Energy Saving Through Design Optimization Of Induction Motors

I. I NTRODUCTION

The purpose of a motor design is to determine motor dimensions which satisfy a given set of specifications under certain constraints and be economical to achieve certain desired performances [Ramarathnam, 1969]. The constraints are commonly determined either by consumers or by certain norms authorities. The constraints demanded by consumers are for examples the horse-power rating, efficiency, power factor and full-load speed, whereas those required by certain norms are for instance the starting current, temperature rise and starting torque. The designer tries to satisfy all those requirements while simultaneously trying to minimize the material, production and operating costs in general.

Designing a motor to be used with constant voltage and frequency supplies will be different to that using variable voltage and frequency supplies. Motor design for the use with current-source inverter will also be different from that with voltage-source inverter.

The objectives can also be distinguished depending on whether the motor will be used for load under constant or variable speed operations. Even if the design

Rini Nur Hasanah is with the Electrical Engineering Departement of Universitas Brawijaya, Malang, Indonesia (corresponding author provide phone 0341-665144; email rini.hasanah@brawijaya.ac.id)

principles are the same, the final configurations could be very different.

Conventionally-supplied motor design concerns the motor design for use with constant voltage and frequency supplies. Such motor is appropriate for constant speed load application. Designing motor for this application will confront various limitations required by norms authorities. The important thing to avoid is for example the high starting current, as it will burden the local power grid when direct on-line starting is carried out. Starting torque must also be considered in order to be able to drive load.

In some applications intended for energy saving, optimum-speed operation and increasing productivity, variable-speed drive systems are required. For such applications, motor design must be adapted for use with variable voltage and frequency supplies. In this design category, some limitations found in the previous conventionally-supplied motor design can be removed, for instance the starting current and torque. Different consideration on starting current limitation gives different view on the treatment of skin effect, for example. Unlike in the preceding category where the skin effect is important to reduce the starting current and to increase the starting torque, it is to be reduced for application with variable voltage and frequency motor design. The breakdown torque consideration is important when motor will be operated under constant power along wide speed-range zone.

II. G ENERAL P ROCEDURES T O D ESIGN A M OTOR As designing a motor means the finding of a

suitable geometry, manufacturing data and performance indexes for given specifications, it comprises the steps of dimensioning (synthesis), sizing, and performance assessment (analysis). General procedure to design a motor includes the following design aspects:

• geometric, • electric, • magnetic, • mechanical, • and thermal aspects.

It is commonly begun by determining the desired specifications of the motor. The assigned magnetic and electric loadings are used to size the magnetic and electric circuits, which consists in adjusting the geometrical data to provide the needed flux and current densities. When they are not fulfilled yet, all dimensions

Energy Saving Through Design Optimization Of

Induction Motors

Rini Nur Hasanah *

must be readjusted and the design process must be

Start

restarted until the desired values are obtained. The coming after stages consist in finding the equivalent circuit parameters to calculate the motor characteristics and performance. If they are still not

- Design specifications satisfactory, the whole design process must be repeated

- magnetic loading with new design values. Repeating the whole process is

- electric loading done according to an adopted strategy until the desired

specifications are met or a satisfactory performance is obtained.

Sizing the electrical The flowchart of a general procedure to design a

and magnetic circuit motor is shown in Fig. 1.

A. Basic Concepts And Design Constraints One of the important indications in designing an

Adjusting the geometrical aspect electric machine is the relation between its dimensions

to its output power. The apparent power developed in an m-phase

Verifying the electric induction motor can be expressed as [Hamdi, 1994]:

and magnetic loading

S o = m 2 πφ f k (1) (

ws N ts ) I () ph

where m phases number

f supplying frequency [Hz]

No Satisfying?

series turn-number per phase ts

Yes ph

I phase current [A]

φ magnetic flux per pole [Wb]

Computing the magnetizing current

winding factor ws

Computing the equivalent circuit parameters The frequency f can be expressed in terms of pole- pairs number p and synchronous speed n :

Computing the complete

f = pn (2) s motor characteristics and performance The series turn-number per phase N

in terms of

ts

total conductor numbers N tot is expressed as:

No Satisfying?

