High voltage (EHV and UHV) transmission facilitates transfer of large amount of power over long distances. However, due to the inherent geometry, the line and substation hardware of EHV and UHV class generate high electric fields, which results in local ionisation of air called corona discharges. Apart from producing audible noise in the form of frying or hissing sound, corona produces significant electromagnetic interferences in the radio range. The limit for this corona generated Radio Interference (RI) has been stipulated by international standards, which are strictly to be followed. In line and substation hardware, corona control rings are generally employed to limit or avoid corona. Standard dimensions of corona rings are not available for EHV and UHV class. In most of the cases, their design is based on either a trial and error method or based on empirical extrapolation. Only in certain specific cases, the dimensioning of the rings is carried out using electric field calculations. In any of these approaches, the unavoidable surface abrasions, which can lead to corona, are not considered. There are also efforts to account for nominal surface irregularity by using a surface roughness factor, which is highly heuristic. In order to address this practically relevant problem, the present work was taken up. The intended exercise requires accurate field computation and a suitable criterion for checking corona onset. For the first part, the Surface Charge Simulation Method is adopted with newly proposed sub-modelling technique. The surface of the toroid is discretised into curvilinear patches with linear approximation for the surface charge density. Owing to its high accuracy, Galerkin’s method of moments formulation is employed. The problem of singularity encountered in the numerical approach is handled using a method based on Duffy’s transformation. The developed codes have also been validated with standard geometries. After a survey of relevant literature the ‘Critical Avalanche Criteria’ is chosen for its simplicity and applicability to the problem. Through a detailed simulation, the effect of avalanche space charge in reducing the corona onset voltage is found to be around 1.5% and hence it is not considered further. For utilities not interested in a detailed calculation procedure for dimensioning of corona rings, design curves are developed for circular corona rings of both 400 kV and 765 kV class with surface roughness factor in the range 0.8 – 1. In the second part of the work, a methodology for dimensioning is developed wherein the inevitable surface abrasion in the form of minute protrusions can be accounted. It is first shown that even though considerable field intensification occurs at the protrusions, such localised modification need not lead to corona. It is shown that by varying the minor radius of the corona ring, it is possible to get a design where the prescribed surface abrasion does not lead to corona onset. In summary, the present work has successfully developed a reliable methodology for the design of corona rings with prescribed surface abrasions. It involved development of an efficient field computation technique for handling minute surface protrusions and use of appropriate criteria for assessing corona inception. It has also provided design curves for EHV and UHV class corona rings with surface roughness factor specified in the range 0.8 – 1.0.