COLEGIO DE INGENIERIA
UNIVERSIDAD DE PUERTO RICO - MAYAGUEZ
INEL 5406
Líneas de Transmisión
Efraín O’Neill-Carrillo, PhD, PE
1
Introducción
Hay diversas estructuras que se usan para
sostener las líneas de transmisión
Pueden ser en metal o en madera, dependiendo del
área, la altura requerida, costos y otros factores:
Construcción
Operación
Mantenimiento
Cost
Capacidad de la línea
Despejos
Hay consideraciones legales, zonificación, e
impacto visual.
La servidumbre depende del voltaje de la línea y
altura de la torre. Puede ser entre 75-150 pies de
ancho.
Impacto en vegetación y el ambiente
http://www.atcllc.com/IT10.shtml
Línea de transmisión: un circuito
Línea de transmisión
Circuito Doble, 138kv, en madera. Otras
líneas (cable and
telefono) pueden usar
la misma estructura.
http://www.atcllc.com/IT10.shtml
Línea de transmisión
Circuito Doble, 138kv, en acero. Se usa
cuando la torre tiene
que aguantar mucho
peso.
http://www.atcllc.com/IT10.shtml
Línea de transmisión
138-kv en acero. La
estructura se oxida
para dar la apariencia
de moho.
http://www.atcllc.com/IT10.shtml
Línea de transmisión
Estructura en H en
madera. Altura más
baja que postes
sencillos.
http://www.atcllc.com/IT10.shtml
Línea de transmisión
Circuito Double 138-kv en torre
enrejada (“lattice”). Este tipo de
estructura es muy fuerte, pero
liviana.
http://www.atcllc.com/IT10.shtml
Línea de transmisión
Circuito doble de
345-kilovolt.
Voltajes Voltajes
mayores requieren
postes más altos y una
servidumbre más
ancha.
http://www.atcllc.com/IT10.shtml
http://www.nrc.gov/reading-rm/doc-collections/nuregs/staff/sr1437/v1/fig005.gif
High-Phase Order Transmission Lines
http://www.nationalgrid.com/uk/LandandDevelopment/DDC/devnearohl_final/appendix2/
Análisis de líneas
Steady state
Transitorio
Sistemas de potencia (baja
frecuencia)
Alta frecuencia en comunicaciones
Conductores
Los conductores usados en líneas de
transmisión grandes son usualmente de
aluminio.
El aluminio es más liviano que el cobre y
cuesta menos (en zonas costeras no se usa
aluminio). Pero conduce menos que el cobre.
Los conductores se sostienen en la torre
usando aisladores de porcelana o polímeros.
Polímeros son más livianos
A mayor temperatura mayor la resistencia
de los conductores
R = r(largo/area); r es proporcional a temp
http://www.atcllc.com/IT10.shtml
Detalle de aisladores
http://ieee-tpc.org/ieee_photos/photos.htm
Conductores
Comúnmente para voltajes de transmisión se usan
conductores tipo “aluminum-conductor steelreinforced” (ACSR).
http://www.anishindustrial.com/aluminium-conductor-steel-reinforced-acsr.html
Line Conductors
 Total conductor area is given in circular mils. One
circular mil is the area of a circle with a diameter
of 0.001 =   0.00052 square inches
 Example: what is the the area of a solid, 1”
diameter circular wire?
Answer: 1000 kcmil (kilo circular mils)
 Because conductors are stranded, the equivalent
radius must be provided by the manufacturer. In
tables this value is known as the GMR and is
usually expressed in feet.
Courtesy of Prof. Tom Overbye, UIUC
Line Resistance
Line resistance per unit length is given by
R =
r
where r is the resistivity
A
Resistivity of Copper = 1.68  10-8 Ω-m
Resistivity of Aluminum = 2.65  10-8 Ω-m
Example: What is the resistance in Ω / mile of a
1" diameter solid aluminum wire (at dc)?
2.65  10-8 Ω-m
m

R 
1609
 0.084
2
mile
mile
  0.0127m
Courtesy of Prof. Tom Overbye, UIUC
Line Resistance, cont’d
 Because ac current tends to flow towards
the surface of a conductor, the resistance
of a line at 60 Hz is slightly higher than at
dc.