N = tot (3)

ts

so that (1) becomes: Yes

2 s ws tot () ph

pnk φ N

I (4) End

Figure 1. Motor design flowchart.

As in general there is only one circuit per phase in The average flux density over the air gap of the

small motors, the conductor current I is the same

machine, usually called the specific magnetic loading, can be expressed as:

cond

as the phase current I .

ph

2p φ

B g_av =

π dl is where d is is the stator bore diameter.

The number of stator ampere conductors per meter of the stator periphery at the air gap, usually called the specific electric loading , can be expressed as:

Jurnal EECCIS Vol. III No. 1 Juni 2009

[www.designprocessing.com] can compute large models = tot cond A I (6) with hundreds of equations and parameters. It consists

π d is

of the following modules:

Finally, the active power output equation is obtained • Pro@DESIGN-Generate analyzes the model, and by substituting (5) and (6) into (4) which results in:

generates automatically a compute object (COB)

P Cd 2 o =

o is ln s (7)

representing the model, including the formal exact

sensibility information. This compute object,

where C o is called the output coefficient:

without any programming, is generated in seconds.

2 • Pro@DESIGN-Compute is a solver that computes

C = 1.11 π B g_av Ak η cos ϕ o (8) s ws the outputs values according to the inputs to with η is the efficiency and cos ϕ is the power

validate the model, and helps to do a sensibility analysis.

factor. • Pro@DESIGN-Optimize finds an optimum using As shown with (7), the output coefficient relates the

the data and the constraints entered into the motor output power to its active parts volume and speed.

specification sheet by the sizing designer. It finds an It is proportional to the product of specific magnetic and

optimum with a high performance SQP gradient- electric loadings.

based algorithm, which is ideal for non-linear The specific magnetic loading determines the

constrained problems typical to engineering, using magnetization requirements of the machine. It influences

the sensibility information. the maximum flux density in the iron parts, magnetising

• Pro@DESIGN-Optimize post-processor gives current and core losses. tables and graphs to analyze the optimization The specific electric loading determines the electric

results.

circuitry requirements in the machine. It influences the The design optimization software is very helpful in temperature rise that can be withstood by the machine, designing process, however up to a certain extent the the required insulation material and the operating initial guess values, which sometimes determines the voltage of the machine. reasonable results, are still dependent on the designer

B. Motor Design Methods expert knowledge. Even so, the Pro@DESIGN enables Generally, two methods to design a motor are known.

the designer to focus his time and talent more in its The first one is undertaken based upon an available

modeling expertise to find better solutions, create better comparable design, whereas the second method is done

models, or work on more designs. by taking advantage of commercial motor design

III. M OTOR D ESIGN O PTIMIZATION products could be useful even for an inexperienced

software. Some software producers claimed that their

Motor design optimization is essentially a problem designer; yet, using both methods, the experience of the

solving involving nonlinear programming techniques. It designer and his ability to take important decisions at

can be one of minimizing the cost, weight, volume, etc. various stages of design to large extent are still required.

being subjected to a set of constraints, while almost all of these functions being nonlinear.

Classical method

Using the classical method, the design steps to follow Known: an initial design,

motor parameters

are shown in Fig. 2. A previously existing motor design is used as a base design. Starting from it, motor performances and characteristics are calculated. As long as they do not correspond to the desired ones, motor

Calculate motor performance parameters values are changed. Some iterations are

sometimes needed before the satisfying performances are finally obtained.

No

State-of-the art method

Change parameters values It is a matter of designing motor with the help of a

Satisfying?

design and optimization commercial software. The

Yes

design optimization software exempts the designer from bulky programming tasks and automates lots of the

Design result

design processes. The designer is just required to model his design in an approximate analytical model

Figure 2. Designing a motor based upon a comparable motor design.

representing technical and economical nonlinear heavily

A. Objective Of Optimization

constrained problems. Optimizing a motor design can be done by As an example, the software Pro@DESIGN

maximizing or minimizing a certain design variable to

Jurnal EECCIS Vol. III, No. 1, Juni 2009

achieve a desired performance under some imposed

vector.

constraints. It is usually formulated as a general The objective function could represent for example nonlinear programming problem and intended to find:

the production cost, annual cost, capitalized cost,

x = xx , ,... x

with

x ≥ 0 (9) efficiency, efficiency, weight, volume, etc.

