inverters for ac motor drive
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Inverters for AC Motor Drives....................................................................................................1
Variable-frequency converter classifications..........................................................................1
Voltage source inverters..........................................................................................................3
Variable-frequency PWM-VSI drives.................................................................................3
Variable-frequency square-wave VSI drives......................................................................8Current source inverters..........................................................................................................9
Variable-frequency CSI drives............................................................................................9
Modulation techniques..........................................................................................................11
PWM with Bipolar Voltage Switching.............................................................................11
PWM with Unipolar Voltage Switching...........................................................................14
Square-Wave Operation....................................................................................................17
Inverters for AC Motor Drives
Variable-frequency converter classifications
The variable-frequency converters, which act as an interface between the utility power system
and the induction motor, must satisfy the following basic requirements:
1. Ability to adjust the frequency according to the desired output speed
2. Ability to adjust the output voltage so as to maintain a constant air gap flux in the
constant-torque region
3. Ability to supply a rated current on a continuous basis at any frequency
Except for a few special cases of very high power applications where cycloconverters areused, variable-frequency drives employ inverters with a dc input. Figure 14-17 illustrates the
basic concept where the utility input is converted into dc by means of either a controlled or an
uncontrolled rectifier and then inverted to provide three phase voltages and currents to the
motor, adjustable in magnitude and frequency.
Fig. 14.17 Variable-frequency converter
These converters can be classified based on the type of rectifier and inverter used in
Fig. 14-17:
1. Pulse-width-modulated voltage source inverter (PWM-VSI) with a diode
rectifier
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2. Square-wave voltage source inverter (square-wave VSI) with a thyristor
rectifier
3. Current source inverter (CSI) with a thyristor rectifier
As the names imply, the basic difference between the VSI and the CSI is the following: In the
VSI, the dc input appears as a dc voltage source (ideally with no internal impedance) to theinverter. On the other hand, in the CSI, the dc input appears as a dc current source (ideally
with the internal impedance approaching infinity) to the inverter.
Fig. 14.18 Classification of variable-frequency converters: (a) PWM-VSI with diode
rectifier; (b) square-wave VSI with a controlled rectifier; (c) CSI with a controlled rectifier.
Figure 14-18a shows the schematic of a PWM-VSI with a diode rectifier. In the square-wave
VSI of Fig. 14-18b, a controlled rectifier is used at the front end and the inverter operates in asquare-wave mode (also called the six-step). The line voltage may be single phase or three
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phase. In both VSI controllers, a large dc bus capacitor is used to make the input to the
inverter appear as a voltage source with a very small internal impedance at the inverter
switching frequency.
It should be noted that, in practice, only three-phase motors are controlled by means of
variable frequency. Therefore, only the dc-to-three-phase-ac inverters are applicable here. The
main emphasis in this chapter will be on the interaction of VSIs with induction motor type ofloads.
Figure 14-18c shows the schematic of a CSI drive where a line-voltage-commutated
controlled converter is used at the front end. Because of a large inductor in the dc link, the
input to the inverter appears as a dc current source. The inverter utilizes thyristors, diodes, and
capacitors for forced commutation.
Voltage source inverters
Variable-frequency PWM-VSI drives
Figure 14-19a shows the schematic of a PWM-VSI drive, assuming a three-phase utility input.
A PWM inverter controls both the frequency and the magnitude of the voltage output.
Therefore, at the input, an uncontrolled diode bridge rectifier is generally used. One possible
method of generating the inverter switch control signals is by comparing three sinusoidal
control voltages (at the desired output frequency and proportional to the output voltage
magnitude) with a triangular waveform at a selected switching frequency, as shown in Fig.
14-19b.
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Fig. 14.19 PWM-VSI: (a) schematic; (b) waveforms.
In a PWM inverter, the harmonics in the output voltage appear as sidebands of the switching
frequency and its multiples. Therefore, a high switching frequency results in an essentially
sinusoidal current (plus a superimposed small ripple at a high frequency) in the motor.
Since the ripple current through the dc bus capacitor is at the switching frequency, the input
dc source impedance seen by the inverter would be smaller at higher switching frequencies.Therefore, a small value of capacitance suffices in PWM inverters, but this capacitor must be
able to carry the ripple current. A small capacitance across the diode rectifier also results in a
better input current waveform drawn from the utility source. However, care should be taken in
not letting the voltage ripple in the dc bus voltage become too large, which would cause
additional harmonics in the voltage applied to the motor.
