2010 3rd International Conference on Computer and Electrical Engineering (ICCEE 2010) IPCSIT vol. 53 (2012) (2012) IACSIT Pre, Singapore DOI: 10.7763/IPCSIT.2012.V53.No.2.37 Etimation of Temperature Rie in Stator Winding and Rotor Magnet of PMSM Baed on EKF Xiaoliang Jiang 1+, Zhongying Zhang 1, Pindong Sun 1 and Z.Q. Zhu 2 1 School of Electrical and Automation Engineering, Nanjing Normal Univerity Nanjing 210042, China 2 Department of Electronic and Electrical Engineering, Univerity of Sheffield Sheffield S1 3JD, UK Abtract Thi paper propoed an etimation approach of temperature rie in tator winding and rotor magnet of a urfaced-mounted permanent magnet (PM) AC motor. By uing the 3rd-order etended Kalman filter (EKF) algorithm in rotating reference frame, tator winding reitance and rotor PM flu-linage can be etimated independently. After comparing the etimation reult of reitance and flu-linage to the rated value meaured at 20 repectively, the correponding temperature rie in tator winding and rotor magnet can be calculated according to ome certain rule. The propoed method wa confirmed to be correct and effective by the imulation reult from MATLAB/SIMULINK. Keyword-PMSM; etended Kalman filter; temperature rie etimation 1. Introduction Thermal condition monitoring and analyi i quite important and neceary for motor, epecially under the circumtance of dynamic operation. Currently, everal method are able to fulfill the ta[1-3]. Tae the thermal equivalent circuit for eample, problem related to temperature field can be tranferred to calculation of thermal path with lumped parameter through employing the thermal equivalent circuit organized by implified thermal ource and thermal reitance. Depite of mall duty of calculation and approimate etimation of average temperature in iron core a well a winding, the etimation error i relatively large and it i not capable of real-time implementation. In addition, ome computational method are once propoed, uch a FEM, equivalent thermal networ, etc. However, thoe method do not wor until the internal tructure of motor i well nown. Furthermore, it i complicated to etablih and analyze the correponding model. Intallation of thermitor or thermocouple during the manufacture proce i another way to monitor dynamic thermal environment of motor, which i normally jut applied to etimate the temperature of tator. So, it i difficult to meaure the temperature of rotor directly. In the control ytem of AC PMSM, EKF i often applied to identify poition and peed of rotor a well a the variation of tator winding reitance and rotor PM flu-linage[4-8]. According to the relationhip between winding reitance and temperature, the variation of temperature in tator can be evaluated by the variation of winding reitance in certain cope. Beide, the variation of PM flu-linage alo reflect the variation of temperature in rotor in term of the relationhip curve between flu and termperature. Therefore, temperature of motor can be etimated and oberved without intalling etra equipment or undertanding motor tructure well. Conequently, uing EKF + Correponding author. E-mail addre: jlgyqf@163.com
to evaluate the variation of winding reitance and PM flu-linage i an economical, convenient and effective method to etimate temperature of motor indirectly. 2. Principle of temperature etimation Conidering the temperature performance of conductance coefficient for copper, temperature of tator can be derived indirectly by comparing the etimation value of winding reitance to the rated value. In the ame way, temperature of rotor can be derived indirectly by comparing the etimation value of PM flu-linage to the rated value due to the temperature enetivity of ferromagnetic material. 