Parameter estimation for condition monitoring of PMSM stator winding and rotor permanent magnets

Transcription

1 Loughborough University Institutional Repository Parameter estimation for conition monitoring of PMSM stator wining an rotor permanent magnets This item was submitte to Loughborough University's Institutional Repository by the/an author. Citation: LIU, K., ZHU, Z.Q. an STONE, D., 213. Parameter estimation for conition monitoring of PMSM stator wining an rotor permanent magnets. IEEE Transactions on Inustrial Electronics, 6(12), pp Aitional Information: Personal use of this material is permitte. Permission from IEEE must be obtaine for all other uses, in any current or future meia, incluing reprinting/republishing this material for avertising or promotional purposes, creating new collective works, for resale or reistribution to servers or lists, or reuse of any copyrighte component of this work in other works. Metaata Recor: Version: Accepte for publication Publisher: c IEEE Please cite the publishe version.

2 Parameter Estimation for Conition Monitoring of PMSM Stator Wining an Rotor Permanent Magnets Kan Liu, Z.Q. Zhu, Fellow, IEEE, an Davi A. Stone Abstract Wining resistance an rotor flux linkage are important to controller esign an conition monitoring of a surface-mounte permanent magnet synchronous machine (PMSM) system. In this paper, an online metho for simultaneously estimating the wining resistance an rotor flux linkage of a PMSM is propose, which is suitable for application uner constant loa torue. It is base on a propose full rank reference/variable moel. Uner constant loa torue, a short pulse of i is transiently injecte into -axis current, an two sets of machine rotor spees, currents an voltages corresponing to i = an i are then measure for estimation. Since the torue is kept almost constant uring the transient injection, thanks to the moment of system inertia an negligible reluctance torue, the variation of rotor flux linkage ue to injecte i can be taken into account by using the euation of constant torue without measuring the loa torue, an is then associate with the two sets of machine euations for simultaneously estimating wining resistance an rotor flux linkage. Further, the propose metho oes not nee the values of -axis inuctances, while the influence from the non-ieal voltage measurement, which will cause an ill-conitione problem in the estimation, has been taken into account an solve by or analysis. This metho is finally verifie on two prototype PMSMs an shows goo performance. Inex Terms conition monitoring, ill-conitione problem, magnetic flux linkage, neural networks, permanent magnet machines, parameter estimation, rotor flux linkage, stator wining resistance I. NOMENCLATURE R Stator wining resistance (Ω). R c Core-loss resistance (Ω). L, L -axis inuctances (H). ψ m Rotor flux linkage (Wb). u, u Actual -axis voltages (V). i, i Actual -axis currents (A). T e Electromagnetic torue (Nm). * Denotes a variable specifie by PI regulator. ^ Denotes an estimate value., 1 Denotes the machine parameter an the measure ata when i = an i, respectively. * * u, u -axis reference voltages measure from the PI regulators (V). u, u Total voltage measurement or in -axis (V). ˆR Estimate stator wining resistance (Ω). Manuscript receive June 14, 212. Revise October 3, 212. Accepte for publication December 24, 212. Copyright (c) 29 IEEE. Personal use of this material is permitte. However, permission to use this material for any other purposes must be obtaine from the IEEE by sening a reuest to pubs-permissions@ieee.org. K. Liu, Z.Q. Zhu an D.A. Stone are with the Department of Electronic an Electrical Engineering, University of Sheffiel, UK ( lkan@live.cn; Z.Q.Zhu@sheffiel.ac.uk;.a.stone@sheffiel.ac.uk). ˆm Estimate rotor flux linkage (Wb). U Distorte voltage ue to the variation of DC bus voltage an zero shift in the amplifier (V). V com Constant of istorte voltage ue to inverter nonlinearity in -axis reference frame (V). Actual DC link voltage (V). V c V m Measure DC link voltage (V). ω, θ Electrical angular spee (ra/s) an rotor position (ra). II. INTRODUCTION ermanent magnet synchronous machines are now wiely employe in inustrial servo rives, electrical/hybri Pelectric vehicles, an win power generators, etc., since they have high torue an power ensity an high efficiency. However, for most applications, it is important to obtain accurate electromagnetic parameters for control system esign [1], [35]-[38], online fault iagnosis [17] an rotor/stator conition monitoring [16]. Traitionally, these machine parameters such as stator wining resistance an rotor flux linkage are measure using aitional instrumentation, which increases system complexity an set up time, an reuires the machine to work on no loa ue to the safety issue in measurement. In reality, it is selom possible that all the reuire instrumentation is available for the parameter measurement, an furthermore, the esire parameter value is usually ifferent on loa from the value on no loa. However, no matter it is for controller esign or conition monitoring, it is preferable that the machine parameters can be observe when it is actually on loa. Thus, in