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ECE 8830 - Electric DrivesTopic 16: Control of SPM Synchronous Motor Drives Spring 2004
IntroductionControl techniques for synchronousmotor drives are similar to those forinduction motor drives. We willconsider both scalar and vector controlfor surface PM motor (both sinusoidaland trapezoidal PM motor) drives,reluctance motor drives, and woundfield synchronous motor drives.
Sinusoidal SPM Motor Drives The ideal synchronous motor torque- speed characteristic at a single frequency excitation is as shown below: TorqueMotoringMode 0 SpeedGeneratingMode
Sinusoidal SPM Motor Drives (cont’d)Thus, the motor either runs at synchronousspeed or doesn’t run at all. Two controlapproaches - open loop V/Hz control andself-control mode.In open-loop V/Hz control, the frequencyof the drive signal is used to control thesynchronous speed of the motor.In self-control, feedback from a shaftencoder is used to effect the control.
Sinusoidal SPM Motor Drives (cont’d)Open-loop V/Hz control is the simplestcontrol approach and is useful whenseveral motors need to be driven togetherin synchrony. Here the voltage is adjustedin proportion to the frequency to ensureconstant stator flux, ψs. An implementationof this control strategy is shown on thenext slide.
Sinusoidal SPM Motor Drives (cont’d)
Sinusoidal SPM Motor Drives (cont’d)The control characteristics are shown inthe figure below:
Sinusoidal SPM Motor Drives (cont’d)Neglecting the stator resistance, and usingthe field flux ψf as the reference phasor, aphasor diagram of the synchronous motoris shown below:
Sinusoidal SPM Motor Drives (cont’d)The torque developed by the motor is given by: P ψ sψ f P Te = 3 sin δ = 3 ψ s I s cos φ 2 Ls 2where Iscosφ is the in-phase component of thestator current and δ is the torque angle.If ωe* is changed too quickly, the system willbecome unstable. The max. rate ofacceleration/deceleration is given by: dω e* 1P = ± ( Ter m TL ) dt J2
Sinusoidal SPM Motor Drives (cont’d)A self-controlled scheme for an SPM motor isshown below:Here the frequency and phase of the inverteroutput are controlled by the absolute positionencoder mounted on the motor shaft.
Sinusoidal SPM Motor Drives (cont’d) The absolute position encoder required for self-controlled drives for synchronous motors are one of two types - an optical encoder or a mechanical resolver with decoder.
Sinusoidal SPM Motor Drives (cont’d)An optical encoder has alternating opaque andtransparent segments. A LED is placed on oneside and a photo-transistor on the other side.A binary coded disk is shown below:With 14 rings (14-bit resolution) a resolutionof 0.04 electrical degrees can be achieved fora four-pole motor with this type of encoder.
Sinusoidal SPM Motor Drives (cont’d)Another type of optical encoder is theslotted disk optical encoder. The belowencoder is specifically designed for a 4-polemotor.
Sinusoidal SPM Motor Drives (cont’d)There are many slots in the outer perimeterand two slots 180° apart on the inner radius.There are four optical sensors S1-S4. S4 islocated on the outer perimeter and the S1-S3sensors are located 60° apart on the innerradius. The sensor outputs are as shown below:
Sinusoidal SPM Motor Drives (cont’d)The block diagram of a resolver with decoderis shown below:
Sinusoidal SPM Motor Drives (cont’d)The analog resolver is basically a 2Φmachine that is excited by a rotor-mountedfield winding. The primary winding of arevolving transformer is excited by anoscillator with voltage V=V0sinωt. The statorwindings of the resolver generateamplitude-modulated output voltages: V1 = AV0 sin ω t sin θ and V2 = AV0 sin ω t cos θ
Sinusoidal SPM Motor Drives (cont’d)The decoder converts the analog voltageoutputs to digital position information. Thehigh-precision sin/cos multiplier multiplies $ $V1 and V2 by cos θ and sin θrespectively. Anerror amplifier takes the difference of thesetwo output signals to generate the signal $ AV0 sin ω t sin(θ − θ ) . The phase sensitivedemodulator creates a dc output that isproportional to $ sin(θ − θ ) . An integralcontroller, VCO, and up-down countertogether generate an estimated θ . Under $steady state conditions the tracking errorwill be zero.
