Accurate and Efficient Torque Control of an Interior Permanent Magnet Synchronous Motor in Electric Vehicles Based on Hall-Effect Sensors

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1 energies Article Accurate Efficient Torque Control of an Interior Permanent Magnet Synchronous Motor in Electric Vehicles Based on Hall-Effect Sensors Lei Yu 1, Youtong Zhang 1, Wenqing Huang 2 1 Laboratory of Low Emission Vehicle, Beijing Institute of Technology, Beijing , China; yulei0724@bit.edu.cn 2 United Automotive Electronic System Co., Ltd., Shanghai , China; hwq086@126.com Correspondence: youtong@bit.edu.cn; Tel.: Academic Editor: Kuohsiu David Huang Received: 4 January 2017; Accepted: 14 March 2017; Published: 21 March 2017 Abstract: In this paper, an effective method to achieve accurate efficient torque control of an interior permanent magnet synchronous motor (IPMSM) in electric vehicles, based on low-resolution Hall-effect sensors, is proposed. The high-resolution position is estimated by a proportional integral (PI) regulator using deviation between actual output power reference output power. This method can compensate for Hall position sensor mounting error, estimate position continuously accurately. The permanent magnetic flux linkage is also estimated based on a current PI controller. Or important parameters, such as d-axis q-axis inductances, stator resistance, loss, are measured offline by experiments. The measured parameters are saved as lookup tables which cover entire current operating range at different current levels. Based on se accurate parameters, a maximum torque per ampere (MTPA) control strategy, combined with feedforward parameter iteration method, can be achieved for accurate efficient torque control. The effectiveness of proposed method is verified by both simulation experimental results. Keywords: hall-effect sensor; position estimation; interior permanent magnet synchronous motor (IPMSM); torque control; electric vehicle 1. Introduction The interior permanent magnet synchronous motor (IPMSM) has been widely used in electric vehicles for its high efficiency high power density. Accurate efficient torque control is essential for automotive drive systems. However, it is difficult to achieve this target because of varying parameters of IPMSM [1]. Although resolver can obtain high-resolution position of IPMSM, it is not suitable to be used in vehicles, considering its high cost, weight, volume. Algorithms based on no position sensors [2] cannot estimate position accurately in all conditions, in addition to high-volume computation. In fact, Hall-effect sensors can be used to realize low cost, weight, volume, high-resolution position. Considering discrete position signals from Hall-effect sensors, it is quite necessary to conduct research on obtaining continuous position signals. The most popular method to estimate position is based on average motor speed [3]. When motor speed varies frequently, this method may cause a very large error failure of control strategy. A vector-tracking observer was proposed to estimate positon in [4]. This method needs to acquire stator voltages, thus increasing cost complexity of system. An improved vector-tracking observer was proposed to eliminate complexity of system in [5]. A method based on back electromotive force (EMF) was proposed in [6]. Although this Energies 2017, 10, 410; doi: /en

2 Energies 2017, 10, of 15 method can obtain accurate speed, it cannot obtain accurate position. A method based on flux estimation was proposed for a slotless permanent magnet synchronous motor (PMSM) in [7]. An improved square root unscented Kalman filter (SRUKF) was proposed to estimate speed position in [8]. Additionally, some studies used linear Hall sensors [9] to estimate position instead of discrete Hall sensors. To achieve accurate efficient control, accurate parameters are essential. There are, mainly, two types of methods proposed to achieve parameter identification. One is based on offline measurements, or is based on real-time estimating arithmetic [1]. The real-time estimating arithmetic based on PMSM model was analyzed in [10]. Some parameters must be assumed to be known since not all parameters are identifiable in steady state. A method was proposed to estimate stator resistance flux linkage by injecting short-period d-axis current into surface PMSM in [11]. However, it is not suitable for application in vehicles. Mechanical parameters of induction motors were estimated by using voltage sensors only in [12]. The variation of d-axis q-axis inductances measured offline [13], or calculated from finite element [14] in consideration of cross saturation were proposed. An analytical calculation method of d-axis q-axis inductances for IPMSM based on winding function ory was proposed in [15]. An adaptive parameter estimator that can achieve maximum torque per ampere (MTPA) control was proposed in [16]. In this paper, an effective method to achieve accurate efficient torque control of an IPMSM in