9. Motor Calculations

Principle: Designing motor circuits requires calculating several parameters: full-load current, starting (inrush) current, torque/speed characteristics, and ensuring appropriate supply and protection. Motors—especially induction motors—draw much higher current on startup (typically 5–8 times full-load current), so calculations must account for voltage drop during start and proper overload protection settings. Additionally, power factor and efficiency influence supply requirements and any necessary corrections.

Full-Load Current (FLC)

FLC is the current drawn when the motor produces its rated horsepower (or kW) at the rated voltage and frequency. It can be calculated from the motor power using the formula:

I = P / (√3 × V × cosφ × η)

where P is the motor shaft output in kW, cosφ is the power factor, and η is the efficiency (both typically given on the motor nameplate). For example, a 15 kW motor at 400 V, with a power factor of 0.89 and 87% efficiency, has its FLC determined accordingly. (In this demonstration, a 12 kW output is assumed if considering a 15 kW input for a 15 kW rated motor.) Manufacturers often publish standard FLC values—for instance, NEMA tables in the NEC provide approximate FLC for common horsepower ratings.

Starting Current and Motor Starting

When an AC induction motor starts, it behaves almost like a short circuit (locked rotor) until it speeds up. The Locked Rotor Current (LRC) is typically 5–7 times the FLC. For example, a motor with a 40 A FLC might have an LRC of around 240 A. This high current persists for a few cycles to a few seconds depending on the motor and the starting method. Key calculations include:

  • Voltage drop during start: Using the source and cable impedances, ensure that the voltage does not sag below acceptable levels (motors usually start at about 80% voltage). If the drop is excessive, consider a soft-starter or reduced voltage starter.
  • Acceleration time: Determine the motor’s acceleration time by examining the torque versus load torque profile. Prolonged acceleration can overheat the motor or stress the supply.
  • Inrush effect on generators: Ensure that, when starting from a generator, the surge does not stall the generator or trip its voltage regulation. In some cases, the motor starting kVA dominates the generator sizing.

Motor Protection and Circuit Elements

A typical motor circuit includes:

  • Breaker/Fuse sizing: As per NEC or IEC, breakers or fuses are sized to allow the high starting current. NEC might permit up to 175% FLC for dual-element fuses or 250% for inverse breakers, with overload relays handling sustained overloads. The upstream device must also handle the LRC.
  • Overload relay setting: Typically set to around 1.1 × FLC (to accommodate a service factor or tolerance). For instance, a 40 A motor might have its overload relay set at about 45 A.
  • Cable size: Cables must be sized to carry the FLC plus a margin and to withstand the short-circuit duration until the breaker clears.

Power Factor and Efficiency

Motors usually operate at a lagging power factor between 0.8 and 0.9. In larger installations, the total reactive power of motors is calculated to properly size power factor correction capacitors. Additionally, motor efficiency is crucial; a higher efficiency motor draws less current for the same output, which can allow for slightly smaller cables and breakers while saving energy over time.

Step-by-Step Example

Consider a 50 HP (~37 kW) three-phase motor, 480 V, with a power factor of 0.88 and 93% efficiency.

  • FLC: Using the kW method,
    FLC ≈ 37 / (√3 × 0.48 × 0.88 × 0.93) ≈ 54 A (Note: NEC tables might list ~65 A for a 50 HP motor at 460 V due to typical lower pf/eff values.)
  • LRC: Assuming ~6× FLC, the LRC is ~324 A. If started across the line, a transformer with 5% impedance would see a voltage dip calculated roughly as 5% × (324/65) ≈ 25%—a significant drop. In practice, industrial systems may mitigate this by having a separate feed for lighting or using soft starters/star-delta starters to limit inrush.
  • Breaker sizing: Per NEC 430.52, an inverse-time breaker for motors >1 HP may be rated up to 250% FLC. For 65 A FLC (by NEC), 250% yields ~162.5 A, so a standard 175 A breaker might be used. This breaker must tolerate the 324 A inrush momentarily.
  • Cable sizing: For a 65 A FLC motor, using the NEC 125% continuous factor (as motor conductors per 430.22 must be at least 125% of FLC) requires conductors to carry about 81.25 A. For example, #3 AWG THHN copper (rated ~85 A) might suffice; alternatively, #2 AWG (rated ~115 A) could be chosen to further reduce voltage drop. For a 50 m run with a conductor resistance of approximately 0.00085 Ω/m, the voltage drop during start (round-trip) is:
    324 A × 0.00085 Ω/m × 2 × 50 m ≈ 25.9 V (≈5.4% drop during start) and ~0.9% at full load (54 A). Adjust conductor size if necessary.
  • Overload relay: Set at roughly 60 A (approximately 110% of 54 A) to avoid nuisance tripping at full load while still protecting the motor.

Niche Applications

  • Motor starting generators: In island or backup generator scenarios, oversizing or using a reduced voltage starter might be necessary because generators have limited surge capacity.
  • Multi-motor starts: When starting two or more large motors together, the combined inrush must be considered—often managed by sequencing the starts.
  • High altitude or temperature: Motors operating at high altitude (with thinner air) or in hot environments may require a larger frame, as their effective rating drops.
  • Synchronous motors: These can supply reactive power when over-excited, improving the overall power factor of the system. Calculations include excitation current and pull-in torque.
  • DC motors or VFDs: For DC motors, armature current is calculated from torque. When using VFDs for AC motors, starting current can be limited (sometimes to about 1.1× FLC), affecting cable and breaker sizing. However, VFDs may introduce harmonics, which require additional considerations.
  • Regenerative braking: If motors feed power back into the system, ensure the system can handle reverse power flow—often managed by active front-end drives or dynamic brake resistors.

Industry Relevance

Motors typically account for 60–70% of industrial electricity consumption. Proper motor circuit calculations are critical for ensuring reliable startup, minimizing voltage sag, and optimizing energy use. In motor control centers (MCCs), these calculations guide the sizing of feeders, breakers, and overload relays. Furthermore, utilities may impose restrictions (such as limiting across-the-line starts above a certain horsepower) to prevent excessive voltage dips and flicker. Efficiency and power factor corrections may justify installing capacitors or selecting higher-efficiency motors to achieve long-term energy savings.

Standards

  • NEC Article 430: Provides detailed requirements for motor circuit sizing, including conductor sizing (430.22), breaker sizing (430.52), and overload relay settings (430.32). It also references NEMA MG-1 for motor performance characteristics.
  • IEC 60947-4-1 and IEC 60204-1: Cover contactors and motor starters, ensuring proper protection and wiring practices.
  • IEEE 399 and IEEE 3004.1: Offer guidelines for motor starting analysis and voltage dip calculations.

Software Tools

  • Motor starting simulation tools: Programs such as ETAP or DIgSILENT simulate motor starting, including dynamic voltage drop and network interactions.
  • Load calculators: Tools that incorporate motor FLC libraries (based on NEC or IEC values) and automatically size breakers and cables.
  • In-house spreadsheets: Custom Excel models often calculate FLC, LRC, recommended breaker and cable sizes, and overload relay settings.
  • Power quality analyzers: Measurements of motor currents and harmonics in existing facilities guide improvements in motor circuit design.
  • Specialty software: Manufacturer-specific tools may simulate both electrical and mechanical aspects (e.g., acceleration profiles, torque curves) to optimize motor selection.

Through careful motor calculations, engineers ensure reliable startup and operation, minimize voltage sag, and optimize both energy use and protection for the motor and the broader electrical network.