Weight optimisation of a salient pole synchronous generator by a new genetic algorithm validated by finite element analysis

Transcription

1 Published in IET Electric Power Applications Received on 5th June 008 Revised on 5th December 008 doi: /iet-epa ISSN Weight optimisation of a salient pole synchronous generator by a new genetic algorithm validated by finite element analysis M. Çelebi Electrical Engineering, Celal Bayar University, Manisa, Turkey mehmed.celebi@bayar.edu.tr Abstract: In this study, a new approach for genetic algorithm (GA) is proposed and compared with conventional GA (CGA) in the weight optimisation of a -MVA salient pole synchronous machine. The main differences between the two algorithms are that, in the newly proposed method, individuals are paired and crossed over based on the Mendelian rules of genetics, and the mutation operator is omitted. The rules concern the segregation of Alleles and the independent assortment of Alleles. This approach is comprehensive and conceptually accurate since its framework uses Mendelian population genetics. The operation CPU time is longer in the new approach when compared to the conventional one but can be ignored in electric machine design since it is not a real-time process. The results of the analytic solution and the new and CGA implementation methods are compared in terms of weight, efficiency and temperature. The results obtained are similar to those of the conventional ones and even better in some cases. A finite element analysis (FEA) is done to realise the machine designs optimised by the new GA (NGA) and CGA for the case of a fixed 4-pole design. Hence the improvement over CGA achieved by NGA has been validated through FEA. Nomenclature b 0 b k b dave B c B d0 B di B dave B ba B pc B br B maxa c C D i width of the slot width of the cooling duct average width of the stator tooth half value of the difference between flux density of the air gap at the middle of the tooth and slot pole flux density of the air gap at the middle of the pole flux density per stator tooth average tooth flux density flux density at the stator yoke flux density at the pole kernel flux density at the pole leg maximum flux density of the air gap of the machine empiric value used in determination of slot size utilisation factor rotor diameter D a G cua G cum G ba G da G ra G pa G total h 0 h p1 I n I mn I r, I s k 0 k e k e stator iron packet exterior diameter copper weight of stator coil copper weight of excitation coil weight of stator yoke weight of stator teeth weight of rotor yoke total rotor pole weight total weight of the machine depth of the slot rotor pole leg height nominal stator current nominal excitation current linear current densities for rotor and stator factor about thickness of the iron of the rotor pole iron filling factor for stator sheets iron filling factor for rotor sheets 34 IET Electr. Power Appl., 009, Vol. 3, Iss. 4, pp & The Institution of Engineering and Technology 009 doi: /iet-epa

2 K l ave L cum L L i L total m n s N O p p cbc P cua P cum P fe P feba P feda P kfri P y P ky R a R m s a s mn S V n q q cua q cum U m w a w m y z 0 u ave total increment in the stator coil resistance related with temperature average length of the excitation coil length of the excitation coil length of armature without cooling ducts fictive armature length total armature length number of phases synchronous speed number of slots total area of the pole leg coil fronts losses stator coil loss excitation coil loss total iron loss iron loss including labour factor teeth loss including labour factor friction loss specific surface loss of pole leg total specific surface loss of pole leg resistance of the stator winding at 758C resistance of the excitation winding at 758C stator coil current density excitation coil current density apparent power nominal voltage number of slots per phase pole stator coil conductor cross-section excitation coil conductor cross-section excitation voltage number of windings per phase of stator coil number of windings per pole of excitation coil reduced coil width by rotor diameter number of conductors at one slot total above-medium excess temperature of stator coil u ave total above-medium excess temperature of excitation coil u umax maximum ampere-turn/pole pair at nominal load p pole pair t 0 slot pitch t p pole pitch