analysis of electromagnetic transients in cross-bonded cable

analysis of electromagnetic transients in cross-bonded cable
ANALYSIS OF ELECTROMAGNETIC TRANSIENTS IN CROSS-BONDED CABLE SYSTEMS
USING FREQUENCY DEPENDENT CABLE MODELS
L. Marti, R.H. Brierley, and T.E. Grainger
ONTARIO HYDRO
700 University Ave., Toronto, Ontario
Canada MSG 1X6
ABSTRACT
This paper describes the selection and use of EMTP
frequency dependent cable models in the design of cross-
bonded High Voltage underground cable transmission
systems. Several types of studies are described, from
frequency scans for harmonic analysis to very fast
transients due to cable energization and reactor switching.
Cable sheath grounding, protection, and design
alternatives are discussed, as well as the impact of
accurate modelling in this type of studies. The
advantages and disadvantages of the models used in a
given type of study are discussed, and general
recommendations are provided.
Keywords: EMTP, Cables, Frequency dependence
1. INTRODUCTION
In recent years there has been a considerable amount of
interest in the modelling of underground cables using
transient analysis programs such as the EMTP. High
capital costs, non-self-restoring insulation, and high
replacement costs in the event of insulation failure are
strong incentives to simulate underground cables with
very high accuracy. In North America, underground
cables are generally viewed as the solution to very
specialized situations where the use of overhead lines is
either impractical, or environmentally and aesthetically
objectionable. In some parts of the world, however, high
voltage underground cable transmission is more the norm
than the exception.
The EMTP has a fair number of cable models, and their
relative merits have been discussed and examined
elsewhere [e.g., 1-2]. However, practical experience with
the more advanced models available is just beginning to
accumulate in a significant way. |
This paper describes some of the "basic" transient studies
carried out at Ontario Hydro for the design of HV cable
systems. Examples based on the simulation of a
relatively large 400 kV transmission system with over
250 km of underground cross-bonded cable circuits are
shown for illustration purposes. The model selection
criteria used in each type of transient simulation 1s
discussed, and some practical guidelines and
recommendations are provided.
2. CABLE MODELS IN THE EMTP
The cable models available in the DCG/EPRI version of
the EMTP used at Ontario Hydro can be classified as
follows:
Lumped-parameter models:
* Nominal 7 |
° Cross-bonded uniform ©
e Exact-7
Distributed-parameter models:
* Distributed constant-parameter (CP)
* Frequency dependent “line” model (FD)
* Frequency Dependent Q (FDQ) "cable" model
Lumped-parameter models.
Lumped or concentrated parameter models consist of
multiphase coupled n-circuits, where R, L, and C are
calculated at a given frequency (normally power
frequency). The distributed nature of the cable
parameters can be approximated to some extent by
cascading a number of these *%-sections. The main
drawback of this type of model is the poor frequency
response beyond the frequency at which the parameters
are evaluated. The most commonly-used types of lumped
parameter models are: |
a) Nominal -circuit.
The series branch of the nominal %-circuit is the series
impedance of the cable, and the shunt branches consist of
half of shunt capacitance of the cable.
b) Cross-bonded uniform-7 cable model.
This model is also known as the Ametani cross-bonded
cable model, and it is probably one of the first dedicated
cable models in the EMTP [3]. It represents a major
section of a cross-bonded cable by combining three
nominal n-circuits, where the coupling of the sheaths to
the main conductors is averaged, and the sheaths
themselves are bundled into a single conductor..
c) Exact-T.
The exact-7 model, is the exact frequency-domain
representation of a cable calculated at a given frequency.
It is not a time domain model and can only be used
during single-frequency steady-state and frequency scan
calculations.
IPST 95 - International Conference on Power Systems Transients
Lisbon, 3-7 September 1995
— major section —
minor secton —# -#— Minor section —# —#— Minor section —#
7
153 3 | |
\
030 100
arresters arresters 1
Fig. 1: Major section of a cross-bonded cable.
2) Distributed parameter models
Distributed-parameter models take into account the
distributed nature of the cable parameters, and they are
based on travelling wave theory. In the time-step loop of
the EMTP, the differential equations that describe the
behaviour of an n-conductor cable system in normal
"phase quantities” are first decoupled into n separate
differential equations by means of a linear transformation.
