Vector control, also called field-oriented control, is a
variable-frequency drive control method where the stator currents of a
three-phase AC electric motor are identified as two orthogonal components
that can be visualized with a vector. One component defines the magnetic flux
of the motor, the other the torque. The control system of the drive calculates
from the flux and torque references given by the drive's speed control the
corresponding current component references. Typically
proportional-integral controllers are used to keep the measured current
components at their reference values. The pulse-width modulation of the
variable-frequency drive defines the transistor switching according to the
stator voltage references that are the output of the PI current controllers.
FOC is used to control the AC synchronous and induction motors. It was
originally developed for high-performance motor applications that
are required to operate smoothly over the full speed range, generate full
torque at zero speed, and have high dynamic performance including fast
acceleration and deceleration. However, it is becoming increasingly attractive
for lower performance applications as well due to FOC's motor size, cost and
power consumption reduction superiority. It is expected that with increasing
computational power of the microprocessors it will eventually
nearly universally displace single-variable scalar volts-per-Hertz
control. Development history
Technical University Darmstadt's K. Hasse and Siemens' F. Blaschke pioneered
vector control of AC motors starting in 1968 and in the early 1970s, Hasse in
terms of proposing indirect vector control, Blaschke in terms of proposing
direct vector control. Technical University Braunschweig's Werner
Leonhard further developed FOC techniques and was instrumental in
opening up opportunities for AC drives to be a competitive alternative to DC
drives. Yet it was not until after the
commercialization of microprocessors, that is in the early 1980s, that general
purpose AC drives became available. Barriers to use of FOC for AC drive
applications included higher cost and complexity and lower maintainability
compared to DC drives, FOC having until then required many electronic components
in terms of sensors, amplifiers and so on.
The Park transformation has long been widely used in the analysis and study of
synchronous and induction machines. The transformation is by far the single most
important concept needed for an understanding of how FOC works, the
concept having been first conceptualized in a 1929 paper authored by Robert H.
Park. Park's paper was ranked second most important in terms of impact from
among all power engineering related papers ever published in the twentieth
century. The novelty of Park's work involves his ability to transform any
related machine's linear differential equation set from one with time varying
coefficients to another with time invariant coefficients.
Technical overview Overview of key competing VFD control
platforms: While the analysis of AC drive controls
can be technically quite involved, such analysis invariably starts with modeling
of the drive-motor circuit involved along the lines of accompanying signal
flow graph and equations. In vector control, an AC induction or
synchronous motor is controlled under all operating conditions like a
separately excited DC motor. That is, the AC motor behaves like a DC motor in
which the field flux linkage and armature flux linkage created by the
respective field and armature currents are orthogonally aligned such that, when
torque is controlled, the field flux linkage is not affected, hence enabling
dynamic torque response. Vector control accordingly generates a
three-phase PWM motor voltage output derived from a complex voltage vector to
control a complex current vector derived from motor's three-phase stator current
input through projections or rotations back and forth between the three-phase
speed and time dependent system and these vectors' rotating reference-frame
two-coordinate time invariant system. Such complex stator current space vector
can be defined in a coordinate system with orthogonal components along d and q
axes such that field flux linkage component of current is aligned along
the d axis and torque component of current is aligned along the q axis. The
induction motor's coordinate system can be superimposed to the motor's
instantaneous three-phase sinusoidal system as shown in accompanying image.
Components of the system current vector, allow conventional control such as
proportional and integral, or PI, control, as with a DC motor.
Projections associated with the coordinate system typically involve:
Forward projection from instantaneous currents to complex stator current space
vector representation of the three-phase sinusoidal system.
Forward three-to-two phase,-to-(,) projection using the Clarke
transformation. Vector control implementations usually assume
ungrounded motor with balanced three-phase currents such that only two
motor current phases need to be sensed. Also, backward two-to-three
phase,-to-(a,b,c) projection uses space vector PWM modulator or inverse Clarke
transformation and one of the other PWM modulators.
Forward and backward two-to-two phase,(,)-to-(d,q) and-to-(,)
projections using the Park and inverse Park transformations, respectively.