a pole pitch factor d 0 air gap at the middle of the pole g fe specific weight of iron s H hysteretic loss material constant s W eddy current loss material constant h efficiency 1 Introduction Genetic algorithms (GAs) are evolutionary and heuristic search algorithms that are based on the basic principles of natural evolution. GAs are now rather widely used for solving electromagnetic design and optimisation problems of electric machines (Table 1). But the difficulty in their use is to find the objective function; in addition, data are read repeatedly in the simulation process, often as much as 50 times, from the graphic representations of the magnetic flux characteristics of the machine and material used in electric machine design process. These graphics can be obtained analytically, but in many cases the error ratio will be outside the tolerated limits. Another difficulty is the determination of the inputs of the objective function that describe power, frequency, dimensions, windings and the electrical parameters of the machine. The output of this function will cover well-known parameters such as reactance, currents, temperatures, efficiencies, weights, losses and torque. All the articles referred in Table 1 use very few characteristics, one of the main differences of this work as mentioned above. An application of a new approach based on two explicit rules of Mendel experiments and Mendel s population genetics for the GA is the second goal of this paper. These rules are segregation of alleles and Table 1 Some GA applications in previous works Ref. no. Machine type Design objectives Number of parameters [1] brushless DC material cost 7 [] general weight 7 [3] squirrel cage induction motor efficiency, torque 138 [4] permanent magnet synchronous motor efficiency 7 [5] permanent magnet synchronous motor flux density, torque density 17 [6] flux switching motor efficiency 7 IET Electr. Power Appl., 009, Vol. 3, Iss. 4, pp doi: /iet-epa & The Institution of Engineering and Technology 009

3 independent assortment of alleles. The doctrinal sense of GA is improved concept-wise by this approach using the Mendelian framework. The new approach is different from the conventional one in terms of crossover, recombination and mutation operators, and it has been simulated for the optimisation of the machine. Details of the new approach are presented in a previous work [7]. The operation CPU time is longer in the new approach when compared to the conventional one because of the massive matrix dimensions carried out, and can be ignored in electric machine design since it is not a real-time process. So the design method proposed in this work has a traditionally complex structure; the objective function is implemented by a MATLAB code. This paper is focused on the weight of the machine, which is one of the main cost parameters. First, a physical description of the machine is given. The weight is analytically solved for a -MVA synchronous machine in terms of the stator and rotor parameters. Then, the results of the analytic solution and the new and conventional GA (CGA) implementation methods are compared in terms of weight, efficiency and temperature optimisation parameters. The results obtained are similar to those of the conventional ones and even better in some cases. Application of the design process The dimensioning process of synchronous machines utilises calculation models based on the theory of electric machines and well experienced knowledge. This work deals with a GA optimisation of a previously analytically designed salient pole synchronous machine [8]. The characteristics are achieved from practical values of former machine designs based on a German school. The purpose of this design is to optimise the machine s weight, efficiency and temperature to correspond to various electrical and mechanical objectives. The GA optimisation is applied for the fixed pole number of 4. The chromosome in the GA process is defined by 11 parameters. The objective function is based on the weight, efficiency and temperature of the machine..1 Functional description of the machine parameters Since there are so many machine parameters and functions of these parameters, we concisely define them all in Table 6 at the end of the paper. The chromosome parameters of the GA and their functions are given in Tables and 3, respectively. The