Switching Angle Design for Pulse Width Modulation AC Voltage Controller Using Genetic Algorithm and Distributed Artificial Neural Network

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1 Swtchg Agle Desg for Pulse Wdth Modulato AC Voltage Cotroller Usg Geetc Algorthm ad Dstrbuted Artfcal Neural Network Pattarapor Jtta, Somyot Katwadvla ad Atthapol Ngaoptakkul Abstract. Ths paper proposes a techque to desg the swtchg agles a PWM AC voltage cotroller usg geetc algorthms (GA) ad dstrbuted artfcal eural etwork (ANN). I the proposed techque, GA s used to evaluate the tur o ad tur off agles of PWM patter to reduce the low order harmoc cotet PWM output voltage. The results from GA are the used to tra the dstrbuted ANN. The advatages gaed from the proposed techque are the reducto of complexty of trag process ad the mprovemet of the ablty of the ANN. I addto, the total harmoc dstorto of voltage, whch calculated from the low order harmoc cotet, s adopted the proposed ftess fucto. Thus, the load value s ot ecessary to be kow before statg the proposed techque. Smulato results show that the proposed techque s superor to the covetoal fxed-durato pulse techque. I. INTRODUCTION Phase cotrol techque ca be used to cotrol the output voltage of AC voltage cotroller. The prcple of ths techque s the phase cotrol le commutated swtchg devce. However, ths techque performs a poor performace terms of hgh harmoc dstorto ad low put power factor. Several years ago, varous techques were proposed to mprove the performace of PWM coverter [, 3]. Garal ad Mostafa [] proposed a geeralzed symmetrcal agle PWM techque for a AC voltage cotroller. Fedyczak et. al. [3] preseted the comparso of basc propertes of sgle-phase seral AC voltage cotrollers usg a bpolar PWM chopper. The comparatve study of the bpolar PWM AC matrx chopper based o full-brdge topology ad the bpolar PWM AC matrx-reactace chopper (MRC) based o Cuk B topology ad auxlary trasformer were descrbed ther paper. Mauscrpt receved Jauary, 0. Ths work s supported by the research fud from Kg Mogkut s Istute of Techology Ladkrabag, Thalad. Pattarapor Jtta, Dr. Somyot Katwadvla ad Dr. Atthapol Ngaoptakkul are wth the Electrcal Egeerg Departmet, Faculty of Egeerg, Kg Mogkut s Istute of Techology Ladkrabag, Thalad. (emal : drsomyotk@gmal.com) Dr. Somyot Katwadvla s also wth the Ceter of Excellece for Iovatve Eergy Systems, Kg Mogkut's Isttute of Techology Ladkrabag, Bagkok 050, Thalad. Artfcal tellget techques were adopted may research areas cludg mechatrocs, electroc, power electrocs, etc. Several artfcal tellget techques such as geetc algorthms (GAs), partcle swarm optmzato, eural etworks, etc. were proposed for solvg the complex problems, whch caot be easly solved by ay aalytcal methods. Somyot ad Proj [0] proposed the geetc algorthms to evaluate the optmal swtchg agles of PWM patter so that the total curret harmoc dstorto ad the voltage error are mmzed. However, ther techque, the load value must be kow before startg the algorthm, ad the complexty of sgle artfcal eural etwork (ANN) used ther paper lmts the sze of trag set. To overcome these problems, ths paper proposes the geetc algorthm (GA) to aalyze the optmal swtchg agles at the specfed voltages, ad uses the dstrbuted eural etwork to approxmate the other agles the specfed rage. I addto, the ftess fucto usg low order harmoc cotet of voltage s proposed; thus, the load value s ot requred for the proposed algorthm. II. CONVENTIONAL PWM AC VOLTAGE CONTROLLER PWM AC voltage cotroller s a power electroc crcut whch ca be used to cotrol the electrcal power from AC source to electrcal load. As show Fg., S ad S perform as the swtchg devces cotrolled by the PWM patter, ad S' ad S' perform as the free-wheelg devces. The Pulse Wdth Modulato (PWM) cotrol [] has hgher effcecy tha the phase cotrol techque; however, the drawbacks of ths cotrol scheme are the hgh swtchg loss ad the complex of cotrol crcut. Normally, the PWM patter s desged by the covetoal fxed durato pulse techque, whch the wdth of pulse cotrols the output rms voltage of the crcut. Fg. shows a example of the output voltage waveform from the covetoal techque. I ths fgure, the swtchg frequecy of PWM s khz; the AC put voltage s 0 V, 50 Hz, ad the umercal calculato of the rms voltage s 60.9 Vrms.

