Motor Vector Control Based on Speed-Torque-Current Map

applied sciences

Article Motor Vector Control Based on Speed-Torque-Current Map

Jianjun Hu 1,2,*, Meixia Jia 2, Feng Xiao 2, Chunyun Fu 2 and Lingling Zheng 2 1 State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China 2 School of Automotive Engineering, Chongqing University, Chongqing 400044, China; [email protected] (M.J.); [email protected] (F.X.); [email protected] (C.F.); [email protected] (L.Z.) * Correspondence: [email protected]; Tel.: +86-139-9607-3282

Received: 1 November 2019; Accepted: 16 December 2019; Published: 20 December 2019

Abstract: In order to effectively extend the mileage of pure electric vehicles, the influence of the electromechanical energy conversion principle and the dynamic control of a permanent magnet synchronous motor (PMSM) on the performance of pure electric vehicles are studied with a dual-motor drive system as a carrier in this paper. A vector control strategy based on the speed-torque-current map of a motor is proposed, considering the bus voltage fluctuation influenced by battery charge and discharge. By constructing a complete vehicle model including the dynamic control model of the motor, the power distribution control strategy of a dual-motor coupling mode considering the dynamic characteristics of the motor is developed and simulated on the MATLAB platform. The results show that the dynamic model of the motor is closer to the actual running conditions. The proposed control strategy effectively reduces the demand power, decreases the energy consumption of the electric drive system, and extends the mileage of the vehicle.

Keywords: control strategy; dynamic control; pure electric vehicle; speed-torque-current map

1. Introduction As the only source of propulsion, the dynamic characteristics and the performance of the motor are very important to vehicles. In order to meet the needs of vehicle research, the study of motors from static control strategy to dynamic control strategy can make the vehicle run more efficiently. The efficiency and torque characteristics of the motor directly determine the effect of the control strategy. It also has a direct impact on the power loss of the motor and the mileage of the vehicle. In recent years, the permanent magnet synchronous motor (PMSM) is increasingly used as the power source in pure electric vehicles. Multi-power source systems are also taken seriously because of their wide efficiency range and multi-mode flexibility [1]. At present, the drive control strategy of a multi-power driven vehicle is mainly designed based on the static characteristics of the transmission system components [2]. In [3], a rule-based control strategy for a dual-motor coupling driven pure electric vehicle is designed to obtain the optimal acceleration performance. In [4], the dynamic programming algorithm is used to optimize the mode switching threshold value of a dual-motor coupling electric drive system with rotational speed coupling mode, and the optimized control strategy significantly improves the economic efficiency of the vehicle. Wang [5] comprehensively considered the problem of motor temperature rise, which leads to its efficiency and torque decline in the process of designing the coordinated control strategy of the whole vehicle powertrain. It effectively reduces the frequency of motor failure due to the temperature rising. Li [6] investigated the PMSM control system through combining the method of rotor field-oriented control and the space vector control strategy. Zhou [7] established the dynamic model of the PMSM and the efficiency model of the inverter

Appl. Sci. 2020, 10, 78; doi:10.3390/app10010078 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 78 2 of 21 module of the motor controller. He studied the speed and torque characteristics of the motor, as well as size and quality characteristics, and designed the control strategy based on torque compensation in the dynamic mode and economic mode. In order to improve the performance of PMSM when it is used as a motor to drive the vehicle, the working principle of this type of motor has been thoroughly analyzed, and its current vector control scheme is optimized [8–15]. Most of the motor dynamic models established by the above scholars are used to study the speed and torque response and energy consumption performance, but the influence of motor dynamic control on the vehicle drive control strategy has not been further studied. Furthermore, if only the static characteristics of components are considered in the formulation of the control strategy of the driving system, there will be a big discrepancy between the operating state of the system and the actual operation process. The influence of dynamic process and control on the performance of the vehicle cannot be ignored; otherwise, performance errors of the vehicle may be caused. The major defects of the static model are as follows. (1) In the static model, the speed and torque of the motor can step change; that is, the working point of the motor can step change instantaneously. However, in practical running, the change of the speed and the torque is not an ideal step process. If the static model is used as the basis of the driving strategy, its dynamic and economy performance have a large deviation from the actual running. (2) The actual operation of the motor is affected by the control parameters, and there is always torque fluctuation. However, these characteristics cannot be reflected in the static model. (3) In the process of coupling drive, the efficiency of different working modes is only considered in the static model, but the mode-switching process and the energy loss are ignored in the process. The dynamic model and control of the motor can fully respond to the whole process of mode operation and mode switching, which is in good agreement with the actual operation process of the motor. The combination of dynamic control and the multi-power vehicle model can reflect the characteristics of speed–torque and energy consumption. Exploring the influence of dynamic control on the performance of multi-power vehicles can be used to guide the formulation of the control strategy of a multi-power coupled electric drive system. The rest of the paper is organized as follows. Section2 introduces the electric drive system configuration and the main parameters that are used in the subsequent strategy. In Section3, a novel vector control strategy of PMSM based on the speed-torque-current map is proposed. Then, the proposed control strategy is validated in Section4 to evaluate the results of the running of the motor controlled by the new strategy.

2. Electric Drive System Conﬁguration and Main Parameters The conﬁguration of the dual-motor drive system [16] is shown in Figure1. The system consists of two drive motors (MG1 and MG2), one planetary gear, three clutches (C1, C2, and C3), one brake (B1), two gear pairs (Gear 1 and Gear 2), and one main reducer (Final Drive). This electric drive system can realize four working modes including MG1 driving alone (M1), MG2 driving alone (M2), torque coupling drive (M3), and speed coupling drive (M4), as shown in Figure2. The vehicle working modes and the corresponding component status are listed in Table1.

Table 1. Vehicle working modes and the corresponding component status. This electric drive system can realize four working modes: MG1 driving alone (M1), MG2 driving alone (M2), torque coupling drive (M3), and speed coupling drive (M4).

Mode MG1 MG2 C1 C2 C3 B Power Flow M1 M C OFF OFF ON OFF Figure2a M2 C M OFF ON OFF ON Figure2b M3 M M OFF ON ON ON Figure2c M4 M M ON ON OFF OFF Figure2d Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 22

B1 C1

MG1 MG2

Gear 2 Gear 1 C3

C2 Final Drive Output shaft

Appl. Sci. 2020, 10, 78 3 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 22

B1 C1 Figure 1. Electric drive system configuration. The system consists of two drive motors (MG1 and MG2), one planetary gear, three clutchesMG1 (C1, C2, and C3),MG2 one brake (B1), two gear pairs (Gear 1 and Gear 2), and one main reducer (Final Drive). Gear 2 Gear 1 C3 Table 1. Vehicle working modes and the corresponding component status. This electric drive system can realize four working modes: MG1C2 driving alone (M1), MG2 driving alone (M2), torque coupling drive (M3), and speed coupling drive (M4). Final Drive Output shaft Mode MG1 MG2 C1 C2 C3 B Power Flow M1 M C OFF OFF ON OFF Figure 2a M2 C M OFF ON OFF ON Figure 2b

M3 M M OFF ON ON ON Figure 2c Figure 1. Electric drive system conﬁguration. The system consists of two drive motors (MG1 and Figure 1. Electric drive system configuration. The system consists of two drive motors (MG1 and M4MG2), one planetaryM gear,M three clutchesON (C1, C2, andON C3), oneOFF brake (B1),OFF two gear pairs (GearFigure 1 and 2d MG2), one planetary gear, three clutches (C1, C2, and C3), one brake (B1), two gear pairs (Gear 1 and Gear 2), and one main reducer (Final Drive). Gear 2), and one main reducer (Final Drive).

