Laplace Transforms
Definition
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one-sided Laplace integeral:
L F (t ) = lim 0 F (t ) e - st dt
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Laplace transform properties superpositioning L [F1 (t ) + F2 (t )] = L F1 (t ) + L F2 (t ) constant stimuli LV =V s ramp stimuli L [I t ] = I s 2
exponent
Chapter 2
The Laplace Transform Method
January 2004
Power System Transients
Functional Transforms
Definition
an operation performed on a function to change it into a new function, typically in a different variable such transformation has the purpose of
Fundamental Notions
Transients
electrical manifestation of a sudden change in circuit conditions
switch opens switch closes network fault
transient period is very short relative to the time spent in steady state operation, but is extremely important
gr
Chapter 10:
Principles of Transient Modeling of
Principles of Transient Modeling of
Power Systems and Components
Introduction
Measuring transient behaviors
taking measurements is difficult, expensive, and hazardous
need to know how components will behave
Chapter 15:
Insulation Coordination
Basic Ideas and Concepts
Transient over-voltages are inherent consequences of
power system operation
sources
switching events can be controlled to some extent by good
design
design
faults and abnormal conditions; and
Chapter 14:
Lightning
Scope of the Lightning Problem
IEEE-EEI Committee study of outages on EHV lines
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lightning is the greatest single cause of outages
accounting for about 26 % for the outages on 230 kV circuits
for about 26 for the outages on 230 k
Chapter 9: Traveling Waves and
Transients on Transmission Lines
Attenuation
Attenuation & Distortion of Travelling Waves
Assumptions and simplifications used in simple two-wire
and simplifications used in simple two
transmission models
far removed from g
Chapter 9: Traveling Waves and
Transients on Transmission Lines
Distributed
Distributed Parameter Elements
There are many important parts of a power system where
lumped parameter modeling is inadequate
approximations are too great
obvious example is a tr
Chapter 8: Electromagnetic Phenomena
Under Transient Conditions
Transient Analysis Using
Maxwells Equations
October 2009
Power System Transients
Page 1
Introduction
Introduction
At this point in the study of transient, more emphasis is
placed on the fie
Chapter 6: Transients in
Chapter 6: Transients in 3-Phase Circuits
Circuits
Introduction
Introduction
No limitation inherent to expanding the study of transient
in single-phase networks to poly-phase networks
poly-phase networks require a little more com
Coil Capacitance
Capacitance to ground of an elementary length x of a coil winding
x Cg 3 x
R0
Lm
Cg
l
Simple model for a coil being switched on no load
27 August 2001
Power System Transients
Coil Capacitance
Steady state operation model
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sees a l
Typical Current and Voltage of Diodes
reverse recovery charge to remove charge carriers from pn junction
Turn-on voltage overshoot not modeled in EMTP like programs
Reason for VFP: Significant ohmic resistance of drift region until space charge layer is d
Power Electronics (PE) Applications
High Voltage DC links (HVDC) Static var Compensation (STATCOM) Load Transfer Switch (e.g. electronic tap changers) Uninterruptible Power Supplies (UPS) Flexible AC Transmission Systems (FACTS) Variable Speed Drives .
Delayed Periodic Functions
Vm
V(t)
0
0
2
3
4
Full-wave rectified output
23 October 2001
Power System Transients
Characteristics of Power Electronics
Common power electronic devices
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Thyristor or Silicon Controlled Rectifier (SCR) Gate Turn Of
Simulating Transmission Lines Typical Applications
Steady State at power frequency w induced voltages at de-energized line segment Steady State at higher frequency w harmonics, power line carrier communication Transients w switching and lightning surges
Two-Wire Transmission Line
S Load
V
S
V
L1 C1
L2 C2
Ln Cn
"Lumpy" representation
Power System Transients
23 October 2001
Charges and Fluxes
Q = C V x dx x I = lim C V =CV x 0 dt t dx =v I =CV v dt
Charge per unit length
Magnetic flux linkage = L I x per
Magnetic Flux Penetration in Metals
Changing magnetic field links other metallic structures besides conventional circuits
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magnetic cores, cubicle walls, structural steel
Linkage within metallic conductors
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inducing emf's, which drive currents in th
Electrostatic Coupling
Q V= C
Power System Transients
16 October 2001
Electrostatic Coupling
16 October 2001
Power System Transients
Electrostatic Coupling Example
16 October 2001
Power System Transients
Electrostatic Coupling Example
16 October 2001
Powe
HW04 Transformer Inrush
Model in EMTDC the magnetizing current of an iron core inductor by means of
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Variable Inductor controlled by Control Blocks modeling the non-linear inductance (see graphic)
Results: Model and Plots
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Current versus time when
Transformer Magnetizing Current
(or B) 1.2 T
v= d dt
stiff v-source !
Non-linear magnetizing curve of iron core
103 0 i (or H) t1
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t2
t
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high 3rd current harmonic in steady state resonance problems with series capacitance ferro-resonance inrush cu
Paper Review
www.ieee.org/organizations/society/power/subpages/authors-folder/authkitfolder/authkit.htm
Guidelines
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Layout: font size, type, graphics, equations Content: new material? Originality, Errors? Clarity of presentation, language Structur
Arc Voltage - Instabilities
Arcing Voltage current
current, voltage
time
Arcing voltage drop
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Not constant due to nonlinear V(I) characteristic Additional "noise" due to thermodynamic processes Essential for low voltage applications => Current limitin
Homework - Comments
Documentation of results are most important
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Plots without comments are not acceptable! Draw at least one conclusion (attempting to explain your results) e.g. "Highest peak of of fault current since voltage is zero at fault incepti
Examples on Board
This lecture consisted of the detailed explanations of the transients associated with the basic LC circuit on the board No lecture notes available
13 September 2001
Power System Transients
Circuit Closing Transients
energizing an RL circuit
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closing a circuit breaker onto a lagging power factor load circuit is reduced to barest essentials for simplicity example: 34.5 kV system load: 15 MW, 0.7 pf
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R V L
27 August 2001
Power System Tr
Post processing Presenting Results
The view graphs should "speak" for themselves
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No curve without label and unit on y and t axis Utilize significance of view graphs Point to curve with arrows Compare scenarios with p.u. values (normalized) Co