IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-22, NO. 4, JULY/AUGUST 1986

A Novel Control Scheme for Current-ControlledPWM Inverters

AKIRA NABAE, MEMBER, IEEE, SATOSHI OGASAWARA, AND HIROFUMI AKAGI

Abstract-A high-performance current-controlled inverter must have aquick current response in transient state and low harmonic currentcontent in steady state. However, in general, these requirements contra-dict each other. A novel control scheme is proposed which is based on thecurrent deviation vector and satisfies both requirements. Experimentalresults showed good agreement with the anticipated performance.

I. INTRODUCTION

HE CURRENT CONTROL strategy plays a mostlimportant role in current-controlled PWM inverters inwhich quick current response and low harmonic currentcontent to suppress torque ripples and acoustic noises arerequired. However, these two requirements contradict eachother. That is, the switching mode, having a high currentderivative, must be chosen to produce the high-speed currentresponse while the switching mode, having low currentderivative, must be chosen to suppress the high currentharmonic content. For the latter purpose, many controlscheme have been published. For example, Holtz et al.proposed the predictive controller [8], and it is an excellentcontrol scheme. However, this controller is not simplebecause it includes complicated calculations.

In this paper the authors propose a novel control schemewhich is not a predictive control but a feedback control. It isable to suppress the high harmonic current in steady state andalso solve the quick current response problem in transientstate.

Fig. 1. PWM inverter circuit.

TABLE IRELATIONSHIPS BETWEEN v(k) AND (Sn, Sv, SW)

v(k) k=O k=I k=2 k=3 k=4 k=5 k=6 k=7

(S. S, S.) 000 100 110 010 011 001 101 111

= 0. Next, the current deviation vector Ai is defined as

Ai=i*F-i

where 1* is the current reference vector. Substituting (2) into(1) produces

LdAi/dt + RAi= (Ldi*/dt + Ri* + eo) - v(k). (3)

II. PRINCIPLE OF CONTROL STRATEGY

Fig. 1 shows a voltage source inverter circuit. The voltageand current equation is expressed as follows:

v(k) =Ldi/dt +Ri+ eo

Generally, RAi can be neglected, compared with LdAildt.Expressing the parentheses on the right side of (3) as e, thefollowing equation are derived:

LdAi/dt e - v (k)(1)

where i is the current vector and eo is the inner induced voltagevector in the load-side. v(k) shows the inverter output voltagevector, and there are eight kinds of u(k), corresponding to theon-off state of the switching devices, as shown in Table I. InTable I, one or zero of switching functions Su, Su, S,,corresponds to the mode in which the upper side device or thelower side device is on-state, respectively. Then, v(O) = v(7)

Paper IPCSD 85-58, approved by the Industrial Drives Committee of theIEEE Industry Applications Society for presentation at the 1985 IndustryApplications Society Annual Meeting, Toronto, ON, Canada, October 6-11.Manuscript released for publication December 21, 1985.The authors are with the Faculty of Engineering, Technical University of

Nagaoka, Kamitomioka-cho, Nagaoka, Niigata, Japan 949-54.IEEE Log Number 8608162.

(4)

e=Ldi*/dt + Ri*+eo (5)

where e means a counter EMF vector at the load terminals,when i = i* is assumed. That is, e is the voltage vector whichlets the load carry the current i* without any current deviation.However, the inverter can output only one voltage vector outof the eight discrete voltage vectors.

