What is the zero-sequence equivalent of a YNy0 transformer?
The first question to ask is: have you got, or can you obtain, the transformer's test certificate? 

Zero sequence impedance may have been measured during the transformer's factory tests. It may be on a separate test certificate specifically for zero sequence impedance. If you can find the measured Z0 from tests, you don't need to delve into the following theory.

In IEC land (where transformers are built and tested to IEC 60076), zero sequence impedance measurement is not a "routine test" so it has to be specially requested. (Hint: If you are specifying a transformer, please ask for the test! It doesn't cost much to run at the factory, and it's quite helpful.)

The second question to ask is: does the transformer have neutral earthing resistors (i.e. LV star point earthed by a 750 amp NER)? It would be unusual (unsafe?) to have a completely floating LV star point.

The third question to ask is: does your transformer have a buried delta tertiary? That considerably changes the answer.

Notwithstanding the above, the full theory is below.



The zero sequence impedance of a Y-Y transformer depends on the transformer's construction and how the windings are earthed.

The case of interest to you is when only one winding of a wye-wye transformer is earthed, i.e. HV grounded-wye, LV ungrounded-wye, or vice-versa. For brevity's sake I'll call this a "YNy0" transformer for the remainder of this post.

NB: technically, it's possible for a YNyn0 transformer to have the LV star point brought out to a bushing, but not connected to anything, so it could also be operated in this way.



Paul M. Anderson's Analysis of Faulted Power Systems, chapter 7.9 Zero Sequence Impedance of Three-Phase Transformers, covers the topic.

Even though the zero-sequence impedance of a theoretical YNy0 transformer is infinite, in practice, the tank of the transformer acts as a weak kind of delta winding. This is the so-called "tank delta" effect.

The table at the end of the chapter essentially says that, for a wye-wye transformer with one of the star points earthed, \$ Z_0 \approx 5 \times Z_1 \$.



A document I have from Eskom (South African power utility) says that a YNy0 transformer has \$ Z_0 \approx 10 \times Z_1 \$, again citing the tank delta effect.

The following text is quoted from Eskom DGL 34-617, "Network planning guideline for transformers".


  4.5.2 Transformer zero sequence impedances
  
  The zero sequence impedance of a transformer installation is dependent on:
  
  
  The transformer zero sequence impedance Z0.
  Transformer star point earthing and NEC, NECR earthing.
  Earthing impedances.
  
  
  In modern PSST software each of the above elements is modelled explicitly. By specifying the transformer zero sequence impedance and it’s earthing (with any associated impedances) the total zero sequence model of the entire transformer installation is simulated in the PSST. In cases where test sheet data is not available, the assumptions below are commonly applied for transformer zero sequence impedance (these are zero sequence values for the transformers. Any grounding impedance must also be modelled in the PSST, and is entered separately):
  
  
  Star/Delta and Delta Star: Z0 = 0.9Z1.
  Star/Zig-zag: Z0 = 0.091Z1.
  Star/Star with both star points earthed: Z0 = 0.85Z1.
  Star/Star with only one star point earthed: Z0 = 10Z1. This is the “tank delta” effect whereby the transformer tank provides a delta winding effect.
  
  
  It is important to note that with Star/Star transformers the transformer zero sequence impedance is
  dependent on the star point earthing. In all other cases the transformer zero sequence impedance is not
  dependent on transformer earthing.




Finally we have old faithful, the J&amp;P Transformer Handbook.

From the J&amp;P Transformer Handbook, 12e:


  2.7 ZERO-SEQUENCE IMPEDANCE
  
  ... the zero-sequence
  impedance varies considerably according to the construction of the transformer
  and the presence, or otherwise, of a delta winding.
  
  The zero-sequence impedance of a star winding will be very high if no delta
  winding is present. The actual value will depend on whether there is a low
  reluctance return path for the third-harmonic flux.
  
  For three-limb designs without a delta, where the return-flux path is through
  the air, the determining feature is usually the tank, and possibly the core
  support framework, where this flux creates a circulating current around the tank
  and/or core framework. The impedance of such winding arrangements is likely
  to be in the order of 75 to 200% of the positive-sequence impedance between
  primary and secondary windings. For five-limb cores and three-phase banks
  of single-phase units, the zero-sequence impedance will be the magnetising
  impedance for the core configuration.
  
  Should a delta winding exist, then the third harmonic flux will create a circu
  lating current around the delta, and the zero-sequence impedance is determined
  by the leakage field between the star and the delta windings. Again the type
  of core will influence the magnitude of the impedance because of the effect
  it has on the leakage field between the windings. Typical values for three
  limb transformers having a winding configuration of core/tertiary/star LV/star
  HV are:
  
  [Z0]LV approximately equal to 80 to 90% of positive-sequence
  impedance LV/tertiary
  
  [Z0]HV approximately equal to 85 to 95% of positive-sequence
  impedance HV/tertiary
  
  where Z0 = zero-sequence impedance.
  
  Five-limb transformers have their zero-sequence impedances substantially
  equal to their positive-sequence impedance between the relative star and delta
  windings.




The assumption I have seen used most often is that a YNy0 transformer has \$ Z_0 = 5 - 10 \times Z_1 \$.

At least one piece of software has this as the default, if you select a "core type" wye-wye transformer (as opposed to "shell type".)