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To increase the visual critical voltage of corona for an overhead line, one solid phase conductor is replaced by a bundle of four smaller conductors per phase, having an aggregate cross-sectional area equal to that of the solid conductor. If the radius of the solid conductor is 40 mm, then the radius of each of the bundle conductors would be
10 mm
20 mm
28.2 mm
30 mm
20 mm
To maintain the same aggregate cross-sectional area, the sum of the areas of the individual bundle conductors must equal the area of the original single conductor. Since the area A=╧Аr2, setting n├Ч╧Аrbundle2тАЛ=╧АR2 leads to rbundleтАЛ=nтАЛRтАЛ, where n is the number of conductors and R is the original radius.
To maintain the same aggregate cross-sectional area, the sum of the areas of the individual bundle conductors must equal the area of the original single conductor. Since the area A=╧Аr2, setting n├Ч╧Аrbundle2тАЛ=╧АR2 leads to rbundleтАЛ=nтАЛRтАЛ, where n is the number of conductors and R is the original radius.
rbundleтАЛ=nтАЛRтАЛ тАФ Relationship between bundle radius and solid conductor radius for equal area
EmaxтАЛ=rln(D/r)VтАЛ тАФ Surface voltage gradient for a conductor of radius r
Bundling conductors increases the effective radius (geometric mean radius) of the phase conductor, which reduces the surface electric field intensity. Because corona inception is highly dependent on the maximum surface voltage gradient, reducing this gradient by increasing the effective surface area improves the visual critical voltage.
Bundling increases the effective surface area, reducing the voltage gradient (E).
Corona loss is inversely proportional to the voltage gradient; lower gradient implies higher corona inception voltage.
The total current-carrying cross-section is preserved to maintain the same resistance (I┬▓R loss).
Bundling also significantly reduces the inductive reactance of the transmission line.
Reduced corona loss and radio interference
Reduced line inductance and surge impedance
Improved power transmission capacity
Increased wind and ice loading
Complex hardware/tower design requirements
Extra High Voltage (EHV) transmission lines (above 220 kV)
Ultra High Voltage (UHV) transmission networks
The calculation r=40/4тАЛ=40/2=20 mm is straightforward. The total area remains A=╧А(40)2=1600╧А, and 4├Ч╧А(20)2=4├Ч400╧А=1600╧А.
Option A is incorrect as it assumes a linear relationship; Option C and D are mathematically inconsistent with the equal-area constraint.
B is correct тАФ By equating the total cross-sectional area, the individual bundle radius is derived as r=R/nтАЛ, resulting in 40/4тАЛ=20 mm.
Always verify if the question asks for 'equivalent radius' based on area (╧Аr2) or 'geometric mean radius' (GMR) used for inductance/capacitance, as they use different geometric formulas.