Found 1006 Articles for Electronics & Electrical

A synchronous motor is not inherently self-starting. Therefore, it requires some auxiliary means of starting. In order to start a synchronous motor, there are following two methods −Starting with an external prime moverStarting with damper windingsSynchronous Motor Starting with an External Prime MoverIn this method of starting a synchronous motor, an external motor is used to drive the synchronous motor as shown in Figure-1.The external motor brings the synchronous motor to synchronous speed and then the synchronous motor is synchronised with the AC supply as a synchronous generator. Then the prime mover (i.e., the external motor) is disconnected. Once synchronised, ... Read More

Losses in Synchronous MotorThe losses that occur in a synchronous motor can be divided into the following categories −Copper Losses or I2R LossesCopper losses or I2R losses occur in the armature winding and rotor winding of the motor. These losses occur due to the resistance of the windings.Core LossesCore losses or iron losses occur in the iron parts of the synchronous motor. The core losses in the motor occur because the various iron parts of the machine are subjected to the varying magnetic field. The core losses consist of eddy current loss and hysteresis loss.Hysteresis Loss - Hysteresis loss occurs ... Read More

The complex power input per phase of the synchronous motor is, $$\mathrm{S_{1φ}=VI^{*}_{a}\:\:\:\:\:\:...(1)}$$Taking excitation voltage (Ef) as the reference phasor, then, $$\mathrm{V=V\angle-δ=V\:cosδ-jVsinδ\:\:\:\:\:\:...(2)}$$$$\mathrm{I_{a}=I_{q}-jI_{d}}$$$$\mathrm{\therefore\:I^{*}_{a}=I_{q}+jI_{d}\:\:\:\:\:\:...(3)}$$Hence, from Eqns.(1), (2)&(3), we get, $$\mathrm{S_{1φ}=(V\:cosδ-jVsinδ)(I_{q}+jI_{d})\:\:\:\:\:\:...(4)}$$For a salient-pole synchronous motor, the quadrature-axis current and direc taxis current are given by, $$\mathrm{I_{q}=\frac{Vsinδ}{X_{q}}\:\:\:\:\:\:...(5)}$$$$\mathrm{I_{d}=\frac{E_{f}-Vcosδ}{X_{d}}\:\:\:\:\:\:...(6)}$$Substituting the values of Iq and Id in Eqn.(4), we have, $$\mathrm{S_{1φ}=(V\:cosδ-jVsinδ)\left(\frac{Vsinδ}{X_{q}}+j\frac{E_{f}-Vcosδ}{X_{d}}\right)}$$$$\mathrm{\Longrightarrow\:S_{1φ}=\left(\frac{v^{2}}{X_{q}}sinδcosδ+\frac{VE_{f}}{X_{d}}sinδ-\frac{v^{2}}{X_{d}}sinδcosδ\right)+j\left(\frac{VE_{f}}{X_{d}}cosδ-\frac{V^{2}}{X_{d}}cos^{2}δ-\frac{V^{2}}{X_{d}}sin^{2}δ\right)}$$$$\mathrm{\Longrightarrow\:S_{1φ}=\left[\frac{VE_{f}}{X_{d}}sinδ+\frac{V^{2}}{2}\left(\frac{1}{X_{q}}-\frac{1}{X_{d}}\right)sin2δ\right]+j\left[\frac{VE_{f}}{X_{d}}cosδ-\frac{v^{2}}{2X_{d}}(1+cos2δ)-\frac{v^{2}}{2X_{d}}(1-cos2δ)\right]}$$$$\mathrm{\Longrightarrow\:S_{1φ}=\left[\frac{VE_{f}}{X_{d}}sinδ+\frac{V^{2}}{2}\left(\frac{1}{X_{q}}-\frac{1}{X_{d}}\right)sin2δ\right]+j\left[\frac{VE_{f}}{X_{d}}cosδ-\frac{v^{2}}{2X_{d}X_{q}}\left\{(X_{d}+X_{q})-(X_{d}-X_{q})cos2δ\right\}\right]\:\:\:\:\:\:...(7)}$$Also, $$\mathrm{S_{1φ}=P_{1φ}+jQ_{1φ}\:\:\:\:\:\:...(8)}$$Comparing Eqns.(7)&(8), we get the real power per phase in watts, $$\mathrm{P_{1φ}=\frac{VE_{f}}{X_{d}}sinδ+\frac{V^{2}}{2}\left(\frac{1}{X_{q}}-\frac{1}{X_{d}}\right)sin2δ\:\:\:\:\:\:...(9)}$$Thus, the total real power for three phases is, $$\mathrm{P_{3φ}=3P_{1φ}=\frac{3VE_{f}}{X_{d}}sinδ+\frac{3V^{2}}{2}\left(\frac{1}{X_{q}}-\frac{1}{X_{d}}\right)sin2δ\:\:\:\:\:\:...(10)}$$The first term on right-hand side of Eqn.(10) is called the excitation power and the second term is called the reluctance power. Also, the reactive power per ... Read More

