Rotor Field Oriented Control of Resonant Wireless Electrically Excited Synchronous Motor

Article Rotor Field Oriented Control of Resonant Wireless Electrically Excited Synchronous Motor

Yong Bao , Zaimin Zhong *, Chengyu Hu and Yijin Qin

School of Automotive Studies, Tongji University, No. 4800 Cao’an Road, Jiading District, Shanghai 201804, China; [email protected] (Y.B.); [email protected] (C.H.); [email protected] (Y.Q.) * Correspondence: [email protected]

Received: 11 September 2019; Accepted: 3 October 2019; Published: 5 October 2019

Abstract: In order to solve the problems of wear and spark of the brush and slip ring in an electrically excited synchronous motor (EESM), based on the principle of magnetic resonance coupling wireless power transfer (MRC-WPT), a resonant wireless excitation system of EESM is designed. By modeling the EESM and analyzing the rotor ﬁeld oriented control (RFOC) method, a control system of the resonant wireless EESM (RW-EESM) is established. Furthermore, the stator current distribution strategy is analyzed. Finally, a test of the RE-EESM prototype is carried out. The test results show that the motor can realize no-load stable operation, and the test speed is maintained at 85 r/min. The results show that the wireless excitation scheme of EESM is feasible, and the RFOC of RW-EESM motor is reasonable.

Keywords: electrically excited synchronous motor; resonant wireless electrically excitation; rotor ﬁeld oriented control

1. Introduction Due to the problems of wear and spark of the brush and slip ring, applications of conventional electrically excited synchronous motors (EESMs) are limited. Brushless rotor excitation is an important development direction of the EESM. Based on the principle of inductive coupling, some scholars have made beneficial explorations in this direction. Zhang et al. proposed a brushless doubly fed machine and studied its electromagnetic characteristics [1]. Xia and Huang proposed dual windings in the rotor side of the synchronous generator to provide the excitation current by capturing the harmonics of the stator armature current through harmonic induction windings [2]. Liu et al. presented a brushless power transferring approach through a high frequency rotating exciter, designed a 48 V 20 kW brushless EESM for mild hybrid vehicles, and studied its torque–speed characteristics, efficiency, copper loss, and temperature rise [3–6]. Hu et al. also designed a brushless EESM [7]. However, the efficiency of the conventional rotor brushless excitation method is low. In addition, a contactless power transfer system based on capacitive coupling was proposed. Ludois et al. designed a wound field synchronous machine base on the principle of capacitive coupling and studied its performance [8–11]. However, its structure is complex and its axial dimension is large. In 2007, Kurs et al. proposed a magnetic resonance coupling wireless power transfer (MRC-WPT) scheme [12], which enriched the technical scheme of wireless power transfer schemes. Jiang et al. proposed and implemented the concept of time-division multiplexing wireless power transfer for separately excited DC motor drives [13]. Ditze et al. examined an inductive power transfer system with a rotary transformer as an alternative solution to slip ring systems for a contactless energy transfer to rotating equipment [14].

World Electric Vehicle Journal 2019, 10, 62; doi:10.3390/wevj10040062 www.mdpi.com/journal/wevj WorldWorld ElectricElectric VehicleVehicle JournalJournal2019 2019,,10 10,, 62 62 22 of 1313

This paper applies the principle of MRC-WPT to the rotor excitation of EESM. A rotor resonant This paper applies the principle of MRC-WPT to the rotor excitation of EESM. A rotor resonant wireless excitation system of EESM is designed. This paper explores the rotor field oriented control wireless excitation system of EESM is designed. This paper explores the rotor ﬁeld oriented control (RFOC) of resonant wireless EESM (RW-EESM). (RFOC) of resonant wireless EESM (RW-EESM). 2. Principle of MRC-WPT 2. Principle of MRC-WPT Taking the inductor/capacitor-inductor/capacitor (LC-LC) topology as an example, the Taking the inductor/capacitor-inductor/capacitor (LC-LC) topology as an example, the principle of principle of MRC-WPT is shown in Figure 1. u is the AC excitation voltage on the primary side. L1 MRC-WPT is shown in Figure1. u is the AC excitation voltage on the primary side. L1 and C1 are the and C1 are the inductor and capacitor on the primary side, respectively. R1 is the parasitic resistance inductor and capacitor on the primary side, respectively. R1 is the parasitic resistance on the primary on the primary side. L2 and C2 are the inductor and capacitor on the secondary side, respectively. R2 side. L2 and C2 are the inductor and capacitor on the secondary side, respectively. R2 and RL are the and RL are the parasitic and load resistances on the primary side, respectively. M is the mutual parasitic and load resistances on the primary side, respectively. M is the mutual inductance of primary inductance of primary and secondary coils. I1 and I2 are the currents on the primary and secondary and secondary coils. I and I are the currents on the primary and secondary sides, respectively. sides, respectively. The1 primary2 side and the secondary side are isolated from each other in space, The primary side and the secondary side are isolated from each other in space, and there is no contact. and there is no contact. Coupling is achieved by mutual inductance between the primary side and Coupling is achieved by mutual inductance between the primary side and secondary side coils. secondary side coils.

