Efficiency Optimal of Inductive Power Transfer System Using the Genetic Algorithms Jikun Zhou *, Rong Zhang, Yi Zhang

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1 International Conference on echanical Science and Engineering (ICSE5 Efficiency Otimal of Inductive Power Tranfer Sytem Uing the Genetic Algorithm Jikun Zhou *, ong Zhang, Yi Zhang Intitute of ytem engineering, China academy engineering of hyic, ianyang, 6999 Keyword: IPT ytem, efficiency otimal, genetic algorithm Abtract. The Inductive ower tranfer (IPT ytem efficiency i determined by kind of arameter. Aim at maximum the ower tranfer efficiency for Inductive ower tranfer (IPT ytem, the efficiency of four baic toology IPT ytem i analyzed. Baed on the analyi, genetic algorithm (GA are ued to otimize IPT ytem arameter to achieve the maximum of the ower tranfer efficiency. Before the GA otimization roce, the IPT ytem are comenated in a reonance condition which can achieve to minimize VA rating of the ower uly and maximum ower tranfer. In the roce of GA otimization, to enure the final olution achieving bifurcation-free oeration, the olution that generate bifurcation henomenon (multi zero hae angle frequency are excluded. The imulation reult verify that the GA can find the bet otimal olution for all toology IPT ytem. Introduction Inductive ower Tranfer (IPT ha been ued in many commercial and indutrial alication due to it ability to tranfer electrical ower without and hyical contact [-]. The IPT ytem include two indeendent mutually couled art called rimary and econdary reectively [4]. The rimary art generate an eentially current i in the rimary coil L with a reonant high frequency witching ower uly. The rimary comenation i ued to minimize the VA rating of the uly. On the econdary art, comenation i alo required to enhance the ower tranfer. A witched mode controller i normally ued to control the ower flow from the econdary coil L to the load. Becaue of large air ga via magnetic couling, the efficiency i a ignification target that mut be conidered when deign of the IPT ytem [6,7]. However, the ytem efficiency i determined by not only one arameter, uch a air ga, oerating frequency, couling coefficient and o on, which make the efficiency otimal deign difficult [9,]. To date, ome analyi and otimal have been undertake. The effect of load and air ga variation are tudied for different toology IPT ytem []. However, the oerating frequency effect i not conidered. The reference [] deign the IPT ytem by uing an otimization algorithm. But the algorithm ignore the effect of couling coefficient. eference [3] analyzed all the arameter that influence the efficiency and reented an otimal algorithm deign method, however, the algorithm cannot enure to find out the mot otimal olution and the bifurcation henomenon i ignored. In thi aer, the GA i elected to efficiency otimal deign of the IPT ytem undertake the reonance condition. In the roce of the GA otimization, the olution that generate bifurcation henomenon are excluded. The imulation verifie that the GA can find the bet otimal olution for all bae toology IPT ytem. Efficiency analye of bae IPT ytem With different comenation, there are four baic toology IPT ytem that called SS, SP, PP, and PS are hown in Fig., where the firt S or P tand for erie or arallel LC comenation of rimary reonance and the econd S or P tand for erie or arallel LC comenation of econdary reonance. The inductor L and L rereent the rimary and econdary coil reectively. The reitance rereent the load on the econdary, while the reitance and rereent the 5. The author - Publihed by Atlanti Pre