reality, online parameter estimation technologies such as moel reference aaptive system (MRAS) [2], recursive least suare (RLS) [17] an extene Kalman filters (EKF) [7] are customarily employe for estimating the esire parameter values rather than using aitional instruments, especially for online monitoring the stator an rotor conitions. However, it is known in system ientification theory that it is impossible to ensure estimation accuracy if the estimation is base on a rank eficient reference/variable moel, an the steay state -axis euation of PMSM shows that it is a rank eficient euation for simultaneously estimating wining -axis inuctances, resistance an rotor flux linkage. Therefore, as etaile in [3], [22], [3] an [34], it is impossible to simultaneously estimate wining resistance an rotor flux linkage using only one set of PMSM states. Taking the metho of [1] for example, it i not take into account the rank of the utilize reference moel, an its estimator faile to estimate the stator wining resistance ue to ill-convergence. For solving this rank eficient problem, some literature [2]-[6], [32]-[34]

3 proposes to estimate each parameter separately by fixing other parameters to their nominal values to get a full rank reference/variable moel. However, what coul be worse is that if the wining resistance an rotor flux linkage are not simultaneously estimate but estimate separately, the estimation of the two parameters will converge to the wrong points [22] ue to the mismatching of un-estimate parameters. For example, the metho in [3] propose two schemes for estimating wining resistance an rotor flux linkage, respectively. In scheme I, the stator wining resistance is estimate while the rotor flux linkage an the inuctance are set to be nominal values. In scheme II, the rotor flux linkage is estimate while the wining inuctance an resistance are set to be nominal values. However, it is verifie in [22] that the metho in [3] will suffer from the mismatch between the nominal an actual parameter values, an similar problem also occurs in the metho presente in [2], which is propose to estimate the wining resistance an inuctance simultaneously while the rotor flux linkage is set to be its nominal value. In practice, parameter values such as PMSM stator wining resistance an rotor flux linkage are both reuire for conition monitoring of stator wining an rotor permanent magnets, for example, their temperature rise. In this case, the estimation of wining resistance an rotor flux linkage shoul be performe simultaneously otherwise this will also suffer from the mismatch between the nominal an actual parameter values. For example, assuming that if there is a variation in the stator wining an the scheme II of [3] is employe for monitoring the variation of rotor flux linkage, the variation of stator wining will influence on the result of estimating rotor flux linkage an it is impossible to istinguish whether this variation comes from the stator wining or the rotor. Thus, the wining resistance an rotor flux linkage shoul be estimate simultaneously an the rank eficient problem shoul be solve prior to the estimator esign. To overcome this rank eficient problem, perturbation signals such as i an DC voltage offset are injecte into the system to buil a full rank reference moel for estimation [7]-[13], [22]. It is firstly reporte in [7]-[9] that by setting the -axis inuctances to be their nominal values, the -axis euation can be mae full rank for simultaneously estimating the wining resistance an rotor flux linkage with the injection of i, in which the variation of inuctance an non-ieal voltage measurement such as the inverter nonlinearities, the variation of DC bus voltage an zero shift in the amplifier, are not taken into account. Taking the metho presente in [8] as an example, it propose to inject alternating -axis current to activate the wining resistance an rotor flux linkage estimation. However, it was prove in [22] that the metho of [8] was sensitive to the amplitue of injecte i because it i not account for the variation of inuctance an non-ieal voltage measurement ue to i. In aition, the metho in [1] proposes to estimate the -axis inuctances, wining resistance an rotor flux linkage simultaneously by two schemes with ifferent convergence spees as well as injecting a three-level perturbation in -axis current. However, the convergence of the estimate parameter was still sensitive to the perturbation an the unstable convergence in some experiments might be cause by saturation. Further, an or analysis base full rank reference/variable moel was propose in [22] for simultaneously estimating the wining resistance, rotor flux linkage an -axis inuctances of a non-salient pole PMSM by a transient injection of i. It took into account the ill-conitione problem (See Appenix B) cause by the variation of -axis inuctances an rotor flux linkage ue to the injecte i. However, it i not take into account the influence from non-ieal voltage measurement. In aition, it is also reporte in [11]-[13] that it is possible to online estimate the wining resistance by transiently superimposing a DC voltage offset in one or more of the machine phases, by which the estimation of wining