Correct cable sizing in three-phase systems ensures safety, efficiency, compliance with NEC standards, and long-term reliability.

Proper conductor selection minimizes voltage drop, prevents overheating, reduces energy losses, and guarantees electrical equipment operates effectively.

Importance of Cable Sizing in Three-Phase Systems

• Safety compliance: Prevents conductor overheating and reduces fire risk.
• Voltage stability: Maintains voltage within permissible limits to protect loads.
• Efficiency: Reduces I²R losses and improves energy efficiency.
• Equipment protection: Ensures motors, transformers, and sensitive devices receive correct voltage/current.
• Code compliance: NEC requires that conductor ampacity, voltage drop, and environmental conditions be considered.

Key NEC References for Cable Sizing

The following NEC articles are fundamental when performing three-phase cable sizing:

• NEC Article 310.15 – Ampacity tables for conductors.
• NEC Article 210.19(A)(1) – Voltage drop recommendations.
• NEC Article 240 – Overcurrent protection coordination with conductors.
• NEC Article 110.14(C) – Termination temperature limitations.
• NEC Annex D Examples – Practical cable sizing methods.

Authoritative reference: NFPA NEC Standards.

Fundamental Formulas for Three-Phase Cable Sizing

The three-phase current and voltage drop are the basis of conductor selection.

1. Three-Phase Current Formula

Where:

• I = Line current (A)
• P = Total power (W)
• V = Line-to-line voltage (V)
• PF = Power factor (0–1, typically 0.8–1.0 for industrial loads)

Common values:

• Industrial PF ≈ 0.85–0.95
• Voltage (V): 208V, 400V, 480V, 600V are typical in NEC practice

2. Voltage Drop Formula (Three-Phase)

Where:

• VD% = Voltage drop percentage
• I = Load current (A)
• L = Length of conductor run (m or ft)
• R = Resistance per unit length of conductor (Ω/m or Ω/ft)
• V = System voltage (V)

NEC recommends:

• ≤ 3% voltage drop for feeders or branch circuits.
• ≤ 5% total (feeder + branch combined).

3. Ampacity Selection Formula

Where:

• Icable = Corrected ampacity of the conductor
• Iload = Load current (A)
• Kadj = Adjustment factor for number of conductors in raceway (from NEC Table 310.15(C)(1))
• Ktemp = Temperature correction factor (from NEC Table 310.15(B)(2)(a))

Common Reference Tables for Three-Phase Cable Sizing (NEC)

Below is a practical table with typical ampacity values for copper conductors with THHN insulation (90°C rating), based on NEC 310.16, assuming 30°C ambient temperature and up to three current-carrying conductors.

Table 1. NEC Copper Conductor Ampacity (THHN, 90°C, ≤3 conductors, 30°C ambient)

Table 2. Aluminum Conductor Ampacity (XHHW-2, 90°C, ≤3 conductors, 30°C ambient)

Voltage Drop Reference Values (Copper Conductors, 75°C)

These resistance values are used in voltage drop calculations for long feeder runs.

Ampacity Correction and Adjustment Factors (NEC Requirements)

In real installations, the ampacity values from NEC Tables 310.16 cannot always be used directly. The NEC requires applying correction factors for ambient temperature and adjustment factors for conductor bundling (more than three current-carrying conductors in a raceway or cable).

1. Temperature Correction Factors (NEC Table 310.15(B)(2)(a))

For conductors with 90°C insulation rating (THHN, XHHW-2, etc.), and 30°C ambient base, apply correction factors:

Example: A THHN conductor in an area with 40°C ambient must be derated to 82% of its table ampacity.

2. Adjustment Factors for More Than Three Conductors (NEC Table 310.15(C)(1))

When more than three current-carrying conductors are installed in the same raceway, cable, or bundled, apply these adjustment factors:

3. Combined Effect

The effective ampacity is calculated as:

Where:

• Iampacity = base ampacity from NEC Table 310.16
• Ktemp = temperature correction factor
• Kadj = adjustment factor for conductor count

Real-World Example 1: Sizing a Feeder for a 100 kW Motor Load (480V, Three-Phase)

Problem Statement:
A 100 kW induction motor at 480V three-phase (PF = 0.9, Efficiency = 95%) must be fed by a copper cable, run length 100 ft. Ambient temperature is 40°C, and the conduit contains 6 current-carrying conductors. Determine the correct conductor size according to NEC, considering voltage drop and derating.

