SwitchingTransients-Example

```Switching Transients Application Example
DIgSILENT PowerFactory *
Abstract
Therefore, transients have to be expected and are observed in the system during the change from the situation before to the situation after switching. Transients are abnormal patterns of current and voltage
that have a limited duration. They frequently exceed
the currents and voltages met during steady-state operation. In order to ensure a safe and reliable operation of the power system, electrical equipment has
to be designed to withstand the stresses caused by
transients.
This example provides an introduction to switching
transients. The application example contains various study cases for the investigation of electromagnetic transient (EMT) phenomena in such as transformer energistaion, overhead line energisation, fault
and load switching as well as the analysis of transient
recovery voltage in PowerFactory. The following topics and functionalities are discussed: Power System
Modelling for Electromagnetic Transients, Electromag- The network model in Figure 1 is used to demonstrate
netic Transients Simulation, Statistical Switching Anal- the use of PowerFactory for the analysis of switching
transients. The network comprises parts of a meshed
ysis.
400 kV transmission system and an underlying 110 kV
sub-transmission system.
1
General Description
The transmission system consists of five substations,
a power plant and two large loads. The power plant is
connected to the substation North via a 400 kV cable
Switching operations in power systems are very com- system. The substations are interconnected by single
mon and must not jeopardize the system’s reliability and double circuit overhead lines according to Figure
and safety. Switching in power systems is necessary 1.
for the following reasons and duties:
The neighbouring network in the West is modelled by
• Taking into or out of service some sections of the a voltage source with an equivalent short circuit power
system, certain loads, or consumers. Typical ex- which acts as slack bus for the system. The transmisamples are: Energisation and de-energisation of sion system in the East is modelled by an equivalent
overhead lines, cables and transformers, switch- load. Shunt reactors and capacitor banks are used for
ing of shunt capacitor banks or shunt reactors.
reactive power compensation.
• Transferring the flow of energy from one circuit
The 110 kV sub-transmission system comprises three
to another, e.g. in a substation from one busbar
substations which are connected to the Central subto another.
station by overhead lines. Furthermore a wind farm
• Isolating certain network components because is connected to the substation through a high voltage
cable system.
of maintenance or replacement.
• Isolating faulted sections of the network in order
to avoid damage and/or system instability. Examples are: terminal fault and short line faults.
2
Simulation Model
Switching in electrical power systems re-configures
the topology of an electrical network. It involves the The investigation of electromagnetic transients remaking and breaking of circuits and causes a distur- quires an accurate representation of relevant power
system components. Depending on the transient bebance of the steady state energy flow.
* DIgSILENT
GmbH, Heinrich-Hertz-Str. 9, 72810 Gomaringen, Germany, www.digsilent.de
DIgSILENT PowerFactory, r4594
1
Switching Transients Example
ing analysed the network model should include:
• Stray inductances and capacitances
• Valid representation of the model for a frequency
range which may vary from DC to several MHz
• Electric arcing model
The following subsections describe the models of the
power system components of the transmission system
• Non-linear saturation characteristics of induc- shown in Figure 1.
tances
• Distributed parameter line models
2
Generator
GT-1
GT-2
0
C Bank
~
SG
Power Plant
9
PP1
PP2
Central
North-East
Inactive
Out of Calculation
De-energised
NPP-1
20 km
Voltage Levels
400, kV
110, kV
33, kV
27, kV
NPP-2
20 km
North1
Shunt Reactor
1
CE-1.1
25 km
North2
West
NC-1
100 km
NC-2
100 km
CE-1.2
25 km
0
WN
100 km
East-1
Grid
CE-2.1
30 km
TR_C1
TR_C2
0
CE-2.2
30 km
WC-1.1
100 km
WC-1.2
100 km
WC-2.1
100 km
WC-2.2
100 km
East-2
WC-1.3
100 km
Wind Farm
8
WFT-1
WC-2.3
100 km
WT
8
CE-3
12 km
West 1
West 2
WF
C4_1.1 C4_1.2
WFT-2
C1_1 C1_2
Figure 1: Single line diagram of the power system
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Switching Transients Example
CCE-1-1
IS.R0.2
IS.R0.1
CB.R0
IS4.3
CNC-1_comp
IS.R6.3
IS4.2
CB4
IS4.1
CE-1.1
25 km
IS7.2
CB7
IS7.1
CE-1.2
25 km
IS3.2
CB3
IS3.1
CE-2.2
30 km
IS2.2
CB2
IS2.1
CE-2.1
30 km
CB1
IS1.1
IS.R3.3
IS.R3.1
NC-2
100 km
CB.R3
IS.R6.2
CB.R6
IS.R6.1
IS.R5.2
CB.R5
IS.R5.1
CNE-1
100 km
IS.R3.2
CNE-2
100 km
CCE-1-2
CNC1
IS.R5.3
IS7.3
IS.R1.3
IS6.3
CB.R4
CB.R1
IS.R1.1
IS6.1
IS.R4.2
IS.R4.3
TR_C2-MV
TR_C2-HV
WC-1.3
100 km
CB.L2
IS3.3
TR_C1-MV
TR_C1-HV
CBS1
IS.L2.3
IS.L2.1
IS6.2
TR_C1
CBS2
CWC1_comp
CB6
IS.L2.2
CWC1
TR_C2
IS.L3.2
CB.L3
IS2.3
IS5.1
CB5
IS5.2
CCE2-1
IS.R4.1
CCE2-2
IS.R1.2
Shunt Reactor
IS.L3.1
IS5.3
CWC2
IS.L3.3
WC-2.3
100 km
IS1.3
IS.L1.1
CB.L1
IS.L1.2
IS1.2
IS.L1.3
CE-3
12 km
IS0.2
CB0
IS.L0.1
IS0.1
CB.L0
C1_1
C4_1.1
CCE-3
IS.L0.2
CWC-2_comp
C4_1.2
C1_2
Figure 2: Detailed substation layout diagram of substation Central
2.1
Transmission Lines
The transmission system contains the following overhead lines (OHL) and cable systems:
• 400 kV double circuit OHL
• 400 kV single circuit OHL
• 400 kV double circuit cable system
• 110 kV double circuit OHL
• 110 kV single circuit cable system
Both cables and overhead lines are modelled based
on their geometry of the corresponding characteristics
of conductors and insulation layers.
Overhead lines can be modelled based on their ge- Figure 3: 400 kV double circuit overhead line structure
ometry and material characteristics of the conductors
and earth return path in PowerFactory.
The Y-values which are entered in PowerFactory corThe geometry is entered in PowerFactory using the respond to the average height of the conductor and
X-Y coordinates of the phase conductors and ground ground wire along the line. The average height inwires as shown in Figure 3. The graph shows the ge- cludes the sag and is calculated as follows:
ometry of the 400 kV and 110 kV double circuit overhead line being used in the network model (Figure 1).
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Switching Transients Example
2
βaverage = βtower − &middot; πsag
3
Apart from the overhead line geometry the phase conductors and earth wires have to be defined. As input
parameter the geometry of the corresponding conductor, its DC-resistance and bundling configuration has
to be entered. The 400 kV overhead line is a bundled
conductor type configuration and comprises 4 subconductors per phase.
The 110 kV overhead lines are untransposed in this
application example.
Phase A
Phase B
Phase C
upper
middle
lower
upper
The specific earth resistivity for the earth return path
middle
is assumed with 100 β¦π for all overhead lines which
corresponds to a typical value [1]. Based on the
lower
above input parameters, PowerFactory calculates the
impedance and admittance matrix for all phases of the
Figure 4: Transposition of the 210 km long 400 kV OHL
WC-1 and WC-2
The impedance and admittance matrix is then used
to calculate the reduced impedance matrix, sequence
impedances and corresponding distributed parameter High Voltage Cables
line models which will be required for the switching
The high voltage cables are modelled in a similar way.
transients studies.