resistance will be epenent of the variation of inuctance an rotor flux linkage. This kin of metho [11]-[13] shoul take into account the influence of injecte DC voltage offset on the system stability an the amplitue of injecte DC bias shoul be minimize. On the other han, the methos in [14]-[16] an [19] propose to estimate the wining resistance an rotor flux linkage with assistance from measuring instruments. For example, the methos presente in [14] an [15] propose to a a loa test to ai the rotor flux linkage estimation an it is effective if the torue is accurately measure. In aition, since it is much cheaper to bury a thermocouple in stator wining than to a a torue transucer, the metho in [16] propose to monitor the variation of rotor flux linkage with the assistance from the measure stator wining temperature. The metho in [19] propose an online multi-parameter ientification metho base on power an torue measurement techniue. Parameters such as copper loss, stator loss, mechanical loss an stray loss are estimate with assistance from high accuracy igital power meter an torue transucer. In aition, it is reporte that in some applications, it is acceptable to estimate the wining resistance an rotor flux linkage approximately by changing the working conition. For example, it is propose in [17] to simultaneously estimate the wining resistance an rotor flux linkage uner varying loa torue, although, this will not be effective uner constant loa torue. It is propose in [18] that the wining resistance can be approximately estimate at low spee while the rotor flux linkage can be approximately estimate at meium an high spee. It is propose in [2] that the wining resistance an rotor flux linkage can be estimate separately before an after the starting of the PMSM. In [21] that the rotor flux linkage can be estimate at stanstill by tuning the PI constants an measuring sets of step responses. In this paper, a metho base on a full rank reference/variable moel is propose for simultaneously estimating the wining resistance an rotor flux linkage of a PMSM, which can be use as conition inicators (such as temperature rises) of stator wining an rotor permanent magnet. Uner constant loa torue, a perturbation of i is transiently injecte into -axis current an two sets of PMSM rotor spees, currents an voltages corresponing to i = an i are then measure for estimation. Since the torue is kept almost constant ue to the system mechanical inertia an fast response of the current-loop PI controller uring the transient injection, the variation of rotor flux linkage ue to injecte i > can be obtaine by using the euation of constant loa torue without measuring the physical loa torue, an is then associate with the two sets of machine euations for simultaneously estimating wining resistance an rotor flux

4 linkage. Different from the existing methos [7]-[1], [2] base on injecting i, the propose estimation oes not nee the nominal value of any parameters, an its accuracy will not suffer from the machine parameter variation ue to i. Furthermore, compare with [21], the propose estimation will not be influence by the variation of -axis inuctances an rotor flux linkage ue to i while the ill-conitione problem cause by non-ieal voltage measurement has been taken into account an solve by optimizing the amplitue of injecte i. The propose metho is experimentally employe for monitoring the stator wining an rotor permanent magnet conitions in a small power PMSM an a relatively large power PMSM, respectively. III. PMSM MODEL Since the cross-coupling effect is usually negligible at steay-state, the -axis euations of the PMSM shown in (1) are usually employe for the parameter estimation of PMSM [1]-[1], [18], [22], an [28]. i R L u i i t L L L i R L u m i i (1) t L L L L Te 1.5p mi L Lii In steay-state, the -axis machine euations can be simplifie as follows [23]: u ( k) Ri ( k) L ( k) i ( k) (2a) u( k) Ri( k) L( k) i( k) m( k) (2b) k is the inex of the iscrete sampling instants in the rive system. However, as can be seen from (2), the rank of (2) is two while there are four parameters such as -axis inuctances, wining resistance an rotor flux linkage. Therefore, it is impossible to ensure the estimation accurately converge to the right point an a current pulse is injecte to obtain one more set of -axis state euation. The schematic iagram for measuring an recoring two sets of rotor spee, -axis currents an voltages is shown in Fig. 1, in which the setup time elay is to ensure the measurement of Data1 is starte after the settling of step transients correlate to the i pulse. From Fig. 1, the two measure sets of PMSM ata correspon to two sets of PMSM state euations an can be combine as a whole system to give: u( k) L( k) i( k) (3a) u( k) Ri( k) m( k) (3b) u( k1) Ri( k1) L( k1) i( k1) (3c) u( k1) Ri( k1) L( k1) i( k1) m( k1) (3) In (3), the variables an parameters with an without the subscripts correspon to the measure ata when i = an i, respectively. k an k 1 are the inex of the k -th an k 1 -th measure instant of Data an Data1, respectively. Since the mechanical an temperature time constants are much larger than the electrical constant, the rotor spee (ω(k )=ω(k 1 )) an wining resistance