Torque-Slip Characteristics of Double-Cage Induction MotorIn a double-cage induction motor, it is assumed that the two cages develop two separate torques. Thus, the total torque developed in the double-cage induction motor is equal to the sum of the two cage torques. The torque-slip characteristics of the two cages and the total torque of the motor is shown in the figure.By changing the individual cage resistances and leakage reactances, the resultant torque-speed characteristics can be modified according to the requirement. The resistances can be changed by changing the cross-sectional area of the rotor bars while the leakage reactance can be changed ... Read More

The graph plotted between the torque and slip for a particular value of rotor resistance and reactance is known as torque-slip characteristics of the induction motor.The torque of a 3-phase induction motor under running conditions is given by, $$\mathrm{\tau_𝑟 =\frac{𝐾𝑠𝐸_2^2𝑅_2}{𝑅_2^2 + (𝑠𝑋_2)^2}… (1)}$$From the eqn. (1), it can be seen that if R2 and X2 are kept constant, the torque depends upon the slip 's'. The torque-slip characteristics curve can be divided into three regions, viz.Low-slip regionMedium-slip regionHigh-slip regionLow-Slip RegionAt synchronous speed, the slip s = 0, thus, the torque is 0. When the speed is very near to the ... Read More

A 3-phase induction motor is an electromechanical energy conversion device which converts 3-phase input electrical power into output mechanical power.A 3-phase induction motor consists of a stator and a rotor. The stator carries a 3-phase stator winding while the rotor carries a short-circuited winding called rotor winding. The stator winding is supplied from a 3-phase supply. The rotor winding drives its voltage and power from the stator winding through electromagnetic induction and hence the name.Working Principle of a 3-Phase Induction MotorThe working principle of a 3-phase induction motor can be explained by considering a portion of it as follows−When the ... Read More

The torque (τ) developed by the rotor of a 3-phase induction motor is directly proportional to −Rotor current (I2)Rotor EMF (E2)Rotor circuit power factor (cos ϕ2)Therefore, $$\mathrm{\tau \propto 𝐸_2𝐼_2 cos \varphi_2}$$$$\mathrm{⇒ \tau = 𝐾𝐸_2𝐼_2 cos \varphi_2 … (1)}$$Where, K is the constant of proportionality.Starting Torque of 3-Phase Induction MotorLet, Rotor resistance/Phase = 𝑅2Rotor reactance/Phase at standstill = 𝑋2Rotor EMF/Phase at standstill = E2∴ Rotor impedance/Phase at standstill, $$\mathrm{𝑍_2 = \sqrt{𝑅_2^2 + 𝑋2^2}}$$Rotor current/Phase at standstill, $$\mathrm{𝐼_2 =\frac{𝐸_2}{𝑍_2}=\frac{𝐸_2}{\sqrt{𝑅_2^2 + 𝑋2^2}}}$$And, Rotor power factor at standstill, $$\mathrm{cos\varphi_2 =\frac{𝑅_2}{𝑍_2}=\frac{𝑅_2}{\sqrt{𝑅_2^2 + 𝑋2^2}}}$$∴ Starting torque, $$\mathrm{\tau_𝑠 = 𝐾𝐸_2𝐼_2 cos\varphi_2 = 𝐾𝐸_2 × (\frac{𝐸_2}{\sqrt{𝑅_2^2 + 𝑋2^2}}) ... Read More

Circuit Diagram and Working Principle of Star-Delta StarterThe figure shows the connection diagram of a 3-phase induction motor with a star-delta starter. The star-delta starter is a very common type of starter and is extensively used for starting the squirrel cage induction motors. It is used for starting a squirrel cage induction motor which is designed to run normally on delta connected stator winding.When the switch S is in the START position, the stator windings are connected in star. When the motor attains a speed about 80 % of rated speed, then the changeover switch S is thrown to the ... Read More

The torque developed by the induction motor is given by, $$\mathrm{\tau_𝑑 =\frac{𝑘 𝑠 𝐸_{20}^2 𝑅_2}{𝑅_2^2 + 𝑠^2𝑋_{20}^2} … (1)}$$Where, k = constant of proportionality, s = fractional slip, E20 = per phase induced EMF in rotor at standstill, R2 = rotor circuit resistance, andX20 = reactance per phase of the rotor at standstillAnd, the value of slip corresponding to maximum torque is given by, $$\mathrm{𝑠_𝑚 =\frac{𝑅_2}{𝑋_{20}}… (2)}$$The speed of a 3-phase induction motor can be varied by changing the supply voltage. Eqn. (1) shows that the torque developed in the motor is proportional to the square of the supply voltage ... Read More

