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1 Transient phenomena
1
Transient Phenomena in Electrical Power Systems
1.1
Introduction
Power system networks are subjected to various forms of transient phenomena ranging
from the relatively slow electromechanical oscillations associated with synchronous
machines and drives to the comparatively fast variations in voltage and current brought
about by sudden changes such as due to lightning strokes. Lightning is a common cause
of faults and subsequent current outages, but faults can and do occur for many other
reasons. Malfunctioning of the system can occur in numerous ways and has a variety of
consequences, e.g. opening of one phase of a three-phase circuit can lead to a
rearrangement of circuit inductances and capacitances in such a manner that a resonant
circuit is produced and excited with large values of voltage and/or current as a
consequence. Transient overvoltages are produced by both opening and closing of a
circuit breaker and their computation and assessment is the particular concern of this
course.
Over the years, the voltages at which electrical power is transmitted over long distances
have been increasing continually and many systems are now in operation at 400 kV,
500 kV, 750 kV and even 1000 kV. The lightning performance of transmission lines
shows an improvement with increasing operating voltage level, because the magnitude
of lightning surges on lines are not greatly affected by the line design. In contrast,
system-generated overvoltages are directly related to the system voltage and their
magnitudes increase as the system voltage increases. As a result, at operating voltages of
400 kV and above, system-generated overvoltages play an increasingly large part in
determining the insulation level of the system. Although the system insulation level must
be sufficiently high in order not to hazard the reliability of the system, at the same time
there are strong economic incentives (minimizing costs) for keeping it as low as possible.
This chapter intends to give a general introduction into transient phenomena, origin and
consequences of transients in simple single- and three-phase circuits. Compared to
steady-state behaviour of power systems at one frequency, where the system can be
described by complex phasor equations easily, mathematical formulation of transient
response of individual equipment and/or the system is rather complex, because in the
transient state, the system response is involved in a wide frequency range. Therefore, it
is important to understand basics of electrical transients and their physical interpretation.
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1 Transient phenomena
1.2
Examples of Transients in Single-Phase Circuits
1.2.1 Introduction
The transient response of any electric circuit can be explained in a simplified manner by
the interaction of following basic electrical parameters:
• Resistance, R
• Inductance, L
• Capacitance, C
All components, whether in a power utility system or industrial circuit possess each of
these parameters to a greater or lesser degree. The resistance, inductance and capacitance
of a circuit are distributed quantities; that is, each small part of the circuit possesses its
share. But it is frequently found that they can be treated as "lumped" parameters,
concentrated in particular branches, without seriously impairing the accuracy of
computations. There are other circumstances, where this technique is not suitable, as in
dealing with long transmission lines, where a different approach will be used.
The parameters L and C are characterized by their ability to store electrical energy, L in
the magnetic field and C in the electric field of the circuit. These stored energies are
functions of the instantaneous current i and voltage v and are, respectively,
(1.1)
In contrast, the parameter R is a dissipater of energy, the rate of dissipation being R@i 2 at
any instant.
Under steady-state conditions the energy stored in the various inductances and
capacitances of a direct current (DC) circuit is constant, whereas in an alternating
current (AC) circuit energy is being transferred cyclically between the L's and C's of the
circuit as the current and voltage rise and fall sinusoidally at the frequency of the supply.
When a sudden change occurs in a circuit, there is generally a redistribution of energy to
meet the new conditions, and in a way, it is this what we are studying when we inquire
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into the nature of transients. The transient behaviour of basic elements L and C are
described by the following equations:
! Inductance
(1.2)
To change the magnetic energy requires a change of current. But change of current in an
inductor causes an induced voltage L di/dt. An instantaneous change of current would
therefore require an infinite voltage to bring it about. Since this is unrealizable in
practice, currents in inductive circuit do not change abruptly and consequently there can
be no abrupt change in the magnetic energy stored. In other words, the magnetic flux
linkage of a circuit cannot change suddenly.
