IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
Improved Direct Torque Control of Permanent Magnet Synchronous Motor in Electric Vehicle Drive Xu Jiaqun *, Tang Renyuan ** and Ouyang Minggao *** * School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing, China. Email:
[email protected] ** National Engineering Research Center for Rare-earth Permanent Magnet Machines, Shenyang University of Technology, Shenyang, China. Email:
[email protected] *** State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, China. Email:
[email protected]
Abstract—In order to improve dynamic performance and reduce switching loss of permanent magnet synchronous motor system in electric vehicle drive, a self-adjusting direct torque control strategy is proposed. Based on the analyses of zero voltage vector in DTC, fuzzy control rules with zero voltage vector are presented to acquire both quick dynamic torque response of PMSM and reduced switching loss of inverter. Simulation and experiment results prove the proposed strategy. Keywords — Direct Torque Control; Permanent Magnet Synchronous Motor; Electric Vehicle
I. INTRODUCTION Permanent magnet synchronous motor (PMSM) has been very attractive in electric vehicle (EV) drive with high efficiency, torque density and power density [1]. And vector control technique is mainly adopted to control PMSM at present [2]. Good dynamic performance and high efficiency are very important to EV drive. With high dynamic torque response and robustness, direct torque control (DTC) has become a competitive control technique to traction motor in EV drive compared to vector control method. DTC was just introduced to PMSM drive, which is different from the application to induction motor[3-7]. Up to now, the application of DTC to PMSM in EV drive has not been studied in detail. The EV in the paper is a small passenger coach driven by an interior permanent magnet synchronous motor (IPMSM), and 24 lead-acid batteries are chosen. Data of the EV is shown in Tab.1.
Good dynamic torque response performance and low switching loss are very important for PMSM and its controller in EV drive. An improved self-adjusting DTC strategy considering zero voltage vectors is presented in this paper. II.
SELF-ADJUSTING DTC WITH ZERO VECTOR
A. Zero Voltage Vector Analysis Space voltage vector and stator field of orientation technique are used in DTC, and α-β plane is divided six regions as Fig.1, the first voltage vector U1 is set up to keep the same direction with α axis. Thus, DTC method can be realized by selecting different voltage vectors based on the change rules of stator flux linkage and electromagnetic torque at any time. Generally, only six voltage vectors from U1 to U6 without zero vector are applied in DTC to ensure dynamic response of PMSM at the cost of switching loss of inverter [5]. Nevertheless, zero vectors including U0 and U7 are very important to improve dynamic performance on basis of reducing inverter loss. IPMSM torque equation is shown as (1) [4,7].
TABLE I. DATA OF THE EV Economic speed, Maximum speed Gradeability Acceleration time (0~20 km/h) Front face area Transmission ratio Radius of wheel
40 km/h 70 km/h 5% 8.5s 2.309 m2 7.21 0.255m
C 2008 IEEE 978-1-4244-1849-7/08/$25.00○
Figure 1. Six regions of α-β plane
IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
Tem
=
3p ψs 4 Ld Lq
[ 2ψ
f
Lq sin δ − ψ s
(L
q
− Ld ) sin 2δ
]
(1)
The relationship between IPMSM parameters and torque value can be calculated according to (1). The results are shown in Fig.2. Parameters of IPMSM system are assured based on vehicle dynamic equation and the EV data in Tab.1, which is shown in Tab.II. In Fig.2, three curves from data1 to data3 are in terms of such stator flux linkage as 0.75ψf, ψf and 1.5ψf, respectively. It is shown that different IPMSM system parameters have an obvious effect on toque. With the zero voltage vector and the load angle φ, torque equation of IPMSM can be expressed as (2).