功率流 B 功率流 B Table 1.Power Vehicle Flow working modes and the correspondingPower Flow component status. This electric drive system can realize four workingC1 modes: MG1 driving alone (M1), MG2C1 driving alone (M2), torque coupling MG2 drive (M3),MG1MG1 and speed coupling MG2driveMG2 (M4). MG1M1 MG2M2

Mode MG1 MG2 C1 C2 C3 B Power Flow C3 C3 M1 C2 M C OFF OFF C2ON OFF Figure 2a M2 C M OFF ON OFF ON Figure 2b M3 M M OFF ON ON ON Figure 2c M4 M M ON ON OFF OFF Figure 2d

功率流 B 功率流（B ） Power Flow （a） Power Flow b C1 C1 MG1 MG2MG2 MG2 功率流 MG1 B MG2 功率流MG1M1 B MG2M2 Power Flow Power Flow C1 C1 C3 C3 MG1M1 MG2M2 MG1M1 MG2M2 C2 C2

C3 C3 C2 C2

（a）（b）

功率流 B 功率流 B Power Flow Power Flow C1 C1 M1 MG2M2 MG1 （c） MG1M1 （d）MG2M2

Figure 2. The power ﬂow of diﬀerentC3 working modes. (a) MG1 driveC3 alone; (b) MG2 drive alone; (c) Figure 2.Torque The power coupling flow drive;C2 of (d different) Speed coupling working drive. modes. (a)C2 MG1 drive alone; (b) MG2 drive alone; (c) Torque coupling drive; (d) Speed coupling drive. The main parameters of the system are shown in Table2.

（c）（d）

Figure 2. The power flow of different working modes. (a) MG1 drive alone; (b) MG2 drive alone; (c) Torque coupling drive; (d) Speed coupling drive. Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 22

The main parameters of the system are shown in Table 2. Appl. Sci. 2020, 10, 78 4 of 21 Table 2. Main parameters of the system.

ComponentTable 2. MainQuantity parameters (Unit) of the system. Value Rated/peak power (kW) 22/46.5 Component Quantity (Unit) Value MG1 Rated/maximum speed (rpm) 2880/5636 Rated/maximumRated/peak power torque (kW) (Nm) 73/154 22 /46.5 MG1 Rated/maximum speed (rpm) 2880/5636 RatedRated/peak/maximum power torque (kW) (Nm) 10/20.5 73 /154 MG2 Rated/maximumRated/peak power speed (kW) (rpm) 3300/8338 10/20.5 MG2 Rated/maximumRated/maximum speedtorque (rpm) (Nm) 29/59 3300 /8338 Planetary gear Rated/maximum Ratio k torque (Nm) 2.6 29/59 Planetary gear Ratio k 2.6 Gear 1 Ratio i1 2.92 Gear 1 Ratio i1 2.92 Gear 2 Ratio i2 1.2 Gear 2 Ratio i2 1.2 FinalFinal drive drive Ratio Ratio ii00 4.05 4.05 TypeType Li-ion Li-ion BatteryBattery pack pack RatedRated voltage voltage (V)(V) 333 333 RatedRated capacity capacity (Ah)(Ah) 78 78

3. Motor Motor Vector Vector Control Strategy Based on Speed-Torque-Current MapMap

3.1. Motor Motor Model Model and and Operation Operation Constraints The motormotor MG1MG1 is is taken taken as anas examplean example for modeling. for modeling. The PMSM The PMSM with three-phase with three-phase and four-pair and four-pairpoles is selected, poles is whoseselected, parameters whose parameters are shown are in Tableshown3. in Table 3.

Table 3. MG1 parameters. Table 3. MG1 parameters.

SymbolSymbol ValueValue

pn 8 8 ϕf 0.0642 Vs φ 0.0642 Vs 2 0.0707 Ld (1e−−2H) L (1e 2H) 0.0707 Lq (1e− H) 0.0707 L −2 ） (1eRs H 0.03540.0707Ω R 0.0354 Ω There is always power loss in the working process of a motor, which leads to the fluctuation There is always power loss in the working process of a motor, which leads to the fluctuation of of speed and torque. The iron loss model can not only reflect the changes of motor voltage, current, speed and torque. The iron loss model can not only reflect the changes of motor voltage, current, flux, and torque, but can also express the changes of the controllable loss including copper loss and flux, and torque, but can also express the changes of the controllable loss including copper loss and iron loss caused by the winding current, which is widely used in the PMSM loss modeling [17]. The iron loss caused by the winding current, which is widely used in the PMSM loss modeling [17]. The equivalent circuit diagram of the PMSM dynamic model employed in this paper is shown in Figure3. equivalent circuit diagram of the PMSM dynamic model employed in this paper is shown in Figure Considering the loss caused by the stator eddy current and hysteresis effect, an iron loss resistance 3. Considering the loss caused by the stator eddy current and hysteresis effect, an iron loss resistance Rc(ω) is added to the equivalent circuit in parallel. R(ω) is added to the equivalent circuit in parallel.

Rs Rs ioq id iod iq ωL i +-q oq icd icq - + ωLqioq ωφf u uq d Rc(ω ) + Rc(ω ) -

（a）（b）

Figure 3. EquivalentEquivalent circuit circuit diagram diagram of the permanen permanentt magnet synchronous motor (PMSM) dynamic model. ( (aa)) d-axis d-axis equivalent equivalent circuit, circuit, ( b) q-axis equivalent circuit. Appl. Sci. 2020, 10, 78 5 of 21

The voltage equivalent equations of the dynamic model are as follows.

" # " # " # ud iod Rs uod = Rs + 1 + (1) uq ioq Rc uoq " # " #" # " # u 0 ωρL i 0 od = − q od + (2) uoq ωLd 0 ioq ωϕf ( i = i i , od d − cd (3) ioq = iq icq −  ωρL i  i = d oq ,  cd Rc  ω−(ϕ + ) (4)  i = f Ldiod cq Rc

The iron loss resistance Rc is calculated by [18]:

1 Rc = . (5) Kh Kf ω

Due to the limits of battery voltage, temperature, the bearing capacity of components, and PWM (pulse width modulation) modulation methods, the current and voltage supply capacity of the inverter is limited respectively to ilim and Udc_lim. The motor armature current is and terminal voltage us expression and constraints are as follows: q 2 2 is = i + i i (6) d q ≤ lim q 2 2 us = u + u U . (7) d q ≤ dc_lim The expressions of electromagnetic torque Te and the motion equation of the PMSM are as follows:

3 h i Te = p ϕ ioq + L Lq i ioq (8) 2 n d d − od dω T = T + J r . (9) e L dt

The relationship between ωr and ω is as follows:

1 1 dθs ωr = ω = . (10) pn pn dt

3.2. Speed-Torque-Current Map Integrated Current Control At present, the control strategies of the motor current mainly include the maximum torque current ratio (MTPA) control, maximum current voltage (MCMV) control, and maximum torque voltage ratio (MTPV) control. MTPA control is a control method aiming to obtain the maximum output torque with the minimum input of a stator current vector within the limits of voltage and current [19,20]. The control equation of its boundary line is as follows:

q 2 2 2 ϕ + ϕ + 4 L Lq iq − f f d − id = . (11) 2(L Lq) d − MCMV control is one of the weak magnetic control methods. Its characteristic is that the current vector and voltage vector are the limits of the current and the voltage of the inverter bus, Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 22

MCMV control is one of the weak magnetic control methods. Its characteristic is that the current vector and voltage vector are the limits of the current and the voltage of the inverter bus, respectively [21]. When the motor speed is adjusted to a certain speed of ω, the control equation of (i, i) in this region is as follows:

Appl. Sci. 2020, 10, 78 6 of 21 ⎧ _ ( ) ⎪ i = . (12) respectively [21]. When the motor speed⎨ is adjusted to a certain speed of ωm, the control equation of ⎪ i =−i −i (iq, id) in this region is as follows: ⎩  r U 2  dc_lim (L i +ϕ )2  ωm − d d f MTPV control enables the motor itoq = achieve the maximum speed by making full use of the  Lq . (12)  q voltage vector supplied by the inverter [22–24]. For2 the2 tab-mounted PMSM, the reference current  id = ilim iq vector and the voltage control equation of MTPV− is as− follows:

MTPV control enables the motor to achieve the−φ maximum speed by making full use of the voltage vector supplied by the inverter [22–24]. For⎧ thei = tab-mounted PMSM, the reference current vector and L the voltage control equation of MTPV is as follows: (13) ⎨ U_ i =− ⎩ ϕLf ω  id = −  Ld U (13)  dc_lim  iq = ω ⎧ − Lq s _ ⎪u = r  2 L Lq  ϕ ϕ 2+8U 2 d− . (14)  f− f dc_lim Lqωs ⎨ =  uq L Lq  d− ⎪ 4 L ω . (14)  u =−U− _q −us ⎩ q  u = U2 u2 d − dc_lim − q To sumTo sumup, up,the therunning running trajectories trajectories of of the the bounda boundariesries ofof thethe threethree control control strategies strategies in thein the d-q d-q coordinate system are shown in Figure4. OA, AB, and BC represent the running trajectories of the coordinate system are shown in Figure 4. OA, AB, and BC represent the running trajectories of the three control strategies (MTPA, MCMV, and MTPV) in the d-q coordinate system, respectively. three control strategies (MTPA, MCMV, and MTPV) in the d-q coordinate system, respectively.