I1 C1 C2 I1 +

u L1 L2 RL — R1 R2

Figure 1. Principle of magnetic resonance coupling wireless power transfer (MRC-WPT). Figure 1. Principle of magnetic resonance coupling wireless power transfer (MRC-WPT). When the primary and secondary sides all operate at the resonant frequency, the resonant frequencyWhen is: the primary and secondary sides all operate at the resonant frequency, the resonant frequency is: 1 1 ω = = . (1) √L1C1 √L2C2 ==11 In the case of power transfer, the resonantω frequencies of primary. and secondary sides should be(1) LC LC equal. The efficiency of power transfer is expressed11 as: 22 In the case of power transfer, the resonant frequencies of primary and secondary sides should ω2M2R be equal. The efficiency of powerη = transfer is expressed Las: . (2) 2 2 (R1(R2 + RL) + ω M )(R2 + RL) ω22MR = L R is much smaller than R , soη . (2) 2 L ()RR()++ R ω22MRR() + 12LLω2M2 2 η . (3) ≈ R R + ω2M2 R2 is much smaller than RL, so 1 L From Equation (3), it can be seen that the efficiency increases with the increase of mutual inductance ω22M and resonant frequency. For the motor rotorη excitation,≈ the distance. of power transfer is short. Thus, + 22 (3) the mutual inductance can be designed to be larger,RR1L andω theM resonant frequency can be designed to be higher. Furthermore, the efficiency of power transfer can be theoretically high. From Equation (3), it can be seen that the efficiency increases with the increase of mutual 3.inductance A Resonant and Wireless resonant Excitation frequency. System For the of motor EESM rotor excitation, the distance of power transfer is short. Thus, the mutual inductance can be designed to be larger, and the resonant frequency can be 3.1.designed The Type to be of Primaryhigher. Furthermore, and Secondary the Coils efficiency of power transfer can be theoretically high. The primary coil is fixed to the stator, and the secondary coil is connected to the rotor. The relative 3. A Resonant Wireless Excitation System of EESM position of the two coils should be consistent to ensure that the mutual inductance is constant, so that the3.1. characteristicsThe Type of Primary of power and Secondary transfer do Coils not change. The two coils can be designed as circular rings, and the coils are in two planes perpendicular to the rotor axis, as shown in Figure2. The primary coil is fixed to the stator, and the secondary coil is connected to the rotor. The relative position of the two coils should be consistent to ensure that the mutual inductance is constant, so that the characteristics of power transfer do not change. The two coils can be designed as circular rings, and the coils are in two planes perpendicular to the rotor axis, as shown in Figure 2. World Electric Vehicle Journal 2019, 10, 62 3 of 13 World Electric Vehicle Journal 2019, 10, 62 3 of 13 World Electric Vehicle Journal 2019, 10, 62 3 of 13 Stator Secondary Primary coil coil StatorRotor Secondary Primary coil coil Rotor P2 P1

P2 P1

Figure 2. A resonant wireless excitation system of the electrically excited synchronous motor Figure(EESM). 2. A resonant wireless excitation system of the electrically excited synchronous motor (EESM). Figure 2. A resonant wireless excitation system of the electrically excited synchronous motor 3.2. The(EESM). Secondary Circuit 3.2. The Secondary Circuit The power transferred to the secondary coil is AC, but the EESM rotor needs DC power. Hence, it 3.2. TheThe Secondary power transferred Circuit to the secondary coil is AC, but the EESM rotor needs DC power. Hence, is necessary to convert the AC power to DC power at the secondary side through rectification and it is necessary to convert the AC power to DC power at the secondary side through rectification and filtering.The power A feasible transferred rectifier filterto the circuit secondary is shown coil inis AC Figure, but3. the The EESM secondary rotor circuit needs isDC rectified power. by Hence, a full filtering. A feasible rectifier filter circuit is shown in Figure 3. The secondary circuit is rectified by a itbridge is necessary and filtered to convert by an inductorthe AC power and a to capacitor DC power to obtain at the DC secondary power, whichside through is then usedrectification to excite and the full bridge and filtered by an inductor and a capacitor to obtain DC power, which is then used to filtering.rotor coil. A feasible rectifier filter circuit is shown in Figure 3. The secondary circuit is rectified by a fullexcite bridge the rotor and filteredcoil. by an inductor and a capacitor to obtain DC power, which is then used to excite the rotor coil.