will be almost constant uring the measuring ata. To reuce the influence on the output torue, the with of the injecte perturbation in the -axis current is limite to a short time, which will be iscusse in the following sections. The recore ata can be use to calculate iteratively until the estimate results converge to the final value in the backgroun application. Since the machine is uner constant loa torue, an the rotor spee is also kept constant, the electromagnetic torue at i = an i can be: T ( k ) 1.5 p i ( k ) (4a) e m Te ( k1) 1.5p mi k1 L L i k1 i k1 ( ) ( ) ( ) (4b) IV. PROPOSED FULL RANK ESTIMATION A. Propose Full Rank Moel an Estimator Design As can be seen from (4), since the electromagnetic torue is constant uring the estimation, the rotor flux linkage after the injection of i can be erive by solving (4): i( k) m m L L i ( k1) (5) i ( k1) Substitute (5) into (3), it becomes: i ( k) u( k1) Ri( k1) m Li ( k1) ( k1) i ( k1) Thus, (6) can be obtaine as follows: 2 u( k1) i( k1) Ri( k1) mi( k) Li( k1) i( k1) ( k1) (6) (3c) multiplie by i (k 1 ) becomes: 2 u( k1) i( k1) Ri( k1) L( k1) i( k1) i( k1) (7) Substitute (7) into (6), it becomes: 2 2 u( k1) i( k1) u( k1) i( k1) Ri( k1) i( k1) mi( k) ( k1) (8) Combine (8) an (3b), it becomes: 2 2 u( k1) i( k1) u( k1) i( k1) Ri( k1) i( k1) mi( k) ( k1) (9a) u( k) Ri( k) m( k) (9b) It can be seen from the erivation process shown in (5)-(9) that all the -axis inuctance terms (L, L, L, L ) an the rotor flux linkage term at i (ψ m ) are cancelle an only two terms, rotor flux linkage at i = (ψ m ) an wining resistance (R), exist in (9), of which the rank number is two. Thus, the wining resistance an rotor flux linkage can be solve from (9) without influence from the variation of -axis inuctances an rotor flux linkage ue to i an (9) can ensure the estimation will correctly converge to the right point. Since the Neural Network technology is wiely employe in machine parameter estimation [22], [24], the Aaline algorithm [25] is utilize to esign the wining resistance an rotor flux linkage estimators, which are erive from (9) an shown in (1) an (11), respectively. The esign processes of the two estimators are etaile in Appenix A.

5 i(a) Fig. 1. Measuring an recoring ata when i = an i, respectively. Fig. 2. Iterative computation processes of propose Aaline NN base estimation strategy. Fig. 3. Schematic iagram of the compensation of measure voltage. ˆ( 1) R ˆ( k ) 2 i ( ) ( ) ( ) ( ( ) ( ) k1 i k1 i k u k1 i k1 Rk u ( k ) i ( k ) u ( k ) i ( k ) O ( k)) (1) 1 1 ˆ m ( k 1) ˆ m ( k ) 2 ( k ˆ )( u( k) u( k)) (11) The schematic iagram of the whole estimation is shown in Fig. 2. The estimation will be starte after the completion of measuring an recoring of Data an Data1. As can be seen from Fig. 2, since Data an Data1 are store in RAM, the numbering can be reset to be k=k =k 1 = at the beginning of the estimation an the two store sets of ata are simultaneously R sent to the propose estimation metho for iterative computation from to N 1 in seuence. Although the propose reference moel (9) is full rank, the accuracy of estimators (1) an (11) still suffers from the ill-conitione problem cause by the non-ieal voltage measurement such as with inverter nonlinearities, the variation of DC bus voltage an zero shift in the amplifier. In Appenix B, the efinition of the ill-conitione problem is briefly introuce an the solution for the ill-conitione problem ue to non-ieal voltage measurement will be iscusse in following section. B. Analysis of Ill-conitione Problem As etaile in [26]-[28], the steay-state euations of a PMSM incluing the voltage nonlinearities can be shown as follows: * u ( ) ( ) ( ) k u ( ) k u Li k i k ( k) R u * ( k ) u ( ) ( ) ( ) k u Li k m i k (12) u cos D( k) Vcom U u sin D( k) V com where u an -axis. V com, u * u an are the total voltage nonlinearities in * u are the constants of istorte voltage ue to VSI nonlinearity an -axis reference voltages are measure from the PI regulators, respectively. ϕ is the angle between voltage vector an -axis. D an D are functions of rotor position θ an the irections of three phase currents, which can be expresse as follows: 2 2 cos( ) cos( ) cos( ) sign( ias ) D sign( ibs ) D 2 sin( ) sin( ) sin( ) sign( ics ) 3 3 1, i sign() i 1, i 1 Toff Ton T Vcom ( Vc Vce V ) (13) 6 Ts where T is the control ea time of the switch; Ton an T off are the turn on/off time elay of the switch; V ce an V are the threshol voltages of the active switch an freewheeling ioe, respectively [29]. From (12), it is evient that terms such as u an u will introuce a istortion into the measure -axis voltages which will cause the estimation result to be ifferent from the actual value. Thus, the measure -axis voltages from the PI regulators shoul be compensate prior to the estimation. Furthermore, since the compensation cannot be 1% accurate, the estimation or ue to non-ieal compensation shoul be analyze an minimize by software approach, for example, or analysis. The compensation for the non-ieal voltage measurement is ivie into three steps: 1. Rea the zero shift voltage V offset of AD converter at spee while V c =. Thus, the actual DC bus voltage can be obtaine by V c =V m -V offset.