The resulting decoupled system of equations is solved in
“modal quantities". The same linear transformation is
then used to convert the modal solution back to phase
quantities. This linear transformation generally takes the
form of a "modal transformation matrix" Q which relates
phase voltages and currents to modal voltages and
currents, with the relationships
=0'-V
phase
— 1.
Lie Q hase
V ode
The distributed parameter models most commonly used
in the EMTP are:
a) Distributed constant-parameter (CP) model.
This model is sometimes referred to as the Dommel line
model. Parameters R, L, and C are assumed to be
constant, and the shunt conductance G is ignored. The
modal transformation matrix Q is assumed to be constant
and real. R, L, and Q are normally calculated at 1 kHz.
Since this model is based on a
representation, only L and C are distributed, and R is
lumped in three places. This mode! is computationally
fast because it produces sparse contributions to the nodal
admittance matrix of the system, and it is more accurate
than concentrated-parameter -circuit representations.
Because Q 1s assumed to be constant and real, it is not
possible to obtain accurate answers at both high and low
frequencies. This model can be quite useful to simulate
secondary cables and for other specialized applications
[4].
b) Frequency Dependent line (FD line) model
This model is also known as the JMARTI overhead line
model. The frequency dependence and distributed nature
of the parameters are well approximated as long as the
modal transformation matrix can be assumed to be
constant and real [5]. While this is probably the most
lossless line
.60-
Magnitude
o
O. OO ETT TA TATI III AA,
0 1 J 10 10 10
Frequency (Hz)
Fig. 2: Magnitude of column 3 of Q for a three-phase
cable (6 curves).
accurate model presently available to simulate overhead
lines, it can run into problems in the case of underground
cables, because the elements of the modal transformation
matrix Q can change quite drastically with frequency, as
shown in Figure 2.
c) Frequency Dependent Q (FDQ) cable model
This model 1s also known as the LMARTI cable model.
It takes into account the frequency dependence of the
cable parameters, as well as the frequency dependence of
the modal ‘transformation matrix Q [6]. It is the most
accurate cable model presently implemented in the
EMTP, and unlike other distributed parameter models, it
can accurately reproduce high and low frequency
phenomena in the same simulation. The FDQ model
requires more resources in terms of storage, but in most
cases 1t 1s only 30% slower than a comparable FD model.
3 MATCHING THE MODEL TO THE SIMULATION
When performing system studies with the EMTP, a
number of factors should be considered in the selection of
cable model: accuracy, computational speed and
suitability for the type of simulation.
To model a cross-bonded cable with the highest accuracy
and detail possible, each major section should be
modelled explicitly, using three six-conductor FDQ
models to represent each minor section. For example, to
model a 25 km cable with 400 m minor sections, a total
of 43 six-conductor FDQ models would be required, and
the time step of the transient simulation would have to be
at least smaller than the travel time the fastest mode of a
400 m minor section (e.g., T = 2.3 ps). The strain on
computational resources due to the small time step would
be very large if several such cables have to be modelled,
and/or statistical studies are needed to study energization
transients.
Computational savings in the order of 30% could be
achieved if an FD model with constant Q were used to
model each minor section. However, the FD model is
unsuitable for the evaluation of sheath voltages and
currents [2], as illustrated in the frequency scan of a
line-to-ground fault termination of a 10 km cable shown
in Figure 3.
IPST ’95 - International Conference on Power Systems Transients
Lisbon, 3-7 September 1995
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Frequency (Hz)
Fig. 3: Magnitude of sheath currents.
The detailed representation of each minor section is not
necessary in all types of system studies. In simulations
where it is not necessary to monitor sheath voltages and
currents (e.g., energization transients, reactor switching,
etc.), it is possible to make some simplifications. The
effect of sheath cross-bonding on core conductors can be
approximated by averaging the core-sheath and sheath-
sheath terms of the impedance and admittance matrices.
Also, the effect of grounding the sheaths at the ends of
each major section can be approximated by assuming that
the sheaths are continuously grounded (i.e., at zero
potential throughout the entire cable length) so that they
can be eliminated. With these approximations, a three-
conductor equivalent of a cross-bonded cable can be
obtained and modelled with an FD model. The main
advantage of this continuously cross-bonded model is that
it does not limit the simulation time step to a fraction of
the travel time of a minor section, thus allowing
significant savings in computational time.
