Hi Steve,
The equivalent circuit of a transformer I am used to in the analysis of power systems is shown here.
By "impedances representing the windings themselves", I mean the complex impedances r1 + jx1 and a^2*(r2 + jx2).
r1 and r2 are the winding resistances. x1 and x2 are derived quantities and depend on the self-inductance of the windings themselves, and the mutual inductance between the windings.
x1 = w * [L11 - a*L21]
where w = 2*pi*f, L11 is the self-inductance of the primary and L21 is the mutual inductance.
x2 = w*[L22 - L12/a]
with L22 the self-inductance of the secondary and L12 the mutual inductance = L21. "a" is the turns ratio of the transformer.
The magnetizing branch is the shunt Gc/Bm combination. Gc represents the I^2*R losses in the core. Bm = 1/(a*w*L21) (Susceptance).
So, with the secondary open-circuited, and neglecing Gc, the equivalent transformer impedance will be r1 + j*w*L11.
Neglecting the magnetizing branch completely leads to the equivalent circuit shown below:
with R1 = r1 + a^2*r2 and X1 = x1 + a^2*x2.
To get an idea of what R1 and X1 are in ohms, consider a 500kV - 345kV three-phase transformer, with an MVA rating of 300MVA. Such transformers typically have an X1 = 8% at the rated voltage and voltampere base.
Referred to the high-voltage side, X1 = 0.08* 500*500/300 = 66.67 ohms. The I^2*R losses are very small compared to the through-impedance, and sometimes R1 is neglected too from the transformer model.
The model you have shown for low frequency analysis is similar to the one I am using, except that the reactances x1 and x2 are not used.
One reference for the equivalent circuit I use is "Power System Analysis" by John Grainger and William Stevenson, Jr.
Ashok
