In a dc machine, the mechanical commutator ensures that current flows
in the machine windings in a manner that will produce useful torque,
even when the rotor changes position and speed. From a modeling and
control standpoint, the presence of the commutator significantly eases
the problem of designing appropriate power-electronic amplifiers for
driving dc machines. Essentially, the problem becomes one of developing
circuitry that can create flexible levels of voltage or current, without too
much concern for the specific waveshape: either a linear amplifier or a
chopper would generally produce adequate results, for example. Only
the relatively slowly varying, average values of the terminal waveforms
prove to be of concern in a well-designed system. In an ac machine,
there is no mechanical commutator, and the electrical excitation of the
stator must be appropriate to ensure sustained torque production. For
a controllable motor drive, this generally means that the drive electronics
must be capable of producing ac waveforms with controllable frequency
and amplitude.
Switching power-electronic drives for ac machines are often (but not
always) constructed as inverters, which operate from a dc input voltage
and which produce a controlled ac output voltage waveform or
waveforms. A dc bus that serves as the input voltage to the inverter can
be created by rectifying a fixed-frequency ac utility service, for example.
Figure 10.24 shows a full-wave rectifier set operating from a three-phase
utility connection. A dc output voltage with relatively low ripple is
produced across the capacitor. If necessary, the level of the dc output
voltage can be controlled by replacing the diodes with controllable
devices, such as silicon-controlled rectifiers. Controlling the firing angle
of these devices permits control of the magnitude of the output voltage.
Of course, a dc bus can be created in other ways. For a single-phase
utility connection, either a single-phase, full-wave rectifier or a firing
angle-controlled rectifier might be used. In an electric-vehicle drive
system, the dc bus would come from a battery rack, and no rectification
would be required.
An inverter uses the dc bus to create ac waveforms with controllable
frequency and amplitude. Figure 10.25 shows a typical inverter
configuration driving a balanced, three-phase, inductive load. This load
could be the wye-connected stator of an induction or PM synchronous
motor, for example. There are a variety of schemes for operating the
switches Q1–Q6 to produce desired ac waveforms. Typically, the ultimate
goal of an inverter drive for an AC machine is to make the machine
appear from an electrical port to be a current-controlled torque source,
just like the PM dc machine. Two approaches for operating the switches
in a three-phase inverter will be discussed briefly here; others may be
found in Reference 13 and especially in Reference 14. The goal of this
section is to reveal how useful ac waveforms can be produced by an
inverter given a DC bus. The waveform analysis presented is
summarized from the excellent discussion in Reference 13.
In a “six-step”, continuous current inverter, the controllable switches
are operated as shown in the top six traces in Fig. 10.26. One leg or
phase of the inverter consists of a top and bottom switch stacked together,
e.g., Q1 and Q4. The stator connections a, b, and c can each be connected
to either the top or the bottom of the dc input voltage by the switches. In
any particular leg of the inverter, the two switches are never turned on
at the same time in order to avoid shorting the input source. Also, in the
continuous current inverter, one of the switches in each leg is always
turned on to provide a path for phase current to flow. To emulate the
behavior of a balanced, three-phase sinusoidal voltage source, the top
or high-side switch in each leg is turned on 120 electrical degrees before
the top switch in the next leg, and remains on for half of the electrical
cycle.
When the high-side switch in a leg is on, the winding connected to
that leg is connected to the top of the dc source. When the high-side
switch is off, the low-side switch in the leg is on, and the winding is
connected to the bottom of the dc source. The voltage between each
stator terminal and point g, therefore, has a waveshape that looks like
the switch state for the high-side switch in that leg. For example, the
voltage Vag has a waveshape like the Q1 switch state trace in Fig. 10.26.
This fact can be used to determine the line-to-line and line-toneutral
voltages seen by the load. For example, the line-to-line voltage
Vab will have a waveshape that looks like the difference of the Q1 and
Q2 waveshapes. This line-to-line voltage is plotted in the seventh trace
in Fig. 10.26. To determine the line-to-neutral voltage for Phase a,
notice that, for stator terminal a, we can use Kirchoff’s voltage law to
discover that
and so on for the other two phases. Because the inverter and load are
balanced and have three phases, we know that
Therefore, the voltage
| |  | (10.11) |
Substituting Eq. 10.11 into Eq. 10.10 reveals that the Phase a line-to-neutral
voltage is
| |  | (10.12) |
The waveshapes of Vag, Vbg and Vcg are identical to the Q1, Q2, and Q3
wave traces in Fig. 10.26. Equation 10.12 and the traces Q1, Q2, and Q3
are used to produce the line-to-neutral voltage waveform Vas for phase a
shown in the last trace in Fig. 10.26. The six-step inverter produces a
line-to-neutral voltage that has a substantial sinusoidal component at
the fundamental frequency, with some obvious harmonic distortion
present at higher, odd harmonics of the fundamental.
The frequency of the output waveforms can, of course, be changed by
varying the time allotted to complete one electrical cycle. In a PM
synchronous machine or “brushless dc motor”, the operation of the
switches in the inverter is often “slaved” or synchronized to the rotor
position, possibly by Hall-effect switches that sense the location of the
rotor. This ensures that the AC waveform produced by the inverter will
have a significant constant component when viewed in the rotor frame,
as is necessary to sustain torque production. In a two-pole machine, for
instance, the inverter would complete one electrical cycle for every
revolution of the rotor. In essence, the inverter operates as an electrical
commutator. The inverter can also be used to drive an induction machine.
This drive could be “open-loop,” i.e., the inverter can provide the induction
motor with a fixed-frequency, balanced voltage set. It could also be
synchronized to the position of the rotor, as would be essential in the
implementation of a field-oriented controller.
In the case of the PM synchronous machine, once the inverter
operation is synchronized to the rotor position, the machine essentially
behaves like a conventional PM dc machine from the standpoint of the
dc input to the inverter. Raising the inverter input voltage will increase
the speed of the machine. The current flowing out of the dc input indicates
the level of torque produced at the shaft of the machine. It is important,
therefore, to be able to control the magnitude of the voltage or current
applied to the machine. This can be done in at least two ways. The first
approach would be to vary the level of the dc input voltage to the inverter.
This might be done either to vary the machine terminal voltage directly,
or perhaps to control the current injected into the machine with a minor
loop. The second, pulse-width modulation approach uses the inverter
switches to chop the voltage applied to the stator. The stator voltages
can always be set to zero by turning on all three high-side, or all three
low-side switches in the inverter (but never the high-side and low-side
switches at the same time for a dc voltage input). The PWM switch
frequency would be set significantly higher than the six-step electrical
frequency. Varying the duty cycle will vary the average voltage applied
to the stator terminals, again permitting voltage control or current
control with a minor control loop.
In a dc machine, the mechanical commutator ensures that current flows
in the machine windings in a manner that will produce useful torque,
even when the rotor changes position and speed. From a modeling and
control standpoint, the presence of the commutator significantly eases
the problem of designing appropriate power-electronic amplifiers for
driving dc machines. Essentially, the problem becomes one of developing
circuitry that can create flexible levels of voltage or current, without too
much concern for the specific waveshape: either a linear amplifier or a
chopper would generally produce adequate results, for example. Only
the relatively slowly varying, average values of the terminal waveforms
prove to be of concern in a well-designed system. In an ac machine,
there is no mechanical commutator, and the electrical excitation of the
stator must be appropriate to ensure sustained torque production. For
a controllable motor drive, this generally means that the drive electronics
must be capable of producing ac waveforms with controllable frequency
and amplitude.
Switching power-electronic drives for ac machines...
More >>
