Warning 127 | [PSS®E] | One or more three-winding transformers may cause static solver instability

Relevant software:

PSS®E

Emitted message:

One or more three-winding transformers with an active tap changer has a winding reactance below PSSE's default minimum impedance threshold.

Description:

This warning is raised when the engine detects a 3-winding transformer configuration that is highly likely to cause numerical instability and immediate divergence during load flow solutions in PSS®E.

PSS®E converts 3-winding transformers from a delta configuration ($Z_{12}$, $Z_{23}$, $Z_{31}$) into an equivalent star/wye configuration ($Z_1$, $Z_2$, $Z_3$) for its internal calculations. The star-point impedances are calculated using equations like: $Z_1 = 0.5 \times (Z_{12} + Z_{31} - Z_{23})$

If the calculated equivalent reactance ($X$) for any winding falls below PSS®E's minimum branch impedance threshold (typically 0.0001 p.u.) PSS®E models attempts to merge the two buses together into a single bus (effectively removing the ideal branch).

However, if that winding is also set to auto-adjust (e.g., automatic tap changing), PSS®E then attempts to calculate the load flow result of a pseudo-merged bus with zero impedance with with different voltages on either end of this ideal branch, causing an instantaneous and massive reactive power mismatch.

tip

You can generally identify this exact issue in the PSS®E log file (psse_log.log) if a simulation diverges immediately and the mismatch log looks like the below.

Largest mismatch: ___ MW ___ Mvar ___ MVA at bus 3WNDTR [] * BUS

Potential issues:

• The network load flow will immediately diverge when the 3-winding transformer tap changes in a model with any reactive power sources, e.g. multiple generators, line susceptance or fixed/switched shunts.
• Massive, unresolvable reactive power mismatches at the 3-winding transformer bus will prevent gridmo from converging the case.

Potential fixes:

• Ensure that the equivalent star-point impedance ($|Z|$) of the delta-wye transform is not zero or below the minimum impedance threshold. Mathematically, make sure that $Z_{ab} \neq Z_{bc} + Z_{ca}$.
• If you are approximating a 3-winding transformer as two 2-winding transformers in series for initial grid connections, apply a small offset to one of the impedances.
  • Example: If $X_{12} + X_{31} = 0.150008$ p.u., and you subtract an $X_{23}$ value of $0.15$ p.u., the result is $0.000008$ p.u. (which is below the 0.0001 threshold).
  • Instead, artificially set $X_{23}$ slightly higher, e.g., to 0.15 + 0.00011 = 0.150011 p.u.
  • This extremely small change is immaterial to your overall study but keeps PSS®E numerically stable.
• Make sure to implement this using the Z pu (winding kV system MVA) option code in PSS®E (this simply changes the units you are entering, not the transformer itself).