Optimization of induction motor design

Seria: E LE K TR Y K A z. 176 N r ko>- 1500

M iroslav SAMEÖ1’

O P T IM IZ A T IO N O F IN D U C T IO N M O T O R D E S IG N

S um m ary. The problem with electric machine optimization can be specified as searching for a compromise between requirements manufacturer’s and user's. Optimum design depends on several parameters, therefore it is very difficult to find real optimum. The evolutionary methods seem to be a way to solve this problem. In this paper there is explained the basic principle of simple Genetic algorithm with binary coding and Simulated Annealing algorithm. Their application to design optimization of a maximum efficiency induction motor is presented as well.

Key w ord s: Genetic algorithm (GA), evaluation function, fitness value, crossover, mutation, Simulated Annealing algorithm (SA)

1. IN TRO DUC TIO N

Squirrel cage induction m otors are w idely used in industry. These motors consume 35% -50% of the total electric energy [5], M anufacturers should be m otivated to manufacture m otors of higher e fficiency. T his is practically executed in Canada. M anufacturers are granted if they m ake m otors of h igher efficiency [2], Factories from Europe that want to export the motors to such a country, have to com ply with strict standards. Production plan of high efficiency machines has SIEM ENS s.r.o. in FrenStat p.R. (Czech R epublic) at present time. The goal of m y work is to design a squirrel double cage induction m otor o f m axim um efficiency.

2. E FFIC IE N C Y IM PR O VEM ENT

For optim ization I have chosen the batch produced squirrel double cage induction m otor with follow ing param eters:

Num ber o f p o le s ... 4 N om inal vo lta g e ...380 V F re q u e n c y ... 50 Hz N om inal p o w e r...18.5 kW W inding jo in t... D E fficie n cy... 90.3 %

T his m otor analysis shows the lay-out of the losses. The stator iron losses and stator winding losses are dom inant, as we can see in Table 1 (the original m otor). I would like to m ention m aterials used in this motor. T he m agnetic core is m ade o f lam inations 0.5 m m width (p i0=2.3 W /kg). The stator w inding is m ade of copper pCu=1/56 n mm2/m. The winding is o f two layers with 5/6 short pitch. T he rotor double cage is m ade of cast aluminium ^pai= 1 /3 4 C im m2/m.

T he efficiency im provem ent of induction m otors is discussed very often nowadays. The authors o f [3] tested m otors with m odified param eters. The original construction was 4 kW , two poles, 400 V, Q s=36, Qr=28, D6=104 mm, Dr=103.2 mm, Dex=180 mm. The design variables were: the core length, the use o f sem i m agnetic slot wedge, the core material, the winding pitch full or 5/6 short, the rotor end ring m aterial Copper or Copper+Fe (the original m otor has Aluminum). The highest efficiency o f the tested m otor w as reached by increasing the core length (0 . 1 2 m instead o f 0.082 m), by using better m agnetic m aterial 0.5 mm CK-37 (1.45 W /kg, 50 Hz, 1 T) instead of 0.63 mm

1) Ing. Miroslav SAME§, vSB - Technical University of Ostrava, Faculty of Electrical Engineering and Informatics, Department o f Theoretical Electrotechnics, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic, tel.

+420/69/699 55 10, +420/69/699 55 55, fax. +420/69/691 95 97, e-mail: miroslav.sames@vsb.cz Num ber of stator slots... 48 Num ber of rotor slots...40 O uter stator diameter... 0.28 m

DK-70 (3.1 W /kg, 50 Hz, 1 T), by using end ring m aterial C opper+Fe and by using full w inding pitch.

T he efficiency increase w as 6.5 % at nominal point (from 85.5% to 92%). See reference [3] for details.

