SVPWM Speed Governing System of IM Based on DSP

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SVPWM Speed Governing System of Induction

Motor Based on DSP

Zhiyong Du,Xianfang WangCollege of Henan Mechanical and Electrical Engineering, Xinxiang, China,453002,e-mail:[email protected] of Information Engineering/Henan Institute of Science and Technology,Xinxiang,China,453003

e-mail: [email protected], [email protected] of Communication and Control Engineering/Southern Yangtze University, Wuxi, China, 214122

Abstract Vector control technology is regard as a kindof controlling manner of AC asynchronous motor, and it isalready become the first method of the high-performancevariable-frequency speed regulating system. Compared withSPWM, SVPWM (Space Vector Pulse Width Modulation)

has been used widely because it has better performance. Thispaper introduced the basic principle of voltage SVPWM andvector control. A full-digital solution with TMS320LF2407using simplified SVPWM control method is presented.Through the experiment of controlling to a practical motor,the resulted shows that this method is feasible, the control-ling system has better dynamic and static performances andcontrolling effect, it would have a prospect widely used.

KeywordsSVPWM, Vector control, Variable-frequency

speed governing system, Dynamic and static performances,

DSP.

I. INTRODUCTION

The development and the application of Pulse Width

Modulation (PWM) technology have optimized perfor-mance of the frequency converter device, and it is applied

to all kinds of AC speed regulating system. In the special

way of vector modulation, the technology of SVPWM

modulation considers the motor and the PWM inverter as

an integer, on the base of the ideal magnetic linkage round

of AC motor of three-phase symmetrical sine voltage

supplied its power, use the effective magnetic linkage

vector produced in different switch modes of inverter to

come close to the criterion circle, that is, use a polygon to

approximate a circle[1]. The SVPWM control method has

some advanced merits compared with classical SPWM

controlling method, for example, direct physical signifi-cance, simple mathematic model, easy computer real-time

controlling, and small torque wave, low noise, simple

control, low cost of power, high effect of utilization of

DC voltage. At present time, this technology would be

applied widely whether in open loop or closed loop speed

governing system.

The traditional SVPWM algorithm adopts largely

trigonometric functions and other nonlinearity functions.

When realized, it would need compute the vector effect

time and store a mass of data in advance [2]. But these

compute is complex, the processing is also very difficult,

therefore, it would be not easy to realize the digital real-

time controlling especially.In this paper, we introduced a simplified SVPWM al-

gorithm, which can realize a conversion speed regulation

system of influence motor. The theoretical analysis and

the experiment results show that this system has some

characteristics, such as realized simply, high utilization

ratio of voltage and small harmonic current, and so on.

Therefore, if adopted this system, the operation quality

of the induction motor would be improved greatly, these

results illustrate that this system would have some higher

practical values.

II . WORKING PRINCIPLES OF SVPWM

A. The Relationship Between Voltage Vector and Mag-

netic Linkage Vector

Where, we suppose that the AC induction motors

power is supplied from an ideal three-phase symmetrical

sine voltage, these stators phase voltage USA , USB , USCis add on three-phase coils respectively, their direction is

always on the axis of each coil, and its value is exchanged

in sine rule following on the time. That is

USA = UA UNUSB = UB UNUSC = UC UN

(1)

In this formula, UA, UB, UC are the three-phase phasevoltage of the inverter output; The Un is the voltages

of the midpoint O that relative to negative potential of

the inverter DC side when the stator winding is star

connection.

The US which is synthesized with the voltage spacevector of the stator winding is as follows

US = USA + USB + USC= 2

3(USA + USB ej

2

3 + USC ej

4

3)

= 23

(UA + UB ej 23 + UC e

j 43)

(2)

The above formula indicated: (1) The voltage space

vector Us that synthesized by three phase voltage space

vectors addition is a space vector rotating with power

source angle frequency speed. (2) In the PWM inverter-

motor system, the analysis of motor stator voltage space

vector can change into the analysis of inverter space

vector [3].

