Problem solving for delta connection of transformer windings

For blocks from the Transformers library, when a three-phase winding is delta-connected, the transformer equation system will contain the following three equations in particular:

where

The three equations given are linearly dependent. If there are no elements on the delta side that have a connection to earth (e.g. in the case of connecting a transformer to a delta-connected load), the system of equations to be solved (complete) may be degenerate. The underdetermination of such a system is that without an additional equation linking the phase voltage to a potential, it is possible to determine the differences between the phase voltages (i.e. line voltages), but it is not possible to determine the phase voltages themselves.

When attempting to simulate models that have isolated neutral sections, errors or incorrect results may occur. The figure below shows a model initialisation error when attempting to simulate a network with an isolated neutral.

The problems of calculating networks with isolated neutral are well known and are found in other modelling software [1, 2].

If it is planned to investigate both symmetrical and asymmetrical modes of operation of networks with isolated neutral, the solution is to connect three-phase active shunts to ground to the windings of transformers connected in delta. The figure below shows a successful run of the model with a three-phase shunt to ground ( = 1e7 Ohm).

The value of the resistance must be large enough so that connecting the shunt does not cause a significant mode change (large leakage current or voltage drop), but also not too large, which would cause numerical problems. The value of the active resistance of the transformer cross branch , which reflects the active no-load losses, can be taken as a value to guide the selection of the value . Based on an analysis of reference data for power transformers, the recommended value for the active resistance of the additional three-phase shunt is 1e7 Ohm. If this leads to numerical problems, it is permissible to reduce the shunt resistance , but it is recommended that it should be at least `100 - 1000 (depending on the tolerance of the error introduced in the problem to be solved).

If it is not planned to investigate unbalanced modes in networks with isolated neutral, it is enough to connect a block Delta Reference (Three-Phase) to the windings connected in delta.

But it should be taken into account that when modelling asymmetrical modes, for example, single-phase earth fault (SPE), usage of Delta Reference (Three-Phase) block leads to physically incorrect results. The figure below shows the effect of the proposed recommendations on the RCD mode (incorrect result with usage of the block Delta Reference (Three-Phase)).