 Resistivity and hence line resistance
increase as conductor temperature
increases (changes is about 8% between
25C and 50C)
 Because ACSR conductors are stranded,
actual resistance, inductance and
capacitance needs to be determined from
tables.
Courtesy of Prof. Tom Overbye, UIUC
ACSR Table Data (Similar to
Table A.4)
GMR is equivalent to r’ Inductance and Capacitance
assume a Dm of 1 ft.
Courtesy of Prof. Tom Overbye, UIUC
Transmission Tower
Configurations
The problem with the line analysis we’ve done so far
is we have assumed a symmetrical tower configuration.
Such a tower figuration is seldom practical.
Therefore in
general Dab 
Dac  Dbc
Typical Transmission Tower
Configuration
Courtesy of Prof. Tom Overbye, UIUC
Unless something
was done this would
result in unbalanced
phases
Transposition
To keep system balanced, over the length of a
transmission line the conductors are rotated so
each phase occupies each position on tower for an
equal distance. This is known as transposition.
Aerial or side view of conductor positions over the length
of the transmission line.
Courtesy of Prof. Tom Overbye, UIUC
Line Transposition Example
Courtesy of Prof. Tom Overbye, UIUC
Line Transposition Example
Courtesy of Prof. Tom Overbye, UIUC
Line
Transposition
http://www.kecrpg.com/KEC%20data/career/Transp
osition%20tower%20in%20india.jpg
Additional Transmission Topics
 Multi-circuit lines: Multiple lines often share a
common transmission right-of-way. This DOES
cause mutual inductance and capacitance, but is
often ignored in system analysis.
 Cables: There are about 3000 miles of
underground ac cables in U.S. Cables are primarily
used in urban areas. In a cable the conductors are
tightly spaced, (< 1ft) with oil impregnated paper
commonly used to provide insulation
– inductance is lower
– capacitance is higher, limiting cable length
Courtesy of Prof. Tom Overbye, UIUC
Additional Transmission topics
 Ground wires: Transmission lines are usually
protected from lightning strikes with a ground wire.
This topmost wire (or wires) helps to attenuate the
transient voltages/currents that arise during a
lighting strike. The ground wire is typically
grounded at each pole.
 Corona discharge: Due to high electric fields
around lines, the air molecules become ionized. This
causes a crackling sound and may cause the line to
glow!
Courtesy of Prof. Tom Overbye, UIUC
Additional Transmission topics
 Shunt conductance: Usually ignored. A small
current may flow through contaminants on
insulators.
 DC Transmission: Because of the large fixed cost
necessary to convert ac to dc and then back to ac,
dc transmission is only practical for several
specialized applications
– long distance overhead power transfer (> 400
miles)
– long cable power transfer such as underwater
– providing an asynchronous means of joining
different power systems (such as the Eastern
and Western grids).
Courtesy of Prof. Tom Overbye, UIUC
Physics of Corona and Gap Discharges
AC and DC Transmission Line Corona
Effects
UV Inspection User’s Group Meeting
February 11-13, 2004
ORLANDO, Florida, USA
By
Dr. P. Sarma Maruvada
Notas en español agregadas por Ing. Ariel Lichtig
exclusivamente para curso teoría de Campos-FIUBA
Introduction
Electrical Design, Operation & Maintenance of HV
Transmission Lines Requires Consideration of:
- Air Insulation
- Corona
- Insulators
All Three Aspects Require Knowledge of Electrical
Discharges in Air, Which May Comprise:
- Partial Breakdown (Corona)
- Complete Breakdown (Gap Discharges)
Corona & Gap Discharges
Corona is an electrical discharge (i.e. partial
breakdown of air insulation) occurring in the high
electric field region, generally in the vicinity of
conducting surfaces, but sometimes also near
insulating surfaces, due to ionization processes in air.
(Resulta de procesos de avalanchas de electrones bajo
condiciones de campo no uniforme que produce que
la avalancha cese antes de llegar a tierra.)
Complete electrical breakdown of air insulation
between two electrodes separated by a very small gap
is known as a micro-gap discharge or simply as Gap
Discharge.
