Speed Sensorless Vector Control of Induction Motor Using Reduced Order Extended Kalman Filter

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1 IJISET - Internatonal Journal of Innovatve Scence, Engneerng & Technology, Vol. 3 Issue 11, November 016 Speed Sensorless Vector Control of Inducton Motor Usng Reduced Order Extended Kalman Flter 1 AkashP P, Mahadev BradarP 1 PG Scholar P P, ProfessorP Department of EEE Poojya Doddappa Appa College of Engneerng, Kalaburag, Karnataka, Inda. Abstract Vector control s a speed control technque used to obtan fast and accurate speed control of nducton motor. Speed sensors degrades relablty hence speed sensorless speed control s proposed. Ths work presents accurate electrcal parameter estmaton such as flux, torque, theta and speed usng reduced order extended Kalman flter based nducton motor control s proposed. The Kalman flter s based on the mnmzaton of the estmaton error and t s sutable for obtanng hgh accuracy estmates of state varables and model parameters and elmnatng measurement noses. Here no need of speed, torque, flux, rotor poston and stator voltage sensors, alternatvely the stator current wll be measured by three current transformers (CT s) wth supportng of mathematcal equatons. The proposed method has some advantages of savng computaton tme n comparson wth the full order extended Kalman flter. The proposed work s mplemented by a hardware usng DSPIC30F4011 controller and smulated wth help of MATLAB SIMULINK R010a verson. Keywords.Vector control, Extended Kalman flter, Current transformers, Speed sensorless, Coordnate transformaton 1. Introducton The nducton machne s the heart of the most wdely used form of electrcal AC drve. Inducton motor can be consdered as the workhorse of the ndustry. Inducton motors are classfed nto sngle phase nducton motor and three phase nducton motor based on gven nput supply. Three phase nducton motors are the most common motors used n ndustral control systems and commercal applcatons. In the past, nducton motors were preferred only for constant speed applcatons. Adjustment of speed of nducton motor was very dffcult and also needs hgh cost. But the rapd growth n power electroncs and semconductor technology results, many knds of nducton motor varable speed drves have been developed and now the nducton motors are very good alternatve for varable speed applcatons. The robustness, low cost, the better performance and the ease of mantenance make the nducton motor advantageous n many ndustral applcatons for general applcatons. A fast and controlled speed response from an nducton motor s obtaned most effectvely f the prncple of vector control s used. Vector control method s also called as feld orented control method. Vector control method s vald for both steady state as well as dynamc state condtons. In vector control t controls not only the ampltude, frequency but also ther phase angle. The man dsadvantages are the huge computatonal capablty and accurate measurements of the motor parameters are requred. In the drect vector control, nformaton about the actual values of the magntude and poston of the rotor flux and rotor speed s necessary. Vector controlled nducton motor drves are wdely used n the ndustral applcatons where hgh performance, lke fast torque and speed responses, are demanded. The man concept of vector control s to decouple the control of nducton motor's flux and torque va coordnate transformatons and to control not only the ampltudes of current and flux but also ther phase angle. The Kalman flter s based on the mnmzaton of the estmaton error and t s sutable for obtanng hgh accuracy estmates of state varables and model parameters and elmnatng measurement noses. A lot of researches are carred out to develop accurate speed estmaton technques. To obtan accurate, hgh performance lke fast torque, speed responses and more relable n three phase nducton motor drve system the vector control method has been proposed. The work s manly focused on speed sensorless speed control of three phase nducton motor usng vector control technque through reduced order extended Kalman flter. For ths purpose of modellng and desgn of nducton motor drve I am developng hardware and smulatng wth help of MATLAB SIMULINK R010a verson.. Modelng of Inducton Motor The IM mathematcal model may perhaps be explaned n the rotatng drect quadrature (d-q) frame as gven below where d and q, V d and V q, ω r, T L,ψ rd and θrepresents stator currents, stator voltages, rotor speed, load torque, drect-axs rotor flux, and flux angle, correspondngly. Parameter τ r = L r / R r ndcates the rotor tme constant and σ = 1 L m L s L r sgnfes the leakage magnetc coeffcent. 44

