Schweitzer Engineering Laboratories SEL-311C - Table 3.1 Phase Distance Calculations

3.2
SEL-311C Relay Instruction Manual Date Code 20060320
Distance, Out-of-Step, Overcurrent, Voltage, Synchronism Check, and Frequency Elements
Distance Elements
Table 3.1 shows the different calculations used for the positive-sequence
polarized mho elements and compensator-distance mho elements. Notice that
the positive-sequence polarized mho element equation is the solution of
Equation 3.1 for the quantity “|Z|,” which represents the relay reach at the
balance point. This equation is in the form of a line drop-compensated voltage
and a polarizing (reference) voltage.
Equation 3.1
As mentioned previously, a digital relay mho element tests the angle between
a line drop-compensated voltage and a polarizing (reference) voltage.
Figure 3.1 through Figure 3.3 show the operating voltages “inside” positive-
sequence polarized mho elements and compensator-distance mho elements.
Note that V1mem is the polarizing voltage for the positive-sequence polarized
mho element and (Z • I – V) is the line drop-compensated voltage. In the
compensator distance phase-to-phase element, the polarizing voltage is the
unfaulted phase-to-phase voltage, and the line drop-compensated voltage is
the faulted phase-to-phase voltage. In the compensator distance three-phase
element, the polarizing voltage is (–jV
AB
– 0.25 • V
C
mem) and the line drop
compensated voltage is (V
AB
– Z • I
AB
).
0ReZIV–• ()Vmem*• []=
Table 3.1 Phase Distance Calculations
Positive-Sequence
Polarized Mho Element
Compensator-Distance Mho Element
Phase A-B Phase-to-Phase Element
Phase B-C Three-Phase Element
Phase C-A
Z
Re V
AB
V
AB
mem*• ()
Re 1 ZI
AB
V
AB
mem*• • ∠()
----------------------------------------------------------------------=
mPP Im V
AB
Z– I
AB
• ()• V
BC
ZI
BC
• –()*[]=
Z
Re V
BC
V
BC
mem*• ()
Re 1 ZI
BC
V
BC
mem*• • ∠()
-----------------------------------------------------------------------=
mABC Im V
AB
Z– I
AB
• ()• jV–
AB
0.25 V
C
mem• –()*[]=
Z
Re V
CA
V
CA
mem*• ()
Re 1 ZI
CA
V
CA
mem*• • ∠()
-----------------------------------------------------------------------=
mPP Phase-to-phase torque calculation.=
Positive torque restrains,
negative torque operates.
Z Impedance measurement=
at the line angle.
mABC Three-phase torque calculation.=
Positive torque restrains,
negative torque operates.
Z Replica line impedance at=
operating or balance point.