sem unit 1
TRANSCRIPT
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UNIT-I
PERMANENT MAGNET SYNCHRONOUS MOTOR
Introduction
Ref: Special Electrical Machines By Gnanavadivel
In conventional Synchronous Motor, the rotor carries the field winding which is excited by a DC
supply to produce the magnetic flux needed for the operation of the motor.
The slip ring and brushes are necessary to excite the field winding by transferring current from a
stationary terminal to the rotating rotor.
Now, the electromagnets and the field magnets are replaced by permanent magnets. This
eliminates the need of slip ring and brushes assembly.
Those motor using permanent magnets to produce the required flux without brushes are calledpermanent magnet synchronous motor or burshless1.1Construction
The construction is very similar to conventional synchronous motor but it differs only in therotor construction as shown in the figure 5.1.
Important parts of the motor are stator and Rotor. The stator consists of outer frame whichencloses the whole machine and protects it from the environmental hazards.
The outer frame is usually made of cast iron (or) steel. Inside the stator frame, stator core is fixed which consist of thin lamination to reduce eddy
current loss and made up of soft magnetic steel material mixed with silicon to reduce the
Hysteresis losses.
The stator core has slots in it which are also laminated. The slots are used to house the polyphase stator winding called armature winding made of copper material.
The thickness of the lamination depends on the frequency of the armature voltage, cost ofthe machine and core loss component of the machine.
Usually for large machine, lap type Double layer winding will be provided but for smallermachines solenoid (or) random winding is used.
The rotor construction can be two types, cylindrical pole type and salient pole type. Usuallycylindrical type of rotor is used to maintain the air gap uniform flux distribution. The permanent magnet made of rare earth magnetic material such as ferrite, cobalt are used. The rotor also consists of damper winding which is used to damp the oscillation near the
synchronous speed and also used to start the motor.
The rotor also carries the shaft and bearing systems. The various types of rotor construction used are
i. Peripheral: the magnets are located on the periphery of the rotor and the fluxis radial.
ii. Interior: interior of the rotor carries the permanent magnets and the flux isdistributed radially.
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iii. Claw-pole (or) Lundell: The permanent magnets in this structure are discshaped. The flux is axial.
iv. Transverse: The permanent magnets are in between the soft iron poles andthe flux is circumferential.
Figure 1.1
Working Principle The operation of the Permanent Magnet synchronous motor is very similar to the
conventional synchronous motor.
This motor is also not self starting hence additional winding is placed on the rotor. Once thesynchronous motor is started by applying voltage at certain frequency and then it is pulled
into synchronism.
The motor speed is decided by the frequency of the supply which excites the phasewindings of the stator.
Necessary torque is produced in the motor for the motor by the interaction of fluxesproduced by the permanent magnet Rotor and the excited stator winding.
The torque produced is called as synchronous Torque. The hunting near the synchronousspeed is possible which is eliminated by using the damper winding.
Due to the presence of the damper winding, the synchronous motor can be started fromzero speed as an induction motor.
The stator phase windings can be excited with variable frequency and the amplitude toachieve wide range of operating characteristics and motor is highly controllable.
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Advantages:
1. Slip rings and brushes are absent, so there is no sparking.2. These motors are flexible as they are highly controllable.3. No DC field excitation is required. So field losses are reduced.4. It requires less space as field windings are absent.5. They have low inertia & friction.6. These motors are reliable and have long life.Disadvantages:
1. The electronic circuitry driving the motor is complex and complicated.2. There is possibility of demagnetization due to excessive currents.3. The flux density produced in the airgap is limited due to permanent magnet.Applications:
1. These motors are used in the applications where constant speed is required such assynthetic fiber drawing, turn table drives in record players, spindle drives in hard disk in
computers.
2. Used for tape drive for video recorders, in the field of aerospace, gyroscope motors andbiomedical instruments like artificial heart pumps.
3. Used in textile and glass industries, hand drills, vacuum cleaners etc.Characteristics features of permanent Magnets synchronous Motor
1. Sinusoidal (or) quasi-sinusoidal distribution of magnetic flux in the airgap.2. Sinusoidal (or) quasi-sinusoidal Current waveforms.3. Quasi-sinusoidal distribution of stator conductors (i.e.) short pitched and distribute (or)
concentric stator winding.
1.2 TORQUE EQUATION OF PM SYNCHRONOUS MOTOR
Ref: Special Electrical Machines By Gnanavadivel
The torque production of the motor can be analyzed in terms of the interaction of the
magnet flux produced by the permanent Magnet with the stator ampere-conductor distribution
in the motor. The figure 5.2 shows the basic concept of the motor with two poles. The stator
conductors are distributed sinusoidally around the stator bore, such that in any angle d, thenumber of conductors is given as
No. of conductors in the small angle d= sin p.d
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Considering that one turn consists of two conductors in series, then number of turns per pole
Np is given as
Np=
Figure 1.2
This means that if all the poles are connected in series, then Ns is automatically equal to the
number of turns in series per phase. The distribution of the turns per pole for two pole andfour pole motors is shown below figure 1.3
Figure 1.3
In the following analysis the angle is in mechanical degree (or) radians.
The stator ampere-conductor distribution is a sinusoidal distribution such that the sine-
distributed current has the same form as the conductor distribution. So that, at the angle d, theampere conductors following in the positive direction (i.e.) out of paper is given as
Ampere conductor in the small angle d=i sin p.d
The rotor magnetic flux distribution is centered on its north d-axis which is displaced by a
positive angle from theaxis of the stator winding which is given as
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B()=sin(P+(/2-))B()=sin(/2+(P-))B()=cos(P-)Where is expressed in electrical radians.
