98 Modern Commercial Wiring Copyright Goodheart-Willcox Co., Inc. Three-Phase Voltage Drop In a three-phase system, voltage drop is calcu- lated with a slightly different equation: VD = √ __ 3 × L × I × R ____________ 1000 or VD = 2 × 0.866 × L × I × R __________________ 1000 where VD = Voltage drop L = One-way length of conductor (in feet) I = Current in the circuit (amps) I R = Conductor resistance as shown in Table 8, 8 Chapter 9 of the Code (in Ohms/1000′) In three-phase wiring, two current-carrying conductors are connected to the equipment. These two conductors are supplying current that_ is not in phase, so the resulting current is √ _ 3 times the nominal current. The current is grounded at the equipment so the factor of two on the length is unnecessary. The second form of the equation shown is identical to the first fi because 2 × 0.866 = √ __ 3 . To determine the maximum allowable con- ductor resistance to maintain a 3% voltage drop in a three-phase system, use the following equation: R MAX = X ______________e)gvolta(line×__03.0×0001 √3 × L × I SAMPLE PROBLEM 6-6 Problem: A 200-ampere panel must be fed f fr om a source (switchgear) that is 460′ away. The switch- c gear supplies 208/120 V, three-phase, four-wire r power. What size THW conductor (copper) is needed d for the feeder? (Assume 3% maximum voltage drop.) d Solution: First, determine the maximum allow o wa ble resistance for the conductor in this three-phase system: ys R MAX = X 1__× _000 _0.03_____l___tage)voinel(×____ √3 √ √ × L × I = 1000 0.03 × ___× ____208 ___V √3 __ × 460′ × 200 A = _______0426 159,349 = 0.0392 ohms/kFT Checking Table 8 of Chapter 9 for a resistance r less than 0.0392 ohms/kFT for an uncoated c co pper con- ductor, we see that 350 kcmil condu uc tor (0.0367 ohm/kFT) is the smallest allowable size. 18 18 250 300 350 1 7 37 37 37 37 — — 0 0.3 9 2.09 2.29 2.47 2 47 1.02 1.16 14.61 16.00 17.30 17 30 0.040 0.046 0.575 0.630 0.681 0 681 0.001 0.002 0.260 0.312 0.364 0 3 64 7.77 7.95 0.0515 0.0429 0.0367 8.08 8.45 0.0535 0.0446 0.0382 42.0 42.8 0.2778 0.2318 0.1984 12.8 13.1 0.0847 0.0707 0.0605 26.5 27.7 0.17 753 0.1463 1 0. 0.1 252 25.5 26.1 0.1687 0.1409 0.1205 0 1 205 0.823 1.06 168 201 235 235 — 0.015 0.082 0.090 0.097 0 097 1620 1620 — — — 400 500 600 37 37 61 1 2.64 2.95 2.52 18.49 20.65 22.68 0.728 0.813 0.893 0.416 0.519 0.626 0.0321 0.0258 0.0214 0.0331 0.0265 0.0223 0.1737 0.1391 0.1159 0.0529 0.0424 0.0353 0 0.1 084 0.0869 0.0732 0.1053 0.0845 0.0704 268 336 404 0.104 0.116 0.099 — — — 0.823 0.823 Table 8 Conductor Properties Area ohm/ km ohm/ kFT oh hm / k kFT ohm/ km ohm/ kFT Uncoated Area Diameter Diam met er Strandi ing Copper Aluminum Copper Conductors Direct-Current Resistanc ce at 75°C (167°F) Coated ohm/ km Circular mils Quantity mm in. mm2 in.2 mm2 Size (AWG or kcmil) i 7 9 0 0 0 0 Copyright © 2016 NFPA