Electromagnetic Transient in Power System and Insulation Coordination Studies

The University of British Columbia Electric Power Group Department of Electrical & Computer Engineering; Power Systems Consultants, Vancouver, Canada

Switching and Lightning Surges in Power Systems Hermann W. Dommel June 2012 Email: [email protected]

Presentation Outline

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• Closing and re-closing operations on transmission lines (line energization) • Reduction of overvoltages in closing and re-closing operations on transmission lines • Computer models for closing and re-closing operations on transmission lines • Examples for closing and re-closing operations on transmission lines • Lightning surges

• Example for temporary overvoltages • Examples for subsynchronous resonance • Example for single-line-to-ground fault on transmission lines The University of British Columbia

Presentation Outline

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• Example for transient recovery voltage • Example for linear resonance after opening a transmission line in parallel with another line • Examples for steady-state coupling between parallel transmission lines • Capacitor switching • Inrush Currents

• Interruption of small inductive currents • Real-time simulators, EMTP-type software • Specific references, general references The University of British Columbia

Closing & Re-closing Operations on Transmission Lines

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• Circuit breakers at both ends I and II cannot close simultaneously.

• Therefore, the voltage surge travelling down the line doubles at the open end.

f openend 

f open-end = 250 Hz for 300 km

1 4

• Low impedance termination (dotted).

f lowZ

1  2 The University of British Columbia


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• In reality, overvoltage can be >2.0 p.u. because: • • • •

not infinite source in A (therefore reflections), line may have "trapped charge" from preceding opening operation, three poles do not close simultaneously, there are multi-velocity waves on a three-phase line (zero-sequence wave speed is slower than positive sequence wave speed), • etc. • Approximate classification (from a paper by M. Erche [1]):

The University of British Columbia


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Closing & Re-closing Operations on Transmission Lines •

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Statistical distribution • Overvoltage is not a single value, but statistically distributed because overvoltage depends on Vsource at instant of closing,

• three poles do not close simultaneously. •

Closing times

• Many cases must be run with different circuit breaker closing times, that are either varied • statistically, • or systematically. The University of British Columbia


•

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Cumulative frequency distribution

from 100 closing operations on digital computers and transient network analyzers (TNA’s).

•

2 % value is often used to define overvoltage with one number



•

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If insulation can withstand the 2 % overvoltage value, then 98 % of switching

operations will statistically be successful. •

2 % of switching operations may statistically cause insulator flashover.

•

By opening circuit breaker and re-closing again, arc will be extinguished (self-restoring insulation).



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Voltage/time curves •

Peak instantaneous overvoltage is not enough to say whether flashover

across insulator occurs. •

Waveshape is also determining factor.

•

For nice laboratory impulses, voltage/time curves can be obtained.

•

Actual waveshapes are much more complicated, but standard impulse waveshapes are needed for laboratory testing,

to meet impulse test standards. •

There are flashover models, such as the integral method, but rarely used:

t2



v( t )  v0 dt  F

t1



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Events in re-closing operations • A fault occurs, usually in one phase. • The transmission line is de-energized (switched off at one end, then on other end). • On unfaulted phases, the current is capacitive when remote end is already switched off. Therefore, current and voltage are 90 ° out of phase. • When current interrupts at current zero, voltage on line is at its maximum (say, at -1.0 p.u.). • If circuit breaker re-closes when source voltage is at its opposite

maximum (say, at +1.0 p.u.), there is a voltage change of 2.0 p.u. • This re-closing operation with “trapped” charge produces the highest overvoltages. The University of British Columbia


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Events in re-closing operations • The overvoltage is now 3.0 p.u.


Reduction of Overvoltages in Closing and Re-Closing

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Operations on Transmission Lines 1. Controlled closing • Contacts close at instant when voltage is close to zero across the contacts. • Requires some prediction of voltage across contacts. • Prediction is easy with a sinusoidal voltage on the source side, and •

zero voltage on the line side,

• or dc voltage on the line side with trapped charge. • Prediction is more complicated when re-closing into trapped charge on a line with shunt reactors.


Reduction of Overvoltages in Closing and Re-Closing

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Operations on Transmission Lines 1. Controlled closing

• Re-closing into trapped charge on a line with shunt reactors: • In this case, there is a beat phenomenon

in voltage across contacts. • Resonance between

shunt reactors and line capacitance usually somewhat below 50 or 60 Hz). The University of British Columbia

Reduction of Overvoltages in Closing and Re-closing

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Operations on Transmission Lines 2. Closing (pre-insertion) resistors

• Close contact I first, then II after 8 to 10 ms. • From [1]:


Reduction of Overvoltages in Closing and Re-closing

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Operations on Transmission Lines 3. Metal oxide surge arresters • At both ends • At both ends and middle. 4. Comparison from [2] & [3] (re-closing into trapped charge with shunt reactors): (staggered closing = close 2nd and 3rd pole 8 and 16 ms later in 60 Hz system)


Computer Models for Closing and Re-closing

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Operations on Transmission Lines •

Feeding network • Simplest model is voltage source behind 50 Hz or 60 Hz “short-circuit

impedance”, both for positive sequence and zero sequence.

• This simple model is reasonable if the feeding network is mostly inductive, as in the case of switching from a power plant:



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Feeding network

• If the feeding network is more complicated, CIGRE recommends to represent the lines in detail one or two substations away from the substation where switching is done. • Beyond the one or two substations away, use the short-circuit

impedances to represent the rest. • Some utilities prefer to represent the large system completely in detail (Hydro-Quebec?).



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Feeding network as equivalent network

• A simplified version of an equivalent network recommended by CIGRE uses the short-circuit impedance (resistance RSC and inductance LSC) in parallel with the surge impedance of the connected

lines, divided by the number of lines, RS = Zsurge/n [4]: • Frequency dependent network equivalent (“FDNE”) creates an R-L-C network that has more or less the same frequency response as the complete network, over the frequency range of interest. Starts from frequency scan of complete network. The University of British Columbia


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Feeding network as equivalent network

• H. Singh and A. Abur developed a time domain model that reaches back more in history [5]:

it   g 0vt   g1vt  t   g 2vt  2t   ... • This can handle travel time delays on transmission lines more easily. • Both FDNE and the time domain model are developed from the full system. • If the equivalent is not used very often, it may be best to work directly with the full system. The University of British Columbia


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Circuit breaker • Normally, the circuit breaker is represented as an ideal switch, • with closing time specified, • and closing taking place at the next time step n·Δt ≥ tclose, or in some

versions at n·Δt closest to tclose. • For slow circuit breakers or circuit switchers, prestrike may have to be taken into account. Contacts start to close Dielectric strength of contacts

Electric closure

t Aiming point

Voltage across contact The University of British Columbia


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Transmission line; constant parameter model • The simplest model is the constant parameter model with constant perunit length parameters R’, L’, C’, both in positive sequence and zero sequence. • In EMTP version that I am familiar with, R’ is not really distributed, but lumped at both ends and the middle.

• Total resistance

R  R' length

must be much less than

characteristic impedance Zchar . • A truly distributed resistance is a special case of line models with frequency dependent parameters,

because Z becomes frequency dependent: Z char 

R'  jL' jC'



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Transmission line; constant parameter model • This model is often accurate enough for switching studies because • frequencies are not very high (maybe to 10 kHz),

• positive sequence parameters are more or less constant in that range.

• Zero seq. parameters are frequency dependent, but if three poles close simultaneously, then there are no zero sequence surges. The University of British Columbia


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Transmission line, frequency-dependent parameter models • Zero sequence parameters are very much frequency dependent.

• This dependence must be taken into account if there are noticeable zero sequence currents and voltages in the transients. The University of British Columbia


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Transmission line, frequency-dependent parameter models • F. Castellanos and J. R. Marti [6] developed a frequency-dependent line model by lumping

R   jLint ernal   in many more places along

lossless line sections, and taking the frequency dependence of these lumped impedances into account. •

R   jLint ernal   represents the resistances and internal

inductances of the conductors and of earth return. • For three-phase lines, these impedances are 3*3 matrices. • It works directly in the phase domain, without having to go through transformation between phase and mode quantities. • Well suited for un-transposed lines.

• This approach works for underground cables as well, with minor modifications [7]. The University of British Columbia


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Transmission line, frequency-dependent parameter models • Most EMTP models are based on fitting propagation factor e-γl and characteristic impedance Zchar(ω) in the frequency domain. • For both positive and zero sequence, find propagation constant



R'   

jL'    jC'

• With approach of J. R. Martí [8], calculate propagation factor A(ω) = e-γl in frequency domain, & convert to weighting function a(t) in time domain. • Before, we picked one history term

going back τ. Now we pick more, using a weighting function a(t). • For efficiency, recursive convolution is used to sum history points with a(t). The University of British Columbia


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Transmission line, frequency-dependent parameter models • The characteristic impedance was a pure shunt resistance Z before. Now it is frequency- dependent. • Approximate Z   

R '    jL'   j C '

with an R-C circuit, as shown at right.