The force on the elementary group of ampere-conductors for a small angle dis in thecircumferential direction and it is given as
F=Bil sinP.cos(P-)
Similarly the corresponding force on the opposite element also will be produced. So two forces
together produces a couple 2 F ron the stator. As equal & opposite couple acts on the rotor andthe total electromagnetic torque on the rotor is the integral of the elementary area over the
whole air gap periphery (i.e.) over P-pole pairs and Torque is given as
T=-P dWhen P=1 then
=-2rBl i T=-2rBl i
T=-2rBl i
T=-2rBl i
T=-2rBl i Integrate the above equation and apply the limits we get the below expression for torque
T=
Maximum positive torque is obtained with =-
(i.e.) rotor north d-axis lagging 90electricalbehind the axis of the stator ampere-conductor distribution.The above analysis has been carried out for a stationary winding. To provide a constant Torque
with the rotor rotating at a steady speed, the stator-ampere-conductor distribution must be
made to rotate in synchronism with the rotor. This can be done by means of poly-phase
winding supplied with poly-phase balanced currents. With P-Pole pairs, if Np=Ns/2 is the
number of sine distributed turns per pole, the total numbers of turns per phase in Ns. If the
phase current flows through all those windings in series, then with balanced sine wave currents
and three phase windings whose axes are 120 apart, the rotating ampere-conductorsdistribution can be derived as
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Rotating ampere-conductors
=icost sin P+icos (t-120) sin (P-120) +icos (t+120) sin (P-120)=
I sin (P-t)
The rotating magnetic flux distribution is given as B()=Bcos(P-t-)The torque provide is obtained using the same expression as for the stationary winding with
(P-t) substituted for P, it is given as,
T=I
Where =-. The angle is called the torque angle and it is positive for motoring and negativefor braking. It is measures in electrical degree (or) radians.
If the phase windings are divided into a parallel paths, the above equation remains valid
provided that I is the total phase current and there is no change in the total number of turns perphase (Ns), but the number of turns in series per phase is the Ns/a.
The Flux Density B in the torque equation is the peak air gap flux density produced by themagnet acting alone and does not include any contribution due to the mmf of the stator
currents. The armature reaction mmf also modifies the air gap flux density but it does not
adversely affect the torque expression, unless it significantly affects the saturation level of the
magnetic circuit.
In normal operation the stator frequency in radians/sec is made equal to the rotational
frequency in electrical radians/sec and it is given as
=2f electrical rad/secThe mechanical angular velocity is given as
The stator ampere-conductors distribution rotates in synchronism with the rotor and the torque
angle is kept constant by means of Vector control(or) field oriented control which requiresa shaft position sensor. If the supply frequency and rotational frequency are unequal, then the
motor will be running asynchronously. So that no average torque will be produced but therewill be a large alternating torque at the beat frequency (or) pole-shipping frequency.
1.3 E.M.F EQUATION OF PM SYNCHRONOUS MOTOR
Ref: Special Electrical Machines By Gnanavadivel
The Emf equation of the motor can be derived by considering the Emf induced in the
elementary group of conductors as shown in figure 5.2 . from the figure drawn the two pole
motor has P=1, for a motor with P-Pole pairs in series, the Emf can be given using the B L V
formulation as
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de=B()lr sin PdBut B()=Bcos(P-t-)
=Bcos(P-(t+))
When we integrate the elementary group of conductors for the complete distribution we get
the instantaneous phase Emf given as
e=2
e=2Bl r
e=2Bl r
e=2Bl r
e=2Bl r
e=2Bl r
Integrate the above equation and apply the limits we get the equation for the instantaneous EMF which
is given as
e=2Bl r sin(t+) volts
e= sin(t+) voltsWhere =2Bl r The R.M.S phase Emf is therefore given as
=
volts
The line-line Emf is
=3 Here again the flux density B is the peak air gap flux density produced by the magnet acting
alone and does not include the contribution of mmf due to stator currents.
The Emf equation can also be derived from Faradays law. In this derivation of Emf, armaturereaction is also taken into consideration. Faradays law is more rigorous then the BLV formation but itis useful to show that for E both methods give the same result.
By Faradays lay, the instantaneous emf induced in the stationary phase winding is given as
e=- volts
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Where is the instantaneous flux linkage.
To calculate the flux linkage, consider the coil formed by the elementary group of conductors within
the angle and assume that the return conductors of coil are located with the angle . Althoughresults are derived for P-pole pairs.
On open circuit, there is no current in the coil and all the flux is due to the permanent Magnet Rotor
The flux through the elementary coil is
(webers)
But B()=Bcos(P-t-)
Integrate the above equation and apply the limits we get the instantaneous Flux which is given as
sin Pcos(t+)(webers)
Where D=2 ris the diameter of stator bore.The flux per pole can be extracted from this expression by putting = and t=0. Thus
=
(webers)
This is the fixed flux that rotates with the rotor. The flux linkage of the elementary coil is
D= [ ]
The total flux linkage of the winding is obtained by integrating the contribution of all the elementary
coil with P-Pole pairs, Thus,
=P
= P
sin P d
=P
d
=P
d
=
d
Integrate the above equation and apply the limits and few get the Instantaneous flux linkage as
= cos(t+)
=cos(t+)
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Where = = The subscript m indicates flux produced by Magnet only.
By Faradays law the instantaneous phase Emf is
e=-
=sin(t+) volts
The r.m.s phase emf is given as
= volts1.4 Inductance of phase winding of PM synchronous Motor
Ref: Special Electrical Machines By Gnanavadivel
Consider the figure 5.2 (ie) single phase, two pole sine-distributed winding. Here we consider
the flux which is produced by the current in the stator winding and we assume that the magnet is un-magnetized while we calculate the inductance by determining the flux linkage of the winding due to its
own current i.
Assume that the steel core in the rotor and stator have infinite permeability, then the mmf is
concentrated entirely across the air gap. Across each air gap, the mmf drop is equal to one half of the
ampere conductors enclosed within the amperes law contours (or) flux line and it is given as
g=
sinPd
Integrate the above equation and apply the limits and we get the following expression
g= cos P
= cos PThe flux density across the gap and the magnet is assumed to be radial and the magnet is assumed to
be equivalent to an airgap of length . Therefore the effective airgap length g is given asg=g+
Hence, B()==cos P= cos PWhere
=The subscript a has been added to indicate the peak airgap flux density to denote that it is generatedby armature current.
By integrating the flux density around the periphery of the airgap, the fundament armature reaction
flux per pole can be determined and given as
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= (webers)
Where again D=2ris the stator bore. This expression is exactly the same form as the flux pole of themagnet and therefore it produces a flux linkage given as
=
The self inductance is obtained as the flux linkage per ampere with turns in series per phase and it isgiven as=
(Henry)The inductance is only half the value which would be obtained with the same number of turns
concentrated into one pole pair spanning 180 degree.
The Inductance which is calculated above is the actual airgap inductance (ie) the value which wouldbe measured with rotor stationary and unmagnetised with the other phases open circuited and withnegligible leakage inductance from the slots (or) the end turns.