However, it is not uncommon for sources to use three-to-two,-to-(d,q) and
inverse projections. While coordinate system rotation can
arbitrarily be set to any speed, there are three preferred speeds or reference
frames: Stationary reference frame where
coordinate system does not rotate; Synchronously rotating reference frame
where coordinate system rotates at synchronous speed;
Rotor reference frame where coordinate system rotates at rotor speed.
Decoupled torque and field currents can thus be derived from raw stator current
inputs for control algorithm development.
Whereas magnetic field and torque components in DC motors can be operated
relatively simply by separately controlling the respective field and
armature currents, economical control of AC motors in variable speed application
has required development of microprocessor-based controls with all
AC drives now using powerful DSP technology.
Inverters can be implemented as either open-loop sensorless or closed-loop FOC,
the key limitation of open-loop operation being mimimum speed possible
at 100% torque, namely, about 0.8 Hz compared to standstill for closed-loop
operation. There are two vector control methods,
direct or feedback vector control and indirect or feedforward vector control,
IFOC being more commonly used because in closed-loop mode such drives more easily
operate throughout the speed range from zero speed to high-speed
field-weakening. In DFOC, flux magnitude and angle feedback signals are directly
calculated using so-called voltage or current models. In IFOC, flux space
angle feedforward and flux magnitude signals first measure stator currents
and rotor speed for then deriving flux space angle proper by summing the rotor
angle corresponding to the rotor speed and the calculated reference value of
slip angle corresponding to the slip frequency.
Sensorless control of AC drives is attractive for cost and reliability
considerations. Sensorless control requires derivation of rotor speed
information from measured stator voltage and currents in combination with
open-loop estimators or closed-loop observers.
Application recap 1. Stator phase currents are measured,
converted to complex space vector in coordinate system.
2. Current vector is converted to coordinate system. Transformed to a
coordinate system rotating in rotor reference frame, rotor position being
derived by integrating the speed by means of speed measurement sensor.
3. Rotor flux linkage vector is estimated by multiplying the stator
current vector with magnetizing inductance Lm and low-pass filtering the
result with the rotor no-load time constant Lr/Rr, namely, the rotor
inductance to rotor resistance ratio. 4. Current vector is converted to
coordinate system. 5. d-axis component of the stator
current vector is used to control the rotor flux linkage and the imaginary
q-axis component is used to control the motor torque. While PI controllers can
be used to control these currents, bang-bang type current control provides
better dynamic performance. 6. PI controllers provide coordinate
voltage components. A decoupling term is sometimes added to the controller output
to improve control performance to mitigate cross coupling or big and rapid
changes in speed, current and flux linkage. PI-controller also sometimes
need low-pass filtering at the input or output to prevent the current ripple due
to transistor switching from being amplified excessively and destabilizing
the control. However, such filtering also limits the dynamic control system
performance. High switching frequency is typically required to minimize filtering
requirements for high-performance drives such as servo drives.
7. Voltage components are transformed from coordinate system to coordinate
system. 8. Voltage components are transformed
from coordinate system to coordinate system or fed in Pulse Width Modulation
modulator, or both, for signaling to the power inverter section.
Significant aspects of vector control application:
Speed or position measurement or some sort of estimation is needed.
Torque and flux can be changed reasonably fast, in less than 5-10
milliseconds, by changing the references.
The step response has some overshoot if PI control is used.
The switching frequency of the transistors is usually constant and set
by the modulator. The accuracy of the torque depends on
the accuracy of the motor parameters used in the control. Thus large errors
due to for example rotor temperature changes often are encountered.
Reasonable processor performance is required; typically the control
algorithm has to be calculated at least every millisecond.
Although the vector control algorithm is more complicated than the Direct Torque
Control, the algorithm is not needed to be calculated as frequently as the DTC
algorithm. Also the current sensors need not be the best in the market. Thus the
cost of the processor and other control hardware is lower making it suitable for
applications where the ultimate performance of DTC is not required.
See also References