Design and Simulation of Speed Control of an Induction motor Taking Core loss and Stray Load

Losses Into Account

Rupak Kanti Dhar, Md. Ehtashamul Haque Department of EEE

American International University-Bangladesh, 82, Road 14, Block B, Kemal Ataturk Avenue, Banani,

Dhaka-1213, Bangladesh E-mail: rupakdhar13@yahoo.com, eh2asham1@yahoo.com

Md. Alinavan Taia, Md. Ratan Sikdar,

Mohammad Abdul Mannan, Department of EEE

American International University-Bangladesh, 82, Road 14, Block B, Kemal Ataturk Avenue, Banani,

Dhaka-1213, Bangladesh E-mail: mdmannan@aiub.edu

Abstract— In order to precisely control the torque and flux, core loss and stray load loss, which are generally neglected, should be considered in the mathematical model of induction motor (IM) to design the controller. Some of literatures have shown how the detuning can be done in the rotor field oriented (RFO) control system to compensate the effects of core loss and stray load loss. But it has seen that the mathematical modeling of detuning process is very complex which makes the complexity in the case of implementation also. In this paper, we design the RFO control system with consideration of both core-loss and stray load loss by including a decoupling control strategy which is easier than the detuning strategy. The effectiveness of the design control system has been verified by the simulation work which has been done by using Matlab/Simulink.

Keywords— induction machines; core losses; stray load losses; vector control; PI controller; decoupling; simulation.

I. INTRODUCTION Vector control accuracy of induction motor drives is

affected by variations of motor parameters and by the phenomena that are not modeled and are therefore unaccounted for in the controller [1]. It appears that the only potential source, which has never been studied before, is the stray load loss, which belongs to the category of unmodeled phenomena. The stray-load loss is that portion of losses in a machine not accounted for by the sum of friction and windage, stator I²R loss, rotor I²R loss and core loss. It’s also defined as additional losses; represent a non-negligible term in the power balance of industrial induction [1, 2]. Stray losses inevitably appear in any ac machine and they have numerous sources. Stray losses in mains supplied ac machines are caused by higher flux density harmonics due to slotting effects, inter-bar rotor currents and skewing. The vector control technique, which is also known as field oriented control (FOC), allows a squirrel-cage induction motor to be driven with high dynamic performance that is comparable to the characteristic of a dc motor [3]. FOC is a control technique used in AC synchronous and induction motor applications. Two types of FOC techniques are used they are direct field oriented control (DFOC) and indirect field oriented control (IFOC). DFOC is complex to implement than IFOC method [4]. To produce high performance in induction Motor (IM) drives by decoupling rotor flux and torque producing

current components of stator current in our work IFOC has been used. The RFO control system has been designed in earlier research where core-loss and stray load losses were not taken in consideration [5]. This is the only paper where the impact of core-loss and stray load loss has been considered to design RFO control by using decoupling control strategy.

II. INDUCTION MACHINE MODEL The equivalent d-q axes synchronously rotating reference frame circuit of IM with consideration of core-loss and stray load loss is shown in Fig. 1. [1]. According to the equivalent circuit the mathematical expressions of an IM: According to the equivalent circuit the mathematical expressions of an IM:

( ) ( ) ⎪⎪⎭

⎪⎪⎬

⎫

−+−+++=

++++=

mmLωaωjrslLωaωjdtmd

mLdt

rdslLrrR0

mmLajωsslLajωdtmd

mLdt

sdslLssRs

iiii

i

iiii

iv

…………………………………………………………........(1)

⎪⎭

⎪⎬⎫

+=

+=

mmLrslLr

mmLsslLs

iiΨ

iiΨ …………………………..………..(2)

Fig. 1. Space vector dynamic equivalent circuit in an

Arbitrary reference frame rotating at ωa with iron loss and stray load loss representation.

