The ground plane represents the earth ground return path for your transmission line or cable system. The ground plane may be approximated with a constant resistivity (default setting), or the user may choose to represent the ground with a frequency-dependent conductivity using Portela's method.
In addition to allowing the adjustment of ground resistivity and permeability, this component also gives the user control over how the complex ground impedance integral (i.e. Carson's Integral) is numerically approximated. Two options are given as described below:
Analytical Approximation: The Transmission Line and Cable Constants program solves the ground impedance integral by analytical approximation. For overhead transmission lines, this is the Deri-Semlyen approximation of Carson's Integral method as described in PSCAD general reference [20]. For underground cable systems, this can either be set as the Saad approximation (EMTDC Chapter 8 reference [29]) or the Wedepohl approximation method of Pollaczek's Integral. For aerial cable systems, the mutual quantities between underground and overhead can either be set as the Ametani or LUCCA approximation (Mutual Impedance with Earth Return).
Numerical Integration: The Transmission Line and Cable Constants program solves the ground impedance integral (either Carson or Pollaczek) through direct numerical integration. Although very accurate, this solution method may add a huge amount of time, as compared with the equivalent Analytical Approximation. This becomes very apparent when solving lines with more than three conductors.
NOTE: It is recommended that Analytical Approximation be selected for most practical situations, due to the huge time savings. The approximation methods are normally accurate to within 5% of the exact solution, however if the user is in doubt, simply run the simulation with each method and compare results.
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More: |
Constructing Transmission Line Systems Constructing Underground Cable Systems |
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Earth Return Representation |
Choice |
Aerial:
The Deri-Semlyen approximation formula is the fastest options in terms of solve speed. Numerical integration is the most accurate, but is very slow by comparison.
Underground (Cables Only):
The approximation formulae are the fastest options in terms of solve speed. Of these options, the Saad approximation (cables only) is the most stable, but requires that the ground permeability be unity. Numerical integration is the most accurate, but is very slow by comparison. NOTE: The Saad formula is derived based on the assumption X / L < 1, where X is the direct horizontal distance between two cables and L is the sum of their depth. This assumption is valid for many practical applications and also this formula gives acceptable accuracy for the case X / L > 1. Between Underground and Aerial (Cables Only):
The LUCCA approximation formula is said to be a widely used and accurate formula and it is as such the default. |
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Resistance is Entered in the Form Of |
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Choice |
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Select either constant resistivity or frequency-dependent conductivity. |
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Resistivity |
REAL |
Literal |
Enter the ground resistivity [Wm] |
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Earth Return Representation is By |
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Choice |
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The approximation formulae are the fastest options in terms of solve speed. Of these two options, the Saad approximation (cables only) is the most stable, but requires that the ground permeability be unity. Numerical integration is the most accurate, but is very slow by comparison.
NOTE: The Saad formula is derived based on the assumption X / L < 1, where X is the direct horizontal distance between two cables and L is the sum of their depth. This assumption is valid for many practical applications and also this formula gives acceptable accuracy for the case X / L > 1. |
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Relative Permeability |
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REAL |
Literal |
Enter the relative ground permeability. |
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Low-frequency conductivity (K0) |
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REAL |
Literal |
[S/m]. This parameter is enabled only if Resistance is Entered in the Form Of | frequency-dependent conductivity is selected. |
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Frequency-dependent parcel of conductivity and permittivity (K1) |
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REAL |
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[S/m]. This parameter is enabled only if Resistance is Entered in the Form Of | frequency-dependent conductivity is selected. |
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Frequency-dependent factor (alpha) |
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REAL |
Literal |
This parameter is enabled only if Resistance is Entered in the Form Of | frequency-dependent conductivity is selected. |