2.1. Etimation of Temperature Rie in Stator Winding A a nonlinear and dramatically coupled ytem with multiple variable, the mathematical model of AC PMSM in rotating reference frame can be decribed a following after ome appropriate implification and aumption: did ud = rid + L ωliq dt diq uq = riq + L + ωlid + ωλ dt (1) where u d, u q, i d, i q are the d-ai and q-ai voltage and current, repectively. λ i the PM flu-linage, r i the tator phae reitance, L i the winding inductance, ω i the angluar peed of rotor. In reality, the change of winding reitance caued by temperature variation i much lower than the change of electrical quantitie. Aume winding reitance remain unchanged while analyzing motor model, then the etimation model for winding reitance can be decribed a following: dr = 0 dt did r ud = i d + ω i q + dt L L diq r λ uq = i q ω i d ω+ dt L L L (2) where tate vector [r i d i q ] T, output vector y=[i d i q ] T, and an abtract epreion of (2) i given by: = f(, u) y = h( ) (3) After linearization by Jacobian matri and dicretization, tate equation of (3) i decribed a following: + 1 ( ) δ w =Γ + y =Δ ( ) δ + v (4) where Γ matri and Δ matri are epreed a:
f(, u) Γ ( ) = I + T 1 0 0 T T = id 1 r ωt L L T T iq ωt 1 r L L (5) h ( ) 0 1 0 Δ ( ) = = 0 0 1 (6) According to phyical law, reitance of winding ha omething to do with the reitivity ρ of copper, while the reitivity ρ i related to temperature T and temperature coefficient α ρ of copper. The relationhip equation i: ρt = ρ20 1 + α ρ ( T 20) (7) where α ρ 0.004/ for copper, ρ 20 i the reitivity of copper at 20, ρ T i the reitivity of copper at T. Then the reitance of copper at T i given by: rt = r20 1 + α ρ ( T 20) (8) Therefore, the relationhip between temperature of tator winding and reitance at correponding temperature can be deduced a: [ ] T = 20 + rt / r20 1 / αρ (9) 2.2. Etimation of Temperature in Rotor Magnet Etimation of rotor PM flu-linage can be realized by employing tochatic filtering algorithm. Baed on the ame principle of tator temperature etimation, aume PM flu-linage remain unchanged while analyzing motor model, then etimation model for PM flu-linage i derived: dλ = 0 dt did r u i d = d + ω i q + dt L L diq r λ uq i q ω ωi d + dt L L L (10) where tate vector [λ i d i q ] T, output vector y=[i d i q ] T. After linearization by Jacobian matri and dicretization, Γ matri and Δ matri are given by:
f(, u) Γ ( ) = I + T 1 0 0 r = 0 1 T ω T L ω r T ωt 1 T L L (11) h ( ) 0 1 0 Δ ( ) = = 0 0 1 (12) The demagnetization characteritic of permanent magnet, i.e. the coercivity, the remanence and the nee point alo vary with temperature. For eample, the remanence B r decreae with temperature. B r at T i: [ α ] BrT = Br 20 1 + Br ( T 20) (13) where B r20 i the remanence at 20, α Br i temperature cofficient of the remanence, for NdFeB magnetic material αbr -0.001/. The PM flu-linage i proportional to Br if the influence of temperature on magnetic aturation i negligible, while the permanent magnet will not be irreveribly demagnetized becaue of temperature rie. Therefore, according to (13), the calculation formulation of flu-linage i epreed by: [ ] λ = λ 20 1 + α Br ( T 20) (14) Conequently, temperature of rotor magnet i derived: [ ] T = + λ λ α 20 / 20 1 / Br (15) 2.3. Recurive Algorithm of EKF A well nown, EKF i an optimal recurive algorithm. During the implementation proce, the recurive equation are given by: ˆ ˆ + 1/ = f( /, u) T P+ 1/ =ΓP/ Γ + Q (16) T T 1 K+ 1 = P+ 1/ Δ[ ΔP+ 1/ Δ + R] ˆ ˆ ˆ + 1/ + 1 = + 1/ + K+ 1( y+ 1 h( + 1/ )) P+ 1/ + 1 = ( I K+ 1Δ) P+ 1/ (17) where the ubcript +1/ denote prediction value and +1/+1 mean eventual etimated value. Q and R are covariance matri of proce noie and meaurement noie, repectively. Γ i the Jacobian matri of partial derivative of f with repect to, i.e. f(, u) Γ = ˆ (18) Δ i the Jacobian matri of partial derivative of h with repect to, i.e.