! Capacitance
(1.3)
To change the electric energy requires a change in voltage. For an instantaneous change
of voltage an infinite current in a capacitor must flow. This is unrealizable, too.
Consequently, the voltage across a capacitor cannot change abruptly nor can the energy
stored in its associated electric field.
The redistribution of energy following a change in the circuit state takes a finite time,
and the process during this interval, as at any other time, is governed by the principle of
energy conservation, that is, the rate of supply of energy is equal to the rate of storage of
energy plus the rate of energy dissipation.
A transient is initiated whenever there is a sudden change of circuit conditions; this is
most frequently occurs when a switching operation takes place. The following examples
studied have been concerned with switching transients. A prime concern is the emphasis
on the physical aspects of what occurs in the circuit. The circuits given have been
generated using graphical preprocessor ATPDraw for ATP-EMTP and the simulations
have been performed using electromagnetic transients program ATP-EMTP.
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1.2.2 Energization of an RL circuit
The single-phase circuit involved in this example is built using ATPDraw and shown in
Fig. 1.1. The load is represented by a series combination of R und L. The sinusoidal
voltage source is defined by the following equation
(1.4)
Fig. 1.1 Energization of a 500-kV shunt reactor
The source is assumed to have negligible internal impedance compared with the load.
Consider a 500-kV system (50 Hz) solidly grounded, supplying a single-phase shunt
reactor with power, S = 10 MVA. X/R ratio of the reactor is 50. The circuit parameters
are obtained as follows:
;
;
;
The peak value of steady-state current can be calculated as Im = 46.66 A.
The current waveforms are shown in Fig. 1.2 for two cases:
(a) switch closes at t = 4.936 ms corresponding to phase angle 2 = 88.85/;
(b) switch closes at t = 9.936 ms corresponding to phase angle 2 = 178.85/.
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50 . 0
50 0
[A ]
[k V ]
37 . 5
37 5
25 . 0
25 0
12 . 5
12 5
0. 0
0
-1 2. 5
-1 25
-2 5. 0
-2 50
-3 7. 5
-3 75
-5 0. 0
0. 00
-5 00
0. 02
0. 04
(f ile E N E R G R L 1. pl4 ; x -v a r t ) c : S R C
-N 1
0. 06
0. 08
[s ]
0. 10
v :S R C
Fig. 1.2 (a) Switch closes at t = 4.936 ms (Q: source voltage; ": current)
20
50 0
[k V ]
[A ]
37 5
0
25 0
-2 0
12 5
-4 0
0
-1 25
-6 0
-2 50
-8 0
-3 75
-1 00
0. 00
-5 00
0. 02
(f ile e nergrl2. p l4; x -v ar t ) c : S R C
0. 04
-N 1
0. 06
0. 08
[s ]
0. 10
v :S R C
Fig. 1.2 (b) Switch closes at t = 9.936 ms (Q: source voltage; ": current)
In both cases the current attains a steady-state peak value of Im and it lags in phase the
voltage by the angle n = 88.85/ after decaying of transients. The solution for current i(t)
can be obtained by the Laplace transform method [1]
(1.5)
where " = R/L : (time constant)–1
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1 Transient phenomena
In case (a) the switch closes at the instant when 2 = n, the transient term becomes zero
and the current wave is symmetrical. On the other hand, if the switch closes when
2 = ± 90/ + n (case b), the transient term attains its maximum amplitude and the first
peak amplitude of the current wave approaches twice of Im (see Fig 1.2b). The rate of
decay of the transient component is determined by the time constant 1/" = 0.159 s of the
circuit.
1.2.3 Double-Frequency Transients
The simplest form of the double-frequency transient is that initiated by opening the
circuit breaker in the simplified 10-kV circuit shown in Fig. 1.3. In this single-phase
circuit, R1 = 33 mS and L1 = 2.1 mH stand for the short-circuit impedance of the 10-kV
source network. Vs is the r.m.s. value of the source voltage. C1 = 2 :F is the equivalent
capacitance of the cable connecting an inductive load to the source. L2 = 30 mH and
C2 = 40 nF represent the inductive load (motor) and its equivalent winding capacitance.