D. Constraint Functions

such that: fkx ( 1 , ) is minimum (maximum)

The constraint functions could be either inequality

(10) gkx ,

i ( 1 ) or equality constraints

being subjected to:

constraints

gkx

i ( 1 , ) ≤ 0 i = 1, 2,3,... r

(11) hkx ,

j ( 1 ) . They could represent the performance

hkx ( 1 , ) = 0 j = 1, 2,3,... s (12)

i properties of the motor, the dimensional and other additional requirements.

A maximizing problem can always be regarded as a The inequality constraints for example are the locked- minimizing one by using the negative of the objective

rotor current, the starting torque, the temperature rise,

function fkx ( 1 , , so that optimizing then means etc, whereas the equality constraints can be the motor )

power rating for example.

finding the optimal value of variables containing in the

vector x , which give the minimum value of fkx ( 1 , )

E. Optimization Techniques

Optimization techniques are basically composed of

and satisfy the given constraints gkx

and

objective function calculation and its corresponding

constraints verification. This technique is carried out by

hkx

. is reached using any deterministic or stochastic

repeating the whole process until sufficient convergence

optimization mathematical method. The optimization is

B. Design Variables And Parameters usually performed with the help of software programs

Design variables are entities that identify a particular and requires significant computer resources. design and will change over a prescribed range during

Three main prerequisites to do an optimization are: the search for the optimal design [Venkataraman, 2002].

• mathematical modeling of the design

A specific design is characterized with the values of a

problem,

complete set of these variables. This set is identified as

• knowledge of computer programming, the design vector x , as shown in (9).

knowledge of optimization techniques.

Nowadays there are available some special-purpose choice of the set of design variables must meet the

In order to apply the techniques of optimization, the

optimization software packages, exempting a designer criterion of linear independence, even in a complex

from an obligation for bulky computer programming or design where the linear relationship may not be very

even to search for the optimization techniques, as apparent.

provided by ProDesign for example. Some other Design parameters identify constants which will not

softwares provide ready-to-use optimization functions, change as different designs are compared. They are

for example Matlab and MathCad. However, the core of primarily predetermined constants in the design, so that

the optimization is still the appropriate mathematical they have no principal role to play in determining the

modeling of the design problem. optimal design [Venkataraman, 2002]. The set of design

IV. D ESIGNING M OTOR ITH parameters is identified as PECIAL . W S O BJECTIVES

A.

C. Objective Function First Case: Minimizing Losses As an application example of motor design and

Objective function (10) establishes mathematical model of the design problem and drives the search for

optimization, minimizing losses objective will be taken. The influence of various design parameters on the

the optimal design. The objective functions must be composed, explicitly or implicitly, of the design

objective value will be observed with the help of ProDesign design and optimization software.

variables. It can be a single objective function or The design variables to be used are stator bore alternatively multi-objective functions. In the single diameter d, stator stack length la, stator slot depth des,

objective function, fkx ( 1 , ) has a scalar value. The stator slot width wes, stator core depth dcs, rotor slot

multi-objective functions drive the search for the depth der, rotor slot width wer, air gap flux density Bg, optimal design using several different design functions,

end ring width wring, end ring depth dring and air gap length gap.

which could be either conflicting or cooperating The stator and rotor windings materials and current

objectives. In multi-objective functions, f ( kx 1 , ) is a densities as well as the stator and rotor slots numbers are

Jurnal EECCIS Vol. III No. 1 Juni 2009

32 fixed during each design and optimization realization.

dl The losses to be minimized are assumed to be

skew a

2 consisted of the stator and rotor joule losses and the

skew

g (25) ( dl B

ag )

stator teeth and core losses.

4 p 22 π

1) Equivalent circuit parameters

K Xm In order to express losses in terms of the design es

K skew = 1 −

(26) N 2

variables, motor equivalent circuit parameters must be

End-leakage reactance:

found in terms of the design variables. They are

consecutively given in (15) – (43).

