Control of Permanent Magnet Synchronous Motor for Traction Application of Electric Vehicles

21 drivetrain system, control structure and control strategy play an important role th Accepted 16 Aug 2021 because they directly affect to the performance and efficiency of the vehicles. The Available online 19th Dec 2021 control structure has to ensure the robustness and reliability even the motor runs Keywords: at high speed, while the control strategy is responsible to improve motor efficiency. Control of PMSM, automotive, These are complex tasks due to the variations of the motor parameters. This paper electric vehicle, optimal control focuses on assessing control structure and control strategy for permanent magnet strategy, motor control synchronous motors that are widely used to provide the vehicle traction force. structure Based on these assessments, a robust structure and an optimal strategy are suggested to control the motor in both base-speed and field weakening areas. This suggestion is verified by simulation to show how well the controller works. â 2020 University of Mining and Geology. All rights reserved Nomenclature 푢d, 푢q direct and quadrature stator voltages 푅s stator resistance 푖d, 푖q direct and quadrature stator currents, 퐿d, 퐿q direct and quadrature stator inductances 휔, 휔e Mechanical and electrical frequencies 훹PM permanent magnet flux linkage 푈max Voltage limit, 푈max = 푈DC⁄√3 푧p number of pole pairs 푇e electromagnetic torque 훹d, 훹q direct and quadrature stator flux linkage 1. Introduction torque demand is provided by the speed controller, while in the torque mode it is an Nowadays, environmental concerns, independent control quantity. Here a question environmental regulations on CO2 and exhaust arises as to how the current references for current emissions are factors driving development of controllers are generated. To answer this electric vehicles (EVs). In this application, question, some control strategies related to permanent magnet synchronous motors optimization algorithms were presented in (PMSMs) are widely used for traction drive literature as summarized by (Nguyen, 2017). because of their advantages, such as such as high They can be classified into three categories: efficiency, high power factor and high power (1) Model-based control (MBC), density (Windisch, Hofmann, 2011). To control (2) Search control (SC), the PMSMs as well as three-phases motors, up to (3) Hybrid control (HC). now field oriented control (FOC) is the most SC and HC strategies base on the iterative loop common method (Quang, Dittrich, 2015). Fig. 1 to seek the optimum point, so they take a long shows the block diagram of the FOC method. As time to achieve the stable state and can cause the can be seen, in the speed mode (dash line) the disturbance in the electromagnetic torque during 153 HỘI NGHỊ KHOA HỌC TOÀN QUỐC VỀ CƠ KHÍ – ĐIỆN – TỰ ĐỘNG HểA (MEAE2021) the search process. Thus, both SC and HC (푖d, 푖q) are selected with respect to the motor strategies are not suitable for applications with speed and the actual DC voltage, which can vary frequent changes in the operating point such as in considerably with the battery state of charge electric vehicles, where the steady state period is (SOC) in EVs. Finally, the suggested structure is short. In contrast, MBC strategies can quickly verified by simulation based on the system achieve the optimal state point and, therefore, parameters in Table 1. they may be suitable for the automotive application (Nguyen, 2017). However, MBC Table 1. Electric system parameters strategies require motor parameters, which are Parameter Value difficult to determine exactly and can be changed Nominal torque 150 Nm due to effect of saturation and temperature. Nominal speed 7000 rpm Because of this disadvantage, MBC strategies are needed to be further developed in the direction of Number of pole pairs 4 considering the variation of motor parameters. Nominal DC-link voltage 400 VDC Direct stator inductance 110 uH UDC V * Quadrature stator inductance 290 uH id * * Current Udq ω* Speed Te Current Reference * Modulation Permanent magnet flux linkage 0.0532 Wb Control