Transmission Line Modelling

Demonstrative Video


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Contents

  • Parameters of the TL

  • Relation of parameters with Electric and Magnetic field

  • Types of Conductors

  • Resistance of TL and variation with temperature

  • Skin effect


Parameters of the Transmission Line

  • An electric transmission line has 4 parameters :

    • Resistance and Inductance form series impedance

    • Capacitance and Conductance form shunt admittance

  • Conductance:

    • exists between conductors or conductors and the ground

    • accounts for the leakage current at the insulators of overhead lines or through insulation of cables

    • leakage at insulators of overhead lines is negligible, conductance is neglected

    • variable no good way to take into account

      • leakage at insulator change appreciably with atmospheric conditions

      • conducting properties due to dirt deposit on insulators

      • Corona variable with atmospheric conditions

      • effect of conductance is negligible amount of shunt admittance


Relation of parameters with electric and magnetic fields

  • Lines of magnetic flux forms a closed loop linking the circuit

  • Lines of electric flux originate from the ’+’ charge on one conductor and terminate on the ’-’ charge on the other conductor

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Magnetic and Electric field associated with a two-wire line

  • Variation of the current causes changes in the number of magnetic flux lines linking the circuit

  • Change in the flux linkage induce a voltage proportional to the rate of change of flux

  • Inductance \(\rightarrow\) Voltage induced \(\rightarrow\) Changing flux \(\rightarrow\) Rate of change of current

  • Capacitance \(\rightarrow\) Charge on the conductors per unit of potential difference between them


Types of conductors

  • Copper replaced by aluminum

    • much lower cost

    • Lighter weight for the same resistance

  • Al conductor has a larger diameter (advantageous) compared to Cu conductor of the same resistance

    • lines of electric flux originating on the conductor will be further apart at the conductor surface for the same voltage

    • lower voltage gradient at the conductor surface

    • Less tendency to ionize the air around the conductor (Corona)

    • AAC all-aluminum conductors

    • AAAC all-aluminum-alloy conductors

    • ACSR aluminum conductor steel reinforced

    • ACAR aluminum conductor alloy reinforced

  • Al alloy conductors have higher tensile strength as compared to ordinary conductors

  • ACSR: central core of steel strands surrounded by layers of Al strands

  • ACAR: central core of higher-strength Al surrounded by layers of electrical-conductor-grade Al


Stranded conductors

  • Alternate layers of wires are spiraled in opposite direction to prevent unwinding

  • outer radius of one layer coincide with inner radius of the next layer

  • provides flexibility for large cross-sectional area

  • number of strands depends on the number of layers and whether all the strands are of the same diameter

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  • Expanded ACSR:

    • has filler such as paper separating the inner steel strands from outer Al strands.

    • Paper gives larger diameter (lower corona) for given conductivity and tensile strength.


Resistance of the transmission line

  • responsible for power loss in the TL

  • The effective resistance of the conductor

    \[R=\dfrac{\mbox{power loss in the conductor}}{|I|^{2}}\Omega\]
    equals to the dc resistance for uniform current distribution
  • DC resistance is given by

    \[R_{0}=\dfrac{\rho l}{A}~\Omega\]
  • dc resistance of the stranded conductor is greater than computed by \(R_0\) because spiralling of the strands make them longer than the conductor itself

  • 1% for 3 strand and 2% for concentrically stranded conductors


Variation of Resistance with Temperature

  • practically linear over normal range of operation

  • extension of the linear portion \(\mapsto\) correction the resistance with temperature
    \(\Rightarrow\) point of interaction with \(t\)-axis at zero \(R\) is a constant of the material

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  • Uniform distribution of current through \(A\) occurs only for dc

  • \(f\) of the ac \(\Uparrow\), non-uniformity becomes more pronounced


Skin Effect

  • The non-uniform distribution of electric current over the surface or skin of the conductor carrying a.c is called the skin effect.

  • In other words, the concentration of charge is more near the surface as compared to the core of the conductor.

  • The ohmic resistance of the conductor is increased due to the concentration of current on the surface of the conductor.

  • : increase in \(f\) causes non-uniform current distribution

  • \(\Rightarrow\) circular conductor \(\mapsto\) current density usually increases from the interior towards the surface

  • \(\Rightarrow\) larger radius conductor \(\mapsto\) current density is oscillatory w.r.t radial distance from the center

\[\mathrm{R_{AC}}=\mathrm{R_{DC}}\cdot k \sqrt{f}\]
Example:

Factors affecting Skin Effect

  • Frequency – increases with the increase in frequency.

  • Diameter – increases with the increase in diameter of the conductor.

  • Shape of the conductor – more in the solid conductor and less in the stranded conductor because the surface area of the solid conductor is more.

  • Type of material – increase with the increase in the permeability of the material.

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