Step 1: Calculate Load Current

Step 2: Select Base Ampacity

From NEC Table 310.16 (90°C, Copper THHN):

• 3/0 AWG = 225 A
• 2 AWG = 130 A

So, 2 AWG is too small. Try 3/0 AWG with 225 A base ampacity.

Step 3: Apply Derating Factors

• Temperature (40°C) → Ktemp = 0.82
• 6 conductors → Kadj = 0.80

Since 148 A ≥ 134 A load, 3/0 AWG copper is acceptable.

Step 4: Check Voltage Drop

Voltage drop formula (resistive only for simplicity):

For 3/0 AWG copper, R = 0.049 Ω/1000ft.

• L = 100 ft → 0.0049 Ω total.

This is well within the NEC recommendation (≤3%).

Final Answer: Use 3/0 AWG copper THHN for this 100 kW, 480V motor feeder.

Real-World Example 2: Long Feeder for a 200A Panel (208V, Three-Phase)

Problem Statement:
A 200A distribution panel at 208V three-phase is located 250 ft away from the main switchboard. Copper conductors are used, with THHN insulation, in a conduit containing 9 current-carrying conductors, ambient temperature 35°C. Determine the correct cable size considering NEC derating and voltage drop.

Step 1: Load Current

The panel is rated at 200A continuous.

Step 2: Base Ampacity Selection

From NEC Table 310.16:

• 4/0 AWG copper = 260 A

Step 3: Apply Derating

• Temperature (35°C) → Ktemp = 0.91
• 9 conductors → Kadj = 0.70

Not sufficient (needs ≥200A). Increase size.

Try 350 kcmil copper (310 A base):

Still below 200 A.

Try 400 kcmil copper (380 A base):

This satisfies ampacity requirement.

Step 4: Voltage Drop Calculation

Resistance for 400 kcmil copper = 0.029 Ω/1000ft.

For 250 ft one-way:

Voltage drop:

Well within NEC recommendation.

Final Answer: Use 400 kcmil copper THHN for the 200A feeder, 208V, 250 ft run.

Frequently Asked Questions (FAQ) about Three-Phase System Cable Sizing – NEC

1. How do you calculate current in a three-phase system?

You need to know three things: the total power of the load, the system voltage, and the power factor. With these values, engineers use standard methods from the NEC to determine the current that flows in each conductor.

2. What is the maximum allowable voltage drop according to NEC?

The NEC recommends that voltage drop should not exceed 3% on a single feeder or branch circuit, and 5% total when considering both feeder and branch circuits together. This ensures good performance and protects electrical equipment.

3. What is the difference between copper and aluminum conductors?

• Copper conductors are more efficient, stronger, and require smaller sizes for the same current, but they are more expensive.
• Aluminum conductors are lighter and more affordable, but they require larger sizes to carry the same current and need special attention at terminations.

4. How do ambient temperature and conduit fill affect cable sizing?

If the cables are installed in hot environments or when many conductors are grouped in the same conduit, their capacity to carry current decreases. The NEC requires applying correction factors in these cases, often leading to the selection of larger conductor sizes.

5. Can I use 90°C rated conductors at their full ampacity?

Not always. Even though the cable insulation may be rated for 90°C, the electrical equipment (such as circuit breakers, lugs, and panels) may only allow 60°C or 75°C terminations. The NEC requires following the lower temperature rating of the equipment, not just the wire.

6. What are the most common voltages in three-phase systems under NEC?

In the United States, the most common three-phase voltages are 208V, 240V, 480V, and 600V. Industrial and commercial facilities frequently use 480V, while 208V is common in commercial buildings.

7. When should aluminum be preferred over copper?

Aluminum is generally preferred in large feeders and service conductors where cost savings and lighter weight are important. Copper is preferred in shorter runs, high-reliability applications, or where space is limited.