Proceedings of 2013 2nd International Conference on Advances in Electrical Engineering (ICAEE 2013)19-21 December, 2013, Dhaka, Bangladesh

978-1-4799-2465-3/13/$31.00 ©2013 IEEE 229

⎪⎪⎭

⎪⎪⎬

⎫

−+=−

+=

rslω)Taj(ωdt

rdslTrr

majωdtmd

cTr

ii

ii

ii

i …………..…….....(3)

⎭⎬⎫

−=

+=+

)qrdrdrqr(3/2)p(eTcmrs

iΨiΨ

iiii …….…..….......(4)

rlrst iii −= ……………………..........(5)

mrsc iiii −+= …………………..….......(6)

Where, sdv , sqv indicate d and q axes stator voltages;

sdi , sqi indicate d and q axes stator currents; rdi , rqi indicate

d and q axes rotor currents; rdΦ and rqΦ indicate d and q

axes rotor fluxes;

sω and slω indicate primary and slip angular frequencies; Rs and Rr indicate stator and rotor resistances; Ls, Lm, Lr indicate stator, mutual, rotor self-inductances respectively; Te and TL indicate electromagnetic and load torques; J, D and Pn indicates moment of inertia, friction coefficient and number of pole pair.

mmLm iΦ = ………………………...….(7)

mmLsslLmsslLs iiΦiΦ +=+= ………………….........(8)

mmLrlrlLmrlrlLr iiΦiΦ +=+= …………………..…(9)

[ ]rdrdrdrdn3/2peT ΦiΦi −= ………………..…..(10) Using (1-10) the first order state space equations can be written as follows:

rsljωm4arRrjωr2arRm2arRs1arRdt

rdΦiΦii

Φ−−−+=

…………………………………………………..............…(11)

r8bmrω8jamsjωr7am6as5adtmd

viiΦiii

++−+−=

……………………………………………………………(12)

r4bs1bmrω12jassjωr11am10as9adt

sdvviiΦii

i−+−−−+−=

…………………………………………….……………….(13)

)LTe(T16arω15adt

rdω−+−= ………………………..(14)

[ ]rdrdrdrdn3/2peT ΦiΦi −= ……………….………….(15) Where,

.16;15;34;

11

;12;711;10;5

9

;1

2;4;2;1

JnP

aJ

Da

slL

bmLb

slLb

slLsamL

aslL

amLa

stL

amLa

slL

amLsRa

rscRb

rscRmL

arlLrscR

rlLcRmLstRa

rscRcR

a

====

===+

=

==−

==

cT

bb

cT

aa

cT

aa

cT

aa

cT

aa 2

3;48;3

7;216;11

5 ===+

=−

=

III. DESIGN OF RFO CONTROLLER FOC was originally developed for high-performance motor applications which can operate smoothly over the full speed range, can generate full torque at zero speed, and is capable of fast acceleration and deceleration but that is becoming increasingly attractive for lower performance applications as well due to FOC's motor size, cost and power consumption reduction superiority [7]. Thus, the model of induction motor is simplified here by means of IFOC since without use of the constraint of IFOC, the calculated desired stator voltage is not suitable to converse actual torque and speed to their reference values. This model can be simplified by means of the concept of IFOC. In an ideal IFOC, the rotor flux linkage axis is forced to align with the d-axis, and it follows those conditions of IFOC, these are:

rrdΨΦ = …………..……………………….….……(16)

0rd =Φ ………………………………….……….(17)

0dt

rdd=

Φ ………………………………………..……(18)

2rd

2rdrr ΦΦΦΨ +== ……………….…………........(19)

Using the conditions of IFOC the required equations found are:

md4arRrωmd2arRsd1arRr8arRdt

rdiiiΨ

Ψ++=+ …….... (20)

0rslωmd4arRrωmd2arRsd1arR =−−+ Ψiii ….........(21) Since rotor flux not only depends on the stator d-axis current but also d-axes magnetizing current and speed, for decoupling control let,

sdesdfsd iii += ......................................................(22)

To obtain the decoupling control strategy the last three-terms should be zero, thus

sdf1arRr8arRdt

rdiΨ

Ψ=+ ……………………….......(23)

