BEE3133 Electrical Power Systems

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BEE3133 Electrical Power Systems

• Chapter 3
• Transmission Line Parameters

Rahmatul Hidayah Salimin revised by Ramdan Razali
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INTRODUCTION
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INTRODUCTION
Transmission line is non ideal, therefore cannot
be assumed that the wires that transmit
electricity are loss less.
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INTRODUCTION

• All transmission lines in a power system exhibit
  the electrical properties of resistance,
  inductance, capacitance and conductance.
• Inductance and capacitance are due to the effects
  of magnetic and electric fields around the
  conductor.
• These parameters are essential for the
  development of the transmission line models used
  in power system analysis.

a model of a transmission line as a resistive
element.
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INTRODUCTION

• The shunt conductance accounts for leakage
  currents flowing across insulators and ionized
  pathways in the air.
• The leakage currents are negligible compared to
  the current flowing in the transmission lines and
  may be neglected.

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RESISTANCE

• Important in transmission efficiency evaluation
  and economic studies.
• Significant effect
• Generation of I2R loss in transmission line.
• Produces IR-type voltage drop which affect
  voltage regulation.

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RESISTANCE

• The dc resistance of a solid round conductor at a
  specified temperature is
• Where
• ? conductor resistivity (O-m),
• l conductor length (m) and
• A conductor cross-sectional area (m2)

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RESISTANCE

• Conductor resistance is affected by three
  factors-
• Frequency (skin effect)
• Spiraling
• Temperature

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RESISTANCE

• Frequency Skin Effect
• When ac flows in a conductor, the current
  distribution is not uniform over the conductor
  cross-sectional area and the current density is
  greatest at the surface of the conductor.
• This causes the ac resistance to be somewhat
  higher than the dc resistance. The behavior is
  known as skin effect.

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RESISTANCE

• The skin effect is where alternating current
  tends to avoid travel through the center of a
  solid conductor, limiting itself to conduction
  near the surface.
• This effectively limits the cross-sectional
  conductor area available to carry alternating
  electron flow, increasing the resistance of that
  conductor above what it would normally be for
  direct current

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RESISTANCE
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RESISTANCE

• Skin effect correction factor are defined as
• Where
• R AC resistance and
• Ro DC resistance.

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RESISTANCE

• Spiraling
• For stranded conductors, alternate layers of
  strands are spiraled in opposite directions to
  hold the strands together.
• Spiraling makes the strands 1 2 longer than
  the actual conductor length.
• DC resistance of a stranded conductor is 1 2
  larger than the calculated value.

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RESISTANCE

• Temperature
• The conductor resistance increases as temperature
  increases. This change can be considered linear
  over the range of temperature normally
  encountered and may be calculated from
• Where
• R1 conductor resistances at t1 in C
• R2 conductor resistances at t2 in C
• T temperature constant (depends on
  the conductor material)

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RESISTANCE

• The conductor resistance is best determined from
  manufacturers data.
• Some conversion used in calculating line
  resistance-
• 1 cmil 5.067x10-4 m2

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Resistivity Temparature Constant of Conductor
Metals
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RESISTANCE

• Example-
• A solid cylindrical aluminum conductor 25km long
  has an area of 336,400 circular mils. Obtain the
  conductor resistance at
• 20C and
• 50C.
• The resistivity of aluminum at 20C is
• ? 2.8x10-8O-m.

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RESISTANCE

• Answer (a)

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RESISTANCE

• Answer (b)

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RESISTANCE

• Exercise
• A transmission-line cable consists of 12
  identical strands of aluminum, each 3mm in
  diameter. The resistivity of aluminum strand at
  20C is 2.8x10-8O-m. Find the 50C ac resistance
  per km of the cable. Assume a skin-effect
  correction factor of 1.02 at 50Hz.

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INDUCTANCE A SINGLE CONDUCTOR

• A current-carrying conductor produces a magnetic
  field around the conductor.
• The magnetic flux can be determined by using the
  right hand rule.
• For nonmagnetic material, the inductance L is the
  ratio of its total magnetic flux linkage to the
  current I, given by
• where ?flux linkages, in Weber turns.

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INDUCTANCE A SINGLE CONDUCTOR

• For illustrative example, consider a long round
  conductor with radius r, carrying a current I as
  shown.
• The magnetic field intensity Hx, around a circle
  of radius x, is constant and tangent to the
  circle.

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INDUCTANCE A SINGLE CONDUCTOR

• The inductance of the conductor can be defined as
  the sum of contributions from flux linkages
  internal and external to the conductor.

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Flux Linkage
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INDUCTANCE A SINGLE CONDUCTOR

• INTERNAL INDUCTANCE
• Internal inductance can be express as follows-
• Where
• µo permeability of air (4p x 10-7 H/m)
• The internal inductance is independent of the
  conductor radius r

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INDUCTANCE A SINGLE CONDUCTOR

• INDUCTANCE DUE TO EXTERNAL FLUX LINKAGE
• External inductance between to point D2 and D1
  can be express as follows

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INDUCTANCE A SINGLE PHASE LINES

• A single phase lines consist of a single current
  carrying line with a return line which is in
  opposite direction. This can be illustrated as

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INDUCTANCE A SINGLE PHASE LINES

• Inductance of a single-phase lines can be
  expressed as below with an assumption that the
  radius of r1r2r.

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SELF AND MUTUAL INDUCTANCES

• The series inductance per phase can be express in
  terms of self-inductance of each conductor and
  their mutual inductance.
• Consider the one meter length single-phase
  circuit in figure below-
• Where L11 and L22 are self-inductance and the
  mutual inductance L12

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SELF AND MUTUAL INDUCTANCES
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SELF AND MUTUAL INDUCTANCES

• L11, L22 and L12 can be expressed as below-

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SELF AND MUTUAL INDUCTANCES

• Flux linkage of conductor i