• Straightforward for “balanced” (perfectly transposed) lines. • On un-transposed lines, transformation matrix approximated as real and constant (not good for double-circuit lines). The University of British Columbia


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Transmission line, frequency-dependent parameter models

• Much progress has been made, particularly for un-transposed lines, mostly with phase domain based models: • T. Noda, N. Nagaoka and A. Ametani [9] developed the ARMA model (auto-regressive moving average).

• A. Morched, B. Gustavsen and M. Tartibi [10] developed the universal model with vector fitting. • B. Gustavsen [11] added many refinements. • A. B. Fernandes and W. L. A. Neves included effects of shunt conductance [14, 15]. • Etc.



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Trapped charge

• There are various ways to represent it, depending on EMTP version. • Simulate the line opening, wait for trapped charge to settle to dc after some oscillations, then close again. May require long simulation time.

• In version which I use, initial conditions can be read in, which override the ac steady-state solution values. Example for line from 1 to 2 with phases A, B, C, read in initial voltages in 1A, 1B, 1C, 2A, 2B, 2C, and read in zero initial currents in 1A-2A, 1B-2B, 1C-2C. • In older versions of EMTP, and maybe ATP, you can connect special voltage sources Vmaxcos(ωt) with a frequency of 0.001 Hz,

(Tstart =

5432.0?), to approximate dc (solving directly for dc requires extensive code changes to handle ωL = 0 and 1/ωC = ). The University of British Columbia

Examples for Closing and Re-closing Operations on

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Transmission Lines •

CIGRE test case for energization of 202.8 km long line from inductive

source [12]

• Source impedance (generator + transformer): Rpos = Rzero = 6.75 Ω; Xpos = Xzero = 127 Ω at 50 Hz. • Line: Z’pos = 0.04 + j 0.318 Ω/km at 50 Hz, C’pos = 11.86 nF/km; Z’zero = 0.26 + j 1.015 Ω/km at 50 Hz, C’zero = 7.66 nF/km;

length = 202.8 km. Constant R’, L’, C’ assumed. • Circuit breaker: closing times, with respect to instant when voltage in phase A goes through zero from positive to negative; TCLOSE-A = 3.05 ms, TCLOSE-B = 8.05 ms, TCLOSE-C = 5.55 ms. The University of British Columbia


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CIGRE test case for energization of 202.8 km long line from inductive source [12]

• Overvoltage at receiving end in phase B; computer results (dashed line) superimposed on family of curves from transient network analyzer

results; time count starts when wave arrives at receiving end The University of British Columbia


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CIGRE test case for energization of 202.8 km long line from inductive source [12] • This case did not have high frequencies, and constant parameter line

model and single Π-circuit gave almost identical results. • In general, I would not recommend Π-circuits (on transient network analyzers, switched line was typically represented by cascade connection of 10 Π-circuits). The University of British Columbia


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CIGRE test case for energization of 202.8 km long line from inductive

source [12] • Trapped charge can increase or decrease the overvoltages. • Depends on polarity of trapped voltage. Trapped charge Overvoltages (p.u.) (p.u.) A B C A B C 0.0 0.0 0.0 2.068 2.166 2.287 0.9 0.8 -0.8 1.368 1.538 1.342 -0.9 -0.8 0.8 3.086 3.172 3.469



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Energization of 400 km long line through closing resistors [13] • This was a field test by CEMIG in Brazil. • Line was switched from a power plant. No other lines were connected. • Line had a three-phase shunt reactor at sending end.

S P T

Sending end

Receiving end

S P

T



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Energization of 400 km long line through closing resistors [13] • Modelling: (1) Find positive and zero sequence impedances looking into power plant (generator with Xd”) , and then model as 3 coupled impedances. (2) Model shunt reactor as 3 coupled impedances. (3) Model line with constant parameters. SOURCE

REACTOR Sending end

[x]

Receiving end

[x] Vs(t) BREAKER

TRANSMISSION LINE



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Energization of 400 km long line through closing resistors [13]

• Voltages at sending end. solid line: field test dotted line: simulation



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Energization of 400 km long line through closing resistors [13] • Voltages at receiving end.

solid line: field test dotted line: simulation

• Going from constant to frequency-dependent parameter models did not improve results much. The University of British Columbia

Lightning Surges •

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The three main causes of lightning overvoltages: • Backflashover: Lightning stroke to tower or ground wire produces overvoltage on tower, which leads to flashover across insulator to line conductor • Direct stroke to conductor • Overvoltages induced into line from nearby lightning stroke to ground


Lightning Surges

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• Simple single-phase study [40].


Lightning Surges

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• Surge arrester characteristic (old silicon-carbide type with gap)


Lightning Surges

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• Volt-time characteristic of 220 kV insulator string


Lightning Surges

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• Results


Surge Function Sources (either Voltage or Current) • Surge function, double exponential:

v( t )  Vmax

e

t

43

e

t



• Used in impulse testing, such as in 1.2/50 μs test.


Surge Function Sources (either Voltage or Current)

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• Impulse shape for 1.2/50 μs test:



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• CIGRÉ surge function, with realistic convex front [41].

v( t )  k1t  k 2t n for 90 % of the front ,and v( t )  k3e ( t t90 ) /  1  k 4 e ( t t90 ) /  2 for the tail .



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• Standler function [42] for convex front and for short tail, such as 8/20 μs impulse for surge arrester testing, which cannot be represented with double exponential function n  t /  

t v( t )  k     e  



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• Heidler function (for convex front; short and long tail) [43] n  t /   1 n 1

 t /  v( t )  k  1  t /  

e



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• Short tail issue discussed by R. B. Standler in [42. p.87] : • Short tails (relative to front), such as 8/20 μs current impulse for surge arrester testing, cannot be represented with double exponential function. • From my own tests, the shortest tail possible with the double exponential function, using front time defined through 10 % and 90 % values, is 8/31 μs, with α = - 69 730 β = - 111 059 Imax = 5.893 for a crest value of Icrest = 1.0. • The shortest tail possible with the double exponential function, using front time defined through 30 % and 90 % values, is 8/28 μs.


Other improvements to lightning surge studies

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• M-phase line models*) • I prefer lossless high-frequency approximation, with

Z surge self

2h D  60  ln , Z surgemutual  60  ln r d

• Tower models for surges

• Models for insulator flashovers • Surge arrester models*) Metal-oxide arresters without gaps nowadays • Cable models*) • Transformer models*) _______________________________________________________ ___ *) See IEEE PES Task Force on Data for Modeling System Transients in: list of references (slide 102) The University of British Columbia

Lightning Surges

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• Electricité de France used a surge generator in outdoor and indoor substations to produce fast surges of the lightning type [39].


Example for Temporary Overvoltages

•

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Energization of a line terminated with transformer or shunt reactor

• Example from M. Erche [1]:

• This case is probably from American Electric Power Corp. • Caused by resonances between harmonics from transformer saturation and line capacitance.



•

52


• Overvoltages can last a long time. The University of British Columbia


•

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• Nonlinear inductances do not keep peak voltages down. • Part of the voltage around voltage zero is “cut out”, because of 90° phase shift between flux and voltage. • VRMS = f(IRMS) must be converted to flux linkage = f (current) (simplified

as 2-slope nonlinearity here)

• This “cut out” produces the harmonics. The University of British Columbia

Examples for Subsynchronous Resonance

•

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Interaction between mechanical resonances on turbine-generator shaft

system and on electric network side • Occurs at frequencies below power frequency. • Most likely to occur on steam turbines, if a transmission line with series capacitors is switched.

• Unlikely to occur on hydro turbines because “stiffer” with higher resonance frequencies. • Can also be caused by control modes in nearby HVDC terminal.


Examples for Subsynchronous Resonance •

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Interaction between mechanical resonances on turbine-generator shaft system and on electric network side • Example from General Electric Co. [17].



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• First IEEE benchmark model [18, 20].



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• First IEEE benchmark model, torque between generator & exciter.



58

• Second IEEE

benchmark model [19, 21].



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• Second IEEE benchmark model, shaft between generator and low

pressure steam turbine.


Examples for Subsynchronous Resonance •

60

Frequency-scan for impedance seen from power plant • Helps to see whether potential for subsynchronous resonance exists.

• Example from [26]:

• Measured: Short circuit was applied for a few cycles. Change in Δv, Δi transformed from time domain to frequency domain, to obtain Z(ω). The University of British Columbia

Example for Single-Line-to-Ground Fault

61

on Transmission Lines •

When a single-line-to-ground fault occurs on a transmission line, there will be overvoltages on the unfaulted phases (typically 1.6 p.u.) • Frequency dependent line model is necessary, because there are large zero sequence currents (Izero = Ipos = Ineg in fault current). • Example [8]:


Example for Transient Recovery Voltage •

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When circuit breaker opens to remove the fault, a “transient recovery voltage” appears across the contacts.

• If rate of rise is too steep or amplitude is too high, circuit breaker may restrike or re-ignite. • Important to include stray capacitances of transformers, busbars, etc. • Initial rate of rise used to be a problem in gas-insulated substations.