2 IJISET - Internatonal Journal of Innovatve Scence, Engneerng & Technology, Vol. 3 Issue 11, November 016 dt = L rr s + L m R r + L m ψ σl s L r τ r σl s L rd + pω r q + L m r τ r ψ q + 1 V rd σl d s d q dt = L rr s + L m R q r σl s L q L m pω r σl s L r ψ rd pω r d + L m r τ r ψ d q + 1 V rd σl q s dθ dt = pω r + L m τ r ψ q rd d d dψ rd = 1 ψ dt τ rd + 1 L r τ m d r dω r = pl m ψ dt L rd q 1 r J T L (1) The stator flux vector Ψ est and the torque generated by the motor, T est, can be estmated wth the help of (1) and (), correspondngly. φsd = (Vsd Rs. sd). dt φsq = (Vsq Rs. sq). dt 4 The prevous equatons only need the stator resstance Rs. The magntude of stator flux s decded by In order to smplfy the nvestgaton, fx m = (L r R s + L m R r ) σl s L r, γ = L m σl s L r, ς = 1 σ L s, k = 1 τ r, ρ = pl m L r, and (1) can be modfed as follows: In ths work, only the stator currents are necessary to be computed for control calculatons, thus leadng to a sensorless nducton drve system. d q d d dt = m d + kγψ rd + pω r q + k L m ψ rd q + ςv d dt = m q γpω r ψ rd pω r d k L m ψ d q + ςv q rd dθ dt = pω r + k L m ψ q rd dψ rd = kψ dt rd + kl m d dω r = ρψ dt rd q 1 J T L... () 3. Desgn of Reduced order Kalman flter In ths approach, the three-phase stator currents are the soltary essental measurements, and these are converted from the three-phase reference frame to a dphase reference frame, and subsequently to the frame of the rotatng feld (d-q) as gven below: d = cos θ 3 a + cos θ 3 π b + cos θ + 3 π c q = sn θ 3 a sn θ 3 π b sn θ + 3 π c Where a, b and c sgnfes the three-phase stator currents, correspondngly and θ represents the estmated flux angle. V d, V q and θ are engaged as feedback to the reduced order extended Kalman flter. (3) Ψ est = (φsd + φsq ) At ths moment, wth the stator flux and the dphase reference frame from the stator currents, together wth the motor poles P, Torque s estmated dependng on the equaton below. T est = 3 P(φsd. sq φsq. sd) (5) Where,φsd and φsq represents the stator flux, sd and sq represents the stator currents Estmated Flux angle can be computed from the equaton gven below. θ = tan 1 φsq (6) φsd 3.1 Speed sensorless speed estmaton Wth the ntenton of estmatng the sensor less speed, the estmated stator flux has to be transformed nto rotor flux dependng on the magnetzng nductance n addton to the secondary nductance per phase. φrd = L m L r φsd; Square of rotor flux, φrd + φrq φrq = L m L r φsq... (7) For the purpose of determnng the speed of rotor feld, the acheved rotor flux has to be transformed nto α, β coordnates, by means of the transfer functon. Speed of rotor feld = (φrd φrβ) (φrq φrα) 3. Speed control.(8) The error takes place between the estmated and set speed; consequently, t s necessary to desgn the requred torque T ref dependng on the speed PI adjuster,.e. T ref = (ω set ω est ) K pω + K ω S (9) 45

3 IJISET - Internatonal Journal of Innovatve Scence, Engneerng & Technology, Vol. 3 Issue 11, November 016 The functon of partcpaton of the PI adjuster s to fne-tune the speed n a small range to make sure the speed trackng precson and the fnal zero statc state error. In the same way, for the purpose of obtanng the desred Vsq, the obtaned reference torque and the estmated torque from sldng mode observer s managed through the torque PI adjuster to acheve the zero statc state torque error. Vsq = T ref T est K pt + K T..(10) S...