0=++ mq4arRrωmd2arRsde1arR iii ……..……….(24)

mqrω14amd13asde iii −−= ………………………….(25)

Here, 1

414,

1

213 a

aa

a

aa ==

For torque control, using (16), (17) and (18) in (15) the expression for torque found:

rqrn3/2PeT iΨ−= ………………………………..……(26)

mq2arn3/2pmdrω4arn3/2psq1arn3/2peT iΨiΨiΨ +−=

……………………………………………...………..….…(27) It is seen that the torque is not-only depends on stator-q-axis current but also depend on Magnetizing dq-axes current. For decoupling control strategy purpose let

sqesqtsq iii += …………………………….......................(28) To obtain the decoupling control strategy the last three-terms should be zero, thus; mdr14mq13sqe ωaa iii +−= …….... (29)

230

It is considered that nt pK 2/3= Using the value of Kt in (27) it is found that:

sqt1artKeT iΨ= …………………………………….… (30)

IV. DESIGN OF PI CONTROLLERS To verify the performance of designed RFO control system

a speed controller was designed considering the impact of core-loss and stray load loss. Here, our aim is to show that, it is possible to design a RFO system using decoupling strategy inspite of detuning technique. PI controller has zero steady state error, less circuit complexity and could performs both for proportional and integral operation [8], so for our work we have used conventional PI controller rather than other controllers to control the speed at transient point. Four controllers were needed to control the speed at transient point. The controllers are rotor flux controller, speed controller, d-axis stator current controller and q-axis stator current controller.

For rotor flux controller, after Laplace transformation of (23) the transfer function found is:

Φ

ΦΨ

i

cK

scT1(s)r

(s)sdf += ……..……...……………….……..…(31)

Where, .;1;33

1

str

rlrscc

rcc RR

LRTaR

TaaK === ΦΦΦ

The expression of PI-flux controller can be written as follows:

(s)esIK

pK(s)sdf ΦΦ

Φi ⎟⎠⎞

⎜⎝⎛ += …………………...…...(32)

(s)r(s)*r(s)e ΦΦΦ −= ………………........………….(33)

Where, r(s)*r ΨΦ = , is reference rotor flux

magnitude. 2rd

2rdrr ΦΦΦψ +==

Again, use (30) in (14). Now, For Speed controller after Laplace transformation of equation (14) the required transfer function found is:

CωK

sCωT1(s)rω

(s)sqt +=

i ……...……………………………...(34)

Where, ;15a16a

CωK;15a

1CωT;

15artK1a16a

CωK ===Ψ

The expression of PI-speed controller can be written as follows:

(s)ωesIωK

pωK(s)sqt ⎟⎟⎠

⎞⎜⎜⎝

⎛+=i ………………...............(35)

)()(*)( ssrse rωωω −= …………………………............(36)

;11

;11

1

aslL

CiTaCiK ==

Using (13) the voltage equation found as,

⎪⎪⎭

⎪⎪⎬

⎫

+=

+=

(s)sqCiK

sCT1(s)qu

(s)sdCiK

sCiT1(s)du

ii

i ………………….…….……...(37)

Thus, the dynamics of the d-axis and q-axis currents are now represented by simple linear first-order differential equations. There, it is possible to effectively control the currents with a PI controller (37) could be written as:

)()( sidesIi

KpiKsdu ⎟

⎟⎠

⎞⎜⎜⎝

⎛+= ……...……....…...........(38)

(s)iqesIi

KpiK(s)qu ⎟

⎟⎠

⎞⎜⎜⎝

⎛+= …………………….......(39)

)()(*)( ssdssdside ii −= ……………….………(40)

)()(*)( ssqssqsiqe ii −= …………………..……(41)

Here, ippp K,K,K φω are the proportional gain constant for speed, rotor flux and d and q axis stator current controller respectively. Again iIIφI K,K,K ω are the integral gain constant for speed, rotor flux and d and q axis stator current controller.