The suitability and validity of the three-conductor FD
representation have been examined in considerable detail
at Ontario Hydro for use in large system studies, both
using frequency scan comparisons with detailed exact-T
representations, and with time domain simulations using
the FDQ model as reference solutions. Figure 4 shows
the conductor voltage of an unfaulted phase of a cross-
bonded cable under line-to-ground fault termination. The
total length of the cable is 25.2 km. The solid trace is
1000-07
800 .0-
=
600. 0-
400.0-
200.0-
0 Y (TITI TT a7 TT | LAAN BALL TT 9" т T TTT TT
10 334 6 10 2 34 6 10 2 34
Frequency (Hz)
Fig 4: Frequency scan of l-t-g voltages, 21 major
sections. Solid = exact-T, Dashed = FD.
the reference response calculated using 21 major sections
modelled explicitly with exact-m models for each 400 m
minor section, and the dashed trace shows the response of
the continuously cross-bonded three-conductor FD model.
For the FD model, Q 1s assumed to be constant and real,
and 1t 1s evaluated at 1 kHz. Figure 5 shows the currents
in the faulted conductor. These results illustrate that the
continuously cross-bonded 3-conductor FD model 1s
sufficiently accurate for transient simulations not
involving the study of sheath overvoltages
4. SYSTEM STUDIES
In the design of an underground cable sub-system, a
number of transient studies should be carried out to
calculate transient and temporary overvoltages in order to
establish insulation and protective equipment
specifications for major system components such as
transformers, reactors and generators. From a modelling
point of view, three basic types of studies can be
considered:
- Frequency scan analysis studies to determine possible
resonant conditions
- Sheath protection studies to determine the
specifications of the arresters used to limit sheath
overvoltages at cross-bonding points.
- Switching transients studies for a number of system
design purposes, such as switching and impulse
insulation strength levels, arrester specification and
circuit breaker specification, to name a few.
From a modelling point of view we will include
temporary overvoltage studies in the same general
category as switching transient studies. The simulation of
temporary overvoltages often involves slow as well as
fast transients, because temporary overvoltages usually
follow some kind of switching activity during which fast
transients may be involved. However, there is no need to
make a modelling distinction when FDQ or three-
conductor FD models are used since given they are
accurate over a wide frequency range.
м
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o
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1 —
2—
т
10 Tr TEE E PT 7° , TEE ET y + УЕ
10 2 34 6 10 2 34 6 10 2 3 4 6 10
Frequency (Hz)
Fig 5: Frequency scan l-t-g fault current, 21 major
sections. Solid = exact-n, Dashed = FD.
IPST *95 - International Conference on Power Systems Transients
Lisbon, 3-7 September 1995
4.1 Frequency Scan Studies
Conceptually, a frequency scan study of system
resonances consists of two parts. First, the frequencies at
which series and parallel resonances take place are
identified by means of driving point impedance
calculations at various points in the system. Second, it
must be assessed if there is a source that will provide the
energy to drive the system into a resonance situation. For
example, if a frequency scan identifies a series resonance
at 150 Hz, it 1s necessary to assess if there is a legitimate
way to obtain a "sustained" 150 Hz energy source. This
150 Hz energy source can be created by a temporary
equipment configuration or contingency situation.
However, unless there is a 150 Hz source of energy for
the duration of the contingency, there will not be any
serious consequences or equipment damage.
The most accurate way to perform harmonic analysis
studies in the EMTP is using exact-7 models. Since
there are no approximations or modal transformations
involved, the exact-7 model is an ideal tool for model
validation and harmonic analysis. For frequency scan
calculations, these x-circuits evaluated at each of the scan
frequencies are stored in a file and read as they are
needed for each steady-state solution of the frequency
scan. Frequency scan studies can, for example, show that
grounding a transformer neutral through a reactor can be
an effective way to limit line-to-ground fault currents in
an overhead system, but can lead into resonant conditions
in a cable system.
4.2 Sheath Protection Studies
For relatively long cables the preferred sheath bonding
method is cross-bonding. The cable is subdivided into
minor and major sections, where the length of a minor
section is usually determined by practical limitations such
as reel size. The sheaths of each minor section are
transposed or “cross-bonded", and grounded at the ends
of each major section (see Figure 1).
