Maximum Power Flow and Line Loadability

The maximum power flow for lossy lines is derived using ABCD parameters in phasor form.

The matrix relationship between the sending-end and receiving-end voltage and current determines the receiving-end current, which calculates the complex power delivered to the receiving end.

From this, the real and reactive power delivered to the receiving end is derived.

Substituting values for a lossless line simplifies the real power equation.

The theoretical maximum real power or steady-state stability limit occurs when the phase angle equals the total series impedance angle.

However, higher series impedance than reactance reduces the maximum real power.

In practice, power lines do not deliver their theoretical maximum power based on rated terminal voltages and a 90-degree angular displacement.

The practical line loadability curve is plotted below the theoretical steady-state stability limit based on a voltage-drop limit of 0.95 or less and a maximum angular displacement of 30 to 35 degrees.

For short lines under 25 kilometers, loadability is limited by the thermal rating of conductor or terminal equipment ratings, not voltage drop or stability.