Implement three-phase transformer with configurable winding connections
Simscape / Electrical / Specialized Power Systems / Fundamental Blocks / Elements
This block implements a three-phase transformer using three single-phase transformers. 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 inductance and resistance of each winding are given in pu based on the
transformer nominal power Pn
and on the nominal voltage of the winding
(V1
or V2
). For a description of per units, refer to the
Linear Transformer and to the Saturable Transformer.
The two windings of the transformer can be connected as follows:
Y
Y with accessible neutral
Grounded Y
Delta (D1), delta lagging Y by 30 degrees
Delta (D11), delta leading Y by 30 degrees
If you select the Y connection with accessible neutral for winding 1, an input port labeled N is added to the block. If you ask for an accessible neutral on winding 2, an extra output port labeled n is generated.
The D1 and D11 notations refer to the clock convention that assumes that the reference Y voltage phasor is at noon (12) on a clock display. D1 and D11 refer respectively to 1:00 p.m. (delta voltages lagging Y voltages by 30 degrees) and 11:00 a.m. (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 |
---|---|---|---|---|---|
0 | 0 | Yy0 | Y | Y | — |
Dd0 | D1 | D1 | abc | ||
1 | –30 | Yd1 | Y | D1 | abc |
Dy1 | D11 | Y | abc | ||
2 | –60 | Dd2 | D11 | D1 | abc |
5 | –150 | Yd5 | Y | D1 | bca |
Dy5 | D11 | Y | cab | ||
7 | +150 | Yd7 | Y | D11 | cab |
Dy7 | D1 | Y | bca | ||
10 | +60 | Dd10 | D1 | D11 | abc |
11 | +30 | Yd11 | Y | D11 | abc |
Dy11 | D1 | Y | abc |
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 [1].
The winding connections for winding 1. Choices are Y
,
Yn
, Yg
(default), Delta
(D1)
, and Delta (D3)
.
The winding connections for winding 2. Choices are Y
,
Yn
, Yg
(default), Delta
(D1)
, and Delta (D3)
.
Select Three single-phase transformers
(default) 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).
Select 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.
Select 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. Default is cleared.
If you want to simulate the transformer in the phasor mode of the Powergui block, you must clear this parameter.
Select to model a saturation characteristic including hysteresis instead of a single-valued saturation curve. This parameter is visible only if the Simulate saturation parameter is selected. Default is cleared.
If you want to simulate the transformer in the phasor mode of the Powergui block, you must clear this parameter.
This parameter is visible only if the Simulate hysteresis parameter is selected.
Specify a .mat
file containing the data for use in the hysteresis
model. When you open the Hysteresis Design Tool of the Powergui block,
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 .mat
file. Use the Save button of
the Hysteresis Design tool to save your model in a new .mat
file.
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 Simulate saturation parameter is selected. Default is cleared.
When the Specify initial fluxes parameter is not selected upon simulation, Simscape™ Electrical™ Specialized 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.
Select Winding voltages
to measure the voltage across the
winding terminals.
Select Winding currents
to measure the current flowing
through the windings.
Select 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.
Select 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.
Select All measurements (V, I, Flux)
to measure the winding
voltages, currents, magnetization currents, and the flux linkages.
Default is None
.
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
Y
, Yn
, or
Yg
, the labels are as follows.
Measurement | Label |
---|---|
Winding 1 voltages |
or
|
Winding 1 currents |
or
|
Fluxes |
|
Magnetization currents |
|
Excitation currents |
|
The same labels apply for winding 2, except that 1
is replaced by
2
in the labels.
If the Winding 1 connection (ABC terminals) parameter is set to
Delta (D1)
or Delta (D3)
, the labels
are as follows.
Measurement | Label |
---|---|
Winding 1 voltages |
|
Winding 1 currents |
|
Flux linkages |
|
Magnetization currents |
|
Excitation currents |
|
Specify the units used to enter the parameters of this block. Select
pu
to use per unit. Select SI
to use
SI units. Changing the Units parameter from
pu
to SI
, or from
SI
to pu
, automatically converts 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 windings. Default is pu
.
The nominal power rating, in volt-amperes (VA), and nominal frequency, in hertz (Hz),
of the transformer. The nominal parameters have no impact on the transformer model when the
Units parameter is set to SI
. Default is
[ 250e6 , 60 ]
.
The phase-to-phase nominal voltage in volts RMS, resistance, and leakage inductance in
pu for winding 1. Default is [ 735e3 , 0.002 , 0.08 ]
when the
Units parameter is pu
and
[7.35e+05 4.3218 0.45856]
when the Units parameter
is SI
.
