Abstract—The dead-time effect in a three-phase voltage source inverter can result in voltage losses, current waveform distortion and torque pulsation. In order to improve the current waveform and decrease the torque pulsation, this paper proposes a dead-time compensation method of SVPWM. This method divides the αi - βi plane into six sectors and compensates the dead-time of SVPWM according to the sector number of stator current vector determined by the α - and β -axis components of the stator current vector in the two-phase static reference frame. In addition, this method can be implemented entirely through software without any extra hardware. Finally experiments based on DSP TMS320F2812 are established and made, and the experiment results indicate that the proposed method is correct and feasible.

Index Terms--dead-time compensation, SVPWM, PMSM, TMS320F2812

I. INTRODUCTION Because the permanent magnet synchronous machine

(PMSM) has a lot of advantages such as high power density, high efficiency, high torque to inertia ratio, high reliability, et al[1], therefore, the PMSM driving system have been widely used in many application fields, especially in hybrid electric vehicles (HEV) in recent years[2]-[6].

In the PMSM driving system, the three-phase voltage source inverter is usually adopted and the IGBT and MOSFET are also used because of their fast switching frequency. For the three-phase voltage source inverter, in order to avoid the short circuit of the dc link occurring when the two switch devices of the same phase are turned on simultaneously, the dead-time is usually inserted in the gate driving switch signals. During the duration of the dead-time, both of the two switch device of the same phase are turned off. The existing of the dead-time will lead to a series of dead-time effect problems such as voltage losses, current waveform distortion and torque pulsation, especially under the condition of small current or low speed.

SVPWM (Space Vector Pulse Width Modulation) is a popular modulation method for three-phase voltage source inverter in motor driving system. In order to improve the current waveform of motors and decrease the torque pulsation of motors, several dead-time compensation methods of SVPWM have been researched and used in the motor driving system[7]-[11]. Most of the

This work was supported by National Natural Science Foundation of China under Project 50707031.

compensation methods are based on the theory of average voltage deviation.

In this paper, a novel dead-time compensation method of SVPWM, which is also based on the theory of average voltage deviation, is proposed. This method divides the

αi - βi plane into six sectors and compensates the dead-time of SVPWM according to the stator current vector angle ϕ determined by the α - and β - axis components of the stator current vector in the α - β reference frame. In addition, this method can be implemented entirely through software without any extra hardware design. Finally experiments are made on the PMSM driving platform based on DSP TMS320F2812 to test and verify the proposed compensation method.

II. DEAD-TIME COMPENSATION METHOD Fig.1 shows the topology diagram of the PMSM

driving system whose invert unit adopts the three-phase voltage source inverter. In Fig.1, Q1, Q2, Q3, Q4, Q5 and Q6 are six IGBTs of the three-phase voltage source inverter, and D1, D2, D3, D4, D5 and D6 are their reverse parallel diodes respectively. In addition, the driving switch signals g1, g2, g3, g4, g5 and g6 are provided by the control unit of the driving system.

Define the phase currents ia, ib and ic are positive when they flow from the inverter to PMSM, and negative when they flow from PMSM to the inverter. There are eight switch combination states for the six IGBTs in the three-phase voltage source inverter, and during the duration of dead-time, there are correspondingly six current combination states for three-phase currents ia, ib and ic according to their polarity:

(1) ia>0, ib<0 and ic<0; (2) ia>0, ib>0 and ic<0; (3) ia<0, ib>0 and ic<0;

Fig.1. Topology Diagram of PMSM Driving System

Dead-time Compensation of SVPWM Based on DSP TMS320F2812 for PMSM

Song Xuelei*, Wen Xuhui, Guo Xinhua, and Zhao Feng Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, P.R.China

E-mail: songxl@mail.iee.ac.cn

(4) ia<0, ib>0 and ic>0; (5) ia<0, ib<0 and ic>0; (6) ia>0, ib<0 and ic>0. It is very important and difficult to detect the zero-

cross point or the polarity of each phase current. Traditionally, if the zero-cross point is detect directly through A/D converter of DSP or MCU, bigger measurement deviation will be led especially under the condition of small current, which will result in bigger dead-time compensation deviation and also affect the result of dead-time compensation. Therefore, this paper adopts an indirectly method to detect the zero-cross point of phase current, which is based on the current vector angle ϕ in the two-phase static reference frame.

