Practice Problems: Protection Systems
Question 1
A protection engineer is designing an overcurrent relay scheme for a 13.8 kV distribution feeder. The maximum load current is 420 A, and the minimum fault current at the remote end of the feeder is 1,850 A. The relay has an inverse time characteristic with a time dial setting (TDS) of 3. The relay curve equation is t = TDS × [(7)/(M0.02 - 1)], where M is the multiple of pickup current. If the pickup setting is chosen as 125% of maximum load current, what is the operating time of the relay for the minimum fault condition?
(a) 0.68 seconds
(b) 0.94 seconds
(c) 1.12 seconds
(d) 1.35 seconds
Question 2
A substation engineer is evaluating a distance relay protecting a 230 kV transmission line. The line has a positive sequence impedance of 0.08 + j0.65 Ω/mile and is 85 miles long. The relay is set for Zone 1 protection covering 80% of the line length. If the relay has an impedance reach accuracy of ±5%, what is the maximum impedance reach setting (in primary ohms) that ensures Zone 1 does not overreach beyond 80% of the line?
(a) 42.8 Ω
(b) 44.6 Ω
(c) 46.2 Ω
(d) 48.5 Ω
Question 3
A relay coordination engineer is setting up differential protection for a three-phase, 50 MVA, 115/13.8 kV transformer with delta-wye connection (delta on high side). The CT ratio on the high voltage side is 300:5 and on the low voltage side is 2400:5. The relay is set with a 25% slope characteristic. During an external fault, the high side CT output is 4.8 A and the low side CT output is 4.5 A (after magnitude compensation). What is the operating current seen by the differential relay?
(a) 0.15 A
(b) 0.30 A
(c) 0.45 A
(d) 0.60 A
Question 4
A utility engineer is analyzing a directional overcurrent ground relay (67N) for a 34.5 kV radial feeder. The relay uses residual voltage polarization with a maximum torque angle (MTA) of 60°. During a ground fault, the zero-sequence current is measured as 850∠-45° A and the zero-sequence voltage is 12,500∠15° V. The relay characteristic angle is defined relative to the polarizing voltage. Will the relay operate for this fault condition?
(a) Yes, the torque angle is 60° within the operating range
(b) Yes, the torque angle is 30° within the operating range
(c) No, the torque angle is 60° outside the operating range
(d) No, the torque angle is 105° outside the operating range
Question 5
A power system protection specialist is setting a time-overcurrent relay on a 480 V, three-phase motor feeder. The motor has a full load current of 125 A and a locked rotor current of 750 A with a starting time of 8 seconds. The relay has an extremely inverse characteristic with the equation t = 80/(M² - 1) where M is the multiple of pickup. If the pickup is set at 1.5 times the full load current, what minimum time dial setting (TDS) will prevent relay operation during motor starting?
(a) 0.45
(b) 0.52
(c) 0.68
(d) 0.75
Question 6
A substation protection engineer is designing a bus differential protection scheme for a five-bay 138 kV substation. The maximum through-fault current on any feeder is 18,000 A. The CT ratio selected is 2000:5. The differential relay has a minimum sensitivity setting of 0.2 A and a maximum slope setting of 50%. What is the minimum internal fault current (in primary amperes) that the relay can detect during maximum through-fault conditions?
(a) 280 A
(b) 360 A
(c) 450 A
(d) 540 A
Question 7
A transmission protection engineer is evaluating the performance of a distance relay on a 345 kV line. The line impedance is 45∠85° Ω. The relay Zone 2 is set to reach 120% of the protected line plus 50% of the shortest adjacent line (impedance 38∠82° Ω). The relay uses a mho characteristic. What is the Zone 2 impedance reach setting?
(a) 68 Ω
(b) 73 Ω
(c) 78 Ω
(d) 83 Ω
Question 8
A protection coordinator is analyzing a generator differential protection scheme for a 100 MVA, 13.8 kV generator. The neutral CT ratio is 4000:5 and the terminal CT ratio is 4000:5. During an internal ground fault at 30% of the winding from the neutral, the fault current is 2,800 A. If the relay has a minimum pickup of 0.3 A secondary, will the relay detect this fault?