Voltage limit circle

Q axis Current limit circle MCMV A B MTPA

MTPV

C O D axis

speed increased

Figure 4. Running trajectories of three current control strategies. MCMV: maximum current voltage; FigureMTPV: 4. Running maximum trajectories torque voltage of three ratio; current MTPA: control maximum strategies. torque currentMCMV: ratio. maximum current voltage; MTPV: maximum torque voltage ratio; MTPA: maximum torque current ratio. To analyze the influence of different current control strategies on the motor speed–torque characteristics, the external characteristics under different strategies are obtained, as shown in Figure5. To analyze the influence of different current control strategies on the motor speed–torque characteristics, the external characteristics under different strategies are obtained, as shown in Figure 5. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 22 Appl. Sci. 2020, 10, 78 7 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 22 MTPA boundaries MCMV boundaries MTPV boundaries PeakMTPA Power boundaries curve PeakMCMV torque boundaries curve MTPV boundaries

Peak Power curve )

Peak torque curve

(

)

(

Torque Torque Torque Torque

Motor Speed (rpm) Figure 5. Speed-torque characteristics of different control strategies. Motor Speed (rpm) Aiming to combineFigureFigure 5. 5.the Speed-torqueSpeed advantages-torque characteristicscharacteristics of the above ofof di differe threefferentnt control control control strategies. strategies strategies,. a comprehensive control strategy is proposed in this paper to expand the motor working range to its maximum within the scopeAimingAiming of to the to combine combineinverter the busthe advantages capacity. advantages ofThe the of principles above the above three of threecontrolthe comprehensive control strategies, strategies, a comprehensivecontrol a comprehensivestrategy control are as strategycontrolfollows: strategy is proposed is proposed in this paper in this to expandpaper to the expand motor the working motor rangeworking to its range maximum to its maximum within the within scope ofthe the scope inverter of the bus inverter capacity. bus The capacity. principles The of principles the comprehensive of the comprehensive control strategy control are as st follows:rategy are as (a) The MTPA control strategy is adopted in the peak torque area to minimize the copper loss and follows: (a) Theiron MTPAloss. control strategy is adopted in the peak torque area to minimize the copper loss and (a)b) ironTheIn the loss.MTPA high- torquecontrol regionstrategy of isthe adopted weak magnetic in the peak field, torque the MCMV area to controlminimize is adopted the copper to transit loss and to (b) Inironthe the MTPV loss. high-torque control regionrange. of the weak magnetic field, the MCMV control is adopted to transit to (b)c) theInMTPV the MTPV high control control-torque is used range.region to extendof the weak the speed magnetic range field, of thethe motorMCMV in control the high is -adoptedspeed region to transit of the to (c) MTPVtheweak MTPV magnetic control control is field. used range. to extend the speed range of the motor in the high-speed region of the weak (c) magneticWithMTPV the control above field. is principles, used to extend the external the speed characteristic range of boundarthe motory ofin currentthe high control-speed is region obtained, of the as weak magnetic field. shown in Figure 6. Compared with the single current control strategy, the designed comprehensive With the above principles, the external characteristic boundary of current control is obtained, as controlWith strategy the above has aprinciples, wider speed the range external under characteristic the same torque, boundar whichy of currentimproves control the utilization is obtained, ratio as shown in Figure6. Compared with the single current control strategy, the designed comprehensive shownof the inputin Figure current 6. Compared vector and with voltage the sing vectorle current and maximizescontrol strategy, the overall the designed working comprehensive range of the control strategy has a wider speed range under the same torque, which improves the utilization ratio controlmotor. strategy has a wider speed range under the same torque, which improves the utilization ratio of the input current vector and voltage vector and maximizes the overall working range of the motor. of the input current vector and voltage vector and maximizes the overall working range of the motor. MTPA boundaries MCMV boundaries MTPV boundaries PeakMTPA power boundaries curve PeakMCMV torque boundaries curve

) MTPV boundaries

Peak power curve Nm

( Peak torque curve

)

(

Torque Torque

Motor Speed (rpm)

FigureFigure 6.6. BoundaryBoundary designdesign ofof comprehensivecomprehensive controlcontrol strategy.strategy. Motor Speed (rpm)

Figure 6. Boundary design of comprehensive control strategy. Appl. Sci. 2020, 10, 78 8 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 22

BasedBased on on the the designed designed current current control control boundary boundary curve, curve, the the speed speed and and torque torque are are traversed traversed and and substitutedsubstituted into into Equations Equations (8) (8) and and (9) (9) to to obtain obtain the the current current of of the the d d axis axis and and q q axis axis of of all all the the work work

points.points. The The resulting resulting speed speed–torque–current–torque–current map map of of the the d d-axis-axis and and q q-axis-axis are are shown in Figure 77..

)

( D D axis current

(a)

) )

( Q axis current

(b)

FigureFigure 7. CurrentCurrent map ofof thethe integrated integrated control control strategy. strategy. (a )( d-axisa) d-axis current current map; map (b); q-axis(b) q- currentaxis current map. map. 3.3. Motor Vector Control Strategy 3.3. MotorIn order Vector to Control solve the Strategy nonlinear problem of the PMSM current in the weak magnetic region, a vectorIn controlorder to strategy solve the is designed nonlinear for problem the motor of basedthe PMSM on the current speed–torque–current in the weak magnetic map, as region, shown ina vectorFigure control8. When strategy the motor is designed runs in thefor weakthe motor magnetic based region, on the thespeed d and–torque q-axis–current currents map are, as obtained shown inusing Figure the lookup8. When table the method. motor runs This in method the weak avoids magnetic the control region, problems the d and caused q-axis by the currents nonlinear are obtainedcurrent, whichusing the in turn lookup extends table the method. weak magneticThis method working avoids region the control of the motor.problems It is caused convenient by the to nonlinearobtain the current current, inwhich the deep in turn weak extends magnetic the region weak by magnetic using the working lookup table. region Besides, of the the motor. following It is convenientproblems can to also obtain be solved: the current it is di inﬃ cult the todeep obtain weak the magnetic current simply region by by using using the the weak lookup magnetic table PI. Bcontroller,esides, the and following the dynamic problems response can ofalso the be motor solved: is slow. it is difficult to obtain the current simply by using the weak magnetic PI controller, and the dynamic response of the motor is slow. Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 22 Appl. Sci. 2020, 10, 78 9 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 22 iq_ref uq_ref + ΔN 转速环SpeedPI PI控 T_ref Speed-Torque 电流环SpeedPI 控制PI SVPWM N_ref controller制器 -current MAP MAP controller器 - id_refiq_ref ud_refuq_ref + ΔN 转速环SpeedPI PI控 T_ref Speed-Torque 电流环SpeedPI 控制PI SVPWM N_ref controller制器 -current MAP MAP controller器 - N_cur N_cur id_ref ud_ref Iq Id Converter逆变器 N_cur N_cur Iq Id Iα IaConverter逆变器 Clarke Park Ib Transmission Transmission Ic Iαβ Ia Clarke Park Ib Transmission Transmission Ic Iβ PMSM

