power electronic drive

EET 421 POWER ELECTRONIC DRIVESO C O C S

Slip-Recovery Drives for W d Fi ld I d ti M tWound-Field Induction Motors

Introd ctionIntroduction

d f ld d h lIn a wound-field induction motor the slip rings allow easy recovery of the slip power which can be electronically controlled to which can be electronically controlled to control the speed of the motor.

Th ld t d i l t t h i t The oldest and simplest technique to invoke this slip-power recovery induction motor speed control is to mechanically vary motor speed control is to mechanically vary the rotor resistance.

Introd ction (cont’d)

INDRAINDRA 20092009

Introduction (cont’d)

Slip power recovery drives are used in Slip-power recovery drives are used in the following applications:

Large-capacity pumps and fan drivesVariable-speed wind energy systemsShipboard VSCF (variable-speed/constant frequency) systemsV i bl d h d / tVariable speed hydro-pumps/generatorsUtility system flywheel energy storage systemssystems

Speed Control b Rotor RheostatSpeed Control by Rotor Rheostat

Recall that the torque slip equation for an Recall that the torque-slip equation for an induction motor is given by:

( )

2

2 2 23 .

2 / ( )sr

ee s r e ls lr

VRPTs R R s L Lω ω

⎛ ⎞= ⎜ ⎟⎝ ⎠ + + +

From this equation it is clear that the torque-slip curves are dependent on the torque slip curves are dependent on the rotor resistance Rr. The curves for different rotor resistances are shown on the next slide for four different rotor resistances (R1-R4) with R4>R3>R2>R1.

Speed Control by Rotor Rheostat (cont’d)(cont’d)

Speed Control by Rotor Rheostat (cont’d)(cont’d)

h l h d dWith R1=0, i.e. slip rings shorted, speed is determined by rated load torque (pt. A). As R increases curve becomes flatter leading Rr increases, curve becomes flatter leading to lower speed until speed becomes zero for Rr >R4.r 4

Although this approach is very simple, it is also very inefficient because the slip energy also very inefficient because the slip energy is wasted in the rotor resistance.

Speed Control by Rotor Rheostat ( t’d)(cont’d)An electronic chopper implementation is An electronic chopper implementation is also possible as shown below but is equally inefficient.

Static Kramer DriveStatic Kramer Drive

Instead of wasting the slip power in the Instead of wasting the slip power in the rotor circuit resistance, a better approach is to convert it to ac line power and return it back to the line. Two types of converter provide this approach:1) St ti K D i l ll 1) Static Kramer Drive - only allows

operation at sub-synchronous speed.2) St ti S h bi D i ll 2) Static Scherbius Drive - allows

operation above and below h dsynchronous speed.

Static Kramer Dri e (cont’d)Static Kramer Drive (cont’d)

A schematic of the static Kramer drive is A schematic of the static Kramer drive is shown below:

Static Kramer Drive (cont’d)The machine air gap flux is created by the stator supply and is essentially constant. The rotor current is ideally a 6-step wave in phase with the rotor voltage.

The motor fundamental phasor diagram referred to the stator is as shown below:

Vs = stator phase voltage, Is=stator current I ’ current, Irf’ = fundamental rotor current referred to the t t i fl stator, ψg = air gap flux,

Im=magnetizing current, and φ=PF angle.


The voltage Vd is proportional to slip, s and the current Id is proportional to torque At a particular speed the torque. At a particular speed, the inverter’s firing angle can be decreased to decrease the voltage VI. This will to decrease the voltage VI. This will increase Id and thus the torque. A simplified torque-speed expression for this implementation is developed next.

Static Kramer Dri e (cont’d)Static Kramer Drive (cont’d)Voltage Vd (neglecting stator and rotor g d ( g gvoltage drops) is given by:

1.35 LsVV

where s=per unit slip VL= stator line voltage

1

LdV

n=

where s=per unit slip, VL= stator line voltage and n1=stator-to-rotor turns ratio. The inverter dc voltage VI is given by:

2

1.35 cosLI

VV

nα

=

where n2=transformer turns ratio (line side to inverter side) and α=inverter firing angle.

2


For inverter operation π/2<α<π In steady For inverter operation, π/2<α<π. In steady state Vd=VI (neglecting ESR loss in inductor)

n=> 1

2

cosnsn

α=

The rotor speed ωr is given by:

if n1=n21(1 ) (1 cos ) (1 cos )nsω ω α ω α ω= − = − = − if n1 n2

Thus rotor speed can be controlled by 2

(1 ) (1 cos ) (1 cos )r e e esn

ω ω α ω α ω

controlling inverter firing angle, α. At α=π, ωr=0 and at α=π/2 , ωr=ωe.