Under balanced steady-state operation, the sheath currents
induced on each minor section are 120 degrees apart, and
the net sum over a major section is zero. This means that
power frequency losses due to sheath currents are
essentially eliminated, except for slight unbalances due to
cable layout. Even these unbalances can be minimized
by also transposing the main conductors at each minor
section as the cable is laid. Under switching and
unbalanced fault conditions, a change in the physical
location of the sheaths at each cross-bonding point
represents an electrical discontinuity. Therefore,
travelling waves will be reflected, and relatively high
transient sheath overvoltages will occur at the sheath
cross-bonding points. These overvoltages are normally
controlled by means of metal oxide surge arresters or
MOVs.
The basic design criterium for the selection of sheath
protection MOVs is to keep sheath overvoltages as low as
practical. Within this general constraint, the MOV
protective level should be high enough to allow the
survivability of the surge arresters under normal switching
operations (e.g., cable energizations), including switching
associated with a fault external to the cable circuit.
The impulse withstand level of sheath insulation can be
expected to be lower than factory specifications after the
cable 1s laid. Furthermore, ageing, humidity and other
environmental factors contribute to lowering the effective
impulse withstand level over the lifetime of the cable. It
is not possible to obtain generic figures regarding the
impulse withstand capabilities after the above factors are
taken into consideration. Therefore, from a practical
point of view, it is necessary that the cable manufacturer
explicitly guarantees the long-term sheath insulation
impulse withstand capability based on the MOV
protective level selected.
All studies for the determination of sheath protection
specification should be carried out using 6-conductor
FDQ cable models (3 cores and 3 sheaths), in order to
obtain an accurate, full-spectrum representation of the
cable. The length of each minor section is usually
determined by the length of cable that will fit on a reel
(e.g., 400 m for a 400 kV cable is more or less typical).
In the EMTP, each cross-bonding point should be
modelled explicitly, and sheath protection MOVs should
be modelled as ZnO arresters. It is not necessary to
model each MOV at every cross-bonding point along the
cable. MOV energy absorption drops sharply after the
first two major sections, and including arrester models in
more than three major sections into the cable (at sending
and receiving ends) is probably unnecessary.
The rest of the system probably does not need to be
modelled in great detail, but it is often a convenient (and
conservative approach) to re-use the same system
representation used in other transients studies (e.g., using
three-conductor) FD models. Compared to the resources
needed to model the cable being studied in detail, the
computational savings that could be achieved using
simpler models on other cables in the system is not
justifiable.
The energy absorbed by the sheath MOVs during cable
energization transients depend on the length of the cable,
the number of cables connected at the sending end, and
the rating of the MOVs. During the energization of a
cable, the arresters closest to the sending end of will
absorb the highest energy. As the number of cables
connected to the sending end increases, the energy MOV
absorption also increases (the effect is similar to that of
back-to-back capacitor bank energization). Arrester
energy absorption drops rapidly after the first major
section. For example, in the energization of a 25 km
cable, the energy absorbed by 6 kV MOVs in the first
cross-bonding point of the first major section was 7 kJ,
whereas in the first cross-bonding point of the second
major section energy absorption dropped to 4.5 kJ.
The MOV duty due to a line-to-ground fault external to
the cable depends on several factors:
1) Number of cable circuits connected to the faulted bus
2) Relative length of the cables contributing current to
the fault
3) System fault level
4) Grounding resistance
IPST *95 - Intemational Conference on Power Systems Transients
Lisbon, 3-7 September 1995
The energy duty of sheath protection MOVs depends
strongly on the core currents during a line-to-ground
fault. The larger the fault current, the higher the energy
absorbed by the arresters.
The number of cable circuits connected to the bus affects
the magnitude of the initial high frequency transient after
the occurrence of a line-to-ground fault. The larger the
number of circuits leaving the bus, the higher the initial
current peak. On the other hand, as the number of cables
connected to the bus increases, the contribution of each
cable to the fault current will be lower. The net result 1s
that the dominating factor is the magnitude of the core
currents; therefore, fewer cables at the faulted bus mean
higher arrester duty. The worst contingency would be if
there were only one cable feeding the fault. In such a
case, the entire fault level contribution (minus fault
current contribution from local generation) would be
carried by one cable. This worst case scenario 1S very
similar to an "internal" cable fault; that is, a fault that
occurs somewhere along the cable (but not at the
terminals). Note that it is not practical or feasible to
specify MOVs that will withstand such extreme
contingencies.