1.5 SYNCHRONOUS REACTANCE OF PM SYNCHRONOUS MOTORRef: Special Electrical Machines By Gnanavadivel
We know that three sine-distributed phase windings carrying balanced three phase
sinusoidal currents produce sine-distributed ampere-conductor distribution which is represented
by the expression.
Three phase Rotating ampere-conductors
=I2
sin(p-t)
This will setup a rotating flux wave in the airgap given as
B()=cos(p-t)Where = I2
This rotating flux wave which is established by armature reaction, generates voltage in all the
three phases.
In each Phase, the voltage is proportional to current I and it is therefore given as the voltage drop ()drops across winding Reactance called as synchronous Reactance . By substituting peak fluxdensity into the expression derived earlier for emf and diving by I we get synchronous Reactance as
follows
w.k.t =
Where =
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= =
Therefore We know that
E=== Where i=I2
Therefore= (ohms)This expression applies to an ideal two poles sine distributed three phase winding with turns in series per phase and it neglects the leakage inductance of the slots and end turns.
1.6. PHASOR DIAGRAMIf the magnets are on the rotor surface and if the shaft cross section is circular, the sine wave
motor is a mom salient Pole synchronous Motor (ie) its d -axis and q-axis synchronous Reactancesare equal. In the steady state with balanced sinusoidal phase currents, the operation can be represented
by the phasor diagram shown in figure 5.4.
Figure 1.4 Phasor diagram of surface magnet sinewave motor
The construction of the phasor diagram is simple and its analysis provides the basis for understanding
the performance characteristic and what happens at different speed & torques.
We know that the o-pen circuit phase emf E is a sinewave which lags behind the magnetic flux by 90electrical.
Its r.m.s value is given as =kf Volts
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The phasor relationship between and the fundamental flux linkage due to the magnet can bewritten as
=j=j Volts
The subscript din the magnetic flux linkage denotes that this phasor is synchronized with the directaxis of the rotor. The subscript i indicates the fundamental space harmonic component. The subscriptq in denotes that it is synchronized with the q-axis. In all phasor diagrams, the d-axis is taken todefined the real axis of the complex plane of the phasor diagram. Note that as the rotor flux rotates in
space, the flux linkage of a stationary phase winding pulsates in time.
The angle defined the position of the physical rotor d-axis at t=0, measured from the positive axis ofthe phase a winding.
Next we determining the current phasor and we read the rotating ampere-conductor distribution of all
three phases taken together. Assuming balanced currents.
=icost=icos(t- )=icos(t+ )
The axes of the three windings are displaced by 120 degree in such a way that the rotor d-axis rotates
past them in the sequence a,b,c. this gives rise to the ampere-conductor distribution given as
Ampere-conductor distribution
=icost sin+ icos(t- )sin(- )+ icos(t+ )sin(+ )=
I2
sin(-t)
The phasor RIrepresents the voltage drop across the phase resistance and it is parallel to I.Similarly, the voltage drop across the synchronous reactance is represented by jI and leads thecurrent phasor by 90. The sum of the back emf and the voltage drop phasor must be equal to theapplied voltage at the terminals. Thus
=E+RI+ jINext, neglect the resistance in order to bring out the essential mechanism of operation. So the below
phasor diagram in the figure 5.5 gives the current and voltage resolved into d-axis and q-axis
components (ie) I= .
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Figure 1.5
In figure 5.5, the current leads the d-axis by angle less than 90, and lags the q-axis by the angle ,where
-=-
The minus sign indicates that the angle is measured from the q-axis in the normal positive direction.
Figure 1.6
The d-axis and q-axis components of current are given by
=-Isin
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= I cosIf is positive, then the armature (or) stator current produces an m.m.f distribution around the air gapthat tends to increase the d-axis flux produced by the magnet. This conduction, the armature reaction is
said to Magnetizing. The flux produced by the stator mmf induces the voltage jin the d-axis andin the q-axis of the phasor diagram. The q-axis component adds to j. The magnet flux densityis increased, so that the operating point moves up the demagnetization characteristics and may end up
in the first quadrant with .In the figure 5.6, is negative and the stator mmf is also negative and demagnetization will occur. Thepower factor angle is given by
=-(demagnetization)
=+(magnetization)
T is less in demagnetization than the magnetization. Therefore, high power
factor can be achieved with operation in the demagnetization Mode.
1.7. CIRCLE DIAGRAM OF PM. SYNCHRONOUS MOTOR
Ref: Special Electrical Machines By Gnanavadivel
The phasor diagram and associated voltage equations can be used to derive control laws and
predict the performance of the sinewave motor in closed analytical form.
If the resistance is neglected, then from phasor diagram (a) and (b)
=-Vsin=-=Vcos=+
is given by the following equation for synchronous Machines on d,q-axistheory, ie
T=3P[ ]Where p is the number of pole pairs and the phase and the phase number is three.
The flux linkages , are r.m.s per phases given by
Therefore the Torque is given by
T= [ ] (Nm)
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The first term is Magnet alignment Torque and the second term is called Reluctance Torque. Insurface Magnet rotor, = =.So, there is no reluctance torque and therefore
T= (Nm)
The above equation is valid even when the resistance is not zero. At a given speed, is fixed by themagnetic flux and the torque is proportional to the q-axis current . Since is itself proportional tospeed.
The amount of current that can be supplied limited by the heat dissipation capability of the motor and
by the current rating of the converter. It can also be limited by the converter voltage, which must
overcome the back Emf and the voltage drops across the synchronous Reactance and the resistance. In
the complex plane of the phasor diagram, the maximum continuous converter current limits thecurrent phasor to a circular locus described by the equation.
=
+
Fig 1.7
This is shown in the figure 5.7. The maximum converter voltage limits the current phasor.To another circular locus with a different radius and a different center and it is derived as follows, if
=+Then = +( ) =Then
=+(
)
The above equation represents the circle with centre at the point (- ). The offset is independent of
frequency and speed since both are proportional to frequency. If the controller is a PWM sine
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wave supply, then at low speeds there is usually sufficient voltage available to cause the voltage
limited locus to enclose the current limit locus, so that maximum current can be obtained at any angle.
The most advantageous angle for the current is obviously along the q-axis, since this maximizes the
torque per ampere. In general at low speeds the PWM duty cycle is low and the phase voltage is
Chopped Down to a value much less than Operation along OQ with torque proportional tocurrent.
