Topic 11: Slip-Recovery Drives for Wound-Field Induction Motors Spring 2004 ECE 8830 - Electric Drives Introduction In a wound-field induction motor the slip rings allow easy recovery of the slip power which can be electronically controlled to control the speed of the motor. The oldest and simplest technique to invoke this slip-power recovery induction motor speed control is to mechanically vary the rotor resistance. Introduction (contd) Slip-power recovery drives are used in the following applications: Large-capacity pumps and fan drives Variable-speed wind energy systems Shipboard VSCF (variable-speed/constant frequency) systems Variable speed hydro-pumps/generators Utility system flywheel energy storage systems Speed Control by Rotor Rheostat Recall that the torque-slip equation for an induction motor is given by: From this equation it is clear that 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. ( ) 22 2 23 .2 / ( )s ree s r e ls lrV R PTs R R s L Le e| |= |\ . + + +Speed Control by Rotor Rheostat (contd) Speed Control by Rotor Rheostat (contd) With R1=0, i.e. slip rings shorted, speed is determined by rated load torque (pt. A). As Rr increases, curve becomes flatter leading to lower speed until speed becomes zero for Rr >R4. Although this approach is very simple, it is also very inefficient because the slip energy is wasted in the rotor resistance. Speed Control by Rotor Rheostat (contd) An electronic chopper implementation is also possible as shown below but is equally inefficient. Static Kramer Drive 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) Static Kramer Drive - only allows operation at sub-synchronous speed. 2) Static Scherbius Drive - allows operation above and below synchronous speed. Static Kramer Drive (contd) A schematic of the static Kramer drive is shown below: Static Kramer Drive (contd) 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, Irf = fundamental rotor current referred to the stator, g = air gap flux, Im=magnetizing current, and |=PF angle. Static Kramer Drive (contd) The voltage Vd is proportional to slip, s and the current Id is proportional to torque. At a particular speed, the inverters firing angle can be decreased 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 Drive (contd) Voltage Vd (neglecting stator and rotor voltage drops) is given by: where s=per unit slip, VL= stator line voltage and n1=stator-to-rotor turns ratio. The inverter dc voltage VI is given by: where n2=transformer turns ratio (line side to inverter side) and o=inverter firing angle. 11.35 LdsVVn=21.35 cosLIVVno= Static Kramer Drive (contd) For inverter operation, t/2 reduction in power factor (|L> |s). The inverter line current phasor is IT. The figure shows IT at s=0.5 for n1=n2. The real component ITcoso opposes the real component of the stator current but the reactive component ITsino adds to the stator magnetizing current. 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 varies, the phasor IT rotates from o=90 at s=0 to o=160 at s=1. Static Kramer Drive (contd) 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 increases. The PF can be improved close to synchronous speed by using a step-down transformer. The inverter line current is reduced by the transformer turns ratio -> reduced PF. Static Kramer Drive (contd) 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 reduced. A starting method for a static Kramer drive is shown on the next slide. Static Kramer Drive (contd) 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 smax value is reached after which switch 1 is opened and the drive controller takes over. AC Equivalent Circuit of Static Kramer Drive 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 Thus the rotor power per phase is given by: 21.35cosL dfV IPn o =' ' 221.35 1' cos3L dl f d dV IP P P I Rn o| |= + = + |\ .AC Equivalent Circuit of Static Kramer Drive (contd) Therefore, the motor air gap power per phase is given by: where Ir=rms rotor current per phase, Rr = rotor resistance, and Pm = mech. output power per phase. ' 2 ''g r r mP I R P P = + +AC Equivalent Circuit of Static Kramer Drive (contd) Only the fundamental component of rotor current, Irf needs to be considered. For a 6-step waveform, Thus, the rotor copper loss per phase is given by: d rf I It6=) 5 . 0 (31 2 2 2 'd r r d d r r rl R R I R I R I P + = + =AC Equivalent Circuit of Static Kramer Drive(contd) The mechanical output power per phase is then given by: Pm = (fund. slip power) (1-s)/s 221.35 (1 )( 0.5 ) cos3 6Lrf r d rfV sI R R In st o ( = + + ( AC Equivalent Circuit of Static Kramer Drive(contd) The resulting air gap power is given by: where: and ' 2 2 Ag rf X rfRP I R Is= +21 ( 0.5 )9X r dR R Rt | |= + |\ .21.35( 0.5 ) cos3 6LA r ddVR R Rn It o = + +AC Equivalent Circuit of Static Kramer Drive(contd) The per-phase equivalent circuit derived from these equations (referred to the rotor) is shown below: Static Kramer Drive Example Example 6.3 Krishnan Torque Expression The average torque developed by the motor = total fundamental air gap power synchronous speed of motor where Pgf = fundamental frequency per-phase air gap power. ' 23 32 2gf rf AeeP I RP PTs e | || | | |= = | | | |\ . \ .\ . Torque Expression (contd) A torque expression in terms of inverter firing angle may be derived (see text pg. 320) resulting in: 22 22 1 2 1 2cos cos cos32see rV P s sT sR sn n n n sno o oe (| | | || | ( ~ + | | |\ . (\ . \ . Torque Expression (contd) The torque-speed curves at different firing angles of the inverter are shown below: Harmonics in a Static Kramer 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 harmonic torque is small compared to average torque and can generally be neglected in practice. Speed Control of a Static Kramer Drive A speed control system for a static Kramer drive is shown below: Speed Control of a Static Kramer Drive (contd) The air gap flux is constant and the torque is controlled by the dc link current Id (controlled in the inner control loop). The speed is controlled via the outer control loop (see performance curves below). Power Factor Improvement As indicated earlier, the static Kramer drive is characterized by poor line PF 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 Drive 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 reverse direction. This can be achieved by replacing the diode bridge rectifier with a thyristor bridge. This is the basic topology change for the static Scherbius drive from the static Kramer drive. Static Scherbius Drive (contd) Static Scherbius Drive (contd) One of the limitations of the previous topology is that line commutation of the machine-side converter becomes difficult near synchronous speed because of excessive commutation angle overlap. A line commutated cycloconverter can overcome this limitation but adds substantial cost and complexity to the drive. Static Scherbius Drive (contd) Another approach is to use a double-sided PWM voltage-fed converter system as shown below: Modified Scherbius Drive for Shipboard VSCF Power Generation Another approach that has been used for stand-alone shipboard power generation is shown below: Modified Scherbius Drive for Ship-board VSCF Power Generation (contd) In this approach an induction generator provides real stator power Pm to a 3u 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 QL is reflected to the rotor as sQL which adds to the machine magnetizing power requirement to give the total reactive power QL of the cycloconverter. This power is further increased to QL at the cycloconverter input by the shaft-mounted synchronous exciter. Modified Scherbius Drive for Ship-board VSCF Power Generation (contd) The slip frequency and its phase sequence are adjusted for varying shaft speed so that the resultant air gap flux rotates at synchronous speed. At subsynchronous speeds the slip power sPm is supplied to the rotor by the exciter and so the remaining ouptut power (1-s)Pm is supplied to the shaft. At supersynchronous speeds, the rotor output power flows in the opposite direction so that the total shaft power increases to (1+s)Pm. Modified Scherbius Drive for Ship-board VSCF Power Generation (contd) Rotor voltage and frequency vary linearly with deviation from synchronous speed. 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 range of slip frequency will be 0->20Hz for a 60Hz supply frequency.