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# Transformer Data Tab | Introduction

**INTRODUCTION**

The HYPERSIM Transformer tools accurately reproduce the behavior of a three-phase linear model, two or three winding transformers at power frequency located in each parameter form of Z-based transformer components respectively.

**Three-limb core: three windings**

- HYPERSIM works with an Inductance matrix transformer model. This model represents only a three-limb or five-limb core. The three single-phase cores are not actually supported (Z0 = Z1).
- Each single-phase transformer is modeled by 3 coupled windings.
- A 3-leg 3-windings transformer with Z0 different from Z1 is modeled by 9 coupled windings ordered in the [L] and [R] matrices in the next section.
- For a 3-leg 2-windings transformer, the transformer is modeled by 6 coupled windings ordered in the [L] and [R] matrices in the next section.

**Inductance Matrix Transformer Model**

The inductance matrix transformer model implements this relationship equation:

Where R1 to R9 represent the winding resistances. Lii represents the self-inductance and the Lij represents the mutual inductance.

The calculation of the inductance matrix transformer is performed by these equations.

**Positive-Sequence and Mutual Reactances**

The zero-sequence self reactances

and mutual reactance

are also computed using similar equations.

Q1i | Three-phase reactive power absorbed by winding i at no load when winding i is excited by a positive-sequence voltage Vnomi with winding j open |
---|---|

Q1j | Three-phase reactive power absorbed by winding j at no load when winding j is excited by a positive-sequence voltage Vnomj with winding i open |

X1ij | positive-sequence short-circuit reactance seen from winding i when winding j is short-circuited |

Vnomi, Vnomj | nominal line-line voltages of windings i and j |

If we extend the two 2x2 reactance matrices in positive-sequence and in zero-sequence, to a 6x6 matrix, and replace the four scalar terms by a 3x3, we have this matrix:

Where the self and mutual terms are given by:

To model the core losses (P1 and P0 in positive and zero-sequence), additional shunt resistances are connected between windings.

The resistances equation is:

The default parameters are for a three-phase 3-windings transformer.

**Enter your own transformer parameters in the Transformer data Tab in the Z-based parameter form, under** **Parameters Tab.**

**See Transformer Data Tab | GUI & Toolbox Icons**

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