The document describes an experiment to study the steady state power limit of a transmission line. It defines the equations for real and reactive power transfer between the sending and receiving ends of a lossless transmission line based on voltage and reactance. A power-angle diagram is drawn by plotting real power transferred versus the phase angle between voltages, showing that maximum power transfer occurs at a phase angle of 90 degrees. The results of the experiment show the steady state power limit is reached at 22W when the phase angle is 81.526 degrees, and that real power transfer varies linearly with changes in the sending end voltage.

1. Cycle II
Experiment 2
Steady State Power Limit of a Transmission Line
Objective:
i) To draw the Power-angle diagram for a transmission line.
ii) To study the change in power transfer for variations in sending-end and receiving-end voltages.
Theory:
The complex power is defined as
𝑃𝑆 − 𝑗𝑄 𝑆 = 𝑉𝑆
∗
𝐼𝑆
Where QS is positive when the reactive power is delivered to the system.
For a lossless short-line representation, having a reactance X, the real power at the two ends will be the same
and equal to:
And the reactive powers are given by:
The above equations show that the transfer of real power between the sending and receiving end is directly
proportional at the two ends. Keeping the magnitudes of the voltages constant, a plot between the power and
the phase angle δ, known as the power angle diagram can be drawn. The maximum power transfer occurs when
δ = 90° i.e. the steady-state power limit is:
Material and Equipment:
Transmission-line model, 3-phase phase-shifting transformer, 3-phase and 1-phase variacs, Voltmeters,
Ammeters and Wattmeters of suitable ratings.

2. Connection Diagram:
Observation Table:
1. Calculating Line Reactance:
V = 154.6 Volts
I = 2.1 Ampere
Z = 73.62 Ω
R = 2.8 Ω
X = 73.57 Ω
2. While varying δ:
|VS| = |VR| = 40V
WS IS cosδ δ (in degrees)
6 0.21 0.925 22.270
8 0.27 0.877 28.754
12 0.37 0.768 39.786
16 0.46 0.642 50.052
20 0.57 0.450 63.227
22 0.71 0.147 81.526
20 0.94 -0.495 119.639
3. While varying |VS|:
|VR| = 40V
VS W I
50 0.21 6
55 0.26 8
62.5 0.38 10

3. Result:
Drawing the power angle curve:
Hence – Steady State power limit is 22W at 81.526o
.
And the curve showing variation of power with sending end voltage:
The variation is linear.
0
5
10
15
20
25
22.270 28.754 39.786 50.052 63.227 81.526 119.639
Power
Angle
Ws
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
50 55 62.5
Power
Sending End Voltage
W