To design rotor flux controller (31), (32), (33) and for speed (34), (35), (36) were used. Again using (37), (38), (39), (40), (41) our required d-axis stator current controller and q axis stator current controller were designed. The value of several parameters and constants are shown in Table 1. The Simulink model of our overall system has been shown in Fig.2. The system has a machine model and a controller. The machine model has two subsystems and the output from the machine had been feedbacked to the controller circuit. From the output bus bar required stator current, rotor flux, torque, magnetizing current and speed are found which is visualized through the scopes. Total controller circuit is consist of four controller which is shown in Fig. 3. Reference speed and the value taken form machine model has been considered as our input for the controller circiut. In Fig. 4.the subsystem-1 of machine model has been shown which is constract using the state space equations. In input basbar four inputs are given and after integrating the state space equation they are feedbacked to input busbar. From Fig. 5. we can observe our subsystem-2 of machine model where core-loss current and rotor leakge current has been calculated according to out derived equations.

All of the controller were designed using PI controller and the value of proportional gain constant and integral gain constant are given in Table 1. In the controller circuit a voltage model is constracted according to our derived equation to find our required d and q axis stator voltege.

231

Speed

Ref

Nm* and Fr*

Vsd

Vsq

ws

TL

IMO

Machine model

IMO

Ref

Vsd

Vsq

ws

Controller

TL0

<Isd><Isd>

<Isq><Isq>

<Imd><Imd>

<Imq><Imq>

<Frd><Frd>

<Frq><Frq>

Is

Rotor Flux

Im

Torque<Te><Te>

<TL><TL>

<Nm><Nm>

<Nm*><Nm*>

Fig. 2. Simulink model of overall system.

3

ws

2

Vsq

1

Vsd

Isdq*

IMO

Udq

d and q axisStator current

control

Udq

Edq

Vsd

Vsq

Voltage model

Isf t

IMO

Isdq*

Subsystem

Ref

IMO

Isf t

ws

Speed and rotor flux controll

IMO

ws

Edq

Edq claculation

2

Ref

1

IMO

Fig. 3. Simulink model of Controller circuits

1

Im1

-a15*u(11)

wr1

Pn

-a1*u(5)-a2*u(7)+a3*u(9)+a4*u(11)*u(6)

Irq

-a1*u(4)-a2*u(6)+a3*u(8)-a4*u(11)*u(7)

Ird

1s

1s

1s

1s

1s

1s

1s

a16

Kt

-a9*u(5)+a10*u(7)-a11*u(9)-u(3)*u(4)-a12*u(11)*u(6)+b1*u(2)

FIsq

-a9*u(4)+a10*u(6)-a11*u(8)+u(3)*u(5)+a12*u(11)*u(7)+b1*u(1)

FIsd

a5*u(5)-a6*u(7)+a7*u(9)-u(3)*u(6)+a8*u(11)*u(6)

FImq

a5*u(4)-a6*u(6)+a7*u(8)+u(3)*u(7)-a8*u(11)*u(7)

FImd

Rr*(a1*u(5)+a2*u(7)-a3*u(9)-a4*u(11)*u(6))-(u(3)-u(11))*u(8)

FFrq

Rr*(a1*u(4)+a2*u(6)-a3*u(8)+a4*u(11)*u(7))+(u(3)-u(11))*u(9)

FFrd

30/pi

4

TL

3

ws

2

Vsq

1

Vsd

TL

Isd

Isq

Imd

Imq

Frd

Frq

Ird

Irq

Te

wr

Vsd

Vsq

ws

Nm

Fig. 4. Simulink Model of Induction Machine (subsystem 1)

232

1

Im2

1/Lrl

1/Lrl

Lm

Lm

1

Im1

<Isd><Isd>

<Ird><Ird>

<Imd><Imd>

<Isq><Isq>

<Irq><Irq>

<Imq><Imq>

<Frd><Frd>

<Frq><Frq>

Icd

Icq

Irld

Irlq

Fig. 5. Simulink Model of Induction Machine (subsystem 2)

