ELEC5205 Chap.9 Overhead Line Parameters and Surges
Overhead Line Parameters and Surges
Compress geometry without losing meaning
Geometric mean distance represents phase spacing, while geometric mean radius represents conductor or bundle construction. Inductance uses self-GMR because internal flux matters; capacitance uses physical radius because a conductor has no internal electric field. These parameters shape surge impedance and travelling-wave behaviour.
Thermal rating, corona onset and lightning exposure remain separate limits that require their own environmental and geometric inputs.
Reduce a transposed geometry carefully
Unequal phase spacings are represented by the cube root of their product when transposition makes each phase occupy every position over the line length. That equivalent is the geometric mean distance.
Conductor construction enters separately through self-geometric mean radius for inductance and physical or bundle-equivalent radius for capacitance. Keeping those quantities distinct prevents a common error in which one convenient radius is inserted into both logarithms.
Units inside a logarithmic ratio must also be consistent.
Predict directions before calculating
Wider phase spacing generally increases inductance and reduces capacitance. A larger effective conductor or bundle radius generally reduces inductance and increases capacitance. Because surge impedance follows the square root of inductance divided by capacitance, bundling tends to lower it.
These direction checks are powerful error detectors. If a numerical result contradicts them, inspect radius choice, spacing product, phase convention and per-metre conversion before trusting calculator precision.
Trace a travelling wave through a junction
A line termination or line-to-cable transition presents a new surge impedance.
The incident voltage and current divide into reflected and transmitted waves so that terminal voltage and current remain compatible at the junction. Reflection sign depends on the relative impedances: a lower-impedance cable tends to reflect voltage with opposite polarity, while an open end produces strong positive voltage reflection.
State the reference direction for current and use one consistent reflection convention throughout the solution.
Keep steady and transient limits separate
Thermal rating depends on resistance, ambient conditions, wind and allowable conductor temperature. Corona depends on surface field, radius, bundle arrangement, air density and surface condition.
Lightning exposure depends on shielding geometry, tower response and insulation coordination. A line may satisfy its steady current target yet remain poorly protected against a surge. A complete design conclusion identifies which limit is being calculated, which environmental variables it assumes, and what protection or geometry addresses the other limits.
What this chapter covers
- 01
Geometric Mean Distance
- 02
Self-GMR
- 03
Line Inductance
- 04
Line Capacitance
- 05
Surge Impedance
- 06
Wave Reflection
Worked example · free
Calculate line parameters
- 2Take the cube root of the spacing product for GMD.
- 4Use self-GMR for inductance and physical radius for capacitance.
- 2Calculate surge impedance and test physical magnitude.
Key terms
- Self-GMR
- Self-GMR is the effective radius used in inductance calculations to account for internal flux linkages.
- Surge Impedance
- Surge Impedance is the voltage-to-current ratio of a travelling wave determined approximately by the square root of L over C.
- Reflection Coefficient
- Reflection Coefficient gives the signed fraction of incident voltage returned by an impedance discontinuity.
Overhead Line Parameters and Surges FAQ
Why do inductance and capacitance use different radii?
Inductance includes internal magnetic flux and therefore uses the conductor self-GMR. Capacitance follows the external electric field and uses physical conductor radius because electric field is zero inside the conductor.
What does conductor bundling change?
Bundling raises effective GMR and capacitive radius. The inductance logarithm decreases, capacitance rises and surge impedance falls, while surface electric field and corona performance also change.
How are transmitted and reflected surge voltages checked?
Calculate coefficients from the two surge impedances, then verify that incident plus reflected voltage equals transmitted voltage at the junction. The sign of reflection shows whether the returned wave reverses polarity.
Exam move
Recompute one unequal-spacing GMD, one bundled-radius direction question and one line-to-cable junction. After each result, predict whether increasing conductor spacing or bundle size should raise or lower L, C and surge impedance. Review thermal and lightning formulas as separate design layers.
Draw voltage and current reference arrows before applying a reflection coefficient, then verify their sums against the receiving surge impedance. Keep a constraint ledger for steady temperature, corona onset and impulse withstand, including the weather and geometry behind each margin. Compare one design change across all three columns so a local benefit is not mistaken for a complete line recommendation.
State whether every result is per phase, per conductor and per unit length, then convert only after the physical model is internally consistent.
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