Pi-Section Line

Purpose

Single-phase pi-section transmission line

Library

Electrical / Passive Components

Description

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

A transmission line is characterized by a uniform distribution of inductance, resistance, capacitance and conductance along the line. However, in many cases these distributed parameters can be approximated by cascading multiple pi sections with discrete components. Fig. 191 illustrates the electrical circuit used for the line model.

Fig. 191 Pi-section transmission line circuit diagram

Let \(l\) be the length of the line and \(n\) the number of pi sections representing the line. The inductance \(L\), the resistance \(R\), the capacitance \(C\) and the conductance \(G\) of the discrete elements can then be calculated from their per-unit-length counterparts \(L'\), \(R'\), \(C'\) and \(G'\) using the following equations:

\[L = \frac{l}{n} L', \qquad R = \frac{l}{n} R', \qquad C = \frac{l}{n} C', \qquad G = \frac{l}{n} G'\]

Parameters

Inductance per unit length

The series line inductance \(L'\) per unit length. If the length \(l\) is specified in meters \((\mathrm{m})\), the unit of \(L'\) is henries per meter \((\mathrm{H}/\mathrm{m})\).

Resistance per unit length

The series line resistance \(R'\) per unit length. If the length \(l\) is specified in meters \((\mathrm{m})\), the unit of \(R'\) is ohms per meter \((\Omega/\mathrm{m})\).

Capacitance per unit length

The capacitance \(C'\) between the line conductors per unit length. If the length \(l\) is specified in meters \((\mathrm{m})\), the unit of \(C'\) is farads per meter \((\mathrm{F}/\mathrm{m})\).

Conductance per unit length

The conductance \(G'\) between the line conductors per unit length. If the length \(l\) is specified in meters \((\mathrm{m})\), the unit of \(G'\) is siemens per meter \((\mathrm{S}/\mathrm{m})\).

Length

The length \(l\) of the line. The unit of \(l\) must match the units \(L'\), \(R'\), \(C'\) and \(G'\) are based on.

Number of pi sections

Number of sections used to model the transmission line. The default is 3.

Initial voltage

A scalar value specifying the initial voltage of all capacitors at simulation start, in volts \((\mathrm{V})\).