Equation (4) shows that dAi/dt is determined by the choiceof v(k). Here, dAi/dt is the most important variable whichcommands the harmonic current content in the steady state andthe current response in the transient state. From (4), LdAi/dtis shown as Fig. 2, when e is detected in the region betweenu(1) and v(2). Fig. 3 shows the deviation-current derivativevectors, derived from Fig. 2. In order to let Ai be smaller, it isnecessary to choose an output voltage vector v(k) such that the

0093-9994/86/0700-0697$01.00 © 1986 IEEE

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(2)

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-22, NO. 4, JULY/AUGUST 1986

U

W(6) V/(21

W 4)

Fig. 2. Output voltage vector v(k) and ILdAi/dt k'

k=3

k=2

Iddti 5

k=6

Fig. 3. Current deviation derivatives IdAi/dt Ik*

corresponding IdAi/dtlk has the opposite direction compo-nent to Ai. Next, assume that the Ai vector is detected in theposition shown in Fig. 3. Then, k = 5 having the largestopposite direction component to Ai is chosen to attain thequick current response, and k = 0 or 7 having the smallestopposite direction component is chosen to suppress theharmonic current. This is the principle of the proposed currentcontrol strategy.

III. SELECTION OF SWITCHING MODE TO SUPPRESS HARMONICCURRENT

A. Selection of Switching Mode

To suppress the harmonic current, it is necessary to choosea switching mode so as to give small dAi/dt. Therefore, theswitching mode to be chosen is limited to the vertices of thetriangle including e, as seen in Fig. 4. That is, if e is detectedin region [I], then the switching mode is chosen out of k = 0,1, 2, 7. Next, it will be explained which mode should bechosen out of the four modes corresponding to vertices of thetriangle including e. It is determined by the position of the Alvector.

In Fig. 4, if the current deviation vector Ai increases in theopposite direction to ldAi/dt lk = 1, the mode k = 1 shouldbe chosen. That is, in Fig. 5, if Ai is detected in regions 0,

0, the mode v(l) is chosen. Fig. 5 shows the region to whichAi belongs. Similarly, if Ai increases in the opposite directionto IdAi/dt k = 2 or IdAi/dtlk = 0, 7, that is, if Ai is detectedin 0, 0) or in 0, 0, then the mode v(2) or v(0), v(7) shouldbe chosen, respectively. (The mode k = 0 or k = 7 isdetermined by judging which mode causes less switching over,compared with the present mode.) If Ai is kept within thehexagon of 6, the switching over does not occur. It isimportant that the v(k) chosen by this method makes lAilsmaller wherever the position of e is within the triangle of [I].

V/(6)VV/n 2)VA6 jK=2 W2~~~K=

Vlo5 )

V/A4)Fig. 4. Hexagon for region of e.

Irk=o 1lEEk-07

Cvik=6 /

CI]k= 2CEM] k= 3C[V] k=0,7

tI]k=0,7 /CR) k= 4[VI k= 5

Fig. 5. Hexagon for region of Ai (e: [I], [III], [V]).

When e belongs to regions [III], [V], the choice of switchingmode is the same as mentioned earlier.When e belongs to regions [II], [IV], [VI], the choice of

switching mode takes place as shown in Fig. 6. In order tojudge the region of Ai, the circuit is easily composed ofcomparators judging the polarity and amplitude of each phasecurrent deviation Aiu, Ai,, and Ai,.

Table II summarizes the relationships among the region ofe, the region of Ai and u(k) to be chosen. In Table II, [I] -

[VI] are the regions of e vector as shown in Fig. 4 and 0 -

0 are the regions of Ai vector as shown in Figs. 5 and 6. Inboth figures, 6 expressing the size of the Al hexagon shows thewindow width of the window comparators [9], and it relates tothe average switching frequency. That is, lAil is regulated soas to be within the 6 value.

Fig. 7 shows the switching frequency feedback circuit. InFig. 7, f,,* is the reference switching frequency to bedetermined by the switching device characteristics, and fs, isthe feedback switching frequency. Both frequencies arecompared, and the deviation is integrated. The output of theintegrator increases, then 6 becomes smaller. On the contrary,it decreases, then 6 becomes larger. As a result, the averageswitching frequency is equalized to the reference switchingfrequency.