i Control ω Generator q Stator resistance 6 mOhm dq i abc i ωe dq sabc 2. Motor Control zp PMSM θs d/dt 2.1. Motor Model and Loss Model Fig. 1. Field oriented control principle The mathematical model of the PMSM is described in the dq-coordinate system as follows One of EVs features is that the motor can run at (Schrửder, 2009): very high speed (called field weakening area), 푑훹d where limitation of current and voltage have to be 푢 = 푅 푖 + − 휔 훹 (2) d s d 푑푡 e q taken into account for determining the current 푑훹q references. For this feature, the motor controller 푢q = 푅s푖q + + 휔e훹d (3) needs be able to operate in both base speed and 푑푡 field weakening areas as well as the control 훹d = 훹PM + 퐿d푖d (4) structure needs to designed to provides a smooth 훹q = 퐿q푖q (5) transition between both (Peters et al., 2012; 3 Schrửder, 2009). Some control structure were 푇e = 푧p(훹d푖q − 훹q푖d) (6) suggested in these references, but there is no 2 assessment being done as to which one is suitable It should be noted that the relationship for the control system of the EV traction drive. between flux linkages and stator current This paper focuses on assessing control components becomes nonlinear due to the structure and control strategy for the traction saturation and temperature effects, especially at control system of EVs. From the assessment, a high load or high speed (Windisch, Hofmann, control structure based on Lookup Tables (LUTs) 2011). Fig. 2 illustrates the flux linkages obtained considering nonlinear saturation effect and iron from FEM simulation for the example motor. losses is proposed. The LUTs are calculated The drive consists of the components inverter utilizing the Maximum-Torque-Per-Ampere and machine, with both causing power strategy with the variation of motor parameters dissipation. In the motor, electrical losses ( 푃loss) obtained from Finite-Element-Method (FEM) are divided into copper losses, iron losses and simulation results. Appropriate state points stray losses (Junggi Lee et al., 2008): 154 HỘI NGHỊ KHOA HỌC TOÀN QUỐC VỀ CƠ KHÍ – ĐIỆN – TỰ ĐỘNG HểA (MEAE2021) 2 2 푃Cu = 1.5푅s(푖d + 푖q) (7) 푃SW = 푓(푖ph, 휉, 푓sw, 푈DC) (11) 훾 2 2 푃Fe = 퐶Fe휔 (휓d + 휓q) (8) Depending on (1) ữ (5) we can design the current controllers by utilizing the FOC method, 푃 = 퐶 휔2 푖2 + 푖2 Str str ( d q) (9) but it is not our objective. In this paper, we focus where 퐶Fe, 훾 and 퐶str are loss coefficients that can on generating the current references for the be varied by motor operating point. current controller based on (6) ữ (10). This is presented in next subsections 3.2 and 3.3. 2.2. Control Strategy Operation in constant torque region As already mentioned, the MBC strategy should be used for the EV traction motor. In the constant torque region, appropriate operation points are chosen by utilizing the optimization control strategy: min⏟ 푃loss(푖d, 푖q) 푠. 푡. 푇e(푖d, 푖q) = 푇e,ref (12) 푖d,푖q Depending on which losses are considered in the loss function 푃loss some MBC strategies were reported in literature (see Error! Reference source not found.). Note that for the MTPA strategy only basic motor parameters such as 푅s, 퐿d, 퐿q and 훹PM are required (see (2)ữ(7)) while other strategies need more experimental parameters (see (8)ữ(11)) that are difficult to determine. In the other words, finding a solution to minimize total power losses is a challenge Fig. 2. Flux linkages from FEM because it requires too much effort to determine In inverter, losses are composed of switching system parameters. It is the reason why using losses and conduction losses of the transistors MTPA strategy is suggested in this paper: and diodes: (Windisch, Hofmann, 2011): min⏟ 푃Cu(푖d, 푖q) 푠. 푡. 