1.8 SPEED-TORQUE CHARACTERISTICS OP PM SYNCHRONOUS
MOTOR
The speed-Torque characteristics can be drawn with respect to the circle diagram shown in the
figure 5.8.As the speed and frequency increases, the current limit locus remains fixed but there comes a
speed at which the radius of the voltage limit locus begins to decrease. This happens when the PWM
duty cycle reaches its maximum and the phase voltage equals the maximum available sine wave from the converter. This point is called as saturated point of the PWM control shown in thick lines.
Figure 1.8
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Figure 1.9
The operation along OQ is still possible, but it is only just possible for the currents to reach its rated
value at Q.The speed at which this happens is called the Corner point speed. It is themaximum speed at which full torque can be developed.
If the speed increases further, the radius of the voltage limit locus decreases. The maximum
current is now at the interaction of the two circles. The decreasing radius of the voltage limit
circledrags the maximum current phasor further and further a head of the q-axis currentdecreases while the d-axis current increases in the negative direction (Demagnetization).This
continuous unit point D, at which speed the maximum current Ic can still be forced into the motor
and it is entirely in the d-axis so that no torque is developed. The power function at this point is
zero and the current is wholly demagnetizing.
The logical OQ and OD together form the limiting locus for the current phasor throughout the
whole speed range and gives rise to torque-speed characteristics. Along OQ maximum torque can
be developed with maximum oriented along q-axis. Along QD the torque decreases until atpoint D, ie T=0 with maximum current still flowing but oriented in the d-axis in the negativedirection. The speed-torque curve is shown in the figure 5.9
The ratio between the speeds at point D and Q is
K==
If we neglect the resistance at Q we have
=0;=;=
and =-.
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The subscript C in the synchronous reactance denotes the value at the corner point frequency.From the phasor diagram
I=j=
And +
=
At point D;
I=== Equating the expressions for
at the two speeds, we get
K=
We can define as the per unit open circuit voltage at the corner point with the maximum r.m.sac voltage of the base voltage, ie.
=
Then k=
At the corner point, the d-axis current is zero and the power factor is given by
cos==
Also, sin= =
==
Where= which is the base value of synchronous Reactance.Where is the per unit synchronous reactance at the corner point.If the speed is increased beyond point D, there is a risk of over current because the back Emf
continues to increase while the terminal voltage remains constant. The current is almost a pure
reactive current flowing from the motor, back to the supply. There is a small q-axis current and a
small torque because of losses in the motor and the converter. The power flow is reversed and this
mode of operation is possible only if the motor over turns the converter. The reactive current islimited by the synchronous reactance and as the speed increase it approach the short circuit currentwhich may be many times the normal rating of the motor winding (or) the converter. The currentis rectified by the fly back diodes and over voltage on the dc side of the converter. An effective
solution is to use an over speed relay to short circuit the phase winding in to a three phase
resistor(or)short circuit, to produce a braking torque without stressingthe converter.
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1.9. CONVERTER VOLT-AMPERE REQUIREMENTS AND TORQUE PER
AMPERE:
Ref: Special Electrical Machines By Gnanavadivel
With a torque angle of 90 degree, the torque per r.m.s ampere of phase current in the three
phase sine wave motor is given as (PM synchronous motor)
=
(Nm/A)
(Ie) it is .Where as in the PM brushless DC motor, assuming 180 magnets arcs, star connection and
120square wave phase currents, the torque per pack ampere of phase current is given as
=4l ()
The r.m.s phase current T is derived from 120square wave I given as
I=i
Where I is the peak (or) flat top value of the phase current is
=
Bl ()
With the above two expressions, the ratio of torque per ampere in the two motor can be compared.
(i.e.) Torque per r.m.s ampere= =
=1.47
With equal peak current, the factor is 1.27
Therefore with equal r.m.s phase current, the torque of the square wave (or) per brushless DC
motor exceeds that of the sine wave (or) synchronous motor by the factor 1.47. The above analysis
neglects many important effects such as armature reaction and losses.4
Now the comparison is to be carried out to the volt-ampere requirements of the Electronic
converter. A very simple estimate of the converter rating can be made in terms of the total KVA
rating of its main switches and per KW of power fed to the motor. The relevant parameters arediscussed below
With respect to the r.m.s current in each switch, if q is the phase number, then
R.M.S =2q x
Where is the r.m.s current in each switch and is the peak voltages across each switch.For the converters normally used in BLDC motor, the peak device voltage is normally equal
to the DC supply voltage, because each switch must block this voltage while the other one in the
same phase leg is conducting. So usually there must be a margin for the voltage spikes caused by
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stray inductance and reverse recovery of diodes. Therefore the DC supply will be used for the
comparison.
With respect to the peak current in each switch.
Peak =2q
Where is the peaks current in each switch.In the case of synchronous motor (or) sine wave motor, the line current are assumed to be wave
and each switch conducts a half sine wave for 180and does not conduct for another 180The r.m.sline switch phase current is
times the rms line current and which will be assumed to be same as
the phase current if the motor is star connected.
The peak device current is equal to the phase current. The relation between the DC supply
voltage V and ac.
The line voltage of the motor is that the peak line-line voltage of the motor is equal to V.
Therefore, =V==
Peak phase voltage.
So we can write
R.M.S switch VA=6V
Peak switch VA=6vi=6v x
Converter power output (kw) =3I=3 x I
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The rms switch =
=3.5
The peak =
=6.9
For the PMBLDC motor, the equation can be written as
R.m.s switch VA=6
Peak switch VA=6 V
The R.M.S switch = =4.9
The peak value =
= 6.0
The results are same for the star and delta connected.
Thus the PMBLDC motor has a slightly better utilization of the peak current capability of the
converter switches. The synchronous motor appears to have a much better utilization of their R.M.Scurrently capability.
1.10 POWER CONTROLLERS OF PM SYNCHRONOUS MOTOR
Ref: Special Electrical Machines By Gnanavadivel
The control for PMSM both in the region of constant torque and in that of flux weakening
could be presented and its schematic controls scheme is shown in the figure 5.10.
Assume that the speed controller drive system, generate the torque command
.
According in the speed error. Depending on the mode of operation Block1 (or) Block2 will be
selected the outputs of these controllers are the stator current magnitude command & torque angle
command. These commands will combine together with the electric rotor position, provide the
phase currents command through the transformation block. The current commands are enforced
with an inverter by current feed back control with any current methods. The rotor position& speed
are obtained with a encoder and a signal conditioners respectively.
