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          Similarly, the balance  is disturbed in the differential    vary with the CT secondary voltage;
        scheme on a fault of any type and a spill current, which      refer to Figure 15.19)
        is the difference between the currents drawn by the two   I,,,  I,. = I,  = circulating currents
        sets of CTs, flows through the relay.  Since the scheme   Ire = spill or differential current through
        functions  on the principle  of  balance  of  currents, it  is   the relay
        imperative that the two sets of  CT parameters,  such as   Vfl, Vfr = V,  = CT secondary voltages under rated
        their  ratio,  secondary  resistance  and  the  magnetizing   conditions (these relays are defined
        current, should be identical, except for the permissible      by both the current and the voltage
        tolerances as discussed in Section 15.10.2. The secondary     settings)
        lead  resistances,  from the  CTs  to  the  relay  terminals,   R, = resistance of the relay coil
        should also be the same, otherwise, spill currents may         VA   whcrc VA is the burden of the
        flow through the relay, even under healthy condition and     =   ~  13
        cause  an unwanted  trip,  or require  a  higher  minimum     relay. This may be specified in terms
        setting of  the relay.  A higher setting  of  the relay  may   of  its current rating  1 A or 5  A or
        jeopardize its sensitivity to detect minor faults. Since it   setting current Ist. Considering this
        is not practical to produce all CTs to be identical, small    to be 1 VArelay at a setting of 0.05 A,
        spill currents under healthy condition are likely and the
        minimum relay setting, IEt, must account for this. Below       R,=--      -400Q
        we consider three different cases to explain the principle         (0.05)’
        of circulating currents, along with the procedure, to select   I,, = relay setting
        the CTs and carry out the relay setting.              R12 = R, = maximum  resistance  of  the
                                                                      connecting  leads  from  the  CT
        Equivalent circuit diagram and selection of                    terminals to the relay terminals. For
                                                                       calculating  this,  for  an  estimated
        class PS CTs                                                   length and size, refer to cable data
        Refer  to  the  control  circuit  diagram  of  Figure  15.24,   in Table 13.15
        drawn for the scheme in Figure 15.22. It is drawn on a   XCT,, XCT2 = XCT = equivalent  excitation reactances  of
        single-phase basis for ease of illustration, where             the CT secondary windings. In ring-
                                                                       type  CTs,  they  are  generally  very
              Ifl, Ir, = If = CT secondary currents                    low and can be ignored for ease of
                  =
            I,,,  lm2 I,  = CTs’ excitation currents (these will       derivation
                                                       RCTI, RCTZ = RCT = equivalent  resistances  of  the  CT
                                                                       secondary windings
                Ll







                c


                                                       The two current through the relay are in opposite directions
                                                       therefore
                                          Differential                         Strictly speaking, these are
                                          relay        Ire = IC2 - IC,         all  phasor  quantities  but
                                                         =    - Im2)  - (If, - I~z)  only their magnitudes are
                                                       Under healthy conditions   considered  for  ease  of
                                                                               illustration,  as quantities
                                                             If1 = If2         of similar parameters such
                                                                               as If,, If2 and I,,,,, I,,   fall
                                                       and  I,,  =Irn2         almost in phase with each
                                                       :.    I,,  = 0          other.
                                                       Hence, in a healthy condition there will be no spill current
                                                       through the relay and it will stay inoperative.
                L2
         (1) Healthy condition, I,,  = lCz - I,,  = 0
                                                       Through-fault condition
         Figure 15.24  Equivalent control circuit diagram for a differential   Refer to Figure  15.25(a). On  a  fault occurring outside
         ground fault protection scheme of  Figure 15.22   the protected  zone, all the CTs that fall in parallel will
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