PMSM Figure 8. Vector control strategy based on the speed–torque–current map. As shown inFigure FigureFigure 8. 8. 8,VectorVector a speed–torque–current control control strategy strategy based based mapon on the the link speed–torque–current speed–torque–current is added to the vector map. map. control strategy between the speed control link and the current control link. The output reference torque T_ of the As shown in Figure8, a speed–torque–current map link is added to the vector control strategy speedAs loop shown and inthe Figure actual 8, motor a speed–torque–current speed are the inputs map to this link link. is added The reference to the vector currents control of the strategy d and between the speed control link and the current control link. The output reference torque T of the qbetween axes corresponding the speed control to the link current and the speed current and controlthe target link. torque The output can be referenceobtained torqueby a lookup T__ref oftable. the speed loop and the actual motor speed are the inputs to this link. The reference currents of the d and q Sincespeed loopthe speed–torque–currentand the actual motor speed map arecontains the inputs the toinformation this link. The of reference the weak currents magnetic of the region d and axes corresponding to the current speed and the target torque can be obtained by a lookup table. Since (includingq axes corresponding the deep weak to the magnetic current region),speed and the the cu rrentstarget oftorque the d can and be q obtainedaxes are byconstrained a lookup intable. the the speed–torque–current map contains the information of the weak magnetic region (including the voltageSince the limit speed–torque–current circle and current limit map circle. contains It solves the theinformation transition ofproblems the weak of currentmagnetic control region in deep weak magnetic region), the currents of the d and q axes are constrained in the voltage limit circle different(including working the deep ranges weak magneticand the problemregion), theof cutorqrrentsue fluctuationof the d and caused q axes byare current constrained or voltage in the and current limit circle. It solves the transition problems of current control in different working ranges over-saturation.voltage limit circle and current limit circle. It solves the transition problems of current control in and the problem of torque fluctuation caused by current or voltage over-saturation. differentCharging working and rangesdischarging and theare alwaysproblem present of torq inue the fluctuation driving process caused of bypure current electric or vehicles, voltage Charging and discharging are always present in the driving process of pure electric vehicles, whichover-saturation. leads to the change of battery SOC (state of charge). The relationship between the battery which leads to the change of battery SOC (state of charge). The relationship between the battery voltage voltageCharging and SOC and is dischargingshown in Figure are always9. The changepresent of in the the battery driving voltage process causes of pure the electricdynamic vehicles, change and SOC is shown in Figure9. The change of the battery voltage causes the dynamic change of bus ofwhich bus voltageleads to amplitude the change [25], of batterywhich in SOC turn (state affects of the charge). d-axis Thecurrent relationship and q-axis between current, the as batterywell as voltage amplitude [25], which in turn affects the d-axis current and q-axis current, as well as the speed thevoltage speed and and SOC torque is shown characteristics in Figure of9. Thethe motor. change of the battery voltage causes the dynamic change ofand bus torque voltage characteristics amplitude [25], of the which motor. in turn affects the d-axis current and q-axis current, as well as the speed and torque characteristics of the motor. 380

360380

340360

340320 Battery voltage (V) voltage Battery 320300 0 0.25 0.50 0.75 1.00 Battery voltage (V) voltage Battery 300 Battery SOC (-) 0 0.25 0.50 0.75 1.00 Figure 9. Relationship betweenBattery battery SOC voltage (-) and state of charge (SOC). Figure 9. Relationship between battery voltage and state of charge (SOC). The external characteristics of the motor under different bus voltages are shown in Figure 10. Figure 9. Relationship between battery voltage and state of charge (SOC). TheIt is external shown characteristics in Figure 10 that of the when motor the under bus voltage different decreases, bus voltages the controlare shown boundary in Figure and 10. the maximumThe external torque characteristics boundary of theof the motor motor move under to thedifferent left, which bus voltages reduces are the shown motor in working Figure range.10. If the influence of bus voltage variation is ignored, the operation of these areas cannot be controlled. When the voltage increases, the bus voltage cannot be fully utilized. When the voltage decreases, the working point may be outside the allowable motor working range, which leads to the over-current or over-voltage protection. The influence of bus current on the motor can also be seen from the perspective of current control of d and q axes, which is shown in Figure 11. When the bus voltage is U1, the motor works at points A1 and A2 to realize torques T1 and T2, respectively. If the bus voltage increases from U1 to U2, then the motor working points are B1 and B2, which improves the utilization ratio of the bus Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 22

160

udc=450V

udc=550V 140 udc=650V

120 Maximum torque

） curve 100 N.m

80 Appl. Sci. 2020, 10, 78 10 of 21 60 电机转矩（ MTPA boundary

voltage. On the contrary,(N.m) Torque if T1 and T2 are the required torques, the motor works at points B1 and B2. 40 curve If the bus voltage decreases from U2 to U1 and the control strategy still takes B1 and B2 as working Appl. Sci.points. 2020, In 10 this, x FOR situation, PEER REVIEW the current regulator saturates and loses its ability to regulate the current. 10 of 22 20

160 0 0 1000 2000 3000 4000 5000 6000 7000udc=450V 8000 udc=550V 140 Motor电机转速（ speedrpm (rpm)） udc=650V

Figure120 10. External characteristics corresponding to different bus voltages. Maximum torque

） curve It is shown in Figure100 10 that when the bus voltage decreases, the control boundary and the maximum torque boundaryN.m of the motor move to the left, which reduces the motor working range. If the influence of bus voltage80 variation is ignored, the operation of these areas cannot be controlled. When the voltage increases, the bus voltage cannot be fully utilized. When the voltage decreases, the 60 working point may 电机转矩（ be outside the allowable motor working range, which leads to the over-current MTPA boundary Torque (N.m) Torque or over-voltage protection.40 The influencecurve of bus current on the motor can also be seen from the perspective of current control of d and q axes, which is shown in Figure 11. When the bus voltage is U1, the motor works at20 points A1 and A2 to realize torques T1 and T2, respectively. If the bus voltage increases from U1 to U2, then the motor working points are B1 and B2, which improves the utilization ratio of the0 bus voltage. On the contrary, if T1 and T2 are the required torques, the 0 1000 2000 3000 4000 5000 6000 7000 8000 motor works at points B1 and B2. If the bus voltage decreases from U2 to U1 and the control Motor电机转速（ speedrpm (rpm)） strategy still takes B1 and B2 as working points. In this situation, the current regulator saturates and loses its abilityFigure Figureto regulate 10. 10.ExternalExternal the characteristicscurrent. characteristics correspon correspondingding to to di differentﬀerent bus bus voltages. voltages.

It is shown in Figure 10 that when the bus voltage decreases, the control boundary and the maximum torque boundary of the motor move to the left, Voltagewhich limit reduces circle the motor working range. If the influence of bus voltage variation is ignored, theQ axis operationCurrent limit of circlethese areas cannot be controlled.

When the voltage increases, the bus voltage cannotMTPA be fully utilized. When the voltage decreases, the B2 working point may be outside the allowable motor working range, whichT2 leads to the over-current A2 B1 T1 or over-voltage protection. The influence of A1bus current on the motor can also be seen from the perspective of current control of d andMTPV q axes, which is shown in Figure 11. When the bus voltage is U1, the motor works at points A1 and A2 to realize torques T1 and T2, respectively. If the bus voltage increases from U1 to U2, then the motor working points are DB1 axis and B2, which improves the utilization ratio of the bus voltage. On the contrary, if T1 and T2 are the required torques, the motor works at points B1U2 and B2U1. If the bus voltage decreases from U2 to U1 and the control strategy still takes B1 and U2>U1B2 as working points. In this situation, the current regulator saturates and loses its ability to regulate the current.

Voltage limit circle Figure 11. Inﬂuence of bus voltage change on the value of the d-q axis current. Figure 11. Influence of bus voltage changeQ axis on theCurrent value limit of circlethe d-q axis current.