• Example from [13, 25]. • Fault current:


Example for Transient Recovery Voltage

63

• For simulation, one can either simulate complete event (fault initiation,

fault clearing). • I prefer “cancellation method”, whereby a current is injected across circuit breaker contacts that cancels the fault current.

• Starts from zero initial conditions. • Network need only be represented to distance away where total travel time > tmax (no reflections coming back beyond that point).



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• Results for fault at 1.2 km from substation:

Solid line = field test; dotted line = simulation. The University of British Columbia


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• Initial rate of rise becomes worse if fault farther away from substation

(“short-line fault” or “kilometric fault”). • Fault moved from

1.2 km to 8.0 km: • Fault current decreases 13.7%. • Initial rate of rise increases.


Example for Linear Resonance after Opening a

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Transmission Line in Parallel with another Line •

Can be studied as a steady-state case at power frequency (60 Hz or 50

Hz) • Best transmission line model is Π-circuit. • For complicated transposition schemes, use one Π-circuit for each section.

• Example from planning study at Bonneville Power Administration:



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Transmission Line in Parallel with another Line •

Can be studied as a steady-state case at power frequency (60 Hz or 50

Hz) • Varying L of shunt reactor showed resonance between

possibility of coupling

capacitance and L.

• L was changed somewhat to avoid resonance at 60 Hz. • Resonance is more likely to occur at harmonic frequencies in such cases. rated current 132 A

rated inductance 6.09 H The University of British Columbia


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Transmission Line in Parallel with another Line

•

A similar case that actually happened on a 345 kV line that was close to an energized 138 kV line is reported in [31] and [32].

•

A case of what might happen on a 765 kV line close to an energized

345 kV line is discussed in [33] for these situations: • No transpositions on both lines. • 345 kV line transposed. • 765 kV line transposed. • Both lines transposed.


Example 1 for Coupling between

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Parallel Transmission Lines •

Three circuits in parallel are modelled as five nine-phase Π-circuits • Coupling is capacitive. • Steadystate case.



70

Parallel Transmission Lines



71


A double-circuit line is modelled as a cascade connection of twelve six-phase Π-circuits. • Coupling is inductive [23]. • Steady-state case.



72

Parallel Transmission Lines • Results from one of many tests.



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From B. C. Hydro and Power Authority [24] • Steady-state case. • A large zero sequence voltage was induced into a 138 kV line from adjacent 500 kV lines. • It distorted the 2½-element revenue metering schemes of two large industrial customers supplied from the 138 kV line. • The two customers were overcharged 3.5% for 15 years. • They received refunds of Can. $ 4 million. • The metering scheme was changed.


Capacitor switching •

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Switching capacitances off • When switching a capacitor or unloaded transmission line off, the capacitance remains charged up.

• 2.0 p.u. overvoltage across contacts half a cycle after opening.

• Modern SF6 circuit breakers are less likely to restrike than older circuit breakers. The University of British Columbia


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Energization of capacitors • Voltage on capacitor cannot change instantaneously, because it is determined by integral:

t

1 vt   v0   C



i  du

0

Equivalent circuit for EMTP studies.

• If voltage is originally zero, bus voltage collapses to zero temporarily after switching on. • Creates voltage collapse on bus, as well as high inrush currents into capacitor bank. The University of British Columbia


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Energization of capacitors • High dv/dt, v, and i may create problems. • From Brunke and Schockelt [16]:


Capacitor switching

•

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Energization of capacitors

• Reduction of transients with: • Closing (pre-insertion) resistors. • Synchronous (controlled) closing, close to zero voltage across contacts.

• Current-limiting reactors in series with capacitor.



78

Effect remote from substation where capacitors are switched • In case shown here, it may have caused phase-to-phase insulation failure 56 km away in a phase-shifting transformer [22]. • Field test and simulation:


Capacitor switching

•

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Back-to back switching of capacitors

• Back-to-back switching: one capacitor bank is energized, and another capacitor bank next to it is switched on. • This is worst condition, as seen in previous case.

• I analyzed a failure where an induction motor was switched on, close to another running induction motor, in a pipeline pumping station. • Both had capacitors connected for power factor correction. • When second motor was switched on with vacuum contactor, the contacts welded together, and contactor could no longer be opened. • After complicated modelling of induction motors, capacitors, etc., it turned out to be so simple I could have solved it with a slide rule. The University of British Columbia

Capacitor switching

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• Both induction motors were 5 m apart through a cable.

• Both had a 600 kVar capacitor, rated 4.16 kV (line-to-line), 83.3 A. • One energized capacitor discharged into the capacitor of the motor being switched on, through whatever inductance is between them. • Creates a very high inrush current, which welded the contacts in this

case.


Capacitor switching

81

• Simulation:

• A current-limiting reactor would solve the problem. The University of British Columbia

Capacitor switching

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• A more likely problem in such cases is overvoltages created by re-

ignitions when opening the vacuum contactor. • This is caused by tendency of vacuum contactors or circuit breakers to chop currents (see next slide). • Surge capacitor on load being switched helps to prevent re-ignition (not

an issue in my case).


Inrush Currents

83

•

When an unloaded transformer is energized, high “inrush currents” may occur that are higher than rated current.

•

Cause is the nonlinear magnetizing inductance, with its nonlinear curve for flux λ = f(i).

• Modern circuit breakers close with high speed. Closing at v = 0 is as probable as closing at v = Vmax (slow contacts used to prestrike close to Vmax). • Since flux is integral of voltage



t

 ( t )   ( 0 )  v  du 0

we get 2 p.u. flux if we close at v = 0, assuming the residual flux λ(0) at t = 0 is zero. The University of British Columbia

Inrush Currents

84

• Residual flux can make the inrush current higher or lower. • There may also be high-frequency overvoltages in energizing threephase banks if the closing times are more than 5 ms apart. This may have caused damages recently.


Inrush Currents

85

•

The inrush current also depends on the tap position of the load tap changer, and by positioning it conveniently, the inrush currents can be reduced.

•

If other transformers are already in operation close to the one being energized, there is “sympathetic interaction” between them that influences the inrush currents [35].

•

By monitoring the flux in the transformer, and by controlling the closing of the circuit breaker contacts, it becomes possible to close at just the right moment to reduce the inrush current to very small values similar to the steady-state exciting current ([36], [37], [38]).


Inrush Currents

•

86

Example from CIGRE Working Group [34]:


Inrush Currents •

87

Example from CIGRE Working Group [34]:


Interruption of Small Inductive Currents •

88

Problem is “current chopping” in circuit breaker opening • Tendency to “chop” if current is small (because of falling v(i) characteristic of arc, arc voltage becomes high when current becomes low).

• Small current is not the problem, but high derivative di/dt. • Can cause overvoltages

di L as dt

.

• Maximum overvoltage factors when interrupting magnetizing currrent of high voltage transformers [1].


Interruption of Small Inductive Currents

89

• Can also happen when switching off reactor-loaded transformers.

• Vacuum circuit breakers have tendency to chop even at higher currents. • For CIGRÉ reports, see [27], [28], [29], [30].


Real-time simulators

90

Playback A “simple” way to test protective relays is to play back simulation results through amplifiers. There is no feedback from relay that may cause other actions. Real-time simulators (not my expertise; J. R. Marti works on it in UBC). Commercially available: • RTDS (Manitoba, Canada) • Hypersim (Quebec, Canada) • OPAL (Quebec, Canada) • etc. The University of British Columbia

EMTP-Type Software

91

• BPA EMTP. Bonneville Power Administration may use ATP now.

• UBC MicroTran. Owned by University of British Columbia. Website: www.microtran.com. • DCG/EPRI EMTP. Was developed from BPA EMTP by Development Coordination Group and EPRI. First commercialized as EMTP96 by Hydro One in Toronto, Canada, then as EMTP-RV by TransÉnergie Technologies (subsidiary of Hydro Quebec), and now by CEA Technologies Inc. (www.emtp.com).


EMTP-Type Software

92

• ATP (Alternative Transients Program). Free, but requires a license. EMTP developers cannot get it.

• PSCAD and EMTDC from Manitoba HVDC Research Centre (www.pscad.com). • DigSILENT from Germany (www.digsilent.de). • NETOMAC (Siemens). • SABER for power electronics.

• SPICE, PSPICE for electronics. • Etc. The University of British Columbia

The End

93

Thank you for your attention! Any Questions?


References

94

[1] K. Ragaller, editor, Surges in High-Voltage Networks. Plenum Press, New York, 1980, p. 63-97.

[2] K. Froehlich, C. Hoelzl, M. Stanek, A.C. Carvalho, W. Hofbauer, P. Hoegg, B.L. Avent, D.F. Peelo, J.H. Sawada, “Controlled closing on shunt reactor compensated transmission lines - Part I: Closing control device development - Part II: Application of closing control device for high-speed autoreclosing on BC Hydro 500 kV transmission line”, IEEE Trans. Power Delivery, Vol. 12, No. 2, pp. 734-746, April 1997. [3] CIGRE Working Group 13.07, “Controlled switching of HVAC circuit breakers – Benefits and economic aspects”, ELECTRA No. 217, pp. 37-47, Dec. 2004. [4] CIGRE Working Group 33.02, Guidelines for representation of network elements when calculating transients. Technical Brochure CE/SC GT/WG 02, 1990.