The winding losses of the motor are represented by R2 = 0.47 S.
Fig. 1.3 Single-phase disconnection of an inductive load (motor)
In general, R1 n TL1 and R2 n TL2. When the switch opens the two halves of the circuit
behave independently. Before switch opening, the 50 Hz voltage will divide in
proportion to the inductances, that is, to a close approximation the voltage of the
capacitors will be
, because L2 o L1 and
(1.6)
When the current passes zero, the switch will open, and the voltage at switch will be at
its peak, because the circuit is dominated by inductances. Following current interruption
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C2 will discharge through L2 with a resonance frequency given by
(1.7)
The influence of R2 is neglected.
Meanwhile C1 is now free to take up the source potential, will oscillate about the peak
value,
, until the losses of the system damp out the disturbance.
10 . 0
[k V ]
7. 5
5. 0
2. 5
0. 0
-2 . 5
-5 . 0
-7 . 5
-1 0. 0
4
5
(f ile S w_O pen 1. pl4; x -v a r t ) v : S W
6
7
8
9
[m s ]
10
v :MO T
Fig. 1.4 Source side (") and load side (Q) voltage transients
20
[k V ]
15
10
5
0
-5
4
5
(f ile S w_O p en1 . p l4; x -v a r t ) v : S W
6
7
8
9
[m s ]
10
-M O T
Fig. 1.5 Transient recovery voltage across circuit breaker contacts
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1 Transient phenomena
The frequency of this oscillation is approximately
(1.8)
Source side and load side transients are depicted in Fig. 1.4. The recovery voltage across
the circuit breaker contacts will be the difference between these two, as shown in Fig.
1.5.
1.2.4 Ferroresonance
In the phenomenon of series resonance, a very high voltage can appear across the
elements of a series LC circuit, when it is excited at or near its natural frequency. From
Fig. 1.6a it is obvious that the voltages VL and VC add to give the applied voltage V. But
because the voltage across the inductor leads the current in phase by 90/, and the
capacitor voltage lags the current by the same amount, the phasor diagram results shown
in Fig. 1.6b. It is seen that both VL and VC can far exceed Vs.
Such resonant conditions are to be avoided in power circuits, but they can occur
inadvertently. The phenomenon is referred to as ferroresonance, since the inductance
involved is usually iron cored and consequently, a series resonance between a nonlinear
inductance and a linear capacitance may occur.
Fig. 1.6 Simple series resonance
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To explain ferroresonance, distortions in the current and in the voltage across the L and
C will be ignored, only the fundamental components will be concerned with. Resistance
of the circuit will be neglected for simplicity. Fig. 1.7 shows a 245-kV ferroresonant
circuit consisting of voltage source, nonlinear inductance, L(I) and capacitance, C. The
nonlinear inductance represents the magnetizing inductance of an 245-kV inductive
voltage transformer (VT) [4]. C = 150 pF is the grading capacitor across the open circuit
breaker. The voltage transformer and the circuit breaker are part of a 220-kV outdoor
switchyard.
Fig. 1.7 245-kV simple ferroresonant circuit
The r.ms. voltage across the inductance can be written as
(1.9)
This voltage leads the current I by 90/. The voltage across the capacitor is given by
(1.10)
the minus sign indicating that it is antiphase with VL and lags the current by 90/. The
total voltage will be
(1.11)
The voltage and current relationships specified by Equations (1.9) and (1.11) are drawn
in Fig. 1.8. The inclined straight line depicts Eq. (1.11) for VL. Since both curves
represent VL in the diagram, the operating point must be where the two curves cross at P.
The capacitor voltage in this instance is PQ and the inductor voltage PB, which modestly
exceeds Vs, whereas the current is given by 0B.