electric vehicles, based on low-resolution Hall-effect sensors, is proposed. A variety of important parameters are estimated for torque control. To obtain high-resolution position, an estimation method based on power closed-loop is proposed with low-resolution Hall-effect sensors. This method can compensate for Hall position sensor mounting error, estimate position continuously accurately. The permanent magnetic flux linkage is estimated based on a current proportional integral (PI) controller. Or important parameters, such as d-axis q-axis inductances, stator resistance, loss are measured offline by experiments. The measured parameters are saved as lookup tables which cover entire current operating range at different current levels. Combined with feedforward parameter iteration method, MTPA control strategy can be achieved based on accurate parameters. As a result, it is an effective approach to realize accurate efficient torque control. MATLAB/SIMULINK models were built to analyze proposed method. Furrmore, experiments were carried out to verify method. 2. Parameter Estimation 2.1. Analysis of IPMSM Energy Model For IPMSM, input comes from inverter. conservation, input can be expressed as follows [17]: According to law of E in = E out + E loss (1) E loss can be expressed as follows: E loss = E Cu + E Fe + E Str + E M (2) From point view of inverter, input can be expressed as follows: E in = 3(v q + v d )/2dt (3) output can be expressed as follows: E out = ω e T e /pdt (4)

3 Energies 2017, 10, of 15 Energies 2017, 10, of 16 where Considering ω e can be obtained cost, from Hall-effect IPMSM used sensors. in vehicles has no torque transducer; hence actual output Considering cannot cost, be obtained IPMSM from used Equation in vehicles (4). However, has no torque if transducer; input hence actual output loss are known, cannot output be obtained from can be Equation obtained (4). from However, Equation if (1). input The IPMSM model can loss be are used known, to estimate output essential parameters, can be obtained such as from Equation permanent (1). magnetic The IPMSM flux linkage model [18], can difference be used of to estimate q-axis essential d-axis inductance parameters, [1]. such In this as paper, permanent magnetic model is flux used linkage to estimate [18], difference high-resolution of q-axis position d-axis based inductance on low-resolution [1]. In this paper, Hall-effect sensors. model is used to estimate high-resolution position based on low-resolution Hall-effect sensors Rotor Position Estimation 2.2. Rotor Position Estimation Rotor Rotor Position Position Estimation Estimation Based Based on on Average Average Motor Motor Speed Speed The The high-resolution high-resolution position position can can easily easily be be estimated estimated through through a method a method based based on on average average speed, speed, where where six six sectors sectors are are classified classified according according to to states states of of Hall Hall sensor s sensor s signals signals [4]. [4]. Assuming Assuming that that speed speed within within a a sector sector is is constant constant average average speed speed in in present present previous previous sectors sectors is is uniform, uniform, speed speed can can be be approximated approximated as as follows follows [3]: [3]: ω e = θ θ θ θ 0 = dθ dθ ω = = e (5) t t t t (5) t 1 t 0 t 1 t 0 where where dθ d isθ is electrical electrical degree degree between between two sectors, two sectors, t 1 t 0 is t 1 t 0 time is interval time interval of previous of previous sector; n sector; n position can position be estimated can be estimated as follows: as follows: θ = 1 + ω e t = θ 1 dθ θ = θ + ω t = θ + t 1 e 1 (6) tt 1 t 0 Similarly, high-resolution position position can can be be obtained, obtained, as as shown shown in in Figure Figure Figure 1. Output signals of Hall sensors resultant position estimation. Figure 1. Output signals of Hall sensors resultant position estimation. θ 1 θ θ 0 θshould be 60 degrees if Hall sensors are aligned accurately. However, in IPMSM, 1 0 should be 60 degrees if Hall sensors are aligned accurately. However, in IPMSM, re is a certain error in hall sensor installation. The back EMF can be used to avoid error eliminate re is a certain third error harmonic. in However, hall sensor large installation. estimation The errors back will EMF occur can be when used this to method avoid is error used in vehicles eliminate where third motor harmonic. speed However, changes frequently. large estimation errors will occur when this method is used in vehicles where motor speed changes frequently Rotor Position Estimation Based on Power Closed-Loop Method Rotor Position Estimation Based on Power Closed-Loop Method For improving accuracy of estimated position, a method based on power closed-loop is proposed For improving to estimate accuracy position, of estimated as shown inposition, Figure 2. a method based on power closedloop is proposed to estimate position, as shown in Figure 2.