X end =

end

2 l a ( d + d es ) (27)

( dl B ag )

Number of turns in series per phase:

k Ns 2 k πτ N

(13) K end = 3.15x10 m

dl B

ph

2 p N es

Ns

ag

ind K Zigzag leakage reactance: Ns = (14)

2 π 2 fk ws

( dl a B g ) g

X zigzag a = K zz 1 2 x

Stator winding resistance per phase:

dw er R s = K Rs

a Kd 3 ) 1 w es

K zz 2 d + K zz 3 − K zz 4 2 + dw

(15) d ( d − 2 ( g

es es

dl B

ag )

dw

2 er

K Rs = s

ph

( K Ns ) (16) zz 5 es zz k 6 N d − 2 g

π 22 p

Rotor resistance per phase:

K zz1 = K Xm

12 N es

d − 2 g − ring

RK

Rr1

zz2 3 − c ) ring ring N 2

2 dw

Rr2

K =+ es 2 K

dl B ag

er er

er (17) K 2

c − 1 N es

(32) ws r ph K Rr1 =

4 m k 2 ρ K 2 ( Ns )

K zz3 =

N er

er (33) K Rr2 =

er K

R (19) zz4

Magnetizing reactance: es (34)

K zz5 =

(35) m =

X Xm

dl

2 zz6

g (20) 2 π

er

( dl B ag )

It is assumed that the total leakage reactance is fm ph 4 µ 0 2 divided equally in the stator and rotor parts, which gives K Xm =

k ws K Ns (21) the following value:

N es pK s

X skew + X zigzag )

X ls = X lr =

X slot + end + X

Slot leakage reactance:

K slot1

d d (36)

X slot =

es

er

( in terms of the design variables as follows. )

slot2

slot3

The stator teeth and core losses are expressed

dl B

P ts = K Pts1 ( d + 2 d es ) dl es a − K Pts2 wdl es es a (37)

K ph = K 2 (23) P cs = K Pcs ( ( d + 2 d es + 2 d cs ) − ( d + 2 d es ) l a slot1 (38)

π 8 fm

Ns

es

where K Pts1 , K Pts2 and K Pcs are: K

slot2 = λ ss

es

d es

K Pts1 = pm ds Fe π (39)

Skew-leakage reactance:

Jurnal EECCIS Vol. III, No. 1, Juni 2009

K Pts2 = pmN ds Fe es (40)

E indstart

I = I + indstart

X K Pcs = pm cs

Fe 4

The core loss resistance can be expressed as:

3) Results

Rc

Table 1 shows a set of design variables values

P ts + P obtained by minimizing losses while confining the

cs

starting and maximum torques as well as starting stator

K 2 Rc = 3 E ind (43)

current between some limiting values. Table 1 The final values during losses minimization iterations

The stator and rotor Joule losses are expressed in terms

Design variables

Final Values

of the design variables as follows.

(44) Stator bore diameter d

P Js = K PJs dw es es ( l a + Kd

Iron core length la

0.01 dwl

2 Stator slot depth des

0.004 P =

( dw er er ) ( d − 2 g − er er a d ring

Stator slot width wes

Jr K PJr1 2 + PJr2

2 Stator core depth dcs

( dl B ag )

( dl B ag ) d ring ring w Rotor slot depth der

Rotor slot width wer

where K PJs , K PJr1 and K PJr2 are:

Air gap flux density Bg

End ring width wring

K = fill es

End ring depth dring

PJs 3 m ph (46) Air gap length gap

K PJr1 = J 2 r ρ r 4 m ph k 2 ws K 2 Ns (47) Starting current

Starting torque

0.8029 PJr2

= J r ρ r m ph k ws K Ns

er

2 K π R p (48)

Maximum torque

In this case, less losses are accompanied with less The total losses are expressed as:

starting and maximum torques. When motor is to be P Loss = P Js + P + P + P (49) used in a wide speed-range operation, the maximum

value obtained is very important to consider. It is

2) Constraints because the motor sometimes needs to develop a torque As constraints, starting torque, maximum torque and

with value almost approaching its maximum torque to starting current are used. Their functions are given as

drive its load.

follows. Using a software like ProDesign, the influence of each design variable on the objective value can be

Starting torque:

2 observed easily. As shown in Fig. 3, when only the p

mU ph Th R r T

influence of air gap flux density on the total losses is to start =

2 π f 2 2 ( be observed, higher the air gap flux density is, less will R

Th + R r )( + X Th + X lr )

be the obtained losses.