The geometry of the single core cable and its correDepending on the frequency of the transient being in- sponding material characteristics are entered in Powvestigated, one of the following models will be used for erFactory. The following layers are included in the
model of the single core cable:
the EMT simulation:
• Lumped parameter model
• Conductor
• Distributed parameter model with constant parameter (frequently known as Bergeron model)
• Sheath
• Distributed parameter model with frequency dependent parameter (frequently known as J. Marti
model)
• Insulation
• Oversheath
• Semiconducting layers
Transposition
The cross-section of the 400 kV single core cable is
displayed in Figure 5. The geometry is entered by
Due to the geometry of the overhead lines, the defining the thickness of each layer. Furthermore the
impedances of each phase differ from each other. In resistivity, relative permittivity and permeability is enorder to mitigate unbalances in the system, overhead tered in PowerFactory.
lines are usually transposed.
In this example the transposition is modelled explicitly for the lines WC-1 and WC-2 between substation
West and Central. The phasing is entered in the line
coupling (ElmTow). Figure 4 shows the transposition
of OHL WC-1 and WC-2.
The other 400 kV overhead lines are transposed circuit wise in *.TypTow by selecting the option Transposition → Circuit Wise. By selecting this option the
positive and zero sequence offdiagonal elements of
the mutual sub-matrices between transposed circuits
are eliminated.
Figure 5: 400 kV single core cable
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Switching Transients Example
The cables are layed directly in ground in flat formation
with a distance of 0.7 m apart. Two cable systems connect the substation North with the Power Plant (see
Figure 1). They are layed in parallel. The layout of
the complete cable system is shown in Figure 6. The
earth resistivity is assumed to be 100 β¦π.
tion of the wind farm with the 110 kV terminal of the
sub-transmission system.
Saturation Model
For simulating non-linear, electromagnetic transients
such as the transformer energisation, the core saturation needs to be included in the model of the transformer.
The saturation is defined in the transformer type. In
this simulation model the magnetising branch of the 3winding transformer is placed at the start point. The
magnetising branch of the 2 winding transformers is
located between the primary and secondary side.
Figure 6: 400 kV double circuit cable system laid in
ground
The non-linear flux-current relationship of the 2winding transformers is modelled using a polynomial
approximation for the saturation curve. As an example
As for overhead lines, internal routines calculate the for a saturation curve Figure 7 shown the magnetising
impedance and admittance matrix of the cable system characteristic of the transformer WFT-1 in Figure 1.
and all required parameters for steady state, dynamic
The saturation characteristic of the 3-winding transand electromagnetic transient analysis.
former is modelled based on open circuit measurement data. They are entered as RMS values (open cirLine Compensation
cuit test). PowerFactory converted them internally to
Shunt reactors are used for the compensation of the current-flux peak values to model the saturation charcharging current of the 400 kV cable system and the acteristic properly.
200 km single circuit and 210 km long double circuit
overhead line connecting substation West and Cen- The residual flux of the transformer is taken into consideration using a parameter event. The residual flux
tral.
is entered in PowerFactory in the dq-frame. The transThey are connected directly to the line at its sending formation of the a-b-c fluxes in the dq-frame is docuand receiving end and are designed to compensate mented in the Technical Reference of the transformer.
approximately 70 % of the charging current.
Furthermore, hysteresis can be included in the transformer core model.
2.2
Transformers
The network model comprises two-winding and threewinding transformers [6], [7].
Transformer Types
3-winding transformers (TR_C1 and TR_C2) are installed in substation Central connecting the 110 kV
sub-transmission system to the 400 kV transmission
system. The transformers have a rated power of
275 MVA. The vector group is YN0yn0d11.
The substation PowerPlant in the North of the network
includes a YNd5 1600 MVA transformer which connects the generator’s 27 kV terminal with the 400 kV
terminal of the transmission grid.
Figure 7: Saturation characteristic of transformer
Furthermore two YNd5 50 MVA transformers are installed in the wind farm and connect the 33 kV substa-
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Switching Transients Example
2.3
Generator
NPP-1
The synchronous machine of the power plant has a
rated power of 1560 MVA and a nominal voltage of
27 kV. Switching transients will not be investigated in
close vicinity of the generator. Therefore the model is
not further described here.
NNPS2_comp
North 1
The wind farm has a rated power of 100 MVA and is
represented by an aggregated wind turbine as shown
in Figure 1. The wind turbine is a full-scale converter
model. The converter is implemented in PowerFactory
using a static generator element, which is configured
to operate as a current controlled voltage source. The
converter currents are controlled using a classical dq rotating reference system current controller in the
EMT simulation.
2.4
NPP-2
NNPS1_comp
NWN1
IS2.2
IS4.2
CB2
CB4
IS2.1
IS4.1
ISa.2
ISb.2
CBa
CBb
ISa.1
ISb.1
IS1.1
IS3.1
CB1
CB3
IS1.2
IS3.2
NNC2
North 2
2.5
Substations
WN
NC
The network model comprises 5 substations:
• Substation West
Figure 8: Substation North with 1 1/2 breaker method
• Substation North
The substation layout includes two-breaker and 1 1/2breaker configuration. The two-breaker configuration
• Substation Power Plant
is shown in Figure 2. In this case the circuit breaker,
branch disconnector and instrumental transformers
• Substation Wind Farm
are duplicated in each branch. Busbar interchange
All substations are modelled in detail as shown in Fig- and isolation of one busbar for maintenance is possiure 2 for substation Central. The substation models ble. One branch breaker can be taken out for maininclude busbars, circuit breakers (CB), disconnector tained at any time without interrupting operation.
switches, surge arresters and shunt reactors for reacThe 1 1/2-breaker design is applied in Figure 8. Fewer
tive power compensation.
breakers are needed here for the same flexibility as
Generally busbars, circuit breakers and disconnec- above. Isolation without interruption is possible. All
tor switches are modelled as ideal elements without breakers are normally closed. Uninterrupted supply is
impedances and as ideal switches. If required, bus- thus maintained even if one busbar fails.
bars will be modelled as distributed parameters lines.
Relevant stray inductances and capacitances of substation equipment (such as instrumental transformers) 2.5.1 Circuit Breakers
will also be considered if necessary.
Circuit breakers (CB) are modelled as ideal switches.
Arcing models and models for re-ignition are available
in PowerFactory but will not be considered in the study
cases which are discussed in this example.
• Substation Central
For Transient Recovery Voltage (TRV) studies the
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Switching Transients Example
breaker capability curve is modelled according to
IEC 62271-100 with a 2-parameter or 4-parameter
curve depending on the voltage level and circuit
breaker rating.
2.5.2
Surge Arresters
Surge arresters are used to protect electrical equipment in substations, such as transformers, circuit
breakers and bushings, against the effects of overvoltages caused by incoming surges. Such overvoltages can be caused by a direct or nearby lightning
strike and other electromagnetic transients such as
e.g. switching operation in the power supply system.
Surge arresters present a nonlinear resistor and are
characterised by a highly non-linear U-I curve. During
normal operating voltages surge arresters have an extremely high resistance and a relatively low resistance
during transient overvoltages.
Metal oxide arresters (MOA) are usually used for
surge arresters and in most cases are connected from
phase to ground. The charactersitic U-I curve of an
surge arrester which is necessary for an EMT study
is usually provided in the vendor datasheet and is entered in PowerFactory in tabular form.