dependent boundary conditions for some of the machine parameters are given in Table 4. For compactness and readability of the paper, we briefly give the necessaries [9]. The three-phase armature winding is assumed to be symmetric and all slots are winded to simplify the process. The weight of copper used at armature coil is h G cua ¼ :9 00L total þ :4 x i 6p 60 þ 18:6 x8 8 x :8V n sin (p=x 6 m)f b (x 3 ) x 8 b k 4:3x 4 fl total (10 3 b k B 6 4 [(100L total 5)x 1=3 1 x =3 ]=[6 5A þ (1=0:9f Is (t p ))]) (1) Table Chromosome parameters of the synchronous machine and related boundary conditions Variables Definition Boundaries Optional conditions Bit Unit x 1 S 1.69, x 1, 60 x 1 ¼ MVA General x p 8, x, 4 1, x, 4 x 6 Q 0.5, x 6, 8, x 6, 4 1 x 4 B d0 0.7, x 4, 1 0.7, x 4, 1 8 T x 5 B di 1.6, x 5, , x 5, T Operational x 9 B ba 1, x 9, 1. 1, x 9, 1. 8 T x 10 B pc 1., x 10, , x 10, T x 11 B br 1, x 11, 1. 1, x 11, 1. 8 T x 3 a 0.5, x 3, , x 3, Geometric x 7 h 0 /b 0 4, x 7, 6 4, x 7, x 8 h 0 3, x 8, 1 7., x 8, cm 36 IET Electr. Power Appl., 009, Vol. 3, Iss. 4, pp & The Institution of Engineering and Technology 009 doi: /iet-epa

4 Table 3 Functions describing the characteristics Functions Eq. no Definition and the corresponding parameter Boundaries Unit f c (x 1, x ) utilisation factor 4, C, 5 f Li /t p (x 1, x ) fictive armature length/pole arc 0.7, L i /t p,.5 f Is (t p ) 13 linear current density for stator 00, I s, 700 A/cm f B max a (t p ) 13 maximum flux density of the air gap of the machine 0.7, B maxa, 1 T f b (x 3 ) 1 pole angle factor 0.5, x 3, 0.75 f hp1 (t p ) length of the pole leg 0, t p, 70 cm f khb (x, D i, D a ) 15 hysteretic correction factor 1, k hb,.4 f kwb (x, D i, D a ) 15 eddy current correction factor 1, k wb,.4. Calculation of copper weight of excitation coil The medium temperature of excitation winding is assumed to be a constant value of 758C. Excitation coils are manufactured from flat windings that have 1-mm width in order to provide heat circulation. The cross-section area and the average length of the excitation winding must be satisfied by the nominal and maximum current densities of excitation coils that are limited between 3 and 4.5 A/mm. The copper weight of excitation coil is 00 " # 1 1=3 G cum ¼ 0 7 p x 1 x A x 6pf c (x 1, x )f Li =t p (x 1, x ) uu þ 33:4 8f hp1 (t p ) max U m þ t p (31:4x 3 þ 8:78) " 100L total c :19k e L total!# ().3 Calculation of the weight of stator yoke The weight of the stator yoke is G ba ¼ 0:1g fe k e p 8 ( f Li =t p (x 1, x )p) x 1 " #1=3 9 Table 4 Dependent boundary conditions related to the synchronous machine Dependent variables Definition Boundaries Unit t 0 slot division, t 0, 5.5 cm b 0 slot width 1.6, b 0, 1.8 cm z 0 number of conductors in a slot 10, z 0, 13 I r s a s mn B pc linear current density for rotor stator current density excitation current density rotor pole flux density 300, I r, 650 A/ cm 3, s a, 5 A/ mm 3, s mn, 4.5 A/ mm 1., B pc, 1.5 T 0:88 3 f c (x 1, x )6x 0vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 u x 1 x (x 8 1) 3 t 0:1x 6pf c (x 1, x )f Li =t p (x 1, x ) 8 0:05A >< >= þ x sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 1 x 3 x 9 k e 6pf c (x 1, x )f Li =t p (x 1, x ) 31=3 1 þ 0:1x 8 4 0:88 3 f c (x 1, x )6x 5 x 4 A >: ( f Li =t p (x 1, x )p) x 1 x 9 k e >; (kg).4 Calculation of the weight of stator teeth The total weight of the teeth is g fe k e 0:88f Li =t p (x 1, x ) =3 p x G da ¼ x 1 x =6pf c (x 1, x ) 1=3 0:1x8 þ 0:5 1 (3) IET Electr. Power Appl., 009, Vol. 3, Iss. 4, pp doi: /iet-epa & The Institution of Engineering and Technology 009

5 "sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 10 3 p 3 x 1 x 3 6pf c (x 1, x )f Li =t p (x 1, x ) # þ 100p(x 8 þ 5) mx x 6 x 8 10 x 7 kg.5 Calculation of the weight of rotary parts The weight of the rotor pole is G pa ¼ 0:1g fe k e 41:056f Li =t p (x 1, x ) p x " # x 1 x 1= pf c (x 1, x )f Li =t p (x 1, x ) 0 c 40t p þ 6:5 f hp1 (t p ) þ 100t p h p1 x 3 :19k e [1:056f Li =t p (x 1, x )(p=x ) B h i 1=3 1] A x 1 x =6pf c (x 1, x )f Li =t p (x 1, x ) The weight of the rotor yoke is 0 G ra ¼ 0:1g fe pk 1:056f Li =t p (x 1, x ) p x " # x 1 x 1=3 11 A 6pf c (x 1, x )f Li =t p (x 1, x ) (40t p þ 6:5) " 50 " x 1 x 6pf c (x 1, x )f Li =t p (x 1, x ) d 0 5(40t # p þ 6:5) þ h p1 4 kg where is the air gap (cm). d 0 ¼ 0:003t p f Is (t p ) f B