Earthing Transformer

Three-phase earthing transformer in zigzag configuration

Libraries:
Simscape / Electrical / Passive / Transformers

Description

The Earthing Transformer block models a three-phase zigzag-connection earthing or grounding transformer. The block allows you to provide an artificial neutral in an ungrounded three-phase power system. The artificial neutral creates a low-impedance path for the zero-sequence current and high-impedance path for the positive-sequence current. To accommodate a phase-to-neutral load, the return path allows a delta-connected supply.

For more information on using a three-phase zigzag-connection earthing or grounding transformer, see Engineering Applications

Equations

This block is implemented in both electrical and magnetic domains, representing the physics of phase windings and magnetic core. The equivalent circuit for the block includes windings, reluctances, and eddy currents.

For a zigzag configuration in magnetic circuit, the a-. b-, and c-phases represent each leg of the magnetic core.

You can obtain the relationship between the electrical and the magnetic properties by applying several mathematical steps based on the magnetic flux conservation rule and on the Hopkinson's law.

For earthing transformers, the couplings between the phases and all the windings are identical. In the equations below:

n is the number of turns of the winding.
R is the magnetizing reluctance between phases.
R_L is the leakage reluctance.
L_eddy is the magnetic inductance due to eddy current losses between phases.

Then the relationship between the inductance matrix in electrical domain and the reluctance matrix in the magnetic domain can be written as:

$L = [\begin{matrix} L_{11} & L_{12} & L_{13} \\ L_{21} & L_{22} & L_{23} \\ L_{31} & L_{32} & L_{33} \end{matrix}] = [\begin{matrix} n^{2} (\frac{2}{R l} + \frac{6}{R}) & - 3 \frac{n^{2}}{R} & - 3 \frac{n^{2}}{R} \\ - 3 \frac{n^{2}}{R} & n^{2} (\frac{2}{R l} + \frac{6}{R}) & - 3 \frac{n^{2}}{R} \\ - 3 \frac{n^{2}}{R} & - 3 \frac{n^{2}}{R} & n^{2} (\frac{2}{R l} + \frac{6}{R}) \end{matrix}]$

The diagonal elements represent the sum of a leakage and magnetizing inductance for each phase, such that:

$L_{l} = \frac{2 n^{2}}{R l}$

Therefore:

$R_{L} = \frac{2 n^{2}}{L_{l}}$

$R = \frac{9 n^{2}}{L_{m}}$

$L_{e d d y} = \frac{9 n^{2}}{R_{m}}$

Ports

Conserving

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~ — Three-phase voltage
electrical

Expandable three-phase electrical conserving port associated with three-phase voltage.

n — Neutral
electrical

Electrical three-phase electrical conserving port associated with the neutral point.

Parameters

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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.

Rated apparent power — Rated apparent power
`100e6` `V*A` (default) | positive scalar

Rated apparent power in SI units. The value must be greater than 0.

Rated voltage — Rated voltage
`24e3` `V` (default) | positive scalar

Rated voltage in SI units. The value must be greater than 0.

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

Rated electrical frequency in SI units. The value must be greater than 0.

Units — Parameterization unit system
`Per unit` (default) | `SI`

System of units for impedance parameterization.

Dependencies

The visibility of other parameters depends on the value of this parameter.

Zero-sequence resistance (pu) — Zero-sequence resistance
`0.01` (default) | positive scalar

Per-unit zero-sequence resistance. The value must be greater than 0.

Dependencies

This parameter is only visible when the Units parameter is set to Per unit.

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

Per-unit zero-sequence reactance. The value must be greater than 0.

Dependencies

This parameter is only visible when the Units parameter is set to Per unit.

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

Per-unit shunt magnetizing resistance. The value must be greater than 0.

Dependencies

This parameter is only visible when the Units parameter is set to Per unit.

Shunt magnetizing reactance (pu) — Shunt magnetizing reactance
`500` (default) | positive scalar

Per-unit shunt magnetizing reactance. The value must be greater than 0.