In the same way, we can define the magnetic linkage

space vector S is

S = SA + SB + SC (3)

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If ignoring the effect of resistant motor stator, then Scan be obtained by integral the voltage space vector to

time.

When the inverter outs put a voltage space vector

Ui(i = 0 7), the magnetic linkage space vectors S canbe expressed as follows:

S = S0 + Ui t (4)

In this form, S0 is an initial magnetic linkage spacevector, is the action time of Ui .

When Ui is a nonzero voltage vector, the magnetic link-age space vector sets off from initial location, whirligig

with the radius

2

3Ul

along the corresponding voltage

space vector direction. While Ui is zero voltage vector,S = S0, the magnetic linkage space vector motion isrestricted. Therefore, chose the operator order and work

time of six nonzero voltage space vector rationally, that

would make the space vectors head turning in clockwise

or in anticlockwise, and would become the certain shape

trace. Choose the different form, being the different

magnetic linkage locus. In general, it makes the magnetic

linkage locus approach a regular polygon or circular.

B. Mathematic Model of Voltage Form PWM Inverter

The power circuit adopted topology structure of the

three-phase voltage class inverter, as show in Fig.1 .The

Up and down switch component s of the inverter bridge

arm cant pass at any the same time. These switch would

be reciprocal state when we dont consider the died area,

Sa, Sb, Sc express three bridge arms state respectively,

1 indicated that the up-bridge arm pass, and 0 in-dicated that the down-bridge arm pass. UA, UB, UC arethe three-phase voltage outputs,Take pursuing negative

voltage shown by Fig.1 as a reference point, We canobtain:

UA = SaUdc, UB = SbUdc, UC = ScUdc

o

A

B

CS c

1 3 5

264

7

+

--

U dc Sa

Sb

Fig. 1. PWM inverter circuit.

Change the three-phase voltage to two-phase dq axissystem according to Clark Transform:

UdUq

=

2

3

1 1

2

1

2

03

2

3

2

UAUB

UC

(5)

The inverter has 8 kinds switch patterns, which

are 000, 001, 010, 011, 100, 101, 110 and 111. So,

we could obtain the 8-voltage space vectors:U0, U60, U120, U180, U240, U300, O000, O111. In thesevectors, O000 and O111 are zero vectors. The Fig.2 isinverters spatial distribution of the eight voltage space

vectors.

d

q

O 000

O 111

U 60 (110)

U 0(100)

U 120 (010)

U180(011)

U 240 (001) U 300 (101)

Fig. 2. Voltage space vectors.

C. Control of Magnetic Linkage Track

While the inverter output the basic voltage space vector

U0 alone, the arrow of the stator linkage vector wouldmove from A to B alone the direction of parallel U0,as show in Fig.3. When moving to B, if we changethe basic voltage space vector into U60, then the vectorarrow of the stator linkage vector also moving fromB to C in correspondingly. In this way, when 6 nonzerovoltage space vectors export alone in turns respectively,

the moving track of the head of stator linkage vector is a regular hexagon, as show in Fig.3.

U 0

U60U120

U180

U240 U300

01

2

34

5

A B

C

DE

F

Fig. 3. Regular hexagon magnetic linkage track.

But there are only six basic nonzero voltage space

vectors, if we want obtain polygon rotating magnetic field

as more as possible, it must has more switch states. One

commonly method is that it can obtain more switch states

use the linearity time combination of these six nonzero

basic voltage space vectors. The basic control principle

was shown as follows.

In Fig.4, Ux and Ux+60 are represent two adjacentbasic vectors of voltage space, Uout is the reference phasevoltage vector of the output, whose amplitude represents

the phase voltage amplitude, whose revolution angular

velocity is to export sine voltage angle frequency. Uoutwas come from the linearity time composed by Ux andUx+60, it is equal to vector sum of

t1TPWM

times Ux

and t2TPWM times Ux+60. Of which, t1 and t2 is the operatetime ofUx and Ux+60 respectively, TPWM is effect timeofUout.

