Implement three-phase transformer with configurable winding connections
This block implements a three-phase transformer by using three single-phase transformers with three windings. For a detailed description of the electrical model of a single-phase transformer, see the Linear Transformer block.
When activated, the saturation characteristic is the same as the one described for the Saturable Transformer block. If the fluxes are not specified, the initial values are automatically adjusted so that the simulation starts in steady state.
The leakage inductances and resistance of each winding are given
in pu based on the transformer nominal power
on the nominal voltage of the winding (
V3). For an explanation of per units, refer
to the Linear Transformer and to the Saturable Transformer.
The three windings of the transformer can be connected in the following manner:
Y with accessible neutral (for windings 1 and 3 only)
Delta (D1), delta lagging Y by 30 degrees
Delta (D11), delta leading Y by 30 degrees
An input port labeled
N is added to the block
if you select the Y connection with accessible neutral for winding
1. If you ask for an accessible neutral on winding 3, an extra outport
n3 is generated.
The D1 and D11 notations refer to the following clock convention. It assumes that the reference Y voltage phasor is at noon (12) on a clock display. D1 and D11 refer respectively to 1 PM (delta voltages lagging Y voltages by 30 degrees) and 11 AM (delta voltages leading Y voltages by 30 degrees).
The conventional notation for a two-winding three-phase transformer uses two letters followed by a number. The first letter (Y or D) indicates a high-voltage wye or delta winding connection. The second letter (y or d) indicates a low-voltage wye or delta winding connection. The number, an integer between 0 and 12, indicates the position of the low-voltage positive-sequence voltage phasor on a clock display when the high-voltage positive-sequence voltage phasor is at 12:00.
The following three figures are examples of standard winding connections. The dots indicate polarity marks, and arrows indicate the position of phase A-to-neutral voltage phasors on high-voltage and low-voltage windings. The phasors are assumed to rotate in a counterclockwise direction so that rising numbers indicate increasing phase lag.
Yd1: The low-voltage winding (d) is lagging high-voltage winding (Y) by 30 degrees. The Winding 2 connection parameter is set to D1.
Dy11: The low-voltage winding (y) is leading high-voltage winding (D) by 30 degrees. The Winding 1 connection parameter is set to D1.
Dy1: The low-voltage winding (y) is lagging high-voltage winding (D) by 30 degrees. The Winding 1 connection parameter is set to D11.
You can represent many other connections with phase shifts between 0 and 360 degrees (by steps of 30 degrees) by combining the +30- or –30-degree phase shift provided by the D1 and D11 block parameter settings and, in some cases, an additional +/–120-degree phase shift obtained by connecting the output terminals of delta winding to the appropriate phases of the network.
The table explains how to set up the Three-Phase Transformer block to obtain common connections.
|Clock Position||Phase Shift (degrees)||Connection||Winding 1 Connection||Winding 2 Connection||Terminals of Delta Winding to Connect to Network ABC Phases|
For example, to obtain the Yd5 connection, set the Winding 1 connection parameter to Y and the Winding 2 connection parameter to D1, and connect the network phases to the winding 2 as follows:
For more details on conventional transformer winding notations, see International Standard IEC 60076-1 .
The winding connection for winding 1.
The winding connection for winding 2.
The winding connection for winding 3.
Three single-phase transformers to
implement a three-phase transformer using three single-phase transformer
models. You can use this core type to represent very large power transformers
found in utility grids (hundreds of MW).
Three-limb core (core type) to
implement a three-limb core three-phase transformer. In most applications,
three-phase transformers use a three-limb core (core-type transformer).
This type of core produces accurate results during an asymmetrical
fault for both linear and nonlinear models (including saturation).
During asymmetrical voltage conditions, the zero-sequence flux of
a core-type transformer returns outside the core, through an air gap,
structural steel, and a tank. Thus, the natural zero-sequence inductance
L0 (without delta winding) of such a core-type transformer is usually
very low (typically 0.5 pu < L0 < 2 pu) compared with a three-phase
transformer using three single-phase units (L0 > 100 pu). This
low L0 value affects voltages, currents, and flux unbalances during
linear and saturated operation.
Five-limb core (shell type) to
implement a five-limb core three-phase transformer. On rare occasions,
very large transformers are built with a five-leg core (three phase
legs and two external legs). This core configuration, also known as
shell type, is chosen mainly to reduce the height of the transformer
and make transportation easier. During unbalanced voltage conditions,
as opposed to the three-limb transformer, the zero-sequence flux of
the five-limb transformer stays inside the steel core and returns
through the two external limbs. The natural zero-sequence inductance
(without delta) is therefore very high (L0 > 100 pu). Except for
small current unbalances due to core asymmetry, the behavior of the
five-limb shell-type transformer is similar to that of a three-phase
transformer built with three single-phase units.
