As you know, three-phase two-winding transformers can produce a phase-shift between the line-to-line or line-to-neutral phasor voltages of one side and the respective line-to-line or line-to-neutral phasor voltages of the other side. This is taken into account as explained in the standard IEC 60076-1 by indicating the vector groups of the transformer.
As may also know, we can analyze balanced three-phase circuits using single-phase (or per-phase) equivalent circuits, whether using per-unit values or real values. In such single-phase circuits, we substitute the three-phase transformer with a single-phase transformer. How is the phase-shift taken into account? At least on the popular textbooks by Grainger & Stevenson and by Glover & Sarma, the authors use a "complex turns ratio". For example, using per-unit values, below are shown per-phase circuits:
Figure 1. Taken from Glover & Sarma's textbook.
Figure 2. Taken from Grainger & Stevenson's textbook.
This is fine, I understand it. But suppose I want to simulate a per-phase circuit (using real values) in a simulator such as Multisim, PSpice, LTspice, etc. and use the AC Analysis mode (which solves for phasor voltages and currents). Is there a way to model the single-phase transformer to include the phase shift (e.g. with a complex turns ratio)?
First attempt
I read the Supported Mathematical Functions, Operators and Constants in Multisim but it looks like there's no support for the imaginary unit, which I'd use to model the complex turns ratio.
I also read the Available Complex Functions in Multisim, but it says the imaginary unit is available only in the Postprocessor. Now, according to this page the postprocessor (and thus the imaginary unt) can be used only after a simulation is run, which is useless in my case.
Second attempt
As you may know, it is possible to model an ideal single-phase transformer using dependent sources. But in such case, to include the phase shift of the three-phase transformer (i.e. the complex turns ratio), I'd need a "complex gain" for the dependent sources. Since Multisim doesn't support the imaginary unit, I can't use a complex gain.
Of course, if it's not possible to model the phase shift of the three-phase transformer in the single-phase transformer, instead of simulating the equivalent single-phase circuit I could simply simulate the actual three-phase circuit. The downside is it'd take more time for me to set up the whole power system.
Best Answer
and
The easiest way (in AC analysis) is to set the applied voltage at the primary to have the appropriate phase shift. I don't use any of the aforementioned simulators so here's how microcap would do it: -
I expect that all Spice simulators will have a similar feature in their voltage sources. See also the numerical shorthand of a voltage source - I've set the phase to be \$\color{red}{30}\$ degrees: -
DC 1 AC 0 \$\color{red}{30}\$ Sin 0 2.5 1meg 0 0 0
Or just use a time delay sub-circuit (if working in transient analysis): -
I can't imagine that LTSpice doesn't have this.