Considering the ﬂuctuation of bus voltage, theMTPA relationship between the actual bus voltage Udc_act B2 and the currents of the d and q axes is as follows: T2 A2 B1 T1 !2 A1 U MTPVdc_act 2 2 = (Lqiq) + (Ldid + ϕf) . (15) ωs

D axis

U2 U1 U2>U1

Figure 11. Influence of bus voltage change on the value of the d-q axis current. Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 22

Considering the fluctuation of bus voltage, the relationship between the actual bus voltage

U_ and the currents of the d and q axes is as follows: _ =(Li) +(Li +φ) . (15) Appl. Sci. 2020, 10, 78 11 of 21

Equation (15) indicates that the bus voltage fluctuation can be corrected by the motor speed. Equation (15) indicates that the bus voltage ﬂuctuation can be corrected by the motor speed. Specifically, when the bus voltage changes, the motor speed can be appropriately increased or Speciﬁcally, when the bus voltage changes, the motor speed can be appropriately increased or decreased decreased by μ times to correct the voltage, as shown in the following equation: by µ times to correct the voltage, as shown in the following equation: μ= _  U_  µ = dc_lim . (16)  Udc_act  _2  U =(Li) +(Li +φ) . (16)  dc_lim = (L i )2 + (L i + ϕ )2  ωsµ q q d d f

Based on on Equation Equation (16), (16), a speed a speed modifier modiﬁer consider consideringing the influence the inﬂuence of bus of voltage bus voltage is added is addedto the speed–torque–currentto the speed–torque–current map link map to linkdevelop to develop a vector a vectorcontrol control strategy, strategy, as shown as shown in Figure in Figure 12. The 12 . real-timeThe real-time bus busvoltage voltage U_U _curobtainedobtained from from the thevoltage voltage sensor sensor is isused used asas the the input input to to the the speed compensator,compensator, and and variable variable N __cps representsrepresents the the speed speed after after the the compensation. compensation.

iq_ref uq_ref + ΔN Speed PI T_ref Speed-Torque Current PI SVPWM N_ref controller -current MAP controller - id_ref ud_ref N_cps N_cur Speed modifier Iq Id Converter U_cur N_cur

Iα Ia Clark Park Ib transformation transformation Ic Iβ

PMSM

FigureFigure 12. 12. VectorVector control control strategy strategy considering considering bus voltage fluctuation. ﬂuctuation.

To validatevalidate the the control control effect effect of theof proposedthe proposed vector vector control control strategy, strategy, a working a working condition condition is designed is designedin which thein which bus voltage the bus and voltage load torque and load are 650torq Vue and are 20650 Nm, V and respectively. 20 Nm, respectively. Besides, the motorBesides, speed the first accelerates from 0 to 1000 rpm, and then again accelerates from 1000 to 5000 rpm after the speed motor Appl.speed Sci. first2020, 10accelerates, x FOR PEER REVIEWfrom 0 to 1000 rpm, and then again accelerates from 1000 to12 5000of 22 rpm afterstabilizes the speed for a short stabilizes period for (around a short 100 period ms). The(around simulation 100 ms). results The are simulation shown in results Figures are 13 andshown 14. in Figures 13 and 14. 6000

(rpm) 4000 Reference speed Actual speed

转速 2000

Speed(rpm) 0 00.050.10.15 Time(s)Time(s)时间(s)

150 Reference torque 100 Actual speed

转矩(Nm) 50

Torque(N.m) 0 00.050.10.15 Time(s)Time(s)时间(s)

200 d-axis current 100 q-axis current 0

d-q轴电流(A) -100 00.050.10.15 D-q axes current(A)D-q Time(s)时间(s)Time(s)

200 A phase current 100 B phase current 0 -100 C phase current 相电流(A) -200 00.050.10.15 Phase current(A) Phase Time(s)时间(s)

FigureFigure 13. Motor13. Motor performance performance without without consideringconsidering bus bus voltage voltage variation. variation.

6000 4000

2000 Reference speed Actual speed 0 00.05 0.15

Speed(rpm) 0.1

Time(s) 150 100 Reference torque Actual speed 50

Torque(N.m) 0 00.050.10.15

Time(s) 200 d-axis current 100 q-axis current 0 -100 D-q axes current(A) axes D-q 00.050.10.15 Time(s)

200 A phase current 100 B phase current 0 C phase current -100

Phase current(A) Phase -200 00.050.10.15 Time(s)

Figure 14. Motor performance considering bus voltage variation.

It is seen from Figure 13 that in the process of speed regulation, torque and current fluctuate greatly due to the effect of the bus voltage changes. However, in Figure 14, the current and torque fluctuations are greatly reduced during the speed regulation period (1000–5000 rpm), when the bus voltage changes are taken into consideration. The results in these two figures indicate that the speed Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 22

6000

(rpm) 4000 Reference speed Actual speed

转速 2000

Speed(rpm) 0 00.050.10.15 Time(s)Time(s)时间(s)

150 Reference torque 100 Actual speed

转矩(Nm) 50

Torque(N.m) 0 00.050.10.15 Time(s)Time(s)时间(s)

200 d-axis current 100 q-axis current 0

d-q轴电流(A) -100 00.050.10.15 D-q axes current(A)D-q Time(s)时间(s)Time(s)

200 A phase current 100 B phase current 0 -100 C phase current 相电流(A) -200 00.050.10.15 Phase current(A) Phase Time(s)时间(s) Appl. Sci. 2020, 10, 78 12 of 21 Figure 13. Motor performance without considering bus voltage variation.

6000 4000

2000 Reference speed Actual speed 0 00.05 0.15

Speed(rpm) 0.1

Time(s) 150 100 Reference torque Actual speed 50

Torque(N.m) 0 00.050.10.15

Time(s) 200 d-axis current 100 q-axis current 0 -100 D-q axes current(A) axes D-q 00.050.10.15 Time(s)

200 A phase current 100 B phase current 0 C phase current -100

Phase current(A) Phase -200 00.050.10.15 Time(s)

FigureFigure 14. 14.Motor Motor performance performance considering bus bus voltage voltage variation. variation.

It is seenIt is seen from from Figure Figure 13 13that that in in the the process process of speed speed regulation, regulation, torque torque and andcurrent current fluctuate fluctuate greatlygreatly due todue the to etheffect effect of theof the bus bus voltage voltage changes. changes. However, However, in inFigure Figure 14, 14the, thecurrent current and torque and torque fluctuationsfluctuations are greatlyare greatly reduced reduced during during the thespeed speed regulation period period (1000–5000 (1000–5000 rpm), rpm), when when the bus the bus voltage changes are taken into consideration. The results in these two figures indicate that the speed voltage changes are taken into consideration. The results in these two figures indicate that the speed modifier with bus voltage regulation well reduces the torque and current fluctuation in the speed regulation process, which is beneficial to the output speed–torque characteristics of the motor.

4. Veriﬁcation of the Proposed Vector Control Strategy

4.1. System Power Distribution Strategy In the actual operation process of the motor, when the output demand is constant, the position of the working point has an impact on the speed regulation process and the energy consumption of the motor. However in the static model, the working point is well determined. Based on vehicle model and PMSM dynamic model established in the previous section, the speed–torque characteristics and the energy consumption characteristics of system are analyzed when the system demand changes. In the coupling modes, the torque distribution strategy and speed distribution strategy are shown in Figures 15 and 16, respectively. Due to the diﬀerence between the static model and the actual operation, the minimum energy consumption point calculated by the static model may not be accurate for the motor. Therefore, the power distribution strategy based on the dynamic control enables the vehicle to operate at the working point with the minimum energy demand, thereby reducing the vehicle energy consumption. Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 22

modifier with bus voltage regulation well reduces the torque and current fluctuation in the speed regulation process, which is beneficial to the output speed–torque characteristics of the motor.

4. Verification of the Proposed Vector Control Strategy

Vehicle condition Motor torque traversal module traversal module input：speed、acceleration、 input：Torque range of MG1&MG2 initial torque of MG1 and MG2 of related speed and target speed. output：actual speed of MG1 output：target torque of MG1&MG2 &MG2

Module of power computation

IGBT switch IGBT switch MG1-MCU MG2-MCU State State

Switch loss、 Switch loss、 Converter Converter Conduction loss Conduction loss Iron loss、 PMSM- Iron loss、 PMSM- Copper Loss MG1 Copper Loss MG2 Mechanical loss Mechanical loss Output Output power power

Power demand of drive system

The target torque value of MG1 and MG2 with the lowest power demand of the driving system under the working condition

FigureFigure 15. 15.Motor Motor performance performance without without consideringconsidering the the bus bus voltage voltage variation variation power power distribution distribution Appl.strategy Sci.strategy 2020 of, the 10 of, xthe torque FOR torque PEER coupling coupling REVIEW mode. mode. 14 of 22

Vehicle condition Motor torque traversal module traversal module input：speed、acceleration、 input：Speed range of MG1&MG2 initial torque of MG1 and MG2 of related speed and target speed. output：actual speed of MG1 output：target speed of MG1&MG2 &MG2

Module of power computation

IGBT switch IGBT switch MG1-MCU MG2-MCU State State

Power demand of drive system

The target speed value of MG1 and MG2 with the lowest power demand of the driving system under the working condition

FigureFigure 16. 16.Motor Motor performance performance withoutwithout consideringconsidering the the bus bus voltage voltage variation variation power power distribution distribution strategystrategy of the of the speed speed coupling coupling mode. mode.