+ Load + Load

Rectifier filter circuit FigureFigure 3.3. The resonant wireless powerpowerRectifier transfertransfer filtersystem.system. circuit 3.3. The Voltage at the PrimaryFigure Side 3. The resonant wireless power transfer system. 3.3. The Voltage at the Primary Side The primary excitation is theoretically a sinusoidal voltage. However, the primary excitation is 3.3. TheThe Voltage primary at the excitation Primary isSide theoretically a sinusoidal voltage. However, the primary excitation is an easily implemented square wave in practice. In the square wave, besides the main fundamental an easily implemented square wave in practice. In the square wave, besides the main fundamental waveThe of energyprimary transfer, excitation there is theoretically are also harmonics, a sinusoidal such voltage. as 3th/5th However,/7th harmonics. the primary The amplitude excitation ofis wave of energy transfer, there are also harmonics, such as 3th/5th/7th harmonics. The amplitude of anthe easily harmonics implemented decreases square rapidly wave with in thepractice. increase In ofthe harmonic square wave, order. besi Furthermore,des the main the fundamental MRC-WPT the harmonics decreases rapidly with the increase of harmonic order. Furthermore, the MRC-WPT wavesystem of has energy a strong transfer, band-pass there characteristic.are also harmonics, Harmonics such haveas 3th/5th/7th little effect harmonics. on the energy The transfer, amplitude so theof system has a strong band-pass characteristic. Harmonics have little effect on the energy transfer, so theharmonic harmonics effect decreases can be ignored. rapidly The with sinusoidal the increase voltage of harmonic can be replaced order. Furthermore, with a square the wave. MRC-WPT systemthe harmonic has a strong effect canband-pass be ignored. characteristic. The sinusoid Harmonal voltageics have can littlebe replaced effect on with the aenergy square transfer, wave. so the3.4. harmonic Rotor Excitation effect can Current be ignored. Regulation The sinusoidal voltage can be replaced with a square wave. 3.4. Rotor Excitation Current Regulation When the motor runs under different conditions, the demand of rotor excitation current may be 3.4. RotorWhen Excitation the motor Current runs underRegulation differe nt conditions, the demand of rotor excitation current may be different, which can be realized by adjusting the voltage at the primary side. For a certain system, when different, which can be realized by adjusting the voltage at the primary side. For a certain system, otherWhen parameters the motor are allruns determined, under differe thent power conditions, on the the load demand can only of berotor adjusted excitation by the current amplitude may be of when other parameters are all determined, the power on the load can only be adjusted by the different,voltage at which the primary can be side. realized In practice, by adjusting changing the the voltage duty ratioat the cycle primary of the side. square For wave a certain can adjust system, the amplitude of voltage at the primary side. In practice, changing the duty ratio cycle of the square whenamplitude other of parameters voltage, and are further all determined, control the rotorthe po excitationwer on the current. load can only be adjusted by the amplitudewave can adjustof voltage the amplitude at the primary of voltage, side. anInd practice, further controlchanging the the rotor duty excitation ratio cycle current. of the square wave4. Model can adjust of EESM the andamplitude RFOC of voltage, and further control the rotor excitation current. 4. Model of EESM and RFOC 4.4.1. Model Model of of EESM EESM and RFOC 4.1. Model of EESM Taking a three-phase salient pole EESM as an example, the assumptions are as follows. The stator 4.1.three-phase ModelTaking of windingsEESMa three-phase are symmetrically salient pole distributedEESM as an in example, space. The the air assumptions gap magnetic are field as is follows. sinusoidally The distributedstatorTaking three-phase ina space.three-phase windings The influence salient are symmetricallypole of magnetic EESM as saturation, distributedan example, core in the space. loss, assumptions and The temperature air gap are magneticas changefollows. field on The the is statormotorsinusoidally three-phase is neglected. distributed windings The normal in space. are direction symmetrically The influence is set by distributed of the magnetic motor in practice. saturation, space. The core air gaploss, magneticand temperature field is sinusoidallychange on the distributed motor is neglected. in space. TheThe influencenormal direction of magnetic is set saturation,by the motor core practice. loss, and temperature change on the motor is neglected. The normal direction is set by the motor practice. World Electric Vehicle Journal 2019, 10, 62 4 of 13