2 D S D S D S Fg. Sgle-phase AC voltage cotroller ad the covetoal PWM sgal [] Fg. Output voltage waveform of the covetoal PWM AC voltage cotroller wth the output rms voltage of 60.9 V III. GA AND DISTRIBUTED ARTIFITIAL NEURAL NETWORK A. Geetc Algorthms (GAs) Geetc algorthm s a searchg algorthm whch ca be used to solve ay optmzato problem by represetg the caddates of the aswer by chromosomes. The adjustmet of the chromosomes s doe by the cocept of evolutoary operatos. Ftess s a fucto whch uses to descrbe the satsfacto level of the chromosome. To geerate the ext geerato populato, several chromosomes are selected to be the parets; chromosome wth hgh ftess has a hgh chace to be selected. A selected geetc operato s the adopted to form a ew chromosome. There are 3 types of geetc operators, reproducto, crossover ad mutato. More formato of GAs ca be see [8]. Geerally, the output waveform of AC voltage cotroller s o-susodal waveform, ad the both the voltage ad the curret from ths crcut ormally cota the harmoc cotet. It s well kow that the curret harmoc causes the curret dstorto, low-put power factor ad loss. The curret dstorto ca be evaluated from the summato of the curret harmocs as show (). Assumg the RL S D load value s kow, the fudametal ad harmoc currets of the AC voltage cotroller ca be determed by (). All compoets ca be determed by applyg the Fast Fourer Trasform (FFT). Addtoally, the total voltage harmoc dstorto ca be determed by (3). THD I R I I V ( fl) V THDv (3) V where THD s the total curret harmoc dstorto, THD s the total voltage harmoc dstorto, v s the th harmoc order, V, I are the rms values of th harmoc voltage ad curret, respectvely, V, I are the rms values of fudametal voltage ad curret, respectvely, RL, are the resstace ad ductace values of load, ad f s the frequecy of the fudametal voltage. I our techque, the calculato of THD cludes the v harmocs from d to 3 th order for cosderg oly low order harmoc cotet. The AC voltage cotroller s used to cotrol the rms output voltage whch ca be evaluated by (4). V rms V (4) As kow by may researchers, the creasg of THD causes the reducto of put power factor. The relatoshp betwee THD ad put power factor ca be see (5). pf.. cos (5) THD where p. f. s the put power factor, ad s the load agle. B. The proposed GA based PWM AC Voltage Cotroller I the proposed techque, the optmal swtchg agles (α) PWM sgal are attempted to be determed so that the total voltage harmoc dstorto calculated from the specfed low order harmoc cotet s mmzed, ad the rms output voltage s acheved. I the proposed techque, the followg parameters must be specfed before startg GA. M s the umber of pulses a quarter cycle of PWM waveform, V drms s the desred rms output voltage, [ o, off, o, off... Mo, Moff ] s the set of swtchg agles a quarter cycle of PWM, ad xo, xoff are the tur-o ad tur-off agles of the x th pulse, respectvely. () ()