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Figure 1.10
1.10.1 CONSTANT TORQUE MODE CONTROLLER
Ref: Special Electrical Machines By Gnanavadivel
The block1 contains the constant torque mode controller with maximum torque per ampere.
The schematic diagram is shown in the figure 5.11.
The speed signal determines the mode of operation of the derive system. In the torque
control mode of operation, if the rotor speed is less than the base speed, then enables bloc1 in the
form of onward transmission of Torque command signal .The torque signal is limited by the maximum torque that could be generated with
maximum permissible stator current phasor. Then the resulting torque signal provides the stator
current magnitude ant torque angle command to the transformation block.
FIGURE 1.11
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1.10.2 FLUX WEAKENING CONTROLLER
Ref: Special Electrical Machines By Gnanavadivel
There are totally three inputs to the block 2, they are the torque request, rotor speed and
maximum permissible stator current. The rotor speed determines the d-axis stator current request
from the function generator. The d-axis stator current along with the maximum stator current
determine the permissible quadrature axis current.
Then this q-axis current determines the maximum electro magnetic torque allowed
within maximum voltage & current constraints .This command is compared with and generated by the speed error and logic sub module adjusts the torque request depending on the
load and maximum capacity of the motor drive system. as a function of the rotor speed. From this
final torque request* and the statord-axis current is computed by using the transformation block.Then the d-axis and q-axis stator current requests are then used to calculate the stator current
phasor magnitude & torque angle request. The torque mode or flux weakening controller mode is
chosen based on the rotor speed is lower or higher than the base speed. The schematics diagram offlux weakening mode of controller is shown in figure 1.12.
Fig 1.12
1.11 MICROPROCESSOR BASED CONTROL OF PM SYNCHRONOUS
MOTOR
In latest emerging trends to control the drive system using fast devices such as
microprocessor. Micro controller, DSP processor are in common uses. Using these controllable
system we can program the drive for its smooth and efficient operation of the drive system. The
microprocessor based has various blocks in its flow of control. Since nowadays microprocessor are
available cheap we find extensive use of it in the closed loop control motors. The microprocessor
will be pre-programmed already by using the data which are available readily. The various input to
the microprocessor are rotor speed, rotor position and motor current. The shaft rotor position is
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detected by the position encoder or by using optical encoder. The speed of the rotor can be driven
from the encoder itself by using signal conditions.
The mode of operation of PM synchronous motor can be decided by the microprocessor whether
the speed is below or above the base speed. The microprocessor sets the reference Torque, current
in the d-axis and q-axis and the torque angle, for the operation of the motor. The microprocessor in
turn drives the inverter with the logic circuit to ensure that the motor runs at a synchronous speed
for different load conditions. The schematic block diagram is shown in the figure 1.13.
Figure 1.13
Application of synchronous motor drive
i. Fiber spinning mills, Rolling mills, Cement mill etc.ii. Ship propulsion, Electric vehicles, Servo and robotic drives.
iii. MAGLEV linear synchronous motor propulsion.iv. Variable frequency starters for 60 Hz wound field synchronous motor.v. Starters/Generators for aircraft engines.
1.12 CONTROL METHODS OF PM SYNCHRONOUS MOTOR
Ref: Special Electrical Machines By Gnanavadivel
The speed of the machine is uniquely related to the frequency supplied by the inverter (or)
cycloconverter. Unlike an induction machine, it will run at synchronous speed (or) will not run atall. There are two control modes of machine:
i. Open loop control, (or) true synchronous machine mode, where the motor speed iscontrolled by the independent frequency control of the converter.
ii. Self control mode, where the variable frequency converter control pulses are derivedfrom an absolute rotor position encoder mounted on the machine shaft.
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1.12.1 Open loop volts/Hertz control
An open loop volts/Hz speed control is an independent frequency control shown in the
figure 5.14. It is the simplest scalar control method of a synchronous machine but it is achieved at
the cost of inferior performance, unlike high performance vector control which will be discussed
later. Here the machines are connected in parallel to the same inverter so that they move in
synchronism corresponding to the command frequency * at the input. The phase voltage * isgenerated through a function generated (FG), where the voltage is essentially maintained
proportional to the frequency so that the stator flux remains constant. The front end of thevoltage fed PWM inverter is supplied from the utility line through a diode rectifier and LC filter.
The machine is normally built with a damper (or) cage winding to prevent oscillatory (or) under
damping behavior during the transient response.
Figure 1.14
The operation of the drive is shown in the figure 1.15 in which the motoring and braking modes are
shown and its corresponding phasor diagram is also drawn.
Figure 1.15 Volts/Hz speed control characteristics in torque speed plane
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Phasor diagram of synchronous (motoring mode only)
Assume for simplicity that initially the load torque on the machine shaft is zero. The machine canbe easily started from standstill condition at point O to point A by slowly increasing the frequency.
At this point, the is gradually increased. At steady state condition =, the operating point willmove vertically along AB in the first quadrant. The torque expression is given as
=P
sin
=3() Where = torque angle = -phase component of the stator current. Therefore withconstant, the angle and the stator current will increase gradually until the rated torque isreached at point B. where wither the limit angle (or) the rated stator current is reached.Usually the inverter current limit is reached before the machine stability limit. The operating point
can be changed from B to C slowly increasing the frequency command and then it can then it can be
brought back to point D by gradually decreasing .At base speed
. The voltage
will saturate. Beyond this point, the machine will enter into field
weakening mode; therefore the available torque will decrease due to reduced as shown. Forvariable speed operation, the motor speed should be able to track the command frequency without
losing synchronism. The rate of * change (or) maximum acceleration/deceleration capability isgiven by the equation
J) = Where J=moment of inertia, = () is the synchronous electrical speed in rps, P=number ofpoles and = mechanical speed in rps. There, the maximum acceleration and decelerationcapabilities are given as.
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=+
)
=-
)
Where - rated torque and -contributes to decelerationAt point A, if
is ramped up, the machine follow the path ABCD. Similarly, the profile during
deceleration will be DEFA.
The recovered electrical energy in deceleration is dissipated in the dynamic braking (DB) installed
in the DC link. The speed reversal is possible by reversible by reversing the phase sequence of the
Inverter. The damper winding prevents hunting (or) oscillatory behavior mentioned before.
