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Transmission Line (Three-Phase)

Three-phase transmission line using lumped-parameter pi-section line model

  • Transmission Line (Three-Phase) block

Libraries:
Simscape / Electrical / Passive / Lines

Description

The Transmission Line (Three-Phase) block models a three-phase transmission line using the lumped-parameter pi-line model. This model takes into account phase resistance, phase self-inductance, line-line mutual inductance and resistance, line-line capacitance, and line-ground capacitance.

To simplify the block-defining equations, Clarke’s transformation is used. The resulting equations are:

V1V2=[R+2RmRRmRRm]I1+[L+2MLMLM]dI1dt

I1+I2=[CgCg+3ClCg+3Cl]dV2dt

I1=TI1

I2=TI2

V1=TV1

V2=TV2

T=13[1201123211232]

where:

  • R is the line resistance for the segment.

  • Rm is the mutual resistance for the segment.

  • L is the line inductance for the segment.

  • M is the value of the Mutual inductance parameter.

  • Cg is the line-ground capacitance for the segment.

  • Cl is the line-line capacitance for the segment.

  • T is the Clarke’s transformation matrix.

  • I1 is the three-phase current flowing into the ~1 port.

  • I2 is the three-phase current flowing into the ~2 port.

  • V1 is the three-phase voltage at the ~1 port.

  • V2 is the three-phase voltage at the ~2 port.

The positive and zero-sequence parameters are defined by the diagonal terms in the transformed equations:

R0=R+2Rm

R1=RRm

L0=L+2M

L1=LM

C0=Cg

C1=Cg+3Cl

Rearranging these equations gives the physical line quantities in terms of positive and zero-sequence parameters:

R=2R1+R03

Rm=R0R13

L=2L1+L03

M=L0L13

Cl=C1C03

Cg=C0

The figure shows the equivalent electrical circuit for a single-segment pi-line model using Clarke’s transformation.

To increase fidelity, you can use the Number of segments parameter to repeat the pi-section N times, resulting in an N-segment transmission line model. More segments significantly slows down your simulation.

To improve numerical performance, you can add parasitic resistance and conductance components. Choosing large values for these components improves simulation speed but decreases simulation accuracy.

Propagation Speeds

The Transmission Line (Three-Phase) calculates the positive-sequence propagation speeds by using these equations:

  • Z1=R1+jωL1 is the series impedance, in Ω/Km.

  • Y1=jωC1 is the shunt admittance, in s/Km.

  • γ1=Z1Y1 is the propagation constant.

  • ν1=ωImag(γ1) is the propagation speed, in Km/s, where ω=2πf.

For zero-sequence propagation speed, the equations are the same but R1, L1, C1, Z1, Y1, γ1, and ν1 are R0, L0, C0, Z0, Y0, γ0, and ν0.

Faults

To model a fault in the Transmission Line (Three-Phase) block, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. In the Add Fault window, specify the fault properties. For more information about fault modeling, see Fault Behavior Modeling and Fault Triggering.

The Transmission Line (Three-Phase) block allows you to model these types of faults at specific position along the transmission line:

  • Single-phase-to-ground fault (a-g, b-g, or c-g)

  • Two-phase fault (a-b, b-c, or c-a)

  • Two-phase-to-ground fault (a-b-g, b-c-g, or c-a-g)

  • Three-phase fault (a-b-c)

  • Three-phase-to-ground fault (a-b-c-g)

Examples

Ports

Conserving

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Expandable three-phase port.

Expandable three-phase port.

Electrical conserving port corresponding to ground connection at ~1 end of the transmission line.

Electrical conserving port corresponding to ground connection at ~2 end of the transmission line.

Electrical conserving port corresponding to ground connection at fault position 1.

Dependencies

To enable this port, set Accessible ground connections at section interface to Yes

Electrical conserving port corresponding to ground connection at fault position 2.

Dependencies

To enable this port, set Accessible ground connections at section interface to Yes

Parameters

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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

Length of the transmission line.

Frequency used for the R, L, C, G specification, where:

  • R is line resistance per unit length.

  • L is the line inductance per unit length.

  • C is the line capacitance per unit length.

  • G is the line conductance per unit length.

Resistance of the transmission line per phase per-unit length.

Self-inductance of the transmission line per phase per-unit length.

Line-line mutual inductance per-unit length. Set this to 0 to remove mutual inductance.

