Implement three-phase transmission line section with lumped parameters
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The Three-Phase PI Section Line block implements a balanced three-phase transmission line model with parameters lumped in a PI section.
Contrary to the Distributed Parameters Line model where the resistance, inductance, and capacitance are uniformly distributed along the line, the Three-Phase PI Section Line block lumps the line parameters in a single PI section as shown in the figure below.
The line parameters R, L, and C are specified as positive- and zero-sequence parameters that take into account the inductive and capacitive couplings between the three phase conductors, as well as the ground parameters. This method of specifying line parameters assumes that the three phases are balanced.
The self and mutual resistances (Rs, Rm), self and mutual inductances (Ls, Lm) of the three coupled inductors, as well as phase capacitances Cp and ground capacitances Cg, are deduced from the positive- and zero-sequence RLC parameters as follows.
Let us assume the following line parameters:
|r1, r0||Positive- and zero-sequence resistances per unit length (Ω/km)|
|l1, l0||Positive- and zero-sequence inductances per unit length (H/km)|
|c1, c0||Positive- and zero-sequence capacitances per unit length (F/km)|
|lsec||Line section length (km)|
The total positive- and zero-sequence RLC parameters including hyperbolic corrections are first evaluated:
kr1, kl1, kc1, kr0, kl0, kc0 — positive-sequence and zero-sequence hyperbolic correction factors
See the PI Section Line block reference page for an explanation on how to compute RLC parameters taking into account hyperbolic corrections.
The Powergui block provides a graphical tool for the calculation of
resistance, inductance, and capacitance per unit length based on the line geometry and the
conductor characteristics. See the
power_lineparam reference page to learn how to
use this tool.
For a short line section (approximately lsec < 50 km), these correction factors are negligible (close to unity). However, for long lines, these hyperbolic corrections must be taken into account in order to get an exact line model at the specified frequency.
The RLC line section parameters are then computed as follows:
The frequency used for specification of per unit length rlc line parameters, in hertz
(Hz). This is usually the nominal system frequency (50 Hz or 60 Hz). Default is
The positive- and zero-sequence resistances in ohms/kilometer (Ω/km). Default is
[ 0.01273 0.3864].
The positive- and zero-sequence inductances in henries/kilometer (H/km). The
zero-sequence inductance cannot be zero, because it would result in an invalid propagation
speed computation. Default is
[ 0.9337e-3 4.1264e-3].
The positive- and zero-sequence capacitances in farads/kilometer (F/km). The
zero-sequence capacitance cannot be zero, because it would result in an invalid propagation
speed computation. Default is
The line section length in kilometers (km). Default is
power_triphaseline example illustrates voltage transients at the
receiving end of a 200-km line when only phase A is energized. Voltages obtained with two line
models are compared: 1) the Distributed Parameters Line block and 2) a PI line model using two
Three-Phase PI Section Line blocks.