The grounding resistance at the sectionalizing and cross-
bonding points also affects, albeit to a lesser extent, the
energy absorbed by the MOVs under fault conditions.
The relationship is not straightforward. A very high
grounding resistance increases sheath overvoltages, while
a very low resistance increases sheath currents. Studies
carried out at Ontario Hydro suggest that a grounding
resistance in the order of 2 to 4 ohms results in the
lowest energy absorption levels for 6 kV rated MOVs.
Beyond the first two major sections, grounding
requirements are not as important, and special grounding
arrangements beyond those required for safety regulations
are probably not necessary.
Depending on the fault level of the system, the overriding
factor in the specification of sheath protection MOVs can
be the energy absorption requirements during external
line-to-ground fault conditions. Under such conditions,
energy requirements due to cable energization tend to be
a relatively small and well-defined factor and they are
simply be added to the energy requirements due to line-
to-ground faults. Note however, that energization
transients produce higher and faster transient overvoltages
900.
800.
700 .—
600.
500.—
Voltage (kV)
400. Ele 77T
Probability 10) 99 90 70 50 30 10 5 2 1
Fig. 5: Probability distribution of peak energization
voltages for 10 buses.
than line-to-ground faults. Therefore, energization
transients must be taken into account in the specification
of the protective level of the selected MOVs.
43 Switching Transients Studies
It is probably unnecessary to use different cable models
in transient simulations where the cable sheaths do not
have to be modelled explicitly. Therefore, we will only
discuss two types of switching surge studies, and consider
them representative examples from a cable modelling
point of view.
4.3.1 Energization Studies
In energization transients studies, cross-bonded cables
should be modelled using FD models. The main reasons
for this choice are:
- For the cables under consideration, the three-
conductor FD model reproduced core voltages and
currents in the mid- to high frequency ranges very
accurately.
- The use of the three-conductor FD model allowed the
use of a larger At than 1t would have been necessary
if each 400 m minor section and each cross-bonding
point had been modelled explicitly.
- ¡Given the large number of simulations required in
statistical studies, the three-phase FD model provided
an advantage in terms of computational speed, without
any practical loss of accuracy, when compared to an
equivalent three-conductor FDQ model.
- Monitoring of sheath voltages and currents 1s not
necessary in this type of simulation.
For modern SF6 breakers, the contact spread can be
assumed to have a normal distribution, and contact spread
values can be less than 2 ms 90% of the time (which
results in a standard deviation 0=1.556 ms). As in the
case of overhead line energization studies, EMTP
"Statistics" should be made, with 100 independent
energizations for each study. The 100 case peaks
(highest voltage reached on any of the three phases for
each case) are retained, and plotted on a (normal)
probability scale (see Figure 5). The truncation level,
which is a best estimate of the maximum overvoltage
which can be produced by the system, can be calculated
from the determined 2% level assuming a Weibull
probability distribution. On the few occasions where the
EMTP actually calculates a slightly higher maximum
value, the higher EMTP value should be used.
4.3.2 Reactor Switching
In the case of long cables, it 1s often necessary to connect
shunt reactors for the purpose of voltage control. These
shunt reactors can be switchable for short term voltage
control, or can be placed on a more or less permanent
basis at the ends of the HV cable itself. Switchable
IPST ?95 - Intemational Conference on Power Systems Transients
Lisbon, 3-7 September 1995
Switching 150MX Tertiary heactor With Reactor Breaker
17.5 Curren E Chopi) - Ne Reactor Breaker Arrester
Voltages: Scale 10" (-5)
Recovery Vig (2nd pk] = 185 kV pk
2.004
1.504 -
4 . ”
] \
Cc. 50 —— = x oo .. / 4. . > . X . \ +, 7
0.00 na o —— —— de и ma ld Lim wee [RR SY 00e ВН
-1.00-
- 1.50 т т т
0.34 0.35 0.36 0.37 0.38 0.39 0.4
Time 10**(-2)
Fig. 6: Shunt reactor switching. Reactor breaker
voltages. No surge arresters.
reactors are usually installed on the tertiary winding of
step-down transformers, to take advantage of low voltage
switchgear. Switching out a reactor produces hi:
frequency transients which may result in arc re-igni:
and re-ignition overvoltages.