Figure 9: Surge arrester π − πΌ characteristic
2.5.3
Reactive Power Compensation
For reactive power compensation a shunt reactor is installed in substation Central. The rated reactive power
of the shunt reactor is 50 Mvar per step. The reactor
is switchable and has 4 steps. Thus, the shunt reactor
can consume a maximum of 200 Mvar.
A capacitor bank is installed at the substation NorthEast with a rated reactive power of 50 Mvar per step.
It is also switchable and has 10 steps.
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Switching Transients Example
3
Switching Transients
be at its peak in steady state operation. However, due
to the initial condition (Ψ equals zero) the flux starts at
zero. As a result the curve of the flux Ψ is shifted by
Switching in electrical power systems re-configures Ψπ upwards in the first cycle of the transient. Thus,
the flux starts at zero and then reaches a maximum of
the network topology for the following purposes:
2Ψπ in the first cycle as indicated in Figure 10 [1].
• Isolation and Earthing
Taking into a account a residual flux of Ψπ in the iron
• Busbar-Transfer Switching
core, the curve is shifted upwards even further as indicated in Figure 10 and reaches a maximum peak
values of Ψπ + 2Ψπ . The magnetization curve is now
• Fault-Clearing
operating in the saturated region and the relationship
between the flux Ψπ and the current π are no longer
The following switching transients are analysed in this
governed by a linear relationship. This causes high
application example:
and distorted inrush currents as shown in the graph.
• Transformer Energisation
ψ
ψR + 2 ψm
ψ, B
2 β ψm
ψR
• Fault-Current Interruption Switching
H, i
The transient phenomena following the above switching actions will result in abnormal patterns of current
and voltage during the transient. The root causes of
the abnormal currents and voltages are described in
the following section.
3.1
u
i
Saturation
For simulating electromagnetic transients such as
transformer inrush currents or ferro-resonance, reactor / transformer core saturation needs to be included
in the model of the transformer. The non-linear behaviour of a typical transformer iron core is shown in
Figure 10 [1].
The solid lines represent the steady state voltage and
flux and current relationship when no saturation occurs. The dashed lines represent the behaviour during a transient, when the core is being saturated (e.g.
during transformer energisation).
Figure 10: Saturation and inrush current
3.2
Travelling Waves
When investigating transient and high-frequency
steady-state phenomena, it is necessary to account
for the distributed-parameter nature of conductors
such as overhead lines, cables and in the case of high
frequency transients, even of busbars.
The magnetic flux Ψ, representing the time-integral of
the voltage, lags in steady state the sinusoidal waveform of the voltage by 90β . Being still in the linear
part of the saturation characteristic, the current is sinusoidal as well. Thus, the current is proportional to
the voltage.
Typically, for low frequency steady-state analysis, lines
and cables are modelled using the well-known lumped
parameter equivalent circuit, thus neglecting the distributed nature without loosing too much accuracy in
the results. In reality, a current in a conductor having
even a very short length, needs a certain time to travel
from its sending end to the remote end [1].
When a completely demagnetised transformer is energised the flux Ψ in the iron core is zero at the instant
of switching. The instantaneous voltage in Figure 10
is zero at this instance. Due to the 90β phase shift
between the flux Ψ and the voltage, the flux ought to
When an overhead line or cable is energised from
the grid as shown in Figure 11, a voltage and current
surge are injected into the line. Before the breaker is
closed, the voltage at both ends of the line is zero.
Upon breaker closing at the sending end of the line,
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Switching Transients Example
the voltage changes instantaneously from zero to the
supply voltage π’π .
At the receiving end of the line, the voltage π’π is still
zero since the surge needs a certain time to travel
from the sending to the receiving end of the line. The
surge propagates with the speed π£ along the line and
arrives at the sending end of the line with a delay equal
with the propagation time π .
The propagation speed π£ is a function of the line inductance πΏ′ and capacitance πΆπΏ′′ . For a lossless line
the propagation speed π£ is calculated by the following
equation [1]:
π’π
π’π
π’π
π’π
π’π
π’π
Figure 11: Voltage surge line energisation
During the transient, the surge is travelling back and
forward until damping and attenuation will eventually
result in a steady state condition. At each electrical boundary the surge is reflected and refracted as
The propagation time constant π is dependent on the
indicated in Figure 11. Electrical boundaries arise
propagation speed v and the line length
when the surge impedance of the network components change, e.g. at an overhead line - cable tran√οΈ
sition or at the open end of a line.
π
π = = π &middot; πΏ′ &middot; πΆ ′
π£
π£=√
1
′
πΏ &middot; πΆ′
Figure 11 shows the voltage surge during the line energisation of an ideal single phase conductor for three
time steps of the transient:
π1
π2
π1
π2
• 1: Breaker is closed at the sending end
• 2: Surge propagates from sending to receiving
end
π’1
π’π
π2 &gt; π1 :
• 3: Reflected surge travels back to sending end
Transient voltage and current surges are thus a function of time and location along the line. Distributed parameter line models are therefore required to analyse
such phenomena. Depending on the transient being
investigated, line models with constant or frequency
dependent parameters are used in simulation models.
π’π
π’1
π’2
π’2
π1
π1
π2
ππ
The constant distributed parameter model in PowerFactory is based on Bergeron’s method, which calculates the voltages and currents at one end of the line
based on the voltage and current at the other end de- Figure 12: Travelling voltages and currents at surge
layed in time. For further information refer to the tech- impedance jump location
nical reference of the line models [4].
With the exception of lossless and distortion-less
lines, the characteristic impedance ππΆ and the propagation constant πΎ are frequency dependent. To handle
PowerFactory uses the approach proposed by J.Marti
[4]. For cable systems the Universal Line Model is
available and offers a high accuracy and a phasedomain formulation [5].
DIgSILENT PowerFactory, r4594
The reflected and refracted voltage and current surge
are a function of the incoming voltage and current
waveform and the surge impedance on both sides of
the boundary. For an ideal surge with a very steep
rise / very short rise time, the reflected and refracted
surges are calculated according to the following equations:
9
Switching Transients Example
interruption must wait for the zero crossing of the current. Depending on the type of circuit-breaker, the device may not be ready to interrupt at the first occurring
current zero after contact separation.
2 &middot; π2
π’2
=
π’1
π1 + π2
π + π1
π’π = 2
π1 + π2
For SF6 circuit breakers, it takes a certain minimum
arcing time before the electric arc extinguishes in the
circuit breaker because sufficient cooling pressure of
the extinction medium must be available and sufficient
contact distance must be reached. For vacuum circuit
breakers sufficient contact distance has to be reached
in order to extinguish the electric arc [2].
π1
2 &middot; π1
=
π2
π1 + π2
π − π2
ππ = 1
π1 + π2
Typical surge impedances for common power system
components are:
πΏπ
• Overhead lines: 200 β¦ to 500 β¦
• Cable systems: 40 β¦ to 70 β¦
πΆπ
π’π
π’πΏ
πΆπΏ
πΏπΏ
• Transformers: 1 πβ¦ to 10 πβ¦
3.3
Transient Recovery Voltage (TRV)
Figure 14: Frequency spectrum of load side oscillation
Transient recovery voltages (TRV) arise both at fault
interruption and load switching. In both cases a circuit
breaker is switching off. The circuit breaker opening
procedure is explained in Figure 13. The switching
command is usually initiated automatically by a relay
that detects a fault in the system or a switching command from the control center to trigger a change in the
operation scenario of the network.