[5] H. Singh and A. Abur, “Multi-port equivalencing of external systems for simulation of switching transients”, IEEE Trans. Power Delivery, Vol. 10, No. 1, pp. 374-382, Jan. 1995. [6] F. Castellanos and J. Martí, “Full frequency-dependent phase domain transmission line model”, IEEE Trans. Power Syst., Vol. 12, pp. 1331-1339, Aug. 1997. The University of British Columbia

References

95

[7] Ting-Chung Yu and José R. Martí, “A robust phase-coordinates frequency dependent underground cable model (zCable) for the EMTP”, IEEE Trans. Power Delivery, Vol. 18, pp. 189-194, Jan. 2003. [8] J. R. Marti, “Accurate Modelling of Frequency-Dependent Transmission Lines in Electromagnetic Transient Simulations”, IEEE Trans. on Power Apparatus and Systems, vol. PAS 101, No.1, pp. 147–157, January 1982. [9] T. Noda, N. Nagaoka and A. Ametani, “Phase Domain Modeling of FrequencyDependent Transmission Lines by Means of an ARMA Model”, IEEE Trans. Power Delivery, vol. 11, no. 1, pp. 401-411,January 1996. [10] A. Morched, B. Gustavsen and M. Tartibi, “A Universal Model for Accurate Calculation of Electromagnetic Transients on overhead Lines and Underground Cables”, IEEE Trans. Power Delivery, vol. 14, no. 3, pp. 1032-1038, July 1999.

[11] B. Gustavsen, “Validation of frequency dependent transmission line models”, IEEE Trans. Power Delivery, vol. 20, no. 2, pp. 925-933, April 2005. [12] CIGRÉ Working Group 13.05, “The calculation of switching surges. Part I. A comparison of transient network analyzer results”, ELECTRA No. 19, pp. 67-78, Nov. 1971. The University of British Columbia

References

96

[13] C.A.F. Cunha and H.W. Dommel, “Computer Simulation of Field Tests on the 345 kV Jaguara-Taquaril line”, (in Portuguese), Paper BH/GSP/12, Presented at “II Seminario Nacional de Producao e Transmissao de Energia Eletrica” in Belo Horizonte, Brazil, 1973 (English translation by D.I. Cameron). [14] A. B. Fernandes anad W. L. A. Neves, “Phase-domain transmission line models considering frequrency-dependent transformation matrices”, IEEE Trans. Power Delivery, vol. 19, pp. 708 - 714, April 2004. [15] A. B. Fernandes and W. L. A. Neves, “Transmissioin line shunt conductance from measurements”, IEEE Trans. Power Delivery, vol. 19, pp. 722 - 728, April 2004. [16] J. H. Brunke and G. G. Schockelt, “Synchronous energization of shunt capacitors at 230 kV”, presented at 1978 IEEE Power Engineering Society Winter Power Meeting, New York, N. Y., Jan. 29 – Febr. 3, 1978, paper no. A 78 148-9. [17] D. H. Baker, “Synchronous machine modeling in EMTP”, IEEE Course Text “Digital Simulation of Electrical Transient Phenomena”, No. 81 EHO 173-5-PWR, IEEE Service Center, Piscataway, N.J., 1980.


References

97

[18] IEEE Task Force, "First benchmark model for computer simulation of subsynchronous resonance", IEEE Trans. Power App. Syst., vol. PAS-96, pp. 15651572, Sept./Oct. 1977.

[19] IEEE Task Force, "Second benchmark model For computer simulation of subsynchronous resonance", IEEE Trans. Power App. Syst., Vol. PAS-104, pp. 1057-1066, May 1985. [20] Microtran Factsheet No. 1, “Subsynchronous Resonance - Test Case 1”, April 2003 (available on website www.microtran.com; click on “Tech Spot”).

[21] Microtran Factsheet No. 2, “Subsynchronous Resonance - Test Case 2”, April 2003 (available on website www.microtran.com; click on “Tech Spot”). [22] R. M. Hasibar, “Examples of electromagnetic transients studies using the BPA EMTP”, Course Notes, EMTP Short Course, University of Wisconsin, Madison, Wisconsin, 1987. Follow-up paper describing transformer failure: R. S. Bayless, J. D. Selman, D. E. Truax, and W. E. Reid, “Capacitor switching and transformer transients”, IEEE Trans. Power Delivery, Vol. 3, pp. 349-357, Jan. 1988. [23] W. G. Peterson, R. M. Hasibar, and D. C. Gentemann, “Grand Coulee – Raver 500 kV double circuit line test July 15-16, 1980”, Div. of System Engineering, Bonneville Power Administration, Portland, OR, U.S.A. The University of British Columbia

References

98

[24] M. B. Hughes, “Revenue metering error caused by induced voltage from adjacent transmission lines”, IEEE Trans. Power Delivery, Vol. 7, pp. 741-745, April 1992. [25] H. W. Dommel, Case Studies for Electromagnetic Transients. Microtran Power System Analysis Corp., Vancouver, Canada, Sept. 1993.

[26] M. B. Hughes, R. W. Leonard, and T. G. Martinich, “Measurement of power system subsynchronous driving point impedance and comparison with computer simulations”, IEEE Trans. Power App. Syst., Vol. PAS-103, pp. 619 – 630, 1984. [27]CIGRE Working Group 13.02, "Interruption of Small Inductive Currents, Chapters 1 and 2", ELECTRA No. 72, pp. 73-103, CIGRE, Paris, Oct. 1980.

[28]CIGRE Working Group 13.02, "Interruption of Small Inductive Currents, Chapters 3, Part A", ELECTRA No. 75, pp. 5-30, CIGRE, Paris, March 1981. [29]CIGRE Working Group 13.02, "Interruption of Small Inductive Currents, Chapters 4, Part A", ELECTRA No. 101, pp. 13-39, CIGRE, Paris, July 1985. [30]CIGRE Working Group 13.02, "Interruption of Small Inductive Currents, Chapters 4: Reactor Switching: Part B: Limitation of Overvoltages and Testing", ELECTRA No. 113, pp. 51-74, CIGRE, Paris, July 1987.


References

99

[31] M. J. Pickett, H. L. Manning, and H. N. Van Geem, “Near resonant coupling on EHV circuits: I – Field investigations”, IEEE Trans. Power App. Syst., Vol. PAS-87, pp. 322-325, Febr. 1968.

[32] M. H. Hesse and D. D. Wilson, “Near resonant coupling on EHV circuits: II – Methods of analysis”, IEEE Trans. Power App. Syst., Vol. PAS-87, pp. 326-334, Febr. 1968. [33] J. J. LaForest, K. W. Priest, A. Ramirez, and H. Nowak, “Resonant voltages on reactor compensated extra-high-voltage lines”, IEEE Trans. Power App. Syst., Vol. PAS-91, pp. 2528-2536, Nov. 1972. [34] B. Holmgrem, R.S. Jenkins, and J. Riubrugent, “Transformer inrush current”, CIGRE Report 12-03, 1968. [35] H.S. Bronzeado, P.B. Brogan, and R. Yacamini, “Harmonic analysis of transient currents during sympathetic interaction”, IEEE Trans. on Power Systems, Vol. 11, pp. 2051-2056, Nov. 1996. [36] J. H. Brunke, and K. J. Fröhlich, “Elimination of transformer inrush currents by controlled switching, Part I”, IEEE Trans. Power Delivery, Vol. 16, pp. 276-280, April 2002. The University of British Columbia

References

100

[37] J. H. Brunke, and K. J. Fröhlich, “Elimination of transformer inrush currents by controlled switching, Part II”, IEEE Trans. Power Delivery, Vol. 16, pp. 281-285, April 2002. [38] E. Portales and A. Mercier, on behalf of CIGRÉ Working Group A3.07, “Controlled switching of unloaded power transformers”, ELECTRA No. 212, pp. 39-47, Feb. 2004.

[39] M. Rioual, “Measurements and computer simulation of fast transients through indoor and outdoor substations”, IEEE Trans. Power Delivery, Vol. 5, pp. 117-123, Jan. 1990. [40] J.R. Marti and H.W. Dommel, "Line models for lightning studies," Trans. Engineering and Operating Division, Canadian Electrical Association, Vol. 28, 1989, 15 pages. [41] CIGRÉ Working Group 33.01, Guide to Procedures for Estimating the Lightning Performance of Transmission Lines. CIGRÉ Techn. Brochure Ref. 63, Paris 1991. [42] R. B. Standler, Protection of Electronic Circuits for Overvoltages. Wiley-Interscience, New York, N.Y. 1989. [43] F. Heidler, "Analytische Blitzstromfunktion zur LEMP-Berechnung (analytical lightning current function for LEMP calculations)", Paper No. 1.9, ICLPProceedings, Munich 1985. The University of British Columbia

General References

101

In addition to the specific references quoted before, advice for Electromagnetic Transient Studies can also be found in the following publications:

IEEE Publications: J. A. Martinez-Velasco, editor, Computer Analysis of Electric Power System Transients. IEEE Press, Piscataway, NJ, U.S.A., 1997. Collection of papers on 619 pages. IEEE PES Special Publication, Modeling and Analysis of System Transients. IEEE Catalog No. 99TP133-0, IEEE Operations Center, Piscataway, NJ, U.S.A., 1998. Put together by a Working Group chaired by A.J.F. Keri: i 1. 2.

