Transmission Line (Three-Phase)
Three-phase power line section with concentrated parameters.
Description
The Transmission Line (Three-Phase) block represents a three-phase transmission line using a U-shaped substitution diagram with concentrated parameters. This model takes into account phase resistance, phase inductance, phase inductance, phase mutual inductance, phase mutual resistance, line capacitance and line earth capacitance.
To simplify the equations defining the block, the Clarke transform is used. As a result, the equations take the form:
Where:
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- is the resistance of the line section.
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- is the mutual resistance of the phases.
-
- eigeninductance of the line section.
-
- value of the Mutual inductance parameter.
-
- ground capacitance.
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- Line capacitance of the line section.
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- Clark transformation matrix.
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- three-phase current through the ~1 port.
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- three-phase current through port ~2.
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- three-phase voltage at port ~1.
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- three-phase voltage at port ~2.
The direct and zero sequence parameters are determined by the diagonal terms in the transformed equations:
Rearranging these equations gives the physical linear quantities in terms of the forward and zero-sequence parameters:
The figure shows the equivalent circuit diagram of one section of line, constructed from a U-shaped substitution diagram using the Clark transform.
To improve accuracy, you can use the Number of segments parameter to repeat the U-shaped section N times, resulting in a transmission line model with N segments. A larger number of segments significantly slows down the modelling process.
Dissemination rates
The Transmission Line (Three-Phase) block calculates the propagation velocities of a direct sequence using these equations:
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- Sequential impedance in `Ω/Km'.
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- bandwidth in
Ω/Km. -
- propagation constant.
-
- propagation rate in
Km/s, where .
For zero sequence propagation velocity, the equations are the same but , , , , , and are equal to , , , , , and .
Ports
~1 - three-phase port
electricity
Three-phase electrical port.
~2 is a three-phase port
electricity
Three-phase electrical port.
g1 - earthing connection at the ~1 end.
electricity
Electrical port, corresponds to the ground connection on the ~1 side.
g2 is the ground connection on the ~2 end.
electricity
Electrical port, corresponds to the ground connection on the ~2 side.
Parameters
Line length, km - transmission line length
1.0 km (by default)
Transmission line length.
Frequency used for rlcg specification - frequency for which RLC parameters are specified
50.0 Hz (By default).
The frequency for which , , , , where:
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- is the resistance of the line per unit length.
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- inductance of the line per unit length.
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- line capacitance per unit length.
-
- conductivity of the line per unit length.
Resistance - specific resistance of the line
`0.02 Ohm/km (by default).
Transmission line resistance per phase per unit length.
Inductance - specific inductance of the transmission line
0.5e-3 Gn/km (by default).
The eigeninductance of the transmission line phase per unit length.
Mutual inductance - specific mutual inductance
0.1e-3 Gn/km (by default).
Mutual inductance of phases per unit length. Set this value to 0 to eliminate mutual inductance.
Line-line capacitance - specific capacitance
0.3e-6 F/km (by default).
Line capacitance per unit length.
Line-ground capacitance - specific ground (leakage) capacitance
`0.1e-6 F/km (by default).
Ground capacitance per unit length.
Mutual resistance - specific mutual resistance of phases
`0.0 (by default).
Mutual resistance of phases per unit length. The value by default is 0.0 (no mutual resistance between phases).
Number of segments - number of segments
1 (By default).
Number of U-shaped segments in the model.