World Electric Vehicle Journal 2019, 10, 62 4 of 13 The axis of rotor excitation winding is called the direct axis (d-axis), and its orthogonal axis is called the quadrature axis (q-axis). In the rotor direct-quadrature (dq) synchronous coordinate system,The the axis stator of rotor and rotor excitation voltage winding equations is called are: the direct axis (d-axis), and its orthogonal axis is called the quadrature axis (q-axis). In the rotor direct-quadrature    (dq)− synchronous coordinate system, uR i ψ  ωψrq the stator and rotor voltage equationsds are:  dd  d  uRi=++  ψωψ , (4)   qsqqrd  dt     u R i  ψ ω ψ  d  ui s Rf d  ψ d  0 r q    fff  d    −   u  =  R  i  +   +    q   s  q   ψq   ωrψd , (4)      dt    where Rs and Rf are the ustatorf and rotor windingRf if resistances,ψf respectively;0 id and iq are the current f components of the stator on the d-axis and q-axis, respectively; i is the rotor excitation current; ψd where Rs and Rf are the stator and rotor winding resistances, respectively; id and iq are the current and ψ are the flux components of the stator on the d-axis and q-axis, respectively; ψ is the rotor componentsq of the stator on the d-axis and q-axis, respectively; if is the rotor excitation current;f ψd and flux;ψq are and the ω fluxr is components the electrical of angular the stator velocity on the of d-axis the rotor. and q-axis, respectively; ψf is the rotor flux; and ωr is the electrical angular velocity of the rotor. ψ LLi0    dd  mdd    ψdψ = Ld000LiLmd   id,    qqq   (5)  ψq  =  0 Lq 0   iq , (5)  ψ  LLi0     ff md f    ψf Lmd 0 Lf if where Ld and Lq are the inductance components of the stator on the d-axis and q-axis, respectively. Lf where Ld and Lq are the inductance components of the stator on the d-axis and q-axis, respectively. Lf is the self inductance of the rotor. Lmd is the mutual inductance on the d-axis. is the self inductance of the rotor. Lmd is the mutual inductance on the d-axis. TheThe torque torque of of EESM EESM is 33 Te ==−p0 ψ()diq ψqid , (6) Tpe0dqqd2 ψ i − ψ i , (6) 2 where p0 is the pole number of the motor. From Equations (11) and (12): where p0 is the pole number of the motor. From Equations (11) and (12): 3 h i Te = 3p0 Lmdi iq + Ld Lq i iq . (7) TpLiiLLii=+−2 f ()− d . (7) e0mdqdqq2 fd The angle between the stator current Is and the d-axis is defined as the torque angle β, as shown The angle between the stator current Is and the d-axis is defined as the torque angle β, as shown in Figure4. in Figure 4.

Is q d β θ r A

Figure 4. Is in the direct-quadrature (dq) synchronous coordinate system. Figure 4. Is in the direct-quadrature (dq) synchronous coordinate system.

The current components on the d-axis and q-axis can be expressed as id = is cos β and iq = The current components on the d-axis and q-axis can be expressed as ii= cos β and is sin β. Hence, ds ii= sin β . Hence, 3 1 2 qs Te = p L i is sin β + L Lq i sin 2β , (8) 2 0 md f 2 d − s where L i i sin β is the excitation31 torque generated by the interaction2 of the stator and rotor currents; md f s TpLii=+−sinβ ()LLi sin 2β , (8) 1 2 e0mdsf dqs and L Lq i sin 2β is the reluctance22 torque caused by the unequal reluctances on the d-axis and 2 d − s q-axis. According to Equation (8), the relationship between torques and β is shown in Figure4. where Liisin β is the excitation torque generated by the interaction of the stator and rotor Frommd Figuref s 5, when the torque angle is between 0 and π/2, that is, the current vector is in the ﬁrst quadrant of the1 dq coordinate system, the total torque can be maximized. Hence, the torque angle can currents; and ()LLi− 2 sin 2β is the reluctance torque caused by the unequal reluctances on the be adjusted to2 makedqs full use of the reluctance torque, which can improve the output torque. d-axis and q-axis. According to Equation (8), the relationship between torques and β is shown in Figure 4. From Figure 5, when the torque angle is between 0 and π/2, that is, the current vector is in the first quadrant of the dq coordinate system, the total torque can be maximized. Hence, the torque WorldWorld Electric Electric Vehicle Vehicle Journal Journal 2019 2019, ,10 10, ,62 62 55 ofof 1313 angleangle cancan bebe adjustedadjusted toto makemake fullfull useuse ofof thethe reluctancereluctance torque,torque, whichwhich cancan improveimprove thethe outputoutput World Electric Vehicle Journal 2019, 10, 62 5 of 13 torque.torque.

33 TTee

22 ββ ππ/2/2

Figure 5. The relationship between torques and torque angle. FigureFigure 5. 5. The The relationship relationship between between torques torques and and torque torque angle. angle. 4.2. RFOC 4.2.4.2. RFOC RFOC According to Equation (7), the total torque is determined by the stator and rotor currents. The RFOC can controlAccordingAccording the motor toto EquationEquation output (7),(7), torque thethe bytotaltotal controlling torquetorque isis thedetermineddetermined stator and byby rotor thethe statorcurrents.stator andand The rotorrotor RFOC currents.currents. system TheThe of RFOCEESMRFOC iscancan shown controlcontrol in Figurethethe motormotor6. outputoutput torquetorque byby controllingcontrolling thethe statorstator andand rotorrotor currents.currents. TheThe RFOCRFOC systemsystem of of EESM EESM is is shown shown in in Figure Figure 6. 6.

