Understanding motor starting characteristics is crucial for designing reliable electrical systems and protecting equipment. Motor starting curve calculations help engineers predict current and torque during startup.
This article explores the Motor Starting Curve Calculator based on IEEE and IEC standards, detailing formulas, tables, and practical examples. Learn how to apply these calculations for optimal motor performance and protection.
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- Calculate starting current for a 15 kW, 400 V, 3-phase induction motor.
- Determine starting torque curve for a 50 HP motor with locked rotor current of 6 times rated current.
- Compute acceleration time for a 30 kW motor with inertia constant of 0.15 s.
- Estimate starting current and torque for a 22 kW motor using IEC standard parameters.
Common Values for Motor Starting Curve Calculations – IEEE and IEC Standards
| Parameter | Typical Range | Units | Description |
|---|---|---|---|
| Rated Power (Prated) | 0.75 – 5000 | kW | Motor rated output power |
| Rated Voltage (Vrated) | 230 – 690 | V | Nominal operating voltage |
| Locked Rotor Current (Ilocked) | 5 – 8 × Irated | A | Current drawn at motor start (locked rotor) |
| Starting Torque (Tstart) | 1 – 2 × Trated | Nm | Torque at motor start |
| Acceleration Time (taccel) | 0.5 – 10 | seconds | Time taken to reach rated speed |
| Inertia Constant (H) | 0.05 – 0.3 | seconds | Stored kinetic energy per kW at rated speed |
| Rated Current (Irated) | Depends on motor size | A | Current at rated load and voltage |
Additional Motor Starting Parameters According to IEC 60034-1 and IEEE Standards
| Parameter | Typical Value | Units | Notes |
|---|---|---|---|
| Slip at Starting (sstart) | 1.0 | – | Rotor speed difference at start (locked rotor) |
| Slip at Rated Speed (srated) | 0.002 – 0.05 | – | Slip during normal operation |
| Starting Power Factor (PFstart) | 0.2 – 0.4 | – | Power factor during motor start |
| Starting Torque Factor (KT) | 0.7 – 2.0 | – | Ratio of starting torque to rated torque |
| Acceleration Torque (Taccel) | Varies | Nm | Torque available to accelerate the motor |
Fundamental Formulas for Motor Starting Curve Calculations
Motor starting curves describe the relationship between torque, current, and speed during startup. The following formulas are essential for calculating these parameters according to IEEE and IEC standards.
1. Locked Rotor Current (Starting Current)
The locked rotor current is the current drawn by the motor at standstill (zero speed).
Ilocked = KI × Irated
- Ilocked: Locked rotor current (A)
- KI: Locked rotor current multiplier (typically 5 to 8)
- Irated: Rated motor current (A)
2. Starting Torque
Starting torque is the torque produced by the motor at zero speed.
Tstart = KT × Trated
- Tstart: Starting torque (Nm)
- KT: Starting torque factor (0.7 to 2.0)
- Trated: Rated torque (Nm), calculated as Prated / ωrated
3. Rated Torque
Rated torque is the torque at rated power and speed.
Trated = (Prated × 9550) / nrated
- Trated: Rated torque (Nm)
- Prated: Rated power (kW)
- nrated: Rated speed (rpm)
4. Acceleration Time
Acceleration time is the time required for the motor to reach rated speed from standstill.
taccel = (J × ωrated) / (Taccel × 9.55)
- taccel: Acceleration time (seconds)
- J: Moment of inertia (kg·m²)
- ωrated: Rated angular speed (rad/s) = (2 × π × nrated) / 60
- Taccel: Acceleration torque (Nm) = Tstart – Tload
5. Torque-Speed Characteristic
The torque at any slip s can be approximated by:
T(s) = Tstart × (s / sstart) × ((1 – s / sstart) / (1 – srated))
- T(s): Torque at slip s (Nm)
- s: Slip at operating point (0 to 1)
- sstart: Slip at start (usually 1)
- srated: Slip at rated speed (typically 0.002 to 0.05)
6. Current-Speed Characteristic
Starting current decreases as speed increases, approximated by:
I(s) = Ilocked × (1 – s)
- I(s): Current at slip s (A)
- Ilocked: Locked rotor current (A)
- s: Slip (0 to 1)
Detailed Real-World Examples of Motor Starting Curve Calculations
Example 1: Calculating Starting Current and Torque for a 15 kW Induction Motor
A 15 kW, 400 V, 3-phase squirrel cage induction motor has a rated speed of 1450 rpm. The locked rotor current multiplier KI is 6, and the starting torque factor KT is 1.5. Calculate the locked rotor current, starting torque, and acceleration time assuming the moment of inertia J is 0.12 kg·m² and the load torque is 50 Nm.
