Three-Phase LoadBalancing Calculator
Balance electrical loads across L1, L2, L3 phases. Calculate neutral current using phasor analysis, optimize load distribution, and ensure BS 7671 compliance.
System Configuration
Affects neutral conductor sizing
Add Electrical Loads
Getting Started
- • Add your electrical loads using the form above
- • Single-phase loads are distributed across L1, L2, L3
- • Three-phase balanced loads affect all phases equally
- • Enable "Auto-Balance" to optimize load distribution
- • The calculator will show phase currents, neutral current, and imbalance percentage
Important Disclaimer
This calculator is provided for informational and educational purposes only. While we strive for accuracy and compliance with BS 7671:2018+A2:2022 regulations, calculations should be verified by a qualified electrician.
Professional Verification Required: All electrical work must be designed, installed, tested, and certified by a competent person in accordance with BS 7671 (18th Edition) and Building Regulations Part P.
No Liability: London Electrical Distributors and its contributors accept no responsibility for any loss, damage, or injury arising from the use of this calculator. Results are estimates and may vary based on specific installation conditions, environmental factors, and local regulations.
Use at Your Own Risk: By using this tool, you acknowledge that electrical design and installation carries inherent risks and should only be undertaken by qualified professionals with appropriate insurance and certification.
Professional Features
Phasor-Based Neutral Current
Accurate neutral current calculation using vector mathematics. Accounts for 120° phase separation for precise results.
Auto-Balance Algorithm
Automatically distributes single-phase loads across phases to minimize imbalance. Accounts for load priority and power levels.
BS 7671 Compliant
Follows BS 7671:2018+A2:2022 regulations for phase balance, neutral sizing, and harmonic content assessment.
Cable Sizing Recommendations
Automatic cable sizing for phase and neutral conductors based on current requirements and harmonic content.
Imbalance Analysis
Real-time phase imbalance percentage calculation with quality ratings (excellent, good, acceptable, poor) and improvement recommendations.
Power Factor Analysis
Calculates real power (kW), apparent power (kVA), and reactive power (kVAR) with weighted average power factor.
Understanding Three-Phase Load Balancing
What is Phase Imbalance?
Phase imbalance occurs when the currents on L1, L2, and L3 are unequal. In a perfectly balanced three-phase system, each phase carries the same current, and the neutral current is zero. In practice, some imbalance is inevitable due to single-phase loads.
Why Does Imbalance Matter?
- Voltage Imbalance: Current imbalance causes voltage imbalance, reducing motor efficiency and lifespan
- Neutral Current: Excessive imbalance increases neutral current, potentially overloading the neutral conductor
- Energy Losses: Imbalanced systems have higher losses in cables and transformers
- Nuisance Tripping: One overloaded phase may trip protective devices unnecessarily
BS 7671 Requirements
BS 7671 Regulation 314.1 requires installations to be divided into circuits to minimize danger and inconvenience in the event of a fault. For three-phase systems, this includes balancing loads to prevent excessive neutral current and voltage imbalance. IEC 61000-2-2 limits voltage imbalance to 2%.
Neutral Conductor Sizing
BS 7671 Regulation 524.2 specifies neutral conductor sizing requirements. For installations with high harmonic content (IT equipment, LED lighting, switch-mode power supplies), the neutral must be the same size or larger than phase conductors, as harmonic currents can cause the neutral current to exceed phase current.
Frequently Asked Questions
How do you calculate neutral current in a three-phase system?
Neutral current is calculated using phasor analysis. Since the three phases are 120° apart, the neutral current is the vector sum of the phase currents. For a perfectly balanced system (equal currents on L1, L2, L3), the neutral current is theoretically zero. For unbalanced systems, neutral current increases. Our calculator uses the formula: In = √[(I1cos0° + I2cos(-120°) + I3cos(120°))² + (I1sin0° + I2sin(-120°) + I3sin(120°))²]
What is an acceptable phase imbalance percentage?
BS 7671 and good electrical practice recommend: Excellent balance: <5% imbalance, Good balance: <10% imbalance (recommended target), Acceptable: <20% imbalance, Poor: >20% imbalance (requires load redistribution). IEC 61000-2-2 specifies voltage imbalance should not exceed 2%, which is typically achieved when current imbalance is kept below 10%.