WPTWPT uuf f systemsystem IIf_reff_ref Id_refd_ref alpha I uudd uualpha TTee TTe_refe_ref Current Current Coordinate Current q_ref Current Coordinate IIq_ref uuqq uubetabeta SVPWMSVPWM InverterInverter EESMEESMwwrr distributiondistribution regulatorregulator transformationtransformation PositionPosition

Figure 6. The rotor ﬁeld oriented control (RFOC) system of EESM. FigureFigure 6. 6. The The rotor rotor field field oriented oriented control control (RFOC) (RFOC) system system of of EESM. EESM. The current distribution module determines the distribution law of the stator and rotor currents accordingTheThe current current to the commanddistribution distribution torque. module module The determines determines current regulator the the distribution distribution calculates law law the of commandof the the stator stator voltage and and rotor rotor according currents currents to accordingtheaccording command toto thethe current commandcommand and the torque.torque. actual TheThe current. currentcurrent The reguregu coordinatelatorlator calculatescalculates transformation thethe commandcommand of the voltagecommandvoltage accordingaccording voltage toisto applied thethe commandcommand to the space currentcurrent vector andand pulse thethe actualactual width current. modulationcurrent. TheThe (SVPWM) coordinatecoordinate module. transformationtransformation Then the ofof control thethe commandcommand signal of voltagethevoltage inverter isis appliedapplied is obtained toto thethe and spacespace the vector controlvector pulsepulse of EESM wiwidthdth is realized. modulationmodulation (SVPWM)(SVPWM) module.module. ThenThen thethe controlcontrol signalsignal of of the the inverter inverter is is obtained obtained and and the the control control of of EESM EESM is is realized. realized. 4.3. Stator Current Distribution Strategy 4.3. Stator Current Distribution Strategy 4.3. StatorThe stator Current current Distribution distribution Strategy must be within the current limit circle: TheThe stator stator current current distribution distribution must must be be within within the the current current limit limit circle: circle: 2 2 2 id + iq ismax (9) iii2222+≤+≤≤ 2 2 iiidqdq s smax max (9)(9) The stator voltage is q TheThe stator stator voltage voltage is is 2 2 us = u + u usmax (10) d q ≤ uuuu=+≤=+≤2222 (10) The voltage equation is mainly restricteduuuusdqsmaxsdqsmax at high speed, so the resistance voltage drop is ignored.(10) Substituting Equation (4) into the upper equation, Equation (10) can be converted to the voltage TheThe voltagevoltage equationequation isis mainlymainly restrictedrestricted atat highhigh speed,speed, soso thethe resistanceresistance voltagevoltage dropdrop isis limit ellipse: ignored.ignored. SubstitutingSubstituting EquaEquationtion (4)(4) intointo thethe upperupper2 equation,equation, EquationEquation (10)(10) cancan bebe convertedconverted toto thethe Lmdif voltage limit ellipse: id + !2 voltage limit ellipse: Ld u + i2 smax . (11) 2 q Lq ≤ Lqωr Ld Hence, the voltage limit equation is an ellipse whose center is L i /i , 0 , the long axis is − md f d 2usmax/ωrLq, and the short axis is 2usmax/ωrLd. World Electric Vehicle Journal 2019, 10, 62 6 of 13

4.3.1. Maximum Torque per Ampere (MTPA) Control at Low Speed Equation (8) can be written as Te = sin β + K2 sin β, (12) K1 where 3 K = p L i i = K i , (13) 1 2 0 md f s f1 s Ld Lq is K2 = − = Kf2is. (14) 2Lmdif

When Te takes the maximum value: q + + 2 1 1 32K2 cos β = − , (15) 8K2

r q 32K2 2 + 2 1 + 32K2 2 − 2 sin β = , (16) 8K2 The current components on d-axis and q-axis are q 1 + 1 + 32K2 i2 − f2 s id = is cos β = , (17) 8Kf2

r q 32K2 i2 2 + 2 1 + 32K2 i2 f2 s − f2 s iq = is sin β = . (18) 8Kf2 From Equations (17) and (18) q 2 (8Kf2id + 1) + 2(8Kf2id + 1) 3 iq = − . (19) 8Kf2

Equation (19) is the MTPA curve, which is essentially the set of tangent points of the current circle and the equal torque curve.