6 (a) (b) Fig. 4. Simulate variation of estimation or R /R a with i uner ifferent i. (a) Case1: u, u u, i =-2A or u, u u, i =2A. Case2: u, u u, i =2A or u, u u, i =-2A. (b) Case1: u, u u, i =-2A. Case2: u, u u, i =2A. 2. V com is compute by using the typical electrical parameters of employe inverter [29]. 3. The compute V offset an V com will be employe for compensating the -axis voltages measure from the output of PI regulators. Fig. 3 shows the above compensation process. By substituting (12) into (9), the wining resistance value incluing the estimation or R ue to u expresse as (14). an u u +u i + u +u i u +u i a i +i i R=R +R = can be (14) where R a is the actual wining resistance an R is the estimation or ue to u an u. ui +ui ui R a = i +i i u i +u i u i i +i i R = (15) Since the estimation is uner constant torue control an the reluctance torue is negligible for a non-salient pole surface mounte PMSM, the -axis current will be almost constant (i =i ) uring the injection of i. Thus, (15) can be simplifie to be (16). u u u i R (16) 2 i i From (16), it is evient that R is a monotonically ecreasing function of i. For parameter estimation, the estimation or R can be acceptable if it is negligible compare with its nominal value. (16) shows that R can be minimize by increasing the amplitue of i or minimizing u an u u. Since it is impossible to minimize u an u u to be zero ue to non-ieal compensation technology, the amplitue of injecte i shoul be optimize for minimizing R. For analysis, assuming that R a =2.5Ω, u =.5an u u =.1, the simulate variation of R with i uner i =2A an i =-2A is epicte in Fig. 4, which shows that R will be either infinite if i is close to zero or close to zero if i is large enough. It can also be explaine that a larger amplitue of injecte i will achieve a larger ratio of signal to measurement or, which can improve the estimation accuracy significantly. Further, as can be seen from (16), since there may be an or cancellation between u an u u, the signs of i, i, u an u u can influence the efficiency of minimizing the estimation or by increasing the amplitue of injecte i. In reality, the signs of u an u u epen on the power evices an are ifferent in various systems while the sign of i epens on the operating moe of the machine. Thus, the sign of i is the only term can be change for achieving the optimal efficiency of minimizing the estimation or, which can be etermine by using or analysis. V. EXPERIMENTAL VERIFICATION A. Harware Platform an Control System To valiate the performance of the propose metho, two prototype PMSMs (Motor1 an Motor2) shown in Fig. 5 are employe for testing an their esign parameters are given in Table I an Table II, respectively. Motor1 is controlle by a TI 2812 DSP an fe by a Mitsubishi PS21867 inverter while Motor2 is controlle by a DS16 boar an fe by a SEMIX 71GD12E4s inverter. In aition, it is obvious that the rate power of Motor1 (15W) is relatively small compare with Motor2 (3kW). Vector control is employe for testing an its schematic iagram is epicte in Fig. 6. B. Experimental Valiation on Motor1 The propose metho is firstly valiate on Motor1. As etaile in subsection B of section VI, the estimation result may suffer from the ill-conitione problem ue to the non-ieal voltage measurement, whilst in reality any voltage compensation cannot be 1% accurate. Thus, the estimation or ue to non-ieal voltage measurement an compensation shoul be minimize by using or analysis.

7 (a) Fig. 5. Prototype PMSMs. (a) Motor1. (b) Motor2. (b) Fig. 8. Measure electrical angular spee (3RPM), -axis currents, an injecte current pulse (Motor1). Fig. 6. Schematic iagram of vector control. Fig. 7. Actual curve of measure variation of R or /R a with i (Motor1). TABLE I DESIGN PARAMETERS AND SPECIFICATION OF MOTOR1 Rate current 4A Rate spee 4 rpm DC link voltage 36V Nominal phase resistance (T=25 o C).33 Ω Nominal terminal wire resistance.43 Ω Nominal self inuctance 2.91mH Nominal mutual inuctance.33mh Nominal -axis inuctances 3.24mH Nominal amplitue of flux inuce by magnets 77.6 mwb Number of pole pairs 5 Number of stator slots 12 Note: Nominal values are measure. TABLE II DESIGN PARAMETERS AND SPECIFICATION OF MOTOR2 Rate current 5A Rate spee 17 rpm DC link voltage 6V Nominal phase resistance (T=2 o C) 1.88 Ω Nominal terminal wire resistance.125 Ω Nominal -axis inuctances 8.18mH Nominal amplitue of flux inuce by magnets mwb Number of pole pairs 14 Number of stator slots 84 Note: Nominal values are measure. Fig. 9. Wining resistance estimation at normal conition (Motor1). Fig. 7 shows the or analysis result of estimate wining resistance at ifferent amplitues of i an the corresponing or analysis process is illustrate below: a. Measure the wining resistance (R a =.373Ω) at stanstill. b. Estimate the wining resistance value (R) by estimator (1). c. The estimation or of (1) ue to ill-conitione problem (or non-ieal voltage measurement) can be R =R R a. As can be seen from Fig. 7 an Table III, the estimation or R ecreases with the increase in the amplitue of i an it can be negligible when i 2A, which is similar to the simulate result of Case2 in Fig. 4 (a). Thus, from the or analysis results of Fig. 7, it is preferable to inject i =2.5A for the parameter estimation throughout this paper. Fig. 8 shows the measure currents an electrical angular spee uring the injection of i, which shows that the influence of injecte i on the spee is negligible thanks to the moment of system inertia. The pulse with of i is set to be 5ms an the ill-conitione problem ue to non-ieal voltage measurement can be well solve by using the or analysis. Fig. 9 an Fig. 1 show the estimate stator wining resistance an rotor flux linkage at normal conition (the room temperature is T=25 o C), from which it is obvious that the estimate parameter values are uite close to the nominal values liste in Table I. In aition, since there exist iron losses (See Appenix C) an temperature rise in wining ue to on-loa, it will cause the estimate wining resistance (.388Ω) slightly larger than the measure wining resistance (.373 Ω) at stanstill.