T he w ays to im prove the induction m otor efficiency [5]:

1. decrease o f the stator w inding losses

• g reater stator w inding section 2. decrease of the rotor w inding losses

• g reater rotor w inding section

• fe w e r turns connected in series in one stator phase cause less rotor current

• using copper

3. decrease of the core losses

• longer m agnetic core (decreasing o f the m agnetic flux density at constant m agnetic flux and less num ber o f turns connected In series in one stator phase)

• better m agnetic m aterial 4. decrease o f the additional losses

• optim al air gap size

• optim al shape and num ber o f stator and rotor slots

• using sem i m agnetic slot wedge 5. decrease of the m echanic losses

• suitable ventilation

• optim al m oto r fram e in order to im prove cooling

• good bearings and lubrication

6. h igher tem perature category o f insulating system - less am ount o f cooling m edia - sm aller ve n tila tor (but the tem perature increase m akes winding losses rise).

A s m entioned in Table 1, the m ain losses arise in the stator winding (38.1 % o f total losses) and in the core m aterial (24.3 % o f total losses). T hat is why there have been chosen the following param eters fo r design o f a high efficiency m otor with m anufacturing possibility considerations:

1. num ber o f turns connected in series in one p h a s e ... N1 = 80-120 2. core le n g th ... I = 0.19-0.30 m 3. diam eter o f stator wire (w ithout in su la tio n )... d = 0.8-0.95 mm

T he core o f the optim ized m otor is m ade up from lam inations with pio=1-8 W /kg instead of Pio=2.3 W /kg in original construction. T he influence o f these fo u r design variables on the motor im portant param eters is discussed in C hapter 4.

G e n etic algorithm and Sim ulated annealing algorithm were used to optim ize this motor. In next chapters the basic principles of these tw o evolutionary m ethods w ill be described.

3. O PTIM IZ IN G M ETH O DS

In com putational design optim ization o f an induction m otor (generally a device) there are two to o ls th a t cooperate to yield the optim um result:

• s e a rc h to o l - this role is played by G A (SA) here. A s every point in the search space represents a d ifferent design, fo r every chrom osom e (in G A case) that is decoded into a point in the search space, the algorithm subm its that particular design to the other tool of the optim ization, th a t is

• a n a ly s is to o l - it is used to obtain a perform ance m easure. The analysis tool task is to solve the equations fo r the subm itted design and to return the relevant param eters back to the search tool.

T he optim izing program uses the m otor com putation (the analysis tool) through the evaluation function. By m eans o f this design the evaluation function is established and “fitness” value is com puted. T his is very im portant step in optim izing process. The evaluation function depends on the problem to be solved, and its form should be as follows:

F (x )= F1(x )= m a x (m in ) 0 )

F ( x ) = a F1( x ) + p — l - r = m ax(m m) (2) F2\x )

f M = + Y ■ F3(x ) +• • • + C Fn(x ) = m ax(m in) (3)

n

F(x )= y ^ ( v a lu e i( x ) - V a lu e^ , ^ ) 2 = min (4)

i=0

x a set o f design variables.

T he sym bols a, p, y and £ stand fo r biases. For exam ple the equation (2) should be used to find m axim um efficiency considering a m inimum weight, the variable F,(x) is the efficiency and the variable F2 is the com ponent weight. The equation (4) should be used to minimize a deviation from a desired characteristic curve.

A s m entioned earlier, my goal is to find m axim um efficiency o f the induction m otor. The evaluation function Is used in both algorithm s. There have to be noticed the GAs search m axim um and SAs look fo r m inim um point of the explored space. Therefore the evaluation function has the form s

F (N U d )= efficie n cy(N 1 ,l,d ) (5)

fo r GA, and

F(N' ld> - * d ^ n 5) (6)

fo r SA algorithm .

T he algorithm s are available on the Internet, the G enetic algorithm on the ftp server, see [1], and the Sim ulated Annealing algorithm on the web page, see [6J. Both algorithms are in the program m ing language C. I im plem ented the electrom agnetic design o f the induction m otor in the program m ing language C, and it stands fo r analysis tool.