4.3.2. Maximum Torque Control under Voltage Limitation When the motor has only a voltage limit and no current limit, the maximum torque per voltage (MTPV) is required. The Lagrange multiplier method is used here. The optimization function is set to be " 2# 3 h i 2 2 usmax F id, iq = p0 Lmdif iq + Ld Lq idiq + λ Ldid + Lmdif + Lqiq . (20) 2 − − ωr From Equation (20)

 ∂F 3  = p0 Ld Lq iq + 2λLd Lmdif + Ldid = 0  ∂id 2 −  ∂F 3 h i 2 . (21)  = p0 Lmdi + Ld Lq id + 2λL iq = 0 ∂iq 2 f − q From the ﬁrst equation in Equation (21), 3p0 Ld Lq iq λ = − . (22) 4Ld Lmdif + Ldid World Electric Vehicle Journal 2019, 10, 62 7 of 13

Substituting from Equation (22) into the second equation in Equation (21), h i Ld Lmdif + Ldid Lmdif + Ld Lq id i2 = − . (23) q 2 L Lq L d − q Substituting from Equation (23) into Equation (11), " # 4Ld 3Lq 2Ld Lq 2 u 2 2 2 + − + − smax = 2Ldid LmdLdif id Lmdif 0. (24) L Lq L Lq − ωr d − d − From Equation (24) b + √b2 4ac i = − − , (25) d 2a where   a = 2L2  d  4L 3Lq  b = d− L L i L Lq md d f . (26)  d−  2Ld Lq 2 u 2  c = − L i smax L Lq md f ωr d− − From Equations (23) and (25), iq can be solved, and then the maximum torque control curve under voltage limitation can be obtained.

4.3.3. Stator Current Distribution Strategy The rotor excitation current is controlled to a constant value, and the stator current is controlled according to diﬀerent speeds. The MTPA strategy is used at low speed, and the MTPV strategy is used at high speed. The rotor excitation current is often not very large. Thus, the center point of the voltageWorld Electric limit Vehicle ellipse Journal is 2019 considered, 10, 62 to be in the current limit circle. The relationship between voltage8 of 13 limit ellipse, current limit circle, MTPA curve, and MTPV curve is shown in Figure7.

iq Voltage limit ellipse

ωr=ωr1 MTPV curve Speed increase A2 MTPA curve

A1 Current limit circle

Figure 7. The limit curves and stator current distribution of resonant wireless EESM (RW-EESM). Figure 7. The limit curves and stator current distribution of resonant wireless EESM (RW-EESM) The rotor excitation current is controlled to a constant value. At diﬀerent speeds, the stator current can beThe controlled rotor excitation as follows. current is controlled to a constant value. At different speeds, the stator currentAt can low be speed, controlled the stator as follows. current is distributed according to the MTPA strategy. According to the requiredAt low torque, speed, the the command stator current current is isdistributed controlled according on the MTPA to the curve. MTPA strategy. According to the required torque, the command current is controlled on the MTPA curve.

As the motor speed increases, the voltage limit ellipse continues to shrink. When the speed ωr1 is reached, the voltage limit ellipse touches the command current A1. Due to the inverter voltage limitation, the motor speed cannot continue to rise. To increase the motor speed, the command current is adjusted leftward from the A1 point along the current limit circle until the current distribution point reaches the A2 point on the MTPV curve. In this process, the motor speed increases and the torque decreases. The above is a method of current distribution, which runs in the whole speed range. A simulation model of the RW-EESM was modeled in Matlab/Simscape and controlled by the above RFOC method. Under the no-load condition, the speed closed-loop control simulation was carried out. When the motor speed was 500 rpm and 1000 rpm, the phase currents were obtained, as shown in Figure 8a,b, respectively.

(a) Motor speed is 500 rpm World Electric Vehicle Journal 2019, 10, 62 8 of 13

As the motor speed increases, the voltage limit ellipse continues to shrink. When the speed ωr1 is reached, the voltage limit ellipse touches the command current A1. Due to the inverter voltage limitation, the motor speed cannot continue to rise. To increase the motor speed, the command current is adjusted leftward from the A1 point along the current limit circle until the current distribution point reaches the A2 point on the MTPV curve. In this process, the motor speed increases and the torque decreases. The above is a method of current distribution, which runs in the whole speed range. A simulation model of the RW-EESM was modeled in Matlab/Simscape and controlled by the above RFOC method. Under the no-load condition, the speed closed-loop control simulation was carriedWorld Electric out. WhenVehicle Journal the motor 2019, 10 speed, x was 500 rpm and 1000 rpm, the phase currents were obtained,9 of as 13 shown in Figure8a,b, respectively.

(a) Motor speed is 500 rpm

(b) Motor speed is 1000 rpm

Figure 8. Phase currents when the motor speed is (a) 500 rpm and (b) 1000 rpm. Figure 8. Phase currents when the motor speed is (a) 500 rpm and (b) 1000 rpm 5. Prototype Veriﬁcation Test 5. Prototype Verification Test Based on the theoretical analysis, a prototype was made. Furthermore, a test on the RW-EESM was carriedBased out. Theon the main theoretical components analysis, in the a circuitprototype and wa theirs made. parameters Furthermore, are shown a test in Tableon the1 .RW The-EESM test resultswas carried are shown out. inThe Figures main 9components and 10. in the circuit and their parameters are shown in Table 1. The test results are shown in Figure 9 and 10.

Table 1. Parameters of MRC-WPT.