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600

xPWM

UT

t 1

602

+x

PWM

U

T

t

d

q

U x

U x+ 60

U out

Fig. 4. The linearity combination of the voltage space vectors.

D. Calculation of the Voltage Vector Operating Time

As mentioned above, the voltage space vector of lin-

earity time combination is

Uout =t1

TPWMUx +

t2TPWM

Ux+60 (6)

In above formula, we projected Uout, Ux and Ux+60to coordinate system 0dq[4]. This formula may be wrotedown:

t1t2

= TPWM

Uxd Ux+60dUxq Ux+60q

1 UoutdUoutq

(7)

After when we would have

obtained Uxd Ux+60dUxq Ux+60q

1

,then can ascertain t1

and t2 right away.In Fig.3, when the inverter alone output zero vectors

O000 and O111, the magnetic linkage vector of themotor stator would be fixedly. According to theses char-

acteristic, intervene the zero vector effects t0 in TPWMperiod, make

TPWM = t1 + t2 + t3 (8)

By such method, it can adjust the angle frequency , andobtain frequency conversions purpose.

E. Ascertain Sector Number

We apart the Fig.3 into six sectors, every sector has asector No.(as show in Fig.3, 0, 1, 2, 3, 4, 5). Only whenwe have known which sector that Uout is located in, thencan ascertain which pair of adjacent basic voltage space

vector would be used to compose Uout.After Uoutd and Uoutq were given, we should calculate

B0, B1, B2 at first.

B0 = UoutqB1 = sin 60

0Uoutd sin 300UoutqB2 = sin60

0Uoutd sin 300Uoutq

(9)

Then calculate the P value

P = 4sign(B2) + 2sign(B1) + sign(B0) (10)

In the form, the sign(x) is a sign function. If x > 0,sign(x) = 1; x < 0,sign(x) = 0.

Finally, according to P value table and look-up TableI,then we can ascertain sector number.

TABLE I

P VALUE AND SECTOR NUMBER RELATION

P

Sector

654321

1 5 0 3 2 1

If we adopt above algorithm, it only needs the plus

minus and logical computation simply, then can ascertain

the location sector where the reference voltage vector be

in, and avoided calculating the complicated nonlinearity

function, this feature have an actual meaning for simpli-

fied the calculation and improve the response speed of

the system. Not only it can decrease the requirement for

controller calculation speed, but also the real time controlcan be realized easily.

III. REALIZATION OF SVPWM ARITHMETIC

THROUGH DSP

A. Event Manager of TMS320LF2407A DSP [5]

Event manager (EV) is a special module, which was

designed for controlling the motor. It can produce all

kinds of PWM waves, and these waves can adjust the

blind area. It can measure the rotating speed, divert and

angle displacement of the motor by the interface of the

increment photo-electricity coder, and measure the pulse

width by capture the power.There are 2 Event mangers in TMS320LF2407A DSP,

which are EVA and EVB. Every event manger has 2 gen-eral timers of16bit, has 8 pulse width modulation passesPWM of 16bit. 3 comparing units with programmingbead area control can produce 3 pairs of absolutely PWMwaves (ie.6 outputs), these 2 timers can produce 2 kindsabsolutely PWM waves. They could be realized: output

the symmetrical and asymmetric PWM wave; avoid out-

put pulse at the same time in up and gown bridges. During

the application of the motor controlled, the PWM circuit

could reduce the CPU overhead for producing PWM

wave and the workload of the user, also could simplifythe control soft for produce the symmetrical pulse width

modulation and symmetrical hardware.

B. Method of Output PWM Wave

We designed the method for produced PWM wave use

the periodic value of the periodic register and the com-

pared value of the comparator based on TMS320LF2407A

DSP. The periodic value is used to produce PWM wave

frequency (or period), the compare value is mainly used

to produce PWM wave pulse width.