Line-line capacitance length, in per-unit.

Line-ground capacitance length, in per-unit.

Line-line mutual resistance per unit length. The default value is 0Ohm/km (no line-line mutual resistance).

Option to model the transmission line as two sections. You must enable this parameter to add a non-intrusive fault in the Transmission Line (Three-Phase) block.

Number of segments in the pi-line model.

Dependencies

To enable this parameter, set Model two line sections to No.

Position of the interface in the pi-line model. If you add a non-intrusive fault, this parameter represents the position of the fault in the pi-line model.

Dependencies

To enable this parameter, set Model two line sections to Yes.

Number of segments in the first section of the pi-line model. If you add a non-intrusive fault, this parameter represents the number of segments before the fault occurs.

Dependencies

To enable this parameter, set Model two line sections to Yes.

Number of segments in the second section of the pi-line model. If you add a non-intrusive fault, this parameter represents the number of segments after the fault occurs.

Dependencies

To enable this parameter, set Model two line sections to Yes.

Option to access the ground connections at the fault position. If you set this parameter to No, the block internally connects the ground connections at the fault position to the electrical reference.

Dependencies

To enable this parameter set Model two line sections to Yes.

Parasitics

Resistance value, divided by the number of segments, that is added in series with every capacitor in the model.

Conductance value, divided by the number of segments, that is added in parallel with every series resistor and inductor in the model.

Faults

To modify the faults, create a fault and, in the block dialog box, click Open fault properties. To open the faults, in the Property Inspector, click the Fault behavior link.

Option to add a fault to the section interface of the pi-line model.

To add a fault, click the Add fault hyperlink.

Dependencies

To enable this parameter, set Model two line sections to Yes.

Type of fault to model. The visibility of related parameters depends on the fault model. Options are:

  • Single-phase to ground (a-g)

  • Single-phase to ground (b-g)

  • Single-phase to ground (c-g)

  • Two-phase (a-b)

  • Two-phase (b-c)

  • Two-phase (c-a)

  • Two-phase to ground (a-b-g)

  • Two-phase to ground (b-c-g)

  • Two-phase to ground (c-a-g)

  • Three-phase (a-b-c)

  • Three-phase to ground (a-b-c-g)

Dependencies

To enable this parameter, add a fault to the Transmission Line (Three-Phase) block by clicking the Add fault hyperlink next to the Section interface fault parameter.

Resistance between the phase connection and the neutral point when the fault is active.

Dependencies

To enable this parameter, add a fault to the Transmission Line (Three-Phase) block by clicking the Add fault hyperlink next to the Section interface fault parameter and set the Fault type parameter to:

  • Single-phase to ground (a-g)

  • Single-phase to ground (b-g)

  • Single-phase to ground (c-g)

  • Two-phase (a-b)

  • Two-phase (b-c)

  • Two-phase (c-a)

  • Two-phase to ground (a-b-g)

  • Two-phase to ground (b-c-g)

  • Two-phase to ground (c-a-g)

  • Three-phase (a-b-c)

  • Three-phase to ground (a-b-c-g)

Resistance between the neutral point and the electrical reference when fault is active.

Dependencies

To enable this parameter, add a fault to the Transmission Line (Three-Phase) block by clicking the Add fault hyperlink next to the Section interface fault parameter and set the Fault type parameter to:

  • Single-phase to ground (a-g)

  • Single-phase to ground (b-g)

  • Single-phase to ground (c-g)

  • Two-phase to ground (a-b-g)

  • Two-phase to ground (b-c-g)

  • Two-phase to ground (c-a-g)

  • Three-phase to ground (a-b-c-g)

Conductance between the phase connection and the neutral point when the fault is not active.

Dependencies

To enable this parameter, add a fault to the Transmission Line (Three-Phase) block by clicking the Add fault hyperlink next to the Section interface fault parameter and set the Fault type parameter to:

  • Single-phase to ground (a-g)

  • Single-phase to ground (b-g)

  • Single-phase to ground (c-g)

  • Two-phase (a-b)

  • Two-phase (b-c)

  • Two-phase (c-a)

  • Two-phase to ground (a-b-g)

  • Two-phase to ground (b-c-g)

  • Two-phase to ground (c-a-g)

  • Three-phase (a-b-c)

  • Three-phase to ground (a-b-c-g)

Extended Capabilities

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

Version History

Introduced in R2013b