Fault currents and inductive load currents (e.g. disconnection of shunt reactors) lag the voltage by around
90β . Thus, the instantaneous voltage at both sides of
the breaker pole is at its peak when the current is interrupted at the current zero-crossing.
Immediately after current interruption a transient voltThe tripping command activates the operating mech- age will oscillate on the load side and source side.
anism and through its kinematic chain separates the Figure 14 shows the equivalent circuit of the load and
contacts in the circuit-breaker. After a certain opening source side after the switching action.
time, the circuit-breaker arcing contacts will open in all
The source side voltage is composed of two compothree poles.
nents, the power frequency voltage (e.g. 50 Hz) and
the transient voltage oscillating between πΏπ and πΆπ .
Breaker state
The frequency of the transient part of the voltage is
calculated by the following formula:
1
1
ππ =
&middot; √οΈ
2π
πΏπ &middot; πΆπ
Switching
command
Contacts start
to separate
Arc extinction in last pole
ο  Current interruption
Contacts fully
separated
arcing time
The oscillation frequency of the voltage on the load
side is defined by πΏπΏ and πΆπΏ and is a single frequency
oscillation in case of linear inductive load.
Total break time
Figure 13: Circuit breaker operation switching off
1
1
ππ =
&middot; √οΈ
2π
πΏπΏ &middot; πΆπΏ
Upon contact separation, an arc is formed in the in- The Transient Recovery Voltage (TRV) is the voltage
terruption chamber of each pole. The actual current across the open circuit-breaker contacts which arises
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Switching Transients Example
immediately after current interruption. It is the differπΏL = 1000 mH; πΆL = 2 πF
ence between the voltage-to-earth at the source side
π’π and load side π’πΏ :
Figure 15 shows that the TRV starts from zero at
current zero, makes an excursion to the momentary
power-frequency voltage, overshoots in a damped
π’TRV = π’π − π’πΏ
oscillatory manner and continues to oscillate until a
steady-state condition is reached. The frequency of
The TRV always consists of at least two oscillatory
the load side oscillation is ππΏ = 3558.8 π»π§ and of
components, the source-side and load-side frequency
the source side ππ = 73.9 π»π§. Important paramecomponent. Depending on the switching action (e.g. ters in a TRV study are the maximum transient recovshunt reactor switching, terminal fault, short line fault ery voltage π and the rate of rise of recovery voltπΆ
interruption) the TRV contains multiple oscillation fre- age (RRRV). Both
parameters are required for circuit
quencies which superimpose.
breaker design studies.
The exemplary TRV for a single phase circuit is shown Current chopping may need be considered as well in
in Figure 15 assuming the following values:
the TRV study for some types of circuit breakers or
switching transients.
πΏS = 17 mH; πΆS = 273 πF
200,00
100,00
0,00
-100,00
-200,00
-300,00
0,00
2,00
Source: Phase Voltage SP in kV
4,00
6,00
8,00
[ms]
10,00
0,00
Load: Phase Voltage SP in kV
4,00
6,00
8,00
[ms]
10,00
200,00
100,00
0,00
-100,00
-200,00
-300,00
2,00
200,00
40,00
100,00
30,00
0,00
20,00
-100,00
10,00
-200,00
0,00
-300,00
0,00
2,00
Circuit Breaker: Voltage Difference in kV
Source: Power Frequency Voltage
4,00
6,00
8,00
Circuit Breaker: Phase Current/Terminal i in A
[ms]
-10,00
10,00
Figure 15: Source side, load side and transient recovery voltage (TRV)
DIgSILENT PowerFactory, r4594
11
Switching Transients Example
4
Study Cases
Large loads are connected to substation North and
North-East, each with a consumption of 1200 MW and
a power factor of 0.9 and 0.98 respectively. For reacThe application example contains several study cases, tive power compensation the capacitor bank at substation North-East is supplying 400 Mvar (tap 8). The
each of them being discussed further below:
shunt reactor at substation Central is tapped to zero
• “Steady State Load Flow Analysis”: Intro- and thus not consuming any active power.
duction to the network model and components.
Load flow calculation and analysis (see section The load flow calculation is configured with automatic
4.1);
tap adjustment of transformers at substation Central
• “Transformer Energisation”: Investigation of and at the wind farm. The load flow calculation will
instantaneous inrush currents caused by the en- determine the active and reactive power flows for all
ergisation of the wind farm transformer WF-1. branches, and the voltage magnitude and phase for
all nodes. Executing the load flow results in the phase
Peak currents and RMS voltage dip. Fourier
voltages displayed in Figure 16. The voltage at subanalysis of the inrush currents (see section 4.2);
station West is the reference voltage with an angle of
• “Overhead Line Energisation”: Investigation 0 β and a symmetrical phase shift of 120 β for each
of transient overvoltages occurring during the phase respectively.
energisation of the 400 ππ overhead line WC-1.
Determination of peak and duration of transient The external grid serves as slack and is supplying
voltages and currents. Statistical switching tool 1900 MW for active power balancing and a reactive
power of 60 Mvar. The voltages of all busbars in
(see section 4.3);
the transmission system and sub-transmission sys• “TRV Analysis of Shunt Reactor
tem, are in the range of 0.99 to 1.03 π.π’. in the steady
ery voltage (TRV) during shunt reactor open- transformers varies between 14 % and 50 %.
ing. Circuit breaker design validation (see section 4.4);
• “TRV Analysis Terminal Fault”: Investigation basis for the calculation of the initial conditions and
of the TRV following a terminal fault at substa- thus the starting point of the EMT simulation.
tion Central. High voltage TRV modelling (see
section 4.5);
[deg]
4.1
Analysis
6,00
5,00
4,00
3,00
The load flow calculation is based on algorithms for
the unbalanced load flow taking into account unbalances resulting from imperfect line transposition of
the multi-phase network and unsymmetrical loads and
generation. The active power control in the load flow
calculation is based on the dispatch of generators and
balanced by the reference machine.
2,00
1,00
-240, -210, -180, -150, -120, -90,0 -60,0 -30,0
30,0 60,0 90,0 120, 150, 180,
[kV]
-1,00
-2,00
-3,00
-4,00
-5,00
-6,00
The external grid connected to substation West rep-7,00
resents the transmission system in the West is used
-8,00
as reference machine (slack). It controls the voltage
West 1: Line-Ground Voltage
North 1: Line-Ground Voltage
C4_1.1: Line-Ground Voltage
to 1 p.u. at substation West. The power plant conNorth-East: Line-Ground Voltage
nected to substation North is set to dispatch 750 MW.
A station controller is used to regulate the voltage at Figure 16: Phase voltages of the transmission system
the HV-side of the Power Plant to 1.02 p.u. The wind
farm connected to the 110 kV sub-transmission system is set to dispatch 30 MW at a power factor of 0.95
overexcited.
DIgSILENT PowerFactory, r4594
12
Switching Transients Example
4.2
Transformer Energisation
This study case investigates the energisation of the
wind farm transformer WF-1. Before energisation, the
complete wind farm is disconnected. The 110 kV HV
cable which connects the wind farm to the point of
common coupling (PCC) at substation Central is already energised and in steady state. The wind farm
transformer WF-1 is energised by closing the circuit
breaker CB4. The residual flux in the transformer core
is assumed to be zero at the time when the transformer is energised (ππ΄ (π‘0 ) = ππ΅ (π‘0 ) = ππΆ (π‘0 ) = 0).
phase C results in a phase current of 2.97 π.π’. in the
saturation curve corresponding to transformer WF-1.
