Alstom MiCOM P546 - Page 469

Application Notes P54x/EN AP/La4
MiCOM P543, P544, P545 & P546
(AP) 6-25
AP
q0 q1 q2
Phase Angle Difference between Two Ends
D
E
A
G
Curve 3
Curve 2
B
C
Po
P
F
Area 2
Area 1
q
Out-of-Step
90
o
0
o
180
o
Curve 1
q3
Figure 6 Power transfer in relation to angle difference θ between 2 ends
The figure above represents power angle curves, with no AR being performed, as follows:
Curve 1 - Pre-fault system operation via parallel lines where transmitted power is Po
Curve 2 - Transmitted power significantly reduced during two-phase to ground fault
Curve 3 - New power curve when the parallel line is tripped (fault cleared)
It can be seen that at a fault instance, the operating point A moves to B, with a lower transfer
level. There is therefore a surplus of power P=AB at the sending end and the
corresponding deficit at the receiving end. The sending end machines start to speed up, and
the receiving end machines to slow down, so phase angle θ increases, and the operating
point moves along curve 2 until the fault is cleared, when the phase angle is θ1. The
operating point now moves to point D on curve 3 which represents one line in service. There
is still a power surplus at the sending end, and deficit at the receiving end, so the machines
continue to drift apart and the operating point moves along curve 3. If, at some point
between E and G (point F) the machines are rotating at the same speed, the phase angle
will stop increasing. According to the Equal Area Criterion, this occurs when area 2 is equal
to area 1. The sending end will now start to slow down and receiving end to speed up.
Therefore, the phase angle starts to decrease and the operating point moves back towards
E. As the operating point passes E, the net sending end deficit again becomes a surplus
and the receiving end surplus becomes a deficit, so the sending end machines begin to
speed up and the receiving end machines begin to slow down. With no losses, the system
operating point would continue to oscillate around point E on curve 3, but in practice the
oscillation is dumped, and the system eventually settles at operating point E.