3. 4.

5. 6. 7. 8.

Modeling and Analysis of System Transients Using Digital Programs - Introduction (A.J.F. Keri, A.M. Gole) Digital Computation of Electromagnetic Transients in Power Systems: Current Status (J.A. Martinez-Velasco) Modeling Guidelines for Power Electronics in Electric Power Engineering Applications (K.K. Sen and L. Tang, H. W. Dommel, K.G. Fehrle, A.M. Gole, E.W. Gunther, I. Hassan, R. Iravani, A.J.F. Keri, R. Lasseter, J.R. Marti, J.A. Martinez, M.F. McGranaghan, O.B. Nayak, C. Nwankpa, P.F. Ribeiro) Modeling Guidelines for Low Frequency Transients (R. Iravani, A.K.S. Chandhury, I.D. Hassan, J.A. Martinez, A.S. Morched, B.A. Mork, M. Parniani, D. Shirmohammadi, R.A. Walling) Modeling Guidelines for Switching Transients ( D.W. Durbak and A.M Gole, E.H. Camm, M. Marz, R.C. Degeneff, R.P. O'Leary, R. Natarajan, J.A. Martinez-Velasco, Kai-Chung Lee, A. Morched, R. Shanahan, E.R. Pratico, G.C. Thomann, B. Shperling, A.J.F. Keri, D.A. Woodword, L. Rugeles, V. Rashkes, A. Sarshar) Modeling Guidelines for Fast Front Transients (A.F. Imece, D.W. Durbak, H. Elahi, S. Kolluri, A. Lux, D. Mader, T.E. McDermott, A. Morched, A.M. Moussa, R. Natarajan, L. Rugeles, E. Tarasiewicz) Modeling Guidelines for Very Fast Transients in Gas Insulated Substations (J.A. Martinez and D. Povh, P. Chowdhuri, R. Iravani, A.J.F. Keri) Modeling and Analysis of Transient Performance of Protection SystemsUsing Digital Programs (A.K.S. Chaudhary and R.E. Wilson, M.T. Glinkowski, M. Kezunovic, L. Kojovic, J.A. Martinez) Bibliography on Modeling of System Transients Using Digital Programs (J.A. Martinez-Velasco and T. E. Grebe)


General References

102

IEEE Power Engineering Society, Tutorial on Electro- magnetic Transient Program Applications to Power System Protection. A. Tziouvaras, Course Coordinator. IEEE Catalog No. 01TP150. IEEE PES Task Force on Data for Modeling System Transients, “Parameter Determination for Modeling System Transients – Part I: Overhead Lines; Part II: Insulated Cables; Part III: Transformers; Part IV: Rotating Machines; Part V: Surge Arresters; Part VI: Circuit Breakers; Part VII: Semiconductors”, IEEE Trans. on Power Systems, Vol. 20, pp. 2038-2094, July 2005. Books (compiled with help from Dr. Luis Naredo): H. H. Skilling, Transient Electric Currents. McGraw-Hill Book Company, Inc., 1937.

H. A. Peterson, Transients in Power Systems. Dover Publications, Inc., New York, 1966 (ISBN 0-486-61685-1). R. Rüdenberg, Electrical Shock Waves in Power Systems. Harvard University Press, 1968. J. P. Bickford, N. Mullineux, and J. R. Reed. Computation of Power-System Transients. IEE Monograph Series 18, Peter Peregrinus Ltd., London, UK, 1976. The University of British Columbia

General References

103

W. D. Humpage, Z-Transform Electromagnetic Transient Analysis in High Voltage Networks. IEE Power Engineering Series 3, Peter Peregrinus Ltd., London, UK, 1982 (ISBN 0-906048-79-6). A. Greenwood, Electrical Transients in Power Systems, 2nd edition. John Wiley & Sons, 1992. P. Chowdhuri, Electromagnetic Transients in Power Systems. Research Studies Press LTD, 1996; John Wiley and Sons, Inc. (ISBN 0 86380 180 3). L. van der Sluis, Transients in Power Systems. John Wiley and Sons, LTD, 2001 (ISBN 0 471 48639 6). N. Watson and J. Arrillaga, Power Systems Electromagnetic Transients Simulation. The Institution of Electrical Engineers, United Kingdom, 2003. L.C. Zanetta Jr., Transitórios Eletromagnéticos em Sistemas de Potencia (in Portuguese). Editora da Universidade de Sao Paulo, Sao Paulo - SP, Brazil, 2003. Antonio E. A. Araújo and Washington L. A. Neves, Transitórios Eletromagnéticos em Sistemas de Energia (in Portuguese). Editora de Universidade Federal de Minas Gerais, Brazil, 2005. Juan A. Martinez-Velasco, Power System Transients: Parameter Determination. CRC Press LLC; 1st edition (Oct 2 2009). The University of British Columbia

General References

104

Antonio Gómez Expósito, Análisis y operación de sistemas de energía eléctrica, McGraw Hill, Madrid, Spain 2002. Antonio Gómez-Expósito, Antonio J. Conejo, Claudio Cañizares, Electric Energy Systems – Analysis and Operation. CRC Press, Boca Raton, Florida, USA, 2009. H. W. Dommel, EMTP Theory Book, 2nd edition. Microtran Power System Analysis Corp., Vancouver, Canada, 1992, latest update January 2005 (there is probably an ATP edition from what I delivered to Bonneville Power Administration in 1986). J. C. Das, Transients in Electrical Systems; Analysis, Recognition, and Mitigation. McGraw-Hill, New York, N. Y., U.S.A., 2010. M. A. Ibrahim, Disturbance Analysis for Power Systems. IEEE Press and John Wiley & Sons, Hoboken, N. J., USA, 2012. This 718-page book contains many cases of disturbances that were recorded on digital fault recorders.


June 18, 2012 New Orleans, Louisiana

IEEE PES Short Course Electromagnetic Transients in Power System and Insulation Coordination Studies

Insulation Coordination Studies Douglas Mader [email protected]

©Copyright Douglas Mader, all rights reserved

Insulation Coordination Process



IEC Standard 60071-1 (2010) 3rd edition published 2006 (amended in 2010)



terms and concepts defined



standard withstand values defined (up to 1200 kV)



standard tests defined





IEEE Standards C62.82.1 (2010) ©Copyright Douglas Mader, all rights reserved

Insulation Coordination Process



IEC Standard 60071-2 published December 1996



application guide for 60071-1





IEEE Standard 1313.2-1999 (R2005)


Insulation Coordination Process IMPORTANT TERMS AND THEIR RELATIONSHIPS EMTP-RV

STRESS

Representative Overvoltage

Coordination Factor

Performance Criteria

kcd k cs Coordination Withstand Voltage

Safety Factors

ka ks

Required Withstand Voltage STRENGTH

Tables

IEC 60071-1

Rated or Standard Insulation Level

Selection of performance criterion leadingMader, to the coordination ©Copyright Douglas all factor is heart of problem

rights reserved

Insulation Coordination

The selection of the dielectric strength of equipment in relation to the voltages which can appear on the system for which equipment is intended, taking into account the service environment and the characteristics of available protective devices.


System Characterization

Um

- The highest voltage for equipment

Range I

- Um

< 245 kV

Range II

- Um

> 245 kV





For the purposes of insulation coordination, overvoltages are divided into four classes:



Temporary Overvoltages (power frequency)

• •

Phase-to-Earth and Phase-to-Phase Longitudinal





Next, 

Slow-Front Overvoltages Phase-to-Earth and Phase-to-Phase





And finally… 

Fast-Front Overvoltages



Combined Overvoltages Phase-to-Phase Longitudinal – in phase and out-of-phase


Representative Overvoltage 81\211.pre

Source – IEC 60071-1


Determining Overvoltage Stresses

After

discussing the various overvoltage stresses, their origins, and typical values, we will explore examples of overvoltage calculation and use a model 230 kV system and computer simulation to illustrate


Determining Overvoltage Stresses  Temporary



Overvoltages (TOV)

Origins Earth Faults (Phase-Earth) Load Rejection Ferroresonance Harmonic resonance Transformer Inrush Machine Self-Excitation 


TOV Determines Insulation Design Usually, especially for long distance transmission, load rejection following loss of system synchronism results in the highest temporary overvoltage.  Generally desirable to limit 1-second value to 1.5 per unit of rated rms voltage.  This is because the maximum TOV determines the required rating of surge arresters. The switching and lightning impulse protective level are determined in turn by the arrester rating. These protective levels in turn determine the insulation design and cost.  Can usually be achieved by an optimum mix of series and shunt compensation including SVC in some cases, and avoiding low harmonic order resonances 