Due to the difference between the static model and the actual operation, the minimum energy consumption point calculated by the static model may not be accurate for the motor. Therefore, the power distribution strategy based on the dynamic control enables the vehicle to operate at the working point with the minimum energy demand, thereby reducing the vehicle energy consumption.

4.2. Simulation Analyses Based on the configuration considered in this paper, two vehicle models which are configured with the static and dynamic models are established for simulation studies. The following three working conditions are employed for verification purposes: 0–100 km acceleration, torque coupling mode, and speed coupling mode.

4.2.1. 0–100 km/h Acceleration Simulation In the simulation of 0–100 km/h acceleration, when the vehicle speed is lower than 60 km/h, the torque coupling mode is adopted; otherwise, the speed coupling mode is adopted. The results are shown in Figure 17. Response delay and torque fluctuation always exist in the actual process of motor speed regulation. Figure 17 shows that due to the response delay, the 0–100 km/h acceleration time resulting from the dynamic model is 14.22 s, which is 0.12 s more than that of the static model (14.10 s). The reason is that the speed and torque response characteristics of the dynamic model are closer to the actual motor operating characteristics. Different from the step response in the mode switching process of the static model, it can be seen from the speed diagram that the time required for the motor to complete mode switching is almost 0.28 s in the dynamic model, which is not shown in the static model. Torque fluctuation always exists in the dynamic model but not in the static model. The fluctuation in the process of mode switching is more apparent, which is shown in the enlarged red circle areas for the torques of MG1 and MG2. In this process, the torque of MG1 is greater than that Appl. Sci. 2020, 10, 78 14 of 21

4.2. Simulation Analyses Based on the configuration considered in this paper, two vehicle models which are configured with the static and dynamic models are established for simulation studies. The following three working conditions are employed for verification purposes: 0–100 km acceleration, torque coupling mode, and Appl.speed Sci. coupling 2020, 10, x mode.FOR PEER REVIEW 15 of 22 of4.2.1. the 0–100static model, km/h Acceleration and the torque Simulation of MG2 is less than that of the static model. The lines of the torque aligned with the static model after 5.57 s because in the mode switching process, the speed In the simulation of 0–100 km/h acceleration, when the vehicle speed is lower than 60 km/h, the regulation of the two motors caused the change of motor torque. This situation is similar to the torque coupling mode is adopted; otherwise, the speed coupling mode is adopted. The results are actual motor operation, indicating that the dynamic model can well reflect the actual motor speed shown in Figure 17. regulation process.

100

50 Dynamic Static 0 Speed(km/h) 0 5 10 15

6000 A 4000

(rpm) C 2000 Dynamic

MG1 Speed MG1 Static 0 B 0 5 10 15 8000 6000 4000

(rpm) Dynamic 2000

MG2 Speed MG2 Static 0 0 5 10 15 200

(Nm) Dynamic Static

MG1 Torque -200 0 5 10 15 100

0 Dynamic

(Nm) Static -100

MG2 Torque MG2 0 5 10 15 Time(s) FigureFigure 17. MotorMotor performance withoutwithout consideringconsidering busbus voltage voltage variation. variation. Comparison Comparison of of the the results results of ofthe the dynamic dynamic model model and and static static model. model.

4.2.2.Response Torque Coupling delay and Mode torque Performance fluctuation alwaysSimulation exist in the actual process of motor speed regulation. Figure 17 shows that due to the response delay, the 0–100 km/h acceleration time resulting from the According to the flow shown in Figure 15, the designed simulation condition of the torque dynamic model is 14.22 s, which is 0.12 s more than that of the static model (14.10 s). The reason coupling mode is as follows: during the period from 0 to 0.05 s, the vehicle speed is adjusted to 18 is that the speed and torque response characteristics of the dynamic model are closer to the actual km/h. In this process, the torque is adjusted to the required torque. After 0.05 s, the vehicle motor operating characteristics. Different from the step response in the mode switching process of the accelerates to 19.7 km/h with 1.8889 m/s2 acceleration during 0.25 s. When the vehicle speed is 18 static model, it can be seen from the speed diagram that the time required for the motor to complete km/h and the acceleration is 1.8891 m/s2, the required torque and speed of the main reducer are 224 mode switching is almost 0.28 s in the dynamic model, which is not shown in the static model. Torque Nm and 720 rpm, respectively. According to the dynamic equation of the torque couple mode, the fluctuation always exists in the dynamic model but not in the static model. The fluctuation in the speeds of MG1 and MG2 are 1494 rpm and 2237 rpm, respectively. Under the corresponding speed process of mode switching is more apparent, which is shown in the enlarged red circle areas for the constraint, the maximum electromagnetic torques of MG1 and MG2 can achieve 153 Nm and 75 Nm, torques of MG1 and MG2. In this process, the torque of MG1 is greater than that of the static model, respectively. The torque intervals of MG1 and MG2 are [−153 Nm, 153 Nm] and [−75 Nm, 75 Nm], and the torque of MG2 is less than that of the static model. The lines of the torque aligned with the respectively. Moreover, the torques of MG1 and MG2 (i.e., T and T ) are also limited by the static model after 5.57 s because in the mode switching process, the speed regulation of the two motors demand torque T of the main reducer, namely: caused the change of motor torque. This situation is similar to the actual motor operation, indicating that the dynamic model can well reflect the actual motor speed regulation process. T =T ∙ (k+1) ∙i ∙η ∙η +T ∙i ∙η. (17)

The motor electromagnetic torque is the sum of the load torque and the speed regulating torque. If the load torque is too large, the motor will lose the ability to regulate the speed. In order to meet the requirements of the output characteristics of the main reducer, the initial and target torques of MG1 are limited in the range of [−2 Nm, 148 Nm] based on Equation (17). Under the same working condition, the torque of MG1 is 88 Nm according to the motor static model control strategy, which is set as the initial MG1 torque. That is, T1 = 88 Nm. In this section, the MG1 target load torque value (T1* = −2 Nm) is taken as an example to analyze the speed–torque Appl. Sci. 2020, 10, 78 15 of 21

4.2.2. Torque Coupling Mode Performance Simulation According to the ﬂow shown in Figure 15, the designed simulation condition of the torque coupling mode is as follows: during the period from 0 to 0.05 s, the vehicle speed is adjusted to 18 km/h. In this process, the torque is adjusted to the required torque. After 0.05 s, the vehicle accelerates to 19.7 km/h with 1.8889 m/s2 acceleration during 0.25 s. When the vehicle speed is 18 km/h and the acceleration is 1.8891 m/s2, the required torque and speed of the main reducer are 224 Nm and 720 rpm, respectively. According to the dynamic equation of the torque couple mode, the speeds of MG1 and MG2 are 1494 rpm and 2237 rpm, respectively. Under the corresponding speed constraint, the maximum electromagnetic torques of MG1 and MG2 can achieve 153 Nm and 75 Nm, respectively. The torque intervals of MG1 and MG2 are [ 153 Nm, 153 Nm] and [ 75 Nm, 75 Nm], respectively. − − Moreover, the torques of MG1 and MG2 (i.e., Tm1 and Tm2) are also limited by the demand torque To of the main reducer, namely:

To = T (k + 1) i η η + T i η . (17) m2· · 2· 2· p m1· 1· 1 The motor electromagnetic torque is the sum of the load torque and the speed regulating torque. If the load torque is too large, the motor will lose the ability to regulate the speed. In order to meet the requirements of the output characteristics of the main reducer, the initial and target torques of MG1 are limited in the range of [ 2 Nm, 148 Nm] based on Equation (17). − Under the same working condition, the torque of MG1 is 88 Nm according to the motor static

Appl.model Sci. control2020, 10, x strategy, FOR PEER which REVIEW is set as the initial MG1 torque. That is, T1 = 88 Nm. In this section,16 of 22 the MG1 target load torque value (T1* = 2 Nm) is taken as an example to analyze the speed–torque − characteristics during during the the transition transition process process of two of motor two motor working working points under points this under working this condition. working condition.The dynamic The response dynamic process response of theprocess two motorsof the two is shown motors in is Figure shown 18 in. Figure 18.