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1 Transient phenomena
Fig. 1.8 Voltage and current relationships in a ferroresonant circuit
If the voltage were applied to the capacitor alone, it would take a much larger current IC,
but if applied to the inductor alone, the current would be the smaller current, IL. The
slope of the inclined line is given by
(1.12)
indicating that if either T or C is reduced the slope will increase and the intersection
point P will progress up the curve. Simultaneously, the voltage VC and VL will increase
sharply. This is demonstrated in Fig. 1.9 which shows the consequences of changing C,
all other parameters remaining constant. In general the capacitor line makes multiple
intersections with the curve VL = TL(I) when the complete characteristic is considered.
Three such intersections for one straight line, designated (a), (b) and (c), illustrate this
point. It is observed that values of VC and VL corresponding to point (a) are negative and
far exceed those corresponding to point (b). VC > VL is for point (a), whereas VC < VL for
point (b). This shows that the current I leads the voltage Vs for condition (a), but lags
behind V for condition (b). Both (a) and (b) are stable operating points, since any slight
variation of I from operating point, will cause voltage changes tending to restore the
current to its initial value. The phase of the voltage at the time of energization effects
which operating point, (a) or (b), will be reached. Point (c) is unstable operating point.
A momentary variation in I would cause changes in VC and VL such as to reinforce the
deviation and destabilize rather than stabilize.
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Fig. 1.9 Effect of increasing C in a ferroresonant circuit
Fig. 1.10 shows the flux-current characteristic of the inductance. The current and voltage
at "VT" across voltage transformer in the circuit (Fig. 1.7) is plotted in Fig. 1.11. The
combination of C = 150 pF and the non-linear characteristic of the inductor results in
typical ferroresonant oscillations, where the voltage across VT reaches very high values.
Increasing the series capacitance to 300 pF causes that the ferroresonance almost
disappears (Fig. 1.12). Also introducing a resistance connected parallel to the inductance
(500 MS) has a limiting effect on ferroresonance as shown in Fig. 1.13.
Fig. 1.10 Flux versus current for the magnetizing
inductance of VT
Power System Transients (Kizilcay)
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1 Transient phenomena
900
0. 090
[ k V]
[ A]
600
0. 052
300
0. 014
0
-0.024
-300
-0.062
-600
-900
0. 00
-0.100
0. 04
(f ile f erro0. pl4; x -v ar t ) v : VT
0. 08
0. 12
0. 16
0. 20
[s]
c : SO U R C E-VT
Fig. 1.11 Ferroresonance in the circuit of Fig. 1.7 (C = 150 pF)
25 0. 0
1. 0
[kV]
[m A]
18 7. 5
0. 6
12 5. 0
62 . 5
0. 2
0. 0
-0. 2
-62 . 5
-12 5. 0
-0. 6
-18 7. 5
-25 0. 0
0. 0 0
-1. 0
0. 0 4
0. 0 8
(f ile f erro1 . pl4; x -v a r t ) v : VT
c : S O U R C E -V T
0. 1 2
0. 1 6
[s]
0. 2 0
Fig. 1.12 Influence of increased C on ferroresonance (C = 300 pF)
250. 0
3
[ k V]
[m A]
187. 5
2
125. 0
1
62. 5
0. 0
0
-62.5
-1
-125.0
-2
-187.5
-250.0
0. 00
-3
0. 04
(f ile f erro0r. pl4; x -v a r t) v : VT
0. 08
0. 12
0. 16
[s]
0. 20
c : SO U R C E-VT
Fig. 1.13 Effect of parallel resistance on ferroresonance
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1 Transient phenomena
1.3
Transients in Three-phase Circuits
In Section 1.2 transients in single-phase circuits have been discussed. Polyphase circuits
are generally more complicated, though little more complex than the single-phase
circuits. Power systems consist of three-phase circuits in general. The complication
arises from the proliferation of three-phase components and branches introduced by the
other two phases and also because of the need to consider mutual coupling between
phases.
