Aerial mode

Mode 1 (first aerial mode) The current of 1/2 flows through phase a returning through phase c, with no current on phase b. Thus, the mode 1 circuit is composed of phases a and c as shown in Figure 1.21b. Because the mode involves no earth-return path in ideal cases, the mode is called the aerial mode. ... 

Mode 2 (second aerial mode) The current of 1/6 flows through phases a and c, and the return current of 1/3 flows back through phase b as illustrated in Figure 1.21c. The propagation characteristics of mode 2 are identical to those of mode 1 in the case of a completely transposed line. If the line is untransposed, the characteristics are different. 

Explain why the modal propagation constants and the modal characteristic impedances for modes 1 and 2 (aerial modes) on a transposed three-phase line become identical. 

The second, third, and fourth distributions correspond to an aerial mode. The second is the positive-sequence mode and the third is the negative-sequence mode. However, the pattern of current distribution varies as frequency changes thus, the fourth distribution can become a negative-sequence mode at a certain frequency. 

The reason for the much smaller wave deformation in the aerial modes than in the earth-return modes is that the conductor internal impedance that contributes mainly to the aerial modes is far smaller than the earth-return impedance that mainly contributes to mode 0. 

Figure 2.8d indicates that aerial mode voltages exist even in the case of voltage application to all phases. This cannot be explained by conventional symmetrical component theory. Modal theory predicts aerial mode components at 28% on the upper phase, 7.6% on the middle phase, and 13% on the lower phase, which agrees well with the field test results of 20%, 4.3%, and 11%, respectively. 

Assuming that the line is transposed and all the phases are simultaneously closed at f = 0, the positive sequence (aerial mode) voltage at the receiving end is given by... 

In the solidly bonded cable, the first three modes (columns) shown in Table 3.3 a-3 express coaxial-propagation modes (that is, the core-to-sheath mode [2]). The other modes (columns) correspond to one of the transformation matrices of an untransposed three-phase overhead line [2]. In this case, mode 4 expresses an earth-return mode and modes 5 and 6 correspond to aerial modes. 

When a line is transposed, all the aerial modes become identical. Thus, a number of different characteristic modes are reduced to two in the three-phase line case and to three in the twin-circuit line case. The different velocities of the aerial modes in an untransposed line cause a spike voltage on a transient voltage waveform, which is characteristic to the untransposed line. 

Modes 1 and 2 (aerial modes) are identical in the transposed line, while those are different in an untransposed line. 

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