Static Kramer Dri e (cont’d)Static Kramer Drive (cont’d)It can be shown (see text) that the torque ( ) qmay be expressed as:

1.35 Ld

VPT I⎛ ⎞= ⎜ ⎟

The below figure shows the torque-speed 12e d

e

T Inω⎜ ⎟

⎝ ⎠

curves at different inverter angles.

Static Kramer Dri e (cont’d)Static Kramer Drive (cont’d)The fundamental component of the rotor pcurrent lags the rotor phase voltage by φrbecause of a commutation overlap angle µ( fi b l ) At li h (see figure below). At near zero slip when rotor voltage is small, this overlap angle can exceed π/3 resulting in shorting of the can exceed π/3 resulting in shorting of the upper and lower diodes.


The phasor diagram for a static Kramer The phasor diagram for a static Kramer drive at rated voltage is shown below:

IIL

Note: All phasors are referred to stator.

Static Kramer Dri e (cont’d)Static Kramer Drive (cont’d)On the inverter side, reactive power is drawn by the line -> reduction in power factor (φL> φs). The inverter line current phasor is I The figure shows I at s=0 5 phasor is IT. The figure shows IT at s=0.5 for n1=n2. The real component ITcosαopposes the real component of the stator pp pcurrent but the reactive component ITsinαadds to the stator magnetizing current. Th t t l li t I i th h The total line current IL is the phasor sum of IT and IS. With constant torque, the magnitude of IT is constant but as slip magnitude of IT is constant but as slip varies, the phasor IT rotates from α=90°at s=0 to α=160° at s=1.


At zero speed (s=1) the motor acts as a At zero speed (s 1) the motor acts as a transformer and all the real power is transferred back to the line (neglecting losses). The motor and inverter only consume reactive power.

At synchronous speed (s=0) the power factor is the lowest and increases as slip i Th PF b i d l increases. The PF can be improved close to synchronous speed by using a step-down transformer The inverter line down transformer. The inverter line current is reduced by the transformer turns ratio -> reduced PF.

Static Kramer Drive (cont’d)Static Kramer Drive (cont d)

A further advantage of the step-down transformer is that since it reduces the inverter voltage by the turns ratio, the device power ratings for the switching devices in the inverter may also be devices in the inverter may also be reduced.

A starting method for a static Kramer drive is shown on the next slide. drive is shown on the next slide.

Static Kramer Drive (cont’d)Static Kramer Drive (cont d)

The motor is started with switch 1 closed and switches 2 and 3 open. As the motor builds up speed, switches 2 and 3 are sequentially closed until desired s value is reached after which until desired smax value is reached after which switch 1 is opened and the drive controller takes over.

AC Equivalent Circuit of Static K D iKramer Drive

Use an ac equivalent circuit to analyze the Use an ac equivalent circuit to analyze the performance of the static Kramer drive. The slip-power is partly lost in the dc link resistance and partly transferred back to the line. The two components are:

Pl=Id2Rd and

2

1.35 cosL df

V IPn

α=

Thus the rotor power per phase is given by:1 351 V I⎛ ⎞' ' 2

2

1.351' cos3

L dl f d d

V IP P P I Rn

α⎛ ⎞

= + = +⎜ ⎟⎝ ⎠

AC Equivalent Circuit of Static K D i ( t’d)Kramer Drive (cont’d)

Therefore the motor air gap power per phase Therefore, the motor air gap power per phase is given by:

' 2 '' 2 ''g r r mP I R P P= + +

where Ir=rms rotor current per phase,Rr = rotor resistance, and Pm’ = mech. output power per phase.

AC Equivalent Circuit of Static K D i ( t’d)Kramer Drive (cont’d)

Only the fundamental component of rotor Only the fundamental component of rotor current, Irf needs to be considered. For a 6-step waveform,

drf IIπ6

=

Thus, the rotor copper loss per phase is given by:

)5.0(31 222'

drrddrrrl RRIRIRIP +=+=3

AC Equivalent Circuit of Static Kramer Dri e(cont’d)Kramer Drive(cont’d)

The mechanical output power per phase is The mechanical output power per phase is then given by:

Pm’ = (fund. slip power) (1-s)/s

2

2

1.35 (1 )( 0.5 ) cos3 6

Lrf r d rf

V sI R R In s

π α⎡ ⎤ −

= + +⎢ ⎥⎣ ⎦⎣ ⎦


The resulting air gap power is given by:The resulting air gap power is given by:

' 2 2 ARP I R I= +

h

g rf X rfP I R Is

= +

2

1 ( 0 )π⎛ ⎞⎜ ⎟where:

d

1 ( 0.5 )9X r dR R Rπ⎛ ⎞

= − +⎜ ⎟⎝ ⎠

1.35( 0 5 ) LVR R R πand

2

( 0.5 ) cos3 6

LA r d

d

R R Rn I

α= + +


The per-phase equivalent circuit derived p p qfrom these equations (referred to the rotor) is shown below:

Torque ExpressionTorque Expression

h d l d b hThe average torque developed by the motor = total fundamental air gap power

synchronous speed of motorsynchronous speed of motor

' 2f f AP I RP P ⎛ ⎞⎛ ⎞ ⎛ ⎞

⎜ ⎟∴ 3 32 2

gf rf Ae

e

P I RP PTsω

⎛ ⎞⎛ ⎞ ⎛ ⎞= = ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠

where Pgf’ = fundamental frequency per-phase air gap power phase air gap power.