4 Energies 2017, 10, of 15 Energies 2017, 10, of 16 P in v, v i, i q q d d v, v, v iu, iv, iw u v w P loss P out P out θ P out P out T e ω e Figure Figure 2. Rotor 2. Rotor position position estimation estimation based based on on power closed-loop method. The reference electromagnetic torque T e can be expressed as follows: The reference electromagnetic torque Te can be expressed as follows: 3 T = pϕ f i dli i e (7) Te = 3 ( ϕ ) 2 oq od oq 2 p f ioq dliod i oq (7) where: where: ( ) 2 1 ω i Li L e q q e q f od = i id = i i cd i= = A 1 id i + ω el q iq R od d cd d c ω e 2L q ϕ f R 2 2 A( c R c R ) c (8) ioq = iq i cq = (8) A 1 iq ( ω e(ϕ f +L d id) + ) 1 ω ϕ Li R c e f d d i = i i = i oq q cq q A R c A = 1 + ω e 2 L d L q (9) R 2 2 c ω LL e d q The reference output power can be expressed A = 1as + follows: (9) 2 R c The reference output power can be Pexpressed out = Te as ω e follows: /p (10) For current closed-loop control, stator P = Tω / p (10) out d-axis e e q-axis current can be expressed as follows: For current i closed-loop control, stator d-axis q-axis current = can be d, = iq, (, ) = ParkTrans(ClarkeTrans(i u, i v, i w ), θ ) (11) expressed as follows: The output voltage of d-axis q-axis can be expressed as follows: i = i, i = i,( i, i ) = ParkTrans(ClarkeTrans( i, i, i ), θ ) d d q q d q u v w (11) (v d, v q ) = ParkTrans(ClarkeTrans(v u, v v, v w ), θ ) (12) The output voltage of d-axis q-axis can be expressed as follows: The input power from inverter to motor P (v,v ) = ParkTrans(ClarkeTrans(v in can be expressed as follows:,v,v ), θ ) d q u v w (12) P in = 3(v q i The input power from inverter to motor P q + v d )/2 (13) in can be expressed as follows: The actual mechanical output power P P out can be expressed as follows: = 3( vi + vi ) / 2 in q q d d (13) P The actual mechanical output power out = P can in P be loss (14) expressed as follows: P out Assuming that estimated position P is= equal P Pto actual position, n out in loss (14) actual electromagnetic torque should be equal to reference electromagnetic torque, actual output power should Assuming be equal that to stimated reference output position power is equal to vice versa. actual Therefore, position, n estimated actual position electromagnetic can be adjusted torque realize should be equal equality to of reference actual electromagnetic output power torque, reference actual output output power. power To achieve should accurate be equal torque reference control, output a PI estimator power with vice robust versa. Therefore, control is designed estimated to obtain position can be adjusted to realize equality of actual output power reference output position in this paper. As shown in Equation (7), permanent flux linkage difference of d-axis q-axis inductances are used to calculate reference electromagnetic torque. These parameters influence

5 Energies 2017, 10, of 16 power. To achieve accurate torque control, a PI estimator with robust control is designed to obtain Energies 2017, position 10, 410 in this paper. 5 of 15 As shown in Equation (7), permanent flux linkage difference of d-axis q-axis inductances are used to calculate reference electromagnetic torque. These parameters influence accuracy accuracy of of position estimation significantly. In this paper, permanent flux flux linkage linkage is is estimated estimated online online difference of of d-axis q-axis inductances is ismeasured offline offline by by experiments Permanent 2.3. Permanent Magnetic Magnetic Flux Flux Linkage Estimation To realize To realize accurate accurate efficient efficient current current control, control, current current PI controller PI controller with with feedforward feedforward control control voltage based on space vector pulse width modulation (SVPWM) is shown in Figure 3 [19]. voltage based on space vector pulse width modulation (SVPWM) is shown in Figure 3 [19]. +_ +_ k p _ d k i _ d s k ad v d _ ff v d +_ SVPWM v d 1 R + L s s d +_ +_ k p _ q k i _ q s k aq v q _ ff v q +_ SVPWM v q 1 R + L s s q Figure 3. Current proportional integral (PI) controller. Figure 3. Current proportional integral (PI) controller. For an For IPMSM, an IPMSM, it is it needed is needed to decouple to decouple d-axis d-axis q-axis q-axis voltages voltages current. The d-axis q-axis voltages q-axis voltages in in rotating rotating coordinate coordinate system system can be can expressed be expressed as as follows: [ ] [ ][ ] [ ][ ] [ ][ ] v 0 i ϕ 0 ω ϕ v d R d s s d e d d R = s 0 = + s 0 ϕ+ ϕ (15) v v 0 i ω 0 ϕ q R + d 0 ω s q + e ϕ d (15) q 0 R s 0 s q ϕ q e ω e q 0 ϕ q The last term of Equation (15) is back EMF. If d-axis q-axis flux linkages are accurate, The last term of Equation (15) is back EMF. If d-axis q-axis flux linkages are accurate, it can be eliminated by decoupling control. The feedforward control voltages can be expressed as it canfollows: be eliminated by decoupling control. The feedforward control voltages can be expressed as follows: [ ] [ ] v d_ f f v d_ ff 0 ω ω ϕ e d = = e ϕ d (16) (16) v q_ f f v _ ω q ff e 0 ϕ ϕq q where v d_ f f v where v q_ f d_ ff v f are d-axis q-axis feedforward control voltages, q_ ff are d-axis q-axis feedforward control voltages, ϕ ϕ d ϕ d are q are ϕ q estimated d-axis q-axis flux linkages. Assuming estimated d-axis v q-axis flux linkages. d_ f b v q_ f b are outputs of PI controller, d-axis q-axis voltages can be expressedassuming as follows: v d_ fb v q_ fb are outputs of PI controller, d-axis q-axis voltages can [ ] [ ] [ ] be expressed as follows: v d v = d_ f b v + d_ f f (17) v q v v q_ v f b v v q_ f f d d_ fb d_ ff = + (17) In steady circumstance, actual current vq vfollows q_ fb vqwell _ ff to reference current, thus differential term of Equation (15) can be eliminated: In steady circumstance, actual current follows well to reference current, thus differential term of Equation [ ] (15) [ can be eliminated: ][ ] [ ][ ] v d R = s 0 0 ω + e ϕ d v q 0 R s ω e 0 ϕ q [ ] [ ] (18) v = d_ f b 0 ω + e ϕ d v q_ f b ω e 0 ϕ q

6 Energies 2017, 10, of 15 Furrmore: [ v d_ f b v q_ f b ] = [ R s 0 0 R s ][ ] + [ 0 ω e ω e 0 ] ϕ d ϕ d ϕ q ϕ q (19) As shown in Equation (19), outputs of current PI controller contain a voltage drop at stator resistance an error of estimated flux linkage. If variation of stator resistance is negligible or can be compensated, error of estimated flux linkage can be obtained from integration term of PI controller, that is: [ ϕ d ϕ q ] = 1ωe [ ]([ v d_ f b_i v q_ f b_i ] [ R s 0 0 R s where ϕ d ϕ q are errors of d-axis q-axis flux linkages between actual estimated value ( ϕ d = ϕ d ϕ d, ϕ q = ϕ q ϕ q ), v d_ f b_i v q_ f b_i are integration terms of PI controller. Then, estimated permanent magnetic flux linkage can be expressed as follows: ][ ]) (20) ϕ f = ϕ d + ϕ d L d = (v q R s )/ω e L d (21) As shown in Equation (21), accuracy of estimated permanent magnetic flux linkage is affected by q-axis voltage (v q ), d-axis q-axis inductances (L d, L q ), stator resistance (R s ), d-axis q-axis current (, ). v q is equivalent to reference voltage, which includes output lag compensation [20] dead time compensation [21]. In this paper, L d, L q, R s are measured offline by experiments. The measured parameters are saved as lookup tables which cover entire current operating range at different current levels. Thus, L d, L q, R s can be considered to be accurate. In fact, R s is approximately accurate with temperature compensation, especially at a high speed when back EMF is much greater than voltage drop at stator resistance., can be obtained from current sensors Hall-effect sensors. Considering electrical angular speed (ω e ) is in denominator, estimation should be avoided at too low speed. 3. Torque Control Strategy 3.1. Feedforward Parameter Iteration Method A variety of parameters are needed for obtaining target current. The position permanent magnetic flux linkage can be estimated, as mentioned above. Or important parameters, such as d-axis q-axis inductances, stator resistance, loss, are measured offline by experiments. The measured parameters are saved as lookup tables which cover entire current operating range at different current levels. The parameters are obtained according to present input current, n target current is calculated according to control strategies. Therefore, parameters do not match target current well [22]. Assuming responding time from zero to maximum torque T emax is t respond, largest change in value of electromagnetic torque in a control period can be expressed as follows: T e_change = T emax 2t respond f (22) The largest change in value of q-axis current in a control period can be expressed as follows: _change = T emax 3pϕ f t respond f (23)