1.12.2 Self control model
A self controlled synchronous machine has close relation with a DC machine. The figure
5.16 shown is the self controlled synchronous motor with permanent in the rotor.
Figure 1.16
The stator winding of the machine is fed by an inverter that generators a variable frequency
variable voltage sinusoidal supply. But in this case instead of controlling the inverter frequency
independently, the frequency and the phase of the output voltage are controlled by an absolute
position sensor mounted on the shaft. The output from the sensor is continues pulse train which is
delayed by an external command.
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A self controlling synchronous machine can be considering similar to a dc motor except the
following difference.
i. Unlike a dc machine, the field is rotating and the armature is stationary.ii. Unlike a mechanical position sensitive inverter we have in this case an electronic inverter
that is controlled by an absolute position sensor.
iii. Unlike stationary fluxes in space, the fluxes and phasor diagram are rotating at synchronousspeed.
The self controlled synchronous machine has several features which is given below.
i. An electric commutator replaces the mechanical commutator and brushes, thus eliminatingthe disadvantages of the DC machine such as maintenance and reliability problems,
sparking, and limitations in speed and explosive environment the limitation of altitude and
the EMI problems.
ii. Because of self control, the machine does not show any stability (or) hunting problem of thetraditional synchronous machine.
iii.
The transient responds can be similar to a DC machineiv. The phase angle between the current and flux can be controlled as necessary by delay
control. The is no longer fixed to the angle as in a DC machine.v. With a high energy magnet, the rotor inertia can be made smaller, which is an advantage in
a fast response servo type drive.
Because of so many favorable characteristics the synchronous machine drivers are exclusively use
self control. The synchronous machines have absolute location of rotor magnetic poles, which is
unlike the location of slipping poles in an induction motor. The sinusoidal PM machines require
continuous information of rotor position with high accuracy. The position encoders can generally
be classified into two types
i. Optical typeii. Resolver type
1.12.3Vector ControlConsider a non salient pole machine with a large efficiency air gap. So that ht
synchronous induction and the corresponding armature flux = is very small that is.for maximum torque sensitivity with the stator current with maximum efficiency wecan set =0 and =which shown in the phasor diagram in which the stator resistance isneglected. Under the above condition, the inverter operates at minimal power rating. The torquedeveloped is given as
= There is the space vector magnitude that is 2and =cos=. The torqueequation indicates that the torque is proportional to torque angle . The vector control diagram for the machine is shown below with the phasordiagram where the stator command current is derived from the speed control loop. Itspolarity is positive for motoring mode but negative for regeneration mode.
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Phasor diagram
Since this is the synchronous machine the slip frequency =0 because the machine always runat synchronous speed (). The magnetizing current , because the rotor flux is suppliedby the PM and unit vector is generated from the absolute position sensor. The vector control
method is somewhat similar to the IM vector control but expect the above points.
Block Diagram: Vector control of SR machine under constant torque region
The rotating frame signals are converted to stator current commands with the help of unit
vector signals (ie) cosand sin as shown. Note that phasor are at quadrature likethe DC machine except, they are rotating at synchronous speed. The machine operates at a
region. As the speed increases, the voltages and increases proportionality to speed andvector control losses its state when the PWM controller saturates at the edges of the constant
torque region.
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Field weakening mode
The speed of the machine can be controlled beyond base speed by field weakeningcontrol. But the field weakening speed angle is small because of a weak armature reaction effect.
This is explained below with phasor diagram and torque speed curve. As the stator voltage tends to
saturate at the edge of the constant torque region and since =, the stator flux must beweakened beyond the base speed so that stator current control remains possible, which meansthat a demagnetizing current must be injected on the stator side. But because of low armaturereaction flux the demagnetizing demands large . Therefore with in the specified statorcurrent rating, it appears weakening of is small which gives small range of field weakeningspeed control.
Phasor diagram
Torque speed curve showing field weakening control above base speed
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It is also possible that with constant ,will increase proportionally with and themachine will get over excited and gives loading P.F. at the terminals.
With lated = is rotated anticlockwise in the a-a locus so that = , here helps in weakening the stator flux alone A-A. At point A,=|| whichcorresponds to zero torque at the speed of is shown in the above figure. It is alsopossible to increase the field weakening range at stator current by increasing the
synchronous inductance from to
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UNIT I
PERMANENT MAGNET SYNCHRONOUS MOTOR
CONSTRUCTIONAL FEATURES :
Construction wise the BLPM sine wave motor is similar to that of BLPM square motor is similar
to that of BLPM square wave motor.
The armature winding and he shape of the permanent magnet are so designed that the flux
density distribution of the air gap is sinusoidal ie the magnetic field set up by the permanent magnet in
the air gap is sinusoidal.
Because of the presence of permanent magnet inthis motor the slip rings and field windings are
absent.
STATOR:
The stator, the stationary members houses the armature winding. By making continuous strips
of soft steel the stator laminations for axial windings are formed.
The thickness of the laminations depends upon the frequency of the armature source voltage.
The cost is also a major constraint for selection of thickness. The yoke of the machine completes
magnetic path.
The armature windings are double layer and lap wound.
Individual coils are connected together to form phasor groups. The phasor groups are
connected together in series/parallel combinations to form star, delta or single phase windings.
Ac windings are generally short pitched to reduce harmonic voltage generated in the windings.
Coils phase groups and phases must be insulated from each other in the end turn regions and the
required dielectric strength of the insulation will depend upon the voltage rating of the machine.
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In this type the permanent magnet are located in the interior of the rotor as shown in fig. The
pattern of flux is generally radial. Interior type rotors are more robust by not earier to construc
compared to peripheral type. They are suitable for high speed applications.
CLAW POLE TYPE ROTOR :-
The following fig, shows the claw pole type rotor configuration:-
The permanent magnets are generally disc shaped and magnetized axially. The long soft extensions of the construction comes out axially from the periphery of the disc like claws or lundell
poles. Hence it is called as claw pole type or lundell type rotor. There is a set of equally spaced
alternate claws on each disc forming alternate north and south poles.
