Transmission Line (Three-Phase)

A section of a three-phase power transmission line with concentrated parameters.

blockType: AcausalElectricPowerSystems.Passive.Lines.ThreePhaseTransmission

Path in the library:

/Physical Modeling/Electrical/Passive/Lines/Transmission Line (Three-Phase)

Description

Block Transmission Line (Three-Phase) It is a three-phase power transmission line according to a U-shaped substitution scheme with concentrated parameters. This model takes into account phase resistance, intrinsic phase inductance, mutual phase inductance, mutual phase resistance, line capacitance, and line ground capacitance.

To simplify the equations defining the block, the Clark transform is used. As a result, the equations take the form:

where

— resistance of the line section;
— mutual phase resistance;
— the intrinsic inductance of the line section;
— parameter value Mutual inductance;
— grounding capacity;
— linear capacity of the line section;
— the Clark transformation matrix;
— Three-phase current through the port ~1;
— Three-phase current through port ~2;
— three-phase voltage at the port ~1;
— three-phase voltage on the port ~2.

The parameters of the forward and zero sequences are determined by the diagonal terms in the transformed equations:

The permutation of these equations yields physical linear quantities in terms of the parameters of the forward and zero sequence.:

The figure shows an equivalent electrical circuit of one section of the line, constructed according to a U-shaped substitution scheme using the Clark transform.

transmission line three phase 1 s

To increase the accuracy, you can use the parameter Number of segments to repeat the U-shaped section N times, resulting in a transmission line model of N segments. A larger number of segments significantly slows down the modeling process.

Propagation speeds

Block Transmission Line (Three-Phase) calculates the propagation velocities of a direct sequence using the following equations:

— serial impedance;
— bandwidth;
— the distribution constant.
— the speed of propagation, where .

For the propagation velocity of the zero sequence, the equations are the same, but , , , , , and equal , , , , , and accordingly.

Ports

Conserving

# ~1 — three-phase port
electricity

Details

Three-phase electrical port.

Program usage name

port1

# ~2 — three-phase port
electricity

Details

Three-phase electrical port.

Program usage name

port2

# g1 — ground connection at the end ~1
electricity

Details

Electrical port, corresponds to the ground connection on the ~1 side.

Program usage name

ground_pin1

# g2 — ground connection at the end ~2
electricity

Details

Electrical port, corresponds to the ground connection on the ~2 side.

Program usage name

ground_pin2

Parameters

Main

# Parameterization — the method of setting line parameters
Balanced impedance | Sequence impedance | Sequence impedance (R, X, B)

Details

The line parameters are set in the following way:

Balanced impedance — set the same series active resistance, series inductance and transverse capacitance for all phases;
Sequence impedance — set the active resistance, inductance and transverse capacitance ( , , ) for the forward and zero sequences;
Sequence impedance (R, X, B) — set the active resistance, inductive resistance and capacitive conductivity ( , , ) for the forward and zero sequences.

The connection parameters between the lines are set in values , , zero sequence, if the option is selected Sequence impedance (R, X, B), and in magnitudes , , zero sequence otherwise.

Values	`Balanced impedance` \| `Sequence impedance` \| `Sequence impedance (R, X, B)`
Default value	`Balanced impedance`
Program usage name	`parameterization`
Evaluatable	No

# Line length — length of the power transmission line
m | um | mm | cm | km | in | ft | yd | mi | nmi

Details

The length of the power transmission line.

Units	`m` \| `um` \| `mm` \| `cm` \| `km` \| `in` \| `ft` \| `yd` \| `mi` \| `nmi`
Default value	`1.0 km`
Program usage name	`line_length`
Evaluatable	Yes

# Frequency used for rlcg specification — the frequency for which the RLC or RXB parameters are set
Hz | kHz | MHz | GHz

Details

At a given frequency, the transmission line parameters are adjusted to more accurately represent the resistances of the forward and zero sequences.

Units	`Hz` \| `kHz` \| `MHz` \| `GHz`
Default value	`50.0 Hz`
Program usage name	`f`
Evaluatable	Yes

Details

The resistance of the transmission line per phase per unit length.

Dependencies