Tem′
=
3p ψ s 4 Ld Lq
[ 2ψ
f
Lq sin δ ′ − ψ s
(L
q
)
− Ld sin 2δ ′
]
(2)
where δ ′ = δ − ϕ . Reduced electromagnetic torque in one control period can be calculated. Assuming control period is 100μs, the proportion of reduced electromagnetic torque vs. rated torque at different rotational speed and stator flux linkage is calculated. For instance, the proportion is less than 2.2% at 3000r/min, and which reduces with a lower rotational speed, even less than 0.37% at 500r/min. The results show that zero voltage vector makes torque reduce appreciably in one control period at different rotational speed. In order to avoid undesired switching loss of inverter and ensure good dynamic response, it is necessary to select zero voltage vector in steady state of PMSM in EV
TABLE II. PARAMETERS OF IPMSM SYSTEM Number of pole pairs, p Armature resistance, Ra Flux linkage, ψf d-axis inductance, Ld q-axis inductance, Lq Rated speed, ωr Maximum speed, ωmax Rated power, PN Maximum power, PN Nominal battery voltage
3 0.0578Ω 0.1252Wb 0.9mH 1.5mH 3000r/min 5500r/min 7.5kW 13kW 240V
requirement is reduced when PMSM system is in steady state, then inverter switching times reduction becomes ideal in order to reduce switching loss. The control method can be realized by the self-adjusting controller considering zero voltage vector. Fuzzy control technique is applied to the self-adjusting DTC strategy. Input variables of the controller are stator flux linkage error, electromagnetic torque error and stator flux linkage degree, and membership function of which are shown in Fig.3. Control variable of DTC system is inverter switching state defined as Ni. Then the ith control rule Ri can be written as follows.
Ri : if Eψ is Ai, ET is Bi and θ is Ci , then Ni. Detailed control rules are presented in Tab.III, and zero voltage vector including U0 and U7 is selected in order to reduce switching loss.
drive.
B. Self-Adjusting DTC In a DTC system, torque loop and flux linkage loop determine the performance of dynamic torque response, torque ripple of PMSM and switching loss of inverter. More quick dynamic torque response is necessary when PMSM system is in dynamic state. Moreover, the dynamic
a) Membership function of flux linkage error (Eψ)
Torque (N.m)
b) Membership function of torque error (ET)
Load angle (deg)
Figure 2. Relationship between torque and IPMSM parameters
c) Membership function of flux linkage degree (θ) Figure 3. Membership function of input variables
IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
TABLE III. CONTROL RULES CONSIDERING ZERO VECTOR
Eψ
θ
ET
θ1 U2 U1 U6 U2 U7 U6 U3 U0 U5 U3 U4 U5
P Z N P Z N P Z N P Z N
PL
PS
NS
NL
θ2 U3 U2 U1 U3 U0 U1 U4 U7 U6 U4 U5 U6
θ3 U4 U3 U2 U4 U7 U2 U5 U0 U1 U5 U6 U1
θ4 U5 U4 U3 U5 U0 U3 U6 U7 U2 U6 U1 U2
θ5 U6 U5 U4 U6 U7 U4 U1 U0 U3 U1 U2 U3
θ6 U1 U6 U5 U1 U0 U5 U2 U7 U4 U2 U3 U4
a) Acceleration time
The ith control decision based on Mamdani rule can be expressed as follows.
μ Ni′ ( n ) = min (α i , μ Ni ( n ) )
(3)
α i = min ( μ Ai ( Eψ ) , μ Bi ( ET ) , μ Ci (θ ) ) (4) Therefore, membership function of control variables can be written as (5).
μ Ni ( n ) = max ( μ Ni′ ( n ) ) III.
(5)
b) Electromagnetic torque Figure 5.