Sinusoidal SPM Motor Drives (cont’d)Vector control of a sinusoidal SPM motoris relatively simple. Because of the largeeffective airgap in this type of motor, thearmature flux is very small so that ψs ≈ ψm≈ ψf . For maximumtorque sensitivity (andtherefore efficiency) we $s I= i .set ids=0 and qs
Sinusoidal SPM Motor Drives (cont’d)The torque developed by the motor can beexpressed as: 3 Pµ Te = ψ f iqs 2 2 µwhere ψ f is the space vector magnitude( 2ψ f ) and ψ f = ψ s cos φ = ψ s cos δ .A block diagram of a vector controlimplementation for a sinusoidal SPM motoris shown in the next slide.
Sinusoidal SPM Motor Drives (cont’d)Note: This vector control scheme is onlyvalid in the constant torque region.
Sinusoidal SPM Motor Drives (cont’d)The upper limits of the available dc-linkvoltage and current rating of the inverterlimit the maximum speed available at ratedtorque to the base speed (ωb). However, itis often desirable to operate at higherspeeds (e.g. in electric vehicles). Abovebase speed, however, the induced emf willexceed the input voltage and so currentcannot be fed into the motor. By reducingthe induced emf, by weakening the air gapflux linkages, higher speeds can beobtained.
Sinusoidal SPM Motor Drives (cont’d)In order to achieve the field weakening, ademagnetizing current -ids must be injectedon the stator side. However, this ids must belarge because of low armature reactionflux, ψa. This small weakening of ψs resultsin a small range of field-weakening speedcontrol.Let us consider next how to extend thevector control scheme to speeds beyondbase speed (ωb), i.e. into the field-weakeningregion.
Sinusoidal SPM Motor Drives (cont’d)A phasor diagram for field-weakeningcontrol is shown below:
Sinusoidal SPM Motor Drives (cont’d)The injected -ids which provides the fluxweakening results in a rotation of the I s $ $vector. At a’, I s = −ids which corresponds tozero torque and maximum speed, ωr1. Atthis condition, δ=0, ψs=ψs’, Vf=Vf’ and Vs=Vs’(see phasor diagram).The field weakening region can beincreased by increasing the statorinductance (see torque-speed diagram onnext slide).
Sinusoidal SPM Motor Drives (cont’d)
Sinusoidal SPM Motor Drives (cont’d)A block diagram of a vector control drivefor a sinusoidal SPM motor including thefield weakening region is shown below:
Sinusoidal SPM Motor Drives (cont’d)In constant torque mode, ids*=0 but in µfield-weakening mode, flux ψ s iscontrolled inversely with speed with -ids*control generated by the flux loop.Within the torque loop, iqs is controlled tobe limited to the value, i = Is * $2 − i 2 qsm ds $ Iswhere is the rated stator current.
Control of Brushless DC MotorDrivesTrapezoidal synchronous permanentmagnet motors have performancecharacteristics resembling those of dcmotors and are therefore often referred toas brushless dc motors (BLDM).Concentrated, full-pitch stator windings inthese motors are used to induce 3Φtrapezoidal voltage waves at the motorterminals. Thus a 3Φ inverter is requiredto drive these motors as shown in thenext slide.