According to using different comparator, there are two

methods to produce PWM wave: One use the timer

and the comparison register to realized, another use thecomparison unit to come true. The PWM wave that the

latter produced can add a blind spot.

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For obtained an output Wave with ideal form, it is

necessary not only set the value of control correctly, but

also need adopt the correct algorithm. For output the

space vector PWM wave, the consumer need sets up

the following register (choose the EVB module): 1)Setthe comparative form control register ARCTRB to define

output form of the compare output part. 2) If enablethe blind port, then must setup the blind port control

register DBT-CONB. 3) Setup the register of timer no.3speriod T3PR, that is the period of stipulating the PWM

waveform. 4) Initialize the comparison register CMPR4 6. 5) Set the comparison control register COMCONBto enable to the compare operation and the pattern of

the space vector PWM. 6) Set the timer no.3 to controlregister T3CON working in continuing increasing/ the

subtraction pattern [6, 7].

C. Seven Sections of Voltage Space Vector SVPWM Wave

To obtain a certain voltage of output, in a on-off cycle,whether how the switch order of the 3 switches state,it is OK if only the relation that was kept between the

switchs state in time was satisfied (7) and (8), this is

not limited for the precedence order of 3 kinds switchstates and the start time, so the optimized control may be

realized that reduced the number of these switch action

and the harmonic wave.

We may arrange the change order of 8 switch states inevery fan sector according the Table II when for making

the inverter change from a switch state to another switch

state, only change a bridge arm switch state, so that to

cut down the number of on/off times in the inverter.

TABLE II

THE STATE ALTERNATION ORDER OF SYMMETRICAL SVPWM

SWITCHES

Time

Sector

0

1

000

5

4

2

3

000

000

000

000

000

011001

011010

111110010

000100110111110100

110

111

111

111

111

101

101

100

001 101

011

101

011

001

000

000

010

010

000

000

000

100

001

T0 /4 T

0/4T

2 /2 T

2/2T

0 /2 T

0/4T

1/2

From Table II, we could know that the 3phase PWMwaves, which produced by symmetrical voltage space

vector, have some features as follows:

(1) Every phase and every PWM waves output only

makes the switch power tube switch one times.

(2) The positive and negative rotate of the motor is only

related to the choice of the fan sector.

(3) Every PWM wave all start and end at the zero

vectors O000, the zero vectors O111inserts in center, andthe zero vectors O000 and O111have the same effects

time.(4) The program of the motor revolution magnetic field

approaches circular is determined by the choice of the

sector TPWM. TPWM would be smaller, the magnetic

field would be more approached circular, but the Tzdecrease is limited by the allowed switch frequency of

the switch component.

(5) Compared with SPWM, its DC voltage utility factor

should be high 0.15, while the output voltage regulatingand controlling, the harmonic wave can be cut down in

an output voltage.

Adopted the control of the voltage space vector PWM,

could avoid unnecessary switch action, reduce switch

frequency, it could cut down the depreciation of the switch

by arranged the zero vectors meticulously.

D. DSP Software Designs of SVPWM Wave

In the program design of the SVPWM wave that

controlled by DSP, the modulation wave frequency was

input by exterior, the carrier frequency and the sampling

frequency are all 20 MHz. The function of frequency (its

domain:0

50HZ) and blind spot would be designed andrealized. The blind spot time is 1.6s, the crystal frequencyof the DSP is 10 MHz, 2 tomes frequency inside, the clockfrequency is 20 MHz, and the counting period is 50ns.

The program is composed of the main program and

the subprogram of the timer underflow interruption. The

task of the main program is initialization, and change

the adjusted ratio of the outside entering frequency into

angle frequency. According to U/F, determine amplitude

of the reference voltage. The function of the interruption

subprogram is work out the value of three comparison

registers in next PWM period during every PWM period,

and is send these values to the comparison register.

