THE THEORY OF VECTOR CONTROL
Ia
Ia+Ib Is =
Ia+Ib+Ic
Ic
Ib
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VECTOR CONTROL
Vector control aims to get the same dynamic
performance or better from an A.C. motor as from a
D.C. machine with certain limitations.
The quantity that needs to be controlled is torque
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TORQUE
In all rotating electromagnetic machinery, Torque
(T) is proportional to the product of current (I)
and field flux ();
[T I] Equation 1
It follows from Equation 1 that we can vary torque
by varying either the current (I), the field flux ()
or both.
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Dynamic Response
Changing the field flux takes a relatively long time (up to
several hundred milliseconds).
To get the best dynamic response it is usually best to keep
constant and alter I.
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DC Motor
In a DC Motor, there are two separate windings, field and
armature.
If in the field winding, builds up magnetic flux along the
d-axis of the motor
To generate torque, current I is injected into the armature
winding, q-axis. Brushes keep the axis perpendicular to
the d-axis, along an axis known as the quadrature or q-
axis.
field n
d-axis
m.m.f.
Field Coil
q-axis
Armature Coil
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DC Motor
The armature rotates so that the part of the
winding carrying current moves away from
the d-axis.
This causes the commutator to switch
current to the part of the armature winding
moving towards the d-axis.
field n
d-axis
m.m.f.
Field Coil
q-axis
Figure 1 Armature Coil
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DC Motor Functional Block
If
If
I T
Figure 2
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AC Motor
In an a.c. squirrel-cage motor the situation is much more
complicated than in a d.c. machine.
This time there is only one winding - on the stator
Both the magnetic field and the m.m.f. are rotating relative
to the stator reference frame.
To complicate things further, the spatial angle between the
field and the m.m.f. is not necessarily a right-angle.
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AC Motor
To understand the theory by which the control of the flux and torque
producing current occurs it is best to consider what is happening at
a frozen "snapshot" in time.
The three windings of the AC induction motor are supplied from an
IGBT transistor bridge and at any one time will have currentso of
magnitude Ia, Ib and Ic flowing in them, phase shifted by 120 from
one another.
Ia
Ib
Ic
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AC Motor
Although current is a scalar (non vector) quantity the resultant of
the 3 phase currents is a vector (Is) in space.
(Is) comprises the flux and torque producing elements and both its
position and magnitude can be varied by controlling the individual
phase currents Ia,Ib & Ic.
Ia
Ia+Ib
Is =
Ia+Ib+Ic
Ic
Ib
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AC Motor
As the real time model of the machine predicts the flux position, (Is)
can be resolved into fixed components relative to the flux.
These components are (Id) the direct component of current which
produces the flux, and (Iq) the perpendicular component of current
that produces the torque. By controlling the three phase currents (Id)
or (Iq) can be controlled independently.
Ib Is
Iq
field axis
Id
stator axis
Ia
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AC Motor
In practice because the flux producing current path is
very inductive and therefore requires a lot of energy to
change, it is kept constant and the torque producing
(low inductive path) current is varied to change the
torque.
In other words, if Id could be kept constant and Iq
varied to give the required torque, it would be
possible to copy the behavior of a separately-excited
d.c. machine.
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AC Motor
Unfortunately Id and Iq are not directly available at the motor
terminals.
However, the stator current is available in terms of stator co-
ordinates, shown as Ia and Ib.
It is possible to calculate Id and Iq if Ia, Ib and the angle are known.
This calculation has to take place continuously in real-time,
(thousands of times per second), which is why vector control has had
to wait for fast microprocessors for it to become feasible.
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Inside the AC Motor
Ia
C Id
Ib Iq Id
T
Figure 4
F
The inputs to the a.c. machine (Ia and Ib) result in the outputs
(magnetic field and torque).
Functional block C represents a transformation from stator co-
ordinates to field-orientated co-ordinates which takes place
inside the machine.
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Inside the AC Motor
Ia
C Id
Ib Iq Id
T
F Figure 4
Any change in the stator co-ordinates Ia and Ib leads immediately to a
change in Id and Iq, determined by feedback of the angle
(represented by functional block F).
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Vector Control
Ia
C Id
Ib Iq Id
T
Figure 4
F
The box C represents a co-ordinate transformation that takes place
"inside" the machine.
To achieve vector control, it is necessary to "compensate" for this
transformation, or, in other words, to "cancel it out".
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Vector Control
Id* Ia
C-1 C Id
Iq* Ib Iq Id
T
Controller Machine
Figure 5
The functional block C-1 that compensates for the co-ordinate
transformation taking place in the machine, gives us vector control.
The inputs Id* and Iq* are reference values for Id and Iq.
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Vector Control
This shows how torque is produced in a vector-controlled machine.
Compare it with Figure 2.
Id * Id
Id*
Figure 6
T
Iq * Iq
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Motor Currents
We have now seen that the magnetizing current controls
the flux in the motor. When the motor turns, this flux
produces a back emf, which is proportional to flux and
rotor speed.
The voltage at the motor terminals will be approximately
equal to this back emf, plus a small stator voltage drop.
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Vector Motor Currents
At light load, i.e.. when the motor is rotating with bare
shaft only, there is no torque component and the current
flowing is entirely magnetizing current.
Id No Load Full Load
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Terminal Volts
If the motor flux is correct, then the terminal volts at
base speed should be approximately equal to the rated
motor voltage. This enables the magnetizing current to
be set up.
In practice the terminal volts should be about 95% of
rated volts, to allow for the extra stator voltage drop
under load.
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Slip
At light load, the applied magnetizing current will rotate
synchronously with the motor shaft. As the load increases, the vector
controller will cause the applied current to rotate slower than the
motor shaft. This is called “SLIP”
The slip frequency will increase linearly as load is applied to the
motor, and may be typically of the order of 1Hz at rated load. That
is, if the motor shaft is rotating at 60Hz, then the motor current will
be rotating at 61Hz.
This slip frequency is necessary to split the motor current into a
magnetizing component and a torque component.
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Rotor Time Constant
The Slip frequency is given by the value of the rotor time constant.
It is important to get it correct in order to ensure the correct split of
the motor current into the torque component and the magnetizing
component.
If the slip frequency is zero, then 100% of the motor current goes to
magnetize the rotor, and none produces torque.
As the slip frequency is increased, the proportion of magnetizing
current decreases.
Slip frequency is inversely proportional to rotor time constant.
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Motor Setup
The aim is to maintain constant magnetizing current for all load
conditions by linearly increasing the slip frequency as load
increases.
If the slip frequency is increased by too little, when load is applied,
the magnetizing current will be too large, and the terminal voltage
will increase.
This is how the rotor time constant is set up.
Increasing rotor time constant decreases slip and increases
terminal volts
Decreasing rotor time increases slip and decreases terminal volts
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Motor Setup
After setting up the magnetizing current with no load on the motor,
the motor is then fully loaded, and the value of rotor time constant
is adjusted to give the correct slip frequency to give the correct
motor terminal volts.
Alternatively it is possible to calculate the value of rotor time
constant which will give the slip frequency written on the motor
nameplate. This is less accurate but doesn’t require the application
of a load.
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Vector Algorithm
Field
Weakening Id Loop Saw Tooth Gain
Mag Current id* ia*
PI
n Torque Scale
Iq Loop C-1 ib* P
Torque
iq*
Demand I
Rotor flux
Tr Slip angle ‘rho’
calc.
Filter Tr
imr id ia
iq ib
Encoder
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