Item Parameter Transfer power Peak 160 W Power supply voltage 30 V Load resistance 10 Ω Self inductance 25 uH Mutual inductance 18 uH Resonant capacitance 100 nF Resonant frequency 100 kHz World Electric Vehicle Journal 2019, 10, 62 9 of 13

Table 1. Parameters of MRC-WPT.

Item Parameter Transfer power Peak 160 W Power supply voltage 30 V Load resistance 10 Ω Self inductance 25 uH Mutual inductance 18 uH Resonant capacitance 100 nF World Electric Vehicle Journal 2019, 10, x Resonant frequency 100 kHz 10 of 13

Figure 9. The excitation voltage and current on the primary side. Figure 9. The excitation voltage and current on the primary side

Figure 10. The resonant capacitor voltage and current on the secondary side World Electric Vehicle Journal 2019, 10, x 10 of 13

World Electric Vehicle Journal 2019, 10, 62 10 of 13 Figure 9. The excitation voltage and current on the primary side

Figure 10. The resonant capacitor voltage and current on the secondary side. Figure 10. The resonant capacitor voltage and current on the secondary side In the test, the resonant frequency was about 105 kHz, which was higher than the design value 100 kHz. Due to the attenuation of capacitance at high frequency, the resonant frequency was higher. Figure9 shows the relationship between excitation voltage and current on the primary side. Furthermore, the two phases were the same. Figure 10 shows the relationship between resonant capacitor voltage and current on the secondary side. Furthermore, the phase difference was 90 degrees. The voltage received at the load side was a stable DC voltage. The test results agreed with the theory. On the basis of an EESM prototype, an MRC-WPT system was used to realize the rotor resonant wireless excitation. The primary coil was fixed to the stator. The secondary coil and the rectifier filter circuit were mounted on the rotor and rotated along with the rotor. The RW-EESM prototype is shown in Figure 11. The rotor resonant wireless excitation system of EESM and the RFOC of RW-EESM were tested and verified. In the test, the rotor excitation was realized by the MRC-WPT system. Under no-load conditions, the motor was controlled by the RFOC approach. The phase current and the rotor position were recorded. The test results are shown in Figures 12 and 13. In the test, the motor ran smoothly, and the speed was stable at about 85 rpm. The sine of the phase currents was good. The results showed that the wireless excitation scheme of EESM was feasible, and the RFOC of RW-EESM motor proposed in this paper was reasonable. World Electric Vehicle Journal 2019, 10, x 11 of 13

In the test, the resonant frequency was about 105 kHz, which was higher than the design value 100 kHz. Due to the attenuation of capacitance at high frequency, the resonant frequency was higher. Figure 9 shows the relationship between excitation voltage and current on the primary side. Furthermore, the two phases were the same. Figure 10 shows the relationship between resonant capacitor voltage and current on the secondary side. Furthermore, the phase difference was 90 degrees. The voltage received at the load side was a stable DC voltage. The test results agreed with the theory. On the basis of an EESM prototype, an MRC-WPT system was used to realize the rotor resonant wireless excitation. The primary coil was fixed to the stator. The secondary coil and the rectifier filter circuit were mounted on the rotor and rotated along with the rotor. The RW-EESM prototype is Worldshown Electric in Figure Vehicle Journal11. The2019 rotor, 10, 62 resonant wireless excitation system of EESM and the RFOC of11 RW of 13- EESM were tested and verified.

World Electric Vehicle Journal 2019, 10, x 12 of 13 Figure 11.11. The RW RW-EESM-EESM prototype.prototype

In the test, the rotor excitation was realized by the MRC-WPT system. Under no-load conditions, the motor was controlled by the RFOC approach. The phase current and the rotor position were recorded. The test results are shown in Figure 12 and 13.

Figure 12. Phase current of RW-EESM. Figure 12. Phase current of RW-EESM

Figure 13. Rotor position of RW-EESM

In the test, the motor ran smoothly, and the speed was stable at about 85 rpm. The sine of the phase currents was good. The results showed that the wireless excitation scheme of EESM was feasible, and the RFOC of RW-EESM motor proposed in this paper was reasonable.

6. Conclusions Based on the principle of MRC-WPT, a rotor resonant wireless excitation system of EESM is designed. Furthermore, the RFOC of RW-EESM is studied. The results suggest the following conclusions. (1) This paper applies the principle of MRC-WPT to the rotor excitation of EESM. A rotor resonant wireless excitation system of EESM is designed. The test results show that the wireless excitation system of EESM is feasible. The new RW-EESM is practical. (2) By modeling the EESM, exploring the RFOC method, and analyzing the stator current distribution strategy, a control system of RW-EESM is established. Finally, the test on the RW-EESM prototype is carried out. Furthermore, the motor can run stably at no-load. The test results show that the RFOC of RW-EESM proposed in this paper is reasonable.

