SYNCHRONOUS MOTOR PHASOR DIAGRAM
• The voltage equation for a synchronous motor
• For an alternator, phasor Ef is always ahead of phasor Vt , just as field poles are ahead of ør , For a synchronous motor, phasor Ef is always behind phasor vt , just as the filld poles are behind ør,
For lagging power factor
For unity power factor
For leading power factor
POWER FLOW THROUGH AN IMPEDANCE
• Two ac voltage source E1 and E2 interconnected through an impedance Z∠θZ. With the current l flowing from E1 to E2.
Here impedance angle θZ is given by
• The power at the source end of the impedance P1 = E1 (component of l in phase with E1)
• The power at the load end P2 = E2 (Component of in phase with E2)
Power Flow in Cylindrical Rotor Synchronous Machine.
• Power input to generator
• Power output of generator
For a cylindrical rotor synchronous motor
• Power input to motor
• Power output of motor
• The power at the shaft for a synchronous motor is Pom minus the rotational losses (friction, windage and core losses). Here Pom is called the mechanical power developed or gross power developed. Similarly the mechanical power input to generator is Pg plus the rotational losses.
• The difference between input (pig or pim) and output (Pog or pom), for either a generator or a motor, must be equal to ohmic loss la2 ra .
• Generally, armature resistance ra is negligible
az = 0 and Zs = Xs
• Power input to generator is at the terminals where the voltage is Ef and power output of the motor Pom is also at the same terminals. The powers Pig and Pom Should therefore be equal and opposite to each other but with δ replaced by (-δ)
Pom = Pig
Similarly Pim = - Pog
maximum Power Conditions
For maximum power output
load angle δ = impedance angle θz.
• maximum power output from a generator is
• maximum power out ( or maximum power developed) in case of a motor
For maximum power input
Load angle , δ = 90 + αZ = 180 - impedance angle θz.
• Maximum power input to generator
• Maximum power input to motor
• Reactive power at the generator output terminals Qog = E2 (component of l in quadrature lagging E2)
• Output terminal for the generator are same as the input terminals for the motor.
Condition For maximum Reactive Power
For a generator
δ + αz = 0
For a motor
δ - αz = 0
when Pim is maximum, δ = 90 + αz , the reactive power under this condition
If ra = 0 then
• An overexcited synchronous machine delivers reactive power whereas an underexcited one absorbs reactive power. Under normal excitation, it neither absorbs nor delivers reactive power.
POWER FACTOR CONTROL
• Power factor of synchronous machine is control by the adjustment of their field excitation.
Effect of field current on synchronous motor power factor
Synchronous motor V-curves and power factor versus field current curves
• When excitation emf is Ef1, the alternator is underexcited and the armature current la1 is leading Vt = Vb = bus-bar voltage.
• For Ef1 , underexcited alternator operates at a leading and absorbs reactive power from infinite bus.
Effect of field current on an alternator connected to infinite bus
• With an increase in field current, excitation emf rises. For excitation emf Ef2 , armature current la2 is im phase with Vt = Vb. Under unity pf operation, the alternator is said to be normally excited and it neither delivers nor absorbs reactive power. For Ef3 more than Ef2, la3 lag Vt. The overexcited alternator operates at a lagging pf and delivers reactive power to infinite bus.
• Just like a synchronous motor, plot of la versus lf is called V-curve of a alternator connected to an infinite bus. The power factor versus field current curve, known as inverted V-curve.
Cylindrical-rotor synchronous Machine
• A generator and is feeding power to an infinite bus of constant voltage Vt.
Salient pole synchronous generator single line diagram and phasor diagram for a lagging pf
• The per phase power delivered to the infinite bus
Salient-pole Synchronous Machine
• The per phase power delivered to the bus.
• The total power consists of a fundamental component and a second harmonic component sin2δ
• For a salient pole synchronous generator, the per phase reactive power in terms of power angle δ and for a lagging power facor is given by
• The synchronizing power coefficient is a measure of the stiffness of electromagnetic coupling between stator and rotor fields. Too large stiffness of coupling means that the motor tends to follow closely, the variation of speed caused by the disturbance in electric power supply. In case there is no power-supply disturbance, then too much stiffness coupling would cause the motor speed to remain practically constant, regardless of the mechanical load fluctuations.
