Winding Impedances

In some cases, the impedances obtained from short-circuit tests (Z12, Z13, Z23) provide a T-equivalent model with negative parameters (Z1, Z2, Z3). This often occurs in the case of transformers with a winding of less power (internal tertiary winding in delta for example).

EMTP supports negative values but may cause numerical problems depending on the parameters of the surrounding elements. Therefore, it is recommended to consider positive values for all the impedance elements. Here is an example of a short-circuit test result that gives negative values.

HYPERSIM does not accept negative values for resistors, inductors and capacitors. They will be automatically replaced by null values. Therefore:

It is recommended to modify z23 so that no negative value results from these equations.

Saturation curve

The saturation characteristic of a transformer is defined by points in a table representing the line segments of a curve (flux, current) in the first quadrant that is symmetric to the third quadrant. 

The following two examples are used to illustrate the criteria followed in HYPERSIM and EMTP to validate a saturation curve. The curve in the figure 1 is valid in both HYPERSIM and EMTP. However, the curve shown in figure 2 is only valid in EMTP. In HYPERSIM, the slops in the saturation curve must be monotonically decreasing.

Please consider the following points when using the saturation model in HYPERSIM: 

• Define a curve with segments that have monotonically decreasing slopes
• The first point must not be (0,0)
• The maximum number of points in the table must be 32