hu (, ) Δ = ˆ (19) Beide, everal initial value are needed for the implementation of algorithm. Different initial value have different influence on the convergence peed. 0 ˆ 0/0 = 0 0 P 0/0 0.1 0 0 = 0 10 0 0 0 20 10 0 R = 0 10 0 0 0 Q = 0 1 0 0 0 1 3. Simulation eperiment and Etimation reult The vector control ytem of PMSM and identification model for different parameter are etablihed in MATLAB/SIMULINK. Some parameter of the motor and the control ytem are lited in Tab.Ⅰ. From Fig.1 to Fig.4, waveform of rotor poition and peed, waveform of voltage and current, identification reult of winding reitance and PM flu-linage a well a temperature rie in tator winding and rotor magnet are given. TABLE I. PARAMETERS OF MOTOR AND CONTROL SYSTEM Rated Current Rated Speed 4(A) 400(rpm) Pole Pair 5 Winding Reitance Flu-linage Winding Inductance Inertia 1(Ω) 0.0776(Wb) 3.366e-3(H) 0.8e-5 Load Torque 1.5(N m) DC Voltage of Inverter 36(V) Fig.1. Speed and angle of rotor
Fig.2.Waveform of voltage and current Fig.3. Identification reult of winding reitance and PM flu-linage Fig.4. Etimation reult of temperature rie in tator winding and rotor magnet etimation error(%) 320 rpm 160 rpm Fig.5.Etimation error of temperature rie in tator winding at different peed It i noticed that temperature variation influence on winding reitance and PM flu-linage imultaneouly. In thi paper, winding reitance and PM flu-linage are etimated independently without conidering the interactive influence. Actually, the temperature coefficient of reitance i nearly 3 time larger than that of flu-linage. However, error analyi and modification of etimation reult are till neceary. With conideration of etreme ituation that the temperature of motor rie to 50 at hort notice, the etimation error of reitance i le than -5.8% by uing the propoed method when no large temperature difference eit between tator and rotor. Therefore, the etimation error of temperature hould alo be retricted in certain cope. If the variation of flu-linage can be timely modified while identifying reitance, then the etimation error will get maller. Fig.5 how the etimation error of tator temperature at different peed. It demontrate that the etimation error get maller when the peed i lower than the rated value. When the peed i about half of the rated value, the etimation error i approimately -1.7%. 4. Concluion temperature( )
Uing etended Kalman filter to etimate temperature of motor i a meaningful dicovery. In thi paper, 3 rd -order EKF algorithm i employed to identify winding reitance and PM flu-linage. Then, temperature rie in tator winding and rotor magnet are etimated indirectly, which help monitoring thermal condition of motor and contribute to lower fault rate, better control performance and longer motor life. The theoretical analyi and etimation reult are confirmed to be correct and valid by imulation reult from MATLAB/SIMULINK. 5. Reference [1] H. M. Li and J. Q. Li, Review on temperature computation and application in electric machine, Journal of North China Electric Power Univerity, vol. 32, no. 1, 2005, pp. 1-5. [2] B. Q. Xu, H. M. Li, L. Zhu, and L. L. Sun, New on-line temperature monitoring method for generator tator and rotor winding, Automation of Electric Power Sytem, vol. 35, no. 1, 2002, pp. 35-38. [3] R. Beguenane and M. E. H. Benbouzid, Induction motor thermal monitoring by mean of rotor reitance identification, IEEE Tran. on Energy Converion, vol. 14, no. 3, 1999, pp. 566-570. [4] X. Zhu, Z. Q. Zhu, and D. Howe, Application of full-order and implified EKF to enorle PM bruhle AC machine, International Journal of Automation and Computing, vol. 2, no. 1, 2006, pp. 179-186. [5] S. Bolognani, R. Oboe, and M. Zigliotto, Senorle full-digital PMSM drive with EKF etimation of peed and rotor poition, IEEE Tran. on Indutrial Electronic, vol. 14, no. 4, 1999, pp. 868-873. [6] Yoon-Ho Kim and Yoon-Sang Koo, High performance IPMSM drive without rotational poition enor uing reduced-order EKF, IEEE Tran. on Energy Converion, vol. 14, no. 4, 1999, pp. 868-873. [7] M. Cernat, V. Comnac, and R. M. Cernat, Senorle control of interior permanent magnet ynchronou machine uing a Kalman filter, Proc. IEEE ISIE (2000), vol. 2, 2000, pp. 401-406. [8] S. Bolognani, L. Tubiana, and M. Zigliotto, EKF-Baed Senorle IPM Synchronou Motor Drive for Flu- Weaening Application, IEEE Tran. on Indutry Application, vol. 39, no. 3, 2003, pp. 768-775.