Impact of PWM-VSI HarmonicsIn a PWM inverter output voltage, since the harmonics are at a high frequency, the ripple in
the motor current is usually small due to high leakage reactances at these frequencies. Since
these high-frequency voltage harmonics can have as high or even higher amplitude compared
to the fundamental-frequency component, the iron losses (eddy current and hysteresis in the
stator and the rotor iron) dominate. In fact, the total losses due to harmonics may even be
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higher with a PWM inverter than with a square-wave inverter. This comparison would of
course depend on the motor design class, magnetic material property, and switching
frequency. Because of these additional harmonic losses, it is generally recommended that a
standard motor with a 5- 10% higher power rating be used.
In a PWM drive, the pulsating torques developed are small in amplitude and are at high
frequencies (compared to the fundamental). Therefore, as shown in Eq. 14-49, they producelittle speed pulsations because of the motor inertia.
Input Power Factor and current waveform
The input ac current drawn by the rectifier of a PWM-VSI drive contains a large amount of
harmonics. Its waveform is shown in Fig. 14-l9b for a single-phase and a three-phase input.
The input inductance LS improves the input ac current waveform somewhat. Also, a small dc-
link capacitance will result in a better waveform.
The power factor at which the drive operates from the utility system is essentially independent
of the motor power factor and the drive speed. It is only a slight function of the load power,
improving slightly at a higher power. The displacement power factor (DPF) is approximately100%, as can be observed from the input current waveforms of Fig. 14-19b.
Electromagnetic braking
The power How during electromagnetic braking is from the motor to the variable-frequency
controller. During braking, the voltage polarity across the dc-bus capacitor remains the same
as in the motoring mode. Therefore, the direction of the dc bus current to the inverter gets
reversed. Since the current direction through the diode rectifier bridge normally used in
PWM-VSI drives cannot reverse, some mechanism must be implemented to handle this
energy during braking; otherwise the dc-bus voltage can reach destructive levels.One way to accomplish this goal is to switch on a resistor in parallel with the dc-bus
capacitor, as is shown in Fig. 14-20a, if the capacitor voltage exceeds a preset level, in order
to dissipate the braking energy.
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Fig 14.20 Electromagnetic braking in PWM-VSI: (a) dissipative braking; (b) regenerative
braking.
An energy-efficient technique is to use a four-quadrant converter (switch-mode or a back-to-
back connected thyristor converter) at the front end in place of the diode bridge rectifier. This
would allow the energy recovered from the motor-load inertia to be fed back to the utility
supply, as shown in Fig. 14-20b, since the current through the four-quadrant converter used
for interfacing with the utility source can reverse in direction. This is called regenerativebraking since the recovered energy is not wasted. The decision to employ regenerative
braking over dissipative braking depends on the additional equipment cost versus the savings
on energy recovered and the desirability of sinusoidal currents and unity power factor
operation from the utility source.
Adjustable-speed control of PWM-VSI drivesIn VSI drives (both PWM and square-wave type), the speed can be controlled without a speed
feedback loop, where there may be a slower acting feedback loop through the processor
controller. Figure 14-21 shows such a control. The frequency of the inverter output voltages is
controlled by the input speed reference signal ref. The input command refis modified for
protection and improved performance, as will be discussed shortly, and the required control
inputs (s or f and Vs signals) to the PWM controller in Fig. 14-21 are calculated. The PWM
controller can be realized by analog components, as indicated by Fig. 14-19b. The control
signals (e.g., va,control) can be calculated from the f and V s signals and by knowing Vd and Vtri.
Fig. 14.21 Speed control circuit. Motor speed is not measured.
A synchronous PWM must be used. This requires that the switching frequency vary in
proportion to f. To keep the switching frequency close to its maximum value, there are jumps
in mf and, hence, in fs as f decreases, as shown in Fig. 14-22. To prevent jittering at
frequencies where jumps occur, a hysteresis must be provided. Digital ICs such as HEF5752V
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are commercially available that incorporate many of the functions of the PWM controller
described earlier.
Fig. 14.22 Switching frequency versus the fundamental frequency.
For protection and better speed accuracy, current and voltage feedback may be employed.
These signals are required anyway for starting/stopping of the drive, to limit the maximum
current through the drive during acceleration/deceleration or under heavy load conditions, and
to limit the maximum dc link voltage during braking of the induction motor. Because of slip,
the induction motor operates at a speed lower than the synchronous speed. It is possible to
approximately compensate for this slip speed, which increases with torque, without measuringthe actual speed. Moreover, a voltage boost is required at lower speeds. To meet these
objectives, the motor currents and the dc link voltage Vd across the capacitor are measured.
