Three-Winding Transformer (Three-Phase)
Three-phase linear non-ideal three-winding transformer with Star and Delta winding connection and saturation consideration.
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Description
Unit Three-Winding Transformer (Three-Phase) represents a linear non-ideal three-phase, three-winding transformer that transfers electrical energy between two or more circuits by electromagnetic induction. The block includes the effects of linear winding leakage and linear core magnetisation. The resistance of the block can be parameterised in relative units. The primary, first secondary and second secondary winding connections, delta-star phase angle and core types are customisable.
The primary and secondary winding configuration options are as follows:
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`Wye with floating neutral' - star with floating three-phase neutral.
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Wye with neutral port- star with three-phase neutral. -
Wye with grounded neutral - star with grounded three-phase neutral.
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`Delta 1 o’clock' - triangle with 30 degrees lag from the star.
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`Delta 11 o’clock' - triangle with 30 degrees ahead of the star.
For more information on the operating modes of a three-phase system connected in a Delta pattern, see Problem solving for delta connection of transformer windings.
Core type options:
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`Three-phase five-limb' - three-phase five-limb core.
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Three-phase three-limb core: `Three-phase three-limb'.
Although the three-phase core is usually cheaper, the five-limb core has the following advantages:
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Lower resistance for the zero sequence current component, i.e. between line and neutral, in case of unbalanced load.
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Greater heat dissipation.
Equations
Three-bar core
This block is implemented in the magnetic domain with usage of blocks Nonlinear Reluctance, Winding and Eddy Current.
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It is important to determine the relationship between the electrical domain parameters from the block mask and the magnetic domain parameters used in the model:
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- number of turns of the primary winding.
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- number of turns of the first secondary winding.
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- number of turns of the second secondary winding.
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- shunt magnetising inductance.
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- zero-sequence inductance.
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- scattering inductance of the primary winding.
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- scattering inductance of the first secondary winding.
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- scattering inductance of the second secondary winding.
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- shunt magnetising resistance.
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- magnetising resistance between phases
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- zero-sequence impedance coefficient
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- primary winding leakage resistance
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- leakage resistance of the first secondary winding
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- leakage resistance of the second secondary winding
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- eddy current loop conductivity
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For three-winding three-phase transformers, the coupling between the different windings in each phase is the same.
Five core
In the case of a transformer with a five-bar core, the additional magnetic flux paths provided by the additional bars can be represented using the zero-sequence magnetic resistances that were originally developed for the magnetic paths through the air in a three-bar core transformer.
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In the five-core model, the magnetic resistances from the phases to the additional windings must be equal to the magnetic resistances between the phases:
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Hence the conclusion:
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Ports
Non-directional
~1 - primary winding terminals
electricity
Three-phase electrical port, corresponds to the phase terminals , and of the primary winding.
n1 is the neutral
electricity
The electrical port associated with the neutral of the primary winding.
Dependencies
To use this port, set the Primary winding connection type parameters to Wye with neutral port.
~2 - terminals of the first secondary winding
electricity
Three-phase electrical port, corresponds to the phase terminals , and of the first secondary winding.
n2 is the neutral
electricity
An electrical port connected to the neutral of the first secondary winding.
Dependencies
To use this port, set the First secondary connection type parameters to Wye with neutral port.
~3 - Second secondary winding terminals
electricity
Three-phase electrical port, corresponds to the phase terminals , and of the second secondary winding.
n3 - neutral
electricity
An electrical port connected to the neutral of the second secondary winding.
Dependencies
To use this port, set the Second secondary connection type parameters to Wye with neutral port.
Parameters
Main
Number of windings - switch between two and three winding transformer
Two (by default) | `Three `
Switching between two and three windings.
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Two- the block simulates a two-winding transformer. -
Three- the block simulates a three-winding transformer.
Rated apparent power, V*A - rated apparent power
`100e6 V*A (by default).
`100e6 V*A (by default)
Rated power passing through the transformer. The value must be greater than 0.
Rated electrical frequency - rated electrical frequency
50 Hz (By default).
The nominal or nominal frequency of the AC mains to which the transformer is connected. The value must be greater than 0.
Primary winding connection type - primary winding configuration
Wye with floating neutral (by 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 (By default) | positive scalar
RMS line voltage applied to the primary winding under normal operating conditions. The value must be greater than 0.
Secondary winding connection type - configuration of the first secondary winding
Wye with floating neutral (by default) | Wye with neutral port | Wye with grounded neutral | Delta 1 o’clock | Delta 11 o’clock.