For this purpose, t0, t1 and t2 must be calculated outaccording to form (7) and (8).

Save scene

Compute the cornerincrease and reference

voltage phase angle

In the secondquadrant

In the first quadrant

In the third quadrant

SS=1,SC=1

SS=1,SC=-1

SS=-1,SC=-1

SS=-1,SC=1

Lookup table of sinand cos ,

And add the signal symbol

ComputeUoutd andUout according to

amplitud and phase angle

Computesector value

Compute address

of the inverse matrix

lable

Compute the head

address of the inverse

matrix lable

Compute the comparative value

0.5C1CMP- 1

0.5C2CMP- 20.25C0CMP-0

Send CMP- 0 to the firs t

Comparative register

Send CMP-0+CMP-1 to the first

Comparative register

to the firstComparative register

Restore scene

Y

N

N

N

Y

Y

Send CMP-0 +CMP-1+CMP-2

Fig. 5. The program flow graph of the timer interruption subprogram.

For programming easily, the period value of the peri-

odic register is equal to TPWM/2, and the Form (7) can

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be simplified:

0.5C10.5C2

=

Uxd Ux+60dUxq Ux+60q

1 UoutdUoutq

(11)

Where,C1 =t1

TPWM/2, C2 =

t2

TPWM/2.

The program flow graph of the timer interruption

subprogram as show in Fig.5

IV. EXPERIMENT RESULTS

Adopting the system designed in this paper, an exper-

iment was carried on with for a 1KW induction motor.These parameters are as the following: the carry frequency

is 20KH z, and the DC bus voltage is 70V.

(a) 30 Hz

(a) 50 Hz

Fig. 6. Current waves of each coil in different frequency.

When the DC bus voltage is 70V, In Fig.6, it shows thecurrent wave of the coil in different frequencies. From this

figure, it is seen clearly that the current wave of the coil

approaches the sin wave. Fig.7 shows the voltage wave

of the coil in different frequencies. From the figure, it isseen clearly the mutual difference of these line voltage of

coil is 1200.

V. CONCLUSION

In this paper, we adopted TMS320F2407 to design a

frequency speed control system of induction motor based

on SVPWM controlling. This is a new method to realize

the Variable-frequency speed governing system. Through

the experiments, it is indicated that this system could

improved the performance of the produced PWM wave in

the condition of non-increase the switch depreciation. At

the same time, it showed that square wave was output by

the wave generator of TMS320LF2407DSP event managemodule, this method simplified the development of soft

and hardware. And the quality and the robust of the

(a) 30 Hz

(a) 50 Hz

Fig. 7. Line voltage waves of each coil in different frequency.

SVPWM wave were also very good. These results illus-

trated that the system has a high control precision and has

good performances of dynamic and static. So, the above

method would have a certain value of popularization and

application..

REFERENCES

[1] Wang Xiao Ming et al, The electric motor DSP is controlled,Press of Beijing University of Aerospace, Beijing, China, 2004.

[2] B.K.Bose, Modern Power Electronics and AC Drives, Mechan-ical industry Press, Beijing, China, 2005.

[3] Huade Li, AC Speed Governing Controlling System, Press of electronic industry, Beijing, China, 2003.

[4] TI Company, AC Speed Governing Controlling System,TMS320LF2407A,TMS320LF2406A, DSP Controllers2002.

[5] Tiezhu Xu, Guoqing Xu, The AC speed regulation controls systembased on the DSP, Electric system and Automatic Proceedings,China, 2002, 14 (6).

[6] li Lin , Xiaojing Li, Yunfeng Jiang, SVPWM vector controls digiti-zation frequency speed regulating system base on DSP, Middle-Mini-type electric motor, China, 2004, 31 (5).

[7] [7] Yang-Gui Jie, Space vector pulse broad modulation methodresearch, Proceedings of the Chinese Society of ElectricalEngineering, China, 2001, 21 (5).

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SVPWM Speed Governing System of IM Based on DSP

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