International Power, Electronics an Materials Engineering Conference (IPEMEC 015) The Efficiency Optimization of Permanent Magnet Synchronous Machine DTC for Electric Vehicles Applications Base on Loss Moel Like Zhao 1, Xiaomin Zhou 1, Dawei Gao 1 School of Mechanical Engineering, University of Science an Technology Beijing, Beijing, 100083, China State Key Laboratory of Automotive Safety an Energy Tsinghua University, Beijing, 100084, China Keywors: Permanent Magnet Synchronous Machine, Direct Torue Control, Loss Moel, Iron Loss Resistance, Efficiency Optimization. Abstract. An efficiency optimization metho of permanent magnet synchronous machine for electric vehicles applications is researche. Consiering iron loss euivalent resistance an irect torue control scheme, the relationship of stator flux an power loss is erive base on loss moel. An then the real-time optimal target flux can be obtaine through the relationship of -axis stator flux, target torue an electric spee at the minimum loss situation. A fitting curve of iron loss euivalent resistance versus spee is obtaine by simulation. This makes the iron loss euivalent resistance closer to the actual value compare with the fixe value. Simulation results show that the motor efficiency has been improve compare with traitional irect torue control. Introuction Compare with conventional internal combustion engine vehicles, the electric vehicles are cleaner, more efficiency an lower noise. It is currently the most promising evelopment irection of the automotive inustry with better ynamic performance [1]. The permanent magnet synchronous motor (PMSM) with small size, light weight, compact structure, highly efficiency is suitable as electric vehicle rive motor. Variable Voltage an Variable Freuency (VVVF), Vector Control (VC), Direct Torue Control (DTC) are the three methos for permanent magnet synchronous motor control []. Direct Torue Control (DTC) has avantages of simple control structure, fast torue response an robustness. Although permanent magnet synchronous motors have higher efficiency compare with asynchronous motors, the loss of the motor is still exist. Wang Jin [3] analyze factors affecting motor s losses an also conclue methos ecreasing losses. Xu Jun-feng [4] an Xu Yan-ping [5] stuie the relationship of current an loss of surface permanent magnet synchronous motor. Chen Xu [6] propose LMC (loss minimum control) base on searching metho. Kang Chang [7] presente a generalize relationship between - current for the LMC of PMSM. It showe that maximum torue per ampere an maximum torue per voltage can be erive as special case of LMC. The - current was treate as irect control value in this metho. A. Dittrich [8] an Naomitsu Urasaki etc. [9] propose a calculation metho for iron loss resistance in the offline manner base on the linear feature between semi-input power an suare of spee electromotive force. The loss of motors inclues iron loss, copper loss, stray loss an mechanical loss [10]. The mechanical loss can t be controlle as it is not irectly relate to current, torue an flux values. Just iron loss an copper loss are escribe in this paper. The loss moel of PMSM The - axis euivalent circuit of PMSM consiering iron loss an copper loss is shown in Figure 1. For control purpose, the iron loss is moelle as a resistance, known as iron loss resistance which is in parallel in the circuit. The - axis current is ivie into iron loss current an excitation current. 015. The authors - Publishe by Atlantis Press 70
