Synchronous Motor V CurvesThe graphs plotted between armature current (Ia) and field current (If) for different constant loads are known as the V curves of the synchronous motor.The power factor of a synchronous motor can be controlled by changing the field excitation, i.e., by variation of field current (If). Also, the armature current (Ia) changes with the change in the excitation or field current (If).Now, let us assume that the synchronous motor is operating at no-load. If the field current (If) is increased from a small value, the armature current (Ia) decreases until Ia becomes minimum. The power factor of ... Read More

Synchronous Motor TorqueThe mechanical power developed (Pm) by any synchronous motor can be expressed as −$$\mathrm{P_{m}=\frac{2πN_{S}\tau_{g}}{60}\:Watts\:\:\:\:\:\:...(1)}$$Also, the mechanical power developed (Pm) is, $$\mathrm{P_{m}=VI_{a}Cos(δ-φ)\:\:\:\:\:\:...(2)}$$Where, NS is the synchronous speed in RPM.τgis the gross-torque in N-m.Therefore, the gross torque of the synchronous motor is given by, $$\mathrm{\tau_{g}=\frac{60}{2π}\frac{P_{m}}{N_{S}}=9.55\times\frac{P_{m}}{N_{S}}N-m\:\:\:\:\:\:...(3)}$$And the shaft torque is given by, $$\mathrm{\tau_{sh}=9.55\times\frac{P_{o}}{N_{S}}N-m\:\:\:\:\:\:...(4)}$$Where, Po is the mechanical power output at the shaft of the motor.From Eqns.(3)&(4), it can be noted that the torque is directly proportional to the mechanical power since the speed of the motor is constant i.e. synchronous speed (NS).Types of Torque in a Synchronous MotorIn order to select a ... Read More

A 3-phase synchronous motor is a 3-phase synchronous machine which is operated as a motor i.e. converts electrical energy input into mechanical energy output.A synchronous motor has a unique feature that is it runs at a constant speed equal to the synchronous speed at all load provided that the load on the motor does not exceed the limiting value. If the load on the motor exceeds the limiting value, then the motor will come to rest and the average torque developed by the motor becomes zero. Because of this, a synchronous motor is not inherently self-starting.A synchronous motor is a ... Read More

Let us first take a look at the block diagram of a synchronous motor −Main Features of Synchronous MotorFollowing are the characteristic features of a synchronous motor −A synchronous motor either runs at synchronous speed or not at all, i.e., while running, it maintains a constant speed from no-load to full load.The speed of a synchronous motor is independent of load.Synchronous motors are not inherently self-starting. Some auxiliary means have to be provided for starting.A synchronous motor will stall if, while running, the load on the shaft is increased beyond the maximum limit that the machine can drive.A synchronous motor ... Read More

An over-excited synchronous motor running on no-load is called the synchronous condenser. It is also known as synchronous capacitor or synchronous compensator or synchronous phase modifier.A synchronous motor can deliver or absorb reactive power by changing the DC excitation of its field winding. It can be made to draw a leading current from the supply with over-excitation of its field winding and therefore, it supplies lagging reactive power (or absorbs leading reactive power).Under-excited Synchronous MotorWhen the synchronous motor is under-excited, then it draws a lagging current form the source and hence supplies leading reactive power (or absorbs lagging reactive power). ... Read More

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