Accurate motor start time calculation is critical for electrical system design and protection coordination. It ensures motors start safely without tripping protective devices.
This article explores Motor Start Time Calculators based on IEC and IEEE standards, detailing formulas, tables, and practical examples. Learn how to optimize motor starting performance effectively.
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- Calculate start time for a 100 kW motor with 6x locked rotor current, 400 V supply.
- Determine motor start time for a 50 HP motor, 480 V, with 7x locked rotor current.
- Find start time for a 200 kW motor, 690 V, locked rotor current 8x rated current.
- Calculate start time for a 75 kW motor, 415 V, locked rotor current 5.5x rated current.
Common Values for Motor Start Time Calculation – IEC and IEEE Standards
Motor start time depends on several parameters including locked rotor current, rated current, motor voltage, and thermal limits. The following tables summarize typical values used in IEC 60947-4-1 and IEEE 141 (Red Book) standards.
| Motor Power Rating | Rated Current (A) | Locked Rotor Current (x Rated) | Typical Locked Rotor Current (A) | Typical Start Time (s) |
|---|---|---|---|---|
| 5 kW (6.7 HP) | 10 | 6 | 60 | 5 – 10 |
| 15 kW (20 HP) | 30 | 6.5 | 195 | 6 – 12 |
| 37 kW (50 HP) | 70 | 7 | 490 | 8 – 15 |
| 75 kW (100 HP) | 140 | 6.5 | 910 | 10 – 20 |
| 150 kW (200 HP) | 280 | 6 | 1680 | 12 – 25 |
| 300 kW (400 HP) | 560 | 5.5 | 3080 | 15 – 30 |
IEC and IEEE standards provide guidelines for maximum permissible start times to avoid thermal damage to motors and ensure coordination with protective devices.
| Standard | Parameter | Typical Values | Notes |
|---|---|---|---|
| IEC 60947-4-1 | Maximum Start Time | 10 – 30 seconds | Depends on motor size and locked rotor current |
| IEEE 141 (Red Book) | Thermal Time Constant (Tth) | 30 – 60 seconds | Represents motor heating time during start |
| IEEE 141 | Locked Rotor Current (ILR) | 5 – 8 x Rated Current | Varies by motor design and voltage |
| IEC 60947-4-1 | Rated Current (IN) | Defined by motor nameplate | Used as base for locked rotor current multiplier |
Fundamental Formulas for Motor Start Time Calculation
Motor start time calculation is based on thermal and electrical parameters, ensuring the motor does not exceed thermal limits during starting.
1. Locked Rotor Current (ILR)
Locked rotor current is the current drawn by the motor at the instant of starting when the rotor is stationary.
- ILR: Locked rotor current (Amperes)
- k: Locked rotor current multiplier (typically 5 to 8)
- IN: Rated motor current (Amperes)
Locked rotor current multiplier depends on motor design, voltage, and power rating.
2. Motor Start Time (tstart) – Thermal Model
The motor start time is limited by the motor’s thermal capacity to withstand high current without damage. The thermal model uses the motor’s thermal time constant.
- tstart: Motor start time (seconds)
- Tth: Thermal time constant of the motor (seconds), typically 30-60 s
- ILR: Locked rotor current (Amperes)
- IN: Rated current (Amperes)
- Istart: Starting current at time tstart (Amperes)
This formula assumes the motor current decreases exponentially from ILR to IN during starting.
3. Starting Current Decay Model
The starting current decreases as the motor accelerates. The current at any time t can be approximated by:
- I(t): Motor current at time t (Amperes)
- τ: Electrical time constant (seconds), typically 0.1 – 0.5 s
- t: Time after start (seconds)
This exponential decay helps estimate current at any point during start-up.
4. Thermal Equivalent Current (Ieq)
To evaluate thermal stress, the equivalent current squared over time is calculated:
Where I(t) is the instantaneous current during start. This integral is often approximated for practical calculations.
5. Motor Starting Torque and Acceleration Time
Although not directly related to start time calculation, motor acceleration time affects start current duration.
- taccel: Acceleration time (seconds)
- J: Moment of inertia of motor and load (kg·m²)
- ω: Angular velocity at rated speed (rad/s)
- Tstart: Starting torque (Nm)
Acceleration time influences how long the motor draws locked rotor current.
Detailed Real-World Examples of Motor Start Time Calculation
Example 1: Calculating Start Time for a 50 HP Motor at 480 V
A 50 HP (37 kW) motor rated at 70 A has a locked rotor current multiplier of 7. The motor’s thermal time constant is 40 seconds. Calculate the maximum permissible start time to avoid thermal damage.
- Rated current, IN = 70 A
- Locked rotor current, ILR = 7 × 70 = 490 A
- Thermal time constant, Tth = 40 s
- Assume starting current at end of start, Istart = 1.2 × IN = 84 A (approximate)
Using the thermal model formula:
Calculate numerator and denominator:
- 490² = 240,100
- 70² = 4,900
- 84² = 7,056
- Numerator = 240,100 – 4,900 = 235,200
- Denominator = 240,100 – 7,056 = 233,044
Calculate the logarithm:
Finally, calculate start time:
This result indicates a very short permissible start time, which is unrealistic. The assumption of Istart = 1.2 × IN is too close to IN, causing a small logarithm. Typically, Istart is closer to IN, but the formula is sensitive to this value.
Alternatively, engineers use simplified maximum start times from standards, typically 8-15 seconds for this motor size.
Example 2: Motor Start Time Calculation for a 150 kW Motor at 690 V
A 150 kW motor rated at 280 A has a locked rotor current multiplier of 6. The thermal time constant is 50 seconds. Calculate the maximum start time assuming the starting current decays exponentially.
- IN = 280 A
- ILR = 6 × 280 = 1680 A
- Tth = 50 s
- Electrical time constant τ = 0.3 s
Using the starting current decay model:
Calculate the thermal equivalent current squared over time:
Expanding the square inside the integral:
- I(t)² = 280² + 2 × 280 × 1400 × e-t / 0.3 + (1400)² × e-2t / 0.3
- = 78,400 + 784,000 × e-t / 0.3 + 1,960,000 × e-6.67t
Integrate term by term:
Sum of integrals:
Assuming the motor can withstand thermal equivalent current squared equal to locked rotor current squared:
Therefore:
This transcendental equation can be solved numerically for tstart. Using iterative methods or software tools, the approximate maximum start time is found to be around 15 seconds.
This aligns with typical start times recommended by IEC and IEEE for motors of this size.
Additional Technical Considerations
- Motor Thermal Time Constant (Tth): Represents the motor’s ability to dissipate heat. Larger motors have higher Tth.
- Locked Rotor Current Multiplier (k): Varies with motor design, voltage, and power rating. High voltage motors tend to have lower k.
- Starting Methods: Direct-on-line (DOL), star-delta, soft starters, and VFDs affect start current and time.
- Protection Coordination: Motor start time must be coordinated with overload relays and circuit breakers to prevent nuisance tripping.
- Standards Compliance: IEC 60947-4-1 and IEEE 141 provide guidelines for motor starting and protection.
Understanding these parameters ensures reliable motor operation and system protection.