8 Fig. 1. Rotor flux linkage estimation at normal conition (Motor1). (a) Fig. 11. Estimate wining resistance an its variation (Motor1). Fig. 12. Estimate rotor flux linkage (Motor1). TABLE III ESTIMATED WINDING RESISTANCE VALUE OF MOTOR1 UNDER DIFFERENT INJECTION SCHEMES Injecte i (A) Estimate R(Ω) i = i = i = i = 1.84 i = i = i =1.913 i = i =2.39 i = For comparison, three resistors are connecte in series with the three phase winings of Motor1 at t=2s. Each resistor is R p =.414Ω an the estimation result after the aition of resistors is shown in Fig. 11. It can be seen that the estimate variation of wining resistance (.426Ω) is close to the actual ae resistor value. Thus, the propose metho is effective in tracking the variation of wining resistance an can be use for the conition monitoring of stator winings. Furthermore, Fig. 12 shows that the variation of wining resistance has almost no influence on the estimation of rotor flux linkage. (b) Fig. 13. Tracking the variation of wining resistance an rotor flux linkage (Motor1). TABLE IV VARIATION OF WINDING RESISTANCE AND ROTOR FLUX LINKAGE AT DIFFERENT TIME POINTS (MOTOR1) Time (minute) Estimate R(Ω) Estimate ψ m (mwb) t= t= t= t= A heater is use to heat the stator an shaft of PMSM for 2 minutes (from t= to t=2minutes). By using an infrare thermometer, the surface temperature of Motor1 is measure to be T=8 o C at t=2 minutes. For comparison, the wining resistance an rotor flux linkage will be estimate at t=, 2, 35 an 6 minutes. Fig. 13 shows the convergence curves of estimate wining resistance an rotor flux linkage at t=, 2, 3 an 6 minutes while the estimate variation of wining resistance an rotor flux linkage are compare in Table IV with their normal values (t= an T=25 o C). From Fig. 13 an Table IV, it is evient that the estimate wining resistance will increase from.388ω to.473ω after 2 minutes heating an the wining resistance value will ecrease to its normal value soon after the heating is remove. Different from the variation of wining resistance, the value of rotor flux linkage will ecrease from 78.8mWb to 72.mWb after 2 minutes heating. In aition, since the rotor is covere by the motor en-caps an has worse heat issipation ability than the stator, the rate at which the rotor flux linkage value increases to its normal value is much slower than the spee of wining resistance. C. Experimental Valiation on Motor2 For comparison, the propose metho is also valiate on Motor2, which is relatively larger than Motor1 an esigne for a small-scale irect-rive win turbine test rig.

