The Current Distribution, Resistance and Internal Inductance of Linear Power System Conductors—A Review of Explicit Equations

This paper reviews the present state of knowledge of explicit equations for calculating the dc and ac current distributions and the resistances and internal inductances per-unit length of linear electrical conductors used in power transmission and distribution systems. These conductors may be homogeneous wire or rod, tubular, triangular, elliptical or rectangular busbars, helically stranded nonmagnetic conductors (AAC or AAAC), or bimetallic stranded conductors, such as the commonly used aluminum conductor steel reinforced (ACSR). In general, the current density in an isothermal homogeneous conductor is uniform with direct current (dc), but with alternating current (ac), skin effect, and proximity effect, can cause nonuniform distribution of current, hence, increased resistance and decreased internal inductance. With stranded steel-cored conductors, the dc density within each section is inversely proportional to its resistivity. However, with ac at power frequency, the spiraling of the currents in the nonferrous layers causes a longitudinal magnetic flux in the steel core, which results in hysteresis and eddy current power loss in the core, and a circular magnetic flux in the nonferrous wires, which results in a nonuniform distribution of current density between the layers of nonferrous wires. These effects give rise to increased resistance and reduced internal inductance. The effects of current amplitude, frequency, temperature, and tensile stress on conductor properties are discussed.