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.

The schematic symbol and input parameters for the three phase two winding variable ratio transformer component are given in Table 1.

Table 1. Three phase two winding variable ratio transformer component
component	component dialog window	component parameters
Three phase two winding variable ratio transformer		Input parameters option (SC and OC tests, Si or p.u.) Nominal Power of the transformer (Sn) Nominal frequency (Hz) Nominal line to line voltage of the primary winding in volts RMS (V1) Nominal line to line voltage of the secondary winding in volts RMS (V2) Positive sequence short circuit voltage (% of nominal phase voltage) (usc1) Positive sequence short circuit losses (Psc1) Core model - Linear, Non-Linear, Rm/Lm neglected Positive sequence no load excitation current (% of nominal current) (ioc1) Positive sequence no load losses (Poc1)
		Winding 1 connection (D or Y) Winding 2 connection (D or Y) Clock number - determines the phase displacement between primary and secondary side voltages
		Enable signal output - passes individual phase voltage and current values to a signal processing output port. Execution rate - defines the execution rate of measurement and signal processing components. Use RMS - passes RMS values for measured voltages and currents.
		Snubber Type - adds a snubber to the current source side of the embedded single phase transformers. Resistance - sets the series resistance value of the snubber if Snubber Type is set to R or RC. Capacitance - sets the series capacitance value of the snubber if Snubber Type is set to RC.

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 one-dimensional 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.

There are two types of tests that are performed to characterize a transformer. Both of the tests are performed on either the primary or the secondary side of the transformer. The tests are:

short circuit test – exciting a set of three-phase windings while the other set of windings is short circuited
open circuit test – exciting a set of three-phase 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 three-phase 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 three-phase 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_{s c}^{d} = 3 \frac{u_{s c}^{d} [%] {(V_{1 n}^{p h})}^{2}}{{100 S}_{n}}

Primary side short circuit resistance is obtained:

R_{s c} = 3 P_{s c}^{d} {(\frac{V_{1 n}^{p h}}{S_{n}})}^{2}

Primary side short circuit inductance:

L_{s c}^{d} = \frac{1}{2 π f_{n}} \sqrt{{(Z_{s c}^{d})}^{2} - {(R_{s c})}^{2}}

Primary and secondary side resistances and short circuit inductances are calculated using:

$R_{1} = \frac{1}{2} R_{s c}$

$R_{2} = \frac{1}{2} R_{s c} {(\frac{N_{2}}{N_{1}})}^{2}$

$L_{1}^{d} = \frac{1}{2} L_{s c}^{d}$

$L_{2}^{d} = \frac{1}{2} L_{s c}^{d} {(\frac{N_{2}}{N_{1}})}^{2}$

From the positive sequence open circuit test results, it is obtained:

$i_{o c}^{d} = \frac{i_{o c}^{d} [%]}{100} I_{1 n}^{p h} = i_{o c}^{d} [%] \frac{S_{n}}{300 V_{1 n}^{p h}}$

$P_{o c}^{d} = 3 \frac{{(V_{1 n}^{p h})}^{2}}{R_{F e}^{d}} \overset{y i e l d s}{\to} R_{F e}^{d} = 3 \frac{{(V_{1 n}^{p h})}^{2}}{P_{o c}^{d}}$

$P_{o c}^{d} = 3 R_{F e}^{d} {(i_{F e}^{d})}^{2} \overset{y i e l d s}{\to} {(i_{F e}^{d})}^{2} = \frac{P_{o c}^{d}}{3 R_{F e}^{d}}$

$i_{m}^{d} = \sqrt{{(i_{o c}^{d})}^{2} - {(i_{F e}^{d})}^{2}}$

$L_{m}^{d} = \frac{1}{2 π f_{n}} \frac{V_{1 n}^{p h}}{i_{m}^{d}}$

Variables description:

S_n - nominal power of transformer

V_1n^ph - primary side nominal phase to phase voltage

f_n - nominal frequency

N₂/N₁ - transfer ration

u_sc^d - short circuit voltage (sc) – positive sequence (d)

Z_sc^d - short circuit impedance (sc) – positive sequence (d)

P_sc^d - short circuit active power (sc) – positive sequence (d)

R_sc - short circuit resistance (sc)

L_sc^d - short circuit inductance (sc) – positive sequence (d)

R₁ - resistance on primary side

R₂ - resistance on secondary side

L_1^d - leakage inductance on primary side – positive sequence (d)

L_2^d - leakage inductance on secondary side – positive sequence (d)

i_oc^d - open circuit (oc) excitation current – positive sequence (d)

i_1n^ph - nominal phase current

P_oc^d - open circuit (oc) losses– positive sequence (d)

R_Fe^d (R_m) - resistance representing the core losses under nominal voltage – positive sequence (d)

i_Fe^d - current due to core losses under nominal voltage – positive sequence (d)

i_m^d - magnetizing current – positive sequence (d)

L_m^d - 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.

Figure 1. Schematic block diagram of three phase two winding variable ratio transformer with corresponding components naming

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