B. Detection of the Region to which e BelongsTo determine the switching mode, it is necessary to detect

the region of the e vector. As mentioned earlier, it is possibleto keep IAiI within 6 value even if the e vector belongs to anyposition among [I] - [VI] shown in Fig. 4. Therefore, it isnecessary to detect only the triangle to which e belongs and notto detect the amplitude and the correct position of e. Here,each phase deviation current is expressed by the new x, y, zaxes rotated clockwise 30° to the u, v, w axes. The followingrelation exists between two coordinates:

[Zj 4 °-1 I ](6)

698

NABAE et al.: CURRENT-CONTROLLED PWM INVERTERS

[I] k=2[W] k=0,7

\ V[I] k=1

LnD k=0,7'0[V] k=5[L] k=66

/ [IElk=3E[W]k= 4

C][k=0,7

Fig. 6. Hexagon for region of Ai (e: [II], [IV], [VI]).

TABLE II

REGION Ai, e, AND SWITCHING MODES

Region Region of A iof e 0i 0 0

[I] 1 2 2 0, 7 0, 7 1[II] 2 2 3 3 0, 7 0, 7[III] 0, 7 3 3 4 4 0, 7[IV] 0, 7 0, 7 4 4 5 5[V] 6 0, 7 0, 7 5 5 6[VI] 1 1 0, 7 0, 7 6 6

ff9*Fig. 7. Switching frequency feedback circuit.

Consider two cases when the present value of k is 0 or 7, or

when k has the values of 1 - 6.1) When k = 0, 7: The vector e and the vector LdAi/dt are

equal from (4). Then, the region of e is uniquely detected byonly the sign (plus or minus) of the deviation-currentderivatives on x, y, z axes.

2) When k = I 6: As explained in the previousparagraph, the switching mode is chosen out of four modescorresponding to the vertices of the triangle including e.

Therefore, if the output voltage is v(l), it can be regarded thate belongs to the region [I] or [VI]. The sign of the deviation-current derivative on the z axis is used to judge the region [I]or [VI]. Plus or minus sign corresponds to the region [VI] or

[I], respectively, from (4). In the case of k = 2 - 6, theregion of e is also detected in the same way. Table IIIsummarizes the results.

In both case, notice that only the sign of dAi/dt is used andthe amplitude of dAi/dt is not used to detect the region of e.

This means that the e detection circuit can be composed of a

simple configuration.

IV. SWITCHING OVER TO QUICK RESPONSE CURRENT CONTROLSCHEME

If Ai becomes large in transient state, it is necessary toswitch over to the quick response current control system. Forthis, it is necessary to choose the switching mode in which thedAi/dt has the largest opposite direction component to Ai, as

TABLE IIIDETECTION OF e

u(k) Ai' Ail Ai' ex y z

0,7 1 0 0 [I]1 1 0 [II]0 1 0 [III]0 1 1 [IV]0 0 1 [VI1 0 1 [VI]

1 - - 1 [VII- _ 0 [II

2 - 0 - [I]_ 1 - III]

3 1 - - [II]0 _ _ [III]

4 - - 0 [III]- - 1 [IVJ

5 - 1 - [IV]- 0 - [V]

6 0 - - [V]1 - - [VI]

Zero indicates minus, one indicates plus.

mentioned in Section II. The mode is uniquely determinedfrom the region of Al as shown in Table IV. In Fig. 8, the twohexagons of Al are shown. A relationship exists between thetwo references; that is, h = 6 + a, where a is some margin.If Ai passes through the h hexagon, then the control system isswitched over from the harmonic current suppression controlsystem to the quick response current control system.

