This article explores effects of Rotor Resistance, supply Voltage, and Frequency on Torque-Speed Curve of Induction motor. Understanding these effects is crucial because induction motors are widely used in industrial, commercial, and residential applications due to their rugged construction and ease of operation. However, their performance and efficiency depend heavily on parameters such as rotor resistance, rotor reactance, supply voltage, and frequency. Therefore, gaining a clear understanding of how these factors impact the torque-speed characteristics ensures proper motor selection and optimal operation.
Effect of Rotor resistance on Torque speed curve
The torque produced by the rotor changes significantly with variations in rotor resistance. However, in a standard squirrel cage induction motor, it is not possible to alter the rotor resistance. In contrast, specially designed slip ring induction motors are equipped with a mechanism to vary rotor resistance externally, as the rotor winding leads are brought out through slip rings and connected to external resistors.
Below is a graphical representation of how rotor resistance affects the torque-speed characteristics of an induction motor
In an induction motor, the slip at which maximum torque occurs (sm) is directly proportional to the rotor resistance (R₂), provided that the rotor reactance (X₂) remains constant. While the magnitude of the maximum torque does not change with variations in rotor resistance, the slip at which it occurs shifts accordingly. As rotor resistance increases, the point of maximum torque moves to higher slip values. This behavior is illustrated in the diagram, where increasing R₂ results in a shift of the maximum torque slip such that sm3>sm2>sm1
However, it is important to note that the maximum torque remains unaffected by changes in rotor resistance. As a result, for a constant load torque TL, the motor’s operating point shifts from A to B to C as the rotor resistance increases. In the torque-speed characteristic curve, this manifests as a rightward shift with increasing rotor resistance. Conversely, reducing the rotor resistance causes the curve to shift leftward, bringing the operating point closer to synchronous speed.
The general equation of starting torque is expressed as follows,
\[Starting Torque (T_{st}) = \frac{kE_2 ^2 R_2}{R_2 ^2 + X_2 ^2}\]
At startup, when the rotor is at standstill and slip s=1the starting torque equation reveals that torque is directly influenced by rotor resistance R2. As a result, increasing rotor resistance R2 leads to a corresponding increase in starting torque
Effect of Supply Voltage on Torque-speed curve
According to the torque equation of an induction motor, the torque produced is directly proportional to the square of the rotor-induced EMF, E22. The rotor EMF E2 itself is proportional to the stator supply voltage E1, and under running conditions,
rotor induced EMF E2=sE1
This implies that torque is also proportional to the square of the supply voltage. Therefore, any change in the supply voltage will result in a significant change in torque at a given rotor speed. As a result, variations in supply voltage have a considerable impact on both the running torque and the maximum torque of the motor. Since T ∝ E22Reducing supply voltage E1 to 50% causes torque to drop to 25%
Effect of change in Supply Frequency
In general synchronous speed of stator magnetic field given as
\[N_s = \frac{120f}{P}\]
This expression shows that the speed of an induction motor is directly proportional to the supply frequency. Under normal conditions, the supply frequency remains nearly constant, typically around 50 Hz. The maximum allowable variation in frequency is ±2 Hz, meaning it can range between 48 Hz and 52 Hz.
However, frequency variations beyond this range can occur in isolated low-power systems, such as those powered by diesel generators or gas turbines. Additionally, supply frequency can be intentionally varied using special control equipment like Variable Frequency Drives (VFDs).
The most noticeable effect of frequency variation is on motor speed, as speed is directly proportional to supply frequency. For example, a 5% change in frequency will result in approximately a 5% change in motor speed.
This becomes critical for machines such as compressors, pumps, and conveyors that rely on constant-speed motors designed to operate at 50 Hz. Running such equipment on a 60 Hz supply causes the motors to operate about 20% faster, which may not be acceptable or safe in many applications.
Operating a 50 Hz Motor on 60 Hz Supply
To operate a 50 Hz motor satisfactorily on a 60 Hz supply, you must increase the supply voltage by a factor of 60/50 = 6/5 = 1.2. In other words, you should raise the voltage to 1.2 times, or 120% of the motor’s rated voltage. This adjustment keeps the new breakdown torque equal to the original breakdown torque, while only slightly affecting the starting torque. Other parameters such as power factor, rotor resistance, impedance, temperature rise, and efficiency generally stay within acceptable limits.
Operating a 60 Hz Motor on 50 Hz Supply
Similarly, you can operate a 60 Hz motor satisfactorily on a 50 Hz supply by reducing the supply voltage in proportion to the frequency ratio. Since 50/60 = 5/6 ≈ 0.83, you should reduce the voltage to approximately 0.83 times, or 83% of the motor’s rated voltage. This adjustment maintains the motor’s magnetic flux at safe levels and ensures reliable performance.
Summary
| Parameter | Impact on Torque-Speed Characteristics |
|---|---|
| Rotor Resistance (R₂) | Shifts curve rightward (higher slip), increases starting torque |
| Stator Voltage (E₁) | Torque ∝ E12, affects torque magnitude at all slips |
| Supply Frequency (f) | Speed ∝ f, affects synchronous speed and requires voltage adjustment to maintain speed |
Conclusion
A thorough understanding effects of Rotor Resistance, supply Voltage, and Frequency on Torque-Speed Curve of Induction motor is essential for accurate motor selection, control, and performance optimization. These parameters directly impact starting torque, slip, efficiency, and overall dynamic behavior. In applications involving fluctuating loads, varying supply conditions, or specialized speed control systems, precise adjustment and coordination of these variables are critical to achieving stable, efficient, and reliable motor operation across the intended operating range