Control of BLDM Drives (cont’d)The inverter can operate in two modes: 1) 2π/3 angle switch-on mode 2) Voltage and current control PWM mode
Control of BLDM Drives (cont’d)The 2π/3 angle switch-on mode is shown inthe below figure:
Control of BLDM Drives (cont’d)The switches Q1-Q6 are switched on so thatthe input dc current Id is symmetricallylocated at the center of each phase voltagewave. At any instant in time, one switch fromthe upper group (Q1,Q3,Q5) and one switchfrom the lower group (Q2,Q4,Q6) are ontogether. The absolute position sensor isused to ensure the correct timing of theswitching/commutation of the devices. At anytime, two phase CEMF’s (2Vc) of the motorare connected in series across the inverterinput. ∴The power into the motor is 2VCId.
Control of BLDM Drives (cont’d)In addition to controlling commutation bythe timing of the switches in the PWMinverter, it is also possible to control thecurrent and voltage output of the inverterby operating the PWM in a chopper mode.This is the voltage and current controlPWM mode of operation of the drive.
Control of BLDM Drives (cont’d)The average output current and voltage areset by the duty cycle of the switches in thePWM inverter. Varying the duty cycle resultsin variable average output current/voltage.Two chopping modes can be used - feedbackmode and freewheeling mode.In feedback mode, two switches areswitched on and off together (e.g. Q1 and Q6)whereas in freewheeling mode, the choppingis performed only on one switch at a time.
Control of BLDM Drives (cont’d)
Control of BLDM Drives (cont’d)Consider the feedback mode with Q1 and Q6as the controlling switching devices. Duringthe time that these switches are on, thephase a and b currents are increasing butduring the time that they are off, thecurrents will decrease through feedbackthrough the diodes D3 and D4. The averageterminal voltage Vav will be determined bythe duty cycle of the switches.
Control of BLDM Drives (cont’d)Now consider the freewheeling mode ofoperation. When Q6 is on Vd is appliedacross ab and the current increases. WhenQ6 is turned off, freewheeling current flowsthrough Q1 and D3 (effectively short-circuiting the motor terminals) and thecurrent decreases (due to the back emf).
Control of BLDM Drives (cont’d)The steady state torque-speed characteristicsfor a brushless dc motor can be easilyderived. Ignoring power losses, the inputpower is given by: Pin = ea ia + ebib + ecic = 2 I dVcThe torque developed by the motor is simply, Pin Te = ωe
Control of BLDM Drives (cont’d)The back emf is proportional to rotor speedand is given by: Vc = Kω rwhere K is the back emf constant and ωr isthe mechanical rotor speed (=P/2) ωe. Thesteady state (dc) circuit equation for anyswitch combination is: Vd = 2 Rs I d + 2Vc
Control of BLDM Drives (cont’d)The torque expression can be rewritten as: Te = K .P.I d = K1 I dwhere P= # of motor poles. If we define thebase torque as: Teb = K1 I d I d = I scwhere Isc is the short-circuit current given by: Vd K1Vd I sc = => Teb = 2 Rs 2 Rs
Control of BLDM Drives (cont’d)The rotor base speed ωrb can be defined as: Vd ω rb = ω r Id =0 = 2KThe torque-speed relationship can be derivedby combining these equations, yielding: ωr = = Te = ω rb 1 − => Te(pu)=1-ωr(pu) Teb where Te(pu)=Te/Teb and ωr(pu)= ωr/ ωrb
Control of BLDM Drives (cont’d)This normalized torque-speed relation is plotted below. Note the droop in the no-load speed due to the stator resistance voltage drop.
Control of BLDM Drives (cont’d)A closed loop speed control system for aBLDM drive with a feedback mode operationof the PWM inverter is shown below:
Control of BLDM Drives (cont’d)Three Hall effect sensors are used to providethe rotor pole position feedback. This givesthree 2π/3-angle phase shifted squarewaves (in phase with the phase voltagewaves). The six step current waveforms arethen generated by a decoder.The speed control loop generates Id* from theωr* command speed. The actual commandphase currents are then generated by thedecoder. Hysteresis current control is usedto control the phase currents to track thecommand phase currents.
