3 Shunt Admittance 3.3 Shunt Admittance and Reactance Matrices 4 Units of Measure

3.4 Shunt Admittance Computations

This discussion of overhead transmission line shunt admittance concludes with a brief dicussion of computing contant factors associated with the potential matrix and reconciling units of measure while evaluating these constants.

3.4.1 Potential Coefficient Unit Conversions

The constant associated with the computation of potential coefficients in Equation 33 depends only upon the medium in which the conductors reside. Assuming that the conductors are suspended in air ( $\epsilon_{r}=1$ ), the potential constant (in F^-1m) is

\frac{1}{2\pi\epsilon_{0}\epsilon_{r}}=\frac{1}{2\pi\cdot 8.8541853\times 10^{% -12}\cdot 1}=1.79751087\times 10^{10}

(43)

To compute potential coefficients in line length units rather than meters, an additional conversion factor m $\to$ u_LL is required, i.e. the multiplier in Equation 33 is actually

\frac{m\to u_{LL}}{2\pi\epsilon}

(m\to u_{LL})1.79751087\times 10^{10}

(44)

which produces potential coefficients with units F^-1 · u_LL. This product is computed once and stored.

3.4.2 Self Potential Unit Conversions

The self potential in Equation 33 is

\frac{ln\left(\frac{D_{ii}}{d_{i}}\right)}{2\pi\epsilon}

When this term is computed, the numerator and denominator of the logarithmic factor must be in the same units. Assuming that the conductor’s diameter (in u_CD) is readily available, the distance must be converted to conductor separation units and the diameter must be converted to a radius. Therefore, the computed logarithmic factor is

ln\left(\frac{D_{ii}}{\frac{d_{i}}{2}(u_{CD}\to u_{CS})}\right)

where u_CD $\to$ u_CS converts conductor diameter to conductor separation units.

Factoring out a constant in this expression

ln\left(c\frac{D_{ii}}{d_{i}}\right)

(45)

where

c=\frac{2}{u_{CR}\to u_{CS}}

(46)

The factor c is computed once and saved.

Note: In the context of the current discussion, the clear choice of unit for capacitive reactance is Ω · u_LL. However, the capacitive reactance found in American reference materials is often MΩ · u_LL or more specifically MΩ · mile. Hence, an additional factor may be required when converting capacitive reactance from computational units to commonly published units (ie. 10^-6 for converting MΩ to Ω).