9 Fig. 17. Wining resistance estimation at 1rpm (Motor2). Fig. 14. Waveforms of measure electrical angular spee, -axis currents, an injecte current pulse (Motor2). Fig. 18. Estimate wining resistance at 15rpm (Motor2). Fig. 15. Actual curve of measure variation of R or/r a with i (Motor2). Fig. 16. Rotor flux linkage estimation at 1rpm (Motor2). Fig. 14 shows the measure electrical angular spee an currents uring the estimation, in which Motor2 is working uner generator moe an the pulse with of i is set to 5ms. Fig. 15 shows the or analysis result of Motor2, which is similar to the simulate result of Case1 in Fig. 4 (b). Thus, from Fig. 15, it is preferable to inject i=1.8a for the parameter estimation of Motor2 throughout this paper. From Figs. 16 an 17, it is obvious that the estimation results at normal conition are close to the nominal values shown in Table II. Fig. 19. Estimate rotor flux linkage at 15rpm (Motor2). Similar to the experimental results of Motor1, the estimate wining resistance value of Motor2 (2.135 Ω) at 1rpm is slightly larger than its nominal value (2.5 Ω) at stanstill, which is cause by the iron losses an temperature rise in wining ue to on-loa. Similar phenomenon also occurs in the experimental results at 15rpm, as epicte in Figs. 18 an 19. For comparison, a set of three resistors are connecte in series with the three phase winings of Motor2 an each resistor is R =1.5Ω. The estimation results after the aition of resistors are epicte in Fig. 2 an Fig. 21, in which show that the estimate abrupt variation in wining resistance (1.155Ω) is close to its actual value (1.5Ω) an there is almost no influence on the estimation of rotor flux linkage. Thus, the propose metho still shows goo performance in tracking the parameter variation of Motor2. In aition, since the rotor outer iameter of Motor2 is as large as 426.4mm an is much larger than that (1mm) of Motor1, it is ifficult to uniformly heat Motor2 an the heating experiment is therefore not uplicate on it.

10 OW (, X) WX i i i i i n Fig. 22. Structure of an Aaline NN i ( k ) i ( k ) i ( k ) Rk ˆ( ) O ( k ) R Fig. 2. Estimate wining resistance an its variation at 1rpm (Motor2). Fig. 21. Estimate rotor flux linkage at 1rpm (Motor2). VI. CONCLUSIONS A new parameter estimation scheme for simultaneously estimating the wining resistance an rotor flux linkage of PMSM has been propose in this paper, which can be use for conition monitoring of machine stator wining an rotor permanent magnet. This metho is base on a propose full rank moel an a short injection of i is neee uring the estimation. Different from existing methos[7]-[1], [2] base on injecting i, the propose metho oes not nee the value of -axis inuctances while the rotor flux linkage variation ue to injecte i is taken into account by using the euation of constant loa torue. In aition, the ill-conitione problem ue to non-ieal voltage measurement is investigate an solve by using the or analysis. The experimental valiation has shown that the propose metho has goo performance in estimating an tracking the variation of wining resistance an rotor flux linkage. Thus, it is suitable for the conition monitoring of non-salient pole PMSM. Further, it has the potential ability to be use for the fault analysis of wining resistance an rotor flux linkage since some real faults, such as wining open/short circuit an amage in the rotor permanent magnet, will cause a significant variation in wining resistance an rotor flux linkage. Appenix A Design Estimators by Aaline NN The mathematical moel of Aaline NN can be shown as follows: n OW (, X) WX (A.1) i i i i i (a) Subnet of wining resistance estimator ( k ˆ m( k) ) ˆ u ( k ) Rki ˆ( ) ( k ) (b) Subnet of rotor flux linkage estimator Fig. 23. Subnets of wining resistance an rotor flux linkage estimators. where W i is the net weight an X i is the input signal. The activation function OW ( i, X i) of the network output noe is a linear function. The general structure of Aaline NN [25] is shown in Fig. 22. As can be seen from (A.1) an Fig. 22, if ( k ) is the measure system output, the weight ajustment can be obtaine via LMS [25]: Wi( k 1) Wi( k) 2 Xi( ( k) O) (A.2) In (A.2), is the convergence factor which ajusts the weight convergence spee. In the propose metho shown in Fig. 2, k will be kept always eual to k 1 for the convenience of estimator esign. Thus, from (9a) an(9b), (A.3) can be obtaine: u ( k ) i ( k ) u ( k ) i ( k ) u ( k ) i ( k ) Ri( k) i( k) i ( k) (A.3) From (A.3), the subnet of wining resistance estimator can be expresse as Fig. 23(a), which shows the input an output of the estimator. Assuming W ˆ i ( k) R( k) k ( ) u( k1) i ( k1) u( k1) i( k1) u( k) i( k) ˆ O OR( k) R( k) i( k1) i( k1) i( k) Xi i( k1) i( k1) i( k) where R ˆ( k) is the estimate wining resistance an the Aaline estimator can be erive from (A.2) by comparing Fig. 23(a) with Fig. 22 an is shown as follows: ˆ( 1) Rk ˆ( ) 2 i ( k ) i ( k ) i ( k ) ( u ( k ) i ( k ) Rk u ( k ) i ( k ) u ( k ) i ( k ) O ( k)) (A.4) 1 1 Similarly, from (9b), the subnet of rotor flux linkage estimator can be expresse as Fig. 23(b), which shows the input an output of the estimator. Assuming W ˆ i ( k) m ( k) k ( ) u ˆ ( k) Rki ( ) ( k) O uˆ ˆ ˆ ( k) R( k) i( k) m( k) ( k) Xi ( k) where ˆ m ( k ) is the estimate rotor flux linkage. Thus, the rotor R

