Q: How do you calculate positive negative and zero sequence impedance?

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No, such a sequence is not posible.

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.

For any index n (>1) calculate D(n) = U(n) - U(n-1). If this is the same for all integers n (>1) then D is the common difference. The sign of D determines whether the common difference is positive or negative.

If the terms get bigger as you go along, the common difference is positive. If they get smaller, the common difference is negative and if they stay the same then the common difference is 0.

The answer depends on what information you have. If you know the first number, a, and the common difference d, (where d is negative), then the nth term is a + (n - 1)*d : exactly the same as in an increasing linear sequence. The only difference is that d is negative instead of positive.

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Negative sequence and positive sequence are the same for a transformer. You would derive using the same connections as done to calculate the positive sequence impedance. Usually the test report will give positive, and often zero sequence impedances (sometimes left off, depending on the type of transformer as the zero sequence sometimes is the same as the positive sequence). The negative sequence is never given to my knowledge, because it is redundant and unnecessary test.

In symmetrical components, there are three types of impedances - positive sequence (balanced), negative sequence (unbalanced), and zero sequence (ground). In a transformer, positive and negative are equal. Ground impedance is determined by the (same factors as the) positive sequence and is based on the flux paths available through the transformer core that can induce ground current.

No, such a sequence is not posible.

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.

could also be negative

Connect positive first, negative last.

In an arithmetic sequence the same number (positive or negative) is added to each term to get to the next term.In a geometric sequence the same number (positive or negative) is multiplied into each term to get to the next term.A geometric sequence uses multiplicative and divisive formulas while an arithmetic uses additive and subtractive formulas.

If the common ratio is negative then the points are alternately positive and negative. While their absolute values will lie on an exponential curve, an oscillating sequence will not lie on such a curve,

There isn't enough information here. Available short circuit fault level can be given as a KVA value for different types of faults, but I assume the questioner is looking for a relationshiop between (transformer?) KVA and available short circuit current - If my assumption is correct, there is no direct correlation without knowing the transformer positive and zero sequence impedances. If these are known, you can assume the source impedance is infinite, and calculate the maximum short circuit current through the transformer as follows: lowside fault current for a 3 phase fault on the lowside of the transformer: lowside kV (line to line) / (1.732 x per unit positive sequence impedance x scalar to real impedance), where scalar to real impedance is equivalent to lowside kV (line to line) ^2 / base kVA. For a L-G fault, do the same with zero sequence impedance.

For any index n (>1) calculate D(n) = U(n) - U(n-1). If this is the same for all integers n (>1) then D is the common difference. The sign of D determines whether the common difference is positive or negative.

Descending (in a sequence) means that a the next number is "more negative" or "closer to negative infinity" or "less positive" or "further from positive infinity" or if n is a number in a sequence and n+1 is the next number then n/n+1 > 1

4/4+4*4=20 is it correct by any means or not ? No this garbage has got nothing to do with negative phase sequence current in 3 phase electrical systems.