Control of BLDM Drives (cont’d)A freewheeling mode close loop currentdrive for a BLDM is shown below:
Control of BLDM Drives (cont’d)In this case the three upper devices (Q1,Q3, and Q5) are turned on sequentially inthe middle of the positive half-cycles ofthe phase voltages and the lower devices(Q2,Q4 and Q6) are chopped sequentially inthe middle of the negative half-cycles ofthe phase voltages to achieve the desiredcurrent Id*. This is all timed through theuse of the Hall sensors and the decoderlogic circuitry. One dc current sensor (Rconnected to ground) is used to monitorall three phase currents.
Control of BLDM Drives (cont’d)The controller section and powerconverter switches outlined by the dottedline can be integrated into a low-costpower integrated circuit. An example of acommercial BLDM controller IC is theApex Microtechnology BC20 (see separatehandout).
Control of BLDM Drives (cont’d)Pulsating torque can be a problem withBLDM motors (see figure below).
Control of BLDM Drives (cont’d)The high frequency component is due toripple current from the inverter and isfiltered out by the motor. The rounding ofthe torque is due to the rounding of thephase voltages (caused by leakage fluxadjacent to the magnet poles) and thisgenerates significant 6th harmonic torquepulsation. A higher number of poles in themachine can help to alleviate this problem.
Control of BLDM Drives (cont’d)The speed range of a BLDM motor can beextended beyond the base speed range(just as in the case of the sinusoidal SPMmotor). This can be achieved by advancingthe angle α which is used to locate theposition of the current waveforms withrespect to the phase voltage waveforms(α=0 locates the current waveforms in thecenter of the voltage waveforms). Also, ifwe change from a 2π/3 conduction mode toa π conduction mode.
Control of BLDM Drives (cont’d)The normalized torque-speed curve forextended range is shown below for differentα angles for 2π/3 conduction mode (solidlines) and π conduction mode (dotted lines).
Simulation of PM Synchronous Motor DrivesProject 5 at the end of Ch. 10 Ong providesa study of a self-controlled permanentmagnet synchronous motor. The motorparameters for the 70 hp, 4-pole PM motorare given in the table below:
Simulation of PM Synchronous Motor Drives (cont’d)The steady state equations used in the simulation aregiven in the following table:
Simulation of PM Synchronous Motor Drives (cont’d) If we assume that the output torque varies linearly with stator current Is, the torque expression can be rewritten as: 2 2 Vs V cos δ − Em V cos δ − Em EmVsK sin 2 δ + s = ( xd − xq ) s + sin δ x xd xd xq q This is a nonlinear equation with a single unknown, δ. Once δ is found, the current and voltage components in the q and d rotor reference frame and the power factor angles and the stationary q, d current components can be calculated.
Simulation of PM Synchronous Motor Drives (cont’d)The steady state curves are shown below:
Simulation of PM Synchronous Motor Drives (cont’d)Some observations from these curves: Output torque ∝ I e and I (almost linear); q q thus torque control can be accomplished by controlling Iqe (or Iq) with Id controlled as shown. The power factor angles = 1/2 torque angle. This results in the phasor diagram shown (for the motoring mode):
Simulation of PM Synchronous Motor Drives (cont’d)A Simulink simulation model for a self-controlled PM drive is shown below:
Simulation of PM Synchronous Motor Drives (cont’d)Some points regarding this simulation model: i and i are used to control the output q d torque. Torque command is implemented using a repeating sequence source. A rate limiter is used to limit the reference torque input to the torque controller. The inner i and i control loops are closed d q loops.
Simulation of PM Synchronous Motor Drives (cont’d) The feedback block uses the stator phase currents and rotor position to generate id and iq. The coordinated reference values for id* and Vs* are generated by separate function generator blocks (Id-Iq and Vs-Tem, respectively) implemented using a curve fit to the steady state data shown earlier. Dynamic simulation results are shown on the next slide.