- 101 - 
 
    = lagging angle of I to Vp 
  θ = directional angle setting 
 
Figure 2.10-9 Directional element 
 
For the element for the fault in phase-bc, the polarizing voltage (Vp
bc
) is given using 
Equation (2.10-29): 
 
 
    
 
 
For  the  element  for  the  fault  in  phase-a,  the  polarizing  voltage  (Vp
a
)  is  given  using 
Equation (2.10-30): 
 
 
 
 
where, 
  V
0
 = voltage in zero-sequence 
  Va = voltage in phase-A 
  Vbc = voltage in phase-bc 
 
In Equation (2.10-29), the Vp
bc
 voltage is subject to the memory action if the close-in 
fault occurs in three-phases; that is, the values of the Va and Vbc voltages are set from the pre-
fault voltages. The  memory  is retained for  two cycles after  the  fault  occurs.  Note that  the 
polarizing voltage (Vpa) in Equation (2.10-30) is not subject to the memory action. 
 
If a close-in fault in three-phases occurs, the Quad element can be enhanced for an offset 
Quad element, as shown in Figure 2.10-10. Similar to issuing the instantaneous trip signal for 
the close-in three-phase fault,  this  enables  the Quad element  to issue a  trip signal with  a 
delayed time together using the memory action.