A Fast Fourier Transform (FFT) is used to investigate
the inrush currents in order to quantify their harmonic
content. The FFT is carried out with a 20 ms window and 64 samples, resulting in a sampling rate of
3200 Hz. Figure 18 shows the FFT of the inrush currents in the same plot. As can be seen, phase C contains a significant DC-component. This is because the
flux in phase C starts at zero when the transformer is
energised, thus resulting in a fluctuating flux between
0 π.π’. and 2 π.π’. (fluctuating around 1 π.π’.).
The EMT simulation is initialised at π‘ = −100 ππ  and
the integration step size is set to π‘ = 100 ππ . The circuit breaker CB4 is closed at π‘ = 0 π . The simulation
results are documented in Figure 17 and Figure 18.
Following the switch event the flux in all three phases
rises proportional to the source voltage at the HV side
of the transformer with a 90β phase shift. The peak
flux arises in phase C and is −1.68 π.π’. which corresponds to a flux of 339.6 π π .
The energisation of the wind farm transformer causes
a voltage drop at the grid connection point (Central
substation). The RMS voltage during the energisation
process is shown in Figure 18. Ahead of energisation
the RMS voltage in all three phases is approximately
1.015 π.π’. The minimum RMS voltage during the energisation occurs in phase C and is 0.99 π.π’. which
corresponds to a voltage dip of approximately 2.5 %.
Usually grid code requirements limit the maximum alDuring the energisation, the fluxes in all three phases lowable RMS voltage dip to 2.0 %. Thus, countermeaexceed 1 p.u. and drive the transformer into satura- sures such as point on wave switching (π ππ ) would
tion. The current-flux relationship is no longer linear have to be considered for the specific case.
and results in high inrush currents which contain harEnergising both transformers instantaneously at π‘ =
monic distortion as described in section 3.1. The non0 π  results in a minimum voltage of 0.97 π.π’.. This will
linear flux-current relationship can also be plotted in
most likely not be acceptable with regard to the grid
PowerFactory and is shown in Figure 17. The peak
code. Taking residual flux into consideration will ininrush current on the HV side of the transformer arises
crease the inrush currents and consequently the RMS
in phase C and is 780 π΄. This is approximately 3 times
voltage dip.
the rated current of 262.4 π΄. Thus, a flux of 1.68 π.π’. in
DIgSILENT PowerFactory, r4594
13
Switching Transients Example
2
3
3
[p.u.]
[p.u.]
[p.u.]
Max. = 1,197 p.u.
1
2
0
1
1
-1
0
0
-2
-1
-1
-3
0
10
-2
20
30
40 [ms] 50
WF: Phase Voltage A
WFT-1: Magnetising Flux A
2
Max. = 1,471 p.u.
0
10
-2
20
30
40 [ms] 50
WF: Phase Voltage B
WFT-1: Magnetising Flux B
Min. = -1,675 p.u.
0
4
800
3,00
[p.u.]
[A]
[p.u.]
2
400
0
0
10
20
30
40 [ms] 50
WF: Phase Voltage C
WFT-1: Mag. Flux c C
2,00
1,00
-2
-400
-4
-800
-6
-1200
0,00
-1,00
0
10
20
30
40 [ms] 50
WFT-1: Magnetising Current, Phase a
WFT-1: Magnetising Current, Phase b
WFT-1: Magnetising Current, Phase c
0
10
20
30
40 [ms] 50
WFT-1: Phase Current A/HV-Side
WFT-1: Phase Current B/HV-Side
WFT-1: Phase Current C/HV-Side
-2,00
-6
-4
-2
0
2 [p.u.] 4
Figure 17: Transformer HV side voltage, magnetic flux in the core, magnetizing current
1,03
[sec.V]
1,02
PCC\RMS Voltage: Phase A
PCC\RMS Voltage: Phase B
PCC\RMS Voltage: Phase C
1,01
1,00
0,99
0,98
0,0
100,0
200,0
300,0
400,0
[ms]
500,0
800,0
[A]
400,0
WFT-1: Phase Current A/HV-Side
WFT-1: Phase Current B/HV-Side
WFT-1: Phase Current C/HV-Side
0,0
-400,0
-800,0
-1200,0
0,0
100,0
200,0
300,0
400,0
[ms]
500,0
500,0
[A]
400,0
WFT-1: Phase A
WFT-1: Phase B
WFT-1: Phase C
300,0
200,0
100,0
0,0
0,000
50,00
100,0
150,0
200,0
[Hz]
Figure 18: RMS voltage dip at PCC, Inrush currents and their harmonic distortion
DIgSILENT PowerFactory, r4594
14
Switching Transients Example
4.3
Line Energisation
The energisation of high voltage overhead lines and
cable systems may cause considerable overvoltages.
With increasing operating voltages of transmission
systems, switching surge overvoltages determine the
insulation design rather than lightning overvoltages.
Transient overvoltages caused by internal line events
such as line switching are one of the main problem in
EHV and UHV systems with regard to insulation coordination and are discussed in this study case. These
transients typically have durations ranging from a few
tens to several thousands of ππ  and belong to the
category of slow front transients. They usually have
complex waveforms with frequencies in the range of
100 Hz to several ππ»π§ superimposed on the power
frequency.
4.3.1
This study case investigates the energisation of the
overhead line WC-1. Before the energisation, the line
is disconnected from the grid and will be energised
from the substation Central while the other end of the
line remains disconnected. The initial condition before
calculation as described in section ??. The surge arresters connected to the overhead line WC-1 are in
service. The network topology is stored in the Operation Scenario Energisation 400 kV OHL WC-1 which
is activated with the Study Case Overhead Line Energisation.
Figure 19: Frequency dependent parameters of the
line model for Mode 1
The EMT simulation is initialised at π‘ = −20 ππ  and
the integration step size is set to π‘ = 10 ππ . A switch
event is defined to close all three phases of the high
voltage circuit breaker CB.L2 simultaneously at π‘ = 0π
as shown in Figure 20. After the breaker contacts are
closed, transient voltage and current surges are injected and travel towards the receiving end at substation West with the propagation speed of approximately
300 π/ππ  .
For the purpose of this analysis a frequency dependent, distributed parameter line model is used for
overhead line WC-1. The change of the line model
compared to the base case is stored in the Variation
Distributed Parameter WC. The modal transformation
matrix is calculated at a frequency of 500 Hz. The minimum and maximum frequency for the approximation
by rational functions of the propagation factor and the
characteristic impedance are 0.01 Hz and 1 MHz respectively.
The frequency dependent parameters of the overhead
line model are displayed in Figure 19 for Mode 1.