(11) Stator Flux Reference Ψ ref = φref ωb ω est (11) Where ωb = 157 rad/s represents the consder base speed φref = ω est s acqured from the sldng mode observer. Fg. 1 Block dagram of the proposed system Vsd = Ψ ref Ψ est K pφ + K φ S In the same way for the purpose of obtanng the desred Vsd, the obtaned stator flux reference and the estmated stator flux from sldng mode observer s managed through the torque PI adjuster to acheve the zero statc state flux error. The obtaned d-q frame voltages V sd and V sq are subsequently gven as feedback to the sldng mode observer to approxmate the necessary electrcal constrants of the nducton motor. Ths evaluaton s performed by takng smply stator current. Inverse park transformaton s exploted to transform the dphase voltage (V sd and V sq ) nto a three phase voltage (V a, V b and V c ) whch s then taken as nput to the Space Vector Pulse Wdth Modulaton. 4. Block dagram and ts explanaton The fgure1 shows the complete block dagram of the proposed work, t conssts of three phase dode brdge rectfer, DC lnk capactance flter, three phase VSI nverter, reduced order extended Kalman flter (sldng mode observer). The operaton of the proposed system s managed by reduced order extended Kalman flter (sldng mode observer) and Pulse Wdth Modulaton. In ths proposed system, there s no necessty for speed, torque, flux, poston and also voltage measurements. The sldng mode observer has the capacty to perfectly approxmate the speed, flux, theta and torque wth the help of the phase currents sensng alone. The sngle phase nput ac voltage s rectfed to dc voltage by..(1) means of dode rectfer and.(13) then the DC lnk voltage VRdcR s gven as nput to the three phase voltage source nverter. The three phase VSI converts dc supply nto three phase ac supply. The SPWM control technque to get the desred output from VSI. Then ths three phase ac supply s gven to stator of the three phase nducton motor. Intally the three phase stator currents are measured through current transformers and then they are converted nto two phase by axs or co-ordnate transformaton usng phase angle(θ) whch s generated byreduced order extended Kalman flter and then these two phase stator currents RsqR and RsdR are gven as nput to the reduced order extended Kalman flter. The reduced order extended Kalman flter uses recursve algorthm and t takes these two phase stator currents as nput and calculates the estmated speed, estmated flux, and estmated torque and phase angle(θ). It compares the reference flux and estmated flux and the result error s processed through a PI controller and t gves the flux controllng component VRsdR. smlarly the reference speed and estmated speed are compared and the result error s processed through a PI controller and t gves the reference torque and agan these reference torque and estmated torque are compared and the result error s processed through a another PI controller and t gves the torque controllng component VRsqR and these flux controllng component VRsd Rand torque controllng component VRsq Rare taken feedback to the reduced order extended Kalman flter. 46

4 IJISET - Internatonal Journal of Innovatve Scence, Engneerng & Technology, Vol. 3 Issue 11, November 016 Then these two phase voltages VRsq Rand VRsd Rare converted back by nverse transformaton usng phase angle (θ) and these three phase reference voltages are gven to PWM drver unt. The drver unt uses snusodal PWM technque compares the carrer sgnal(trangular wave) and the gven three phase reference sgnal(snusodal wave) and generates the PWM pulses of wdth vared accordng to the three phase reference voltage sgnal and these PWM sgnals are gven to the MOSFET swtches n the VSI for swtchng acton. As the three phase reference voltage s vared accordng to the set speed and n turn PWM sgnal pulse wdth s vared accordng to the three phase reference voltage and n turn the output of VSI s vared accordng to the PWM pulses and n turn the nput of the motor s the output of VSI and n turn the speed of motor s vared as the nput of the motor s vared, hence we wll get desred set speed and ths type the speed of three phase nducton motor s controlled. 4. Smulaton results and dscusson Fg 4. a) Set speed v/s actual speed, b) Electromagnetc torque, c) Stator current Ra Rwaveforms From the fgure 4.