# Line Loadability – Universal Line Loadability Curve

Loadability of line is defined as the extent of load which can flow through the line without exceeding the limitations. Line Loadability is expressed in percentage of Surge Impedance Loading of line. The limiting factor for line loading are: thermal limit, voltage drop limit and steady state stability. The loading of line shall not exceed these limits in any case.

Thermal limit corresponds to heating of transmission line and interposes a limit on current which can flow. Though of overhead transmission line, thermal limit is quite high but this cannot be neglected while deciding loading.

Voltage drop limit corresponds to drop in receiving end voltage. In case the loading of line is very high compared to Surge Impedance Loading (SIL), there will be a huge drop in receiving end voltage. A voltage drop of 5% is normally permissible.

Steady State limit shall be considered for long line. As the power transfer equation is inversely proportional to reactance X, increase in line length increases the reactance and hence decreases the power transfer capability.

P = VrVsSinδ /X

A steady state stability margin of 30% is usually adopted. Steady State stability margin is defined as the percentage loading of line.

Steady State stability = (Pmax – Plim) / Pmax

Pmax = Maximum Power Transfer Capability (when load angle δ is 90°)

Plim = Actual Power Transfer taking place

30% steady state stability margin will result in,

0.3 = (Pmax – Plim) / Pmax

0.7Pmax = Plim

0.7 VrVs /X = VrVsSinδ /X  (since δ = 90°)

δ = 44°

This means that for permissible steady state stability margin of 30°, load angle should be kept at 44°.

### Universal Line Loadability Curve

Based on the three limitations, loadability of line is defined for different voltage and length of line. A plot of line loading with respect to length of line applicable for all voltage level was first derived by St. Clair. This plot is known as ST. Clair Curve or Universal Line Loadability Curve. In determining the line loadability curve, it is assumed that a voltage drop of 5% and steady state stability margin of 30% are permissible. Figure below shows the Universal Line Loadability Curve.

As can be seen from the above loading curve, the limit to line loading are limited by the following factors:

1) Thermal limit for Short Line (Length up to 80)

2) Voltage drop limitation for medium line (length up to 320 km)

3) Steady State Stability Limitation for Long Lines (line length more than 320 km)

Once can easily suggest the maximum loading capability of transmission line for different line length using the above power transfer capability curve or Universal Line Loadability Curve. For example, if line length is 300 km, then line loadability will be around 1.5 times of Surge Impedance Laoding.