Type of first secondary winding.
Secondary rated voltage, V - RMS mains voltage applied to the first secondary winding
4160 (By default) | `positive scalar'.
RMS line voltage applied to the first secondary winding under normal operating conditions. The value must be greater than 0.
Tertiary winding connection type - Secondary winding configuration
Wye with floating neutral (by default) | Wye with neutral port | Wye with grounded neutral | Delta 1 o’clock | Delta 11 o’clock.
Type of second secondary winding.
Tertiary rated voltage, V - RMS mains voltage applied to the second secondary winding
4160 (By default) | `positive scalar'.
RMS line voltage applied to the second secondary winding under normal operating conditions. The value must be greater than 0.
Core type - Core type
Three-phase three-limb (by default) | `Three-phase five-limb'.
Core type.
Impedances
Primary winding resistance, pu - primary winding resistance, o.u.
0.01 (by default) | `positive scalar `
Primary winding resistance, p.u. The value must be greater than 0.
First secondary winding resistance, pu - First secondary winding resistance, p.u.
0.01 (by default) | `positive scalar'.
Resistance of the first secondary winding. The value must be greater than 0.
Second secondary winding resistance, pu - resistance of the second secondary winding, o.e.
0.01 (by default) | `positive scalar'.
Resistance of the second secondary winding. The value must be greater than 0.
Leakage reactance - account for magnetic flux losses.
Exclude (by default) | Include.
Enable modelling of magnetic flux losses.
Primary leakage reactance, pu - magnetic resistance of primary winding, o.u.
0.001 (by default) | positive scalar.
Magnetic flux loss in the primary winding, o.u. The value must be greater than 0.
Dependencies
To use this parameter, set the Leakage reactance parameters to Include.
First secondary leakage reactance, pu - magnetic resistance of the first secondary winding, o.u.
0.001 (by default) | `positive scalar'.
Magnetic flux loss in the first secondary winding, o.u. The value must be greater than 0.
Dependencies
To use this parameter, set the Leakage reactance parameters to Include.
Second secondary leakage reactance, pu - magnetic resistance of the second secondary winding, o.u.
0.001 (by default) | `positive scalar'.
Magnetic flux loss in the second secondary winding, o.u. The value must be greater than 0.
Dependencies
To use this parameter, set the Leakage reactance parameters to Include.
Magnetising resistance - Magnetizing resistance consideration
Exclude (by default) | Include.
Enables the modelling of the magnetizing resistance in the transformer core.
Shunt magnetising resistance, pu - active resistance of the magnetising branch, o.u.
500 (by default) | positive scalar.
Active resistance of the magnetising branch, o.u. The value must be greater than 0.
Dependencies
To use this parameter, set the Magnetising resistance parameters to Include.
Magnetising reactance - Magnetizing reactance accounting
Exclude (by default) | Include.
Enable modelling of magnetic effects of the transformer core.
Magnetic saturation representation - Magnetic saturation representation
None (by default) | Lookup table (phi versus i)
Select whether and how to represent magnetic saturation.
Dependencies
To use this parameter, set the Magnetising reactance parameter to `Include'.
Current vector (pu), i is the vector of current values, o.e.
[0, .002, 1, 2] (by default).
Vector of current values, o.u. The first value must be 0, the rest are strictly ascending.
Dependencies
To use this parameter, set the Magnetising reactance parameter to Include' and the Magnetic saturation representation parameter to `Lookup table (phi versus i).
Magnetic flux vector (pu), phi is a vector of flux values, o.e.
[0, 1.2, 1.5, 1.51] (by default).
Vector of magnetic flux values, o.u. The first value must be 0, the rest are strictly ascending.
Dependencies
To use this parameter, set the Magnetising reactance parameter to Include' and the Magnetic saturation representation parameter to `Lookup table (phi versus i).
Shunt magnetising reactance, pu - magnetizing branch reactance, o.u.
500 (by default) | positive scalar.
Magnetising branch reactance at linear area operation, o.u. The value must be greater than 0.
Dependencies
To use this parameter, set the Magnetising reactance parameter to Include and the Magnetic saturation representation parameter to Lookup table (phi versus i).
Zero sequence reactance, pu - zero sequence reactance
0.5 (by default) | `positive scalar'.
Zero sequence reactance in o.u. The value must be greater than or equal to the magnetic flux losses of the primary winding.
Dependencies
To use this parameter, set the Core type parameters to `Three-phase three-limb'.