Author Contributions: Conceptualization, Z.Z.; methodology, Y.B.; software, C.H.; validation, Y.B. and Y.Q.; formal analysis, Y.B. and C.H.; writing—original draft preparation, Y.B.; writing—review and editing, Y.B.; funding acquisition, Z.Z. World Electric Vehicle Journal 2019, 10, x 12 of 13

World Electric Vehicle Journal 2019, 10, 62 Figure 12. Phase current of RW-EESM 12 of 13

FigureFigure 13. 13Rotor. Rotor position position of of RW-EESM. RW-EESM 6. Conclusions In the test, the motor ran smoothly, and the speed was stable at about 85 rpm. The sine of the phaseBased currents on the wa principles good. The of MRC-WPT, results show aed rotor that resonant the wireless wireless excitation excitation scheme system of EESM of EESM was isfeasible, designed. and the Furthermore, RFOC of RW- theEESM RFOC motor of proposed RW-EESM in this is paper studied. was reasonable. The results suggest the following conclusions. 6. Conclusions(1) This paper applies the principle of MRC-WPT to the rotor excitation of EESM. A rotor resonant wirelessBased excitation on the systemprinciple of EESMof MRC is-WPT, designed. a rotor The resonant test results wireless show excitation that the wirelesssystem of excitation EESM is systemdesigned. of EESM Furthermore, is feasible. the The RFOC new RW-EESM of RW-EESM is practical. is studied. The results suggest the following conclusions.(2) By modeling the EESM, exploring the RFOC method, and analyzing the stator current distribution(1) This strategy, paper a applies control the system principle of RW-EESM of MRC is-WPT established. to the rotor Finally, excitation the test on of theEESM. RW-EESM A rotor prototyperesonant is wireless carried excitationout. Furthermore, system ofthe EESM motor is can designed. run stably The at no-load. test results The show test results that the show wireless that theexcitation RFOC of system RW-EESM of EESM proposed is feasible. in this The paper new is RW reasonable.-EESM is practical. Author(2) Contributions: By modelingConceptualization, the EESM, exploring Z.Z.; methodology, the RFOC methodY.B.; software,, and C.H.; analyzing validation, the stator Y.B. and current Y.Q.; formaldistribution analysis, strategy, Y.B. and C.H.; a control writing—original system of RW draft-EESM preparation, is established. Y.B.; writing—review Finally, the and test editing, on the Y.B.; RW funding-EESM acquisition,prototype Z.Z. is carried out. Furthermore, the motor can run stably at no-load. The test results show that Funding:the RFOCThis ofresearch RW-EESM was proposed funded by thein this National paper Natural is reasonable. Science Foundation of China (Grant No. 51575392). Conflicts of Interest: The authors declare no conflict of interest. Author Contributions: Conceptualization, Z.Z.; methodology, Y.B.; software, C.H.; validation, Y.B. and Y.Q.; formal analysis, Y.B. and C.H.; writing—original draft preparation, Y.B.; writing—review and editing, Y.B.; References funding acquisition, Z.Z. 1. Zhang, F.; Li, Y.; Wang, X. The design and FEA of brushless doubly-fed machine with hybrid rotor. In Proceedings of the 2009 International Conference on Applied Superconductivity and Electromagnetic Devices, ASEMD 2009, Chengdu, China, 25–27 September 2009; IEEE: Piscataway, NJ, USA, 2009; 5306627, pp. 324–327. 2. Xia, Y.; Huang, S. Influence of field current pulsation on no-load voltage waveform of armature windings. Electr. Mach. Contrl. 2012, 16, 21–25. 3. Liu, Y.; Pehrman, D.; Lykartsis, O.; Tang, J.; Liu, T. High frequency exciter of electrically excited synchronous motors for vehicle applications. In Proceedings of the 2016 22nd International Conference on Electrical Machines, ICEM 2016, Lausanne, Switzerland, 4–7 September 2016; IEEE: Piscataway, NJ, USA, 2016; 7732554, pp. 378–383. 4. Tang, J.; Liu, Y. Design and Experimental Verification of a 48 v 20 kW Electrically Excited Synchronous Machine for Mild Hybrid Vehicles. In Proceedings of the 2018 23rd International Conference on Electrical Machines, ICEM 2018, Alexandroupoli, Greece, 3–6 September 2018; IEEE: Piscataway, NJ, USA, 2018; 8507259, pp. 649–655. 5. Tang, J.; Liu, Y.; Rastogi, Y.; Sharma, N.; Shukla, T. Study of Voltage Spikes and Temperature Rise in Power Module Based Integrated Converter for 48 V 20 kW Electrically Excited Synchronous Machines. In Proceedings of the 2018 IEEE Applied Power Electronics Conference and Exposition, APEC 2018, San Antonio, TX, USA, 4–8 March 2018; IEEE: Piscataway, NJ, USA, 2018; 8341011, pp. 210–217. World Electric Vehicle Journal 2019, 10, 62 13 of 13

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