematic diagram of a 400/132-kV-system for urban load;

Figure 11.3		228
Figure 11.3		229