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In my experience, the zero sequence of transformers is not calculated, it is directly tested following ANSII/IEEE guidlines for Z1no, Z2no, and Z1ns tests (for three phase, three winding transformers). Rough estimations of zero sequence impedance can be determined based on the positive sequence and core form of the transformer. A Shell type core will have a zero sequence of ~100% the positive sequence because the flux stays in the core / follows the same path as it does for positive sequence currents. For a core type, the zero sequence will be ~80-90% typically, because the flux must travel outside the core. This is for three winding transformer.
yes. A zero common difference represents a constant sequence.
These are called the second differences. If they are all the same (non-zero) then the original sequence is a quadratic.
If the first two numbers are 0, 1 or -1 (not both zero) then you get an alternating Fibonacci sequence.
Goemetric sequence : A sequence is a goemetric sequence if an/an-1is the same non-zero number for all natural numbers greater than 1. Arithmetic sequence : A sequence {an} is an arithmetic sequence if an-an-1 is the same number for all natural numbers greater than 1.