V. SYSTEM CONFIGURATION

Fig. 9 shows the control circuit configuration. Each phasecurrent deviation is attained from the difference between eachphase current reference and each phase feedback current. Theregion to which At belongs is judged by the vector compara-tor. The sign of each phase deviation current derivative andpresent switching mode are input to ROM1, and the region towhich e belongs is judged by Table III. The signals of regionsAl and e and the present switching mode are input to ROM2.The switching mode which gives the low harmonic currentcontent is chosen by Table II. The mode to attain quick currentresponse is chosen by Table IV through the output signal of thevector comparator, and it is switched over through the Aiamplitude comparator and compared with the reference valueh. The comparator of fs and fsA' calculates 6 and keeps theaverage switching frequency constant. The low-pass filter (50,uts) in the e region detection circuit is effective in killing thenoises caused by the derivator. Fig. 10 shows the experimental1l.5-kW permanent magnet synchronous motor servo system.The motor ratings are given in Table V.

VI. EXPERIMENTAL RESULTS

A. Steady StateFig. 11 shows the comparison of harmonic current between

the conventional hysteresis comparator control scheme and theproposed control scheme in steady state. Both average

699

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. IA-22, NO. 4, JULY/AUGUST 1986

REGION OF AiTABLE IV

AND SWITCHING MODE (QUICK CURRENT RESPONSESYSTEM)

Ai v(k)

o 1o 2o 3o 4( 50 6

'I

Fig. 8. Hexagon to switching over two states.

. to drivecircuit

_v

0F

Fig. 9. Control circuit configuration.

m

PS: Position Sensor

TG: Tacho GeneratorFig. 10. Experimental ac servo system.

TABLE VRATING OF PERMANENT MAGNET SYNCHRONOUS MOTOR

Rated output 1.5 kWRated speed 1200 r/minRated current 12.6 A (crest value)Number of poles 4Armature resistance 0.75 0Armature inductance 5.8 mHArmature linkage flux due to

permanent magnet 0.35 WbMoment of inertia 50.1 kg cm2

switching frequencies are 2 kHz. The proposed controlscheme shows lower harmonic current content.

Fig. 12 shows the comparison of the motor acoustic noiselevel between both control schemes in the "no-load" opera-tion. The proposed control scheme shows the lower acousticnoise level, especially in the low-speed region.

B. Transient State

Fig. 13 shows the transient response characteristics. High-speed current response of about 2 ms is attained to about 60 A

700

NABAE el al.: CURRENT-CONTROLLED PWM INVERTERS

f=OHz 6A/div.2ms/div f=OHz 6Aldiv.2ms/div

(a) (b)

Fig. 11. Comparison of harmonic current in steady state. (a) Hysteresis

comparator control scheme. (b) Proposed control scheme.

2

al

60

56

52

48

hysteresis comparatorcontrol scheme

mproposedcontrol schemce

0 300 600 900 1200 1500

rotor speed Erpmn

Fig. 12. Comparison of noise levels.