Figure 20: Energisation of OHL WC-1 at substation
Central
DIgSILENT PowerFactory, r4594
15
Switching Transients Example
Max. =552,791 kV
600
300
0
-300
-600
-900
0
L2: Phase Voltage A in kV
T1.6: Phase Voltage A in kV
4
8
12
16
[ms]
20
4
8
12
16
[ms]
20
8
12
16
[ms]
20
500
250
0
-250
Min. =-394,306 kV
-500
-750
0
L2: Phase Voltage B in kV
T1.6: Phase Voltage B in kV
500
250
0
-250
Min. =-410,437 kV
-500
-750
0
L2: Phase Voltage C in kV
T1.6: Phase Voltage C in kV
4
Figure 21: Transient phase-to-ground voltages at the sending and receiving end during the energisation of
OHL WC-1
1200
[A]
800
WC-1.3: Phase Current A/Terminal j
WC-1.2: Phase Current A/Terminal j
WC-1.1: Phase Current A/Terminal j
400
0
-400
-800
0
300
600
900
1200
[us]
1500
1200
[A]
800
WC-1.3: Phase Current B/Terminal j
WC-1.2: Phase Current B/Terminal j
WC-1.1: Phase Current B/Terminal j
400
0
-400
-800
0
300
600
900
1200
[us]
1500
300
[A]
0
WC-1.3: Phase Current C/Terminal j
WC-1.2: Phase Current C/Terminal j
WC-1.1: Phase Current C/Terminal j
-300
-600
-900
-1200
0
300
600
900
1200
[us]
1500
Figure 22: Transient phase currents during the energisation of OHL WC-1
DIgSILENT PowerFactory, r4594
16
Switching Transients Example
Figure 21 shows the transient voltage at the sending
and receiving end of overhead line WC-1 during the
energisation process. The voltage surges are injected
at the sending end of the overhead line and then duplicated and reflected at the receiving end (substation
West). Then the surges travel back to substation Central. Due to attenuation, the magnitude of the wave
decreases and the waveform is distorted, as it propagates along the line. The current and voltage wave
shapes become dissimilar, though they were the same
initially. The following maximum overvoltages arise
during the energisation of overhead line WC-1:
• Phase A: 516 kV
• Phase B: 400 kV
• Phase C: 420 kV
the switch event) is varied randomly by &plusmn; 10 ππ . Furthermore, the scatter time corresponding to the mechanical delay of the closing time of each individual
phase of the breaker is varied randomly by 0...1 ππ  in
each simulation. Figure 25 shows the maximum overvoltages for the π = 100 EMT simulations executed
automatically by the statistical tool in PowerFactory.
Figure 25 documents the maximum line-to-earth overvoltages at substation West resulting from each simulation executed during statistical analysis. The plot
documents the overvoltages resulting from the energisation of overhead line WC-1 from substation Central
for all three phases.
As demonstrated, the overvoltages significantly depend on the breaker closing time and also the operation scenario, such as e.g. energisation from substation West or Central. For economic reasons the
insulation design for self-restoring insulation is usually
not based on the maximum prospective overvoltage
of all investigated cases. Instead the design is based
on a probabilistic approach to withstand only a certain
percentage, e.g. 98%, of the prospective overvoltages
which are calculated in a statistical analysis.
Figure 22 shows the current surge along the line. In
phase A a current surge of approximately 1080 A is injected into the line, in phase B the amplitude is 845 A
and in phase C 267 A. The propagation time of the
first line segment is approximately 234 ππ . Thus the
injected current surge arrives at the first point of transposition only after 234 ππ  which can be observed in
Figure 22. The surge arrives at SS West (open end
of overhead line WC-1) approximately 712 ππ  after the According to the insulation coordination standard IEC
60071-2 first the maximum overvoltages are detercircuit breaker is closed.
mined using EMT simulations. The maximum overThe overvoltages resulting from line energisation voltages are documented in Figure 25 and are based
highly depend on the magnitude of the injected surge on the statistical analysis. As a next step, the repat the sending end of the line. The magnitude of the resentative overvoltage πππ is derived from the maxinjected surge depends mainly upon the voltage in- imum overvoltages. Secondly, the coordination withstantaneous value (point on the waveform) at which stand voltage πππ€ is calculated from the representathe circuit-breaker contacts close electrically. Since tive overvoltage using the coordination factor πΎπ , as
the point on the waveform of the voltage depends on follows:
the circuit breaker closing instant, statistical studies
should usually be performed. As the circuit breaker
πππ€ = πππ &middot; πΎπ
closing time is of random nature in reality, all potential
breaker closing times and thus overvoltages should be
The coordination factor πΎπ makes allowance for limevaluated.
itations in the modelling, shape and duration of an
The randomness of the circuit breaker closing time overvoltage. For the deterministic approach (non-self
is modelled in PowerFactory by means of statistical restoring insulation) in the insulation coordination πΎπ
analysis. The statistical analysis tool in PowerFactory is usually 1.0 . For a probabilistic approach it is based
runs a number of π simulations. In each simulation on the statistical analysis.
the breaker closing time is varied randomly within a
defined range. Additionally, breaker pole scattering For that purpose, the risk of failure π(π ) is calcucan be included in the statistical analysis in order to lated based both on the probability distribution of the
account for deviations in the closing time between the overvoltage π (π ) and the probability of the insulation
strength π (π ) and is illustrated in Figure 23.
three phases.
An example of a statistical switching analysis is pro∫οΈ
vided in this section. The overhead line WC-1 from
π(π ) = π (π ) &middot; π (π ) ππ
the previous simulation is used for this purpose. For
the statistical analysis, 100 simulations are run. For
each simulation the breaker closing time (defined in Figure 23 shows the probability distribution of the
DIgSILENT PowerFactory, r4594
17
Switching Transients Example
overvoltages and the failure probability of the dielectric strength of the insulation. According to the figure,
a voltage of 1.5 π.π’. is most likely. For that voltage the
failure of the insulation is very small. Thus, the risk
of failure R(U) is also relatively small. For higher voltages, e.g. 2 π.π’., the probability for overvoltages is
smaller. However, the probability of insulation failure is
much higher. Thus, the overall risk of failure is higher.
For very high overvoltages the risk of insulation failure
is significant. However, the probability of such high
overvoltages is almost zero and thus the risk of failure
is also nearly zero.
Table 1: Statistical overvoltages for different bands
around the mean π
1
f(U)
0,8
Probability in p.u.
The insulation for self-restoring insulation, such as
overhead lines, is usually designed for the 98 %
percent value of the prospective voltage stresses.
The statistical tool in PowerFactory determines the
prospective overvoltage π for a defined probability
π (π ) (e.g. 98%). The analysis is based on the π number of EMT simulations executed during the statistical
analysis. In this example (π = 100 EMT simulations)
the statistical results in Table 1 are obtained for energisation of overhead line WC-1 from the substation
Central.
P(U)
R(U)
0,6
0,4
ππππ
π (π )
π
π’πππ₯
(π − π, π + π)
65.9 %
471 ππ
492 ππ
(π − 2π, π + 2π)
95.5 %
471 ππ
548 ππ
(π − 3π, π + 3π)
99.73 %
470 ππ
593 ππ
0,2
0
-3
-2
-1
0
1
2
3
4
Stress, e.g. voltage in p.u.
The coordination withstand voltage πππ€ is chosen
based on the 2 % probability and is equal to 564 ππ
in this case. This means that only 2% of the simulated
overvoltages exceed this value.
Figure 23: Risk of failure π(π )
In the following insulation coordination study the required withstand voltage πππ€ is now determined
based on the coordination withstand voltage πππ€ and
The distribution of the breaker closing time and thus
using the safety factor πΎπ  and altitude correction facthe transient overvoltages π (π ) is usually a normal
tor πΎπ :
distribution. Consequently, a normal distribution function can be assumed for the breaker closing time and
the resulting overvoltages:
πππ€ = πππ€ &middot; πΎπ  &middot; πΎπ
1 π’−π 2
1
√
&middot; π− 2 &middot;( π )
π&middot; 2&middot;π
Finally, the standard withstand voltage ππ€ is selected
according to the tables in IEC 60071-1. In case the
required withstand voltage πππ€ exceeds the desired
The mean π of the distribution function and the stan- standard withstand voltage defined in IEC 60071-1,
dard deviation π are determined using the statistical the prospective overvoltages can be reduced by additool in PowerFactory. The normal distribution function tional surge arresters, pre-insertion resistors or point
is shown in Figure 24 and shows the probability versus on wave switching.
standard deviation π in general.