Maximum torque:

m ph U 2

2 Th T max =

R Th + R Th + ( X Th + X lr )

Starting rotor current:

R Th + R r )( + X Th + X lr )

Figure 3 The influence of air gap flux density on the total losses

Starting air gap induced voltage: As seen in Fig. 4, this losses reduction is essentially

2 2 produced by the reduction in rotor joule losses (45).

E indstart = I rstart R r + X lr (53)

Starting stator current:

Jurnal EECCIS Vol. III No. 1 Juni 2009

34 nowadays. This trend is being strengthened mainly by

the advances in power- and micro-electronics technology together with those in the field-oriented control methods. An appropriate combination of inverter supply-system and field-oriented control method will give the induction motor a better opportunity to get more and more important roles in adjustable-speed drive-systems.

The required speed and torque characteristics of an induction motor are determined by the type of its application. In an application requiring a wide speed- range, the use of field-weakening method is advisable.

Figure 4 The influence of air gap flux density on each However, for a given set of induction motor parameters, component of losses its torque and speed capability are limited by the

maximum values of inverter current and voltage used. The influence of stator bore diameter on the total

losses is shown in Fig. 5.

Figure 7 Total losses minimization iteration s

Figure 5 The influence of stator bore diameter on the total losses

As shown in Fig. 6, such form of curve is caused principally by the decreasing rotor Joule losses and the increasing stator Joule losses.

Figure 6 The influence of stator bore diameter on each component of losses

If we let all design variables change while putting the starting and maximum torques as well as stator starting current as constraints, the losses minimization iterations are shown in Fig. 7. The iterations of the stator teeth and core losses are shown in Fig. 8, whereas those of the stator and rotor Joule losses are given in Fig. 9.

B. Second Case: Adjustable-Speed Motor Design The use of induction motor in a variable-speed drive-

system is more and more common and desirable

Jurnal EECCIS Vol. III, No. 1, Juni 2009

Figure 8 Stator teeth and core losses iterations during losses Figure 9 Stator and rotor Joule losses iterations during losses minimization

minimization

Operating characteristics Its total phase-impedance can be found as follows:

In order to design a motor being capable of working r + jL ω jL ω in a wide speed-range using an inverter supply voltage,

lr m the conventional motor equivalent circuit, where all

Z total_init =

+ jL ω

ls parameters are referred to stator, should be rearranged

(55) + j ω L

( + L m lr )

to form its associated rotor flux-based equivalent circuit in order to facilitate the field oriented performance

− ω 2 A + jB ω study. Other assumptions, where the stator winding

C + jD ω resistance, iron saturation and losses are neglected, are

where

A = L + L L + L − L taken. 2 ( m ls )( m lr ) m (56)

Rearranging the steady-state induction motor

equivalent circuit into the rotor flux-based one to nullify

m + L ls ) (57)

the series inductance in rotor branch is derived in the following paragraphs.

C = r (58) The original conventional equivalent circuit without

s stator resistance and magnetizing resistance is shown in

D = ( L m + L lr ) (59)

Fig. 10.

Jurnal EECCIS Vol. III No. 1 Juni 2009

T = LII o T (69)

The limiting current and voltage imposed by

the inverter are expressed as:

jωL

2 2 I 2 N ≥ I + I T (70)

≥ ( L l + L o ) I + LI l T (71)

Figure 10 Induction motor equivalent circuit with ignored

stator and magnetizing resistances

For various operating conditions, the required With all leakage inductances being referred to the

torque-producing stator-current components as a rotor flux, the equivalent circuit becomes:

function of flux-producing stator-current component are

as follows:

• constant-torque operation:

LI o

• constant-current condition:

T = I N − I (73)

Figure 11 Induction motor equivalent circuit with all leakage inductances being referred to the rotor flux

• constant-voltage condition:

22 as follows:

Its associated total phase-impedance can be expressed

(74) r

jL 2 ω L

Z total_fin = '

+ jL ω l

The constant-torque operation results in a hyperbolic

+ jL ω

(60) curve of torque-producing current as a function of flux-

producing current, as shown in Fig. 12.

