rotor field oriented control strategy with harmonic currents closed-loop control for five-phase...

ISSN 1068�3712, Russian Electrical Engineering, 2014, Vol. 85, No. 5, pp. 334–343. © Allerton Press, Inc., 2014.

334

1 1. INTRODUCTION

With the advancements of modern power electron�ics technology and motor control theories, theinverter�feed driving technology of motor removes thelimitation on the number of motor phase. In recentresearches, multiphase motors are gaining more andmore attentions due to their advantages of improvedtorque quality, reduction of stator current per phaseand increase of fault tolerance. Multiphase motors,with the merits stated before, are applied widely, espe�cially on ship propulsion, electric vehicle, and aero�space and so forth.

Multiphase motor possesses plenty of advantageswhen compared to their three�phase counterparts.Firstly, for the given machine’s output power, mul�tiphase motor can reach it with low�voltage powerdevice easily, while conventional three phase motorhas to use high�voltage power device to gain the samepower. Secondly, the torque ripple of multiphasemotor is ameliorated, by reducing its’ amplitude andincreasing its’ frequency. Thirdly, multiphasemachines’ fault tolerance is superior to three�phasemachines, based on the fact that multiphase motorspossess a larger number of redundancy phases, whichgenerally means the improved reliability [1–3]. Thelast but not the least, more phases in multiphasemachines brings about more control freedoms, which

1 The article is published in the original.

means the control strategy of machines can be morediversity and precise [4].

The growing interest in multiphase electrical driveshas required the extension of control schemes andmodulation techniques already well known for three�phase drives. In recent researches, more and morecontrol strategies, which traditionally are adopted inthree�phase machines, are applied to multiphasedrives to improve their performance. Duran et al. [5]proposed two SVPWM methods that are capable ofreducing the peak–to–peak common�mode voltage(CMV) by 40 and 80% compared to standard five�phase modulation strategies. Reduction of the CMV isdone at the expense of higher phase voltage and cur�rent distortion. Levi [6] introduced a predictive torquecontrol for five�phase induction motors as an alterna�tive to Field Oriented Control (FOC) and DirectTorque Control (DTC) methods and comparison ofthree methods is presented in the article.

While, in the process of extending three�phasemachines control schemes and modulation tech�niques to multiphase machines, one significant differ�ence between traditional machines and multiphasemachines should be sure to get attention [7]. Low�orderharmonics are particularly problematic and their effectis more significant in multiphase drives. H.A. Toliyatinjected third�order harmonic current into a five�phase induction motor to improve the magnetic fieldand increase the motor output torque. In the researchthey keep the amplitude of air�gap magnetic flux den�

Rotor Field Oriented Control Strategy with Harmonic Currents Closed�Loop Control for Five�Phase Induction Motor1

Yin Rongsena, Yang Jiaqianga, *, and Xu Jianhuab

aCollege of Electrical Engineering Zhejiang University, Hangzhou, 310027 ChinabJiangyin Zhenjiang Steel Structure Co., Ltd., Jiangyin City, 214400 China

*e�mail: [email protected] February 3, 2014

Abstract—In order to solve the problems of harmonic currents in the conventional vector control of mul�tiphase induction motor, the rotor field oriented control (RFOC) strategy with harmonic current closed�loopcontrol is proposed in the paper. Based on the transform theory of the multiphase system and the RFOC strat�egy of three�phase induction motor, the mathematical modulation of RFOC for five�phase induction motoris modeled. The fundamental current and the second order harmonic current can be controlled indepen�dently after being decoupled. The proposed strategy is implemented with a board microcomputer that usesTMS320F28335 DSP. The experimental results show that the proposed RFOC strategy with harmonic cur�rent closed�loop control has outstanding dynamic and static performance.

Keywords: five�phase induction motor, rotor field oriented control, harmonic current, closed�loop control

DOI: 10.3103/S1068371214050101

RUSSIAN ELECTRICAL ENGINEERING Vol. 85 No. 5 2014

ROTOR FIELD ORIENTED CONTROL STRATEGY 335

sity and stator copper loss equal to the value when sup�plied by fundamental harmonic current. However, theyoke air�gap magnetic flux density exist wave distor�tion and a problem of yoke saturation was found.G. Yepes expanded harmonic current control strategyfor nonlinearities compensation used in three�phasesystems to symmetrical multiphase machines [8].However no experiments were conducted to confirmthe proposed idea.