7 Energies 2017, 10, of 15 In fact, torque dem varies frequently for IPMSM used in vehicles, target current is calculated according to actual torque dem. It is difficult to define an equation to calculate mismatch between parameters current. For a given torque dem, starting with present parameters ( d-axis q-axis inductances, stator resistance, loss), one set of d-axis q-axis current is obtained, which is calculated by control strategies (such as MTPA). The obtained current is used for a new set of motor parameter calculation (using parameter lookup tables). Anor set of d-axis q-axis current is calculated with new parameters. This recursive calculation is carried out until differences between new output current previous one have reached a defined minimum error [22]. The feedforward parameter iteration method follows five steps: (1) Obtain present motor parameters ( d-axis q-axis inductances, stator resistance, loss) from lookup tables; (2) Calculate one set of d-axis q-axis current using control strategies; (3) Calculate motor parameters with current from step 2 using lookup tables; (4) Calculate anor set of d-axis q-axis current with new set of motor parameters from step 3 using control strategies. (5) If current error is within tolerance between current previous step, iteration is complete. Orwise, return to step Maximum Torque Per Ampere Control Strategy The MTPA control strategy is an efficiency optimization algorithm which only considers copper loss. The aim of optimization algorithm is to realize minimum copper loss for a given torque. Since copper loss is proportional to square of stator current, it is essential to find minimum stator current for a given torque. The MTPA control strategy can be expressed as follows: i cd = 0 i cq = 0 i od = i cd = i oq = i cq = T e = 3 2 p ( ϕ f + ( L d L q ) id ) min P Cu = 3 ( ) 2 2 R s i 2 2 d + = 3 2 R s i 2 d + 2T e 3p (ϕ f + ( ) ) L d L q id (24) (25) (26) For an IPMSM, L d = L q, Equation (26) has no explicit solutions for a given torque. If control parameter is q-axis current [23] or amplitude of stator current [24], explicit solution of can be expressed by as follows: or explicit solution of can be expressed by i s as follows: = ϕ f ϕ 2 f + 4 ( ) 2iq L q L 2 d 2 ( ) (27) L q L d = ϕ f ϕ f ( L q L d ) 2is 2 4 ( L q L d ) (28)

8 Energies 2017, 10, of 15 normalizing Equation (25), it can be expressed as follows: where T en = n (1 n ) (29) i b = ϕ f / ( L q L d ), Teb = 1.5pϕ f i b n = /i b, n = /i b, T en = T e /T eb (30) Equation (29) shows that output torque depends on d-axis q-axis current. For a given T en, n n have no unique solution. Substituting Equation (29) into Equation (26), MTPA control strategy can be expressed as follows: min { P Cu = 3 2 R si b 2 [ ]} i 2 dn + T en 2 (1 n ) 2 For a given IPMSM, R s i b are certain, MTPA control strategy can be expressed as follows: { } min i 2 dn + T en 2 (1 n ) 2 (32) solving Equation (32): T en = n (n 1) 3 T en = n 2 ( i 2 qn) Although relationship between normalized torque stator current can be obtained, Equation (33) has no explicit solutions eir. However, n n can be obtained from lookup tables, as shown in Figure 4. One of current can be obtained from lookup tables. The or Energies 2017, 10, of 16 current can be obtained from lookup tables directly or calculated by first current. (31) (33) Figure4. 4. Lookup tablesof of n n n to Tto en. T en. The MTPA T e control strategy only needs two lookup tables, which are independent of motor ω parameters, hence it is widely used in IPMSM for e its simplicity small amount i i θ of calculations. The IPMSM control system with MTPA control q strategy is shown in Figure 5. dl v q v d i v u T eb ϕ f i q θ T e i b i vd v q q FW v d _ fb _ i v q _ fb _ i v d v q θ V dc V dc