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PRINCIPLE OF OPERATION :
i. The permanent magnet synchronous motor stator is a cleric 3 stator and employingpermanent magnets in rotor. In this motor field windings and slip tings are absent.
ii. The motor is driven by sine wave voltage coupled with the given rotor position. Thestator flux together with the rotor flux which is generated by a rotor magnet defines the
torque and thus speed of the motor.
iii. The permanent magnet synchronous motor is fed by directly from a 3supply.iv. When the armature winding draws a currently, the current distribution within the stator
armature winding depends upon the rotor position and the turning on process of the
devices in the control circuit.
v. The sine wave voltage output is to be applied to the 3winding system in such a waythat angle between the stator flux and the rotor flux is kept close to 90 to get themaximum generated torque. To meet this criterion the motor requires electronic controfor proper operation.
vi. The armature supply frequency is changed in proportion to the rotor speed changes sothat the stator field always moves at the same speed as the rotor.
vii. The rotor position sensor is required for accurate tracking of the speed in order toprevent the motor from pulling out of step and to avoid instability due to the change in
torque or frequency. The PMSM drive is widely used in high performance servo drives
in spite of its high cost. For starting the large synchronous motor the machine is operated
in self controlled mode.
EMF EQUVATION :-
Ref : Special Electrical Machines by gnanavadivel.
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Let at + = 0, the axis of the coil coincides with polar axis. Consider a full pitch single turn
armature coil.
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Let the rotor be revolving with an angular velocity of wm mech rad / sec.
Flux density at the at the strip B sin pIncremental flux in the strip d
d = x area swept by the conductor= x (lrd)
d = sin lrd = lrd
= lr * +
= =
=
e = -N
Emf induced in the single turn coil N = 1
e = -N
= * +
=
= 2 lr wm sin PwmtLet the armature winding be such that all the per phase are full pitched and
concentrated.
Let Tph be the number of turns connected in series per phase. Thus the emf
induced per phase is the algebraic sum of the emf due to individual turns.
eph = 2 lr wm sin x Tph= 2 lr wm Tph sin Pwmt
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eph = ph sin Pwmt = 2 l rwn Tph maximum value of induced emf
Eph =
Eph = l r wm Tpheph = ph sin Pwmt
= ph sin p t
= ph sin wetWe = Angular velocity in electrical rad / sec
m = maximum value of flux per pole in sinusoidal distribution. = BA
= Bav x x l
= x l
m =
rl = ---------------------------------- (1)
RMS value of the induced emf per phase
Eph = r l Tph wm ------------------ (2)Sub equ (1) in equ (2)
Eph = x x wm x Tph
= x x x Tph
= x
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=
Eph = 4.44 f
The above equation is the Rms value of the induced emf / phase of an ideal BLPMSNW motor.
TORQUE DEVELOPED IN A BLPM SNW MOTOR :-
Ref : Special Electrical Machines by Gnanavadivel
Let the ampere conductor density distribution is A sin pLet the axis of the ampere conductor density distribution be displaced from the axis of
the flux density distribution by an angle ( )
B = Sin [ ( )]
= Sin [ ]
= = cos
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Force experienced by the conductors in the strip = df
df = B x A d x l= cos (p
df = B A sin pcos (p Let r Torque experienced by the ampere conductor in the strip = dF x r
dT
PROPERTIES OF TORQUE DEVELOPED IN A PRACTICAL BLPM SNW MOTOR
A.p turn density distribution of a phase winding consisting of full pitched coil is Tph
Fundamental component of the Amp-turn distribution of a phase winding is
4/iTph\In a practical BLPM SNW motor chorded coils and are accommodated in skewed
slots. Therefore for getting the fundamental component of the Amp-turn distribution in this
case. The turns per phase is modified as kw1.Tph. Thus the fundamental component of the
Amp-turns per phase
=4/I kwTph.
When a balanced 3phase sinusoidally varying AC currents is passed through the 3phase
balanced windings then the total sinusoidally varying Amp turns density distribution is
=x
The axis of phase winding are displaced byelec. rad (or)
mech rad. The current in
the winding are also balanced. The armature winding is said to be balanced. If all the
3 windings are exactly identical in all aspects. But there axis are mutually displaced by The 3 armature current is said to be balanced when the 3 currents areexactly equal but mutually displaced in phase by 120
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= 4.44 f (Ka Ia) Kw Tph.Xa = 4.44 f Ka Kw Tph.
= Xa Iaa = - j xa Iaal = emf induced perphase in the armature winding due to armature leakage flux
( = 4.44 f al Kwl Tph = Kal Ia = 4.44 f Kal Ia kal TphXal = -jIa x al
Eal = - jIa x al
VOLTAGE EQUATION :-
+ f + a + al = Iara + f +
+ f =Iara _ JIa (Xa + Xal)= Ia [la + j (Xa + Xal]
+ f = IaZs = - f + IaZs
Fig shown is phasor diagram for permanent magnet synchronous motor.
Let EMF Eq in X axis
= -
f + IaZs
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OA = mf = main field fluxOB = Ef = emf induced perphase due to mfof = Ia = , power angleCD = Iara
OE = V
DE = Iaxs
CE = IaZs
Input power = 3 = 3 (q + IaZs) a= 3 aq a + a Ia (ra + jXs)= = 3 (q Ia + a2Ia ra + 0)
Input power = power converted to mechanical + copper loss
Electro magnetic Torque developed =
Pm = 3 Eq Ia Cos (90-)Pm = 3 f| Ia sin T =
N.M
can be resolved into two component d X q setup an mmf along the direct axis= setup an mmf along the Quadiature axis.
= q + ZsI = q + q
=
q +
ra + j
Xs
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= q + (d + q) ra + j (d + q) Xs. = q + d ra + q ra + jd Xs + jq Xs
TORQUE SPEED CHARACTERISTICS :-
Fig shows torque speed characteristics of PMSM the frequency is varied from 0 to f, the
PMSM developed maximum torque. Again we increasing the frequency the torque will
reduced and goes to zero at a frequency of FD
SELF CONTROLLED PMSM DRIVE EMPLOYING TOAD COMMUTATED THYRISTOR
INVERTOR :
Ref : Special Electrical Machines by Gnanavadivel.
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A CLOSED 100P SPEED CONTROL OF LOAD COMMUTATED INVERTER FED
SYNCHRONOUS MOTOR :-
(i) Self control ensure that for all operating points the armature and rotor field movesexactly at the same speed. The torque angle is adjusted electronically.
(ii) Hence there is an additional controllable parameter causing greater control of themotor behavior. By varying the firing of the semiconductor switched of an inertorthe torque angle is set electronically.
(iii) The drive employs two converters, which are termed here as source side convertorand load side converter. Inductance Ld reduces ripples and interfering with two
converters.