R s i io L R s i io L i i i i U R i w e U R i w e (a) The euivalent circuit of -axis (b) the euivalent circuit of -axis Figure 1 the euivalent circuit The - axis flux an the electromagnetic torue are calculate as the formula (1), (), (3) shown. Li o f (1) Li o () Te 1.5np fio L L ioio (3) where ψ is the axis flux, ψ is axis flux, L is the axis inuctance, L is the axis inuctance, ψ is the rotor flux, i is the axis excitation current, i is the axis excitation current, n is the pole pairs, T is the electromagnetic torue. Accoring to the formula (1), (), the excitation currents can be calculate as the formula (4), (5) shown. i f o L (4) (5) The i, i can be calculate as formula (6), (7) shown by applying the Kirchhoff s first law for noe A, B in Figure 1. i io ii (6) i io ii (7) Where i is the axis current, i is the axis current, i is the axis iron loss current, i is the axis iron loss current. The formula (8), (9) can be obtaine by applying the Kirchhoff s secon law to the right sie loop in the Figure 1. i o L plio elioi i 0 (8) pl i L i R i 0 o e o f i i (9) Where p is the ifferential operator, ω is the electric spee, R is the iron loss resistance. In the steay state, p0. The steay-state iron loss current expression is shown as formula (10), (11). eli o ii (10) eli o f ii (11) The iron loss P an copper loss P are compute shown as formula (1), (13). 1.5 e Li o 1.5e f Li o Piron 1.5 ii ii (1) eli o e Li o f Pcu 1.5Rs i i 1.5R s io i o R i R i (13) The final power losses incluing both copper loss an iron losses can be represente as formula (14). Ploss Piron Pcu (14) 71
Accoring to the formula (4), (5), (1), (13),, (14), formula (15) cann be obtaine. P a b c e R a L L LR i LR i L LR i Where (5) into (3), the relationship of Tan ψ is obtaine as formula (16). f f (16) The relationship of P an Ψ incluingg unknownn uantity Ψ, T, ω can be obtaine by substituting formula (16) into formula (15).. In the steay state, T, ω are constant values. So, the power losss P is only relate to t Ψ. The flux corresponing to the minimum loss of this torue value can be obtaine by erivation the power losses P with respect to Ψ as shown in formula 17. Formula (17) can be rewritten as formula (18). Also Accoring value can target flux s e s e, the R Rs e Rs e Rse Rse R s f Rs f e Rs f b,c,, e, f. L factor expressions 3 a 6auz 3 u z, a1 az ckuz 3, 3 z u eku a0 ckz z k TeLL, u 3 n p (L L),z 3nL p f. to the formula (18), the optimal axis flux value can be b obtaine.. The targett axis flux be obtaine by substituting the target axis flux value into euation (16). The stator value corresponing to the minimum loss can be obtaine shown ass the euation (19). The estimate of euivalent iron loss resistance loss 4 3 a 4 a3 a a a Loss resistance in minimum loss iron moel is a changing value. There are ifferent ways to estimate the resistance off-line. This paper estimatess the iron loss l resistance by finite element analysis. Motor finite element moel is shown in Figure. Dimensions of the moel are liste in Table 1. T el L 3n p L are bk u Ploss 0 = uekz, as: a 4 L Substituting formula f (4), L 1 0 a L 0 f 3 au, a 6 au z u, 3 4 3 (15) (17) (18) (19) Figure Motor finite element moel Table 1 Dimensions of the motorr name value DiaGap of Statorr 161..9(mm) DiaYoke of Stator 69..4(mm) DiaGap of Rotorr 160..4(mm) DiaYoke of Rotor 110..64(mm) Slots 48 The input power can be expresse as formula (0). Pin U i U i R i i s e R i e io i o (0) 7
Where the first term is the copper loss, thee secon term is the iron loss, an the thir term is the output power. The Electromotivee Force (EMF) is proportional to the t suare of the iron loss l an the ratio is the inverse of the iron loss euivalent resistance. The simulation parameters of the motor are liste in Table. Table The motor parameters use in the simulation Stator resistance(ω) 0.069 axis inuctance (H) 0.00 axis inuctance (H) 0.006 Rotor flux( (Vs) 0.158 Pole pairs 4 By changing the -axis current at the spee of 837.758ra/s, a set of iron losss is recore shown in Table 3. Changing the -axis current only affects the -axis flux. The T fitting curve shown in Figure 3 is acuire by using a linear fitting algorithm. The slope of thee curve is the euivalent iron losss resistance at this spee. Table 3 A sett of iron loss at the electric spee of o 837.758 ra/s ω ψ (V) Piron (w) 37.05 61.1584 7514.88 74.5987 33354.1 90.9784 39754.94 104..1844 46717.18 11..8611 5440.89 139..7776 636.07 157..0671 7097.7 174..5733 80180.84 191..8711 Figure 3 The fitting curve of iron power loss an EMF at 837.758 ra/s In the same manner, the iron losss resistance at other spees can be obtaine shown in Table 4. It can be seen that the iron loss resistance increasess with spee increasing. Table 4 The iron loss resistance at ifferent spee Spee [ra/s] Iron loss resistance[ω] 418.879 35..1 68.3185 30..7 837.758 396..8 1047..198 456..4907 156..637 51..5 73