V. SIMILATION AND RESULTS Stator current (Is) depends on stator d-axis and stator q-axis current. From (22) it is seems stator d-axis current (Isd) depends on flux producing d-axis stator current (Isdf) and Stator d-axis current ripple component (Isde). Again from (25) Stator d-axis current ripple component (Isde) is proportional to d-axis magnetizing current (Imd) and q-axis magnetizing current (Imq) which are constant. As a result (Isde) remain constant. So finally stator d-axis current (Isd) totally depends on flux producing d-axis stator current (Isdf). Again from (23) flux producing d-axis stator current (Isdf) is proportional to rotor flux (�r) which is dependent on stray load. The stator q-axis current (Isq) is the summation of torque producing q-axis stator current (Isqt) and q axis ripple current(Isqe). From (27) it is known that Isq is dependent on load torque. On the other hand from (29) it is found that q-axis ripple current only depend on magnetizing currents which are constant. So, stator q-axis current (Isq) is only dependent on torque producing q-axis stator current (Isqt). Here load torque remains constant with time. The initial value of stator d-axis stator current and q-axis stator current was set at 12.2506A and 9.2436A respectively. From Fig. 6. it is found that without the two overshoots in the q-axis stator current (isq) the values are remain same as its initial value all the time. We observed the two d and q axis currents individually in our matlab/Simulink. It was observed that, for both Isd and Isq an overshoot was occurred at t=2 s because the reference speed was stepped up from 500 rpm to 1000 rpm at 50% load torque. At t=6 s when reference speed step down from 1000 rpm to 500 rpm two individual overshoots was also observed. But for the d-axis stator current the value of the overshoots in the transient points are too small almost negligible and in between the transient points there was a little fluctuation observed for considering the stray load. But for the q-axis stator current no fluctuation observed between the transient points and two considerable overshoots were observed at transient points.

Total stator current is the summation of stator d axis and stator q axis current. In this simulation work, the gains of current controller are chosen as KPi= 0.5688 and KIi=1.6094×103

consequently. Total rotor flux is the summation of rotor d-axis and rotor q-axis flux. From (16 and 17) it could be said that d-axis flux is equal to rotor flux and q-axis flux is zero. From (23) the concept is found that rotor flux is dependent on Isdf. From Fig. 7. it is seem that rotor q axis flux is remaining zero and rotor d-axis flux is changing with the stator d-axis current where the initial value of rotor d-axis flux is setup at 0.8939 Weber. Two overshoots are observed at t=2s and t=6s when the reference speed is changing. In this simulation work, the gains of current controller are chosen as KPi= 0.5688 and KIi=1.6094×103consequently. Here rated speed is considered Nm=500 rpm and at 50% load the reference speed was stepped up from 500 rpm to 1000 rpm. From (14) and (15) it’s known that stray load losses have no effect on speed response, but torque is related to speed which is affected by SLL. For SLL consideration during controller design speed remains constant after transient points because it is concerned with torque. Fig. 8. shows speed response of the proposed controller for step change of reference speed where the reference speed steps up from 500 rpm to 1000 rpm at t = 2 s and again the speed steps down from 1000 rpm to 500 rpm at t = 6 s. Two overshoots are observed at the transient points where the speed is changed. In this simulation work, the gains of speed controller are chosen as KIω=1.9900 and KPω=0.1571 consequently. Two overshoots at the transient points can be improved by using advance PI controller logics. From (26) it’s found that torque is dependent on rotor flux and rotor current. Here both two components are constant. From Fig. 9. it is observed that torque remain constant at 24.1014 N-m as load torque. Only two overshoots are seen in the transient points at t=2 s and t=6 s. So, stray load loss has no affect on torque response. When ramp signal is taken as input signal two very small overshoots are observed at t=2.5 s and t=6 s. From Fig. 10. we can observe that the overshoot is very small but the duration of the overshoot is little bit large for ramp input than step input. Fig. 11. shows torque response with ramp change of reference speed. From the figure we can see that torque response remain same as initial all the time. Two overshoots are observed at the transient points. The duration of the overshoots are also longer for the ramp input which might be harmful for induction machine. All the controllers were checked for different types of roots like root=10, 50. For root 10 small overshoots occurred at transient points but response curve was shifted right from the reference curve and overshoot duration was higher. For root 50 the overshoots at the transient points was increased but the overshoots duration remained very small. Also the response curve was also shifted right from the reference curve. For the IM increment in the overshoot duration is not acceptable because machine coil could be burnt. So, root 25 is suitable in these aspects.