In order to solve the problem of harmonics in mul�tiphase machines, the rotor field oriented control(RFOC) strategy with second order harmonic currentclosed�loop control for the five�phase inductionmotor is proposed in the paper. Based on the transfor�mation theory of P–pair poles and N–phase system[9], the mathematical modulation of five�phaseinduction motor is molded. Furthermore, a five�phaseinduction machines with sinusoidal winding distribu�tion is examined experimentally and the recordedexperimental waveforms prove the outstanding perfor�mance of the proposed strategy.

The structure of this paper is as follows: the mathe�matical model of five�phase induction motor is pre�sented in chapter 2. Chapter 3 introduces the conceptsof rotor field oriented control of five�phase inductionmotor based on open�loops of harmonic currents andclosed�loops of harmonic currents respectively. Chap�ter 4 describes the experimental results and analysis.Experimental results of RFOC strategy based onopen�loops of harmonic and closed�loops are com�pared and differences between them presented clearly.The conclusions are summarized in the chapter 5.

2. MATHEMATICAL MODEL OF FIVE�PHASE INDUCTION MOTOR

This work considers one of the attractive mul�tiphase induction motor drive, as an alternative tostandard three�phase drives, drive with a symmetricalfive�phase induction machine (spatial displacementθ = 2π/5) with distributed windings and a two�levelfive�phase inverter [10]. Figure 1 presents the two�level five�phase induction motor drive scheme.

2.1. Voltage and Torque Equations of Five�Phase Induction Motor

Generally, in the rectangular coordinates, the volt�age equations of multiphase induction motor can bepresented as formula (1):

(1)

Among formula (1): U, I, R and L are voltage, cur�rent, resistance and inductance matrices respectively;subscript s represents stator, subscript r representsrotor and subscript sr represents mutual inductances.

In the rotor field oriented control strategy, the volt�age and current of stator are transformed into directcomponent in the d–q coordinate system. It is conve�nient to control the multiphase induction motor, forthere is no coupling of motor among d–q plane. Theequations of each d–q plane of multiphase inductionmotor can be listed respectively. For the five�phaseinduction motor, the equations of voltage and torque,

Us

Ur

Rs 0

0 Rr

Is

Ir

ddt��

Ls Lsr

LsrT Lr

Is

Ir

.+=

e ise d isd c isc b isd a isa

vscvsb

vsa

vsc

+b

–a–b

VDC

2��

VDC

2��

vse

2π5

�� +a

–e

+e

+d–d –c

+c

Fig. 1. Schematic diagram of the symmetrical two�level five�phase induction motor drive.

336


YIN RONGSEN et al.

which come from the fundamental harmonic in thed1–q1 plane and the second order harmonic in the d2–q2

plane, can be expressed respectively from formula (2)to (5):

(2)

(3)

(4)

(5)

where p is differential operator, 1 and 2 represent har�monic order respectively; Ls1 = Lm1 + Ls01, Lr1 = Lm1 +Lr01, Ls2 = Lm2 + Ls02, Lr2 = Lm2 + Lr02; usd1, usq1 thed�axis and q�axis stator voltage of the fundamentalharmonic respectively; usd2, usq2 are the d�axis andq�axis stator voltage of the second order harmonicrespectively; isd1, isq1 are the d�axis and q�axis statorcurrent of the fundamental harmonic respectively; ird1,irq1 are the d�axis and q�axis rotor current of the funda�mental harmonic respectively; isd2, isq2 are the d�axisand q�axis stator current of the second order harmonicrespectively; ird2, irq2 are the d�axis and q�axis rotorcurrent of the second order harmonic respectively;Lm1, Ls01, Lr01 are stator magnetizing inductance, sta�tor leakage inductance and rotor leakage inductanceof the fundamental harmonic respectively; Lm2, Ls02,Lr02 are stator magnetizing inductance, stator leakageinductance and rotor leakage inductance of the secondorder harmonic respectively; Rs is stator resistance;Rr1, Rr2 are rotor resistance on the fundamental har�monic and the second order harmonic respectively;ω, ωr are stator electrical angle velocity and rotor elec�trical angle velocity respectively; Te1, Te2 are electro�magnetic torque on the fundamental harmonic andthe second order harmonic respectively; P is numberof poles.