The fitting curve is shown in Figure 4. The regression coefficient of the fitting curve is 0.991 which means that the formula well escribes the tren of iron loss resistance. The iron loss resistance satisfies the formula (1). 0.39e 108 (1) Iron loss resistance (Ω) 600 500 400 300 00 100 0 y = 0.39x + 108.0 R² = 0.991 0 500 1000 1500 Electric Spee (ra/s) Figure 4 The curve of iron loss resistance an spee Analysis of Simulation Results The simulation is conucte at the electrical spee of 837.758 ra/s. Accoring to the formula (1), the iron loss euivalent resistance is 383.6 Ω at this spee. The target torue steps from 30NM to 50NM at 0.0s. The loss minimization irect torue control an traitional irect torue control are simulate in the same situation respectively. The simulation results are shown in Figure 5, 6. Efficiency(%) 100 90 80 70 60 50 40 X: 0.015 Y: 96.79 X: 0.03 Y: 94.9 Efficiency(%) 100 90 80 70 60 50 40 X: 0.015 Y: 96.94 X: 0.03 Y: 96.3 30 30 0 0 10 10 0 0 0.005 0.01 0.015 0.0 0.05 0.03 0.035 0.04 Time(s) 0 0 0.005 0.01 0.015 0.0 0.05 0.03 0.035 0.04 Time(s) Figure 5 Efficiency of traitional irect torue control Figure 6 Efficiency of loss minimum irect torue control Using traitional DTC metho, the motor efficiency is 96.79% when the target torue is 30NM an the efficiency is 94.9% when the target torue is 50NM. Using the metho of loss minimization DTC, the motor efficiency is 96.94% when the target torue is 30NM an the efficiency is 96.3% when the target torue is 50NM. It can be seen that the motor efficiency improves 0.15% when the target torue is 30NM an the efficiency improves 1.33% when the target torue is 50NM compare with the traitional DTC. Conclusions This paper proposes a loss minimum control metho through ajusting the flux reference ynamically base on loss moel. The relationship between euivalent iron loss resistance an spee is acuire by finite element simulation uner ifferent conitions. The iron loss resistance increases linearly with spee increasing. Using the propose LMC metho, motor efficiency is improve compare with traitional irect torue control. 74
Acknowlegements We woul like to acknowlege the financial support by National Natural Science Founation of China through Grant No.5104017 an the project No.KF1413 supporte by the Science Fun of State Key Laboratory of Automotive Safety an Energy. References [1] Liu Wei-Gang. Stuy an Implementation of Direct Torue Control of PMSM Motor for Electric Vehicle Driving System. Chonging: Chonging University, 011. [] Xu Yan-Ping. Research on Direct Torue Control Methos of Decreasing Torue pples for Permanent Magnet Synchronous Motors. Xian: Xi an university of technology, 008,8. [3] Wang Jin. Core Loss Research an Design of Super Premium Efficiency PMSM. Shenyang: Shenyang University of Technology, 009. [4] Xu Jun-Feng, Feng Jiang-hua, Xu Jian-ping. Direct Torue Control of Permanent Magnet Synchronous Machine Consiering Loss Moel. Power Electronics, 39(), pp.4-8, 005. [5] Xu Yan-Ping, ZHONG Yan-ru. Simulation of Minimum Loss Control for PMSM. Journal of System Simulation,19(), pp.583-586, 007. [6] Chen Xu. Research on Loss Minimization Control Metho of Permanent Magnet Synchronous Motor. Beijing: North China University of Technology, 013. [7] Kang Chang. Loss Minimization Control of Permanent Magnet Synchronous Machine For Electric Vehicle Applications. Montreal: Concoria University, 013. [8] A. Dittrich. Moel Base Ientification of The Iron Loss Resistance of An Inuction Machine. In Proc. Power Electronics an Variable SpeeDrives, Lonon, U.K., Sept. 1998, IEEE Conf. Pub. No. 456, pp. 500 503. [9] Naomitsu Urasaki, TomonobuSenjyu, Katsumi Uezato. A Novel Calculation Metho for Iron Loss Resistance Suitable in Moeling Permanent Magnet Synchronous Motors. IEEE transaction on energy conversion, 18(1), pp.41-47,003. [10] Francesco Fabio Quattrone. Dynamic Moelling of Losses in Electric Machines for Active Loss Control. Leibniz University Hannover. 011, 6. 75