− ω 2 E + jF ω The relation between the torque-producing and flux- =

G producing current components under operation with + jH ω

constant-current condition results in a form of circle where

E = LL ol (61) I

' with a centre (0,0) and a radius N , as shown in Fig.

( 13. L o + L )

H = L o (64)

en rr

n g 1 equations: T=1 p.u.

Equating (55) and (60), will result in the following

ci

T=0.6 p.u.

ro

rr

( T=0.2 p.u. L m + L lr )

L to 2 0

m (66)

o ( L m + L lr )

flux-producing current I λ [p.u.]

LL L L

l = ls +

( Figure 12 Various constant-torque operating conditions

m lr

≅ L ls + L (67)

lr )

lr

When the operating current value N is smaller than developed torque can be stated as:

As described in [Bianchi, 1997], the rotor flux and

the flux-producing current component, (73) gives an

λ= LI o (68)

imaginary number. When its absolute value is taken, the relation between the two current components is shown in

Jurnal EECCIS Vol. III, No. 1, Juni 2009

the left part of Fig. 13. The right-part of Fig. 13 shows used on adjustable frequency controllers. However, a the relation when the imaginary part is ignored.

motor which is designed for best performance on a single frequency is not the optimum motor for use on an

adjustable-frequency system. If a high performance level

.u

p .u

of the system is imperative, either the controller or the

I 1.5 0.8 t

I=1 p.u.

motor should be designed specifically.

en

u rr I=0.2 p.u.

rr en u 0.6

The advance in power-electronic technology and its

n g 1 n g c I=0.6 p.u.

ever-increasing development are almost always able to

d u ci I=0.6 p.u.

d u ci ro 0.4

fulfill such an expectation. On the other side, the

p 0.5 I=1 p.u. ro p 0.2 u e-

e- u

I=0.2 p.u.

inherent complexity of induction motor design makes

rq

rq

0 0 the achievement in this case is not so advanced as that of 0.5 1 1.5 2 to 0 0 0.2 0.4 0.6 0.8 1

to

the control side.

flux-producing current I λ [p.u.]

flux-producing current I λ [p.u.]

p .u .] 0.8 .] 0.5 .u

Figure 13 Various constant-current operating conditions

T 0.6 F W [ F 0.4

Under constant-voltage operation the torque-

producing current component as a function of flux-

producing current component forms an ellipse with t in g

centre (0,0) and an ellipticity -w , as shown in

fl u

Fig. 14. Various values of stator angular frequency are

0 0.5 1 1.5 2 fl

given. The left-part of Fig. 14 represents (74) with the stator angular frequency [p.u.] imaginary values are replaced with their corresponding

stator angular frequency [p.u.]

Figure 15 Flux-weakening torque as a function of stator absolute values. The right-part of Fig. 14 represent (74)

angular frequency when the imaginary values are ignored.

Contrary to the common practice, where the working

p .u .]

.] .u 8 3

characteristics of a motor are obtained from a given set

I T [ 2.5 t of motor and drive inverter, in order to obtain an 6 en

2 rr appropriate motor being capable of working and en rr t ω=1 p.u.

g c ω=3 p.u.

4 g c 1.5 resulting the desired characteristics, motor design should

ci n

n ci

consider the volt-ampere rating of the driving inverter

ro d u

ω=1 p.u.

1 ω=2 p.u.

e- p 2 ω=2 p.u.

ω=3 p.u.