11 flux linkage estimator can be erive from (A.2) by comparing Fig. 23(b) with Fig. 22 an is shown as follows: ˆ m ( k 1) ˆ m ( k ) 2 ( k ˆ )( u( k) u( k)) (A.5) R ˆ( k) is transfe from (A.4) in each step of estimation. Appenix B Ill-conitione Problem Consier systems x y 2 x y 2 an x 1.1y 2 x 1.1y 2.1 The system on the left has solution x=2, y= while the one on the right has solution x=1, y=1. The coefficient matrix is calle ill-conitione because a small change in the constant coefficients or in the variables (x, y) will result in a large change in the solution. For a coefficient matrix A, the conition number (con(a)) is utilize to juge whether it is a well-conitione matrix, which is efine as follows: con(a) v = A -1 v A v (B.1) where v is the operator norm of matrix A, which can be 1, 2 or. The system euations are calle ill-conitione if con(a) v is much larger than 1, or else, they are calle well-conitione. Appenix C Core-loss Resistance Assuming that R c is the core-loss resistance (or iron-loss resistance) cause by the rotor-pm an stator armature-reaction fluxes, the PMSM voltage euations in steay-state conition can be written as [19], [31]: 2 Lm i u Rei Li+ L Rc t (C.1) i u Rei Li m+ L t 2 LL ( k1) L where Re R an 1 [19]. Thus, Rc Rc compare with (1), it is obvious from (C.1) that the resistance term R e incluing the wining resistance an core-loss term will be slightly larger than the wining resistance R at stanstill. Thus, in real application, the heat resistance losses of a PMSM shoul be larger than its copper loss. Taking Motor2 as an example, the estimate value of iron loss versus copper loss at full loa by using SPEED software is 26% an is not negligible. Furthermore, by taking into account the core-loss resistance, (9) will become (C.2). u( k1) i ( k1) u( k1) i( k1) ( k 2 2 1) L Rei( k1) i( k1) m( k1)( i( k) i( k1)) (C.2) Rc u( k) Rei( k) m( k) ( k1) L where i( k) i( k1) in real application. Thus, C.2 Rc can be simplifie to be: u( k1) i ( k1) u( k1) i( k1) 2 2 Rei( k1) i( k1) m( k1) i( k) (C.3) u( k) Rei( k) m( k) (C.3) has the same form as (9) but with a larger resistance term R e >R. Thus, in real application, the estimate wining resistance base on (9) will be slightly larger than the measure wining resistance at stanstill ue to the core-loss resistance (or iron losses). REFERENCES [1] S. Ichikawa, M. Tomita, S. Doki, an S. Okuma, Sensorless control of permanent-magnet synchronous motors using online parameter ientification base on system ientification theory, IEEE Trans. In. Electron., vol. 53, no. 2, pp , Apr. 26. [2] L. Liu, an D.A. 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Luomi, A combination position an stator-resistance observer for salient PMSM rives: esign an stability analysis, IEEE Trans. Power Electron., vol. 27, no. 2, pp , Feb Kan Liu receive the B.Eng. an Ph.D. egrees in automation (control theory an control engineering) from the Hunan University, China, in 25 an 211, respectively. He is currently working in the Department of Electronics an Electrical Engineering at the University of Sheffiel. His research interest focuses on brushless AC motor parameters estimation by control theory, sensorless control an nonlinearity compensation for voltage source inverter output voltage. Z. Q. Zhu (M 9 SM F 9) receive the B.Eng. an M.Sc. egrees in electrical an electronic engineering from Zhejiang University, Hangzhou, China, in 1982 an 1984, respectively, an the Ph.D. egree in electrical an electronic engineering from the University of Sheffiel, Sheffiel, U.K., in From 1984 to 1988, he was a Lecturer with the Department of Electrical Engineering, Zhejiang University. Since 1988, he has been with the University of Sheffiel, where he was initially a Research Associate an was subseuently appointe to an establishe post as Senior Research Officer/Senior Research Scientist. Since 2, he has been a Professor of Electrical Machines an Control Systems with the Department of Electronic an Electrical Engineering, University of Sheffiel, an is currently Hea of the Electrical Machines an Drives Research Group an Director of Sheffiel Siemens Win Power Research Centre. His current major research interests inclue esign an control of permanent magnet brushless machines an rives, for applications ranging from automotive, aerospace, to renewable energy. He is a Fellow of IEEE. Davi A. Stone receive the B.Eng. egree in electronic engineering from The University of Sheffiel, Sheffiel, U.K., in 1984 an the Ph.D. egree from Liverpool University, Liverpool, U.K., in He returne to The University of Sheffiel as a member of Acaemic Staff specializing in power electronics an machine rive systems in the Department of Electrical an Electronic Engineering. His current research interests are in hybri-electric vehicles, battery charging, electromagnetic compatibility, an novel lamp ballasts for low pressure fluorescent lamps.