When a reactor is switched out of service, the vo: . :
across the reactor oscillates at very high frequency und
eventually decays as the energy stored in the reactor is
dissipated via reactor losses. The frequency of oscillation
depends on the size of the reactor, and the stray
capacitances across the reactor (and breaker bushings).
The magnitude of the transient voltage across the reactor
also depends on the magnitude of the current chopped,
which in turn, depends of the type of breaker and voltage
level. The magnitude of the voltage across the breaker
depends on the voltage across the reactor as well as the
voltage on the "source side”. The reactor and source-side
voltages oscillate at different frequencies, therefore, the
magnitude of the transient recovery voltage across the
breaker is generally the sum of the magnitudes of source-
side and reactor voltages.
Consider, for example, switching out a 150 MVA shunt
reactor connected to the 66 kV winding of a
400/230/66 kV autotransformer bank, with cables
connected to the 400 kV and 230 kV buses. Figure 6
shows the Transient Recovery Voltage (TRV) across the
breaker terminals, as well as the reactor and source side
voltages. The assumed current chopping level is 7.5 A.
The cable was modelled assuming the sheaths are
continuously cross-bonded and grounded. This simulation
indicates that TRV voltages in the order of 185 kV peak
or 3.4 pu can be produced. If no action is taken to
control the recovery voltage across the breaker, the
magnitude and fast rate-of-rise of the TRV, would result
in breaker re-strike.
Surge arresters at both the shunt reactor and at source
side of the breaker (tertiary terminals of the
autotransformer) would limit overvoltages at the reactor
terminals, but would not be sufficient to limit the voltages
across the breaker terminals. On the other hand,
connecting 54 kV surge arresters across the contacts of
the circuit breaker terminals would limit the recovery
voltage to 86 kV or 1.6 pu, and it would eliminate the
risk of re-ignition.
4. CONCLUSIONS
When using the EMTP to carry out system studies, it is
desirable to have very high accuracy within reasonable
limits imposed by computer resources. It is also desirable
to have as few modelling choices as possible, because the
design engineer should be more concerned with the
studies being conducted than with EMTP-specific
modelling details and idiosyncrasies.
For underground cross-bonded cables, three models
and/or modelling techniques can cover most of the
transient simulations used in transients system studies:
1. Exact-m representations for
frequency scan studies.
steady-state, and
2. Explicit modelling of a the cross-bonded cable under
consideration using six-conductor FDQ models for
each minor section to examine sheath overvoltages
for sheath protection studies.
3. Three-conductor FD models where sheaths are
assumed to be continuously transposed and grounded
for simulations where core voltages and currents are
important. A six-conductor FD model, on the other
hand, 1s not generally suitable for the simulation of
sheath overvoltages.
ACKNOWLEDGMENTS
The authors would like to thank Dave Peelo and Jack
~ Sawada from B.C. Hydro, and Mike Foty and Atef Morched
from Ontario Hydro for their useful discussions and practical
insights.
REFERENCES
[1] H.W. Dommel, "The EMTP" Theory Book, Second
Edition. The University of British Columbia, 1994.
[2] L. Marti "Simulation of Electromagnetic Transients
in Underground Cables using the EMTP",
Proceedings APSCOM 93, Hong Kong, December
1993.
[3] N. Nagaoka and A. Ametani, "Transient Calculations
on Crossbonded Cables". IEEE Transactions on
Power Apparatus and Systems, pp. 779-787, April
1983. |
[4] H.W. Dommel, "Simulating travelling waves inside
and outside GIS enclosures with the EMTP",
Electricity Today - Canada, Vol. 7 No. 3, March
1595.
(5 "KR. Marti, "Accurate modelling of frequency-
cependent transmission lines in electromagnetic
transients simulations”, IEEE Trans. Power App.
Syst., vol. PAS-101, pp. 147-157, Jan. 1982.
[6] L. Marti, "Simulation of Transients in Underground
Cables with Frequency-Dependent Modal
Transformation Matrices". [EEE Transactions on
Power Delivery, Vol. 3, No. 3, pp.1099-1110, July
1988.
IPST ’95 - International Conference on Power Systems Transients
Lisbon, 3-7 September 1995
10
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