Dependencies

This parameter is only visible when the Units parameter is set to Per unit.

Zero-sequence resistance — Zero-sequence resistance
`0.0576` `Ohm` (default) | positive scalar

Zero-sequence resistance in SI units. The value must be greater than 0.

Dependencies

This parameter is only visible when the Units parameter is set to SI.

Zero-sequence inductance — Zero-sequence inductance
`1.728` `H` (default) | positive scalar

Zero-sequence inductance in SI units. The value must be greater than 0.

Dependencies

This parameter is only visible when the Units parameter is set to SI.

Shunt magnetizing resistance — Shunt magnetizing resistance
`2880` `Ohm` (default) | positive scalar

Shunt magnetizing resistance in SI units. The value must be greater than 0.

Dependencies

This parameter is only visible when the Units parameter is set to SI.

Shunt magnetizing inductance — Shunt magnetizing inductance
`2880` `H` (default) | positive scalar

Shunt magnetizing inductance in SI units. The value must be greater than 0.

Dependencies

This parameter is only visible when the Units parameter is set to SI.

More About

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Engineering Applications

To facilitate grounding and detection of an earth fault, earthing transformers provide a ground path to either an ungrounded "Y" or a delta-connected system. They are typically used to:

Provide a relatively low impedance path to ground, thereby maintaining the system neutral at or near ground potential.
Limit the magnitude of transient overvoltages when re-striking ground faults occur.
Provide a source of ground fault current during line-to-ground faults.
Permit the connection of phase-to-neutral loads when desired.

Extended Capabilities

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

Version History

Introduced in R2019a

Earthing Transformer

Description

Equations

Ports

Conserving

~ — Three-phase voltage electrical

n — Neutral electrical

Parameters

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

Rated apparent power — Rated apparent power 100e6 V*A (default) | positive scalar

Rated voltage — Rated voltage 24e3 V (default) | positive scalar

Rated electrical frequency — Rated electrical frequency 60 Hz (default) | positive scalar

Units — Parameterization unit system Per unit (default) | SI

Dependencies

Zero-sequence resistance (pu) — Zero-sequence resistance 0.01 (default) | positive scalar

Dependencies

Zero-sequence reactance (pu) — Zero-sequence reactance 0.3 (default) | positive scalar

Dependencies

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

Dependencies

Shunt magnetizing reactance (pu) — Shunt magnetizing reactance 500 (default) | positive scalar

Dependencies

Zero-sequence resistance — Zero-sequence resistance 0.0576 Ohm (default) | positive scalar

Dependencies

Zero-sequence inductance — Zero-sequence inductance 1.728 H (default) | positive scalar

Dependencies

Shunt magnetizing resistance — Shunt magnetizing resistance 2880 Ohm (default) | positive scalar

Dependencies

Shunt magnetizing inductance — Shunt magnetizing inductance 2880 H (default) | positive scalar

Dependencies

More About

Engineering Applications

Extended Capabilities

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

Version History

See Also

~ — Three-phase voltage
electrical

n — Neutral
electrical

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

Rated apparent power — Rated apparent power
`100e6` `V*A` (default) | positive scalar

Rated voltage — Rated voltage
`24e3` `V` (default) | positive scalar

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

Units — Parameterization unit system
`Per unit` (default) | `SI`

Zero-sequence resistance (pu) — Zero-sequence resistance
`0.01` (default) | positive scalar

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

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

Shunt magnetizing reactance (pu) — Shunt magnetizing reactance
`500` (default) | positive scalar

Zero-sequence resistance — Zero-sequence resistance
`0.0576` `Ohm` (default) | positive scalar

Zero-sequence inductance — Zero-sequence inductance
`1.728` `H` (default) | positive scalar

Shunt magnetizing resistance — Shunt magnetizing resistance
`2880` `Ohm` (default) | positive scalar

Shunt magnetizing inductance — Shunt magnetizing inductance
`2880` `H` (default) | positive scalar

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