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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