More detailed equations are listed as follows tomake the modulation of five�phase machines morecomprehensible. The stator flux linkage equations offive�phase machines are presented as formula (6):

(6)

The rotor flux linkage equations of five�phasemachines are presented as formula (7):

(7)

The air gap flux linkage equations of five�phasemachines are presented as formula (8):

(8)

2.2. Coordinate Transformation of Multiphase System

Generally, for a n�phase symmetrical system,Matrix Cs shown in formula (9), is used to transformthe voltages and currents of stator to synchronous ref�erence frame under constant power condition [4–6].

Among formula (9), ξ = 2π/n; if n is odd, the lastrow in the matrix should be deleted; ϕ1 = ∫ωdt, ϕ2 =∫2ωdt, ϕ3 = ∫3ωdt, …, ϕ

v = ∫vωdt, and they are electri�

cal angle velocity of rotor. Cs is an orthogonal matrix,

usd1

usq1

urd1

urq1

Rs Ls1p+ ωLs1– Lm1p ωLm1–

ωLs1 Rs Ls1p+ ωLm1 Lm1p

Lm1p ω ωr–( )Lm1– R1r Lr1p+ ω ωr–( )Lr1–

ω ωr–( )Lm1 Lm1p ω ωr–( )Lr1 Rr1 Lr1p+

isd1

isq1

ird1

irq1

,=

Te1 PLm1 isd1irq1 ird1isq1–( ),=

usd2

usq2

urd2

urq2

Rs Ls2p+ ωLs2– Lm2p ωLm2–

ωLs2 Rs Ls2p+ ωLm2 Lm2p

Lm1p ω ωr–( )Lm2– Rr2 Lr2p+ ω ωr–( )Lr2–

ω ωr–( )Lm1 Lm2p ω ωr–( )Lr2 Rr2 Lr2p+

isd2

isq2

ird2

irq2

,=

Te2 PLm2 isd2irq2 ird2isq2–( ),=

urd1 0, urq1 0, urd2 0, urq2 0,= = = =

ψsd1 Ls1isd1 Lm1ird1+=

ψsq1 Ls1isq1 Lm1irq1+=

ψsd2 Ls2isd2 Lm2ird2+=

ψsq2 Ls2isd2 Lm2idr2.+=⎩⎪⎪⎨⎪⎪⎧

ψrd1 Lr1ird1 Lm1isd1+=

ψrq1 Lr1irq1 Lm1isq1+=

ψrd2 Lr2ird2 Lm2isd2+=

ψrq2 Lr2ird2 Lm2isr2.+=⎩⎪⎪⎨⎪⎪⎧

ψmd1 Lm1 isd1 ird1+( )=

ψmq1 Lm1 isq1 irq1+( )=

ψmd2 Lm2 isd2 ird2+( )=

ψmq2 Lm2 isq2 irq2+( ).=⎩⎪⎪⎨⎪⎪⎧



composed of many pairs of d–q components. That is,the first and the second rows constitute d1–q1 subspace

while the third and the fourth rows constitute d2–q2subspace, and so on.

(9)

Multiple phase induction motor contains manyorthogonal d–q planes, which means the inductionmotor has a large amount of control degrees of free�dom. For the five�phase system, it possesses d1–q1 andd2–q2 plane, having two control degrees of freedom.

The diagram of five�phase induction motor coordi�nate transformation is shown in Fig. 2.

According to the formula (9) and Fig. 2, the coor�dinate transformation matrix of five�phase system is asformula (10).

