Three phase two winding variable ratio transformer
This section describes the three phase two winding variable ratio transformer
The three phase two winding variable ratio transformer is modeled as three single phase variable ratio transformers, meaning that only magnetic coupling between windings of the same phase are taken into account.
The magnetization inductance Lm can be modeled as linear or with saturation. Core losses are modeled as a shunt resistance Rm. Both Lm and Rm are modeled on the primary side of the transformer. It is possible to neglect Lm and Rm by selecting Lm/Rm neglected in the Core model property. For more information on the core model, please refer to Core model.When the Core model property is set to Lm/Rm neglected, the primary inductance L1 may be degenerated. If it is desired to preserve L1, a snubber can be defined under the stability tab to provide an alternative current path at the transformer primary. Alternatively, the Refer L1 to secondary checkbox provides the option to refer the effects of inductance L1 to the secondary side of the transformer. If this option is selected, inductances L1 and L2 are replaced with a single variable inductor L2_var on the transformer secondary.
component  component dialog window  component parameters 

Three phase two winding variable ratio transformer 







The ratio input is used ot set the turns ratios of each of the three internal transformers. The input can either be a single value or an array. If a onedimensional input is provided, the given ratio will be assigned to each transformer. If an array is provided, the entries in index positions 0, 1, and 2 will be assigned to phases A, B, and C respectively.
 short circuit test – exciting a set of threephase windings while the other set of windings is short circuited
 open circuit test – exciting a set of threephase windings while the other set of windings is open circuited
Measurement results obtained from these tests and other information given on the transformer’s nameplate provide the necessary data for transformer characterization and modeling.
Winding excitation in the tests is threephase positive sequence voltage. In addition to that, when characterizing a transformer and making a transformer model that includes mutual inductances between phases, it is necessary to perform the same tests, but with excitation being threephase zero sequence voltage.
Parameters of the equivalent circuit are calculated as follows. During the short circuit test, the magnetization branch is considered shorted by the short circuited winding. So, primary side short circuit impedance is obtained:
${Z}_{sc}^{d}=3\frac{{u}_{sc}^{d}\left[\%\right]{\left({V}_{1n}^{ph}\right)}^{2}}{{100S}_{n}}$Primary side short circuit resistance is obtained:
${R}_{sc}=3{P}_{sc}^{d}{\left(\frac{{V}_{1n}^{ph}}{{S}_{n}}\right)}^{2}$Primary side short circuit inductance:
${L}_{sc}^{d}=\frac{1}{2\pi {f}_{n}}\sqrt{{\left({Z}_{sc}^{d}\right)}^{2}{\left({R}_{sc}\right)}^{2}}$Primary and secondary side resistances and short circuit inductances are calculated using:
${R}_{1}=\frac{1}{2}{R}_{sc}$
${R}_{2}=\frac{1}{2}{R}_{sc}{\left(\frac{{N}_{2}}{{N}_{1}}\right)}^{2}$
${L}_{1}^{d}=\frac{1}{2}{L}_{sc}^{d}$
${L}_{2}^{d}=\frac{1}{2}{L}_{sc}^{d}{\left(\frac{{N}_{2}}{{N}_{1}}\right)}^{2}$
From the positive sequence open circuit test results, it is obtained:
${i}_{oc}^{d}=\frac{{i}_{oc}^{d}\left[\%\right]}{100}{I}_{1n}^{ph}={i}_{oc}^{d}\left[\%\right]\frac{{S}_{n}}{300{V}_{1n}^{ph}}$
${P}_{oc}^{d}=3\frac{{\left({V}_{1n}^{ph}\right)}^{2}}{{R}_{Fe}^{d}}\stackrel{yields}{\to}{R}_{Fe}^{d}=3\frac{{\left({V}_{1n}^{ph}\right)}^{2}}{{P}_{oc}^{d}}$
${P}_{oc}^{d}=3{R}_{Fe}^{d}{\left({i}_{Fe}^{d}\right)}^{2}\stackrel{yields}{\to}{\left({i}_{Fe}^{d}\right)}^{2}=\frac{{P}_{oc}^{d}}{3{R}_{Fe}^{d}}$
${i}_{m}^{d}=\sqrt{{\left({i}_{oc}^{d}\right)}^{2}{\left({i}_{Fe}^{d}\right)}^{2}}$
${L}_{m}^{d}=\frac{1}{2\pi {f}_{n}}\frac{{V}_{1n}^{ph}}{{i}_{m}^{d}}$
Variables description:
S_{n}  nominal power of transformer
V_{1nph}  primary side nominal phase to phase voltage
f_{n}  nominal frequency
N_{2}/N_{1}  transfer ration
u_{scd}  short circuit voltage (sc) – positive sequence (d)
Z_{scd}  short circuit impedance (sc) – positive sequence (d)
P_{scd}  short circuit active power (sc) – positive sequence (d)
R_{sc}  short circuit resistance (sc)
L_{scd}  short circuit inductance (sc) – positive sequence (d)
R_{1}  resistance on primary side
R_{2}  resistance on secondary side
L_{1d}  leakage inductance on primary side – positive sequence (d)
L_{2d}  leakage inductance on secondary side – positive sequence (d)
i_{ocd}  open circuit (oc) excitation current – positive sequence (d)
i_{1nph}  nominal phase current
P_{ocd}  open circuit (oc) losses– positive sequence (d)
R_{Fed} (R_{m})  resistance representing the core losses under nominal voltage – positive sequence (d)
i_{Fed}  current due to core losses under nominal voltage – positive sequence (d)
i_{md}  magnetizing current – positive sequence (d)
L_{md}  magnetizing inductance – positive sequence (d)
The topology of the three phase two winding variable ratio transformer is designed to match that of the Three phase two winding transformer. A schematic block diagram of the three phase two winding variable ratio transformer with the corresponding component arrangement and naming is shown in Figure 1.
It should be noted that terminals N1 and N2 can be connected with the rest of the circuit in Schematic Editor only if the corresponding side is wye (Y) connected.
Analog output signals from Enable signal output
When the Enable signal output checkbox is checked, a vector of internal variables of the transformer is passed to the output port out. These values are the primary and secondary voltages and currents for the individual single phase transformers. Each of the analog output signals is instantaneous in nature by default. If the Use RMS option is checked, the RMS values of each output will be returned instead.
Analog output variable name  Description 

Vprm_a  Primary voltage of the phase A transformer 
Iprm_a  Primary current of the phase A transformer 
Vsec_a  Secondary voltage of the phase A transformer 
Isec_a  Secondary current of the phase A transformer 
Vprm_b  Primary voltage of the phase B transformer 
Iprm_b  Primary current of the phase B transformer 
Vsec_b  Secondary voltage of the phase B transformer 
Isec_b  Secondary current of the phase B transformer 
Vprm_c  Primary voltage of the phase C transformer 
Iprm_c  Primary current of the phase C transformer 
Vsec_c  Secondary voltage of the phase C transformer 
Isec_c  Secondary current of the phase C transformer 