To represent the instantaneous three-phase ac motor currents, a current io at the inverter input,
as shown in Fig. 14-21, is measured. The following control options are described:
1. Speed control circuit. As shown in Fig. 14-21, a speed control circuit accepts the speed
reference signal r,refas the input that controls the frequency of the inverter output voltages.
By the ramp limiter, the maximum acceleration/deceleration rates can be specified by the user
through potentiometers that adjust the rate-of-change allowed to the speed reference signal.
During the acceleration/deceleration condition, it is necessary to keep the motor current i o and
the dc-bus voltage Vd within limits.
If the speed regulation is to be improved, to be more independent of the load torque, it also
accepts an input from the slip compensation subcircuit, as shown in Fig. 14-21 and explained
in item 3 below.
2. Current-limiting circuit. A current-limiting circuit is necessary if a speed ramp limiter as in
Fig. 14-21 is not used. In the motoring mode, ifs is increased too fast compared to the motor
speed, then sl and, hence, io would increase. To limit the maximum rate of acceleration so
that the motor current stays below the current limit, the actual motor current is compared with
the current limit, and the error, through a controller, acts on the speed control circuit by
reducing the acceleration rate (i.e., by reducing ms).
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In the braking mode, ifs is reduced too fast, the negative slip would become large in
magnitude and would result in a large braking current through the motor and the inverter. To
restrict this current to the current limit during the braking, the actual current is compared with
the current limit, and the error, fed through a controller, acts on the speed control circuit by
decreasing the deceleration rate (i.e. , by increasing s). During braking, the dc-bus capacitor
voltage must be kept within a maximum limit. If there is no regenerative braking, adissipation resistor is switched on in parallel with the dc-bus capacitor to provide a dynamic
braking capability. If the energy recovered is larger than that lost through various losses, the
capacitor voltage could become excessive. Therefore, if the voltage limit is exceeded, the
control circuit decreases the deceleration rate (by increasing s).
3. Compensation for slip. To keep the rotor speed constant, a term must be added to the
applied stator frequency, which is proportional to the motor torque Tem, as can be seen from
Fig. 14-6:
s = r,ref+ k18Tem (14-50)
The second term in Eq. 14-50 is calculated by the slip compensation block of Fig. 14-21 . Oneoption is to estimate Tem. This can be done by measuring the dc power to the motor and
subtracting the losses in the inverter and in the stator of the motor to get the air-gap power P ag.
From Eqs. 14-3 and 14-18c, Tem can be calculated.
4. Voltage boost. To keep the air gap flux ag constant, the motor voltage must be (as found by
combining Eqs. 14-38b and 14-25)
Vs = k19s + k20Tem (14-51)
Using Tem as calculated in item 3 above and knowing mf, the required voltage can be
calculated from Eq. 14-51. This provides the necessary voltage boost in Fig. 14-21.
It should be noted that, if needed, the speed can be precisely controlled by measuring the
actual speed and thereby using the actual slip in the block diagram of Fig. 14-21. By knowing
the slip, the actual torque can be calculated from Eq. 14-27, thereby allowing the voltageboost to be calculated more accurately.
Variable-frequency square-wave VSI drives
The schematic of such a drive was shown in Fig. 14-18b. The inverter operates in a square-
wave mode, which results in phase-to-motor-neutral voltage, as shown in Fig. 14-24a. With
the square-wave inverter operation each inverter switch is on for 180 and a total of three
switches are on at any instant of time. The resulting motor current waveform is also shown in
Fig. 14-24b. Because of the inverter operating in a square-wave mode, the magnitude of the
motor voltages is controlled by controlling Vd in Fig. 14-18b by means of a line-frequency
phase-controlled converter.
Voltage harmonics in the inverter output decrease as V1/h with h = 5, 6, 11, 13, . . ., where V,
is the fundamental-frequency phase-to-neutral voltage. Because of substantial magnitudes of
low-order harmonics, harmonic currents calculated from Eq. 14-47 are significant. These
harmonic currents result in large torque ripple, which can produce troublesome speed ripple at
low operating speeds.
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Fig. 14.24 Square-wave VSI waveforms
Assuming a continuously flowing current through the rectifier, and for simplicity, ignoring
the line-side inductances,
Vd = 1.35 VLL cos (14-52)
where VLL is the line-line rms line voltage. From Eq. 8-58, the motor line-line voltage for a
given Vd is
VLLmotor= 0.78Vd (14-53)
From Eqs. 14-52 and 14-53,
VLL1motor = 1,05VLLcos = VLLcos (14-54)
which shows that the maximum line-line fundamental-frequency motor voltage (at = 0) is
approximately equal to VLL. Note that the same maximum motor voltage (equal to the line
voltage) can be approached in PWM-VSI drives only by overmodulation. Therefore, in both
PWM and square-wave VSI drives, the maximum available motor voltage in Fig. 14-12b isapproximately equal to the line voltage. This allows the use of standard 60-Hz motors, since
the inverter is able to supply the rated voltage of the motor at its rated frequency of 60 Hz.