Representation of TOV A one minute duration power frequency overvoltage:



-

a maximum value

-

a set of peak values

-

a complete statistical distribution


Determining Overvoltage Stresses Slow-Front



Overvoltages (SFOV)

Origin Line energization and reclosing Faults and fault clearing Load rejection Switching of inductive and capacitive currents Slow front lightning overvoltages (of minor importance) 

Important particularly in range II


Representation of SFOV

Surge Arrester Protection - deterministic method - truncation values if Ups > Ut - Ups if Ups < Ut



No Surge Arresters - deterministic method - truncation values - statistical method




Statistical Representation of SFOV



(no surge arrester limitation) Usually characterized by a statistical (Weibull or Gaussian) probability distribution of standard switching impulses (250/2500 us) with the following parameters:




Statistical Representation of SFOV



Distribution Definition

Ue2 Up2 Se

Sp Ut

- overvoltage phase-to-earth in per unit having 2% probability of being exceeded - same as Ue2 but phase-phase - standard deviation of the distribution phase-earth in per unit - standard deviation of the distribution phase-phase in per unit = U50 + 3S (truncation)(Weibull) ©Copyright Douglas Mader, all rights reserved

SFOV Studies



Per Unit Base 2

Um

 phase-to-earth peak

3


Determining Overvoltage Stresses Fast-front

Overvoltages (Lightning)

a) Begins with lightning current probability distribution and front time probability distribution and a spacial distribution of stroke termination points. b) Because of separation effects, each piece of equipment has a different representative overvoltage which is a statistical quantity.


Selection of Surge Arresters

TOV1



-

1 second temporary overvoltage capability basis of application (ANSI)

-

IEC uses 10 seconds

-

gives one point on the "No-Prior-Energy" curve


Selection of Surge Arresters 

Determine TOV1 (10) -

use computer simulation to determine TOV envelope and arrester energy for such origins as -

load rejection (model complete machine and controls) transformer inrush ferroresonance dynamic overvoltage associated with HVDC determine earth fault factor from X1 X0 R0


Selection of Surge Arresters


Coordination Withstand Voltage 

Performance criteria, coordination factor, and the selection of the Coordination Withstand Voltage UCW = kC · Urp

 

kcd  Deterministic kcs  Statistical

For temporary overvoltage (Power Frequency) Kcd = 1.0. - main considerations are pollution and extreme wind.


UCW for SFOV with Surge Arrester Limitation For

Equipment protected by surge arresters use deterministic or conventional method



select arrester rating by temporary overvoltage



for slow front overvoltages



- by EMTP-RV studies, determine protective level Ups at equipment


UCW for SFOV with Surge Arrester Limitation 

For Slow Front Overvoltages If Ups < 0.7 Ue2  kcd = 1.1 for phase-earth or if Ups < 0.5 Ue2  kcd = 1.1 phase-phase



If 0.7 < Ups/ Ue2  If 0.5 < Ups/ Ue2  

1.2 0.9

use graph (p - e) use graph (p - p)

This adjustment to kcd takes into account the skewing of the probability distribution due to the control by the arrester.



Note also that where the degree of limitation of Ue2 by arresters is large, the limited values of Up2 can approach 2xUps. ©Copyright Douglas Mader, all



rights reserved

KCD for SFOV Limited by SA 81\211.pre



Self-Restoring Insulation Application

of Weibull Distribution to "m" 5 Insulations X m 1+ 4

Pm = 1 - (1 - P)m yielding Pm(X) = 1 - 0.5 and Zm = Z/m1/5

U50m = U50

and - 4(Z - Zm ) = U50 - 4Z (1 - 1/m1/5) ©Copyright Douglas Mader, all rights reserved

Self-Restoring Insulation 81\211.pre



Self-Restoring Insulation Example: - 100 insulators - For each, U50 = 1600 kV Z = 100 kV Zm=100 / (100)1/5

Then: -

and

-

= 39.8 kV

U50m= U50 - 4 (Z - Zm) = 1600 - 4 x (100 - 39.8) = 1359.2 kV

P(u)%

50

16

10

2

1

0.1

0

U (kV)

1600

1500

1475

1400

1370

1310

1200

Um(kV)

1359

1319

1308

1280

1268

1244

1200


SFOV UCW for Unprotected Equipment



i.e. No Surge Arrester Protection applies in particular to slow-front overvoltages



Usually consists of self-restoring insulation



kC determined by a risk-of-failure calculation Ut R=  f(U) P(U) dU U50-4z Computer calculation (laborious) 


SFOV UCW for Unprotected Equipment

81\211.pre



Simplified Statistical Method for SFOV 

Simplified by relating risk-of-failure to the ratio of the voltages corresponding to two reference probabilities. 

the statistical withstand voltage U90 = U50 - 1.3Z



the 2% overvoltage U2



KCS = U90 /U2 statistical coordination factor



Choice of KCS is the key performance criteria. ©Copyright Douglas Mader, all rights reserved

Simplified Statistical Method for SFOV



Simplified Statistical Method for SFOV 

Example  100 insulators Let Ue2 1200 kV Se = 100kV 



For one insulator U90(10% F.O. prob.) = 1475 kV KCS = 1475 = 1.23 1200 R = 10-5

For 100 insulators U90 = 1308 kV KCS = 1308 = 1.09 1200 R = 10-3 ©Copyright Douglas Mader, all rights reserved

UCW for FFOV with Surge Arrester Limitation

Fast



Front Overvoltages

For fast-front overvoltages kcd = 1.0 and the protective level at the equipment takes into account separation effects, which can be quite large at higher values of Um


UCW with Surge Arrester Limitation



For simple arrangements of equipment with close-by arresters and terminal capacitance less than a few hundred picofarads, we would expect the protective level at the equipment to approach: Ucw Up S T

= = = = =

Up + 2ST arrester lightning impulse protective level steepness in kV/s equivalent time in microseconds + a1 + a 2 +  c

c

= light speed in m/s (~ 300) ©Copyright Douglas Mader, all rights reserved

Effect of Separation Distance



Safety and Correction Factors  Correction

and safety factors are applied to obtain the Required Withstand Voltage 

Altitude Correction (IEC 721-2-3 (1990)) Applied to external (atmosphere-exposed) insulation

ka

= bm e(H/8150)

}

ka = e

b

=

H

= altitude in meters ©Copyright Douglas Mader, all rights reserved

H m 8150

Exponent ‘m’ for Altitude Correction Factor

For

switching-impulse required withstand: m is determined from the figure as a function of UCW and the insulation configuration


Exponent ‘m’ for Altitude Correction Factor 81\211.pre



Exponent ‘m’ for Altitude Correction Factor For

lightning impulse required withstand and shortduration power-frequency withstand voltages of air gaps: m



= 1

For

polluted insulator continuous power frequency withstand: m



= 0.5 - 0.8 (standard units - fog units)


Mixed Insulation at High Altitudes



If ka >1.05 the required withstand voltage of external insulation can be greater than that for the internal. Example transformer winding versus bushings



Either: - over design the internal insulation - external insulation separately tested on a dummy - air clearances equal to or greater than tables A1 - A3.




Required Withstand Voltage 

Safety Factors aging unknowns tolerances - assembly, quality control, installation test dispersion 

External Insulation kS= 1.05

Internal Insulation kS = 1.15

Then URW = ka kS UCW

* may be up to 1.2 or more for GIS in Range II ©Copyright Douglas Mader, all rights reserved

Conversion of URW to Standard Test Voltages 

In range I, we specify and test short-duration power frequency withstand



lightning impulse withstand



In range I, we must convert the required switching impulse withstand voltage into an equivalent shortduration power-frequency withstand voltage or lightning impulse withstand voltage.



Table 2 of IEC 60071-2 Section 5.2 provides conversion factors.




Conversion of URW to Standard Test Voltages 81\211.pre

Source – IEC 60071-2 ©Copyright Douglas Mader, all rights reserved

Conversion of URW to Standard Test Voltages 

In range II, we specify switching impulse withstand voltage phase-earth and phase-phase





lightning impulse withstand voltage

We must convert the required power frequency withstand voltages phase-earth and phase-phase to an equivalent switching impulse withstand voltage. Table 3 of IEC 60071-2 Section 5.2 provides conversion factors.