(10)

Cs2n��

ϕ1( )cos ϕ1 ξ–( )cos ϕ1 2ξ–( )cos ⋅⋅⋅ ϕ1 n 1–( )ξ–( )cos

ϕ1( )sin– ϕ1 ξ–( )sin– ϕ1 2ξ–( )sin– ⋅⋅⋅ ϕ1 n 1–( )ξ–( )sin–

ϕ2( )cos ϕ2 2ξ–( )cos ϕ2 4ξ–( )cos ⋅⋅⋅ ϕ2 2 n 1–( )ξ–( )cos

ϕ2( )sin– ϕ2 2ξ–( )sin– ϕ2 4ξ–( )sin– ⋅⋅⋅ ϕ2 2 n 1–( )ξ–( )sin–

ϕ3( )cos ϕ3 3ξ–( )cos ϕ3 6ξ–( )cos ⋅⋅⋅ ϕ3 3 n 1–( )ξ–( )cos

ϕ3( )sin– ϕ3 3ξ–( )sin– ϕ3 6ξ–( )sin– ⋅⋅⋅ ϕ3 3 n 1–( )ξ–( )sin–

� � � ⋅⋅⋅ �

ϕv

( )cos ϕv

vξ–( )cos ϕv

2vξ–( )cos ⋅⋅⋅ ϕv

v n 1–( )ξ–( )cos

ϕv

( )sin– ϕv

vξ–( )sin– ϕv

vξ–( )sin– ⋅⋅⋅ ϕv

v n 1–( )ξ–( )sin–

1/ 2 1/ 2 1/ 2 ⋅⋅⋅ 1/ 2

1/ 2 1– / 2 1/ 2 ⋅⋅⋅ 1– / 2

.=

Cs25��

ϕ1( )cos ϕ12π5

��–⎝ ⎠⎛ ⎞cos ϕ1

4π5

��–⎝ ⎠⎛ ⎞cos ϕ1

6π5

��–⎝ ⎠⎛ ⎞cos ϕ1

8π5

��–⎝ ⎠⎛ ⎞cos

ϕ1( )sin– ϕ12π5

��–⎝ ⎠⎛ ⎞sin– ϕ1

4π5

��–⎝ ⎠⎛ ⎞sin– ϕ1

6π5

��–⎝ ⎠⎛ ⎞sin– ϕ1

8π5

��–⎝ ⎠⎛ ⎞sin–

ϕ2( )cos ϕ24π5

��–⎝ ⎠⎛ ⎞cos ϕ2

8π5

��–⎝ ⎠⎛ ⎞cos ϕ2

12π5

��–⎝ ⎠⎛ ⎞cos ϕ2

16π5

��–⎝ ⎠⎛ ⎞cos


��–⎝ ⎠⎛ ⎞sin– ϕ2

8π5

��–⎝ ⎠⎛ ⎞sin– ϕ2

12π5

��–⎝ ⎠⎛ ⎞sin– ϕ2

16π5

��–⎝ ⎠⎛ ⎞sin–

1

2�� 1

2�� 1

2�� 1

2�� 1

2��

.=

C

D E

isβ

B

is

isα α = A

–

αisα

isd

d

θ

is –

isd

isβ

βqβ

Fig. 2. Coordinate transformation of five�phase induction motor.

338


YIN RONGSEN et al.

3. ROTOR FIELD ORIENTED CONTROLOF FIVE�PHASE INDUCTION MOTOR

The vector control of five�phase induction motor,whose dynamic response is good, is a high perfor�mance control strategy. It has the ability to transforma complicated and coupled model of five�phase induc�tion motor into a simple and linear one. Meanwhile,stator current is also decomposed into excitation com�ponent and torque component so that they can becontrolled independently. The RFOC strategy is usedextensively in the AC drive systems.

In the paper, the five�phase induction motor is usedto conduct the experiment.

(1) The RFOC strategy with harmonic currentopen�loops. The decoupling components of funda�mental harmonic current in the d1–q1 plane, id1 andiq1, are controlled with two closed�loops. Meanwhile

the second harmonic current in the d2–q2 plane, id2and iq2 are controlled with open�loops.

(2) The RFOC strategy with harmonic currentsclosed�loops. The decoupling components of funda�mental harmonic current in the d1–q1 plane and thesecond order harmonic current in the d2–q2 plane, id1,iq1, id2 and iq2 are all controlled with closed�loopsrespectively.

3.1. RFOC Strategy with Harmonic Current Open�Loop Control

The vector control of three�phase system is com�mon and can be extended to the five�phase system.The fundamental current can be decoupled into exci�tation component and torque component under for�mula (10) to control independently.

