Two-Winding Transformer (Three-Phase)

Three-phase linear nonideal wye- and delta-configurable two-winding transformer with saturation capability

Libraries:
Simscape / Electrical / Passive / Transformers

Description

The Two-Winding Transformer (Three-Phase) block represents a linear nonideal three-phase two-winding transformer that transfers electrical energy between two or more circuits through electromagnetic induction. The block includes linear winding leakage and linear core magnetization effects. You can parameterize the block impedance using per-unit values. The primary and secondary winding types, delta-wye phase angle, and core types are configurable.

The configuration options for both the primary and secondary windings are:

Wye with floating neutral — Star or T configuration with Floating Neutral (Three-Phase)
Wye with neutral port — Star or T configuration with Neutral Port (Three-Phase)
Wye with grounded neutral — Star or T configuration with Grounded Neutral (Three-Phase)
Delta 1 o'clock — Mesh configuration with a lagging 30 degree phase shift relative to the voltage of a connected wye configuration
Delta 11 o'clock — Mesh configuration with leading 30 degree phase shift relative to the voltage of a connected wye configuration

Options for the core type are:

Three-phase five-limb
Three-phase three-limb

Although a three-limb core is typically less expensive, a five-limb core offers these advantages:

Lower impedance for the zero-sequence component of current, that is between the line and neutral, in the case of an unbalanced load
Greater heat dissipation

Equations

Three-Limb Core

This block is implemented in the magnetic domain using basic magnetic reluctances, windings, and eddy currents blocks.

It is important to determine the relation between the electrical domain parameters from the block mask and the magnetic domain parameters used in the model:

n₁ is the number of the primary winding turns.
n₂ is the number of the secondary winding turns.
L_m is the shunt magnetizing inductance.
L₀ is the zero-sequence inductance.
L_p is the primary winding leakage inductance.
L_s is the secondary winding leakage inductance.
R_m is the shunt magnetizing resistance.
R is the magnetizing reluctance between phases.
$R = \frac{n_{1}^{2}}{L_{m}}$
R₀ is the zero sequence reluctance.
$R_{0} = \frac{1}{3} \frac{n_{1}^{2}}{L_{0} - L_{p}}$
Rl₁ is the primary winding leakage reluctance.
$R l_{1} = \frac{n_{1}^{2}}{L_{p}}$
Rl₂ is the secondary winding leakage reluctance.
$R l_{2} = \frac{n_{2}^{2}}{L_{s}}$
L_eddy is the conductance of eddy current loop
$L_{e d d y} = \frac{n_{1}^{2}}{R_{m}}$

For two-winding transformers (three-phase), the coupling between different windings in each phase is identical.

Five-Limb Core

In the case of a five-limb transformer, the extra magnetic flux paths provided by the extra limbs can be represented by zero sequence reluctances, which are originally designed for magnetic paths through the air in the three-limb transformer.

In a five-limb model, the magnetic reluctances from the phases to the extra limbs are supposed to be equal to the magnetic reluctances between phases.

$R = R_{0}$

Therefore we deduce:

$R = R_{0} = \frac{n_{1}^{2}}{L_{m}}$

Display Options

You can display the transformer per-unit base values in the MATLAB^® command window using the block context menu. To display the values, right-click the block and select Electrical > Display Base Values.

Variables

To set the priority and initial target values for the block variables before simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. You can specify nominal values using different sources, including the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

Examples

Three-Phase Asynchronous Drive with Sensor Control

Control and analyze the operation of an Asynchronous Machine (ASM) using sensored rotor field-oriented control. The model shows the main electrical circuit, with three additional subsystems containing the controls, measurements, and scopes. The Controls subsystem contains two controllers: one for the Grid-Side Converter (AC/DC) and one for the Machine-Side Converter (DC/AC). The Scopes subsystem contains two time scopes: one for the Grid-Side Converter and one for the ASM. When the model is executed, a Spectrum Analyzer opens and displays frequency data for the A-Phase Supply Current.