9 Energies 2017, 10, of 15 Figure 4. Lookup tables of i dn n to T en. T e dl ω e v d v q i θ i v u T eb ϕ f i q θ T e i b i vd q v q v d _ fb _ i v q _ fb _ i v d v q θ V dc FW V dc Figure 5. Maximum torque per ampere (MTPA) control algorithm. Figure 5. Maximum torque per ampere (MTPA) control algorithm. 4. Simulation Experimental Results 4. Simulation Experimental Results 4.1. Simulation Results 4.1. Simulation Results MATLAB/SIMULINK models were developed to examine proposed method. A 75-kW MATLAB/SIMULINK IPMSM for a new models vehicle application were developed is used in tothis examine paper, its proposed parameters method. are shown A in 75-kW IPMSM Table for1 a[1]. new vehicle application is used in this paper, its parameters are shown in Table 1 [1]. Table 1. Parameters of interior permanent magnet synchronous motor (IPMSM). Table 1. Parameters of Parameter interior permanent magnet Symbol synchronous Value motor (IPMSM). Number of pole pairs p 6 Parameter Stator resistance Symbol Rs 4.23 Value mω NumberMagnet of pole pairs flux linkage p ϕf Wb Stator resistance d-axis inductance R s Ld mω mh Magnet flux q-axis linkage inductance φ f Lq mh Wb d-axis inductance DC linkage voltage L d Vdc mh V q-axis inductance Maximum speed L q nb 4000 Rpm mh DC linkage Peak voltage current V dc Ipk Apk V Maximum speed n Rated power b 4000 Rpm Pr 75 kw Peak current I pk 570 Apk Peak torque Tmax 540 Nm Rated power P r 75 kw Coefficient of RSac to RsDC Peak torque T μ 0.1 max 540 Nm Coefficient of R Sac to R sdc µ 0.1 Hysteresis current coefficient K h Eddy current coefficient K e Stray loss coefficient c Str Mechanical friction torque T fric 5.24 Windage torque coefficient c wind The simulation model is shown in Figure 6. The PWM frequency is set as 10 khz PI current regulating frequency is set as 20 khz. The dead time voltage drop of power device are ignored in simulation (in actual application, dead time voltage drop of power device will be compensated, so simplification is valid at this stage). Iron loss mechanical frictional loss are also ignored in simulation. To make simulation more accurate, stator resistance d-axis q-axis inductances are measured offline. In fact, only varying trends but not accurate values of se parameters are needed in simulation, because y are just used to verify effectiveness of proposed method. The simulation results are shown in Figures 7 9 at different conditions. As shown, actual electromagnetic torque follows well with reference electromagnetic torque based on accurate estimated measured parameters; hence accurate torque control is achieved. The simulation

10 Energies 2017, 10, of 16 Hysteresis current coefficient Kh Energies 2017, 10, 410 Eddy current coefficient Ke of 15 Stray loss coefficient cstr Mechanical friction torque Tfric 5.24 results under any orwindage condition torque alsocoefficient verify effectiveness of proposed method (except cwind zero-speed zero-torque condition under which d-q axis voltages reference power are zero. In that The case, simulation position model is shown estimator in Figure flux 6. linkage estimator cannot function). Figure 6. Simulation model. The PWM frequency is set as 10 khz PI current regulating frequency is set as 20 khz. The dead time voltage drop of power device are ignored in simulation (in actual application, dead time voltage drop of power device will be compensated, so simplification is valid at this stage). Iron loss mechanical frictional loss are also ignored in simulation. To make simulation more accurate, stator resistance d-axis q-axis inductances are measured offline. In fact, only varying trends but not accurate values of se parameters are needed in simulation, because y are just used to verify effectiveness of proposed method. The simulation results are shown in Figures 7 9 at different conditions. As shown, actual electromagnetic torque follows well with reference electromagnetic torque based on accurate estimated measured parameters; hence accurate torque control is