(a) t s clear that the speed of the nducton motor s catchng the set speed 1000 rpm from 0.0 to 1.0 sec and 600 rpm from 1.0 to.0 seconds. From the fgure 4.(b) t can be concluded that the torque s remanng constant of magntude N-m. From the fgure 4.(c) the stator current of magntude 3.5A, 65 Hz frequency for duraton 0.0 to 1.0 second and same magntude but frequency of 40 Hz for duraton from 1.0 to.0 seconds hence t s clear that the frequency of stator current s varyng accordng to the change n speed by keepng magntude constant. Fg 4.1 Block dagram of complete smulaton system The Block dagram of the complete smulaton system s shown n Fgure 4.1. The smulaton of the work s smulated for the tme duraton from 0.0 seconds to.0 seconds and the results are observed and they are presented below. CASE: Gven step nput for a speed 1000r.p.m from 0.0 to1.0 seconds and 600r.p.m from 1.0 second to.0 seconds: Fg 4.3 Three phase stator current varaton waveform 47

5 P IJISET - Internatonal Journal of Innovatve Scence, Engneerng & Technology, Vol. 3 Issue 11, November 016 From the fgure 4.3 the three phase stator currents of magntude 3.5A, 65 Hz frequency for duraton 0.0 to 1.0 second and same magntude but frequency of 40 Hz for duraton from 1.0 to.0 seconds. The three phase stator currents are snusodal n shape and are balanced that s all 0 three phase have same magntude wth 10P phase dfference and the frequency of three phase stator current s varyng accordng to the change n speed by keepng magntude constant. Fg 4.5 a) VRdc R, b) Three phase reference voltage waveforms From the fgure 4.5(a) t s clear that the VRdc Rs the pulsatng dc voltage approxmately magntude of 35 volts remanng constant. Fg 4.4 a) VRalpha beta R, b) Stator flux waveforms From the fgure 4.4(a) VRalpha beta Rs of magntude 0 volts for duraton 0 to 1.0 second and magntude of 130 volts for duraton 1.0 to.0 seconds. The two phase stator voltage VRalpha beta Rs two phase snusodal voltage and whose magntude s varyng accordng to the speed change. From The fgure 4.5(b) three phase reference voltager Rs of magntude 0 volts for duraton 0.0 to 1.0 second and magntude of 130 volts for duraton 1.0 to.0 seconds. The three phase reference voltage s snusodal voltage and whose magntude s varyng accordng to the speed change. From the fgure 4.4(b) t can be concluded that the stator flux s remanng constant of magntude of 1 Weber. The stator flux s snusodal and two phase contanng both quadrature and drect components of stator flux and t s mantaned to constant magntude of 1 Weber rrespectve of speed change. Fg 4.6 PWM sgnal waveform From the fgure 4.6 t can be concluded that the contnuous square wave PWM pulses are generatng and are suppled to VSI. 48

6 IJISET - Internatonal Journal of Innovatve Scence, Engneerng & Technology, Vol. 3 Issue 11, November Expermental setup and ts results The fgure 5. shows the stator voltage waveform of peak to peak magntude of 8.4 volts and rms magntude of.4 volts wth frequency 5.8 Hz. Fg. 5.1 Expermental set up of hardware The fgure 5.1 shows the expermental set up of the hardware unt. It conssts of sngle phase ac power supply, three phase dode brdge rectfer, dc lnk capactor flter, three phase voltage source nverter, current transformers, control relay crcut, DSPIC30F4011 Controller, MOSFET drver unt and three phase nducton motor. Fg 5.3 Stator current waveform The above fgure represents the stator current waveform. The magntude of stator current s approxmately 0.3 amps, 50 Hz. The hardware s connected as shown n fgure 5.1. The requred supples are turned on then the motor starts to run. The speed of motor s set to 1000 rpm and the three parameters are measurng through Dgtal Storage Osclloscope are stator voltage, stator current and PWM pulses and they are represented below Fg 5.4 PWM pulses waveform The above fgure represents the PWM pulse sgnal waveform. These waveforms are the PWM pulses generated by drver crcut and are gven to the MOSFET swtches for swtchng acton. The PWM pulse s of magntude 60 volts. Fg 5. stator voltage waveform 49