MG1 torque

) MG2 torque

( Torque Torque

Time(s)

)

rpm (

Speed MG1 speed MG2 speed

Time (s)

Figure 18. ChangesChanges of of speed speed and and torque torque of MG1 MG1 and MG2 MG2..

Figure 18 demonstrates the change of the two motor speeds, as the vehicle speed is adjust adjusteded to 18 kmkm/hat/hat,, nono loadload conditioncondition duringduring the the period period of of 0–0.045 0–0.045 s. s. In In the the period period of of 0.045–0.05 0.045–0.05 s, s, the the torques torques of ofthe the two two motors motors are are adjusted adjusted to the to demandthe demand torque torque corresponding corresponding to the to condition the condition (i.e., 18 (i.e. km,/ h18 vehicle km/h vehiclespeed and speed 1.8991 and m1.8991/s2 acceleration. m/s2 acceleration. At the momentAt the moment of 0.05 of s, the0.05 motor s, the motor MG1 is MG1 loaded is loaded by the by target the target torque of −2 Nm, and the torque of MG2 is calculated from the real-time load torque and the load torque of MG1. In the torque coupling mode, the torques of MG1 and MG2 can be coupled arbitrarily, as long as the output torque of the vehicle meets requirements. This means that countless combinations of the torques of MG1 and MG2 exist. The economy of each combination can be measured by the demand power of the electric drive system. According to the flow shown in Figure 16, the MG1 target torque

is traversed to obtain the corresponding demand power of the electric drive, as shown in Figure 19.

)

（

(

System demandpower Demand Power DemandPower

MG1MG target1 target torque（N. m()Nm)

Figure 19. Demand power under different MG1 target torques. Appl. Sci. 2020, 10, x FOR PEER REVIEW 16 of 22

characteristics during the transition process of two motor working points under this working condition. The dynamic response process of the two motors is shown in Figure 18.

MG1 torque MG2 torque Torque (Nm) Torque

Time(s)

Speed (rpm) Speed MG1 speed MG2 speed

Time (s)

Figure 18. Changes of speed and torque of MG1 and MG2.

Figure 18 demonstrates the change of the two motor speeds, as the vehicle speed is adjusted to 18 km/hat, no load condition during the period of 0–0.045 s. In the period of 0.045–0.05 s, the torques Appl. Sci. 2020 10 of the two, motors, 78 are adjusted to the demand torque corresponding to the condition (i.e., 1816 ofkm/h 21 vehicle speed and 1.8991 m/s2 acceleration. At the moment of 0.05 s, the motor MG1 is loaded by the torquetarget oftorque2 Nm, of − and2 Nm, the and torque the oftorque MG2 of is MG2 calculated is calculated from the from real-time the real-time load torque load torque and the and load the − torqueload torque of MG1. of MG1. InIn the the torque torque coupling coupling mode, mode, the the torques torques of of MG1 MG1 and and MG2 MG2 can can be be coupled coupled arbitrarily, arbitrarily, as as long long as as thethe output output torque torque of of the the vehicle vehicle meets meets requirements. requirements This. This means means that that countless countless combinations combinations of of the the torquestorques of of MG1 MG1 and and MG2 MG2 exist. exist. The The economy economy of of each each combination combination can can be be measured measured by by the the demand demand powerpower of of the the electric electric drive drive system. system. According According to to the th ﬂowe flow shown shown in Figurein Figure 16, 16, the the MG1 MG1 target target torque torque is traversedis traversed to obtain to obtain the correspondingthe corresponding demand demand power power of the of electricthe electric drive, drive, as shown as shown in Figure in Figure 19. 19. System demand power（kW) demand System Demand Power Demand(kW) Power

MG1MG1 target target torque（N.m)torque (Nm)

Figure 19. Demand power under different MG1 target torques. Figure 19. Demand power under different MG1 target torques. When the demand torque is constant in the torque coupling mode, the torque of MG1 is 88 Nm on the point of the allocated power obtained from the static model. In the dynamic model, the demand power of the electric drive system first decreases and then increases with the increase of the MG1 target torque, as shown in Figure 19. Note that the starting point T ∗ = 2 Nm, the final point T ∗ = 148 Nm, 1 − 1 and the trough point T1∗ = 68 Nm are employed in the simulation studies, as shown in Table4.

Table 4. Demand power under diﬀerent MG1 target torques.

MG1 Target Torque/Nm MG1 Power/kW MG2 Power/kW Demand Power/kW 2 0.248 25.856 26.104 − 68 13.476 8.073 21.549 88 17.814 4.007 21.822 148 32.297 5.157 27.140 −

The motor static model cannot reflect the loss during the transition process of the motor working point, so the optimal power distribution scheme of the two motors cannot be obtained when the power demand of the system is fixed. If the vehicle demand torque is constant, MG1’s target torque is too high, which results in MG1 working near the peak torque. If the target torque of MG1 is too small, then MG2 will work near its peak torque, and vice versa. These situations will lead to an increase in system losses and lower efficiency. The transformation law of demand power with MG1 target torque is shown in Figure 19, when the demand torque is constant. Table4 shows that when the MG1 target torque is 148 Nm, the demand power of the electric power system reaches a maximum of 27.140 kW. When the target torque is 88 Nm in the static model, the average demand power of the system is 21.822 kW. When the target torque is 68 Nm (obtained from the dynamic model), the demand power of the system has a minimum of 21.549 kW, which is 1.27% lower than the average power consumption obtained by the static model, and 20.6% lower than the maximum demand power of the electric drive system. Appl. Sci. 2020, 10, 78 17 of 21

4.2.3. Speed Coupling Mode Performance Simulation In the speed coupling mode, when the required torque is constant, the speeds of both motors can change within a certain range, and the system power consumption corresponding to different speed combinations is also different. According to the flow shown in Figure 16, the simulation condition is designed as follows: from 0 to 0.05 s, the vehicle speed is adjusted to 60 km/h. In this process, the torque is adjusted to the demand torque. Then, the vehicle travels from the initial speed of 60 km/h to the target speed of 60.43 km/h, with an acceleration of 0.48 m/s2 for 0.25 s. Under the above conditions, the demand torque and speed of the main reducer are 75 Nm and 2430 rpm, respectively. The corresponding torques of MG1 and MG2 are 51 Nm and 24 Nm, respectively. Under the restriction of corresponding speed, the maximum speeds of MG1 and MG2 are 5600 rpm and 8500 rpm, respectively. The speed ranges of MG1 and MG2 are [ 5600 rpm, 5600 rpm] and [ 8500 − − rpm, 8500 rpm], respectively. In addition, the speeds of MG1 and MG2 are also constrained by the demand speed of final drive, which is described as follows:

ωm1 k + ωm2 ωo = · . (18) i (k + 1) 0· To meet the requirements of the main reducer output characteristics, the speed range of MG1 under this condition is [ 295 rpm, 5600 rpm] based on Equation (18). − The target speed n1∗ = 3590 rpm of MG1 is taken as an example to analyze the speed–torque characteristics during the working point transfer process. The dynamic responses of MG1 and MG2 areAppl. shown Sci. 2020 in, 10 Figure, x FOR 20PEER. REVIEW 18 of 22

MG1 torque

) MG2 torque

( Torque

Time(s) )

rpm MG1 speed (

MG2 speed Speed Speed

Time (s)

FigureFigure 20.20. Changes of speed and torque of MG1 and MG2.MG2.