2 International Conference on echanical Science and Engineering (ICSE5 elf-reitance of L and L reectively. I I I I V in C L C L I V in C L L C I (a SS (b SP I I I I C V in C L V in C L L C (c PS L I I (d PP Fig. Four baic toologie of IPT ytem The voltage Vin i the outut voltage of the converter. The imedance of the econdary Z whoe value deend on the econdary comenation a given by Z L Larallel econdary C L eri econdary C / L The reflected imedance Z i deendent on the tranformer couling and oerating frequency, which i given by Z ( Z To achieve maximum ower tranfer, The caacitor C i choen to comenate the large leakage inductance of the econdary coil L to achieve reonance condition. Where, ω i the inherent frequency of the econdary art. C (3 L The caacitor C i choen to cancel the reactive art of the circuit een by the ource, to achieve maximum ower tranfer with minimum VA rating of the uly. With different toologie, the calculation of rimary caacitor C for different toology IPT ytem are hown in Table.. Table. Primary caacitor C SS PP L / L L ( ( L / L SP ( L / L PS L L L ( L ( When oerated at the econdary inherent frequency, the efficiency of the ytem i given by [] (4 ( ( ( L ( L L (5 5. The author - Publihed by Atlanti Pre

3 International Conference on echanical Science and Engineering (ICSE5 Where k LL (6 Where k i couling coefficient and ubitent (6 into (4 and (5, the ytem efficiency can be given by k LL (7 ( ( k L L ( L L k LL k LL (8 Efficiency otimal with genetic algorithm When deign the IPT ytem, the efficiency uually i conidered firt. From (7 and (8, it can be een that, four geometrical arameter, oerate frequency ω, rimary inductor L, econdary inductor L and couling coefficient k need to be otimal to achieve maximum ower tranfer. Therefore, the efficiency otimal roblem i a maximization of the obective function with four geometrical arameter, which can be given by (, L, L, k arallel econdary fob (9 (, L, L, k eri econdary However, it i difficult to find the otimal arameter with all of the four arameter with traditional numeric otimal algorithm. The genetic algorithm have become increaing imortant for thi tye of otimization roblem by eeking the otimal olution of the obective function with imulating the roce of evolution and adatation of living organim. The GA that reented by Holland i a comutational otimization aradigm modeled on the concet of biological evolution [4]. It oerate a oulation of random olution to an otimization roblem. A fitne function i ued to evaluate the quality of all oible olution. The olution with high quality are elected to create the next generation.therefore, the GA can be ued to otimal the IPT ytem by not uing any comlex mathematical information in the earching roce. During the otimal roce of the IPT ytem, to enure the zero hae angle frequency i equal to the reonance frequency, bifurcation henomenal mut be avoided. The neceary criteria i tabulated in Table..[5] Table. Neceary criteria for bifurcation-free oeration SS Toology L ( k SP and PP Toologie k L k PS Toology L k The olution that diatify the neceary criteria hould be eliminated. oreover, the four dimenion ω L L and k alo ha max and minimize value, and are given by k_ min k k L L L L L L _ max _ min _ max _ min _ max The Proce of GA otimal can be denotated a fllow. Ste: Chromoone coding 5. The author - Publihed by Atlanti Pre3 3 _ min _ max (

4 International Conference on echanical Science and Engineering (ICSE5 In thi aer, tatic binary tring i ued to code the four dimenion. Auming that the length of one dimenion i m, the total length of the chromoome i 4m. The chromoome can be given by X x4, x3, x, x [, L, L, k] ( xi bi * m bi * m bi * mm ( The decimal value can be calculated by x x i* m i_ max i_ min id i _ min ( i* m (3 m i* mm x x b Ste: Fitne evaluate Creating an initial oulation of N individual for evolution after chromoome coding wa done. Then calculate the obective function value for every individual. To enure the ytem which ha multi zero hae angle are not elected to coy and exit in next generation, the obective function hould be divided by fob ( X one zero hae angle f ob ( X multi zero hae angle Conidering efficiency otimal i a maximization roblem, the fitne function i equal to the obective function, and i give by f X f X (5 int ( ob ( Ste3: GA oerator The GA oerator contain reroduction, croover, and mutation oerator. In thi aer, roulette wheel election i ued in reroduction mechanim while ingle oint croover and ingle oint mutation are ued for croover and mutation reectively. The efficiency otimal deign of IPT ytem with GA i reented in Fig.. Start (4 Initial value,, Select toology Create N individual by random [ω, L, L, k] Evaluate all individual No Croover utation Satify the Termination criterion? Ye Calculate C bae Table. C=/Lω eroduction Finih Fig. Efficiency otimal reult with GA In the GA arameter, et the maximum number of generation T=5, the number of individual N=, the croover robability Pc=.6, the mutation robability Pm=., the length of the chromoome m=, and the four dimenion are given by. k.6 3μH L μh 3μH L μh 5kHz 5kHz The GA otimal roce i hown in Fig.3 and the final olution are hown in Table.4 (6 5. The author - Publihed by Atlanti Pre4 4

