Date Code 20011026 Maintenance and Testing 7-47
SEL-321/321-1 Instruction Manual
()()
()( )()
*T1II0k1ANG1Z1Im
*T1IVIm
X
AA
AA
AG
°∠⋅⋅⋅+⋅∠
°∠⋅
=
Equation 7.18
When T = 0°, as it does in the example relay settings, Equation 7.18 can be further
Simplified using the following identity:
()()
()()
()
()
0k1IANG1Z1Im
*IVIm
X
*III
2
A
AA
AG
AA
2
A
+⋅⋅∠
=
⋅=
Equation 7.19
If we select a value for V
A
, it then becomes possible to use Equation 7.19 to calculate
the magnitude and angle of I
A
required to test the Zone 2 ground quadrilateral
distance element reactive reach.
For the example, select V
A
= 40.0 ∠0°. To simplify the reactance calculation, select
the angle of I
A
= -90° with respect to V
A
. For the Zone 2 element, XG2 = 9.36 Ω,
∠Z1ANG = 83.97°, and k0 = 0.726∠-3.69°.
()
()()
°−∠+⋅°∠⋅
°∠⋅°∠
=
69.3726.0197.831ImI
90I00.40Im
36.9
2
A
A
The result of computing the imaginary portion of V
A
⋅ I
A
*
when I
A
lags V
A
by 90° is:
()
AAAA
IV90I0VIm ⋅=°∠⋅°∠
Substituting this into the equation above yields:
()
71.1I
I0.40
36.9
2
A
A
⋅
⋅
=
Solving for the magnitude of I
A
yields:
()()
amps49.2I
71.139.9
0.40
I
A
A
=
⋅
=
The Zone 2 ground distance element is forward-reaching in the example relay
settings. Thus, it is supervised by the forward directional element 32QF, as well as
the 50L2 and 50G2 phase and residual overcurrent elements. Applied phase current
must exceed the 50L2 setting, applied residual current must exceed the 50G2 setting,
and applied 3I2 must exceed the 50QF setting.
The 50L overcurrent elements operate based upon the magnitude of the phase
current. Using the current connections shown in Figure 7.6, the magnitude of I
A
is
equal to the magnitude of the applied test current.
With a 50L2 setting of 0.90 amps, 50L2 picks up when I
TEST
is greater than 0.90
amps.
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