When should the neutral conductor be the same size as the phase conductors?
BS 7671 Regulation 524.2 requires the neutral to be the same size as phases when: 1) The system has high harmonic content (IT equipment, LED lighting, switch-mode power supplies), 2) Neutral current exceeds 50% of phase current, 3) The installation serves predominantly non-linear loads. For balanced installations with low harmonic content and phase conductors ≤16mm², the neutral can be 50% of the phase size, with a minimum of 2.5mm².
How does the auto-balance feature work?
The auto-balance algorithm distributes single-phase loads across L1, L2, and L3 to minimize imbalance. It works by: 1) Processing high-priority loads first, 2) Sorting loads by power (largest first) for optimal distribution, 3) Assigning each load to the phase with the lowest current, 4) Accounting for existing three-phase loads. This ensures the most balanced distribution possible while respecting load priorities.
What power factor should I use for different load types?
Typical power factors by load type: Resistive heating/incandescent lights: 1.0, LED lighting: 0.95, Induction motors (full load): 0.85, Induction motors (part load): 0.7-0.8, Fluorescent lighting: 0.85, IT equipment: 0.9, Air compressors: 0.85, Welding equipment: 0.7. Our calculator includes these typical values for easy selection.
Complete Three-Phase Electrical Calculations Guide
Star (Y) vs Delta (Δ) Configurations
Three-phase systems can be wired in two configurations, each with distinct voltage and current relationships.
Star (Y) Connection
- • Line Voltage = √3 × Phase Voltage
- • Line Current = Phase Current
- • VL = 400V, VP = 230V (UK supply)
- • Neutral point available
- • Used for: Distribution systems, motors
Delta (Δ) Connection
- • Line Voltage = Phase Voltage
- • Line Current = √3 × Phase Current
- • VL = VP = 400V
- • No neutral point
- • Used for: Motors, transformers, high power
The √3 Factor Explained:
The √3 (≈1.732) factor comes from vector addition of two phase voltages at 120° apart. Using cosine rule: VL² = VP² + VP² - 2(VP)(VP)cos(60°) = 3VP², therefore VL = √3 × VP.
Three-Phase Power Calculations
Three-phase power formulas are essential for sizing cables, protection, and understanding system capacity.
Balanced Three-Phase Power:
P = √3 × VL × IL × cos(φ)
P = 3 × VP × IP × cos(φ)
S = √3 × VL × IL (Apparent power, kVA)
Q = √3 × VL × IL × sin(φ) (Reactive power)
Current from Power:
IL = P ÷ (√3 × VL × cos(φ))
IL = S ÷ (√3 × VL)
For 400V system, 1kW @ PF=0.85:
IL = 1000 ÷ (1.732 × 400 × 0.85) = 1.70A
| Load (kW) | PF=1.0 | PF=0.85 | PF=0.8 |
|---|---|---|---|
| 10kW | 14.4A | 17.0A | 18.0A |
| 22kW | 31.8A | 37.4A | 39.7A |
| 50kW | 72.2A | 84.9A | 90.2A |
Current values for 400V three-phase balanced load at various power factors
Unbalanced Loads and Neutral Current
Real-world three-phase systems are rarely perfectly balanced. Single-phase loads connected line-to-neutral create imbalance, causing neutral current to flow.
Neutral Current Calculation (Phasor Method)
IN = √[(I1cos0° + I2cos(-120°) + I3cos(120°))² +
(I1sin0° + I2sin(-120°) + I3sin(120°))²]
For I1=30A, I2=20A, I3=25A: IN ≈ 8.7A (calculated using phasor addition)
Imbalance Percentage
Imbalance = (Max Phase - Min Phase) ÷ Avg × 100%
- • <5%: Excellent
- • <10%: Good (target)
- • <20%: Acceptable
- • >20%: Poor - requires redistribution
Voltage Imbalance Effects
- • 2% voltage imbalance → 20% motor I²R losses increase
- • 3% imbalance → motor derating required
- • 5% imbalance → significant motor damage risk
- • IEC 61000-2-2 limits: max 2% voltage imbalance
Harmonic Currents in Three-Phase Systems
Non-linear loads (LED lighting, VFDs, IT equipment) generate harmonic currents that can cause the neutral current to exceed phase current even in balanced systems.