Conversion of URW to Standard Test Voltages

81\211.pre

Source – IEC 60071-2 ©Copyright Douglas Mader, all rights reserved

Rated/Standard Insulation Level





Select a set of standard insulation values closest to each of the values of URW for the various overvoltage classifications. Where possible, design the insulation to correspond to a Standard Insulation Level which is defined as a set of rated insulation levels related as a group to Um and corresponding to one line in the IEC tables. ©Copyright Douglas Mader, all rights reserved





June 18, 2012 New Orleans, Louisiana

Electromagnetic Transients in Power System and Insulation Coordination Studies

Study Examples Using EMTP

Douglas Mader [email protected]

1

Circuit Breakers and Switches EMTP



Models for Circuit Breakers

Ideal Switch 

Acts as an ideal Switch: Impedance = 0 before current zero Impedance =  after current zero

Assumes - Prospective currents and voltages are unaffected by the interruption process itself  Has primary use in breaker specification and overvoltage studies 

2

Circuit Breakers and Switches EMTP 



Models for Circuit Breakers

Simple time controlled  Closes at t ≥ t close  Opens at t ≥ t open and current < Imargin or at the next zero crossing if Imargin = 0

Heuristic (Statistical and Systematic) Models the externally-observed circuit breaker operation - pole spread, restrike, reignition, prestrike Useful for overvoltage studies (statistical overvoltage distribution) Interrupts also as an ideal switch 3

Circuit Breakers and Switches Ideal 



Switch – Random/Systematic

By combining the statistical distribution of overvoltages with the statistical properties of breakdown strength of insulation, it becomes possible to determine a risk of flashover or insulation failure Let Pd (U) be the known probability of flashover for a known overvoltage U. and let p(U) be the probability of occurrence of an overvoltage of magnitude U. The overall risk of failure is then: 

R= -

Pd(U) p(U) dU 4

Circuit Breakers and Switches Point

on Wave delay

 Toffset



= 1./f ((1-X) Dmin + X Dmax) 360.

X is a random uniformly distributed number between 0 and 1

 Dmin

and Dmax are the min. and max. angles respectively of a window in a sinusoidal waveform of frequency f

5

Circuit Breakers and Switches Typical 

Parameter Values and Practical Advice

Typical Pole Spans Standard Deviation Mean Closing Time







6-10 ms (3.5-5.5 for newer springhydraulic mechanisms 1-1.67 ms (.6-.8 ms) 16-20 ms

Higher statistical overvoltages associated with larger pole span Make sure minimum absolute close time after random calculation is > 0.0 Typically 200 shots used If you have a fast machine use more for better accuracy

6

Circuit Breakers and Switches Typical



Parameter Values and Practical Advice

Select the ideal switch output tab option to get the actual switching times of the worst case and re-run it to observe the waveshape



For point on wave use uniform law



Use Gaussian law for closing times at ±3 std dev

7

Circuit Breakers and Switches Pre-insertion 



Resistors in Breakers

Common method of reducing line switching or capacitor switching overvoltages Typical Insertion Time 7-10 ms Must be no less than twice the line travel time



Simulated by an independent statistical auxiliary contact in series with the resistor and a statistical main shorting contact dependent on the auxiliary contact with mean closing time 7-10 ms. The standard deviation of the 8 auxilliary contact is typically half that of the main contact.

Circuit Breakers and Switches Preinsertion

Resistors

B

A

R

A. Auxilliary Contact B. Main Contact R. Resistor 9

Circuit Breakers and Switches Test System for Lab Exercises x"=.0546 200

5

4 11kV

50MVA 0.9PF 222MVA 10%

1 61MVAC 200 10% 200 MVA

220 kV 16km 7

145km

2

193km

24km 220kV

12

9.1% 200MVA

220kV

9.1%

10 400MVA 0.9PF

13

500MVA

200MVA

66kV

9.1%

11kV 11

50MVAC 180

x"=.02186

6

9.1% 500MVA

100MVA

500

11kV

X"=.08744

220kV 11kV

220kV 97km

x"=.1421

8 290km

50 50MVA 9.1% 200 MVA 0.9PF

290km 220kV

230kV SYSTEM

GENERAL FEATURES 10 DRAFT\DJM\PAKGEN.PRE

Circuit Breakers and Switches Example







Set up a statistical three phase switch to leave a trapped charge on line 1-2 by opening and another to reclose the line against trapped charge. (Make a subcircuit). Obtain the overvoltage distribution at the BUS2 end. Add a pre-insertion resistor to the reclosing breaker and repeat. Capacitor Switching

11

Circuit Breakers and Switches Transient









Recovery Voltage

Breakers rated in terms of magnitude and rate of rise ANSI and IEC standards have now been harmonized with IEC 62271-100, but studies for older ANSI breakers need to respect the applicable edition of C37 Indoor and Outdoor breakers distinguished Prospective TRV envelope is best simulated by EMTP ideal switch

12

Circuit Breakers and Switches Transient 



Recovery Voltage

IEC Rating method is also divided into two groups at Um=100 kV, the same as ANSI. The 2-parameter test characteristic applies to Class S1 and S2 breakers rated at or below 100 kV and the parameter values are obtained from Tables 1 and 2 of 62271-100:    

Uc = is a function of Um t3 is function of Um t3 = T2/1.138 td,t',u' allow for the effect of bus/breaker capacitance

Uc

U'

0

td

t'

t3

13

Circuit Breakers and Switches Transient 

recovery Voltage

Above 100 kV, the 4-parameter test characteristic applies and parameters are obtained from Tables 3, 4, and 5 of 62271-100:   

U1 = 0.8 Uc t1 is function of Um t2 = 3t1

Uc

U1

U'

0

td

t'

t1

t2

14

Circuit Breakers and Switches Simple Circuit for Overdamped TRV

300 mH

~

100 km

E cos ωt

15

Circuit Breakers and Switches Simple Circuit for Underdamped TRV With With Short Line Fault

3 mH

E cos ωt

~

1 km

.25 uF

16

Circuit Breakers and Switches Transient







Recovery Voltage

Important for Initial rate of rise to represent the bus side capacitances. Distributed parameter lines may be necessary for extensive buswork Breaker capability curve can be generated in Controls and plotted against the actual TRV Entergy actual example

17

Lightning Overvoltages Modeling and Analysis Lightning Overvoltages 

Three causes - all associated with overhead lines 1. 2. 3.





Backflashover Direct Strokes to Phase (shielding failure) Induced (nearby strokes to ground)

Direct strokes to station are usually ignored because perfect shielding via masts or wires is assumed. Studies focus primarily on line performance (backflashover and shielding failure events) and arrester application © Douglas J. Mader

18

Lightning Overvoltages Modeling and Analysis 

Backflashover 





Above typically about 50 kA strokes to towers or overhead ground wires can produce voltages on the tower high enough to cause flashover of the line insulation. Steep wavefront surge imposed on the affected phase conductor which is attenuated in steepness and magnitude through propagation by earth resistance and corona Reflections from adjacent towers and the footing act to limit the overvoltage peak as does coupling to phase conductors. © Douglas J. Mader 19

Lightning Overvoltages Modeling and Analysis Shielding Failure  Occur when a flash misses the shield wires or tower and terminates directly on a phase conductor.  Prospective overvoltage at stricken point is:

V60 Zs 

I Zs V = + V60 (t) 2 = instantaneous power frequency voltage = conductor surge impedance

Most involve strokes of a few kA but can involve subsequent strokes of greater magnitude (<80 kA) and steepness than first stroke but with shorter tail © Douglas J. Mader

20

Lightning Overvoltages Modeling and Analysis

© Douglas J. Mader

21


© Douglas J. Mader

22

Lightning Overvoltages Modeling and Analysis Shielding Failure IEEE 1243-1997 (R2008) 

S

= 10•I.65 (m, kA) (Love)



I

= 0.029S1.54 (kA, m)



ß

= 0.36 + .168 In (43 - [hG+ hφ)]/2) (hG+ h φ) /2 < 40 m



ß

= .55S

h > 40 m © Douglas J. Mader

23

Lightning Overvoltages Modeling and Analysis Important Parameters (CIGRE) lI - Initial Crest Current l Final Crest Current F T Tail Duration h t d30= T30 /.6 = Rise time from 30% of peak to 90% of peak of lI S m = maximum steepness (at crest of lI ) 





All parameters are generally approximated by log-normal distributions Lightning stroke has a concave wavefront © Douglas J. Mader

24

Lightning Overvoltages Modeling and Analysis T10

T30

T[us]

ITrig I10

Tan 10

TANG (Sm)

I30

Definition of front parameters for a lightning current impulse of negative polarity

I[ka]

I90 II IF

PEAK © Douglas J. Mader

25

Lightning Overvoltages Modeling and Analysis • CIGRE Distribution for Key Parameters

© Douglas J. Mader

26

Lightning Overvoltages Modeling and Analysis Modeling Guidelines 

Stroke Modelling 



Modelled generally as an ideal current source. Stroke Surge Impedance is an inverse function of peak current (up to ~35 - 40kA) Zst = 6897 – 158.45IF (Mazur & Ruhnke 2001) (3000 ohms at 25 kA)



Double exponential type models inadequate. © Douglas J. Mader

27

Lightning Overvoltages Modeling and Analysis Modeling Guidelines 

Stroke Modelling 

Simulation of concave wavefront is important for lightning protection. Peak current amplitude Maximum steepness at 90% of current peak. Average steepness between 30% and 90% of current peak. 