푇e(푖d, 푖q) = 푇e,ref (13) 푃Cond = 푓(푖ph, 휉, 휑) (10) 푖d,푖q Table 5. Model-based control strategy for PMSM Strategy Considered Losses Reference Maximum Torque Per (Meyer, Bửcker, 2006) 푃 = 푃 Ampere (MTPA) loss Cu (Schrửder, 2009) (Junggi Lee et al., 2008) Minimum motor losses 푃 = 푃 + 푃 + 푃 loss Cu Fe Str (Peters et al., 2012), 푃 = 푃 + 푃 + 푃 (Pohlenz, Bửcker, 2010) Minimum total losses loss Cu Fe Str + 푃Cond + 푃SW (Windisch, Hofmann, 2011) 155 HỘI NGHỊ KHOA HỌC TOÀN QUỐC VỀ CƠ KHÍ – ĐIỆN – TỰ ĐỘNG HểA (MEAE2021) To overcome the problem of motor parameter 훹PM are obtained from FEM simulation variations, the MTPA control characteristic is considering the saturation and iron loss effects. As calculated by using the FEM simulation results (see can be seen, when the speed increases, the control Fig. 2). Thus, both nonlinear saturation and iron characteristics are moved to the direction of loss effects are taken into account. Fig. 3 shows decreasing the direct stator current. The torque is comparison of two MTPA characteristics obtained maintained equal to its reference or it is controlled by using nominal motor parameters (nominal to reach the maximum value if input power is trajectory - red) and by using FEM simulation limited. Thus, this strategy is called Maximum- results (FEM-based trajectory - blue). Both Torque-Per-Watt (MTPW). Note that at low speed characteristics are calculated from (13) by using where the voltage limitation can be neglected, the Matlab-Optimization-Toolbox. It can be seen that MTPW characteristic is coincided with FEM-based for high torque or high speed the operating point MTPA one in Fig. 4 differs significantly from the nominal trajectory. The reason is the variations of the motor inductances at high current due to the magnetic saturation. Due to lack an explicit formula for the MTPA strategy, LUT is used for the FEM-based MTPA strategy. Operation in field weakening region MTPA control strategy will be maintain as long Fig. 3. MTPA characteristics as the point (푖d, 푖q) is still located within limitations of the current and voltage (Meyer, Bửcker, 2006; Schrửder, 2009): Speed 2 2 2 increasing 푖d + 푖q ≤ 퐼max (14) 2 2 2 푢d + 푢q ≤ 푈max (15) As MTPA point (푖d, 푖q) is outside the limitations (14) and (15), it has to be re-calculated so that the copper losses reach minimum while the torque is Fig. 4. Control characteristics maintained equal to its reference or reached as 2.3. Control Structure maximum as possible. So the loss minimization problem (13) can be rewritten as: Fig. 5 summarizes some block diagrams of current reference generator reported in literature min⏟ 푃 (푖 , 푖 ) Cu d q (Lee et al., 2008; Schrửder, 2009; Pohlenz, Bửcker, 푖 ,푖 d q 2010; Windisch, Hofmann, 2011; Peters et al., 푇e(푖d, 푖q) → 푚푎푥 ≤ 푇e,ref (16) 2012). In Fig. 5a and Fig. 5b the current references 2 2 2 푠. 푡. {푖d + 푖q ≤ 퐼max are calculated offline based on MTPA strategy (13) 2 2 2 and used as LUT. To avoid using LUTs, structures 푢 + 푢q ≤ 푈max d in Fig. 5c and Fig. 5d use the outputs of the PI- The problem (16) can be solved by numerical controllers as q - axis current reference while d - method such as using Matlab-Optimization- axis current reference is calculated based on an ToolBox. Fig. 4 shows the results including control explicit formula, which is the solution of (13) when characteristics with constant speed for the neglecting the variation of the motor parameters. Fig. 5. Current reference generator diagrams The structures in Fig. 5a ữ Fig. 5d can be applied simulation motor. Here the parameters 퐿d, 퐿q and 156 HỘI NGHỊ KHOA HỌC TOÀN QUỐC VỀ CƠ KHÍ – ĐIỆN – TỰ ĐỘNG HểA (MEAE2021) * only for motor operation in constant torque id * Te MTPA region, not appropriate for EV traction. Lookup Table * iq To control the motor operating in both constant torque and field weakening regions, the structures (a) LUT-based MTPA 1 in Fig. 5e and Fig. 5f supplement I-controllers with * * is id * Conversion from voltage feedback. In the constant torque region, the Te MTPA Polar to Lookup Table Cartesian * I-controllers are inactive by using saturation β iq Coordinates blocks and the current reference are generated by (b) LUT-based MTPA 2 the MTPA strategy. In the field-weakening region, the I-controller are active and the d-axis current * ω* iq * MTPA id reference is moved so that the state point (푖d, 푖q) PI Calculation * ω iq lies on the voltage limit curve. In this way, the d- axis flux linkage is reduced and the motor can (c) Formula-based MTPA operate in the field-weakening region. The main * disadvantage of these structures is that they need * i * T q e MTPA id PI convergence time to achieve a new steady state. Calculation * iq Te ,est Thus, they are not suitable for the EV traction, i dq where the operating point is changed frequently. Torque Estimation To overcome the problem of convergence time, in this paper the LUT-based open-loop control (d) Formula-based MTPA with torque estimation * * structure is proposed in Fig. 5g. By utilizing motor iq1 iq * parameters from FEM simulation, the current Te MTPA Lookup Table * id1 references are calculated offline founded on the MTPW strategy (16). When neglecting the stator i* d resistance, at steady-state the voltage components U*dq in (2) and (3) can be rewritten as 푢d = −휔e훹q and 푢q = 휔e훹d. Thus, torque limit 푇lim can be Udc Kp calculated under conditions (14) and (15) as (e) LUT-based MTPA with voltage feedback 1 follows: * * is i d * Conversion from Te Current Angle Polar to * 2 2 2 Lookup Table Cartesian i β β' q 푖 + 푖 ≤ 퐼 Coordinates d q max max⏟ 푇 (푖 , 푖 ): { 2 (17) e d q 2 2 푈max U* 훹 + 훹 ≤ ( ) dq 푖d,푖q d q 휔 1 e Udc All offline results are then used as LUTs. In this way, we can avoid the problem of convergence (f) LUT-based MTPA with voltage feedback 2 time and the motor can runs in both constant * torque and field weakening regions with the id * * Te Te, sat MTPW smooth transition between both. The simulation Lookup Table * iq results shown in Fig. 6 demonstrates this remark. Tlim 3. Conclusion ωe ω zp Lookup In this paper, the realization of a Lookup-Table- Table Udc based open-loop control structure for a permanent (g) Proposed LUT-based open-loop control magnet synchronous motor based on the Maximum-Torque-Per-Watt strategy is presented. Because the proposed control strategy utilizes the 157 HỘI NGHỊ KHOA HỌC TOÀN QUỐC VỀ CƠ KHÍ – ĐIỆN – TỰ ĐỘNG HểA (MEAE2021) Finite-Element-Method simulation results to [2] Meyer M, Bửcker J. (2006). Optimum calculate the stator current references for the Control for Interior Permanent Magnet Fig. 6. Simulation results: motor runs in speed mode, at 10000 rpm and 100 Nm. controller, variations of motor Synchronous Motors (IPMSM) in Constant parameters due to saturation and effect of iron Torque and Flux Weakening Range. 2006 losses on the motor model are considered. 12th International Power Electronics and Simulations using a subcompact electric vehicle Motion Control Conference. IEEE. model demonstrate that the presented structure is capable for the constant torque region as well as [3] Nguyen CD. (2017). Loss minimization for the flux-weakening region and provides a control of three-phase motors. Shaker. smooth transition between both. [4] Peters W; Wallscheid O; Bửcke J. (2012). A It should be noted that for strategies based on precise open-loop torque control for an the Finite-Element-Method, the knowledge of the interior permanent magnet synchronous machine such as geometries and materials is motor (IPMSM) considering iron losses. required. In addition, the machine models are IECON 2012 - 38th Annual Conference on time-consuming to create and verify, and sometimes they need to be refined repeatedly to IEEE Industrial Electronics Society. ensure that the results are accurate. [5] Pohlenz D, Bửcker J. (2010). Efficiency The proposed approach can be applied for improvement of an IPMSM using Maximum other motor types such as induction motors and Efficiency operating strategy. Proceedings synchronous reluctance motors. This is a target of of 14th International Power Electronics and further research. Motion Control Conference EPE-PEMC References 2010. IEEE. [1] Junggi Lee, Kwanghee Nam, Seoho Choi, [6] Quang NP, Dittrich JA. (2015). Vector Soonwoo Kwon. (2008). Loss Minimizing control of three-phase AC machines. Control of PMSM with the Use of Polynomial Springer. Approximations. IEEE Industry Applications [7] Schrửder, D. (2009). Elektrische Antriebe - Society Annual Meeting. Regelung von Antriebssystemen. Springer. 158 HỘI NGHỊ KHOA HỌC TOÀN QUỐC VỀ CƠ KHÍ – ĐIỆN – TỰ ĐỘNG HểA (MEAE2021) [8] Windisch T, Hofmann W. (2011). Loss minimization of an IPMSM drive using pre- calculated optimized current references. IECON, Australia. 159