(11)

According to the equations of voltage and torque ofmultiphase induction machines, the equations of d–qaxis stator currents on the d1–q1 plane can be obtainedrespectively from formula (12) to (14):

(12)

(13)

(14)

Where: Tr1 = Lr1/Rr1; ψrd1 is d�axis rotor linkage ofthe fundamental harmonic.

The harmonic voltages should be controlled at out�put side of the inverter to make the amplitude of har�monic voltages of output voltage zero. The diagram of

RFOC strategy with harmonic current open�loops inthe five�phase IM is shown in Fig. 3.

3.2. RFOC Strategy with Harmonic Current Closed�Loop Control

To control the harmonic currents in the multiphaseIM supplied by voltage source inverter, the RFOCstrategy with harmonic current closed�loop control isadopted. There are four closed�loops of currents tocontrol the fundamental harmonic in the d1–q1 planeand second order harmonic current in d2–q2 plane fordecoupling respectively.

According to formula (9) and the vector control ofthree�phase system, the vector control strategy of five�phase system can be reached. Then through formula(15), the fundamental current can be decomposed intoexcitation current and torque current to be controlledindependently, as formula (2).

(15)

To control the second order harmonic current inthe five�phase induction motor, which is supplied byvoltage source inverter, the second order harmonic

current also should be controlled with closed�loops.According to formula (9), the transform matrix forthe second order harmonic current is presented as

Cs25��

ϕ1( )cos ϕ12π5

��–⎝ ⎠⎛ ⎞cos ϕ1

4π5

��–⎝ ⎠⎛ ⎞cos ϕ1

6π5

��–⎝ ⎠⎛ ⎞cos ϕ1

8π5

��–⎝ ⎠⎛ ⎞cos


��–⎝ ⎠⎛ ⎞sin– ϕ1

4π5

��–⎝ ⎠⎛ ⎞sin– ϕ1

6π5

��–⎝ ⎠⎛ ⎞sin– ϕ1

8π5

��–⎝ ⎠⎛ ⎞sin–

.=

isq11p��

Lr1Te1

Lm1ψrd1

��,=

isd11 Tr1p+

Lm1

��ψrd1,=

ωs1 ω ωr–( )Rr1Lm1isq1

Lr1ψrd1

��.= =

Cs25��

ϕ1( )cos ϕ12π5

��–⎝ ⎠⎛ ⎞cos ϕ1

4π5

��–⎝ ⎠⎛ ⎞cos ϕ1

6π5

��–⎝ ⎠⎛ ⎞cos ϕ1

8π5

��–⎝ ⎠⎛ ⎞cos


��–⎝ ⎠⎛ ⎞sin– ϕ1

4π5

��–⎝ ⎠⎛ ⎞sin– ϕ1

6π5

��–⎝ ⎠⎛ ⎞sin– ϕ1

8π5

��–⎝ ⎠⎛ ⎞sin–

.=



formula (16). Through it, the second order harmoniccurrent can be decomposed into excitation current

and torque current as formula (4) to be controlledindependently.

(16)

The diagram of RFOC strategy with harmonic cur�rent closed�loop control in the five�phase inductionmotor is showed in Fig. 4.

After being decoupled, the fundamental harmoniccurrent and the second order harmonic current can becontrolled independently. In each d–q plane, the exci�tation current and the torque current are controlledindependently as well. This RFOC strategy with har�monic current closed�loop control definitely makesthe control of induction motor more convenient.

4. EXPERIMENTAL RESULTS AND ANALYSIS

In order to examine the proposed RFOC strategywith harmonic current closed�loop control, experi�ments were conducted using a five�phase inductionmotor supplied by five�phase voltage source inverter.The parameters of the five�phase induction motor arelisted in the Appendix. The results of experiments areas follows.

The five�phase induction motor is controlled byRFOC strategy with the second order harmonic cur�rent closed�loop control. Figure 5 shows the wave�

forms of excitation current id and torque current iq inthe initial start�up period of five�phase inductionmotor.

From Fig. 5, it can be seen that the excitation cur�rent id grows from 0 to 1.2 A immediately and remainsstable. While the torque current iq firstly increases to9.0 A in 500 ms, then remains in this state for 3000 msand finally decreases to 0 A within more than one sec�ond. Figure 5 proves that the static performance offive�phase machine meets requirement.