For convenient analysis and illustration, place the three-phase currents ia, ib, ic in the three-phase static reference frame and the two current components αi , βi of the current vector in the two-phase static reference frame into the same figure, which is shown in Fig.2. According to the polarity of three-phase currents ia, ib, ic, the αi - βi plane in the two-phase static reference frame can be divided into six sectors: I(1), II(2), III(3), IV(4), V(5) and VI(6).

For each sector in the αi - βi plane, there is a corresponding dead-time compensation rule. In other words, once the sector which the current vector belongs to is known, the dead-time effect can be compensated according to the corresponding compensation rule. Therefore, recognizing the sector number of the current vector is the key problem.

In this paper, the sector number is determined by the current vector angle ϕ which can be calculated through the α - and β -axis components of the stator current vector. Equation (1) shows the calculation method of the current vector ϕ , and equation (2) shows the relationship between the sector number and the current vector ϕ .

)1,0()arctan( =+= kii

kα

βπϕ (1)

ai

bi

ci

αi

βi si

0>ai0<ai

0>bi

0>ci

0<bi

0<ci

ϕ

Fig.2. Current Polarity and Current Vector Angle ϕ

TABLE I DEAD-TIME COMPENSATION RULES TABLE OF SVPWM

Sector I II III IV V VI ia + + - - - +

ib - + + + - -

ic - - - + + +

Δ Ta -Tcom - Tcom + Tcom + Tcom + Tcom - Tcom Δ Tb + Tcom - Tcom - Tcom - Tcom + Tcom + Tcom Δ Tc + Tcom + Tcom + Tcom - Tcom - Tcom - Tcom

1 ( 6 6)2 ( 6 2)3 ( 2 5 6)

sector4 (5 6 7 6)5 (7 6 3 2)6 ( 2 6)

π φ ππ φ ππ φ π

π φ ππ φ ππ φ π

− < <⎧⎪ < <⎪⎪ < <⎪= ⎨ < <⎪⎪ < <⎪

− < < −⎪⎩

(2)

For three-phase voltage source inverter, the essence of dead-time compensation is to compensating the voltage deviation. However, in the digital motor driving and control system, voltage regulation is implemented through pulse width modulation, that is, through regulating the duty cycle of voltage pulse which has something to do with the pulse width T in one PWM period Tpwm. Therefore, in fact it is the pulse width T that is compensated in the practical application. TABLE I shows the dead-time compensation rules corresponding with the polarity of three-phase currents ia, ib, ic and the sector number of the current vector in the αi - βi plane. It

can be seen that for different sectors of the αi - βi plane, the compensation values are correspondingly different.

In one word, the proposed dead-time compensation method can be carried out through the following steps:

(1) Calculate the current vector angle ϕ through the α - and β -axis components of the stator current vector in the two-phase static reference frame according to equation (1).

(2) Determine the sector number through the current vector angle ϕ according to equation (2).

(3) Execute the dead-time compensation algorithm according to the compensation rules table TABLE I.

III. EXPERIMENTS In order to test and verify the proposed dead-time

compensation method of SVPWM, experiments are established and made. The experiment system consists of PMSM, three-phase voltage source inverter, control platform, dynamometer, heat dissipation system, et al. The type of IGBT in the inverter is CM600DY-24A produced by Mitsubishi. The control platform is based on DSP TMS320F2812 produced by Texas Instrument. It is a special motor control DSP which has many advantages and can implement high-performance motor control such as FOC (Field Oriented Control) and DTC (Direct Torque Control). The main parameters of the control object

PMSM used in experiments are listed in TABLE II. For different pulse width compensation values of

0.76 sμ , 1.10 sμ , 1.33 sμ and 1.60 sμ , the dead-time compensation experiments are all made. Fig.3 shows the experiment waveforms of three-phase stator currents and the sector number of stator current vector for different pulse width compensation values, and Fig.4 shows the corresponding frequency spectrums.

