# Transmission Line Corona Calculations

The air at the surface of the conductor can be ionised when the voltage gradient at the conductor surface exceeds the allowable critical gradient [1, 4]. This ionisation creates a heat source very close to the conductor surface which can affect the rating of the conductor . However, corona effects are commonly ignored in rating calculations as this ionisation is usually considered during the line design stages. Nevertheless, there are some instances where corona needs to be considered, such as the uprating of an existing line to a higher operating voltage.

The critical surface voltage gradient for a conductor surface was initially derived experimentally by F.W. Peek . The following equation summarises this phenomenon where the conductor (or conductor bundle) is surrounded by a cylinder at zero potential . A similar equation can be derived for the critical surface voltage gradient where there are parallel conductors or a single conductor above an earthed plane . where δ is the relative air density, and m is the surface irregularity factor and D is the conductor diameter, or the effective diameter of the conductor bundle.

The surface factor depends on the conductor stranding, the presence of surface scratches and foreign matter such as pollution or even water droplets. Various reports give guidance in the selection of the irregularity factor, such as  which notes that values between 0.5 and 0.65 should be used for new, dry conductors. After several months ageing this value rises to around 0.9, but this may fall when pollution or dust affects the conductor surface. During rainfall, the surface irregularity factor falls to between 0.7 and 0.75 if the rainfall intensity is less than 2mm per hour. Lower values should be selected for higher intensity rainfall in accordance with [1, 3, 4].

The critical surface voltage gradient needs to be compared with the electric field gradient at the conductor surface. For a conductor (or conductor bundle) is surrounded by a cylinder at zero potential, this equates to : where V is the three-phase rms line voltage, and d1 is the conductor diameter, or the effective diameter of the conductor bundle, and d2 is the diameter of the zero potential cylinder.

Similar equations can be derived for the ‘parallel conductor’ and the ‘conductor to plane’ scenarios described in , respectively, where S is the separation between the parallel conductors and h is the height above the ground plane: ## References

 M.G. Comber, D.W. Deno, L.E. Zaffanella “Corona Phenomena on AC Transmission Lines” Chapter 4 in Transmission Line Reference Book 345kV and Above, EPRI, revised 2nd edition, EL-2500 1987
 M.G. Comber, L.E. Zaffanella “Corona Loss” Chapter 7 in Transmission Line Reference Book 345kV and Above, EPRI, revised 2nd edition, EL-2500 1987
 F.W.Peek, “Dielectric Phenomena in High Voltage Engineering”, 1929 McGraw Hill
 V.T. Morgan, “The Thermal Rating of Overhead-Line Conductors. Part 1. The Steady State Thermal Model”, Electric Power Systems Research, 5 (1982) 119-139