An Investigation into AC Transmission Line and Active Power Flow

This report delves into the intricacies of active power flow within AC transmission lines, examining the crucial relationship between voltage drop, phase shift, and power transfer efficiency. It elucidates how the current flowing through the transmission line directly impacts voltage drop and, consequently, the active power conveyed from the sending to the receiving end. The report highlights the significance of phase shift between voltage sine waves in facilitating power transfer, emphasizing that the active power is directly proportional to the sender end voltage and the sine of the phase shift angle. Furthermore, it explores the impact of line inductance, with shorter lines exhibiting higher power transfer capabilities. The report also touches upon FACTS devices and HVDC systems, providing a comprehensive understanding of power system control and enhancement techniques. The document is a valuable resource for students seeking to grasp the fundamental principles of AC transmission line operation and power flow management.

AC TRANSMISSION LINE AND ACTIVE POWER FLOW
The value of voltage drop is dependent on the ac transmission line current. For the transmission of the
useful power P from the sender end to the receiver end, then it is essential for load voltage available at the
receiver ER lags behind voltage from the source at the sender end ES. This scenario is explained by the
fact that current will only flow from the sending terminal to the receiving end when voltage sine waves at
both ends are not in phase. Zero current will flow into the system is the two voltages are in phase and
equal. The instantaneous value for one of the voltage must be greater than the other signal. The difference
in the instantaneous value is mainly determined by the phase shift angle that also depends on phase shift
between two sinusoidal waves in terms of their load value in the compensated system. As a result, the
above influence directly affects the amount of the ac transmission line currents. This current has
therefore, affects active power conveyed over the ac transmission line. The active power from the sender
to the receiver is found by the equation below.
P= E2
S
X L
Sinθ
Where
P is active power , ES is senders phase voltage , XL represents theinductive line reactance∧whose receiver /sender p
. Therefore, the active power at the receiving end is directly proportional to the square of the sender end
voltage and sin of phase shift angle θ . The graph showing the relationship between active receiving end
power and phase shift angle is as shown below.
From the graph, no active component of power is transferred once phase shift voltage is zero. However,
active power begins to be realized when angle of the phase shift increases. The maximum power is
transferred at 900phase shift angle between the receiver and the sender is equal to.
Pmax = E2
S
X L

Beyond 900, the active power transfer begins to diminish and becomes difficult to compensate using
shunt capacitance. For this reason voltage compensation in executed at phase shift well below 900. Also,
the maximum active power supplied to the receiver is achieved when line inductive inductance is small.
Shorter transmission lines are capable of transferring high power since line inductance is less in the small
distance transmission network. A graphical summary of the effects of phase shift having different
reactance is as shown below.