max a (t p ) 1 # 1=3.6 Calculation of the objective function x (4) (kg) The total weight function as a function of the chromosome parameters X for the task machine is G(X ) ¼ G cua þg cum þ G ba þ G da þ G pa þ G ra (kg) (8) The next step is to determine the function of efficiency of the machine as a second design objective. (5) (6) (7).7 Calculation of copper losses of the machine The essential well-known loss about electric machine design is the copper loss caused by the increase in the temperature of stator windings. The winding resistance will increase depending on the winding type because of the current concentration at the surface of conductors at higher frequencies. These additional currents will also increase the copper loss by an additional factor. The exact stator coil loss function is 8 1 þ 9: L b cu h 9 kcu >< n cu h l P cua ¼ 3In ave b cu >= 0 R " a # 100L >: þ10 5 c l ave m >; cu (W) Both b cu, b kcu and h cu, h kcu are non-isolated and isolated width and height of conductors, respectively. n cu and m cu are, respectively, the numbers of partial conductors and conductors in one layer. c ¼ y/t p ¼ 0.89 is the winding factor for double layer windings of the machine [8]. The excitation coil copper loss is (9) P cum ¼ I mnr m (W) (10) where R m ¼ r t L cum =q cum, R m ¼ U m w m =1:05u umax and R m ¼ U m(30t p 8f hp1 (100t p ) þ 33:4) 1:05u u max (V) (11).8 Coil front losses of the machine This loss is calculated using empirical formulas [8]. The loss per frontal connection is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p cbc ¼ Ir (100t p )=d 0 7:14 (W) (1) The total loss is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P kcbc ¼ pd i 0:0114 Ir (100t p ) 3 =d 0 714: (W).9 Calculation of the iron losses of the machine (13) Iron losses are produced at the stator yoke and tooth of the machine, and must be calculated separately. The iron losses are categorised as hysteretic and eddy current losses in the classical machine literature. The eddy current losses change with the inductive and ohmic resistances of the laminated steel. Then, including the effects of harmonics and labour 38 IET Electr. Power Appl., 009, Vol. 3, Iss. 4, pp & The Institution of Engineering and Technology 009 doi: /iet-epa

6 factor, the hysteretic loss per kilogram steel is p fe ¼ s H B f 100 þ s WB f (W=kg) (14) 100 and the eddy current loss per kilogram steel is " f P feba ¼ 1:5 s H f khb (x, D i, D a ) 100 # f þs W f kwb (x, D i, D a ) x 100 9G ba (W) (15) The stator teeth loss is P feda ¼ 1:5p 1 B daveg da (W) (16) where p 1 is the specific iron loss factor under Calculation of surface losses of the poles of the machine and friction losses The specific surface loss of the pole leg is P y ¼ k 0 (10 4 Nn s ) 1:5 B c t 0 (W=m ) (17) 0:1 The total surface loss is P ky ¼ O p P y (W) (18) The frictional loss of a -MVA machine is approximately 0.3% of the total power and is obtained from the special characteristic [10] a 4-pole machine, the analytical design of which is given in [8]. The CGA is simulated 10 times for each parameter set and the results are averaged. To determine the generation number at which the GA performs best, the initial and sub-population sizes (ipop and subpop) are fixed, and crossing over and mutation ratios are assumed constant as the generation number is varied. Then, the procedure is repeated for the initial population size of 00. The result obtained for ipop ¼ 00 is enough to make an effective comparison. The yoke weight constitutes one of the main weights of the machine. The weight minimisation will produce a value of 7 m for the exterior diameter of the stator yoke for a 4- pole machine, and a value of 174. m corresponding to a number of 1 (Fig. 1). The total weight is similar to the yoke weight since the parameter set fn s, D i, t p, b k, d 0, L total, z k, L, L i g is fixed in the 4-pole machine. The variation of the total weight of the machine as the algorithm progresses as depicted in Fig. 1 shows the minimised weights of various parts of the machine as a function of pole number and rotor diameter, summarising the major results of this paper. The minimum weight of 5545 g is determined as 1 poles (if the only criterion is weight), eventually, though it is close to that for 14. The weight of the machine decreases as the armature length increases since increased armature