The phase-to-phase nominal voltage in volts RMS, resistance, and leakage inductance in
pu for winding 2. Default is [ 315e3 , 0.002 , 0.08 ]
when the
Units parameter is pu
and
[3.15e+05 0.7938 0.084225]
when the Units parameter
is SI
.
The magnetization resistance Rm, in pu. Default is 500
when the
Units parameter is pu
and
1.0805e+06
when the Units parameter is
SI
.
The magnetization inductance Lm, in pu, for a nonsaturable core. The Magnetization inductance Lm parameter is not accessible if the
Saturable core parameter on the Configuration tab is selected. Default is 500
when the
Units parameter is pu
and
2866
when the Units parameter is
SI
.
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)
. Default is 0.5
when the Units parameter is pu
and
2.866
when the Units parameter is
SI
.
This parameter is available only if the Simulate saturation
parameter on the Configuration tab is selected. Default is [
0,0 ; 0.0024,1.2 ; 1.0,1.52 ]
when the Units parameter is
pu
and [0 0;0.66653 1910.3;277.72 2419.7]
when the Units parameter is SI
.
The saturation characteristic for the saturable core. Specify a series of current/ flux pairs (in pu) starting with the pair (0,0).
Specify initial fluxes for each phase of the transformer. This parameter is available
only if the Specify initial fluxes and Simulate
saturation parameters on the Configuration tab are
selected. Default is [ 0.8 , -0.8 , 0.7 ]
when the
Units parameter is pu
and [1273.5
-1273.5 1114.3]
when the Units parameter is
SI
.
When the Specify initial fluxes parameter is not selected upon simulation, Simscape Electrical Specialized 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 overwrite any previous values.
The Advanced tab of the block is not visible when you set the
Simulation type parameter of the powergui block to
Continuous
, or when you select the Automatically handle
discrete solver parameter of the powergui block. The tab is visible
when you set the Simulation type parameter of the powergui
block to Discrete
, and when the Automatically handle
discrete solver parameter of the powergui block is cleared.
When selected, a delay is inserted at the output of the saturation model computing magnetization current as a function of flux linkage (the integral of input voltage computed by a Trapezoidal method). This delay eliminates the algebraic loop resulting from trapezoidal discretization methods and speeds up the simulation of the model. However, this delay introduces a one simulation step time delay in the model and can cause numerical oscillations if the sample time is too large. The algebraic loop is required in most cases to get an accurate solution.
When cleared (default), the Discrete solver model parameter specifies the discretization method of the saturation model.
Select one of these methods to resolve the algebraic loop.
Trapezoidal iterative
—Although this method produces
correct results, it is not recommended because Simulink® tends to slow down and may fail to converge (simulation stops), especially
when the number of saturable transformers is increased. Also, because of the Simulink algebraic loop constraint, this method cannot be used in real time. In
R2018b and previous releases, you used this method when the Break Algebraic
loop in discrete saturation model parameter was cleared.
Trapezoidal robust
—This method is slightly more accurate
than the Backward Euler robust
method. However, it may produce
slightly damped numerical oscillations on transformer voltages when the transformer is at
no load.
Backward Euler robust
—This method provides good accuracy
and prevents oscillations when the transformer is at no load.
The maximum number of iterations for the robust methods is specified in the Preferences tab of the powergui block, in the Solver details for nonlinear elements section. For real time applications, you may need to limit the number of iterations. Usually, limiting the number of iterations to 2 produces acceptable results. The two robust solvers are the recommended methods for discretizing the saturation model of the transformer.
For more information on what method to use in your application, see Simulating Discretized Electrical Systems.
The power_transfo3ph
circuit uses the Three-Phase Transformer block where the saturable core is simulated. Both
windings are connected in a Y grounded configuration. The neutral points of the two windings are
internally connected to the ground.
The 500 kV/ 230-kV saturable transformer is energized on the 500-kV system. Remanent fluxes
of 0.8 pu, −0.4 pu, and 0.4 pu have been specified respectively for phases A, B, and C. Run the
simulation and observe inrush currents due to core saturation. See also the power_xfonotation
model that
shows four types of three-phase Yd and Dy transformer connections.
[1] IEC. International Standard IEC 60076-1, Power Transformer - Part 1: General, Edition 2.1, 2000–04. "Annex D: Three-phase transformer connections." 2000.
Linear Transformer, Multimeter, Saturable Transformer, Three-Phase Transformer (Three Windings), Three-Phase Transformer Inductance Matrix Type (Two Windings)