SYNCHRONOUS MACHINE STABILIYT
• A synchronous machine connected to an infinite bus is said to be working in a stable condition, if it is in synchronism or in step with the bus.
• The tendency of a synchronous mechine to develop forces so as to maintain synchronism and equilibrium is called stability.
• A stability limit represents the maximum power flow possible, when the synchronous machine is operating with stability.
Steady state stability Limit
• The maximum power flow possible through a particular point without loss of stability, when the power is increased very gradually.
• The steady-state limit can be improved upon as follows:
• A synchronous machine operates satisfactorily, if the mechanical speed to the rotor is equal to the stator field speed.
• Any departure from these conditions, gives rise to synchronizing forces which tend to maintain this equality.
• Phenomenon, involving the oscillations of the rotor about its final equilibrium position, is called hunting.
• During the rotor oscillations or hunting. the orientation of phasor Ef changes relative to fixed voltage Vt and because of this reason, hunting is also called phase-swinging.
Reduction of Hunting
• Damper windings.
• Use of flywheels which helps in maintaining the
rotor speed constant.
• By using suitable synchronizing power coefficient.
• Damper windings consist of low- resistance copper. brass or aluminium bars embedded in slots in the pole-faces of salient-poles machines. The projecting ends of the bars are connected to short circuiting strips of the same material asused for the bars. Sometimes interpolar connectors are omitted to form incomplete type of damper winding.
• In damper winding techniques, for reducing hunting resistance (Rd) of damper windings should be minimum, While for good starting torque, damper bars should have a low resistance therefore we have to make compromise in the value of damper winding resistance. it should be in between two.
• In alternator, the value of damper winding resistance should be low for minimizing hunting.
EFFICIENCY OF SYNCHRONOUS MACHINES
• The various losses in synchronous machines are:
(a) friction and winding loss and
(b) open circuit core loss.
(c) l2 R loss in armature winding.
(d) l2 R loss in armature winding.
(e) in iron and
(f) in the armature conductors.
• The combination of direct load loss and stray load losses is referred to as shot circuit load loss.
The Stray load loss consists of two components, namely:
• iron losss or core loss due to armature leakage flux and
• armature ohmic loss due to skin effect and eddy currents in the armature conductors.
POWER FLOW DIAGRAMS
• NO- load rotational loss
Pr = Friction and windage loss + open-circuit loss pr + vf lf = constant losses Short=circuit load loss - 3la2.ra + stray- load loss.
• Maximum efficiency in a synchronous machine occurs when variable losses = constant losses. or 3la2.ra = Pr +Vf .lf where lam is the armature current at which maximum efficiency occurs in the synchronous machine.
• Total alternator losses = F.W.loss + open-circuit core loss + short-circuit load loss + field - circuit loss.
= Wf + W2 + W3 + Vf lf
STARTING OF SYNCHRONOUS MOTOR
• A synchronous motor is not self starting. It can be started by the following two methods.
Stator field rotates at NS
at starting Nr = 0
Let, Ns = 1500 rpm
At starting rotor field stationary and stator field is rotating at h higher speed that is synchronous. Due to the interaction between rotor and stator poles, the torque developed reverses after each half revolution of stator field. Due to its inertia rotor can not respond so quickly hence it remains stationary that's whey synchronous motor is non self-stationary that's why synchronous motor is non self- starting if by some external means rotor is made to rotate at a speed close to synchronous then due to the locking of stator and rotor field rotor will continue to rotate at synchronous speed.
• Solid copper (cu) or Aluminium (Al) are embedded in the slots cut in the pole shoe and short circuited by end rings like squirrel cage induction motor (SCIM).
At starting no-field excitation is given, so there is relative motion between damper winding and stator field.
Ns - Nr = Ns - 0 = Ns
• AT Starting no excitation is given to the rotor, Due to the relative motion between damper winding and stator field the induced current in damper winding opposes the relative motion and hence starting torque is produced due to induction motor principle and rotor start rotating at a speed some what less than synchronous. Now dc excitation is given and stator and rotor field remains continue to rotates at synchronous speed, when rotates at synchronous speed there is no relative motion between damper winding and stator field. No induced current in the damper winding hence no role of the damper winding in steady state.