achieved. The simulation results under any or condition also verify effectiveness of proposed method (except 6. zero-speed zero-torque condition Figure under 6. which Simulation d-q model. axis voltages reference power are zero. In that case, position estimator flux linkage estimator cannot function). The PWM frequency is set as 10 khz PI current regulating frequency is set as 20 khz. The dead time voltage drop of power device are ignored in simulation (in actual application, dead time voltage drop of power device will be compensated, so simplification is valid at this stage). Iron loss mechanical frictional loss are also ignored in simulation. To make simulation more accurate, stator resistance d-axis q-axis inductances are measured offline. In fact, only varying trends but not accurate values of se parameters are needed in simulation, because y are just used to verify effectiveness of proposed method. The simulation results are shown in Figures 7 9 at different conditions. As shown, actual electromagnetic torque follows well with reference electromagnetic torque based on accurate estimated measured parameters; hence accurate torque control is achieved. The simulation results under any or condition also verify effectiveness of proposed method (except zero-speed zero-torque condition under which d-q axis voltages reference power are zero. In that case, position estimator flux linkage estimator cannot function). Energies 2017, 10, of 16 Figure 7. Flux linkage estimation torque control under maximum torque conditions Figure 7. Flux linkage estimation torque control under maximum torque conditions (1000 (1000 rpm/540 Nm). rpm/540 Nm). Figure 8. Flux linkage estimation torque control under rated conditions (2000 rpm/358 Nm). Figure 8. Flux linkage estimation torque control under rated conditions (2000 rpm/358 Nm).

11 Energies 2017, 10, of 15 Figure 8. Flux linkage estimation torque control under rated conditions (2000 rpm/358 Nm). Figure Flux linkage estimation torque control in in flux weakening region (2800 rpm/256 Nm) Experimental Results The effectiveness of of proposed method was tested experimentally with IPMSM as Table 1 shows. A dynamometer was usedto emulate load. Adigital signal signal processor (DSP) (DSP) was was used usedto to carry carryout out real-time algorithm. Six-pack insulated gate bipolar transistors (IGBT) were used as as power switches. switches. A LiFePO A LiFePO4 4 battery battery pack (288 pack V/180 (288 Ah) V/180 wasah) usedwas a power used as source. a power The experimental source. The bench experimental is shownbench in Figure is shown 10. in Figure 10. Energies 2017, 10, of 16 Figure Figure Experimental Experimental bench. bench. The experimental results are shown in Figures The experimental results are shown in Figures As shown in Figures 11 12, minimum position error is less than one electrical As shown in Figures 11 12, minimum position error is less than one electrical degree degree maximum position error is less than five electrical degrees. However, maximum position error is less than five electrical degrees. However, maximum maximum position error with average speed based estimation method is around ten position error with average speed based estimation method is around ten electrical degrees [4]. electrical degrees [4]. Furrmore, output torque of motor is always accurate. Furrmore, output torque of motor is always accurate. Figure 11 shows that voltage of battery drops dramatically to 250 under rated conditions, Figure 11 shows that voltage of battery drops dramatically to 250 V under rated conditions, hence, motor enters flux-weakening region. Compared with simulation results, q-axis hence, motor enters flux-weakening region. Compared with simulation results, q-axis current decreases, whereas d-axis current increases, magnetic saturation is not so serious. Thus, current decreases, whereas d-axis current increases, magnetic saturation is not so serious. Thus, estimated flux linkage in experiment is slightly greater than simulation result. estimated flux linkage in experiment is slightly greater than simulation result.

