Rt = 0.0054 pu (transf. ZBase)
1-st step in
calculation
ZBase = 0.9522 Ω (generator)
Xd' = 0.2960 · 0.952 = 0.282 Ω
Rs = 0.0029 · 0.952 = 0.003 Ω
ZBase (13.8 kV) = 0.6348 Ω
Xt = 0.100 · 0.6348 = 0.064 Ω
Rt = 0.0054 · 0.635 = 0.003 Ω
Xline = 300 · 0.4289 = 128.7 Ω
Rline = 300 · 0.0659 = 19.8 Ω
(X and R above on 230 kV basis)
Xe = Z
e
· sin (φ) = 10.52 Ω
Re = Z
e
· cos (φ) = 1.05 Ω
(Xe and Re on 230 kV basis)
2-nd step in
calculation
Xd' = 0.2960 · 0.952 = 0.282 Ω
Rs = 0.0029 · 0.952 = 0.003 Ω
Xt = 0.100 · 0.6348 = 0.064 Ω
Rt = 0.0054 · 0.635 = 0.003 Ω
Xline= 128.7 · (13.8/230)
2
= 0.463
Ω
Rline = 19.8 · (13.8/230)
2
= 0.071
Ω
(X and R referred to 13.8 kV)
Xe = 10.52 · (13.8/230)
2
= 0.038 Ω
Re = 1.05 · (13.8/230)
2
= 0.004 Ω
(X and R referred to 13.8 kV)
3-rd step in
calculation
ForwardX = Xt + Xline + Xe = 0.064 + 0.463 + 0.038 = 0.565 Ω; ReverseX = Xd' = 0.282 Ω (all referred to gen. voltage 13.8 kV)
ForwardR = Rt + Rline + Re = 0.003 + 0.071 + 0.004 = 0.078 Ω; ReverseR = Rs = 0.003 Ω (all referred to gen. voltage 13.8 kV)
Final
resulted
settings
ForwardX = 0.565/0.9522 · 100 = 59.33 in % ZBase; ReverseX = 0.282/0.9522 · 100 = 29.6 in % ZBase (all referred to 13.8 kV)
ForwardR = 0.078/0.9522 · 100 = 8.19 in % ZBase; ReverseR = 0.003/0.9522 · 100 = 0.29 in % ZBase (all referred to 13.8 kV)
Settings ForwardR, ForwardX, ReverseR, and ReverseX.
• A precondition in order to be able to use the Out-of-step protection and construct a
suitable lens characteristic is that the power system in which the Out-of-step
protection is installed, is modeled as a two-machine equivalent system, or as a single
machine – infinite bus equivalent power system. Then the impedances from the
position of the Out-of-step protection in the direction of the normal load flow can be
taken as forward.
• The settings ForwardX, ForwardR, ReverseX and ReverseR must, if possible, take
into account, the post-disturbance configuration of the simplified power system. This
is not always easy, in particular with islanding. But for the two machine model as in
Table
32, the most probable scenario is that only one line is in service after the fault
on one power line has been cleared by line protections. The settings ForwardX,
ForwardR must therefore take into account the reactance and resistance of only one
power line.
• All the reactances and resistances must be referred to the voltage level where the Out-
of-step relay is installed; for the example case shown in Table
32, this is the generator
nominal voltage VBase = 13.8 kV. This affects all the forward reactances and
resistances in Table
32.
• All reactances and resistances must be finally expressed in percent of ZBase, where
ZBase is for the example shown in Table 32 the base impedance of the generator,
ZBase = 0.9522 Ω. Observe that the power transformer’s base impedance is different,
ZBase = 0.6348 Ω. Observe that this latter power transformer ZBase = 0.6348 Ω must
be used when the power transformer reactance and resistance are transformed.
1MRK 506 369-UUS - Section 8
Impedance protection
Line distance protection REL670 2.2 ANSI 471
Application manual
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