3.1. Genetic algorithm

G A is inspired by m echanism o f natural selection, a biological process in which stronger individuals are likely to be winners in a competing environm ent. Search space is tested stochastically w ithout stringent m athem atical form ulation such as the traditional gradient-type of optim izing procedure. GA w orks with a population o f potential solutions. The population consists of chrom osom es. Each chrom osom e is m ade-up from genes. Design variables are regarded as the genes o f a chrom osom e and it is structured by a string o f values in binary form.

There is necessary criteria generally known as “fitness” value. It is used to reflect the degree of

“goodness” o f the chrom osom e fo r solving the problem, and this value is closely related to the evaluation value. Through genetic evolution, better chrom osom es (a better solution o f the problem ) has higher chance to m ove up to the new population.

Creation o f the new population:

• evaluation - calculating of each chrom osom e fitness value by evaluation function,

• selection - the population is divided into two parts, better and worse, by a fitness value,

• crossover - the new population Is made from better part of form er population by m eans of operator crossover. W orse part o f the population is replaced by new chromosomes,

• m utation - som e bits o f the new population chrom osom es are changed from 0 to 1 (or from 1 toO ).

W e repeat these fo u r points until the end condition is reached. This condition should be m axim um num ber o f populations (in this case), the am ount of individual’s variation between d ifferent generations, or a predefined fitness value.

T he genetic algorithm structure including input values is shown in Fig. 1. The fitness (efficiency) im provem ent from initial generation to generation 200 is shown in Fig. 2.

The genetic algorithm s, their m odifications and applications are discussed in [1],

Fig. 1. The structure of the genetic algorithm

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Fig. 2. The fitness value progress

3.2. Simulated annealing algorithm

T he basic idea cam e up from therm odynam ics. To grow a crystal, w e start y heating a row of m aterials to a m olten state. Then we reduce the tem perature o f this crystal rnlt until the crystal structure is done T he m aterial has m inim um energy at the end of annealing procss.

The searching space is exploring stochastically by the algorithm . In the begining w orse points in the neighbourhood o f the current point are also accepted. This property is ven important because the algorithm is able to escape from a local m inimum . Than with decreasig tem perature the probability o f accepting these w orse points is less than at high te m p e ra tu re .. worse or a better point is determ ined by evaluation function as m entioned above.

The basic evolutionary m ethods, the hill clim bing, the tabu search and the imulated annealing algorithm are detailed discussed in [4].

4. RESULTS

T he design variables, the original and the optimized m otor param eters are nown in Table 1.

T able 1 T he original and the optim ized m otor comparing

Subscripts: 1 - stator, 2 - rotor

Param eter Original

m otor

O ptim ized m otor num ber o f turns connected in series in one phase N1 [-] 124 8 8

core length I [m] 0.19 0.3

diam eter o f sta to r w ire (w ithout insulation) d [m m] 0 . 8 0.85

core m aterial (0.5 m m w idth) P,o [W /kg] 2.3 1 . 8

Iron losses (hysteresis and eddy current) APpei [W] 480.5 388.3 APf <,2 [W] ⁰ (neglected) 0 (neglected)

S urface losses AP, [W] 2.3 2.5

AP2[W] 41.5 44.3

P ulse losses APp, [W] 4.7 3.8

APp2 [W] 15.1 1 1 . 8

M echanical losses APm[W] 1 0 0 1 0 0

A dditional losses APd [W] 1 0 1 . 8 1 0 1 . 8

W inding losses APji [W] 753 609

A P j2[W] 477 351

T otal losses AP [W] 1 976 1 612

efficiency q [%] 90.3 92.0

rated torque M [Nm] 1 2 0 . 8 1 2 0 . 0

rated pow er fa cto r cosip [-] 0 . 8 6 0.85

rated speed n [m in'1] 1463 1472

m otor cost* cost

[units] 684.36 1 130.47

'The motor cost is calculated in units: the original motor - the core material costF.=S units/kg, the stator winding costcu=30 units/kg, the rotor winding cost*i=20 units/kg; the optimized motor - the core material costf.=7.5 units/kg, the c o s tc and the cost« remain the same.