(a) Yes, differential current is 0.84 A
(b) Yes, differential current is 1.05 A
(c) No, differential current is 0.21 A
(d) No, differential current is 0.15 A
Question 9
A relay engineer is commissioning a reverse power relay (32) for a 25 MW cogeneration facility connected to the utility grid at 69 kV. The relay is set to trip if power flows from the utility to the facility for more than 5 seconds at levels exceeding 2% of rated capacity. The PT ratio is 69,000:120 V and the CT ratio is 250:5. What is the minimum secondary power (in watts) that will initiate the reverse power trip sequence?
(a) 14.4 W
(b) 17.3 W
(c) 20.8 W
(d) 24.0 W
Question 10
A distribution engineer is setting up an adaptive reclosing scheme for a 23 kV overhead feeder with underground cable sections. The overhead section can withstand 4 reclose attempts with intervals of 2-10-15-30 seconds. However, for faults on the cable section, only 1 reclose attempt is permitted after 30 seconds. The fault detection system identifies cable faults by impedance signature. If a permanent fault occurs on the cable after the first unsuccessful reclose, what is the total time before lockout?
(a) 30 seconds
(b) 32 seconds
(c) 60 seconds
(d) 62 seconds
Question 11
A consultant is evaluating a phase distance relay protecting a parallel transmission line configuration. Each line has an impedance of 25 + j80 Ω. During a single-line-to-ground fault on one line while both are in service, the relay on the faulted line measures an apparent impedance of 18 + j58 Ω. The mutual coupling zero-sequence impedance is 2 + j15 Ω. If the Zone 1 setting is 80% of the line impedance (83.8 Ω magnitude), will Zone 1 operate?
(a) Yes, measured impedance is 61.0 Ω
(b) Yes, measured impedance is 67.0 Ω
(c) No, measured impedance is 83.8 Ω
(d) No, measured impedance is 91.2 Ω
Question 12
A protection engineer designs a negative-sequence directional element (46) for a 161 kV transmission line. During a phase-to-phase fault, the negative-sequence current is 2,450∠-120° A and the negative-sequence voltage is 48,500∠30° V. The relay's maximum torque angle is set at -90°. The operating characteristic requires the angle between V2 and I2 to be within ±90° of the MTA. Will the relay declare a forward fault?
(a) Yes, the characteristic angle is -150° indicating forward fault
(b) Yes, the characteristic angle is 150° indicating forward fault
(c) No, the characteristic angle is -150° indicating reverse fault
(d) No, the characteristic angle is 150° indicating reverse fault
Question 13
A utility protection specialist is setting a voltage-controlled overcurrent relay (51V) for a 12.47 kV feeder. The relay pickup is set at 600 A with voltage control enabled below 70% of nominal voltage. During a fault, the current is 4,200 A and the voltage drops to 6,500 V (line-to-line). The relay inverse time characteristic at normal voltage gives an operating time of 0.8 seconds for this current level. The voltage-controlled multiplier reduces operating time by a factor of \( \text{V}_\text{multiplier} = (0.7 × \text{V}_\text{nominal})/\text{V}_\text{actual} \) when voltage is below 70%. What is the actual relay operating time?
(a) 0.43 seconds
(b) 0.54 seconds
(c) 0.68 seconds
(d) 0.80 seconds
Question 14
A substation engineer is configuring a breaker failure protection scheme for a 230 kV breaker. The breaker failure relay (50BF) is set with a timer of 150 milliseconds and a minimum current supervision of 0.5 A secondary. The CT ratio is 1200:5. During a fault with 8,500 A primary current, the breaker fails to open. All five surrounding breakers must trip. If each breaker has an operating time of 3 cycles (60 Hz system), what is the total fault clearing time from initial trip command?
