U14EET402- UNIT 2-11. POWER FLOW IN TRANSMISSION LINES

Consider the following model depicting the transfer of AC power between two buses across a line:

Figure 1. Simple AC power transmission model

Where  is the voltage and phase angle at the sending end

 is the voltage and phase angle at the receiving end

 is the complex impedance of the line.

 is the current phasor

The complex AC power transmitted to the receiving end bus can be calculated as follows:

At this stage, the impedance is purposely undefined and in the following sections, two different line impedance models will be introduced to illustrate the following fundamental features of AC power transmission:

• The power-angle relationship
• PV curves and steady-state voltage stability

Power-Angle Relationship

In its simplest form, we neglect the line resistance and capacitance and represent the line as purely inductive, i.e. . The power transfer across the line is therefore:

Where  is called the power angle, which is the phase difference between the voltages on bus 1 and bus 2.

We can see that active and reactive power transfer can be characterised as follows:

Plotting the active power transfer for various values of , we get:

Figure 2. Active power transfer characteristic for a lossless line

The figure above is often used to articulate the Power-Angle Relationship. We can see that in this simple model, power will only flow when there is a phase difference between the voltages at the sending and receiving ends. Moreover, there is a theoretical limit to how much power can be transmitted through a line (shown here when the phase difference is 90^o). This limit will be a recurring theme in these line models, i.e. lines have natural capacity limits on how much power they can transmit.