It should be noted that usually 1000 runs are recommended for a statistical switching study in order to en0,4
sure the statistical significance of the study.
Probability overvoltages in p.u.
π (π’) =
0,3
0,2
68.5 %
0,1
95.5 %
99.7 %
0
-4
-3
-2
-1
0
1
2
3
π 4
DIgSILENT PowerFactory, r4594
Figure 24: Probability distribution of switching overvoltages
18
overvoltages in kV
Switching Transients Example
600
500
400
300
200
Phase A
100
Phase B
Phase C
0
0
20
40
60
80
100
number of simulation n
probability in %
100
Phase A
80
Phase B
Phase C
60
40
20
0
350
400
450
500
550
600
voltage in kV
Figure 25: Probability distribution of energisation overvoltages for OHL WC-1
TRV Analysis of Shunt Reactor the model in order to do the TRV analysis.
Switching off
For reactive power compensation a shunt reactor is
installed at substation Central as shown in Figure 2.
The shunt reactor is a three-phase five-leg core type
with a rated reactive power of 200 Mvar. The reactor is switchable and has 4 steps. Thus, it is able to
consume 0 π π£ππ, 50 π π£ππ, 100 π π£ππ, 150 π π£ππ and
200 π π£ππ. The reactor is connected directly to the
400 kV busbar via a 400 kV circuit breaker.
In this study case the transient recovery voltage (TRV)
is analysed when the shunt reactor in substation Central is switched off. Before disconnecting, the shunt
reactor is operated at step 2, supplying the grid with
200 Mvar of reactive power. The reactor is then disconnected by opening the CB. The objective of this
study case is to analyse the transients following the
reactor drop out.
For the purpose of this analysis the variation Detailed
CB model shunt reactor is activated which contains
a more detailed model of CB.R4 with a two parameter curve according to IEC 62271-100 to model the
dielectric strength of the breaker during the transient.
Furthermore, winding capacitances of the shunt reactor and additional stray capacitances are included in
DIgSILENT PowerFactory, r4594
Figure 26 shows a simplified single line diagram of the
most important components of the switching bay of the
shunt reactor. The shunt reactor is tapped at step 1.
The inductance of the reactor is 10.19 π». The capacitance on the source side of the CB corresponds to the
lumped capacitances of the instrumental voltage and
current transformers. They are assumed to be equal
to 4 ππΉ . The capacitances on the shunt reactor side
mainly represent the winding stray capacitances of the
shunt reactor and are assumed to be equal to 1 ππΉ .
68.51 ππ»
4 ππΉ
1 ππΉ
10.19 π»
4.4
Figure 26: Equivalent circuit diagram showing the
source inductance and stray capacitances of the shunt
reactor bay
The network impedance at the shunt reactor is calcu-
19
Switching Transients Example
lated using the Frequency Sweep Calculation Tool in
PowerFactory. The inductance is 68.51 ππ» at substation Central in case the shunt reactor is out of service.
Based on the network capacitances and inductances
the approximate oscillation frequency can be calculated as described in section 3.3. The load side oscillation frequency is approximately 1.58 kHz:
ππ =
parameters for the TRV envelope are based on the
maximum peak voltages π’π and rate of rise of recovery
voltage ππππ . In this example the following parameters are assumed for the breaker capability curve:
• Peak TRV voltage π’πΆ : 787 ππ
• Time to π’πΆ : 112 ππ
1
1
= 1.58 ππ»π§
&middot; √οΈ
2π
πΏπ &middot; πΆπ
Figure 28 shows the transient oscillation voltage on
the shunt reactor side after disconnecting the device
together with the phase currents through the circuit
breaker connecting the reactor with substation Central.
The first zero-crossing occurs in phase A after the circuit breaker is triggered by a simulation event. At π‘ =
0.607 ππ  the current in phase A is zero and the breaker
is opened. Then, 3.404 ππ  later at π‘ = 4.011 ππ  the
current in phase C goes to zero and the ideal switch
is opened for that phase. In phase B the switch is
opened at π‘ = 7.314 ππ .
Due to the 90β phase shift between the interrupted
current and the supply voltage (inductive load), the
voltage in each phase of the isolated shunt reactor is
at its peak when the breaker contacts separate. Thus,
the stray capacitances in each phase are charged with
energy πΈπΆ when the current is interrupted. The stored
energy πΈπΆ is:
1
πΈπΆ = &middot; πΆ &middot; π’2
2
The energy is now oscillating between the inductance
and capacitance until the transient is damped out and Figure 27: Equivalent circuit of source and load side
the load side voltage is zero. Figure 28 shows the
transient oscillation on the load side. The peak value
of the voltage is approximately 315 ππ and the fre- In the investigated case the maximum peak voltages
quency corresponds to the resonant frequency of the and RRRV of the TRV are within the defined limits for
circuit in Figure 26. Applying a Fast Fourier Trans- all three poles. The following results are obtained:
former (FFT) to the load side transient voltage results
• Phase A: π’π = 626 ππ ; ππππ = 2.57 ππ /ππ
in the plot in Figure 27. The dominant frequency is
between 1.8 kHz and 1.9 kHz as predicted by the sim• Phase B: π’π = 625 ππ ; ππππ = 2.47 ππ /ππ
plified hand calculation.
• Phase C: π’π = 627 ππ ; ππππ = 2.53 ππ /ππ
Following the current interruption in each phase, the
TRV, as described in section 3.3 arises across the The interruption of small inductive currents frequently
breaker poles. The TRV for each phase is depicted results in current chopping and virtual current chopin Figure 29 together with the breaker capability curve ping which might lead to re-ignition and even multiple
of the CB. According to IEC 62271-100 the TRV en- re-ignitions. Both effects can easily be included in the
velope is defined by a two-parameter curve. The input breaker model used for this study.
DIgSILENT PowerFactory, r4594
20
Switching Transients Example
600
[kV]
400
200
0
-200
-400
0
T1: Phase Voltage A
T1: Phase Voltage B
T1: Phase Voltage C
4
8
12
16
[ms]
20
8
12
16
[ms]
20
200
[A]
100
0
-100
-200
-300
0
4
CB phase A: Phase Current/Terminal i
CB phase B: Phase Current/Terminal i
CB phase C: Phase Current/Terminal i
Figure 28: Load side oscillation voltagesand phase currents in the high voltage circuit breaker
1000
500
0
-500
-1000
-1500
0,0
2,5
CB phase A: Voltage Difference in kV
TRV Limit Phase A T10: TRV_limit_neg
TRV Limit Phase A T10: TRV_limit_pos
5,0
7,5
10,0
[ms]
12,5
0,0
2,5
CB phase B: Voltage Difference in kV
TRV Limit Phase B T10: TRV_limit_neg
TRV Limit Phase B T10: TRV_limit_pos
5,0
7,5
10,0
[ms]
12,5
0,0
2,5
CB phase C: Voltage Difference in kV
TRV Limit Phase C T10: TRV_limit_neg
TRV Limit Phase C T10: TRV_limit_pos
5,0
7,5
10,0
[ms]
12,5
1000
500
0
-500
-1000
-1500
1000
500
0
-500
-1000
-1500
Figure 29: Transient recovery voltage (TRV) and dielectric strength of circuit breaker
DIgSILENT PowerFactory, r4594
21
Switching Transients Example
CBS2
IS.L2.1
IS.L2.2
IS.L3.2
IS.L1.1
CB.L1
IS.L1.2
IS.L1.3
CWC-2_comp
IS.L0.2
IS.L0.1
π£
4&middot;π
Before the fault, the transmission system is in steady
state as described in section ??.The short circuit is
applied on the line side of the circuit breaker CB.L2
as depicted in Figure 30. To simulate the fault, a 3phase short circuit is triggered at π‘ = 0 π . After 50 ππ
switch events are triggered to isolate the faulted part
of the network. The following circuit breakers have to
be opened:
• CB.L2.1 (substation Central)
• CB.W.1 (substation West)
• CB.W.1 (substation West)
The current in each circuit breaker is interrupted at the
following current zero of each individual phase. The
line is re-connected after clearing of the fault. However, the re-closure action of the line is not simulated
in this study case since the investigation focuses on
the TRV capability of the HV circuit breaker during the
Terminal fault.