α is the current vector angle representing the

0 0 B 0.2 0.4 0.6 0.8 1

to 0 0 0.5 1 1.5 2 to

angle formed by the torque- and flux-producing current

flux-producing current I λ [p.u.]

flux-producing current I λ [p.u.]

components at rated condition and being chosen during

Figure 14 Various constant-voltage operating conditions the drive design, the limiting inverter current as a function of current vector angle for some values of

o ratio is shown in Fig. 16. It shows that for a (69), (73) and (74), the torque as a function of stator

At the onset of the field-weakening operation, both

limiting current-and-voltage values are attained. Using

given value of L / L ratio, there is a definite current

angular frequency in the field-weakening region can be

expressed as: vector angle value which will require a minimum inverter current value.

L + L 22 o I − N

22 Fig. 17 shows the values of total inductance L o

− LI

being responsible for the flux production as a function T

FW L o

lo Observing (75), above a certain frequency

of current vector angle for some values of L / L ratio.

It can be observed that lower the L / L o ratio value,

l value, it results in imaginary numbers. The left-part of

Fig. 15 shows the torques when the absolute values of o value is. It can also be seen that for a

higher the L

(75) is taken, whereas the imaginary values of (75) are

given value of L / L o ratio, there is a definite current

ignored in the right-part of Fig. 15.

vector angle value which will result in a maximum o L

Design characteristics

value. A higher L value represents a smaller machine

To fulfill the need of a variable-speed drive system,

actually the standard motors designed for general

size.

purpose constant frequency application can often be

Jurnal EECCIS Vol. III No. 1 Juni 2009 Jurnal EECCIS Vol. III No. 1 Juni 2009

N W T F 1 F 0.8 a=0.05 I 4 L /L

l o =0.4 p.u. n t

e 0.8 e u b=0.15 rq

c=0.25

rr u l o =0.3 p.u.

a e=0.55

3 L /L =0.2 p.u.

L /L =0.1 p.u.

stator angular frequency [p.u]

li m 1

stator angular frequency [p.u]

current vector angle α Figure 18 Field-weakening torque as a function of angular

B [deg]

frequency for various L / L o ratio values

Figure 16 Limiting inverter current as a function of current

vector angle for various L / L o ratio values

α B [deg]

] T F 1.4 d W F 1.25 .u a=80 p 5

=0.1 p.u.

in 0.8 a n in g 0.75 t e=30

=0.2 p.u. x i -w L /L u 0.2 x -w l 0.25

fl

0 u fl

ci 2 L /L =0.3 p.u.

stator angular frequency [p.u]

stator angular frequency [p.u]

ro L /L =0.4 p.u.

-p

u x 1 Figure 19 Field-weakening torque as a function of angular r fl

frequency for various values of current vector angle α with

to B

ro 0 0 10 20 30 40 50 60 70 80 90 a given L / L ratio value

current vector angle α

B [deg]

Finally, some general remarks can be drawn as

Figure 17 Total inductance being responsible for the flux

follows:

production as a function of current vector angle for various • the smallest motor size and the lowest inverter L / L

l o ratio values rating cannot be obtained simultaneously in a design .

For a given value of L / L ratio and current-vector • the choice of current vector angle α is determined

B from the desired design characteristics:

design-angle α , there is a definite maximum

B o high torque-capability is obtained with a frequency that can be achieved by a motor. Fig. 18

low value of α , but with higher motor shows the curves of torque as a function of angular B

size (lower inductance L ) and lower frequency for various values of L / L o ratio. It is

power-factor (higher inverter current-

shown that higher the ratio of L / L

l o , lower the

rating I )

maximum flux-weakening frequency is. The right-part o high power-factor and low inverter of Fig. 18 is obtained by ignoring the imaginary values

current-rating are obtained with a high of torque, whereas the left-part is obtained by taking

value of α , but with a lower torque-

their corresponding absolute values.