233

Table 1: parameter values at rated condition

VI. CONCLUSION From the simulation and analysis results, it was obtained that the torque control capability was much improved and the speed estimation error for RFO control system was reduced. The designed controller has simplicity over detuned RFO controller which is more preferable for practical implementation. The performance of the controller were checked for different types of load torque and reference signal and after examine the result we could reached to the conclusion that controller was able to control stator current, rotor flux, speed and torque at transient point. Due to consideration of core-loss and stray load loss sensitivity on measurement errors of electrical values and torque become higher. The overshoots occurred at the transient points could be vanish using advance technologies. Through the Matlab /Simulation it is shown that for RFO control delivers better performance when the impact of core loss and stray load losses are considered. So the future induction machine controller should be manufactured taking core-loss and stray load losses into account.

References [1] Emil Levi, “Impact of Stray Load Losses on Vector Control Accuracy in

Current-Fed Induction Motor Drives,” IEEE Transactions On Energy Conversion , VOL. 21, NO. 2, June 2006.

[2] A. Lamine ,"Modelling And Detunning Assessment Due To Stray Loadlosses In Vector Controlled Induction Machines,” Industrial Electronics Society, 2007. IECON 2007. 33rd Annual Conference of the IEEE.

[3] Mohammad Abdul Mannan, Asif Islam, Mohammad Nasir Uddin, “ Fuzzy-Logic Based Speed Control of Induction Motor Considering Core Loss into Account,” Intelligent Control and Automation, 2012, 3, 229-235 .doi:10.4236/ica.2012.33026 Published Online August 2012

[4] Bimal k.Bosh,“Modern Power Electronics And Ac Drives,” 2002Prentice Hall PTR .

[5] Muhammad H.rashid,"Power Electronics Circuit,Devices,And Applications,” Prentice Hall Of India Third Edition 2007.

[6] Hiware, R.S. ; IPS, G.H.R.C.E., Nagpur, India ; Chaudhari, J.G.,“Indirect Field Oriented Control for Induction Motor,” published in Emerging Trends in Engineering and Technology (ICETET), 2011 4th International Conference on Date 18-20 Nov. 2011

[7] Bimal k.Bosh,“Modern Power Electronics And Ac Drives,” 2002Prentice Hall PTR .

Parameter and Constant value Rated speed, Nm 1436.r rpm

Developed torque, Te 49.85 N-m Load torque, TL 24.1013 N-m Slip speed, ωsl 13.2994 rpm

friction coefficient, D 0.011N-m/rad/s Inertia, J 0.017

Proportional speed gain constant ,KPω 0.1571 Integral speed constant ,KIω 1.9900

Integral flux constant, KIf 47.9048 Proportional flux gain constant, KPf 15.7085

Integral current constant, KIi 1.6094×103 Proportional current gain constant ,KPi 0.5688

Fig. 6. Stator d-axis and q-axis current with Step Change of Reference

Speed (where, root = 25)

Fig. 7. d-axis and q-axis rotor flux with Step Change of Reference

Speed (where, root = 25)

Fig. 8. Speed response with Step Change of Reference Speed (where,

root = 25)

Fig. 9. Torque response with Step Change of Reference Speed (where,

root = 25)

Fig. 10. Speed response with Ramp Change of Reference Speed (where,

root =25)

Fig. 11. Torque response with Ramp Change of Reference Speed (where, root = 25)

234