Voltage drop formulas
Voltage drop calculations using the DC-resistance formula are not always accurate for AC circuits, especially for those with a less-than-unity power factor or for those that use conductors larger than 2 AWG.
Table 1 allows engineers to perform simple ac voltage drop calculations. Table 1 was compiled using the Neher–McGrath ac-resistance calculation method, and the values presented are both reliable and conservative. This table contains completed calculations of effective impedance (Z) for the average ac circuit with an 85 percent power factor (see Calculation Example 1).
The basic assumptions and the limitations of Table 1 are as follows:
- Capacitive reactance is ignored.
- There are three conductors in a raceway.
- The calculated voltage drop values are approximate.
- For circuits with other parameters, the Neher–McGrath ac-resistance calculation method is used.
Calculation Example #1
A feeder has a 100 A continuous load. The system source is 240 volts, 3 phase, and the supplying circuit breaker is 125 A. The feeder is in a trade size 1¼ aluminum conduit with three 1 AWG THHN copper conductors operating at their maximum temperature rating of 75°C. The circuit length is 150 ft, and the power factor is 85 percent.
See the solution //
STEP-1 // Find the approximate line-to-neutral voltage drop.
Using the Table 1 column “Effective Zat 0.85 PF for Uncoated Copper Wires”, select aluminum conduit and size 1 AWG copper wire. Use the given value of 0.16 ohm per 1000 ft in the following formula:
STEP-2 // Find the line-to-line voltage drop:
STEP-3 // Find the voltage present at the load end of the circuit:
Calculation Example #2
A 270 A continuous load is present on a feeder. The circuit consists of a single 4-in. PVC conduit with three 600-kcmil XHHW/USE aluminum conductors fed from a 480 V, 3-phase, 3-wire source. The conductors are operating at their maximum rated temperature of 75°C.
See the solution //
STEP-1 // Using the Table 1 column “XL (Reactance) for All Wires”, select PVC conduit and the row for size 600 kcmil. A value of 0.039 ohm per 1000 ft is given as this XL. Next, using the column “Alternating-Current Resistance for Aluminum Wires”, select PVC conduit and the row for size 600 kcmil. A value of 0.036 ohm per 1000 ft is given as this R.
STEP-2 // Find the angle representing a power factor of 0.7.
Using a calculator with trigonometric functions or a trigonometric function table, find the arccosine (cos-1) θ of 0.7, which is 45.57 degrees. For this example, call this angle.
STEP-3 // Find the impedance (Z) corrected to 0.7 power factor (Zc):
STEP-4 // As in Calculation Example 1, find the approximate line-to-neutral voltage drop:
STEP-5 // Find the approximate line-to-line voltage drop:
STEP-6 // Find the approximate voltage drop expressed as a percentage of the circuit voltage:
STEP-7 // Find the voltage present at the load end of the circuit:
Conclusion // According to 210.19(A)(1), Informational Note No. 4, this voltage drop does not appear to be excessive.
TABLE 1 //
Alternating-Current Resistance and Reactance for 600-Volt Cables, 3-Phase, 60 Hz, 75°C (167°F)
Three Single Conductors in Conduit //
Reference // National Electrical Code Handbook – Mark W. Earley, P.E., Jeffrey S. Sargent, Christopher D. Coache and Richard J. Roux (National Fire Protection Association, Quincy, Massachusetts)