Let, Ef=Excitation voltageV= Terminal voltage per phase applied to the armatureIa=Armature current per phase drawn by the motor from the supplyRa= Effective armature resistance per phaseXS=Synchronous reactance per phase of armature windingCosφ= Power factorδ=Torque angleThe voltage equation of a cylindrical rotor synchronous motor is, $$\mathrm{V=E_{f}+I_{a}(R_{a}+jX_{S})\:\:\:\:\:\:...(1)}$$$$\mathrm{\Longrightarrow\:V=E_{f}+I_{a}R_{a}+jI_{a}X_{S}\:\:\:\:\:\:...(2)}$$The phasor diagrams of a 3-phase cylindrical rotor synchronous motor operating at different power factors can be drawn with the help of eqn.(2).Phasor Diagram at Lagging Power FactorThe phasor diagram of the synchronous motor operating at a lagging power factor Cosφ is shown in Figure-1.Consider the synchronous motor is taking a lagging current from the supply. ... Read More

The excitation voltage of synchronous motor refers to the DC supply given to the rotor to produce the required magnetic flux. The excitation voltage (Ef) of a synchronous motor can be determined for different power factors using complex algebra.Let the supply voltage (V) be taken as the reference voltage. Thus, $$\mathrm{V=V\angle0°=V+j0\:\:\:\:\:\:...(1)}$$Then, the armature current at different power factors is given as follows, For lagging power factor −$$\mathrm{I_{a}=I_{a}\angle-φ=I_{a}cosφ-jI_{a}sinφ\:\:\:\:\:\:...(2)}$$For unity power factor −$$\mathrm{I_{a}=I_{a}\angle0°=I_{a}+j0\:\:\:\:\:\:...(3)}$$For leading power factor −$$\mathrm{I_{a}=I_{a}\angle+φ=I_{a}cosφ+jI_{a}sinφ\:\:\:\:\:\:...(4)}$$Now, the excitation voltage of the synchronous motor is given by, $$\mathrm{E_{f}=V-I_{a}Z_{S}\:\:\:\:\:\:...(5)}$$Where, ZS is the synchronous impedance and is given by, $$\mathrm{Z_{S}=R_{a}+jX_{S}\:\:\:\:\:\:...(6)}$$Case 1 – Excitation Voltage ... Read More

Consider an under-excited (i.e., Ef < V), 3-phase cylindrical rotor synchronous motor driving a mechanical load. The figure shows the per phase phasor diagram of the motor. Since the motor is under-excited, it will be operating at a lagging power factor cos φ.In practice, for a synchronous motor, XS>>Ra, then the armature resistance (Ra) of the motor can be neglected. Since Ra is neglected, the armature copper loss will be zero. Therefore, the mechanical power developed (Pm) by the synchronous motor is equal to the input power (Pi) to the motor.Also, Ra= 0, Er=IaXS, thus the armature current (Ia) lags ... Read More

Hunting in Synchronous MotorHunting is the phenomenon of oscillation of the rotor about its steady state position or equilibrium state in a synchronous motor. Hence, hunting means a momentary fluctuation in the rotor speed of a synchronous motor.In a synchronous motor, when the electromagnetic torque developed is equal and opposite to the load torque, such a condition is known as "condition of equilibrium" or "steady state condition".In the steady-state, the rotor of the synchronous motor runs at synchronous speed, thereby maintaining a constant value of torque angle (δ). If there is a sudden change in the load torque, then the ... Read More

Assume that initially, the rotor of a synchronous motor is stationary. When a pair of rotating stator poles sweeps across the stationary rotor poles at synchronous speed, the stator poles will tend to rotate the rotor in one direction and then in the other direction. As a result, the rotor experiences a torque first in one direction and then in the other. However, the rotor has high inertia and the stator field slides by so fast that the rotor cannot follow it. As a result, the rotor cannot move and hence the resultant starting torque is zero, i.e., a synchronous ... Read More

Assume that the rotor of a synchronous motor is stationary. When a pair of rotating stator poles sweeps across the stationary rotor poles at synchronous speed, the stator poles will tend to rotate the rotor in one direction and then in the other direction. As a result, the rotor experiences a torque first in one direction and then in the other. However, the rotor has high inertia and the stator field slides by so fast that the rotor cannot follow it. As a result, the rotor cannot move and hence the resultant starting torque is zero.But, if the rotor poles ... Read More

A synchronous motor is a doubly-excited system, i.e., it is connected to two electrical systems −A 3-phase supply is connected to the armature winding.A DC supply is connected to the rotor field winding.The figure shows the equivalent circuit for one phase of a three-phase synchronous motorLetV = Terminal voltage per phase applied to the motorEf = Excitation voltageIa = Armature current per phase drawn by the motor from the supplyRa = Effective armature resistance per phaseXS = Synchronous reactance per phase of the motor armature windingZS = Synchronous impedance per phase of the armatureBy applying KVL in the equivalent circuit ... Read More