If selected, implements a saturable three-phase transformer. See also the Saturation characteristic parameter on the Parameters tab.
Select to model a saturation characteristic including hysteresis instead of a single-valued saturation curve. This parameter is visible only if the Saturable core parameter is selected.
This parameter is visible only if the Simulate hysteresis parameter is selected.
.mat file containing the data to
be used for the hysteresis model. When you open the Hysteresis
Design Tool of the Powergui, the default hysteresis loop
and parameters saved in the
hysteresis.mat file are displayed. Use the Load button
of the Hysteresis Design tool to load another
Use the Save button of the Hysteresis
Design tool to save your model in a new
If selected, the initial fluxes are defined by the Initial fluxes parameter on the Parameters tab. The Specify initial fluxes parameter is visible only if the Saturable core parameter is selected.
When the Specify initial fluxes parameter is not selected upon simulation, Simscape™ Power Systems™ software automatically computes the initial fluxes to start the simulation in steady state. The computed values are saved in the Initial Fluxes parameter and will overwrite any previous values.
Winding voltages to measure the voltage
across the winding terminals of the Three-Phase Transformer block.
Winding currents to
measure the current flowing through the windings of the Three-Phase
Fluxes and excitation currents (Im + IRm) to
measure the flux linkage, in volt seconds (V.s), and the total excitation
current including iron losses modeled by Rm.
Fluxes and magnetization currents (Im) to
measure the flux linkage, in volt seconds (V.s), and the magnetization
current, in amperes (A), not including iron losses modeled by Rm.
All measurements (V, I, Flux) to measure the winding voltages, currents,
magnetization currents, and the flux linkages.
Place a Multimeter block in your model to display the selected measurements during the simulation. In the Available Measurements list box of the Multimeter block, the measurements are identified by a label followed by the block name.
If the Winding 1 connection (ABC terminals) parameter
is set to
the labels are as follows.
Winding 1 voltages
Winding 1 currents
The same labels apply for winding 2 and winding 3, except that
1 is replaced by
2 or by
If the Winding 1 connection (ABC terminals) parameter
is set to
Delta (D11) or
Delta (D1), the labels
are as follows.
Winding 1 voltages
Winding 1 currents
Specify the units used to enter the parameters of the Three
Phase Transformer block. Select
pu to use per unit.
SI to use SI units. Changing the Units parameter from
pu, will automatically
convert the parameters displayed in the mask of the block. The per
unit conversion is based on the transformer rated power Pn in VA,
nominal frequency fn in Hz, and nominal voltage Vn, in Vrms, of the
The nominal power rating, in volt-amperes (VA), and nominal
frequency, in hertz (Hz), of the transformer. Note that the nominal
parameters have no impact on the transformer model when the Units parameter is set to
The phase-to-phase nominal voltage in volts RMS, resistance, and leakage inductance in pu for winding 1.
The phase-to-phase nominal voltage in volts RMS, resistance, and leakage inductance in pu for winding 2.
The phase-to-phase nominal voltage in volts RMS, resistance, and leakage inductance in pu for winding 3.
The magnetization resistance Rm, in pu.
The magnetization inductance Lm, in pu, for a nonsaturable core. The Magnetization inductance Lm parameter is not accessible if the Saturable core parameter is selected.
The Inductance L0 of zero-sequence flux path return, in pu, for the three-limb core transformer type.
This parameter is visible only if the Type parameter
is set to
Three-limb core (core type).
This parameter is accessible only if the Saturable core parameter is selected.
The saturation characteristic for the saturable core. Specify a series of current/ flux pairs (in pu) starting with the pair (0,0).
Specifies initial fluxes for each phase of the transformer. This parameter is visible only if the Specify initial fluxes and Saturable core parameters are selected on the Configuration tab.
When the Specify initial fluxes parameter is not selected upon simulation, Simscape Power Systems software automatically computes the initial fluxes to start the simulation in steady state. The computed values are saved in the Initial Fluxes parameter and will overwrite any previous values.
When you use the block in a discrete system, you will get an algebraic loop. This algebraic loop, which is required in most cases to get an accurate solution, tends to slow down the simulation. However, to speed up the simulation, in some circumstances, you can disable the algebraic loop by selecting Break Algebraic loop in discrete saturation model. You should be aware that disabling the algebraic loop introduces a one-simulation-step time delay in the model. This can cause numerical oscillations if the sample time is too large.
uses two Three-Phase Transformer blocks. Two Multimeter blocks are
used to measure the phase A voltage (or AB for delta connections)
of each winding