From Fig. 6, it can be seen that the five�phaseinduction motor’s speed grows from 0 to 1000 rpmsmoothly, then it maintains at a steady speed. In thegrowth process of speed, the amplitude of stator phasecurrent is 10.0 A, while the speed maintains at a steadyspeed the phase current’s amplitude is 1.8 A. Thedecrease of phase current is caused by the decrease oftorque current iq. The changes of phase current’s fre�quency are happening in the growth process of speedas well.

Figure 7 shows the stator current waveform underα–β coordinates when the five�phase induction motorruns steadily at 1000 rpm without load, which adopt

Cs25��

ϕ2( )cos ϕ24π5

��–⎝ ⎠⎛ ⎞cos ϕ2

8π5

��–⎝ ⎠⎛ ⎞cos ϕ2

12π5

��–⎝ ⎠⎛ ⎞cos ϕ2

16π5

��–⎝ ⎠⎛ ⎞cos


��–⎝ ⎠⎛ ⎞sin– ϕ2

8π5

��–⎝ ⎠⎛ ⎞sin– ϕ2

12π5

��–⎝ ⎠⎛ ⎞sin– ϕ2

16π5

��–⎝ ⎠⎛ ⎞sin–

.=

isd1*

isd1*

Park t–1 Clarke t–1

PI

PI

PI

Udc+ –

usd1*

usq1*

usα1*

usβ1*

+ ––

ωr

ωr*

α, β a, b, c, d, eisβ1*

isα1*d, qα, β


Speed Sensor

iaibicidie

–d, q

α, β

usα1* = 0

usβ1* = 0

α, β

a, b, c, d, eθ

ua

ubucud

ue

SPWMFive

phaseSPWM

Fivephase

IM

Fig. 3. RFOC strategy with harmonic current open�loop control in the five�phase IM.

340


YIN RONGSEN et al.

RFOC strategy with harmonic current open�loop.Figure 7a is electric current loop for the fundamentalcurrent and Fig. 7b is electric loop for the second har�monic current. From Fig. 7, it can be easily attendedthat when adopt RFOC strategy with harmonic cur�

rent open�loop, the fundamental current and the sec�ond harmonic current both exist. The second har�monic current is relatively small compared to the fun�damental current, however it still distorts the phasecurrent and influence machines performance.

Figure 8 shows the stator current waveform underα–β coordinates when the five�phase induction motorruns steadily at 1000 rpm without load, which adoptRFOC strategy with harmonic current closed�loop.Figure 8a is electric current loop for the fundamentalcurrent and Fig. 8b is electric loop for the second har�monic current.

Compared to Fig. 7, Fig. 8 shows that when adoptRFOC strategy with harmonic current closed�loop,the electric current loop for the fundamental currentdoes not changed much, while the electric currentloop for the second harmonic current turn into a spot.The main difference between Fig. 7a and Fig. 8a is thatloop of later is more smooth, which means that thereis less distortion for the fundamental current inFig. 8a. It should be pointed out that the radius of sec�ond harmonic current loop in Fig. 7b and Fig. 8b aresimilar.

Generally, machines run under the condition withload. Therefore, Fig. 9 and Fig. 10 presents the wave�form of electric current adopt RFOC strategy withharmonic current open�loop and RFOC strategy withharmonic current closed�loop respectively, when themachine runs with 5 N load.

Figure 9 presents the stator current waveformunder α–β coordinates when the five�phase inductionmotor runs steadily at 1000 r/min with 5 N load,which adopt RFOC strategy with harmonic currentopen�loop. Figure 9a is electric current loop for thefundamental current and Fig. 9b is electric loop for the

6 A/div

id = 0

iq = 0 1s/div

id

iq

Fig. 5. Waveforms of id and iq in the Start�up period.

