Question 8.5: Steady-State Currents Calculate the steady-state currents on......
Steady-State Currents
Calculate the steady-state currents on the 13.8 kV bus, fault-point F2, in the system of Example 7.2, according to IEC and ANSI methods.
IEC Method
The steady-state current is the summation of the source current through the transformer and the generator steady-state current:
I_{k} = I_{k,PSU} + I_{kG} = I^{\prime \prime}_{K,PSU} + λ_{max}I_{rG}
Substitution of λ_{min} gives the minimum steady-state current; λ_{max} and λ_{min} are calculated from Figure 8.8; and I_{rG} = 4.69 kA, I^{\prime \prime}_{kG} = 30.99 kA, and ratio I^{\prime \prime}_{kG}/I_{rG} = 6.61. Also from Table 6.1, the generator X_{d–sat} = 1.949. From Series One curves in Figure 8.8, λ_{min} = 0.5 and λ_{max} = 1.78. Therefore, the maximum generator steady-state current is 8.35 kA, and the minimum generator steady-state current is 2.345 kA. The source steady-state current is equal to the initial short-circuit current (25.53 kA); therefore, the total steady-state short-circuit current is 33.88 kA maximum and 27.88 kA minimum.
ANSI Method
The source current from Example 7.2 is 27.69 kA. From Table 6.1, the generator transient reactance is 0.278 on machine MVA base. The generator contribution is, therefore, 16.87 kA, and the total steady-state current is 44.56 kA.
| TABLE 6.1 Generator Data |
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| Description | Symbol | Data | |
| Generator 112.1 MVA, 2-pole, 13.8 kV, 0.85 PF, 95.285 MW, 4690 A, 0.56 SCR, 235 field V, wye connected |
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| Per unit reactance data, direct axis | |||
| Saturated synchronous | X_{dv} | 1.949 | |
| Unsaturated synchronous | X_{d} | 1.949 | |
| Saturated transient | X_{dv}^{\prime} | 0.207 | |
| Unsaturated transient | X_{d}^{\prime} | 0.278 | |
| Saturated subtransient | X_{dv}^{\prime \prime} | 0.164 | |
| Unsaturated subtransient | X_{d}^{\prime \prime} | 0.193 | |
| Saturated negative sequence | X_{2v} | 0.137 | |
| Unsaturated negative sequence | X_{2I} | 0.185 | |
| Saturated zero sequence | X_{0v} | 0.092 | |
| Leakage reactance, overexcited | X_{0I} | 0.111 | |
| Leakage reactance, underexcited | X_{LM,OXE} X_{LM,UXE} |
0.164 0.164 |
|
| Per unit reactance data, quadrature axis | |||
| Saturated synchronous | X_{qv} | 1.858 | |
| Unsaturated synchronous | X_{q} | 1.858 | |
| Unsaturated transient | X_{q}^{\prime} | 0.434 | |
| Saturated subtransient | X_{qv}^{\prime \prime} | 0.140 | |
| Unsaturated subtransient | X_{q}^{\prime \prime} | 0.192 | |
| Field time constant data, direct axis | |||
| Open circuit | T_{d0}^{\prime} | 5.615 | |
| Three-phase short-circuit transient | T_{d3}^{\prime} | 0.597 | |
| Line-to-line short-circuit transient | T_{d2}^{\prime} | 0.927 | |
| Line-to-neutral short-circuit transient | T_{d1}^{\prime} | 1.124 | |
| Short-circuit subtransient | T_{d}^{\prime \prime} | 0.015 | |
| Open circuit subtransient | T_{d0}^{\prime \prime} | 0.022 | |
| Field time constant data quadrature axis | |||
| Open circuit | T_{q0}^{\prime} | 0.451 | |
| Three-phase short-circuit transient | T_{q}^{\prime} | 0.451 | |
| Short-circuit subtransient | T_{q}^{\prime \prime} | 0.015 | |
| Open circuit subtransient | T_{q0}^{\prime \prime} | 0.046 | |
| Armature dc component time constant data | |||
| Three-phase short circuit | T_{a3} | 0.330 | |
| Line-to-line short circuit | T_{a2} | 0.330 | |
| Line-to-neutral short circuit | T_{a1} | 0.294 | |