7 n1t 1TIndustral IJISET - Internatonal Journal of Innovatve Scence, Engneerng & Technology, Vol. 3 Issue 11, November Concluson A model to control the speed of three phase nducton motor by vector control method usng reduced order extended Kalman flter has been successfully mplemented for ½ HP, 440V, 0.75A, 50Hz three phase nducton motor. The hardware of proposed work s mplemented by usng DSPIC30F4011 controller and the work s smulated wth help of MATLAB SIMULINK R010a verson. The outputs of smulaton and hardware are taken and are found qute satsfactory. The stator voltage of peak to peak magntude of 8.4 volts and r.m.s magntude of.4 volts wth frequency 5.8 Hz s obtaned. The magntude of stator current s approxmately 0.3 amps, 50 Hz and the PWM pulse s of magntude 60 volts. The accurate and fast speed control s acheved. The accuracy of speed control s acheved by mnmzng estmaton errors by usng reduced order extended Kalman flter. A fast control s acheved by savng computaton tme compared wth full order Kalman flter. The accuracy and relablty of system s mproved by replacng the speed sensors wth current transformers. The problem as dynamc response and couplng effect of scalar control are solved. The problem of speed sensors as error n measurement tself and low relablty are solved. Easy of mantenance due to not present of mechancal commutators, bushes, slp rngs and speed sensors. Performance of proposed drve has been found qute satsfactory by accurate and fast controllng the speed of three phase nducton motor. Ths type of speed control of three phase nducton motor can be used n ndustres where a hgh performance drve lke fast and accurate speed control and hgh relablty s requred. References [5] L-Cheng Za, Chrstopher L. DeMarco and Thomas A. Lpo "An extended Kalman flter approach to rotor tme constant measurement n PWM nducton motor drves," n Industry Applcatons, IEEE Transactons on, vol.8, no.1, Jan/Feb 199 pp [6] TsugutoshOhtan, Noryuk Takada and Koj Tanaka"Vector control of nducton motor wthout shaft encoder," n Industry Applcatons, IEEE Transactons on, vol.8, no.1,, Jan/Feb 199, pp [7]Juanjuan Sun and Yongdong L "Voltage-Orented Vector Control of nducton motor: Prncple and dynamc performance mprovement" n1t 1TPower Electroncs and Applcatons, 009. EPE '09. 13th European Conference on, vol, no Sept. 009 pp.1-10 [8] Francesco Alonge, FlppoD Ippolto and AntonnoSferlazza"Sensorless Control of Inducton-Motor Drve Based on Robust Kalman Flter and Adaptve Speed Estmaton" Electroncs, IEEE Transactons on1t 1T, vol.61, no.3, March 014 pp [9] AsgharTaher and Mohsen Mohammadbeg "Speed sensor-less estmaton and predctve control of sx-phase nducton motor usng extended kalman flter" n1t 1TPower Electroncs, Drve Systems and Technologes Conference (PEDSTC), 014 5th1T 1T, vol., no., 5-6 Feb. 014 pp [10] Bmal K. Bose Modern Power Electroncs and AC Drves publshed by Dorlng Kndersley (Inda) Pvt. Ltd. Sxth Impresson, 009 Author s profle: Akash, PG Scholar Dept of EEE, Poojya Doddappa college of engneerng, kalaburag, Karnataka, Inda, akashandure9945@gmal.com Mahadev Bradar, Professor, Dept. of EEE, Poojya Doddappa Appa College of Engneerng, Kalaburag, Karnataka, Inda, [1] Young-Seok Km, Sang-Uk Km and Iee-Woo Yang Implementaton of a speed sensor-less vector control of nducton motor by reduced-order extended Kalman flter" n Appled Power Electroncs Conference and Exposton, APEC '95. Conference Proceedngs 1995, Tenth Annual, vol. no.0, vol.1, 5-9, Mar 1995, pp [] G.Garca Soto, E.Mendes and A.Razek "Reduced-order observers for rotor flux, rotor resstance and speed estmaton for vector controlled nducton motor drves usng the extended Kalman flter technque" n Electrc Power Applcatons, IEE Proceedngs - vol.146, no.3, May 1999, pp.8-88 [3] Young-Real Km, Seung-K Sul and Mn-Ho Park "Speed sensorless vector control of nducton motor usng extended Kalman flter" n Industry Applcatons, IEEE Transactons on, vol.30, no.5, Sep/Oct 1994, pp [4] A. Dell'Aqula, F. Cupertno, L. Salvatore and S. Stas "Kalman flter estmators appled to robust control of nducton motor drves" n Industral Electroncs Socety, IECON '98. Proceedngs of the 4th Annual Conference of the IEEE, vol.4, 31 Aug-4 Sep 1998, pp

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