12 degree maximum position error is less than five electrical degrees. However, maximum position error with average speed based estimation method is around ten electrical degrees [4]. Furrmore, output torque of motor is always accurate. Figure 11 shows that voltage of battery drops dramatically to 250 V under rated conditions, hence, motor enters flux-weakening region. Compared with simulation results, q-axis Energies current 2017, 10, decreases, 410 whereas d-axis current increases, magnetic saturation is not so serious. Thus, 12 of 15 estimated flux linkage in experiment is slightly greater than simulation result. Figure 11. Experimental results under rated conditions (2000 rpm/358 Nm). Energies 2017, 10, Figure Experimental results under rated conditions (2000 rpm/358 Nm). 13 of 16 Energies 2017, 10, of 16 Figure 12 shows almost same results with simulation except that flux linkage decreases due to increment of temperature. Under maximum torque conditions, reluctance torque is greater than or conditions; hence less current is needed to obtain same output torque. Therefore, torque control is more efficient. Figure 13 shows efficiency of motor drive system, including motor inverter. As shown, maximum efficiency of motor drive system can reach 0.94 around rated conditions, minimum efficiency of system is above 0.8. Thus, efficient control has been realized. Figure 12. Experimental results under maximum torque conditions (1000 rpm/540 Nm). Figure Figure 12. Experimental 12. Experimental results results under under maximum maximum torque conditions (1000 (1000rpm/540 rpm/540 Nm). Nm). Figure 13. Efficiency of motor drive system. Figure 13. Efficiency of motor drive system. Figure 13. Efficiency of motor drive system. 5. Conclusions 5. Conclusions In this paper, an effective method to achieve accurate efficient torque control of an IPMSM in electric In this vehicles, paper, an based effective on low-resolution method to achieve Hall-effect accurate sensors, efficient is proposed. torque Assuming control of that an IPMSM d- axis in electric q-axis vehicles, inductances, based on stator low-resolution resistance, Hall-effect loss sensors, are known is proposed. (measured Assuming offline), that highresolution d- axis q-axis inductances, position stator permanent resistance, flux linkage are loss estimated are known online (measured based offline), on IPMSM highresolution model. Combined position with permanent feedforward flux linkage parameter are estimated iteration online method, based MTPA on control IPMSM strategy model. is achieved Combined based on with accurate feedforward parameters. parameter The simulation iteration method, experimental MTPA results control show

13 Energies 2017, 10, of 15 Figure 12 shows almost same results with simulation except that flux linkage decreases due to increment of temperature. Under maximum torque conditions, reluctance torque is greater than or conditions; hence less current is needed to obtain same output torque. Therefore, torque control is more efficient. Figure 13 shows efficiency of motor drive system, including motor inverter. As shown, maximum efficiency of motor drive system can reach 0.94 around rated conditions, minimum efficiency of system is above 0.8. Thus, efficient control has been realized. 5. Conclusions In this paper, an effective method to achieve accurate efficient torque control of an IPMSM in electric vehicles, based on low-resolution Hall-effect sensors, is proposed. Assuming that d-axis q-axis inductances, stator resistance, loss are known (measured offline), high-resolution position permanent flux linkage are estimated online based on IPMSM model. Combined with feedforward parameter iteration method, MTPA control strategy is achieved based on accurate parameters. The simulation experimental results show that, by using this method, accurate efficient torque control can be realized. By using low-resolution Hall-effect sensors instead of resolvers, electric vehicles can reduce cost, weight, volume. Since position estimation is based on a power closed-loop, IPMSM can output accurate torque even if estimated position has some errors. Since flux linkage power calculations are related to speed, proposed method may have some drawbacks in low-speed region. However, this method provides a relatively more effective way to achieve efficient accurate control of IPMSM, particularly when IPMSM works under high-power, high-speed working conditions. Moreover, method proposed in this paper can also be applied in or types of motors in electric vehicles, such as in-wheel motors, surface PMSM, PM-assisted synchronous reluctance motors. Author Contributions: This paper is results of hard work of all of authors. Lei Yu Wenqing Huang conceived designed proposed method. Lei Yu Youtong Zhang conceived performed experiments; Lei Yu analyzed data; Lei Yu wrote paper. All authors gave advice for manuscript. Conflicts of Interest: The authors declare no conflict of interest. Nomenclature E in E out E loss E Cu E Fe E str E M v u, v v, v w v d, v q v d, v q i u, i v, i w, id, i q i cd, i cq n, n i s FW ω e Input Output Energy loss Copper loss Iron loss Stray loss Mechanical loss Stator three phase voltages Stator d-axis q-axis voltages Reference stator d-axis q-axis voltages Stator three phase current Stator d-axis q-axis current Reference stator d-axis q-axis current d-axis q-axis iron loss current Normalized stator d-axis q-axis current Stator current d-axis field-weakening current Rotor electrical angular speed

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