TABLE II

MAIN PARAMETERS OF PMSM USED IN EXPERIMENTS

Parameters Unit Value

Number of Phases - 3

Number of Pole Pairs - 5

Rated Power kw 52

Rated Speed rpm 2500

Rated Torque Nm 200

Permanent Magnetic Flux Wb 0.104

Inductance (d/q) mH 0.33/0.50

Resistance of Stator Winding Ω 0.024

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

5

10

sect

or

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

ia(A

)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

ib(A

)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

Time(s)

ic(A

)

(a) No Compensation

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

5

10

sect

or

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

ia(A

)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

ib(A

)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

Time(s)

ic(A

)

(b) Pulse Width Compensation Value = 0.76 sμ

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

5

10

sect

or

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

ia(A

)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

ib(A

)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

Time(s)

ic(A

)

(c) Pulse Width Compensation Value = 1.10 sμ

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

5

10

sect

or

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20ia

(A)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

ib(A

)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

Time(s)

ic(A

)

(d) Pulse Width Compensation Value = 1.33 sμ

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

5

10

sect

or

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

ia(A

)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

ib(A

)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-20

0

20

Time(s)

ic(A

)

(e) Pulse Width Compensation Value = 1.60 sμ

Fig.3. Experiment Waveforms of Three-phase Stator Currents

Here, the CPU frequency of DSP is set at 150MHz, the switching frequency of IGBTs in three-phase voltage inverter is set at 10kHz, the dead-time is set at 3.2 sμ through the hardware and software of DSP, the motor control method adopts FOC algorithm, the dc link voltage is set at about 330V, and the phase current is controlled at about 10 A.

0 2 4 6 8 10 12 14 160

5

10

15

Frequency Order

Mag

nitu

de(A

)

(a) No Compensation

0 2 4 6 8 10 12 14 160

5

10

Frequency Order

Mag

nitu

de(A

)

(b) Pulse Width Compensation Value = 0.76 sμ

0 2 4 6 8 10 12 14 160

5

10

15

20

Frequency Order

Mag

nitu

de(A

)

(c) Pulse Width Compensation Value = 1.10 sμ

0 2 4 6 8 10 12 14 160

5

10

15

20

Frequency Order

Mag

nitu

de(A

)

(d) Pulse Width Compensation Value = 1.33 sμ

0 2 4 6 8 10 12 14 160

5

10

Frequency Order

Mag

nitu

de(A

)

(e) Pulse Width Compensation Value = 1.60 sμ

Fig.4. Frequency Spectrum of Stator Current (Phase A)

It can be seen from Fig.3 and Fig.4 that, compared with experiment results of no compensation, through the proposed dead-time compensation algorithm the three-phase stator current waveforms of PMSM are all improved effectively and the harmonic components of three-phase stator currents are also decreased effectively. Especially when the pulse width compensation value is set at about 1.10 sμ , compared with experiment results at the other pulse width compensation values of 0.76 sμ , 1.33 sμ and 1.60 sμ , the compensation result is the best and the harmonic components of three-phase stator currents are the least. Therefore, the proposed dead-time compensation method is correct and feasible.

IV. CONCLUSIONS The proposed dead-time compensation method can be

implemented easily through software algorithm without any extra hardware design. So long as the current vector angle ϕ is determined by the α - and β -axis components of stator current vector in the two-phase static reference frame, the dead-time compensation algorithm can be carried out effectively according to the corresponding dead-time compensation rules table. Finally experiments are established and made on the PMSM driving platform based on DSP TMS320F2812 and the results indicate that the proposed method can improve the current distortion and decrease the torque pulsation effectively, especially when the pulse width compensation value is equal to about 1.10 sμ . Therefore, the proposed method is correct and feasible.

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