Tools › Building Systems › Lighting and Electrical › Voltage Drop and Short Circuit › Example
480 V, 1,500 kVA radial system: feeder voltage drop, bus fault currents by the ohmic method and the TM 5-811-14 per-unit example
| Tool | Voltage Drop and Short Circuit |
| Source | U.S. Department of the Army (1991). Coordinated Power System Protection. TM 5-811-14 (Appendix G Example 5, Figure G-21, eqs 4-1 to 4-3 and G-1 to G-5); U.S. Department of the Army and U.S. Air Force (1995). Electrical Power Supply and Distribution. TM 5-811-1 / AFJMAN 32-1080 (Figures 4-1 and 5-2); Institute of Electrical and Electronics Engineers (1993). IEEE Std 141-1993 (ohmic method and the approximate drop form, as mathematics). |
| Level | Professional |
Problem
A 1,500 kVA, 5.75 % Z (X/R 7) transformer on a 500 MVA utility (X/R 15) supplies a 480 V main bus with 600 kVA of motors (X″ 0.25, X/R 6). A 400 A, 0.85 power-factor feeder of two 3/0 copper conductors per phase runs 200 ft to panel DP-1, then 2/0 for 100 ft to MCC-1 and 4 AWG for 75 ft to LP-1 (steel conduit, 75 °C). Find the feeder voltage drop (exact phasor, IEEE 141 approximate and resistive forms), the smallest size for 3 %, the drop at a 2,000 A, 0.30 power-factor motor start, and the bolted three-phase and line-to-ground fault, X/R, first-cycle peak and half-cycle rms current at every bus with the device ratings (65 / 65 / 42 / 22 kA).
Inputs to Enter
- Voltage drop: 480 V three-phase, 400 A, pf 0.85, 2 × 3/0 AWG stranded copper at 75 °C, 200 ft, reactance by the geometric estimate at 1 in spacing (non-magnetic), limit 3 %, table ampacity 200 A per conductor, start 2,000 A at pf 0.30
- Short circuit: 480 V, 60 Hz, utility 500 MVA X/R 15, transformer 1,500 kVA 5.75 % X/R 7 (Z0/Z1 1.0), motors 600 kVA X″ 0.25 X/R 6, runs 2 × 3/0 (200 ft, 65 kA), 2/0 (100 ft, 42 kA), 4 AWG (75 ft, 22 kA), steel conduit factor 1.25, device test X/R 6.6, clearing 0.1 s
Answers
- R(3/0, 75 °C) = 0.0767 Ω per 1,000 ft, X = 0.0422 (estimate); run R 0.00767 Ω, X 0.00422 Ω; exact drop 6.055 V = 1.261 % (sending end held 6.055 V), approximate 6.054 V, resistive 5.312 V, TM 5-811-1 kVA form 1.261 %; 2 AWG is the smallest size for 3 % with two per phase; start 22.34 V = 4.66 %
- Z_base 0.1536 Ω, I_fl 1,804 A, I_inf = I_fl · 100/5.75 = 31,378 A; source contribution 29,826 A, motor contribution 2,887 A (4 × 722 A); main bus: Z1 0.00119 + j0.00839 Ω, X/R 7.07, I_3φ 32,712 A, I_L-G 32,255 A, peak 75,922 A, half-cycle rms 44,157 A, 65 kA device derated to 64.1 kA, adequate
- DP-1 17.02 kA (X/R 1.54), MCC-1 10.37 kA, LP-1 5.72 kA; conductor withstand at 0.1 s 70.3 / 27.9 / 8.74 kA against 17.0 / 10.4 / 5.72 kA
- TM 5-811-14 Example 5 (test script): I_base = 2,000 kVA/(√3 · 0.48 kV) = 2,405.6 A, X″ at MP 4 = (0.033 ‖ 2.45 ‖ 1.89 + 0.231) ‖ 4.6 = 0.249 pu, I″ = 9,661 A (manual 9,661); eq 4-1 to 4-3: 241 A, 861 A, 1,378 A; eq G-1: 119 A; TM 5-811-1 Figure 5-2: 4.28 %, Figure 4-1: 10 kA
Notes
The tool's default inputs are the voltage-drop case; choosing the short-circuit analysis loads the radial system. The system and its X/R values are illustrative (stated on the page); every number is reproduced by test_voltage_drop_short_circuit.php (369 checks) with an independent numpy complex-arithmetic and nodal-network reference in References/Voltage-Drop/checks/. TM 5-811-14 misprints its equations G-22 to G-24 denominators and applies the base-change voltage ratio inverted in eqs G-25 to G-31; the test reproduces the printed numbers and records the slips.