Acceleration performance of EV
SIMULATION AND EXPERIMENT
A. System Simulation Block diagram of self-adjusting PMSM DTC system in EV drive is shown in Fig.4. Based on the proposed strategy and math model [3], simulation results are given. Acceleration performance of EV with reference speed of 20km/h is shown in Fig.5, which indicates that vehicle speed can reach the reference speed in 8.5 second, electromagnetic torque keeps the maximum value during the acceleration process, and then reduces gradually near the reference vehicle speed. Electromagnetic torque and load torque are equal at the reference speed. Gradeability performance of EV with 5% degree is shown in Fig.6. With the reference creep speed of 5km/h, electromagnetic torque keeps the maximum value during
a) Vehicle creep speed
ψ s*
−
Te*
ψs
−T
e
isα isβ
ψs
ψ sα ψ sβ
θ
isα
ia
u sα u sβ
uDC
isβ
ib
b) Electromagnetic torque Figure 4. Block diagram of PMSM DTC system
Figure 6. Gradeability performance of EV
IEEE Vehicle Power and Propulsion Conference (VPPC), September 3-5, 2008, Harbin, China
the acceleration and climbing process, and then reduces gradually near the reference speed, and electromagnetic torque and load torque are equal at the reference speed. The EV can reach the reference creep speed in 7 second, and then maintain the creep speed. Good dynamic performance is obtained, and switching loss reduces due to the selection of zero voltage vector in steady state. B. System Experiment With TMS320F240 DSP and intelligent power modules, the IPMSM system with self-adjusting DTC approach is developed. In the system, the hysteresis control method is used in both torque and flux observer. An encoder is applied to measure PMSM speed. Such parameters as DC input voltage and phase current need measuring in real time to determine torque and flux. Space voltage vectors are chosen in accordance to PMSM operation mode. Waveform of IPMSM back-EMF is shown in Fig.7, and actual stator current waveform at 80 r/min is given in Fig.8. Good sine wave characteristic is helpful to improve system efficiency and reduce torque ripple. Stator flux linkage waveform at 100 r/min is shown in Fig.9. Orthogonal stator flux linkage components fluctuate
T 1>
1>
2>
1) Ch 1: 2) Ch 2:
500 mVolt 50 ms 500 mVolt 50 ms
Figure 9. Waveform of stator flux components
in a sinusoidal pattern, which illuminates that the locus of stator flux linkage is a good circular shape in space, and that is very availability to reduce the fluctuation of electromagnetic torque and electrical loss. Experiment results indicate feasibility of the proposed strategy. IV. CONCLUSION Complicated PMSM operating modes in EV drive make it difficult to acquire satisfied performance based on regular DTC method. In this paper, a self-adjusting DTC strategy combined with the fuzzy rules and zero voltage vector is presented. Simulation and experiment results prove the feasibility of the proposed strategy. REFERENCES [1]
1) Ref B:
50 Volt 5 ms
[2]
Figure 7. Waveform of IPMSM back-EMF [3]
[4]
[5] 1>
2>
[6] 1) Ch 1: 2) Ch 2:
1 Volt 200 ms 1 Volt 200 ms
Figure 8. Waveform of stator current
[7]
Jung-woo Park, Dae-Hyun Koo and etc. Improvement of Control Characteristics of Interior Permanent-Magnet Synchronous Motor for Electric Vehicle[J]. IEEE Trans. on Industry Applications..2001, 37(6): 1754~1760. Konghirun M, Xu L. A fast transient-current control strategy in sensorless vector-controlled permanent magnet synchronous motor. IEEE Trans. on Power Electonics, .2006, 21(5): 1508~1512. Jun-Koo Kang,Seung-Ki Sul, “New direct torque control of induction motor for minimum torque ripple and constant switching frequency,” IEEE Trans. on Industry Applications, vol. 35 (5), pp. 1076~1082, 1999. Zhong L, Rahman M F, Hu WY, Lim K W, Rahman M A, “A direct torque controller for permanent magnet synchronious motor drives,” IEEE Trans. on Energy Conversion, vol. 14 (3), pp.637~642, 1999. MF Rahman,L.Zhong, “Voltage switching tables for DTC controlled interior permanent magnet motor,” Proceedings of IECON'99, vol. 3 (29), pp. 1445 –1451, 1999. Faiz J, Mohseni-Zonoozi SH. A novel technique for estimation and control of stator flux of a salient-pole PMSM in DTC method based on MTPF. IEEE Trans. on Industrial Electonics, .2003, 50(2): 262~271. L.Zhong, M.F. Rahman. Analysis of direct torque control in permant magnet synchronous motor drives[J]. IEEE Trans. on Power Electronics.1997, 12(3): 528~535.