5 International Conference on echanical Science and Engineering (ICSE5 Efficiency SS PS SP PP Generation Fig.3 Efficiency otimal reult with GA Obervation of Figure 3 reveal that the GA can find the bet otimal olution for all toology IPT ytem. On the other hand, in the beginning of the roce, not all the bet olution in each oulation i being roagated to the ubequent generation. That becaue the olution with the highet efficiency may be not atify the neceary criteria of bifurcation-free. Table.3 Otimized reult of different toologie Parameter SS SP PS PP L(μH C(μF..7.. L(μH C(μF k f(khz η(% Concluion Thi aer ha reented an otimization cheme baed on the GA for the efficiency otimal deign of the IPT ytem. Before the GA otimization roce, the ytem i comenated in a reonance condition to minimize the VA rating of the ower uly and achieve maximum ower tranfer. During the GA otimization roce, the olution that diatify the neceary criteria hould be eliminated to avoid bifurcation henomenal occur in the finally olution. The imulation verifie that the GA otimization can find the bet otimal olution for all toology IPT ytem. eference [] Huang, Shyh-Jier;Lee, Tong-Shing;Pai, Fu-Sheng;Huang, Tzyy-Haw. ethod of feedback detection for looely couled inductive ower tranfer ytem with frequency-tracking mechanim. IEEE th International Conference on Power Electronic and Drive Sytem (PEDS, 3: [] Wu, Pengfei, Shi, Liming, Cai, Hua, Li, Yaohua. An inductively couled ower tranfer ytem baed ower control for motor drive of rail tranit vehicle. 7th International Conference on Electrical achine and Sytem, 4: -5. [3] J. T. Boy, G. A. Covic, and A. W. Green. Stability and control of inductively couled ower 5. The author - Publihed by Atlanti Pre5 5

6 International Conference on echanical Science and Engineering (ICSE5 tranfer ytem. IEEE Proceeding Power Alication. vol. 47, no., : [4] B. Lee and K. Han. Proceeding of the Eighth International Conference on Electrical achine and Sytem.vol., 5: [5] H.L. Li, A.P. Hu, G.A. Covic and C.S. Tang. Otimal couling condition of IPT ytem for achieving maximum ower tranfer. electronic letter t January 9, Vol. 45 No. [6] Han, K.H., Lee, B.S., and Baek, S.H.: The deign evaluation of inductive ower-tranformer for eronal raid tranit by meauring imedance. Journal of Alied Phyic, 8: 3-5 [7] oradewicz AJ, Kazmierkowki P. Contactle energy tranfer ytem with FPGA-controlled reonant converter. IEEE Tranaction Indutry Electronic ;57(9:38 9. [8] Sallan J, Villa JL, Llombart A, Sanz JF. Otimal deign of ICPT ytem alied toelectric vehicle battery charge. IEEE Tranaction Indutry Electronic, 9;56(6:4 9. [9] Saeed Haanzadeh, Sadegh Vaez-Zadeh. Efficiency analyi of contactle electrical ower tranmiion ytem. Energy Converion and anagement, 3;65: [] Z. ichalewicz, Genetic Algorithm + Data Structure =Evolutionary Program, Genetic Programming and Evolvable achine, Sringer, Berlin,997: The author - Publihed by Atlanti Pre6 6