SimPowerSystems

PI Section Line

Implement a single phase transmission line with lumped parameters

Library

Elements

Description

The PI Section Line block implements a single-phase transmission line with parameters lumped in PI sections.

For a transmission line, the resistance, inductance, and capacitance are uniformly distributed along the line. An approximate model of the distributed parameter line is obtained by cascading several identical PI sections, as shown in the following figure.

Unlike the Distributed Parameter Line block, which has an infinite number of states, the PI section linear model has a finite number of states that permit you to compute a linear state-space model. The number of sections to be used depends on the frequency range to be represented.

A good approximation of the maximum frequency range represented by the PI line model is given by the following equation:

where

• N: Number of PI sections
• v: Propagation speed in km/s = L in H/km, C in F/km
• l: Line length in km

For example, for a 100 km aerial line having a propagation speed of 300 000 km/s, the maximum frequency range represented with a single PI section is approximately 375 Hz. For studying interactions between a power system and a control system, this simple model could be sufficient. However for switching surge studies involving high-frequency transients in the kHz range, much shorter PI sections should be used. In fact, accurate results would probably only be obtained by using a distributed parameters line model.

Dialog Box and Parameters

Frequency used for RLC specifications

Frequency used to compute the line parameters, in hertz (Hz).

Resistance per unit length

The resistance per unit length of the line, in ohms/km ().

Inductance per unit length

The inductance per unit length of the line, in henries/km (H/km).

Capacitance per unit length

The capacitance per unit length of the line, in farads/km (F/km).

Length

The line length in km.

Number of pi sections

The number of PI sections. The minimum value is 1.

Measurements

Select Input and output voltages to measure the sending end (input port) and receiving end (output port) voltages of the line model.

Select Input and output voltages to measure the sending end and receiving end currents of the line model.

Select All voltages and currents to measure the sending end and receiving end voltages and currents of the line model.

Place a Multimeter block in your model to display the selected measurements during the simulation. In the Available Measurements list box of the Multimeter block, the measurement is identified by a label followed by the block name.

Measurement	Label
Sending end voltage (block input)	Us:
Receiving end voltage (block output)	Ur:
Sending end current (input current)	Is:
Receiving end current (output current)	Ir:

Example

The psbpiline.mdl demo shows the line energization voltages and currents of a PI section line.

The results obtained with the line modeled by one PI section of 100 km and 10 PI sections of 10 km are shown.

See Also
Distributed Parameter Line

Permanent Magnet Synchronous Machine

Powergui