Gap Discharges in Air
Gap Discharges may Occur:
Between metallic hardware parts of
transmission and distribution lines;
Between metallic and insulating surfaces;
On the surface of polluted insulators
Corona Effects on AC and DC
Transmission Lines
For both ac and dc lines:
Corona (power) Loss (CL)
Electromagnetic Interference (EMI) (Includes
RI, TVI, etc.,)
Audible Noise (AN)
Ozone, NOx etc.
For dc lines:
Space Charge Effects
Corona-generated Hum Noise
Sound Pressure Level, dB above 20 µ PA
Oscillatory movement of the ionic space charge
creates hum noise at twice power frequency;
Figure shows lateral profile of hum noise
70
60
50
40
0
10
20
30
40
Lateral Distance From Center Phase, m.
50
Corona Effects Design Criteria
Corona Loss
- Economic Choice of Conductor Bundle
Total Cost
B
A
por pérdidas
dc1
dm
dc2 por radiointerferencia
Conductor Diameter, d
Corona Effects Design Criteria (at 1 MHz)
Radio Interference
USA
RI from power
systems is governed
by the FCC Rules
Canada
Design Limits
Nominal
Phase-toPhase Voltage
(kV)
Interference
Field
Strength
(dB above
1 μV/m)
Below 70
70 – 200
200 – 300
300 – 400
400 – 600
Above 600
43
49
53
56
60
63
Corona Effects Design Criteria
Audible Noise
USA
 The Environmental Protection Agency (EPA)
published guidelines for AN in general.
 However, each state is responsible to legislate
noise regulations and these regulations may
vary widely from state to state.
 The EPA document recommends that the daynight average sound level, Ldn, be limited to
55 dB(A) outdoors and 45 dB(A) indoors.
“Bundles”
http://ieee-tpc.org/ieee_photos/photos.htm
Sajita, catenaria, flecha (“sag”)
http://ieee-tpc.org/ieee_photos/photos.htm
Limits Affecting Max. Power
Transfer
 Thermal limits
– limit is due to heating of conductor and hence
depends heavily on ambient conditions.
– For many lines, sagging is the limiting constraint.
– Newer conductors limits can limit sag. For
example, in 2004 ORNL working with 3M
announced lines with a core consisting of ceramic
Nextel fibers. These lines can operate at 200
degrees C.
– Trees grow, and will eventually hit lines if they
are planted under the line.
Courtesy of Prof. Tom Overbye, UIUC
Other Limits Affecting Power
Transfer
 Angle limits
– while the maximum power transfer occurs when
line angle difference is 90 degrees, actual limit
is substantially less due to multiple lines in the
system
 Voltage stability limits
– as power transfers increases, reactive losses
increase as I2X. As reactive power increases
the voltage falls, resulting in a potentially
cascading voltage collapse.
Courtesy of Prof. Tom Overbye, UIUC
Transmission Line Equivalent
Circuit
Our current model of a transmission
line is shown below
Units on
z and y are
per unit
length!
For operation at frequency  , let z = r + j L
and y = g +jC (with g usually equal 0)
Courtesy of Prof. Tom Overbye, UIUC
Three Line Models
Long Line Model (longer than 200 miles)

l
sinh  l Y ' Y tanh 2
use Z '  Z
,

l
2 2 l
2
Medium Line Model (between 50 and 200 miles)
Y
use Z and
2
Short Line Model (less than 50 miles)
use Z (i.e., assume Y is zero)
Courtesy of Prof. Tom Overbye, UIUC
Modelos de línea
Corta (menos de 50 millas)
Zs= R + jX (“lumped”)
Mediana (50 a 200 millas)
Parametros ABCD (modelos  o T)
Zs, Yc
Modelo de línea larga
Distancia > 200 millas
Parametros distribuidos
Zo=√(Zs/Yc);  =a+jb= ZsYc
Constante de atenuacion a
Cambio de fase b
Valor de V e I en cualquier punto x de
la linea
Vsend(x)=Vrcosh (x)+ IrZoYsinh(x)
Isend(x)=Ircosh (x)+ (Vr/Zo)Ysinh(x)
Modelos de línea
http://www.lexic.us/definition-of/transmission_line