length improves torque performance and thus decreases the weights of the copper and iron at the same power. Fig. depicts the average results of the 4-pole machine obtained by the CGA. Each machine configuration is simulated up to 30th generation until the algorithm stabilises. The algorithm is run 10 times P kfri ¼ 10 4 x 1 ( 0:0039x þ 0:406) (W) (19) The final efficiency function h(x ) ¼ P n =(P n þ P cua þ P cum þ P feba þ P feda þ P ky þ P kfri ) (0) which is a part of the optimisation procedure. Till now, all parameters are obtained for design optimisation. Now, we can include efficiency and weight function into our GA process. Tables and 4 summarise the dependent and independent boundaries, whereas the optional conditions demonstrate the task machine. The operation ends with this step; both the boundary conditions and the objective function are expressed for the GA optimisation. 3 Comparison of the results 3.1 With the CGA In this section, we compare our results with those found by the CGA. All calculations are made for the optimisation of Figure 1 Total weight of the task machine against the rotor diameter for variable pole numbers and ipop ¼ 300. G cua and G cum are the stator and rotor copper weights, G da is the stator teeth weight, G ba is the stator yoke weight, G ra is the rotor yoke weight and G pa is the rotor pole weight IET Electr. Power Appl., 009, Vol. 3, Iss. 4, pp doi: /iet-epa & The Institution of Engineering and Technology 009

7 Figure CGA simulation results for a 4-pole machine where ipop ¼ 00, subpop ¼ 10, p m ¼ 0., p c ¼ 0.5 for each generation at a fixed initial population in order to eliminate the disadvantages of random procedures like mutation and crossover, and the average values are shown. 3. With the new GA Introducing a new aspect to GA, the new method does not involve mutation and crossover, unlike the CGA. Since Mendel s population genetics is taken as the basis, judging by the high accuracy of the results that Mendel s genetics produce the new GA (NGA) is constructed on more logical and effective grounds. The main advantage of the NGA is that it is not necessary to obtain the ratio of well-known recombination and crossover operators of CGA or pursue Table 5 Doctrinal differences between applications of CGA and the new approach CGA NGA parameter set chromosome gamete initial population yes yes sub-population yes yes recombination chromosome gamete groups groups crossing over between chromosomes Punett square for the same gamete group mutation exist exist generation number phenotype and genotype dominance and recession independent no no related to subpopulation number yes yes Figure 3 Simulation results of the NGA for a 4-pole machine correspond to a sub-population size of 8 them. However, the CPU time is long compared to the CGA. Thus, the algorithm of the new approach cannot be used in real-time processes. Therefore the new approach accepts comparison with the CGA for only non-real-time processes such as design processes, and in such a comparison the CPU run-time is of no concern. The differences between CGA and the new approach are summarised in Table 5 [7]. In the new approach, the number of genotypes decreases with the number of subpopulations according to a power law. Each couple of data produces an individual, which exists from two gametes: one from male and one from female, each couple of points defines the recessive character of phenotype and genotype of the individual (machine parameters). Dominant characters have priority to the recessive characters in expression for Mendelian population genetics; each phenotype always shows the same character with the first character of genotype. Figs. 3 and 4 are related to the new approach for a 4-pole machine, where unlike the CGA very few generations are required, since the number of subpop ¼ gnþ1, where gn is the number of generations. The top axes in these figures Figure 4 Simulation results of the NGA for a 4-pole machine correspond to a sub-population size of IET Electr. Power Appl., 009, Vol. 3, Iss. 4, pp & The Institution of Engineering and Technology 009 doi: /iet-epa

