Power loss due to corona is directly proportional to

Question

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Option C: Supply frequency

Explanation & Concepts:
Corona power loss ($P_c$) is directly proportional to the supply frequency ($f$). This relationship is derived from Peek's formula, which shows that ionization losses per cycle increase linearly with the frequency of the alternating voltage supply.

Working Principle: Corona is an electrical discharge caused by the ionization of fluid surrounding a conductor. As the frequency increases, the number of cycles per second increases, meaning the air around the conductor undergoes ionization and de-ionization processes more frequently, leading to higher cumulative energy dissipation per unit time.

Key Formulas: $P_c = 242.2 	imes \frac{f + 25}{\delta} \sqrt{\frac{r}{d}} (V - V_c)^2 	imes 10^{-5}$ — Peek's formula for corona loss; $P_c \propto f$ — Proportionality relationship

Key Points: Corona loss is observed to be directly proportional to $(f + 25)$, where $f$ is in Hertz.; Higher frequency leads to a greater number of ionization cycles per second, increasing the heat and noise dissipation.; Corona is more prevalent in HV and EHV lines where the surface electric field intensity exceeds the dielectric strength of air.

Advantages: Used as a natural indicator of line insulation stress.; Prevents transient overvoltages by dissipating energy during surges.

Disadvantages: Causes power loss in transmission lines.; Leads to radio and television interference due to harmonic generation.; Produces ozone, causing corrosion of conductors.

Applications: Design of high voltage transmission lines.; Used in electrostatic precipitators and laser printers.

Additional Info: Dielectric strength of air at NTP is approximately $30 kV_{peak}/cm$ (or $21.1 kV_{rms}/cm$).. Option A is incorrect because increasing spacing between conductors increases the distance, which actually reduces the potential gradient and thus reduces corona loss.. Option B is incorrect because increasing the radius (r) of the conductor reduces the electric field intensity ($E = V/r \ln(D/r)$), thereby reducing corona loss.

Answer: C is correct — Power loss due to corona increases linearly with an increase in the frequency of the power supply as defined by Peek's formula.

Exam Tip: Remember that while corona increases with frequency, it is inversely proportional to the logarithm of the conductor spacing ($D$) and decreases with an increase in conductor radius ($r$).

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Option A: Spacing between conductors

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Option B: Radius of conductor

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Option D: None of above

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