60_-60rpm

-20ms- 20ms -

~~~600WMn0- o C =

6-' 60

iu 60A 60A4

0-1-(a) (b)

Fig. 13. Transient response characteristics. (a) Hysteresis comparatorcontrol scheme. (b) Proposed control scheme.

step variation in both control schemes. Also, the lowerharmonic current content is seen in the proposed controlscheme. That is, this control scheme has excellent controllabil-ity in both transient state and steady state by switching over

both states.

VII. CONCLUSION

The authors propose a novel control scheme for current-controlled PWM inverters. It has high-speed current responsecharacteristics in transient state and low harmonic currentcontent in steady state. The features of the proposed controlscheme are summarized as follows. 1) The circuit configura-tion is simplified by using the feedback control and ROM's. 2)It is independent of the load constants. 3) The averageswitching frequency is kept constant. 4) The output harmoniccurrent content is decreased, and the low acoustic noise leveldrive system is realized. 5) High-speed current response is

attained in the transient state. Experiments using the perma-

nent magnet synchronous motor servo system verified these

conclusions.

REFERENCES

[1] K. R. Jardan, S. B. Dewan, and G. R. Slemon, "General analysis of

three-phase inverters," IEEE Trans. Ind. Gen. Appl., vol. IGA-5,pp. 672-678, 1969.

[2] V. K. Heintze, H. Tappeiner, and M. Weibelzahl, "Pulswechselrichter

zur Drehzahlsteuerung von Asynchronmachinen," Siemens Rev., vol.

45, no. 3, p. 154, 1971.

[3] A. Schonung and D. Stemmler, "Static frequency changers with

subharmonic control in conjunction with reversible variable speed ac

drives," Brown Boveri Rev., pp. 557-577, Aug./Sept. 1974.

[4] A. Abbondanti, J. Zubek, and C. J. Nordy, "Pulse width modulated

inverter motor drives with improved modulation," IEEE Trans. Ind.Appl., vol. IA-Il, pp. 695-703, 1975.

[5] G. S. Buja and G. B. Indri, "Optimal modulation for feeding ac

motors," IEEE Trans. Ind. Appl., vol. IA-13, pp. 38-44, 1977.

[6] A. B. Plunkett, "A current controlled PWM transistor drive," in

IEEE-IAS Conf. Rec., 1979, pp. 785-792.

[7] G. Pfaff, A. Weschta, and A. Wick, "Design and experimental results

of a brushless ac servo-drive," in IEEE-IAS Conf. Rec., 1982, pp.692-697.

[8] J. Holtz and S. Stadtfeld, "A predictive controller for the stator current

vector of ac machines fed from switched voltage source," in JIEE

IPEC-Tokyo Conf. Rec., 1983, pp. 1665-1675.

[9] D. M. Brod and D. W. Novotny, "Curren, control of VSI-PWM

inverters," in IEEE-IAS Conf. Rec., 1984, pp. 418-425.

[10] A. Kawamura and R. G. Hoft, "Instantaneous feedback controlled

PWM inverters with adaptive hysteresis," IEEE Trans. Ind. Appl.,vol. IA-20, pp. 769-775, 1984.

[11] P. D. Ziogas, E. P. Wiechmann, and V. R. Stefanovic, "A computeraided analysis and design approach for static voltage source inverters,"in IEEE-IAS Cenf. Rec., pp. 900-907, 1984.

Akira Nabae (M'79) was born in Ehime Prefec-

ture, Japan, on September 13, 1924. He received

the B.S. degree from Tokyo University, Tokyo,Japan, in 1947, and Dr.Eng. degree from Wasada

University, Japan.He joined Toshiba Corporation in 1951. From

1951 to 1970, he was engaged in the research and

development of rectifier and inverter technology at

Tsurumi Works Engineering Department. From

1970 to 1978, he was involved in research and

development of power electronics, especially ac

drive systems at the Heavy Apparatus Engineering Laboratory. Also, from

1972 to 1978, he was nonoccupied Lecturer of Waseda Uriversity, Japan.Since 1978, he has been a Professor at the Technological University of

Nagaoka, Japan. He is now interested in the energy conversion and control

systems.Dr. Nabae is a member of the Institute of Electrical Engineers of Japan.

Satoshi Ogasawara was born in Kagawa Prefec-

ture, Japan, on July 27, 1958. He received the B.S.

and M.S. degrees in electrical and electronic engi-neering for Technological University of Nagaoka,Niigata, Japan, in 1981 and 1983, respectively.

Since 1983, he has been an Assistant Professor at

the Technological University of Nagaoka. He is

engaged in research on ac drive systems.

.l lMr.Ogasawara is a member of the Institute of

lElectrical Engineers of Japan.

Hirofumi Akagi was born in Okayama Prefecture,Japan, on August 19, 1951. He received the B.S.

degree from Nagoya Institute of Technology, Na-goya, Japan, in 1974 and the M.S. and Ph.D.

degrees from Tokyo Institute of Technology, To-

kyo, Japan, in 1976 and 1979, respectively, all inelectrical engineering.

Since 1984, he has been an Associate Professor at

the Technological University of Nagaoka, Japan.He is engaged in research on ac motor drive systemsand reactive power compensator systems.

Dr. Akagi is a member of the Institute of Electrical Engineers of Japan.

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