8 Table 6 Total results for analytic method: CGA and NGA Symbol Unit Analytic CGA NGA method 4 poles 4 poles S kva V n V p D i cm D a cm L total cm N Q.5 w a w m z q cua mm q cum mm d 0 mm u ave 8C u ave 8C G total ton weight reduction 6.5% 6.6% give the number of gametes for each generation, and show how the genotype numbers reduce. The bold drawn curves show phenotypes and genotypes of the population. The new method gives results similar to those of the CGA, but with slightly better degree of optimisation. Each algorithm is simulated 10 times and average values are taken, and the results are compared with CGA. The reduction of the number of simulations in the new algorithm does not affect the best solution even if it produces new mid-genotypes, supporting the concept of the new approach. For example, the first pair of points [7183, 7519] of the weight curve in Fig. 3 shows the genotype Rr of the individual, where the first is dominant and the second is recessive. However, the last pair of points has similar values, and as such defines an RR dominant character. The genotype of this individual could be of either RR two-dominant or rr two-recessive genes. However, since it is the last generation, it should be RR dominant. Thus, the phenotype and the genotype of this individual are the same. Fig. 3 indicates three pairs of integers, where one of them has one dominant and one recessive character (first pair), and the others have two dominant, which reflect the basic concept of Mendelian genetics. Fig. 4 characterises the algorithm for different subpop number and indicates seven pairs of integers. The last pair of points [7180, 7198] expresses the final value (two dominant), which results in the optimal solution of 7180 in Figs. 3 and 4. Table 6 summarises the minimum weight and related machine parameters determined by the CGA and the NGA. The theoretical reduction of the machine weight is given at the end of the table. A 6.6% reduction is obtained for 4 poles. It is interesting to note that when the pole number doubles, the rotor diameter approximately doubles as well. Table 7 shows the arrangements of the windings and related parameters. Tables 8 and 9, and Fig. 5 show finite element analysis (FEA) results for the realisation of the designs optimised by CGA and NGA. The FEA method is used for testing algorithm results in the real world; they show that all the boundary conditions in Table were satisfied by FEA. The first columns of CGA and NGA groups are the implementation of GAs and the second columns are FEA validations with the same geometric and electric parameters in Table 8. The column of analytic method describes the machine in [9], and the neighbouring one shows also an FEA check. Table 8 shows that the parameters found by FEA based on the analytic design and those directly computed by the analytic design are almost the same. The FEA analysis based on the Table 7 Three-phase, two-layer winding arrangements of different machine configurations Number of slots Number of parallel branches Number of conductors per slot Coil pitch Stator winding factor A-A-A B B-C-C-C A A-B- B-B C C -A B B B-C-C A A A-B-B C C C-A A A-B-B C C-A-A B B-C- C A A-B A A-B-B C C-A-A B B-C- C A A-B IET Electr. Power Appl., 009, Vol. 3, Iss. 4, pp doi: /iet-epa & The Institution of Engineering and Technology 009

9 Table 8 Total results for analytic method: CGA and NGA by FEA Parameters Unit Analytic method FEA CGA NGA 4 poles FEA 4 poles FEA total exciting ampere-turn stator current density A/mm exciting current density A/mm rotor pole flux density T air gap flux density T efficiency % total weight ton Table 9 Important factors of the machines for analytic design: CGA and NGA designs by FEA FEA analysis CGA NGA Important factors Unit Analytic design 4 poles 4 poles short-circuit ratio (SCR) no load line voltage THD % full load line voltage THD % Figure 5 Flux density analysis of the two designed machines by FEA a Analytic design b 4-pole design by NGA 33 IET Electr. Power Appl., 009, Vol. 3, Iss. 4, pp & The Institution of Engineering and Technology 009 doi: /iet-epa