Open Model

Three-Phase Asynchronous Drive with Sensorless Control

Control and analyze the operation of an Asynchronous Machine (ASM) using sensorless rotor field-oriented control. The model shows the main electrical circuit, with three additional subsystems containing the controls, measurements, and scopes. The Controls subsystem contains two controllers: one for the Grid-Side Converter (AC/DC) and one for the Machine-Side Converter (DC/AC). The Scopes subsystem contains two time scopes: one for the Grid-Side Converter and one for the ASM. When the model is executed, a Spectrum Analyzer opens and displays frequency data for the A-Phase Supply Current.

Open Model

Three-Phase Bridge Cycloconverter

A three-phase bridge cycloconverter. The cycloconverter consists of 36 thyristors and has the capacity to lower the frequency of the input voltage. The Control subsystem implements the cycloconverter RMS voltage control. It also provides pulse generation for the firing of the thyristors. The Visualization subsystem contains scopes that allow you to see the simulation results. The simulation time, t, is 1 second. The load increases when Load1 switches on at t = 0.75 seconds.

Open Model

Ports

Conserving

expand all

~1 — Primary winding voltage
electrical

Expandable three-phase electrical conserving port associated with the three-phase, [a1 b1 c1], voltage of winding 1.

n1 — Primary winding neutral point
electrical

Electrical conserving port associated with the primary winding neutral point.

Dependencies

This port is only visible when the Main parameter Winding 1 connection type is set to Wye with neutral port.

~2 — First secondary winding voltage
electrical

Expandable three-phase electrical conserving port associated with the three-phase, [a2 b2 c2], voltage of the first secondary winding.

n2 — First secondary winding neutral point
electrical

Electrical conserving port associated with the first secondary winding neutral point.

Dependencies

This port is only visible when the Main parameter Winding 2 connection type is set to Wye with neutral port.

Parameters

expand all

Modeling option — Whether to model composite or expanded three-phase ports
`Composite three-phase ports` (default) | `Expanded three-phase ports`

Whether to model composite or expanded three-phase ports.

Composite three-phase ports represent three individual electrical conserving ports with a single block port. You can use composite three-phase ports to build models that correspond to single-line diagrams of three-phase electrical systems.

Expanded three-phase ports represent the individual phases of a three-phase system using three separate electrical conserving ports.

Main

Rated apparent power — Apparent power at rated capacity
`100e6` (default) | positive scalar

Apparent power flowing through the transformer when operating at rated capacity. The value must be greater than 0.

Rated electrical frequency — Connected network electrical frequency
`60` (default) | positive scalar

Rated or nominal frequency of the AC network to which the transformer is connected. The value must be greater than 0.

Winding 1 connection type — Primary winding configuration
`Wye with floating neutral` (default) | `Wye with neutral port` | `Wye with grounded neutral` | `Delta 1 o'clock` | `Delta 11 o'clock`

Primary winding type.

Primary rated voltage — RMS line voltage applied to the primary winding
`4160` (default) | positive scalar

RMS line voltage applied to the primary winding under normal operating conditions. The value must be greater than 0.

Winding 2 connection type — Secondary winding configuration
`Wye with floating neutral` (default) | `Wye with neutral port` | `Wye with grounded neutral` | `Delta 1 o'clock` | `Delta 11 o'clock`

Secondary winding type.

Secondary rated voltage — RMS line voltage applied to the secondary winding
`24e3` (default) | positive scalar

RMS line voltage applied to the secondary winding under normal operating conditions. The value must be greater than 0.

Core type — Number of limbs
`Three-phase three-limb` (default) | `Three-phase five-limb`

Number of limbs that comprise the magnetic circuit.

Impedances

Primary winding resistance (pu) — Primary winding power loss
`0.01` (default) | positive scalar

Per-unit power loss in the primary winding. The value must be greater than 0.

Secondary winding resistance (pu) — Secondary winding power loss
`0.01` (default) | positive scalar

Per-unit power loss in the secondary winding. The value must be greater than 0.