AsAs shownshown inin FigureFigure 20 20,, in in the the period period of of 0–0.045 0–0.045 s, thes, the speed speed of theof the two two motors motors are are adjusted adjusted to the to speedthe speed when when the vehicle the vehicle speed speed is 60 kmis 6/h.0 k Inm/h the. In period the period of 0.045–0.05 of 0.04 s,5– the0.05 torques s, the torques of the two of the motors two aremotors adjusted are adjusted to the demand to the demand torque corresponding torque corresponding to the condition to the condition (i.e., 60 km (i.e./h,speed 60 km/h and speed 0.48 m and/s2 acceleration).0.48 m/s2 acceleration). At the moment At the ofmoment 0.05 s, theof 0.05 MG1 s, speedthe MG1 is adjusted speed is to adjusted the target to speedthe target of 3590 speed rpm; of meanwhile,3590 rpm; meanwhile the torque, the of MG1 torque increases of MG1 and increases that of and MG2 that decreases of MG2 as decreases these two as motors these two need motors extra torqueneed extra to overcome torque to the overcome rotational the inertia rotational force inertia when force the speed when changes. the speed changes. AccordingAccording to to the the power power distribution distribution ﬂow in flow Figure in 16 Figure, all of the 16, energy all of consumption the energy corresponding consumption tocorresponding the target speed to the n1* target of MG1 speed can be n1* obtained. of MG1 When can be the obtained. vehicle Whenspeed is the 60.43 vehicle km/ h, speed the range is 60.43 of n1*km/h, is [the295 range rpm, of 5600 n1* is rpm]. [−295 When rpm, 5600 the initial rpm]. speedWhen ofthe MG1 initial is speed set to 3242of MG1 rpm, is set the to target 3242 speedrpm, the of − MG1target traverses speed of in MG1 the intervaltraverses of in [ the295 interval rpm, 5600 of rpm][−295 torpm, obtain 5600 the rpm] demand to obtain power the of demand the electric power drive of − the electric drive system. The demand power of the system, corresponding to different target speeds

of MG1, is shown in Figure 21.

)

( Demand power power Demand

MG1 target speed (rpm)

Figure 21. Demand power corresponding to different target speeds.

The optimal speed of MG1 n1* obtained from the static model of the motor is 3590 rpm. In the dynamic model, it is seen from Figure 21 that with the increase of target speed n1* of MG1, the system demand power first decreases and then increases. The following points of the MG1 target speed n1* are selected in the simulation studies: the starting point of the decreasing function is −295 rpm, the trough point is 1867 rpm, and the final point of the increasing function is 5600 rpm. Table 5 shows the demand power at different MG1 target speeds. Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 22

MG1 torque MG2 torque Torque (Nm)

Time(s)

MG1 speed MG2 speed Speed (rpm)

Time (s)

Figure 20. Changes of speed and torque of MG1 and MG2.

As shown in Figure 20, in the period of 0–0.045 s, the speed of the two motors are adjusted to the speed when the vehicle speed is 60 km/h. In the period of 0.045–0.05 s, the torques of the two motors are adjusted to the demand torque corresponding to the condition (i.e., 60 km/h speed and 0.48 m/s2 acceleration). At the moment of 0.05 s, the MG1 speed is adjusted to the target speed of 3590 rpm; meanwhile, the torque of MG1 increases and that of MG2 decreases as these two motors need extra torque to overcome the rotational inertia force when the speed changes. According to the power distribution flow in Figure 16, all of the energy consumption corresponding to the target speed n1* of MG1 can be obtained. When the vehicle speed is 60.43 Appl.km/h, Sci. 2020the ,range10, 78 of n1* is [−295 rpm, 5600 rpm]. When the initial speed of MG1 is set to 3242 rpm,18 of 21the target speed of MG1 traverses in the interval of [−295 rpm, 5600 rpm] to obtain the demand power of system.the electric The demanddrive system. power The of thedemand system, power corresponding of the system, to di correspondingﬀerent target speeds to different of MG1, target is shown speeds inof Figure MG1, 21 is. shown in Figure 21. Demand Demand power (kW)

MG1 target speed (rpm)

FigureFigure 21. 21.Demand Demand power power corresponding corresponding to to di differentﬀerent target target speeds. speeds.

TheThe optimal optimal speed speed of of MG1 MG1n 1n1* obtained* obtained from from the the static static model model of of the the motor motor is is 3590 3590 rpm. rpm. In In the the dynamicdynamic model, model, it isit seenis seen from from Figure Figure 21 that 21 withthat thewith increase the increase of target of speedtarget n1* speed of MG1, n1* of the MG1, system the demandsystem powerdemand first power decreases first decreases and then increases.and then Theincreases. following The pointsfollowing of the points MG1 of target the MG1 speed target n1* are selected in the simulation studies: the starting point of the decreasing function is 295 rpm, the speed n1* are selected in the simulation studies: the starting point of the decreasing −function is −295 troughrpm, the point trough is 1867 point rpm, is and 1867 the rpm, final and point the offinal the poin increasingt of the function increasing is 5600 function rpm. is Table 56005 rpm.shows Table the 5 demandshows the power demand at diff powererent MG1 at different target speeds.MG1 target speeds.

Table 5. Demand power of the electric drive system at diﬀerent MG1 target speeds.

MG1 Target Speed/rpm MG1 Power/kW MG2 Power/kW Demand Power/kW 295 7.615 16.291 23.906 − 1867 14.347 7.745 22.092 3590 21.53 2.013 23.543 5600 31.56 2.965 28.595 −

Table5 shows that the power of MG1 increases and that of MG2 decreases, with the increase of the MG1 target speed n1*. When the optimal speed (3590 rpm) obtained by the static model is taken as the target speed of MG1, the average demand power of the drive system is 23.543 kW, which is not the minimum demand power of the electric drive system under this condition. When the MG1 target speed n1* is 5600 rpm, the maximum power demand of the electric drive system is 28.595 kW. This is because when the target speed of MG1 is 5600 rpm, the speeds of motor MG1 and MG2 need to be adjusted from 3242 rpm to 5600 rpm, and from 733 rpm to 4165 rpm, respectively. This is a large − speed regulation process, which leads to power loss. When the target speed of MG1 is 1867 rpm, the minimum demand power of the electric drive system can be obtained, i.e., 22.092 kW. This minimum value is 6.16% lower than the average demand power obtained from the static model and 22.74% lower than the maximum demand power of the electric drive system.

5. Conclusions In this paper, the mechanical and electrical energy conversion mechanism and dynamic control of PMSM are studied in order to analyze the impact on the performance of pure electric vehicle. Considering the influence of bus voltage fluctuation on motor performance, a vector control strategy based on the speed–torque–current map is designed. In this study, three working conditions were formulated, including the 0–100 km/h acceleration condition, speed coupling condition, and torque Appl. Sci. 2020, 10, 78 19 of 21 coupling condition. They have been used to study the dynamic characteristics and energy consumption characteristics of the double motor coupling mode. The simulation results show that compared to the static control model, the dynamic control model can better reflect the actual working process of the motor. In the torque coupling mode, the minimum demand power of the system, corresponding to the optimal MG1 target torque, is obtained from the dynamic characteristics of the motor. This power is 1.27% lower than that obtained from the static model and 20.6% lower than the maximum demand power of the system. In the speed coupling mode, the minimum demand power of the system, corresponding to the optimal MG1 target speed, is also obtained from the dynamic characteristics of the motor. This power is 6.16% lower than the demand power corresponding to the MG1 target speed obtained by the static characteristics and 22.74% lower than the maximum demand power of the system. The above results show that the proposed vector control strategy based on the dynamic model of the speed–torque–current map achieves optimal power distribution of the electric drive system, and effectively reduces the energy consumption of the electric drive system and extends the mileage of the car. This research results in this article lay a theoretical foundation for further improving the dynamic performance of electric vehicles.

Author Contributions: J.H. wrote the first draft of the manuscript, proposed the design method. M.J. designed the process of control strategy and the performance simulation method, completed the verification of the strategy, and dealt with the simulation data. F.X., L.Z., and C.F. provided insights and additional ideas on presentation. All authors have read and agreed to the published version of the manuscript. Funding: This work was funded by the Chongqing Key Research and Development Program (Project No. cstc2018jszx-cyztzx0047), and the National Key Research and Development Program of China under Grant 2018YFB0106100. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature id Armature current vector of the d-axis iq Armature current vector of the q-axis ud Voltage vector of the d-axis uq Voltage vector of the q-axis icd Iron loss current of the d-axis icq Iron loss current of the q-axis iod Current vector of the d-axis ioq Current vector of the q-axis Ld Inductance of the d-axis Lq Inductance of the q-axis Rs Copper loss resistance Rc Iron loss resistance ϕf Flux Ω Electrical angular velocity ρ Salient pole ratio Kf Eddy current loss coeﬃcient Kh Hysteresis loss coeﬃcient is Armature current us Terminal voltage Te Electromagnetic torque pn Number of pole pairs TL Load torque J Moment of inertia ωr Angular velocity θs Electrical angle n1* Target speed fsw Inverter switching frequency Appl. Sci. 2020, 10, 78 20 of 21

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