Carson’s impedance

Even in the case of Pg = 100 Q m, a transient of a 10 ns time region cannot be simulated by Pollaczek s and Carson s impedances [8, 9, 10-11]. It should be noted that most frequency-dependent line models are not applicable in these models because they are based on Pollaczek s and Carson s impedances. 

Pollaczek s and Carson s impedances are for a horizontal conductor. In reality, there are a number of nonhorizontal conductors, such as vertical and inclined ones. Although many papers have been published on the impedance of vertical conductors such as transmission towers, it is still not clear if the proposed formulas are correct. The empirical formula in Reference 12 is almost identical to an anal5 cal formula [13], which agrees quite well with the measured results. However, the anal5 cal formula requires further investigation to confirm if the derivation is correct. 

An important step prior to starting voltage analysis is the determination of line impedance. Quite often, impedance tables are used for standard conductors. However, for greater accuracy, Carson s equations are recommended (Kersting, 1992). 

A modification of Carson s equations is now used widely in calculating self-and mutual impedances in ohm per mile. The equations are... 

There were no computers in the 1920s thus, it was impossible to use Pollaczek s impedance [8]. Carson derived the same formula as Pollaczek, neglecting the earth permittivity (i.e., =... 

Again, assuming x is infinite, Pollaczek s, Carson s, or Sunde s impedance is obtained ... 

This equation is identical to the impedance derived for an infinite horizontal conductor in Reference 6, which is an approximation of Carson s earth-return impedance, as already explained in Section I.2.2.2. 

FIGURE 1.62 Self-inductance and capacitance of a finite horizontal conductor, (a) Inductance, (b) Capacitance, exp. experimental result, cal.-fin. calculated result of finite line impedance, cal.-inf. calculated result of Carson s infinite line impedance. 

Table 1.11 shows measured and calculated results of the surge impedance of a horizontal conductor. It is clear that the proposed formula shows more accuracy than Carson s. The accuracy of the proposed formula increases as x/h decreases, corresponding to the characteristic of the inductance. A similar observation has been made in different measurements in Reference 44. 

In fhe 1920s, fhere was no compufer, and fhus if was impossible to use Pollaczek s impedance. Carson derived fhe same formula as fhe Pollaczek s one neglecfing fhe earfh permiffivify, fhaf is, e = eo in Equation 1.23, and furfher he derived a series expansion of fhe infinite integral in Equafion 1.21. The defail of Carson s expansion formula is explained in many publications, for example. Ref. [10]. 

S. L. Carson, M. E. Orazem, O. D. Crisalle, and L. H. Garcia-Rubio, "On the Error Structure of Impedance Measurements Series Expansions," Journal of The Electrochemical Society, 150 (2003) E501-E511. 

---