The three-phase systems can be solidly grounded at their neutrals, they can be
completely isolated from ground, or they can be grounded through a neutral impedance
of some kind. The transient voltages caused by switching operations or other
disturbances (faults) will often depend upon the neutral point treatment. In a system
where the neutral is solidly grounded, the three phases are virtually independent and
behave like three independent single-phase circuits if the ground impedance itself is
negligible and mutual inductive coupling between phases is omitted. Thus, if a circuit
breaker opens to clear a fault or shed a load, the c.b. poles interrupt the current in each
phase independently at current zero-crossing. The transient recovery voltage across the
breaker poles or load can be determined by the single-phase methods.
The situation is different when the neutral is ungrounded, or grounded through an
impedance, for example through a arc suppression coil, the inductance of which forms
a parallel resonant circuit with the line-to-ground capacitances. Suppose we are
switching off a Y-connected capacitor bank which has no connection at the neutral as
shown in Fig. 1.14. The 15 Mvar capacitor bank is connected to 10-kV busbar
(Vpeak = 8.165 kV). The neutral point of the bank is isolated. 1 nF connected to neutral
shown in Fig. 1.14 represents the small stray capacitance.
Fig. 1.14 Three-phase capacitor bank switching
Power System Transients (Kizilcay)
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1 Transient phenomena
Under steady-state conditions when the bank is energized, the symmetry of the circuit
will cause the neutral point N of the capacitor bank to be at ground potential. Suppose
that when the switch is opened, phase A interrupts first. The current IA will reach zero
when the voltage VA is at its peak. This can be seen in Fig. 1.15, where waveforms of
capacitor voltage and current of phase A are plotted. The current in phase A is
interrupted at t = 10 ms. The other poles B and C of the switch remain closed. Once the
capacitor of phase A is disconnected, there is nowhere for the charge on CA to go, it
remains trapped and this capacitor will retain Vpeak. Phases B and C form now a single
circuit in which the current I = IB = –IC flows. This unsymmetry causes the potential of
the neutral point, N, to rise with respect to ground as shown in Fig. 1.15. Hence phase A
follows the voltage of the neutral with a displacement of Vpeak.
10
1 50 0
[k V]
[A]
5
1 00 0
0
5 00
-5
0
-1 0
-5 0 0
-1 5
-1 0 00
-2 0
-1 5 00
0
10
20
(f ile C a p3 p h 1. p l4 ; x -v ar t ) v : C A P A
30
v :N
40
50
[m s ]
60
c : S R C A -C A P A
Fig. 1.15 Waveforms of phase A current ()) and voltage (") of the
disconnected capacitor CA, and of neutral point voltage (Q)
1500
[ A]
1000
500
0
-500
-1000
-1500
0
10
20
(f ile c ap3ph3 .pl4; x -v ar t ) c : SR C A -C APA
30
c : SR C B -C APB
40
50
[m s]
60
c : SR C C -C APC
Fig. 1.16 Three phase switch opening. Phase currents A: ", B: Q, C: )
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1 Transient phenomena
Since the neutral point is not effectively grounded, after opening of phase A, the
remaining poles B and C of the switch interrupt the current at the same time at zerocrossing as depicted in Fig. 1.16. The waveforms of the capacitor voltages to ground are
plotted in Fig. 1.17 when the capacitor bank is entirely disconnected. Due to charges
trapped on the capacitors after three-phase switching off, the voltages of capacitors and
of the neutral point remain constant.
15
[k V ]
10
5
0
-5
-1 0
-1 5
0
10
(f ile c ap3 ph 3. p l4; x -v ar t ) v : C A P A
20
v :C A PB
30
v :C A PC
40
50
[m s ]
60
v :N
Fig. 1.17 Phase to ground voltages of the capacitor bank and voltage of the
neutral after three-phase disconnection of the bank
If the neutral of three-phase capacitor bank and the source neutral are solidly grounded,
the analysis for a single-phase circuit would apply to the individual phases of the threephase circuit. For completeness, that case is shown in Fig. 1.18. The three-phase
interruption is plotted in Fig. 1.19, whereas voltages to ground of the three capacitors are
shown in Fig. 1.20.
