TRANSMISSION LINE PARAMETERS

An electric transmission line has four parameters which affect its ability to fulfill its function as part of a power system: resistance, inductance, capacitance, and conductance.

Conductance between conductors or between conductors and the ground accounts for the leakage current at the insulators of overhead lines and through the insulation of cables. Since leakage at insulators of overhead lines is negligible, the conductance between conductors of an overhead line is assumed to be zero.

Capacitance exists between the conductors and is the charge on the conductors per unit of potential difference between them.

The resistance and inductance uniformly distributed along the line form the series impedance. The conductance and capacitance existing between conductors of a single-phase line or from a conductor to neutral of a three-phase line form the shunt admittance.

TYPES OF CONDUCTORS

Symbols identifying different types of aluminum conductors are as follows:

AAC- all-aluminum conductors
AAAC- all-aluminum alloy conductors
ACSR- aluminum conductor, steel reinforced
ACAR- aluminum conductor, alloy reinforced

Aluminum alloy conductors have higher tensile strength than the ordinary electrical-conductor grade of aluminum. ACSR consists of a central core of steel strands surrounded by layers of aluminum strands. ACAR has a central core of higher-strength aluminum surrounded by layers of electrical-conductor-grade aluminum.

RESISTANCE ON TRANSMISSION LINES

DC resistance

The resistance R of a conductor of uniform cross section can be computed as

where:

l is the length of the conductor, measured in meters [m]

A is the cross-sectional area of the current flow, measured in square meters [m²]

ρ (Greek: rho) is the electrical resistivity (also called specific electrical resistance) of the material, measured in Ohm · meter (Ω m). Resistivity is a measure of the material's ability to oppose electric current.

For practical reasons, any connections to a real conductor will almost certainly mean the current density is not totally uniform. However, this formula still provides a good approximation for long thin conductors such as wires.

Temperature dependence

Near room temperature, the electric resistance of a typical metal increases linearly with rising temperature, while the electrical resistance of a typical semiconductor decreases with rising temperature. The amount of that change in resistance can be calculated using the temperature coefficient of resistivity of the material using the following formula:

where:

T is its temperature,

T₀ is a reference temperature (usually room temperature),

R₀ is the resistance at T₀, and

α is the percentage change in resistivity per unit temperature.

The constant α depends only on the material being considered. The relationship stated is actually only an approximate one, the true physics being somewhat non-linear, or looking at it another way, α itself varies with temperature. For this reason it is usual to specify the temperature that α was measured at with a suffix, such as α₁₅ and the relationship only holds in a range of temperatures around the reference.

This table shows the resistivity and temperature coefficient of various materials at 20 °C (68 °F)

Material------- Resistivity (Ω·m) at 20 °C----- Temperature coefficient* [K−1]
Silver------------ 1.59×10−8-------------------------------- 0.0038
Copper--------- 1.72×10−8-------------------------------- 0.0039
Gold------------- 2.44×10−8-------------------------------- 0.0034
Aluminium----- 2.82×10−8-------------------------------- 0.0039
Calcium-------- 3.36x10−8
Tungsten------- 5.60×10−8------------------------------- 0.0045
Zinc-------------- 5.90×10−8------------------------------- 0.0037
Nickel----------- 6.99×10−8
Iron-------------- 1.0×10−7---------------------------------- 0.005
Platinum------- 1.06×10−7-------------------------------- 0.00392
Tin--------------- 1.09×10−7-------------------------------- 0.0045
Lead------------ 2.2×10−7---------------------------------- 0.0039
Manganin----- 4.82×10−7-------------------------------- 0.000002
Constantan---- 4.9×10−7--------------------------------- 0.000 008
Mercury-------- 9.8×10−7---------------------------------- 0.0009
Nichrome[6]-- 1.10×10−6--------------------------------- 0.0004
Carbon[7]----- 3.5×10−5--------------------------------- −0.0005
Germanium[7]-- 4.6×10−1------------------------------- −0.048
Silicon[7]------ 6.40×10-2-------------------------------- −0.075