Found 1006 Articles for Electronics & Electrical

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

The 3-phase input power fed to the stator of a 3-phase induction motor is given by, $$\mathrm{𝑃_{𝑖𝑠} = \sqrt{3} 𝑉_𝐿𝐼_𝐿 cos \varphi_i = 3 𝑉_{𝑠𝑝ℎ} 𝐼_{𝑠𝑝ℎ} cos \varphi_i}$$Where, VL = Line voltageIL = Line currentVsph = Stator phase voltageIsph = Stator phase currentcos \varphii = input power factorStator LossesStator copper losses or I2R losses in the stator winding resistances, which are given as follows −$$\mathrm{𝑃_{𝑠𝑐𝑢} = 3 𝐼_{𝑠𝑝ℎ}^{2} 𝑅_{𝑠𝑝ℎ}}$$Hysteresis and eddy current losses in the stator core, which are known as stator-core losses and are given by −$$\mathrm{𝑃_{𝑠𝐶} = 𝑃_{𝑠ℎ} + 𝑃_{𝑠𝑒}}$$Therefore, the power output of the stator will be, ... Read More

The rotor speed (Nr) of an induction motor is given by, $$\mathrm{𝑁_𝑟 = (1 − 𝑠)𝑁_𝑠}$$And the synchronous speed is given by, $$\mathrm{𝑁_𝑠 =\frac{120𝑓}{𝑃}}$$Therefore, $$\mathrm{𝑁_𝑟 = (1 − 𝑠) (\frac{120𝑓}{𝑃}) … (1)}$$It is clear from eqn. (1) that the speed of the induction motor can be changed by varying the frequency (f), number of poles (P) or slip (s).Speed Control of Induction Motor by Pole Changing MethodBy changing the stator poles, the speed of the induction motor can be changed. The number of stator poles can be changed by, Multiple Stator WindingsMethod of consequent poles, andPole-Amplitude Modulation (PAM)The pole changing ... Read More

Theory and Circuit DiagramThe no-load test or open-circuit test of an induction motor enables us to determine the efficiency and the circuit parameters of the equivalent circuit of the 3-phase induction motor. The circuit arrangement for the no-load test of the induction motor is shown in the figure.In the no-load test, the motor is uncoupled from the load and the rated voltage at the rated frequency is applied to the stator of the motor to run it. To measure the input power, two-wattmeter method is used.A voltmeter and an ammeter being connected as shown in the circuit diagram (see the ... Read More

An induction machine can also work as a generator without any external supply system. It's called an isolated induction generator. To provide the necessary excitation in the machine, a delta connected capacitor bank is connected across the terminals of it (see the figure).The presence of residual magnetic flux is necessary to provide the initial excitation in the machine. If there is no residual magnetic flux, then, initially, the machine has to run as an induction motor to create residual magnetic flux.At no load, the induction motor is run slightly above the synchronous speed with the help of a prime mover. ... Read More

In a conventional 3-phase induction motor, a balanced 3-phase supply is fed to the stator of the motor from the supply mains. Whereas, in an inverted or rotor fed induction motor, the rotor has 3-phase windings and being fed with the 3-phase balanced supply from the AC mains. The rotor windings of the inverted induction motor must be in star configuration.Construction of Inverted Induction MotorThe figure shows the block diagram of a typical inverted or rotor fed induction motor.The stator of the inverted or rotor fed induction motor has three phase windings which are short-circuited. The rotor also has 3-phase ... Read More