Tail is important Tail duration



(energy). © Douglas J. Mader

28

Lightning Overvoltages Modeling and Analysis Concave Front l t n SN tf

where

= = = = = =

At + Btn time in µs 1 + 2(SN -1) (2 + 1/SN) Smtf / l front time td30

A

=

1 n -1

B

=

1 tnn (n-1)

tn

=

0.6 tf

0.9

l n - Sm tn

[Sm tn - 0.9 l ] 3SN2 /(1 + SN2 )

© Douglas J. Mader

29

Lightning Overvoltages Modeling and Analysis Tail l1e-(t-tn)/t1 - l2 e-(t-tn)/t2 time to half value (th - tn )/ ln 2 0.1 l / Sm

l th t1 t2

= = = =

l1

=

t1 t2 t1 -t2

Sm + 0.9 l t2

l2

=

t1 t2 t1 -t2

Sm + 0.9 l t1

© Douglas J. Mader

30

Lightning Overvoltages Modeling and Analysis Approximations  IEEE (5 kA < l < 200 kA) 1 P

l

=

l 31

1 +

2.6

1 P

S

= 1 +

S 24

4

log I =

0.30

log S=

0.20

Ramp function front at Sm to lpeak  Ramp function tail from I peak through th 

Adequate for studies and can easily be used in hand © Douglas J. Mader calculations

31

Lightning Overvoltages Modeling and Analysis For steel towers model tower as a distributed single phase lossless line with surge impedance: (Chisholm 1985) Zavg = 60 In cot

(

(

1 tan -1 2

Ravg h1+ h2

))

where Ravg = r1 r2 r3 h1 h2

= = = = =

r1 h2 + r2 (h1 + h2) + r3 h1

h1 + h 2 Tower Top Radius (m) Tower Midsection Radius (m) Tower Base Radius (m) Height from Base to Midsection (m) Height from Midsection to Top (m)

(based on surge impedance of conical sections) © Douglas J. Mader

32

Lightning Overvoltages Modeling and Analysis Tower Surge Impedance 





Propagation velocity in towers can vary from 70% of light speed in broad cross-section lattice steel towers with many cross arms to just under lighjt speed in tall towers with narrow cross section Surge impedance of guy wires should be evaluated separately and placed in parallel Surge impedance of a vertical wire of length h/2 is about 10% more than that of a horizontal wire at h/2 © Douglas J. Mader 33

Lightning Overvoltages Modeling and Analysis Earth Electrode Model 

Model the footing resistance and transient response Ro =

 2 g

ln (11.838g2/A) (Chisholm 2001)

Ro =

low current earth resistance (Ω)

g

geometric sum of length + width + depth (m)

=

ρ =

resistivity of earth (-m)

A = total surface area of electrode (m2)

© Douglas J. Mader

34

Lightning Overvoltages Modeling and Analysis Earth Electrode Model 

Add a contact resistance correction term Rc = L



=

 L

(Chisholm 2001)

total length of all the wires in the grid

For concrete piers use the area of the concrete in the previous equation and the contact resistance based on the resistivity of concrete (70-250 ohmmeters) © Douglas J. Mader

35

Lightning Overvoltages Modeling and Analysis Line Insulators Represent by flashover in parallel with capacitance  Capacitance for suspension units ~ 80 pF/unit  Simulate flashover characteristic by built in leader development, equal area integration models or  Volt-time curve models built using controls 

CIGRE volt-time curve: V

=

[

d

=

gap in metres

0.2

400 +

]

710 d (kV) t.75

µs < t < 16 µs © Douglas J. Mader

36

Lightning Overvoltages Modeling and Analysis Line Insulators 

Leader Development Model: tc = time to breakdown = ti + ts + tl ti = corona inception time (assumed=0) ts = streamer propagation time 1/ts = 1.25(E/E50)-0.95 (1/usec) E = max gradient in gap before breakdown (kV/m) E50 = average gradient at CFO © Douglas J. Mader

37


Leader Development Model: For tl

dL/dt = K V(t)(V(t)/(g-L) - Eo) (kV,m) V(t) = voltage across the gap in kV L = leader length in m g = gap length in m

© Douglas J. Mader

38


Leader Development Model:

Gap Config.

Polarity

K(m2/kV2sec) Eo(kV/m)

Air Gaps,Post Insulators

+ -

0.8 1.0

600 670

Cap and Pin Insulators

+ -

1.2 1.3

520 600

© Douglas J. Mader

39

Lightning Overvoltages Modeling and Analysis Line Insulators Integration Model (d < 2m):

DE =to ʃ t(UAB(t) - Uo)k dt

UAB > Uo

When the area reaches DE, at t=tf , flashover is initiated Voltage Uo corresponds approximately to the voltage defining the dielectric withstand of an air gap subjected to a conventional lightning impulse of +ve polarity © Douglas J. Mader

40

Lightning Overvoltages Modeling and Analysis Corona Attenuation and Distortion 





Important for proper calculation of lightning overvoltages coming into a station from an overhead line Complex phenomena - difficult to simulate accurately over a wide range of line physical parameters Affects mainly the wavefront by introducing a time delay to the peak and a reduction in the steepness which become more pronounced with increasing propagation distance © Douglas J. Mader

41

Lightning Overvoltages Modeling and Analysis Corona Attenuation and Distortion





Few laboratory measurements available to provide data (Maruvada, et al IEEE 1977) - cage data only

Most models start with the assumption of a cylinder surrounding the conductor in corona. The cylinder represents the boundary of the ionization (space charge, attachment and recombination processes) © Douglas J. Mader

42




The corona onset or inception voltage is constant for a given conductor configuration, however time lags associated with the electron avalanche process can delay the onset for faster wavefronts such as lightning The total capacitance within the region of ionization increases dynamically as a result of particle redistribution

© Douglas J. Mader

43


© Douglas J. Mader

44








Time domain models must be distributed at discrete intervals between short (50 m or less) sections of distributed line. Can be costly in terms of computer resources (time and memory). A number of models similar in approach have been prepared (Suliciu, Gary, etc.). EMTP-RV uses a quasi three-phase Suliciu model © Douglas J. Mader

45

Lightning Overvoltages Modeling and Analysis Substation Components 

Model substation busbar sections as untransposed distributed parameter lines between bus supports but if distance between supports < 3m, combine sections



Between each section lump the bus insulator and support structure capacitance - for cap& pin: 123kV - 80 pF 400kV - 120 pF less (10-50) for post/NCI 765kV - 150 pF



Make sure sections accurately locate major equipment

© Douglas J. Mader

46


Model large lumped capacitances such as CVT = 4 - 10 nF, the higher values with lower voltages) Magnetic PT ~550 pF CT = 150-1000 pF with increasing voltage Dead Tank Breaker ~50pf each side to ground 6-10 pF longitudinal Live Tank Breaker 5pF to ground, 10pF longitudinal Plus any grading or TRV capacitors Bus support structures - three phases 100 ohm Zs - one phase 300 ohm Zs - ground resistance 0.1 ohm 

© Douglas J. Mader

47


Cables and GIS: Be careful to model short cables and GIS bus section lengths accurately and watch out for voltage buildup (standing waves) if any cables/bus sections can be fed single-ended



Watch out for voltages between sheath and ground. These are usually the most critical and should be modeled using an untransposed cable with transformation matrix evaluated at high frequency. Any cross bonding and sheath ground resistance/arrester protection must be included.



© Douglas J. Mader

48


Modeling Guidelines for GIS Bus sections are lossless DP lines with Z typically 50-60 ohms and propagation velocity about 95% of light speed.



Accurate overall length is important, however rigorous spacer to spacer resolution is only important for VFT analysis. For lightning, try to avoid representing individual bus sections of less than 3 metres as DP lines. Divide and lump the spacer capacitance at each end of each bus section.



© Douglas J. Mader

49


Modeling Guidelines for GIS spacers - ~ 20 pF magnetic PT - ~ 100 - 300 pF (400-800 kV) closed circuit breaker - DP line of the length of the breaker, velocity of .95c and Z calculated from average diameter of breaker conducting elements from end to end. Add lumped phase-earth caps. Open circuit breaker - same but divided at open contact and grading capacitors across opening. Model closing resistor as separate breaker. Disconnectors - include length as DP line add shunt cap of ~25-50 pF 

© Douglas J. Mader

50


Modeling Guidelines for GIS surge arrester capacitance ~ 100-200 pF cable terminals ~ 60-80 pF plus length as DP line SF6-Oil bushing ~ gas filled ~20-40 pF ~ capacitive ~ 100-300 pF ground switch ~ 20-40 pF Elbow - additional ~ 20-40 pF Bus end - additional 3-5 PF for spherical shield 

© Douglas J. Mader

51


Power transformers 





If possible use wideband transformer model esp. for surge transfer studies where winding ratio > 10:1, if not use the L-C matrix unless you do parametric study As a minimum, model transformers as input capacitance including bushings [typical HV-G values of large units are 4 - 40 nF (shell) 1 - 20 nF (core)] in shunt with surge impedance of about 5000 ohms

Consider possible open breaker conditions and lines © Douglas J. Mader 52 out of service

Lightning Overvoltages Modeling and Analysis IEEE SPDC WG 3.4.11 Model (Station Class or IEC Class 4-5)

© Douglas J. Mader

53


© Douglas J. Mader

54


© Douglas J. Mader

55

Electromagnetic Transient in Power System and Insulation Coordination Studies

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