Question 8.2: Calculate the fault current contributions of the following a......
Calculate the fault current contributions of the following asynchronous machines, directly connected to a bus, using ANSI and IEC methods. Calculate first-cycle (IEC peak) currents and the interrupting (breaking) currents at contact parting times of two and three cycles, 60 Hz basis, and IEC minimum time delays of 0.03 and 0.05 s approximately. Compare the results.
● 320 hp, 2-pole, 2.3 kV induction motor, X_{lr} = 16.7%
● 320 hp, 4-pole, 2.3 kV induction motor, X_{lr} = 16.7%
● 1560 hp, 4-pole, 2.3 kV induction motor, X_{lr} = 16.7%
These results of ANSI calculations are shown in Table 8.6, while those of IEC calculations are shown in Table 8.7. Most of the calculation steps for asynchronous motors are in common with those for synchronous motors, as illustrated in Example 8.1. The motor-locked rotor reactance of X_{lr} = 16.7% on a motor kVA base is used in both calculation methods; however, the resistances are based on recommendations in each standard. Factor q must also be calculated for asynchronous motors and it is given by Equation 8.36.
q = 1.03 + 0.12 ln m for t_{min} = 0.02 s
= 0.79 + 0.12 ln m for t_{min} = 0.05 s
= 0.57 + 0.12 ln m for t_{min} = 0.10 s
= 0.26 + 0.10 ln m for t_{min} ≥ 0.25 s (8.36)
This requires m equal to the motor-rated power in megawatts per pair of poles to be calculated on the basis of motor power factor and efficiency. The symmetrical breaking current is then given by (8.37).
I_{b,sym} = μqI^{\prime \prime}_{k} (8.37)
A comparison of results again shows divergence in the calculated currents. In ANSI calculations, the interrupting duty current for a 320 hp two-pole motor is twice that of the four-pole motor, 0.28 kA versus 0.14 kA. This is so because a prior impedance multiplying factor of 1.5 is applicable to a two-pole 320 hp motor, and this factor is 3 for a four-pole 320 hp motor. IEC calculation results for a two-pole motor is only slightly higher, 0.235 kA. The IEC calculations consider decay of currents from asynchronous motors, while ANSI/IEEE does not. There is no direct comparison of the asymmetrical motor currents in Table 8.7.
| TABLE 8.6 ANSI Fault Current Calculations from Asynchronous Motors Directly Connected to a Bus |
||||||||
| Description | X_{lr} on Equipment MVA Base | X/R | Impedance Multiplying Factors | First-Cycle Calculations | Interrupting Duty Calculations | |||
| First Cycle | Interrupting | First-Cycle Current (kA sym.) | First-Cycle Current (kA peak) | 3-Cycle Contact Parting Time (kA rms) | 2-Cycle Contact Parting Time (kA rms) | |||
| 320 hp, 2-pole induction motor, 2.3 kV (kVA = 285) |
16.7 | 15 | 1 | 1.5 | 0.427 | 1.095 | 0.28 | 0.28 |
| 320 hp, 4-pole induction motor, 2.3 kV (kVA = 285) |
16.7 | 15 | 1.2 | 3 | 0.356 | 0.909 | 0.14 | 0.14 |
| 1560 hp, 4-pole, 2.3 kV induction motor (kVA = 1350) |
16.7 | 28.5 | 1 | 1.5 | 2.028 |
5.441 |
1.35 | 1.35 |
| TABLE 8.7 IEC Fault Current Calculations from Asynchronous Motors Directly Connected to a Bus, Three-Phase Short-Circuit |
|||
| Description | 300 hp, 2-Pole, 2.3 kV Induction Motor (kVA = 285), Power Factor = 0.9, Efficiency = 0.93 | 300 hp, 4-Pole, 2.3 kV Induction Motor (kVA = 285), Power Factor = 0.9, Efficiency = 0.93 | 1500 hp, 4-Pole, 2.3 kV Induction Motor (kVA = 1350), Power Factor = 0.92, Efficiency = 0.94 |
| I_{LR}/ I_{rM} | 6 | 6 | 6 |
| I^{\prime \prime}_{k}I_{rM} | 6.6 | 6.6 | 6.6 |
| m (electric power per pair of poles) (MW) | 0.256 | 0.128 | 6.21 |
| R_{M}/X_{M} | 0.15 | 0.15 | 0.15 |
| k_{M} | 1.65 | 1.65 | 1.65 |
| μ (0.05 s) | 0.79 | 0.79 | 0.79 |
| μ (0.03 s) | 0.83 | 0.83 | 0.83 |
| q (0.05 s) | 0.63 | 0.54 | 0.73 |
| q (0.03 s) | 0.79 | 0.66 | 0.86 |
| I^{\prime \prime}_{kM} | 0.473 | 0.473 | 2.229 |
| i_{pM} (kA crest) | 1.104 | 1.104 | 5.201 |
| i_{bsym} (0.05 s) kA | 0.235 | 0.202 | 1.285 |
| i_{bsym} (0.03 s) kA | 0.31 | 0.259 | 1.591 |
| I_{DC} (0.05 s) kA | 0.029 | 0.029 | 0.136 |
| I_{DC} (0.03 s) kA | 0.101 | 0.101 | 0.479 |
| i_{basym} (0.05 s) | 0.237 | 0.204 | 1.292 |
| i_{basym} (0.03 s) | 0.326 | 0.278 | 1.661 |