Step 1: Calculate Rated Current (Irated)
Using the formula for rated current in a 3-phase motor:
Irated = Prated / (√3 × Vrated × PF × η)
Assuming power factor PF = 0.85 and efficiency η = 0.9:
Irated = 15000 / (1.732 × 400 × 0.85 × 0.9) ≈ 28.3 A
Step 2: Calculate Locked Rotor Current (Ilocked)
Ilocked = KI × Irated = 6 × 28.3 = 169.8 A
Step 3: Calculate Rated Torque (Trated)
Trated = (Prated × 9550) / nrated = (15 × 9550) / 1450 ≈ 98.8 Nm
Step 4: Calculate Starting Torque (Tstart)
Tstart = KT × Trated = 1.5 × 98.8 = 148.2 Nm
Step 5: Calculate Rated Angular Speed (ωrated)
ωrated = (2 × π × nrated) / 60 = (2 × 3.1416 × 1450) / 60 ≈ 151.8 rad/s
Step 6: Calculate Acceleration Torque (Taccel)
Taccel = Tstart – Tload = 148.2 – 50 = 98.2 Nm
Step 7: Calculate Acceleration Time (taccel)
taccel = (J × ωrated) / (Taccel × 9.55) = (0.12 × 151.8) / (98.2 × 9.55) ≈ 0.019 s
Note: The acceleration time seems very short due to the small inertia; in practice, inertia may be higher, or load torque may vary.
Example 2: Motor Starting Current and Torque Curve for a 50 HP Motor
A 50 HP (37.3 kW) motor operates at 460 V, 1770 rpm. The locked rotor current is 7 times rated current, and starting torque is 1.2 times rated torque. Calculate the starting current, starting torque, and plot the torque-speed curve at slips 1.0, 0.5, 0.1, and 0.02.
Step 1: Calculate Rated Current (Irated)
Assuming PF = 0.9 and efficiency η = 0.92:
Irated = (Prated × 1000) / (√3 × V × PF × η) = (37300) / (1.732 × 460 × 0.9 × 0.92) ≈ 51.5 A
Step 2: Calculate Locked Rotor Current (Ilocked)
Ilocked = 7 × 51.5 = 360.5 A
Step 3: Calculate Rated Torque (Trated)
Trated = (Prated × 9550) / nrated = (37.3 × 9550) / 1770 ≈ 201.3 Nm
Step 4: Calculate Starting Torque (Tstart)
Tstart = 1.2 × 201.3 = 241.6 Nm
Step 5: Calculate Torque at Various Slips
Using the torque-slip formula with sstart = 1 and srated = 0.02:
| Slip (s) | Torque T(s) (Nm) |
|---|---|
| 1.0 | 241.6 × (1 / 1) × ((1 – 1 / 1) / (1 – 0.02)) = 0 Nm (start slip, torque at zero speed) |
| 0.5 | 241.6 × 0.5 × ((1 – 0.5) / 0.98) ≈ 61.6 Nm |
| 0.1 | 241.6 × 0.1 × ((1 – 0.1) / 0.98) ≈ 22.2 Nm |
| 0.02 | 241.6 × 0.02 × ((1 – 0.02) / 0.98) ≈ 4.8 Nm |
Step 6: Calculate Current at Various Slips
Using the current-slip formula:
| Slip (s) | Current I(s) (A) |
|---|---|
| 1.0 | 360.5 × (1 – 1) = 0 A |
| 0.5 | 360.5 × (1 – 0.5) = 180.3 A |
| 0.1 | 360.5 × (1 – 0.1) = 324.5 A |
| 0.02 | 360.5 × (1 – 0.02) = 353.3 A |
Note: The current at slip 1.0 (locked rotor) is maximum, decreasing as slip reduces.
Additional Technical Considerations for Motor Starting Curve Calculations
- Standards Compliance: IEEE Std 112 and IEC 60034-1 provide guidelines for motor testing and parameter definitions.
- Starting Methods: Direct-on-line (DOL), star-delta, autotransformer, and soft starters affect starting current and torque curves.
- Thermal Limits: High starting currents cause thermal stress; calculations help ensure motor protection devices are correctly rated.
- Load Characteristics: Load torque profile influences acceleration time and starting torque requirements.
- Inertia Effects: Total inertia includes motor rotor and load; accurate inertia values improve acceleration time predictions.
- Power Supply Impact: Voltage dips during starting affect current and torque; calculations can include supply impedance.