A s we can see in this table, the optim ized m otor is longer and it has better m agnetic m aterial (Pio=1.8 W /kg), the sta to r w ire diam eter increases thanks to less num ber of turns connected in series in one stator phase. It m ust be rem inded that the m otor diam eter (the outer stator diam eter D2= 0.28 m) is the sam e in both cases. T he iron losses (hysteresis and eddy current) as w ell as the w inding losses decreased rapidly. T he operating point param eters are listed in the last lines o f the table. T he torque-speed curves com parison is shown in Fig. 3.

It is interesting to follow the m otor cost price. The cost covers only m ain materials, the m agnetic core and w indings m aterials. The cost is calculated in units. The optimized motor cost increased a lm ost twice. In practice we have to design a new stator fram e and the m otor cost keeps rising. But the total losses decreased by 364 W . The energy saving depends on the m otor service.

T he im portant advantage o f this optim ization result m ust be pointed out: the stator and the rotor shape lam inations rem ain the same.

The m otor shaft needs to be recalculated if its sag is in tolerance. If it is not satisfied there are two options: the first - using better shaft m aterial (the rotor lam inations shape remain the same), the second one - using new rotor lam inations shape with larger hole fo r the bigger shaft. The second change m akes the m agnetic flux density in the rotor yoke increase, but the magnetic flux density decreased approxim ately by 1 0% in the optim ized motor.

Using the m agnetic slot wedge is very im portant fo r suppression o f harmonics in the m agnetic field. It is possible to increase the m otor efficiency by several per cent [7].

5. C O N C LU S IO N S

In this paper there are presented tw o evolutionary m ethods, the Genetic algorithm and the S im ulated annealing algorithm , used fo r to design of the induction m otor o f maximum efficiency.

T he optim ized m otor efficiency increased from 90.3 % to 92 % thanks to increasing the m otor length, decreasing the num ber o f turns connected in series in one phase, increasing the diam eter of sta to r w ire and using better m agnetic m aterial. The m ain advantage o f this optimization is the same shape o f the stator and rotor lam inations (at com pliance the conditions discussed in previous chapter). T he optim ization has the following disadvantages: the robust construction of optimized m otor, the higher starting current and increasing the cost price (approximately twice). But the payback depends on the m otor service and accruing the energy prices. Using the m agnetic slot w edge is very useful and it can bring another significant im provem ent o f the efficiency.

REFER E N C ES

1. M ichalew icz Z.: G enetic algorithm s + data structures = evolution programs, 310 rev. and extended ed., Springer 1996; the source code of author's algorithm is available on: ftp.uncc.edu, the folder coe/evol, the file prog.c.

2. K o sfa l P.: A synchronnl m otory s vysokou u iin n o s tl (in Czech), Diplom ova p ric e 1996, Departm ent of electrical m achines and apparatus, Technical university of Ostrava.

3. Haataja J., Pyrhdnen J., Kurronen P.: Im proving the efficiency of squirrel cage induction motors:

technical and econom ical consideration, IEEE/KTH Stockholm Power Tech Conference, Stockholm , Sweden, June 18-22,1995, p. 217-222.

4. M ichalew icz Z., Fogel D. B.: How to solve it: Modern Heuristics, Springer 2000.

5. C h m elik K.: N ik la d y na provoz asynchronnlch m otoru (in Czech), Elektrotechnika v praxi, no. 1, Vol. 2, 2000, p. 24-33.

6. Ingber L.: Lester Ingber's Code and R eprint Archive, http://w w w .ingber.com /.

7. Liska F., Kopacka V., Becvar L.: A plikace m agneticky vodivych klinu (in Czech), Elektrotechnicky obzor, no. 10, 1976.

Recenzent: Dr hab. inz. W ie sla w Jazdzyriski

W plyn^to do Redakcji dnia 15 lutego 2001 r.