In a square-wave drive, from Eq. 14-54 and assuming Vs/f to be constant.
r/r,rated=VLL1motor/VLL=cos (14-55)
From Eqs. 6-47a and 14-55, the drive operates at the following power factor from the line
(assuming that a sufficiently large filter inductor is present in Fig. 14-18b at the rectifier
output):
Line power factor ~ 0.955 cos ~ 0.955 r/r.rated(14-56)
which shows that the line power factor at the rated speed is better than that of an induction
motor supplied directly by the line. At low speed, however, the line power factor of a square-
wave drive can become quite low, as seen from Eq. 14-56. This can be remedied by replacingthe thyristor rectifier by a diode rectifier bridge in combination with a step-down dc-dc
converter.
Current source inverters
Variable-frequency CSI drives
Figure 14-18c shows the schematic of a CSI drive. Basically it consists of a phase-controlled
rectifier, a large inductor, and a dc-to-ac inverter. A large inductor is used in the dc link,
which makes the input appear as a current source to the inverter.
Since the induction motor operates at a lagging power factor, circuits for forced commutationof the inverter thyristors are needed, as shown in Fig. 14-25a. These forced-commutation
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circuits consist of diodes, capacitors, and the motor leakage inductances. This requires that the
inverter be used with the specific motor for which it is designed. At any time, only two
thyristors conduct: one of the thyristors connected to the positive dc bus and the other
connected to the negative dc bus. The motor current and the resulting phase voltage waveform
are shown in Fig. 14-25b. In a CSI drive, the regenerative braking can be easily provided
without any additional circuits.
Fig. 14.25 CSI drive: (a) inverter; (b) idealized phase waveforms.
In the past, the fact that line-frequency thyristors with simple commutation circuits act as the
inverter switches was a very important asset of CSI drives. With the availability of
controllable switches in ever-increasing power ratings, nowadays CSI drives are used mostly
in very large horsepower applications.
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Modulation techniques
PWM with Bipolar Voltage Switching
Here the diagonally opposite switches (TA+, TB-) and (TA-, TB+) from the two legs in Fig. 8-11
are switched as switch pairs 1 and 2, respectively. With this type of PWM switching, theoutput voltage waveform of leg A is determined by comparison of vcontrol and vtri in Fig. 8-12a.
Fig. 8.11 Single-phase full-bridge inverter.
The output of inverter leg B is negative of the leg A output; for example, when TA+ is on and
vAo is equal to dV
2
1+ , TB- is also on and vBo = dV
2
1 . Therefore
vBo(t) = -vAo(t) (8-17)
and
vo(t) = vAo(t) - vBo(t) = 2vAo(t) (8-18)
Fig. 8-12 PWM with bipolar voltage switching.
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The vo waveform is shown in Fig. 8-12b. The peak of the fundamental-frequency component
in the output voltage ( )1oV is)0.1( 1 = adao mVmV (8-19)
and
)0.1(
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Fig. 8.13 Inverter with fictitious filters.
With these assumptions, vo in Fig. 8-13 is a pure sine wave at the fundamental output
frequency 1,
tVvvooo 11 sin2 == (8-22)
If the load is as shown in Fig. 8-13, where eo is a sine wave at frequency 1, then the output
current would also be sinusoidal and would lag vo for an inductive load such as an ac motor:
)sin(2 1 = tIi oo (8-23)
where is the angle by which io lags vo.
On the dc side, the L-C filler will filter the high-switching-frequency components id, and id
would only consist of the low-frequency and dc components.
Assuming that no energy is stored in the filters,
)sin(2sin2)()()( 11* == tItVtitvtiV oooodd (8-24)
Therefore
21
*
)2cos(cos)( ddd
oo
d
oo
d iItV
IV
V
IV
ti +== (8-25)
)2cos(2 12 = tII dd (8-26)
where
cosd
oo
d
V
IVI = (8-27)
and
d
oo
d
V
IVI
2
12 = (8-28)
Equation 8-26 for id shows that it consists of a dc component Id, which is responsible for the
power transfer from Vd on the dc side of the inverter to the ac side. Also, i d* contains asinusoidal component at twice the fundamental frequency. The inverter input current id
consists of id* and the high-frequency components due to inverter switchings, as shown in Fig.