(iv) The source side converter is a 6 pulse line commutated thyristor converter,(v) For a firing angle rand 0< < 90it works as a line commutated fully controlled
rectifier delivering +ve vds and positive Id. For a firing angle range 90< < 180it work as a line commutated inverter delivering ve Vds and +ve Id.
0< < 90 - it works a rectifier giving +ve Vds90< < 90- it works a inverter giving ve vds
For 0< < 90 ; 90< < 90 and with Vds Vds the source side converterworks as a rectifier and load side converter as an inverter causing power fww from ac source
to the motor, thus giving motoring operation.
(vi) Consequently the power flow fww reverses and machine operates in regenerativebraking. The magnitude of torque depends on (Vds-Vds) speed can be changed bycontrol of line side converter firing angles.
ADVANTAGES:-
(i) It does not require commutation circuits.(ii) Frequency of operation can be higher.(iii) If can operate power levels beyond the capability of forced commutation.
APPLICATIONS :
(i) Compressors(ii) Blowers
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(iii) Conveyers(iv) Steel rolling mins(v) Air craft
CLOSED 100P CONTROL :-
(i) It employs outer speed control 100p and inner current control with a limiter, likea dc motor. The terminal voltage sensor generates reference pulses of the same
frequency as the machine induced voltages. The phone delay circuit shifts the
reference pulses suitably to obtain control at a constant commutation lead angel
rc.(ii) Depending on the sign of speed error is set to provide motoring (or) braking
operation speed wm can be sensed either from the terminal voltage sensor (or)
from a separate tacho meter. An increase in reference speed wm produces a + ve
speed error.(iii) rc value is set for motoring operation. The speed controller and current limiter
set dc link current reference at maximum permissible value.
(iv) The machine accelerates fast when close to the derived speed, the current limiterset the dc link current reference at the maximum permissible value.
(v) Similarly reduction in reference speed produces ve speed error. This sets for regenerative braking operation and the motor decelerates when speed error
changes sign value is set for motoring operating and the drive settles at thedesired speed.
ADVANTAGES :-
(i) High efficiency(ii) Four quadrant operation with regenerative braking is possible.(iii) High power ratings and run at high speeds.
APPLICATIONS :-
(i) Compressors(ii) Blowers(iii) Fans(iv) Pumps(v) Conveyors(vi) Stell rolling mills.(vii)
Mainline traction
(viii) Ship propulsion
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VECTOR CONTROL OF BLPM SNW NOTOR :-
Ref : Special Electrical Machines by Gnanvadivel
Electromagnetic torque developed due to the interaction of the current carrying
conductor and magnetic field.
Fig shows flux axis is in quadrature with the armature mmf axis. Each and every
armature conductor experiences a force which contributes the torque.
The torque contributed by armature conductors have the same direction. It is observed that
the steady an dynamic performance such an arrangement are better.
SECOND CASE :-
Angle between the axis of the flux and the armature mmf axis different from . Inthis case some conductors developed torque in one direction, while the other developed in the
opposite direction.
Its observed that both the steady state and dynamic performance of such a motor are
poor. For a BLPM SNW motor to have better steady state and dynamic performance. It is
essential that the armature mmf axis and the axis of the PM are to be in quadrature in all
operating conditions.
I = Id + Iq
Id = Direct axis current
Iq = Quadrature axis current
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VECTOR CONTROL:-
(i) Knowing the values of the derived torque and speed and also the parametersand voltage to which the motor subjected to its possible to compute values of id
ref and iq ref for the desired dynamic and steady steady state performance theref. values of id and iq are transformed into ref. values of currents namely ia ref,
ib ref, ic ref.
(ii) These currents are compared with actual currents and error values actuate thetriggering circuitry which is also influenced by rotor position sensor and speed
sensor.
MICROPROCESSOR BASED CONTROL OF PMSM :-
(i) A block diagram of the controlled PMSM drive is shown in fig. PMSM is fedfrom a current source. Dc luck converter system. Which consists of a sckbridge rectifier connected to a 3 SCR converter through rectifier is operatedfrom 3 ac supply lines and its gating signals are provided by digitallycontrolled firing circuit.
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(ii) The optical en coder which is composed of a coded disk attached to the motorshaft and four optical sensors providing rotor speed and position signals.
(iii) The inverter triggering pulses are synchronized to the rotor position referencesignals with a delay angle determined by an B.bit control input. The inverter
SCTS are naturally commutated by the machine voltages during normal
operation.
(iv)
The speed signal which is a pulse train of frequency propositional to the motorspeed is fed to a programmable counter used for speed sensing.
(v) The stator current is defected by current sensor an amplified by optically isolatedamplifier. The output signals are multiplied and converted to digital form by a
high speed analog to digital converter.
(vi) The main functions of the microprocessor are monitoring and control of thesystems variables for the purpose of obtaining desired driver features. It can also
perform various auxiliary fasts such as protection. diagnosis display.
(vii) In normal operation commands are fetched from the input-output terminals andsystem variables are sensed and fed to CPU. After processing themicroprocessor issues control signals to the input rectifier, the machine inverter
so as to provide the programmed drive characteristics.
SYNCHRONOUS REACTANCE :
The synchronous reactance is the reactance employed to account for the voltage
effects in the armature circuit produced by the actual armature leakage reactance and the
change in the air gap flux caused by armature reaction.
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For an ideal two pole sine-distributed 3 winding with Ns turns in series per phaseneglecting the leakage inductance of the slots and end turns, the expression for synchronousreactance is given by armature reaction.
For an ideal two pole sine distributed 3 winding with Ns turns in series per phaseneglecting the leakage inductance of the slots and end-turns, the expression for synchronous
reactance is given by.
Xs = (3 N2 lr1 ) / (8p2g) ohms = Permeabilityr1 = Stator bore radios
l = Stack length
= Angular velocity in mech / radP = Pole pairs
g = Effective airgap length allowing for magnet
CONVERTER VOLT AMPERE REQUIREMENTS :-
The volt ampere per watt of shaft power of PMSM is defined as the volt ampereproduct required in the ratings of the semiconductor devices in the converter. The eg
calculations are all based on a two phase PMSM and it was assumed that each phase wassupplied by a full bridge circuit requiring a total of eight transistors. The nominal convector
volt-amperes, based on rms current in each device times peak current times the number os
switching devices, is therefore.
X 8 X = 8VI
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