Torque of 3-Phase Induction Motor under Running ConditionLet the rotor circuit of 3-phase induction motor at standstill has per phase resistance R2, per phase reactance X2 and per phase induced EMF E2. If ‘s’ is the slip under running condition of the motor, then, $$\mathrm{Rotor \:reactance/phase , 𝑋′_2 = 𝑠 𝑋_2}$$$$\mathrm{Rotor \:EMF/phase , 𝐸′_2 = 𝑠 𝐸_2}$$$$\mathrm{\therefore \:Rotor \:impedance/phase , 𝑍′_2 = \sqrt{𝑅_2^2 + (𝑠 𝑋_2)^2}}$$$$\mathrm{Rotor\:impedance/phase ,𝐼′_2 =\frac{𝐸'_2}{𝑍′_2}=\frac{𝐸'_2}{\sqrt{𝑅_{2}^{2} + (𝑠 𝑋_2)^2}}… (1)}$$$$\mathrm{Rotor\: power \:factor, cos \varphi′_2 =\frac{𝑅_2}{𝑍′_2}=\frac{𝑅_2}{\sqrt{𝑅_{2}^{2} + (𝑠 𝑋_2)^2}}… (2)}$$Therefore, $$\mathrm{Running\:torque, \tau_𝑟 \propto 𝐸′_2 𝐼′_2 cos \varphi′_2 … (3) +}$$$$\mathrm{\because 𝐸′_2 \propto Magnetic\:flux (\varphi)}$$$$\mathrm{\therefore \tau_𝑟 = 𝐾 \varphi 𝐼′_2 ... Read More

Circuit Diagram and Working PrincipleIn a rotor resistance starter, a star connected variable resistance is connected in the rotor circuit through slip-rings. The full voltage is applied to the stator windings. The connection arrangement of the rotor resistance starter is shown in the figure.At the instant of starting, the handle of variable resistance (rheostat) is set to ‘OFF’ position. This inserts maximum resistance in series with each phase of the rotor circuit. This reduces the starting current and at the same time starting torque is increased due to external rotor resistance.As the motor accelerates, the external resistance is gradually removed ... Read More

When 3-phase supply is fed to the stator winding of the 3-phase induction motor, a rotating magnetic field (RMF) is produced. This magnetic field is such that its poles do not remain in a fixed position on the stator but go on shifting their positions around the stator. For this reason, it is known as rotating magnetic field (RMF) or RMF.Mathematically, it can be shown that the magnitude of this rotating magnetic field is constant and is equal to 1.5 times of the maximum flux ( ϕm) due to current in any phase.The speed of the rotating magnetic field is ... Read More

For a 3-phase induction motor, the full-load torque is given by, $$\mathrm{\tau_{𝐹.𝐿} \propto\frac{𝑠𝑅_2}{𝑅_2^2} + (𝑠𝑋_2)^2… (1)}$$Where, s is slip corresponds to full-load.The starting torque is given by, $$\mathrm{\tau_𝑠 \propto \frac{𝑅2}{𝑅_2^2 + 𝑋_2^2} … (2)}$$And the maximum torque is given by, $$\mathrm{\tau_𝑚 \propto\frac{1}{2 𝑋_2}… (3)}$$Therefore, (1) Ratio of maximum torque to full-load torque −$$\mathrm{\frac{\tau_𝑚}{\tau_{𝐹.𝐿}}=\frac{𝑅_2^2 + (𝑠𝑋_2)^2}{2 𝑠 𝑅_2 𝑋_2}}$$Dividing the numerator and denominator on RHS by $𝑋_2^2$, we have, $$\mathrm{\frac{\tau_𝑚}{\tau_{𝐹.𝐿}}=\frac{(𝑅_{2}⁄𝑋_{2})^2 + 𝑠^2}{2 𝑠 (𝑅_{2}⁄𝑋_{2})}}$$$$\mathrm{⇒\frac{\tau_𝑚}{\tau_{𝐹.𝐿}}=}$$$$\mathrm{\frac{𝑠_𝑚^2 + 𝑠^2}{2 𝑠 𝑠_𝑚}… (4)}$$Where, $$\mathrm{𝑠_𝑚 =\frac{𝑅_2}{𝑋_2}= Slip\:corresponding \:to \:maximum\: torque}$$(2) Ratio of maximum torque to starting torque −$$\mathrm{\frac{\tau_𝑚}{\tau_𝑠}=\frac{𝑅_2^2 + 𝑋_2^2}{2 𝑅_2 𝑋_2}}$$Dividing the numerator and denominator ... Read More