Fig. 1.18 Switching off of a Y-connected capacitor
bank with solidly grounded neutral
Power System Transients (Kizilcay)
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1 Transient phenomena
15 00
[A ]
10 00
50 0
0
-5 00
-1 00 0
-1 50 0
0
10
20
(f ile c ap3 ph 5. p l4; x -v ar t ) c : S R C A -C A P A
30
c : S R C B -C A P B
40
c:SR C C
50
[m s ]
60
-C A P C
Fig. 1.19 Three-phase interruption of capacitor currents (A: ", B: Q, C: ))
90 00
[V ]
60 00
30 00
0
-3 00 0
-6 00 0
-9 00 0
0
10
(f ile c ap3 ph 5. p l4; x -v ar t ) v : C A P A
20
v :C A PB
30
40
50
[m s ]
60
v :C A PC
Fig. 1.20 Voltages of the disconnected capacitors (A: ", B: Q, C: ))
The current of each capacitor is interrupted at zero-crossing of the phase current
independently. Since the voltage reaches its peak when the current crosses zero value for
a capacitance, all three capacitor voltages remains at the peak value after disconnection
of phases because of trapped charges.
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1.3.1 Typical Power System Transients
Electrical transients in power systems are manifold. Over the years through the
experience in the operation of power systems, especially due to malfunction of the
system, different kinds of transient phenomena have been identified and investigated. In
the following important topics of transient phenomena are given:
! Lightning overvoltages
– direct lightning strokes
– indirect lightning strokes, back flashover
– induced lightning overvoltages
– protection by surge arresters
! Switching transients
– energization and re-energization of lines and cables
– energization of transformers
– capacitor switching
– reactor switching
– circuit breaker duty, current chopping, restriking phenomena
– load rejection
– ferroresonance
– motor startup
– power electronics applications
– harmonic distortion
! Faults
– symmetrical and unsymmetrical faults
– fault clearing
– short-line faults
– shaft torsional oscillations
– transient stability
! Very fast transients in GIS (gas-insulated switchgear)
– disconnector operations
– faults (fast breakdown of the gas gap)
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1 Transient phenomena
1.4
Stresses on Equipment caused by Transients
Electrical transients in power systems may cause stresses on equipment. These are
mainly due to overvoltage and/or overcurrent. In the following the origin and typical
characteristics of overvoltages and overcurrents will be briefly described.
1.4.1 Overvoltages
In general the overvoltages caused by the transients are important in a power system
because of their stresses exerted on the insulation or on protective devices like surge
arresters. The overvoltages can be classified regarding their origin or duration/shape.
Regarding origin of overvoltages, a distinction can be made between internal and
external overvoltages. Internal overvoltages are caused by an excitation within the
system such as faults or switch closing and opening without any influence from outside.
In contrary, external overvoltages arise by an excitation exerted from outside of the
system. Lightning stroke is typical cause of external overvoltages. Fig. 1.21 summarizes
the classification of overvoltages.
Fig. 1.21 Classification and origin of overvoltages
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1 Transient phenomena
The classification of overvoltages for insulation coordination studies is given in the norm
IEC 71-1 Insulation Co-ordination, Part 1: Definitions, principles and rules [2].
Characteristics of voltages and overvoltages are specified according to [2] as follows:
• Continuous (power frequency) voltage: Power frequency voltage, considered
having constant r.m.s. value, continuously applied to any pair of terminals of an
insulation configuration.
• Temporary overvoltage: Power frequency overvoltage of relatively long duration.
• Slow-front overvoltage: Transient overvoltage, usually unidirectional, with time to
peak 20 :s < Tp # 5000 :s, and tail duration T2 # 20 ms.
