three winding autotransformer impedence 3

[backer86]

I am trying to evaluate the impedence of an autotransformer with a tertiary winding. The problem is that I am getting negative value for primary winding impedence, how is that possible?

Zhx = 10% on 30MVA
Zxy = 9% on 10MVA
Zhy = 15% on 30MVA

I am using 100MVA as base.
H: high voltage winding
X: low voltage winding
Y: tertiary winding.

Any help is appreciated.

 

[prc]

Yes. It is possible to have negative impedance for one circuit of a three winding transformer.

This was first explained by the great GE transformer designer A Boyajian of Pittsfield factory in 1924( AIEE Feb 1924 Paper Theory of three circuit Transformers) and later included in his book (with LF Blume) Transformer Engineering(1938)

Negative impedance means when one circuit is loaded terminal voltage dips while the terminal voltage of the circuit with negative impedance boosts up.But not more than one branch can be negative as net impedance between two pairs of winding must be always positive ie inductive.Also negative reactance of any branch shall be smaller than either one of the positive reactances in other branches.

This small negative reactance in one branch occurs due to certain winding arrangements when the leakage flux between two loaded windings stray in to the idle winding.

 

[davidbeach]

The negative impedance happens because the T-model, while very useful mathematically, has no physical meaning. Just as with a real transformer, the model will never have a negative impedance from terminal to terminal.