In the following figure of an equivalent TX line model is there any mutual inductance between the inductors?
Dear Mr. Ray, as I can figure out, you are refering to the distributed line model, where current and voltage are not examined as in most circuit cases, because here the electromagnetic wave and the wave impedance take place. The distributed parameters are taken into consideration in order to determine the wave impedance of the line. If this is the case you may not consider mutual inductances.
On the other hand, if the wave phenomenon is not taken into account and the line is being considered as a normal circuit, then, YES, there is a mutual inductance between reactors. For instance in a 3phase line, each line has an inductance, but there is also a mutual inductance between lines, or even between line and earth.
If the line is not long and/or the frequency is low the mutual inductance could be calculated. If the line is too long or the frequency is high, then the wave effect takes place, the circuit elements are embeded into the wave impedance and the mutual inductance may be ignored.
Yes there is mutual inductance between the inductors. The value depending on the aiding or opposing connections of inductors.
Technically, YES, there is mutual inductance. Nevertheless, factor in (if inclusive) the effect of line transposition, which grossly reduces these effects over a long distance: i.e. transforming the 3-phase line sequence from abc - cab - bca over a transposition cycle.
Do recall, these are equivalent circuits based on approximations. I have attached a brief with details herewith.
The mutual inductance is present in the actual wording of inductance line parameter because the inductance parameter depends on the configuration of the line. Search the formulation.
physical interpretation of each phase conductor, N and ground and flux distribution may help to understand it better
Even though there is mutual inductance betwen inductors while using a distributed transmission line modeling mutual inductance is normally neglected. Even for lumped modeling when the transmission line is transposed again mutual indunctances are neglected.
In the textbook used in Tsinghua University, it is written that the effect of mutual inductance has been considered in the equivalent transmission line model based on the assumption that the system is 3-phase symmetrical. Hope that may help you.
Really there will be mutual inductance between two parallel lines. But in transmission line modeling we neglect this mutual inductance term, since the effect of it is negligible. Normally the transmission lines will be located at some minimum distance, so the effect will be less. But in cables, the distance is less and we take care of mutual inductance, called inductive coupling. Twisting of wires in cable is one solution to reduce this effect. In some cases, magnetic shielding also used.
Thanks for the observation. Agreed that a transposed is taken as a symmetrical line. But that is only an approximation and that is how an approximation arises.
There is a mutual inductance in the equivalent of a poly-phase transmission line. However, the calculations of electromagnetic transients with constant parameter line models are done in the modal domain. Each conductor is solved independently. Finally, the effects of coupling impedance among the conductors are taking into account by transforming the modal domain variables into phase domain variables. This is done via a constant transformation matrix.
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