Vertical conductor

When the conductors i and j are at the same vertical position, that is, = h , K=hm Equation 1.253 is simplified in the following form  

If the earth is assumed to be perfectly conducting, the earlier equation is further simplified  

When the bottom of a single conductor (d=r) is on the earth surface, that is, h-X = 0, 

The admittance of the vertical conductor system is evaluated from Equation 1.251. 

---

For the purpose of a numerical estimate, we may assume an intense lightning current of crest value i = 100 k amp and a ground resistance of R= lOQ. The inductance of a single vertical conductor is about 160 j H per 100 m and the rate of rise of the front of the lightning, as reported by Llewellyn (J ), may be taken as 50k amp/ /4 u sec. If the height of the chimney above ground is 10 m, the top of the lightning conductor is raised to a potential with respect to true earth which amounts to ... 

In all situations where several conductors are joined in one system, the vertical conductors should be connected both at the top and near the ground line. The angles and the prominent portions of a building being the most liable to be struck, the conductors should be carried over and along these projections, and therefore along the ridges of the roof. The conductors should be connected to any outside metal on the roofs and walls, and specially to the foot of rain-water pipes. 

Still within the PCB editing stage, the layout phase is followed by the routing phase. This routing (manual and automatic) implements the mtercomiection list in a PCB conductive pattern composed of traces, planes, and vias (vertical conductors). 

To analyze a transient in a distributed-parameter line, a traveling-wave theory is explained for both single- and multiconductor systems. A method to introduce velocity difference and attenuation in the multiconductor system is described together with field test results. Impedance and admittance formulas of unusual conductors, such as finite-length and vertical conductors, are also explained. 

There are a number of papers on nonuniform lines [30,31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48-49]. EMC-related transients or surges in a gas-insulated substation and on a tower involve nonuniform lines, such as short-line, nonparallel, and vertical conductors. Pollaczek s [7], Caron s [8], and Sunde s [50] impedance formulas for an overhead line are well known and have been widely used in the analysis of the transients mentioned earlier. However, it is not well known that these formulas were derived assuming an infinitely long and thin conductor, that is, a uniform and homogeneous line. Thus, impedance formulas are restricted to the uniform line where the concept of per-unit-length impedance is applicable. 

This section explains impedance and admittance formulas of nonuniform lines, such as finite-length horizontal and vertical conductors based on a plane wave assumption. The formulas are applied to analyze a transient on a nonuniform line by an existing circuit theory-based simulation tool such as the EMTP [9,11]. The impedance formula is derived based on Neumann s inductance formula by applying the idea of complex penetration depth explained earlier. The admittance is obtained from the impedance assuming the wave propagation velocity is the same as the light velocity in free space in the same manner as an existing admittance formula, which is almost always used in steady-state and transient analyses on an overhead line. 

First, it is necessary to clarify a problem to be discussed in this section, that is, a nonuniform line or a nonhomogeneous line. Figure 1.57 shows a typical example of transient voltage responses measured on a vertical conductor with radius r = 25 mm and height h = 25 m [41,42]. 

Thus, it can be said that the voltage waveform at a vertical conductor is distorted due to the nonuniformity of the vertical conductor at every height (position). That is, the characteristic impedance (impedance and admittance in general) of the vertical conductor is position dependent. 

TABLE 1.12 Measured and Calculated Surge Impedances of Vertical Conductors... 

Calculate the surge impedance of a vertical conductor given in Table 1.12 by using the following approximation, and discuss the results in comparison with measured results, as well as Wagner s and Sargent s formulas, in the table ... 

Hara, T. et al. 1988. Basic investigation of surge propagation characteristics on a vertical conductor. Trans. lEE Jpn. B-108 533-538 (in Japanese). 

Ametani, A., Y. Kasai, J. Sawada, A. Mochizuki, and T. Yamada. 1994. Frequency-dependent impedance of vertical conductor and multiconductor tower model. lEE Proc.-Gener. Transm. Distrib. 141(4) 339-345. 

A model circuit for an EMTP simulation is shown in Figure 6.17. In the figure, is the surge impedance of a distribution pole, which is represented by a lossless distributed line with a propagation ve-locity of 300 m/ps. The surge impedance is evaluated by the following formula of a vertical conductor [27] ... 

Yutthagowith, R, A. Ametani, N. Nagaoka, and Y. Baba. 2010. Influence of a measuring system to a transient voltage on a vertical conductor. lEEJ Trans. EEE 5 221-228. 

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. 

Hara, T., O. Yamamoto, M. Hayashi, and C. Uenosono. 1989. Empirical formulas of surge impedance for single and multiple vertical conductors. Trans. lEE Jpn. 110-B 129-136. 

---