Leakage reactance — Leakage reactance modeling
`Exclude` (default) | `Include`

Whether to model magnetic flux losses.

Primary leakage reactance (pu) — Primary winding magnetic flux loss
`0.001` (default) | positive scalar

Per-unit magnetic flux loss in the primary winding. The value must be greater than 0.

Dependencies

To enable this parameter, set Leakage reactance to Include.

Secondary leakage reactance (pu) — Secondary winding magnetic flux loss
`0.001` (default) | positive scalar

Per-unit magnetic flux loss in the secondary winding. The value must be greater than 0.

Dependencies

To enable this parameter, set Leakage reactance to Include.

Magnetizing resistance — Magnetizing resistance modeling
`Exclude` (default) | `Include`

Whether to model the transformer core losses.

Shunt magnetizing resistance (pu) — Transformer core losses
`500` (default) | positive scalar

Per-unit losses in the transformer core. The value must be greater than 0.

Dependencies

To enable this parameter, set Magnetizing resistance to Include.

Magnetizing reactance — Magnetizing reactance modeling
`Exclude` (default) | `Include`

Whether to model magnetic effects of the transformer core.

Magnetic saturation representation — Representation of the magnetic saturation
`None` (default) | `Lookup table (phi versus i)`

Choose if and how you want to represent the magnetic saturation.

Dependencies

To enable this parameter, set Magnetizing reactance to Include.

Current vector (pu), i — Per unit vector of currents
`[0, .002, 1, 2]` (default)

Per unit vector of currents. The first value must be 0. This parameter must be strictly ascending.

Dependencies

To enable this parameter, set Magnetizing reactance to Include and Magnetic saturation representation to Lookup table (phi versus i).

Magnetic flux vector (pu), phi — Per unit vector of magnetic flux
`[0, 1.2, 1.5, 1.51]` (default)

Per unit vector of magnetic flux. The first value must be 0. This parameter must be strictly ascending.

Dependencies

To enable this parameter, set Magnetizing reactance to Include and Magnetic saturation representation to Lookup table (phi versus i).

Shunt magnetizing reactance (pu) — Transformer core magnetic effects
`500` (default) | positive scalar

Per-unit magnetic effects of the transformer core when operating in its linear region. The value must be greater than 0.

Dependencies

To enable this parameter, set Magnetizing reactance to Include and Magnetic saturation representation to None.

Zero sequence reactance (pu) — Zero sequence reactance
`0.5` (default) | positive scalar

Per-unit zero sequence reactance. The value must be greater than or equal to the primary winding magnetic flux loss.

Dependencies

To enable this parameter, set Core type, a Main parameter, to Three-phase three-limb.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2019a

Two-Winding Transformer (Three-Phase)

Description

Equations

Display Options

Variables

Examples

Three-Phase Asynchronous Drive with Sensor Control

Three-Phase Asynchronous Drive with Sensorless Control

Three-Phase Bridge Cycloconverter

Ports

Conserving

~1 — Primary winding voltage electrical

n1 — Primary winding neutral point electrical

Dependencies

~2 — First secondary winding voltage electrical

n2 — First secondary winding neutral point electrical

Dependencies

Parameters

Modeling option — Whether to model composite or expanded three-phase ports Composite three-phase ports (default) | Expanded three-phase ports

Main

Rated apparent power — Apparent power at rated capacity 100e6 (default) | positive scalar

Rated electrical frequency — Connected network electrical frequency 60 (default) | positive scalar

Winding 1 connection type — Primary winding configuration Wye with floating neutral (default) | Wye with neutral port | Wye with grounded neutral | Delta 1 o'clock | Delta 11 o'clock

Primary rated voltage — RMS line voltage applied to the primary winding 4160 (default) | positive scalar

Winding 2 connection type — Secondary winding configuration Wye with floating neutral (default) | Wye with neutral port | Wye with grounded neutral | Delta 1 o'clock | Delta 11 o'clock

Secondary rated voltage — RMS line voltage applied to the secondary winding 24e3 (default) | positive scalar