(a) 200 milliseconds
(b) 250 milliseconds
(c) 300 milliseconds
(d) 350 milliseconds
Question 15
A protection coordinator is analyzing a dual-setting instantaneous overcurrent relay (50) on a 4.16 kV industrial switchgear. The relay has a high-set at 12,000 A and a low-set at 4,000 A. The low-set is enabled only when a downstream tie breaker is closed, indicating parallel source operation. During maintenance, the tie breaker is open and a bolted three-phase fault occurs 50 feet from the relay location on a cable with impedance of 0.05 + j0.08 Ω per 1000 ft. The source impedance is 0.01 + j0.15 Ω. What is the fault current magnitude?
(a) 14,850 A
(b) 15,920 A
(c) 17,240 A
(d) 18,560 A
Question 16
A renewable energy facility protection engineer is setting up a loss-of-field relay (40) for a 15 MW, 13.8 kV synchronous generator connected to a wind farm collector system. The generator's direct-axis synchronous reactance is Xd = 1.85 per unit and transient reactance is X'd = 0.28 per unit on a 15 MVA base. The relay is configured with an offset mho characteristic on the R-X diagram. If the relay diameter is set at 1.0 per unit on the generator base, what is the relay diameter in primary ohms?
(a) 10.2 Ω
(b) 12.7 Ω
(c) 15.3 Ω
(d) 18.8 Ω
Question 17
A consultant is reviewing synchrophasor-based out-of-step protection for a 500 kV interconnection between two utility systems. The equivalent impedances are: System A = 2 + j25 Ω, Tie line = 5 + j45 Ω, System B = 3 + j30 Ω. The electrical center is determined by equal angular swings. During a disturbance, the impedance locus enters the protected zone at a rate of 15 Ω per cycle (60 Hz). If the out-of-step blocking zone is centered at the electrical center with a diameter of 40 Ω, what is the time duration the impedance locus remains in the blocking zone?
(a) 1.5 cycles
(b) 2.0 cycles
(c) 2.7 cycles
(d) 3.2 cycles
Question 18
A protection engineer is evaluating a restricted earth fault (REF/64) protection scheme for a 45 MVA, 115/13.8 kV transformer with solidly grounded wye on both sides. The neutral CT ratio is 2000:5 and the residual connection of phase CTs (ratio 2000:5) on the 13.8 kV side forms the differential element. During an external ground fault, the neutral CT carries 1,850 A and the residual connection carries 1,820 A due to CT errors. What is the differential current seen by the relay?
(a) 0.075 A
(b) 0.150 A
(c) 0.225 A
(d) 0.300 A
Question 19
A utility engineer designs undervoltage load shedding (UVLS) for a 138 kV substation serving critical industrial loads. The scheme has three stages: Stage 1 at 92% voltage with 2-second delay sheds 20% load, Stage 2 at 88% voltage with 1-second delay sheds 30% additional load, Stage 3 at 85% voltage with 0.5-second delay sheds remaining 50%. During a system disturbance, voltage drops from 100% to 84% in 4.5 seconds following a linear trajectory. Assuming each stage successfully executes when its voltage threshold is crossed and required delay expires, what percentage of load remains connected after all stages execute?
(a) 0%
(b) 30%
(c) 50%
(d) 70%
Question 20
A transmission protection engineer analyzes a pilot wire differential scheme (87L) for a 25-mile, 230 kV line. The scheme uses metallic pilot wires with a capacitance of 0.06 μF/mile. The relay operating threshold is set at 0.1 A differential current. During heavy load transfer of 1,200 A with a power factor of 0.85 lagging, charging current in the pilot wire creates an imbalance. If the pilot wire charging current at 60 Hz is approximated by \( I_c = 2πfCV \), where V is proportional to the voltage difference across terminals (estimated at 5% of nominal for this load angle), what is the approximate charging current contribution to relay imbalance (secondary amperes, CT ratio 600:5)?
(a) 0.02 A
(b) 0.05 A
(c) 0.08 A
(d) 0.12 A
