PROBLEMS 1. Given a polyphase directional relay, each element of which develops maximum torque when the current in its current coil leads the voltage across its voltage coil by 20°. Assuming that the constant in the torque equation is l.0, and neglecting the spring torque, calculate the total torque for each of the three conventional connections for the following voltages and currents: Vbc = 90 + j0 Vab = –30 + j50 Vca = –60 – j50 Ia = 25 + j7 I b = –15 – j l8 I c = –2 + jl0 2. Figure 22 shows a percentage-differential relay applied for the protection of a generator winding. The relay has a 0.l-ampere minimum pickup and a 10% slope (defined as in Fig. 19). A high-resistance ground fault has occurred as shown near the grounded-neutral end of the generator winding while the generator is carrying load. As a consequence, the currents in amperes flowing at each end of the generator winding have the magnitudes and directions as shown on Fig. 22.
Fig. 22. Illustration for Problem 2.
Assuming that the CT’s have a 400/5-ampere ratio and no inaccuracies, will the relay operate to trip the generator breaker under this condition? Would the relay operate at the given value of fault current if the generator were carrying no load with its breaker open? On the same diagram, show the relay operating characteristic and the points that represent the operating and restraining currents in the relay for the two conditions. 3. Given two circuits carrying a-c currents having rms values of I1 and I2, respectively. Show a relay arrangement that will pick up on a constant magnitude of the arithmetic (not vector) sum of I1 and I2.
PROTECTIVE RELAY TYPES
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