Journal of Reliable Power - SEL

15
B. Adaptive Resistance Element
Fig. 29 shows the quadrilateral distance element
characteristic that uses the adaptive reactance element of the
previous design with an adaptive resistive element.
X
Adaptive Reactance Element
setting of 11.52 ohms and an impedance reach (Zset) setting of
120 percent of ZL1. The mho distance element has a reach of
120 percent of ZL1. The sensitivity of all the distance
elements is 0.05 • Inom.
Fig. 30, Fig. 31, and Fig. 32 show the Rf coverage of mho
and quadrilateral distance elements. We observe that the Rf
coverage is severely reduced as the fault approaches the end of
the line. As expected, the mho element is the one with less Rf
coverage, and the adaptive resistance element has the greatest
Rf coverage, especially for power flow in the forward
direction, δ equal to 10 degrees.
20
18
Mho Distance Element
Quadrilateral Distance Element
Adaptive Resistive Element
Z LINE
Adaptive
Resistive
Element
16
14
Rset = 11.52 ohms
δ = -10 degrees
R
Fault Resistance (ohms)
12
10
8
6
Fig. 29. Quadrilateral distance element characteristic with adaptive
resistance element
The adaptive resistive element calculates Rf according to
(38) and (39), and compares the minimum of the two
calculation results against the resistive setting.
j⋅θ
L1
( )
j⋅θ
L1
*
( )
Im
⎡
V • I2 • e
⎢
R2 =
⎣
Im
⎡
I • I2 • e
⎢⎣
Im
⎡
V • I
⎢
Rα
=
⎣
Im
⎡
I • I
⎢⎣
⎤
⎥⎦
⎤
⎥⎦
*
j⋅θ
L1
( α • e )
j⋅θ
L1
*
( α • e )
⎤
⎥⎦
⎤
⎥⎦
*
(38)
(39)
Equation (38) is equivalent to (11) and (12). It uses a
different form of phase comparator equation. Equation (39)
uses the alpha component (Iα = I1 + I2).
C. Resistive Coverage
To compare the resistive coverage of the traditional
distance elements with the adaptive resistive element, we use
the system in Fig. 4 and perform the tests discussed in the
following sections.
1) Faults at Multiple Locations
We calculate the maximum Rf that the distance elements
can detect for an A-phase-to-ground fault for m values from 0
to 1 and load angles of δ equal to –10, 0, and 10 degrees. The
quadrilateral distance elements have a resistive reach (Rset)
4
2
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fault Location (pu)
Fig. 30. Rf coverage of mho and quadrilateral distance elements for
δ equal to –10 degrees
Fault Resistance (ohms)
8
7
6
5
4
3
2
1
Mho Distance Element
Quadrilateral Distance Element
Adaptive Resistive Element
Rset = 11.52 ohms
δ = 0 degrees
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fault Location (pu)
Fig. 31. Rf coverage of mho and quadrilateral distance elements for δ equal
to 0 degrees
Adaptive Phase and Ground Quadrilateral Distance Elements | 79