6.2 A/div

speed

Phasecurrent

1000 rpm

Times:1s/div

Fig. 6. Waveforms of speed and phase current.

isd1*

isq1*


PI

PI

PI

Udc+ –

usα1*

usβ1*

+––

ωr

ωr*

α, β a, b, c, d, e

d, qα, β


Speed Sensor

ia

ibicidie

– d, q

α, β

α, β

a, b, c, d, e

θ

uaubucud

ue

SPWMFive

phaseSPWM

Fivephase

IM

isq2*isd2*

–

PI

PI

usd1*

usd2*

usq1*

usq2*

isα1

isα2isβ2

–usα2*

usβ2*

isβ1

Fig. 4. RFOC Strategy with harmonic current closed�loop control.



second harmonic current. From Fig. 9, it can be seenthat when adopt RFOC strategy with harmonic cur�rent open�loop, the fundamental current and the sec�ond harmonic current both exist. The second har�monic current is relatively small compared to the fun�

damental current, however it still distorts the phasecurrent and influence machines performance.

Figure 10 shows the stator current waveform underα–β coordinates when the five�phase induction motorruns steadily at 1000 rpm with 5 N load, which adopt

(a)

Fundamental current Second harmonic current

(b)

Fig. 7. Electric current loop for machine adopt RFOC strategy with harmonic current open�loop runs without load.

(a)


(b)

Fig. 8. Electric current loop for machine adopt RFOC strategy with harmonic current closed�loop runs without load.

342


YIN RONGSEN et al.

RFOC strategy with harmonic current closed�loop.Figure 10a is electric current loop for the fundamentalcurrent and Fig. 10b is electric loop for the secondharmonic current. Compared to Fig. 9, Fig. 10 showsthat when adopt RFOC strategy with harmonic cur�rent closed�loop, the electric current loop for the fun�damental current become more smooth and full, while

the electric current loop for the second harmonic cur�rent turn into a small spot, whose radius is not onlysmaller than that of the electric current loop in Fig. 9b,but also smaller than that of the spot in Fig. 8b.

Comparing Fig. 9 and Fig. 10, the most obviousdifference is that the second harmonic current isrestricted distinctly when adopt the RFOC strategy

(a)


(b)

Fig. 9. Electric current loop for machine adopt RFOC strategy with harmonic current open�loop runs with 5 N load.

Second harmonic current

(b)(a)

Fundamental current

Fig. 10. Electric current loop for machine adopt RFOC strategy with harmonic current closed�loop runs with 5 N load.



with harmonic current closed�loop. The same conclu�sion can be attended when compare Fig. 7 and Fig. 8.The effect of restriction for the second harmonic cur�rent is even more obvious. In the same time, theimpact on the fundamental current is very tiny and theelectric current loop maintains almost the same state.

Comparing Fig. 8 and Fig. 10, the spot in Fig. 10bis smaller than the spot in Fig. 8b, which means thatthe RFOC strategy with harmonic current closed�loophas better performance when machine runs with loads.Tally with the actual situation that machines usuallyruns with load.

The experimental results above show that the pro�posed RFOC strategy with harmonic current closed�loop can restrict the second harmonic current andimprove the machine’s performance.

5. CONCLUSIONS

Based on the mathematical modulation of five�phase induction motor, RFOC strategy with the har�monic current closed�loop control is proposed in thepaper. From the paper’s analysis and experimentalresults we can obtain the following conclusions:

(1) After being decoupled, the fundamental currentand the second harmonic current of the five�phaseinduction motor can be controlled independently inthe five�phase system according to RFOC strategywith harmonic current closed�loop control.

(2) The five�phase induction motor possesses twocontrol freedoms and for multiphase motor, therecould be many control freedoms. Owing to the manydegrees of freedom, the proposed RFOC Strategy withharmonic current closed�loop can restrict the har�monic current and enhance machine’s performance.

6. APPENDIX

The parameters of the five�phase induction motorused in the experiment are as follows:

7. ACKNOWLEDGMENT

Thanks the anonymous reviewers for their valuableremarks and comments. This work is supported byThe National Basic Research Program of China(2013CB035604), the National Natural ScienceFoundation of China (51177150), the AeronauticalScience Foundation of China (Project 2013ZB76004)and Jiangsu province incubation program for Scienceand technology enterprises to be listed (BE2013811).

This work is supported by The Natural ScienceFoundation of Zhejiang Province (LY14E070004).

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Power 3 kW

Phase voltage 155 V

Phase current 3.87 A

Poles 1

Speed 1000 rpm

Torque 20 N m

rotor field oriented control strategy with harmonic currents closed-loop control for five-phase...

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