Influence of current-vector angle α B on the field-

capability.

weakening torque capability for a given value of

3) Design procedure

l To design an induction motor for operation in an weakening frequency will be obtained if the current-

L / L o ratio is shown in Fig. 19. As seen, higher flux-

adjustable-speed drive system, the desired torque-speed vector angle is smaller.

operating range should be known previously. The operating range may comprise the constant-torque and the field-weakening regions. The constant-torque operation is normally carried out up to the rated operation speed. Above this speed, another strategy

Jurnal EECCIS Vol. III, No. 1, Juni 2009

39

must be adopted because in this operating region the with its associated constraint functions must be built nominal voltage of the driving inverter would have been

using the design variables and parameters. The objective attained. Increasing the speed beyond that rated

along with the constraint functions must be resolved condition can be realized by weakening the flux while

using some known optimization techniques. To solve the maintaining the supply-voltage at its nominal value.

optimization problem, some commonly used optimizing Consequently, the required motor parameters and the

algorithms are available. Some known calculation volt-ampere ratings of the driving inverter must be

softwares, for example Matlab, MathCad, etc., provide determined to meet the need.

ready-to-use optimizing functions based on some Steps to design an induction motor being capable of

commonly known algorithms. Design software with working in the field-weakening region are as follows:

optimizing capability, for example ProDesign, is also

1) Determine the desired field-weakening available commercially. Optimization included design performance

software forms the state-of-the art design method. The • the flux-weakening torque T FW key in optimization, which is also the difficulty at the

• the flux-weakening angular frequency same time, resides at the construction of objective and ω constraints functions using the design variables and

FW parameters. It is not always easy to construct a group of

2) Determine the required ratio of total leakage independent equations in order that the optimization inductance to rotor-flux producing inductance

algorithm can be applied appropriately.

L l / L o and the current vector angle at base

The description of energy saving through motor design optimization in this article is completed with

condition α B some examples of design with special objectives. An

3) Calculate the

required

inductance

induction motor design with minimized losses has been

corresponding to rotor-flux production o L , the taken as a case example. The description of how to

design an induction motor being operated in an

total leakage inductance L l and the inverter adjustable speed environment has also been presented. current rating I N

VI. A CKNOWLEDGEMENTS

4) Determine the base operating values of the desired motor: the base torque, the base angular

The author would like to thank The Swiss Federal frequency, the base voltage, the base current

Commission of Scholarship and The Integrated and the base inductance

Actuators Laboratory of the Ecole Polytechnique

5) Find the peak stator current and the motor Fédérale de Lausanne for having financed and made inductance

possible the accomplishment of my researches some

6) Choose the poles number, maximum stator results of which are presented in this article. tooth flux density, maximum stator iron yoke

flux density, the stator slot height, stator slot- BIBLIOGRAPHY width, winding coefficient and number of stator

slots per pole per phase.

[1] Bianchi, N. and Bolognani, S. (1997) “Design procedure of a

vector

motor for flux-weakening operations”, Conference Record of the Thirty-Second IAS

controlled

induction

V. C ONCLUSION A ND O UTLOOK Annual Meeting, IEEE Industry Application Conference, In this article, a global view on how to design IAS’97., Volume:1, Page(s):104-111.

[2] _________. (1997). “Parameters and volt-ampere ratings of a

induction motor is described. Beginning with the

field-oriented induction motor drive for flux-weakening

description of design problem, various different

applications”, Eight International Conference on Electrical

objectives based on the types of supply as well as loads machines and Drives. Conf. Publ. No. 444, Page(s): 46-50.

[3] Hamdi, E.S. (1994). Design of Small Electrical Machines, New

to drive are given. Basic concepts and a general

York: John Wiley & Sons Inc.

procedure to design a motor is followed with the

[4] Ramarathnam, R. (1969). Optimization of Polyphase Induction

description of two common motor design methods, the

Motor Design . Bombay: IIT Master of Technology Thesis. [5] Venkataraman, P. (2002) Applied Optimization with MATLAB

classical one being based on a previously available

Programming . New York: John Wiley & Sons.

design and the state-of-the art method involving the use of commercial design including optimization software. It can be concluded that using both methods, up to a certain extent the experience of the designer is still required at various design stages. It is still unconceivable to have an independent, unique and general program being capable to do the design job completely and giving satisfactory results.

Completing the motor design, optimization is necessary. Beginning with determining the objective of optimization, an objective function to optimize along

Jurnal EECCIS Vol. III No. 1 Juni 2009