10 4-pole NGA gives more significant results: a 10.8% weight reduction is obtained. Although in Table 9, total harmonic distortion (THD) percentages found by FEA based on the CGA and NGA are greater than those found by the analytic design, they are in an acceptable range. However, GA designs give good short circuit ratios (SCRs), which are the important factor of the machine. If we take FEA results in Table 8 as reference, NGA proves to be better than CGA for the 4-pole design. Although the GA design is validated by FEA based on an old machine design procedure, there is no doubt that modern technologies such as water cooling or superconducting designs will reduce weight by greater ratios than conventional ones. Meanwhile, the main design principles do not change drastically over the years, except for improvements in cooling, material, conductor and manufacture technologies. However, since GA is conceptually accurate and comprehensive, it can efficiently be applied for modern machine designs once the algorithm modules are implemented for different technologies. For example, the heat equations module can be easily changed to describe water cooling instead of air cooling. 4 Conclusion In this study, a new approach for GA is proposed and compared with CGA in the optimisation of a salient pole synchronous machine. The main differences between the two algorithms are that, in the newly proposed method, individuals are paired and crossed over based on the Mendelian rules of genetics, and the mutation operator is omitted. The rules concern the segregation of alleles and the independent assortment of alleles. This approach is comprehensive and conceptually accurate since its framework uses Mendelian population genetics. It is hence potentially useful in modern machine design, once algorithm modules are adapted for different cooling, conductor or material technologies. The details of the new approach have been presented in a previous work [7]. The operation CPU time is longer in the new approach when compared to the conventional one because of the massive matrix dimensions carried out, and can be ignored in electric machine design since it is not a real-time process. So the design method proposed in this work has a traditionally complex structure; the objective function is implemented by a MATLAB code. The weight is analytically solved for a -MVA synchronous machine in terms of the stator and rotor parameters. The results of the analytic solution and the NGA and CGA implementation methods are compared in terms of weight, efficiency and temperature optimisation parameters. The results obtained are similar to those of the conventional ones and even better in some cases. A 6.5% and 6.6% reduction with respect to the analytical weight is obtained by the CGA and the NGA, respectively, for a 4-pole machine. Thus, the new method performs comparably to the CGA, even slightly better. Finally, an FEA analysis is done to realise the machine designs optimised by the NGA and CGA. Although there is not much difference in the optimal weights computed by the CGA and NGA, the design based on NGA surpasses that on CGA in the weight obtained by FEA for the case of the fixed 4-pole design. 5 References [1] BIANCHI N., BOLOGNANI S.: Brushless DC motor design: an optimization procedure based on genetic algorithms. IEE EMD97 Conf., No. 444, 1997 [] BIANCHI N., BOLOGNANI S.: Design optimization of electric motors by genetic algorithms. IEE Proc. Electr. Power Appl., 1998 [3] PALKO S., JOKINEN T.: Optimization of squirrel cage induction motors using finite element method and genetic algorithms. Eighth Int. Conf. Electrical Machines and Drives, pp. 1 5 [4] SIM D.-J., CHO D.H., CHUN J.-S., JUNG H.-K., CHUNG T.-K.: Efficiency optimization of interior permanent magnet synchronous motor using genetic algorithms, IEEE Trans. Magn., 1997 [5] SUDHOFF D.S., CALE J., CASSIMERE B., SWINNEY M.: Genetic algorithm based design of a permanent magnet synchronous machine. IEEE Int. Conf. Electric Machines and Drives, 005, pp [6] CHAI K., POLLOCK S.C.: Using genetic algorithms in design optimization of the flux switching motor. IEE Power Electronics Machines and Drives Conf., 00, pp [7] ÇELEBI M.: A new approach for the genetic algorithm, J. Stat. Comput. Simul., 009, 79, (3), pp [8] BODUROĞLU T.: Electric machinery notes (İstanbul Technical University Press, 1986), vol. 3, no., pp. 4, 6, 8, 9, 45, 107, 113, 14, 18, 00, [9] ÇELEBI M.: Weight optimization of salient pole synchronous generator by a new genetic algorithm, PhD thesis, Department of Electric and Electronics Engineering, Yıldız Technical University, 003 [10] ALGER A.L., EKSERGIAN R.: Yoke core losses in induction machines, J.A.I.E.E (IEEE), 190, p. 906 IET Electr. Power Appl., 009, Vol. 3, Iss. 4, pp doi: /iet-epa & The Institution of Engineering and Technology 009