The breaker capability curve is modelled according to
the limits defined in IEC62271-100 for a voltage level
of 420 kV. The relevant parameters for the envelope
curve are listed in Table 2 and define a 4-parameter
envelope. The envelope curve defines the maximum
transient voltages which are allowed after the fault interruption across the breaker poles and represents the
dielectric strength of the breaker.
DIgSILENT PowerFactory, r4594
CB.L3
IS.L3.3
0,0
0,00
91,4
ππ =
IS.L2.3
CB.L2
C4_1.1
CB.L0
0,0
0,00
91,4
The detailed breaker model is stored in the Variation
TRV Analysis Terminal Fault which is activated with WC-2.3
the study case TRV Analysis Terminal Fault. Furthermore, all lines connected to the faulted terminal
are modelled as distributed parameter lines. The frequency for travel-time estimation ππ is chosen based
on the line lengt π and propagation time of each line
according to the following equation:
CWC1_comp
CWC1
In this section the transient recovery voltage across
the breaker poles of the circuit breaker CB.L2 in substation Central is analysed, following a terminal fault
on the line side of the circuit breaker. For the purpose WC-1.3
of this analysis the CB.L2 is modelled by detailed circuit breaker model. The breakers include a model of
the dielectric strength during the transient according
to IEC 62271-100.
CBS1
0,0
0,00
91,4
TRV Analysis Terminal Fault
CWC2
4.5
C4_1.2
Figure 30: Fault location of terminal fault
The limits in Table 2 correspond to the short-circuit
duty tests T100, T60 and T30. The duty test T100 corresponds to a short circuit current equal to the short
circuit rating of the CB. In the duty test T60 the short
circuit current is only 60 % of the short circuit rating of
the CB.
Table 2: Parameters of TRV envelope of 420 kV circuit
breakers; terminal faults (T)
Curve
π‘1 /ππ
T100
π’1 /ππ
334
π‘2 /ππ
167
ππΆ /ππ
624
T60
334
11
669
666
T30
-
-
687
137
668
Figure 31 shows the short circuit current flowing from
substation Central to the fault location at the beginning
of overhead line (OHL) WC-1.3. Initially the current
through the circuit breaker is in steady state. At time
π‘ = 0π  the fault is initiated with zero fault impedance
(ππ ππ’ππ‘ = 0 β¦ and ππ ππ’ππ‘ = 0 β¦).
The steady state load current changes into a significantly higher short circuit current in an oscillatory
manner as shown in Figure 31. After a few ππ  the
short circuit current is nearly in steady state. At time
22
Switching Transients Example
π‘ = 50 ππ  a switch event triggers the CBs to open. The The maximum peak voltages π’π and rate of rise of reshort circuit current is then interrupted at the following covery voltage ππππ during the transient for the difcurrent zero (zero-crossing) in each phase.
ferent phases are as follows :
• Phase A:
π’π = 529 ππ ; ππππ = 0.32 ππ /ππ
During the short circuit the terminal voltage at substation Central drops from a peak line-to-earth voltage
of 328.3 ππ to 0 ππ and afterwards returns approximately to its original value. The peak short circuit current through the circuit breaker connected to substation Central is 16.7 ππ΄.
As described in section 3.3 a transient recovery voltage arises across the circuit breaker poles after the
current is interrupted. The TRV appearing across the
circuit breaker poles is the instantaneous values sum
of the voltage from the source and the line side phaseto-earth voltage and is shown in Figure 32. The plot
shows the TRV arising in phase A, B and C together
with the breaker capability curve of the circuit breaker
CB.L2.
30
• Phase B:
π’π = 497 ππ ; ππππ = 0.24 ππ /ππ
• Phase C:
π’π = 489 ππ ; ππππ = 0.14 ππ /ππ
The maximum withstand voltage of the CB for the
T100 duty is 624 ππ and the maximum RRRV is
0.32 ππ /ππ . The transient recovery voltage (TRV)
therefore does not exceed the limits defined in
IEC62271-100. For this particular case a high voltage circuit breaker with a fault current ratio of 100%
of its rated short circuit capability is sufficient for the
application.
Short Circuit
Switch Event
[kA]
20
10
0
-10
-20
600
0
IS.L2.3: Phase Current A/Terminal i
IS.L2.3: Phase Current B/Terminal i
IS.L2.3: Phase Current C/Terminal i
20
40
Short Circuit
60
80
[ms]
100
60
80
[ms]
100
Switch Event
[kV]
300
0
-300
-600
-900
0
C4_1.1: Phase Voltage A
C4_1.1: Phase Voltage B
C4_1.1: Phase Voltage C
20
40
Figure 31: Short circuit current through the CB.L2 during the transient and voltage at substation Central
DIgSILENT PowerFactory, r4594
23
Switching Transients Example
1000
500
0
-500
-1000
-1500
50
54
CB phase A(1): Voltage Difference in kV
TRV Limit Phase A: TRV_limit_neg
TRV Limit Phase A: TRV_limit_pos
58
62
66
[ms]
70
50
54
CB phase B(1): Voltage Difference in kV
TRV Limit Phase B: TRV_limit_neg
TRV Limit Phase B: TRV_limit_pos
58
62
66
[ms]
70
50
54
CB phase C(1): Voltage Difference in kV
TRV Limit Phase C: TRV_limit_neg
TRV Limit Phase C: TRV_limit_pos
58
62
66
[ms]
70
1200
800
400
0
-400
-800
1000
500
0
-500
-1000
-1500
Figure 32: Transient recovery voltage (TRV) and dielectric strength of circuit breaker
References
[1] Juan A. Martinez-Velasco: “Power System Transients: Parameter Determination”, CRC Press,
2009, ISBN 978-1420065299
[2] R. Smeets; L. Sluis; M. Kapetanoviae; D. Peelo;
A. Janssen: “Switching in Electrical Transmission
and Distribution Systems”, Wiley, 2014,
ISBN 978-1118381359
[3] Allan Greenwood: “Electrical Transients in Power
Systems”, Wiley-Interscience, 1991,
ISBN 978-0471620587
[4] DIgSILENT PowerFactory
DIgSILENT PowerFactory, r4594
Line Models”, PowerFactory 2018, DIgSILENT
GmbH, Gomaringen, Germany, 2018
[5] DIgSILENT PowerFactory
Technical Reference Documentation “Cable System”, PowerFactory 2018, DIgSILENT GmbH,
Gomaringen, Germany, 2018
[6] DIgSILENT PowerFactory
Technical Reference Documentation “TwoWinding Transformer”, PowerFactory 2018,
DIgSILENT GmbH, Gomaringen, Germany,
2018
[7] DIgSILENT PowerFactory
Technical Reference Documentation “ThreeWinding Transformer”, PowerFactory 2018,
DIgSILENT GmbH, Gomaringen, Germany,
2018
24
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