Earth-Return Impedance

Note Some oil companies specify a lower disconnection time tdis than 5.0 seconds, e.g., 1.0 second. This significantly increases the disconnection current by a factor of about 3.0 times. This ensures a much lower permissible limit to Zioopf, and thereby making it more necessary to use an earth leakage circuit breaker. Indirectly this reduction in time should be accompanied by ensuring that the earth return impedance Z r (and Zer) is kept very low i.e. as far below... 

Zg the conductor outer-media (space/earth return) impedance... 

The outer-media impedance of an underground cable (insulated conductor) is the same as the earth-return impedance because the underground cable is surrounded by only the earth ... 

This is the reason space impedance is often confused with earth-return impedance. In fact, when earth-return impedance is derived from Maxwell s equation, space impedance appears as a part of earth-return impedance [7,8]. 

Earth-return impedance at a low frequency can be easily evaluated by an approximate formula derived from Equation 1.16 under the assumption that hg hi, h2i... 

Pollaczek derived the following earth-return impedance in 1926 [7] ... 

In Equation 1.21, Q - jP is often called the correction term of earth-return impedance, or the earth-return impedance correction. It should be clear that gives the space impedance. nil is called the intrinsic propagation constant of the earth. 

Pollaczek derived a general formula that can deal with earth-return impedances of overhead conductors, underground cables, and multiconductor systems composed of overhead and underground conductors in the following form [7,13] ... 

Discuss the difference between conductor internal impedance and earth-return impedance based on the results of Problems 1.1 and 1.4. 

Derive a low-frequency approximate formula of the earth-return impedance from Equation 1.15 under the condition that hg h,-, hj. 

Similar to the conductor internal impedance explained earlier, the earth-return impedance in Equation 1.15 is frequency dependent as the penetration depth hg is frequency dependent. Equation 1.15 is approximated considering ln(l + x) for a small x by... 

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. 

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. 

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. 

Ametani, A., Y. Miyamoto, and J. Mahseredjian. 2014. Derivation of earth-return impedance of an overhead multi-conductor considering displacement currents. lEE Japan Trans. PE, 134 936-940. 

Each element of the impedance matrix is composed of the cable internal impedance and the cable outer media (earth-return) impedance, as explained in Chapter 1 of this volume. In the overhead line case, the conductor internal impedance is composed of only one impedance (i.e., the outer surface impedance of a conductor). The cable internal impedance consists of the following six components [1] ... 

Ametani, A., T. Yoneda, Y. Baba, and N. Nagaoka. 2009. An investigation of earth-return impedance between overhead and underground conductors and its approximation. IEEE Trans. EMC 51(3) 860-867. 

Earth is stratified, as is well-known, and its resistivity varies significantly at the top layer depending on the weather and climate. The earth-return impedance of an overhead conductor above the stratified earth was derived in Reference 16, and the stratified-earth effect was investigated in Reference 17. The stratified-earth effect may be far more significant than the accurate evaluation of the homogenous earth-return impedance of Pollaczek and Carson, and this requires further investigation. 

Earth resistivity, as mentioned earlier, is weather/climate dependent. The resistivity after the rains is lower than that measured during dry days. Also, it may be frequency dependent. The frequency dependence of earth permittivity may be far more significant than that of earth resistivity. Furthermore, water (H2O), which is a dominant factor for earth permittivity, is extremely temperature dependent [18]. As a result, the error due to the uncertainty of earth resistivity and permittivity might be far greater than that due to the incompleteness of the earth-return impedance derived by Carson and Pollaczek. This should be remembered as a physical reality that is important in engineering practice. 

Earth-return impedance has been well discussed, and its effect on the wave-propagation characteristic and the transient waveform is well-known, as is clear from a number of publications. Earth-return admittance [8,9,39,40], however, is neglected in most studies on wave propagation and surge characteristics, and its significant effect is not well understood [8,9,40, 41, 42 3]. 

Nakagawa, M., A. Ametani, and K. Iwamoto. 1973. Further studies on wave propagation in overhead lines with earth return—Impedance of stratified earth. Proc. lEE 120(2) 1521-1528. 

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