• Fast-front overvoltage: Transient overvoltage, usually unidirectional, with time to
peak 0.1 :s < T1 # 20 :s, and tail duration T2 # 300 :s.
• Very fast-front overvoltage: Transient overvoltage, usually unidirectional with time
to peak Tf # 0.1 :s, total duration < 3 ms, and with superimposed oscillations at
frequency 30 kHz < f < 100 MHz.
Overvoltage may occur between one phase conductor and earth or between phase
conductors having a peak value exceeding the corresponding peak of the highest voltage
of equipment, Um. Um is the highest r.m.s. value of phase-to-phase voltage for which the
equipment is designed in respect of its insulation. Overvoltage values (phase to earth) are
expressed in p.u. as overvoltage factor, unless otherwise indicated:
(1.13)
1.4.2 Overcurrents
Overcurrents initiated by transients may cause thermal and mechanical stresses on
equipment. The classification of overcurrents can be made analog to overvoltages.
Internal overcurrents get their energy from the system. Typical example is short circuit
Power System Transients (Kizilcay)
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1 Transient phenomena
currents caused by faults in power systems. They are mainly power frequency
overcurrents superimposed by high frequency oscillations. Depending on inception
angle, they may be asymmetric with high peak value. The duration of the s.c. current
plays a role for thermal stress, whereas the peak value is responsible for mechanical
stress due to magnetic force. External overcurrents arise from direct and indirect
lightning strokes. They may have very high amplitude and are of very short duration.
1.5
Electrical Transients and Associated Frequency Ranges
The study of electrical transient phenomena in power systems involves a frequency
range from DC to about 50 MHz or in specific cases even more. Above power frequency
these usually involve electromagnetic phenomena, whereas below power frequency also
transients of the electromechanical type in rotating machines can be involved.
Table 1.1 gives an overview on the various origins of transients and their most common
frequency ranges. Minimum frequency values below power frequency indicate the
frequency band required to represent main time constants of the relevant transients.
Table 1.1 Origin of electrical transients and associated frequency ranges
Origin
Transformer energization,
ferroresonance
Load rejection
Fault clearing
Fault initiation
Line energization
Line reclosing
Transient recovery voltage
Terminal faults
Short line faults
Multiple restrikes of circuit breaker
Lightning surges,
Faults in substations
Disconnector switching and faults in GIS
1-20
Frequency range
(DC) 0.1 Hz – 1 kHz
0.1 Hz – 3 kHz
50 Hz – 3 kHz
50 Hz – 20 kHz
50 Hz – 20 kHz
(DC) 50 Hz – 20 kHz
50 Hz – 20 kHz
50 Hz – 100 kHz
10 kHz – 1 MHz
10 kHz – 1 MHz
100 kHz – 50 MHz
Power System Transients (Kizilcay)
1 Transient phenomena
In some cases the total duration of electrical transients may last longer than indicated in
the above table, e.g. saturation of large transformers during energization, but normally
shorter time periods of study is of real interest.
Representation of all system components which are valid within the large frequency
range of 0 to 50 MHz is practically not possible. For this reason, those physical
characteristics of a specific network element that play significant role in the transient
phenomena to be studied, should be given detailed consideration for the modeling. The
representation of the individual network elements must therefore correspond to the
specific frequency range of the particular transient phenomenon. In [3] the frequency
ranges of electrical transients given in Table 1.1 are classified as four typical groups with
overlapping frequency ranges for which specific models of components may be
established. Table 1.2 shows these groups related to the actual steepness of overvoltages.
Table 1.2 Classification of frequency ranges for modeling of system components
Group
Frequency range
time-domain
characteristic
Representation
mainly for
I
0.1 Hz – 3 kHz
low frequency oscillations
temporary
overvoltages
II
50 Hz – 20 kHz
slow front surges
switching
overvoltages
III
10 kHz – 3 MHz
fast front surges
lightning
overvoltages
IV
100 kHz – 50 MHz
very fast front surges
restrike
overvoltages
Power System Transients (Kizilcay)
1-21