Torque Expression (cont’d)Torque Expression (cont d)

fA torque expression in terms of inverter firing angle may be derived (see text pg 320) resulting in:(see text pg. 320) resulting in:

22 2⎡ ⎤⎛ ⎞ ⎛ ⎞⎛ ⎞22 2

2 1 2 1 2

cos cos cos3

2s

ee r

VP s sT sR sn n n n sn

α α αω

⎡ ⎤⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎢ ⎥≈ − + −⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

Torq e E pression (cont’d)Torque Expression (cont’d)

The torque-speed curves at different firing The torque speed curves at different firing angles of the inverter are shown below:

Harmonics in a Static Kramer Dri eKramer Drive

The rectification of slip-power causes harmonic currents in the rotor which are reflected back into the stator. This results in increased machine losses. The h i i ll d harmonic torque is small compared to average torque and can generally be neglected in practice neglected in practice.

Speed Control of a Static K D iKramer Drive

A speed control system for a static Kramer A speed control system for a static Kramer drive is shown below:

Speed Control of a Static K D i ( t’d)Kramer Drive (cont’d)

The air gap flux is constant and the torque g p qis controlled by the dc link current Id (controlled in the inner control loop). The

d i t ll d i th t t l speed is controlled via the outer control loop (see performance curves below).

Power Factor ImprovementPower Factor Improvement

d d l hAs indicated earlier, the static Kramer drive is characterized by poor line PF because of phase controlled inverter because of phase controlled inverter.

One scheme to improve PF is the commutator-less Kramer drive - see Bose text pp. 322-324 for description.

Static Scherbius DriveStatic Scherbius Drive

The static Scherbius drive overcomes the The static Scherbius drive overcomes the forward motoring only limitation of the static Kramer drive.

Regenerative mode operation requires the slip power in the rotor to flow in the p preverse direction. This can be achieved by replacing the diode bridge rectifier with a th i t b id Thi i th b i t l thyristor bridge. This is the basic topology change for the static Scherbius drive from the static Kramer drive the static Kramer drive.

Static Scherbi s Dri e (cont’d)Static Scherbius Drive (cont’d)

Static Scherbi s Dri e (cont’d)Static Scherbius Drive (cont’d)

f h l f hOne of the limitations of the previous topology is that line commutation of the machine-side converter becomes difficult machine-side converter becomes difficult near synchronous speed because of excessive commutation angle overlap. A g pline commutated cycloconverter can overcome this limitation but adds

b t ti l t d l it t th substantial cost and complexity to the drive.

Static Scherbi s Dri e (cont’d)Static Scherbius Drive (cont’d)Another approach is to use a double-sided ppPWM voltage-fed converter system as shown below:

Modified Scherbius Drive for Shipboard VSCF Po er GenerationShipboard VSCF Power Generation

Another approach that has been used for Another approach that has been used for stand-alone shipboard power generation is shown below:is shown below:

Modified Scherbius Drive for Ship-board VSCF Power Generation (cont’d)

In this approach an induction generator In this approach an induction generator provides real stator power Pm to a 3Φ 60Hz constant voltage bus which is equal to the turbine shaft power and the slip power fed to the rotor by a cycloconverter. The stator reactive power Q is reflected to the rotor as reactive power QL is reflected to the rotor as sQL which adds to the machine magnetizing power requirement to give the total reactive p q gpower QL’ of the cycloconverter. This power is further increased to QL” at the

l t i t b th h ft t d cycloconverter input by the shaft-mounted synchronous exciter.


The slip frequency and its phase sequence are The slip frequency and its phase sequence are adjusted for varying shaft speed so that the resultant air gap flux rotates at synchronous resultant air gap flux rotates at synchronous speed.

At subsynchronous speeds the slip power At subsynchronous speeds the slip power sPm is supplied to the rotor by the exciter and so the remaining ouptut power (1-s)Pm g p p ( ) m is supplied to the shaft. At supersynchronous speeds, the rotor output power flows in the

it di ti th t th t t l h ft opposite direction so that the total shaft power increases to (1+s)Pm.


Rotor voltage and frequency vary linearly with deviation from synchronous speed. For example if the shaft speed varies in For example, if the shaft speed varies in the range of 800-1600 rpm with 1200 rpm as the synchronous speed (s=±0.33) the as the synchronous speed (s ±0.33) the range of slip frequency will be 0->20Hz for a 60Hz supply frequency.

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