Earth-return mode

Figure 1.24 shows an example of the frequency dependence of attenuation constant a and propagation velocity c for the earth-return mode and the self-characteristic impedance Zq for a phase of a 500 kV overhead transmission line. 

In Table 1.6, the first kind of distribution corresponds to the so-called zero-sequence mode and is mode 0 in the same polarity case and mode 3 in the opposite polarity case. If the line is single circuit, there is no opposite polarity mode, and the first kind of distribution is the same as mode 0 distribution, which was explained in Section I.4.4.I. Mode 0 is often called the first zero-sequence mode (earth-return mode), and mode 3 is called the second zero-sequence mode (intercircuit zero-sequence mode). 

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. 

Mode 0 (earth-return mode) no significant difference. 

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. 

The reduced transformation matrix of a cross-bonded cable is shown in Table 3.3b-3. The composition of the top left 3x3 matrix (the first three modes) is similar to that of an overhead transmission line. The current of the third mode returns from the equivalent sheath instead of the earth. The fourth mode expresses the equivalent earth-return mode of the cross-bonded cable system. 

The attenuation and velocity of the earth-return mode (mode 4) in both cable models are identical. 

Assume that the sample cable in Section 3.2.4 is buried as a single-phase cable. Find the impedance and admittance matrices for the single-phase example cable using EMTP. Use the Bergeron model and calculate the impedance and admittance matrices at 1 kHz. From the impedance and admittance matrices found in (1), find the phase constants for the earth-return mode and the coaxial mode using the voltage transformation matrix... 

From the impedance and admittance matrices found in (1), find the phase constants for the earth-return mode and the coaxial mode... 

The basic corrosion instrumentation requirement involves the measurement of potential difference. Currents are measured as the potential across a resistor (R ) as shown in Fig. 1.2, where the potential difference is again determined with an operational amplifier. More sophisticated measurements such as polarisation characteristics and zero resistance ammetry involve the use of potentiostats which again use operational amplifiers in a differential mode. The potentiostat is an instrument for maintaining the potential of an electrode under test at a fixed potential compared with a reference cell, and the basic circuit is similar to that for potential measurement with the earth return circuit broken to an auxiliary electrode in the electrochemical cell. Such a circuit would maintain the potential of the test electrode at the reference cell potential. This potential may be varied by inserting a variable potential source (V ) in the input circuit as shown in Fig. 1.3. The actual cell potential (V ) and the current required to polarise the test electrode to this potential may be measured using the basic circuits shown in Figs. 1.1 and 1.2 respectively. 

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. ... 

The earth-return impedance is far greater than the conductor internal impedance thus, the latter can be neglected. However, in a steady-state analysis such as fault and load flow calculations in a multiphase line, the positive-sequence (mode 1) component is important, and the conductor internal impedance is dominant for the positive-sequence component. 

Because the cable is installed in a tunnel (that is, the cable is in air), the attenuation constant and the propagation velocity of mode 4 (earth return) and modes 5 and 6 (the first and second inter-sheath) in the solidly bonded cable show similar characteristics to those of an overhead line [1]. The attenuation constants of modes 5 and 6 are much smaller and the propagation velocity is much greater in the solidly bonded cable than those in the other modes. 

The current of 1/3 following to the positive direction on each phase and the return current 1 have to flow back through the earth. Because the return current flows through the earth, the mode "0" component is called "earth-return" component. A circuit corresponding to the mode 0 can be drawn as Figure 1.21a. The mode 0 component involves the earth-return path of which the impedance is far greater than the conductor internal impedance as explained in Section 1.5.1,... 

The upward dc currents flow with little spreading in a rapidly increasing conductivity profile to the ionosphere, where they combine to establish the ionospheric potential and return to earth in fair-weather regions. In the ionosphere, the very lowest frequency ac currents will follow similar trajectories. The ionosphere and earthformacavity resonator with characteristic frequencies that are multiples of 7 Hz, so that above afew hertz these Schumann resonances must be considered. At higher frequencies, complex modes dominate the ac propagation. However, much of the ac energy is at lower frequencies, where a simpler viewpoint prevails. 

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