Why Third Harmonics Add in the Neutral
Fundamental currents (50Hz) are 120° apart and cancel in a balanced system. Third harmonic currents (150Hz) are 3×120° = 360° apart, meaning they are in-phase and add together instead of cancelling.
Neutral current (high harmonics) = 3 × Phase × %3rd Harmonic
Example: 30A phase × 33% 3rd harmonic = 30A neutral!
| Load Type | Typical 3rd Harmonic | Neutral Sizing |
|---|---|---|
| Resistive loads | <5% | 50% of phase (min 2.5mm²) |
| LED lighting | 15-30% | Same as phase |
| IT equipment | 30-50% | Same as or larger than phase |
| VFDs | 20-40% | Same as phase |
Reference: BS 7671 Regulation 524.2 and Appendix 4, Section 11
Three-Phase Motor Circuits - Cable and Protection Sizing
Motor circuits require special consideration for starting current, voltage drop during start, and protection coordination.
Motor Starting Current
- • DOL (Direct-On-Line): 6-8 × FLC
- • Star-Delta: 2-3 × FLC initially
- • Soft Starter: 2-4 × FLC
- • VFD: 1.0-1.5 × FLC
Protection Selection
- • Type D MCB for motor circuits
- • MCCB with adjustable thermal-magnetic
- • Overload relay: 1.0-1.2 × FLC setting
- • Allow 10× In for 5-20 seconds starting
| Motor kW | FLC (400V) | Start Current (DOL) | Min Cable (short run) |
|---|---|---|---|
| 4kW | 8.5A | 51-68A | 2.5mm² |
| 7.5kW | 15.6A | 94-125A | 4mm² |
| 11kW | 22.5A | 135-180A | 6mm² |
| 22kW | 42.5A | 255-340A | 16mm² |
FLC based on typical 4-pole motor at 0.85 PF. Always verify with motor nameplate data.
Three-Phase Voltage Drop Calculations
Voltage drop in three-phase circuits uses a modified formula compared to single-phase. The BS 7671 limit is 5% (20V on 400V system) or 3% for lighting.
Three-Phase Voltage Drop Formula:
Vd (line-to-line) = √3 × mV/A/m × L × I ÷ 1000
Or using 3-core/4-core SWA tables directly which already account for √3
Worked Example: 22kW Motor at 50m
Given: 22kW motor, 42.5A FLC, 50m cable run, 10mm² 4-core SWA
From BS 7671 Table 4D4A: 10mm² 4-core SWA = 3.8 mV/A/m (3-phase)
Calculation: Vd = (3.8 × 50 × 42.5) ÷ 1000 = 8.08V
Percentage: (8.08 ÷ 400) × 100 = 2.02% ✓
Common Three-Phase Applications in the UK
Commercial Kitchens
- • Combination ovens: 10-30kW
- • Induction hobs: 10-20kW
- • Dishwashers: 10-15kW
- • Typical total: 50-100kW
- • Usually resistive loads (PF ≈ 1.0)
EV Charging (Commercial)
- • 22kW AC chargers: 32A per phase
- • 50kW DC chargers: 80A supply
- • 150kW DC chargers: 250A supply
- • Load management for multiple units
- • High power factor (near unity)
HVAC Systems
- • Chillers: 20-200kW
- • Air handling units: 5-50kW
- • Cooling towers: 5-30kW
- • Motor loads (PF 0.8-0.85)
- • VFDs increasingly common
Data Centres
- • UPS systems: 10-500kVA
- • PDUs: balanced distribution
- • High harmonic content (IT loads)
- • Oversized neutrals essential
- • Redundant supplies (2N, N+1)
Professional Reference
For complex three-phase installations, consult:
- BS 7671:2018+A2:2022 - Requirements for Electrical Installations
- IEC 61000-2-2 - Electromagnetic Compatibility (voltage limits)
- IET Guidance Note 1 - Selection and Erection of Equipment
- CIBSE Guide K - Electricity in Buildings
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