8-14.
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Fig. 8-14 The dc-side current in a single-phase inverter with PWM bipolar voltage switching.
In practical systems, the previous assumption of a constant dc voltage as the input to the
inverter is not entirely valid. Normally, this dc voltage is obtained by rectifying the ac utility
line voltage. A large capacitor is used across the rectifier output terminals to filter the dc
voltage. The ripple in the capacitor voltage, which is also the dc input voltage to the inverter,
is due to two reasons: (1) The rectification of the line voltage to produce dc does not result ina pure dc as discussed in dealing with the line-frequency rectifiers. (2) As shown earlier by
Eq. 8-26, the current drawn by a single-phase inverter from the dc side is not a constant dc but
has a second harmonic component (of the fundamental frequency at the inverter output) in
addition to the high-switching-frequency components. The second harmonic current
component results in a ripple in the capacitor voltage, although the voltage ripple due to the
high switching frequencies is essentially negligible.
PWM with Unipolar Voltage Switching
In PWM with unipolar voltage switching, the switches in the two legs of the full-bridge
inverter of Fig. 8-11 are not switched simultaneously, as in the previous PWM scheme. Here,
the legs A and B of the full-bridge inverter are controlled separately by comparing v tri with
vcontrol and vcontrol, respectively. As shown in Fig. 8-15a, the comparison of vcontrol with the
triangular waveform results in the following logic signals to control the switches in leg A:
vcontrol>vtri: TA+ on and vAN=Vd (8-29)
vcontrolvtri: TB+ on and vBN=Vd (8-30)
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-vcontrol
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The waveforms of Fig. 8-15 show that there are four combinations of switch on-states and the
corresponding voltage levels:
1. TA+, TB- on: vAN=Vd, vBN=0; vo=Vd2. TA-, TB+ on: vAN=0, vBN= Vd; vo=-Vd3. TA+, TB- on: vAN=Vd, vBN= Vd; vo=0
4. TA-, TB+ on: vAN=0, vBN=0; vo=0
We notice that when both the upper switches are on, the output voltage is zero. The output
current circulates in a loop through TA+ and DB+ or DA+ and TB+ depending on the direction of
io. During this interval, the input current id is zero. A similar condition occurs when both
bottom switches TA- and TB- are on.
In this type of PWM scheme, when a switching occurs, the output voltage changes between
zero and +Vd or between zero and Vd voltage levels. For this reason, this type of PWM
scheme is called PWM with a unipolar voltage switching, as opposed to the PWM with
bipolar (between +Vd and -Vd) voltage-switching scheme described earlier. This scheme has
the advantage of effectively doubling the switching frequency as far as the output
harmonics are concerned, compared to the bipolar voltage-switching scheme. Also, thevoltage jumps in the output voltage at each switching are reduced to Vd, as compared to 2Vd
in the previous scheme.
The advantage of effectively doubling the switching frequency appears in the harmonic
spectrum of the output voltage waveform, where the lowest harmonics (in the idealized
circuit) appear as sidebands of twice the switching frequency. It is easy to understand this if
we choose the frequency modulation ratio mf to be even (mfshould be odd for PWM with
bipolar voltage switching) in a single-phase inverter. The voltage waveforms vAN and vBN are
displaced by 180 of the fundamental frequency f1 with respect to each other. Therefore, the
harmonic components at the switching frequency in vAN and vBN have the same phase
(ANBN = fm180 = 0, since the waveforms are 180 displaced and m f is assumed to be
even). This results in the cancellation of the harmonic component at the switching frequency
in the output voltage vo = vANvBN. In addition, the sidebands of the switching-frequency
harmonics disappear. In a similar manner, the other dominant harmonic at twice the switching
frequency cancels out, while its sidebands do not. Here also
)0.1( 1 = adao mVmV (8-32)
and
)0.1(4
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Fig. 8.16 The dc-side current in a single-phase inverter with PWM unipolar voltage switching.
By comparing Figs. 8-14 and 8-16, it is clear that using PWM with unipolar voltage switching
results in a smaller ripple in the current on the dc side of the inverter.
Square-Wave Operation
The full-bridge inverter can also be operated in a square-wave mode. Both types of PWM
discussed earlier degenerate into the same square-wave mode of operation, where the switches
(TA+, TB-) and (TB+, TA-) are operated as two pairs with a duty ratio of 0.5.
As is the case in the square-wave mode of operation, the output voltage magnitude given
below is regulated by controlling the input dc voltage:
do VV
4 1 = (8-36)
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