Core type — Number of limbs Three-phase three-limb (default) | Three-phase five-limb

Impedances

Primary winding resistance (pu) — Primary winding power loss 0.01 (default) | positive scalar

Secondary winding resistance (pu) — Secondary winding power loss 0.01 (default) | positive scalar

Leakage reactance — Leakage reactance modeling Exclude (default) | Include

Primary leakage reactance (pu) — Primary winding magnetic flux loss 0.001 (default) | positive scalar

Dependencies

Secondary leakage reactance (pu) — Secondary winding magnetic flux loss 0.001 (default) | positive scalar

Dependencies

Magnetizing resistance — Magnetizing resistance modeling Exclude (default) | Include

Shunt magnetizing resistance (pu) — Transformer core losses 500 (default) | positive scalar

Dependencies

Magnetizing reactance — Magnetizing reactance modeling Exclude (default) | Include

Magnetic saturation representation — Representation of the magnetic saturation None (default) | Lookup table (phi versus i)

Dependencies

Current vector (pu), i — Per unit vector of currents [0, .002, 1, 2] (default)

Dependencies

Magnetic flux vector (pu), phi — Per unit vector of magnetic flux [0, 1.2, 1.5, 1.51] (default)

Dependencies

Shunt magnetizing reactance (pu) — Transformer core magnetic effects 500 (default) | positive scalar

Dependencies

Zero sequence reactance (pu) — Zero sequence reactance 0.5 (default) | positive scalar

Dependencies

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

~1 — Primary winding voltage
electrical

n1 — Primary winding neutral point
electrical

~2 — First secondary winding voltage
electrical

n2 — First secondary winding neutral point
electrical

Modeling option — Whether to model composite or expanded three-phase ports
`Composite three-phase ports` (default) | `Expanded three-phase ports`

Rated apparent power — Apparent power at rated capacity
`100e6` (default) | positive scalar

Rated electrical frequency — Connected network electrical frequency
`60` (default) | positive scalar

Winding 1 connection type — Primary winding configuration
`Wye with floating neutral` (default) | `Wye with neutral port` | `Wye with grounded neutral` | `Delta 1 o'clock` | `Delta 11 o'clock`

Primary rated voltage — RMS line voltage applied to the primary winding
`4160` (default) | positive scalar

Winding 2 connection type — Secondary winding configuration
`Wye with floating neutral` (default) | `Wye with neutral port` | `Wye with grounded neutral` | `Delta 1 o'clock` | `Delta 11 o'clock`

Secondary rated voltage — RMS line voltage applied to the secondary winding
`24e3` (default) | positive scalar

Core type — Number of limbs
`Three-phase three-limb` (default) | `Three-phase five-limb`

Primary winding resistance (pu) — Primary winding power loss
`0.01` (default) | positive scalar

Secondary winding resistance (pu) — Secondary winding power loss
`0.01` (default) | positive scalar

Leakage reactance — Leakage reactance modeling
`Exclude` (default) | `Include`

Primary leakage reactance (pu) — Primary winding magnetic flux loss
`0.001` (default) | positive scalar

Secondary leakage reactance (pu) — Secondary winding magnetic flux loss
`0.001` (default) | positive scalar

Magnetizing resistance — Magnetizing resistance modeling
`Exclude` (default) | `Include`

Shunt magnetizing resistance (pu) — Transformer core losses
`500` (default) | positive scalar

Magnetizing reactance — Magnetizing reactance modeling
`Exclude` (default) | `Include`

Magnetic saturation representation — Representation of the magnetic saturation
`None` (default) | `Lookup table (phi versus i)`

Current vector (pu), i — Per unit vector of currents
`[0, .002, 1, 2]` (default)

Magnetic flux vector (pu), phi — Per unit vector of magnetic flux
`[0, 1.2, 1.5, 1.51]` (default)

Shunt magnetizing reactance (pu) — Transformer core magnetic effects
`500` (default) | positive scalar

Zero sequence reactance (pu) — Zero sequence reactance
`0.5` (default) | positive scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.