3 Start Specfy Geetc parameters & AC voltage cotroller : M, Vdrms o o off off Mo Moff Create a frst populato radomly Fg. 3 Example of output voltage of PWM AC voltage cotroller whch M = 3 Evaluate ftess value usg (6) Ge = Ge + Fg. 3 presets the example of PWM waveform that has the umber of pulses a quarter cycle (M) = 3. Ths waveform s symmetrcal. The boudary of each swtchg agle ca be specfed easly. The detals of specfyg boudares of the agles ca be see [0]. I ths problem, α s the chromosome GA, ad the equato of ftess fucto s modfed as the followg: ftess f Vdrms Vrms a THD V V b v drms rms V V a (6) k f drms rms Where Vrms s the rms output voltage of the PWM AC voltage cotroller wth the swtchg agle (α), Vdrms s the desred rms output voltage, a s the acceptable value of the voltage error calculated from the absolute of the dfferece betwee Vdrms ad Vrms, b s the specfed umber whch s used to avod the equal to zero of the deomator, ad k s the low value umber whch s assged whe the rms output voltage s ot wth the specfed boud, a. I ths research work, the parameters (6) are specfed as follows: a =, b =0.00 ad k =0.. These values ca be adjusted properly depedg o the desg. Fg. 4 represets the flowchart of the proposed techque. The stoppg codto s specfed by a maxmum geerato. Ths procedure ca be summarzed as follows: Step Specfy the geetc parameters, e.g. operato probablty, populato sze, maxmum geerato, M, V, drms etc. Step Create the frst populato radomly. Step 3 Evaluate the ftess value of each chromosome (α) by (6). Select the chromosome whch has the maxmum ftess value as the soluto of curret geerato. Step 4 Whe the curret geerato s less tha the maxmum geerato, fd a ew populato by geetc operators ad the retur to step 3. If the curret geerato s the maxmum geerato, the stop. The chromosome that has the maxmum ftess value s the optmal soluto of the problem. Check Codto Stop END YES NO Fg 4 Flowchart of GAs. Create a ew populato ext geerato B. Dstrbuted artfcal eural etwork Several sets of the optmal swtchg agles ad all specfed voltage outputs evolved by GA are the optmal solutos for several gve output voltages. I ths paper, the optmal agles each output voltage from the GA process wll be used to tra the dstrbuted ANN usg the Leveberg-Marquardt back-propagato. Fg.5 shows the structure of dstrbuted artfcal eural etwork adopted ths paper. The put ode of dstrbuted ANN s the desred output voltage, ad the output odes are the swtchg agles, α. I ths case, the dstrbuted ANN approxmates the optmal agles every operatg pot. More formato about the dstrbuted artfcal eural etworks ca be see [9].

smulato study are specfed as follows: the put voltage s 0

= 300 mh, M = 3, cross-over probablty = 0.

, populato sze = 000, maxmum geerato = 0, ad the agle 3off

Examples of the voltage ad curret waveforms are show Fg. 6.

6 Examples of waveforms from the proposed techque ad the

4 o off (c) 3off Fg. 5 Dstrbuted Artfcal Neural Network for AC voltage Cotroller (d) IV. THE ANALYSIS AND SIMULATION RESULTS The parameters our smulato study are specfed as follows: the put voltage s 0 Vrms, 50 Hz, output voltage [ 40, 0], RL load: R = 40 Ω, L = 300 mh, M = 3, cross-over probablty = 0.6, mutato probablty = 0., populato sze = 000, maxmum geerato = 0, ad the agle 3off s assged as 90. Examples of the voltage ad curret waveforms are show Fg. 6. (e) (a) (b) (f) Fg. 6 Examples of waveforms from the proposed techque ad the techque [0] (at 80 V, R = 40 Ω, L = 300 mh) (a) Curret waveform [0], (b) Curret waveform (the proposed techque), (c) Voltage waveform [0], (d) Voltage wave form (the proposed techque), (e) Spectrum of curret waveform [0], (f) Spectrum of curret waveform (the proposed techque)

Fgs. 6(a) to 6(d) show the waveforms at the desred voltage 80 V. As see these fgures, the waveforms from the proposed techque ad the techque [0] are dfferet. However, cosderg Fgs.

5 Fgs. 6(a) to 6(d) show the waveforms at the desred voltage 80 V. As see these fgures, the waveforms from the proposed techque ad the techque [0] are dfferet. However, cosderg Fgs. 6(e) ad 6(f), the low order harmoc cotet of the proposed techque s better tha that of the techque [0]. Fg. 7 shows the total harmoc dstortos of curret whe the voltage output s vared from 40 to 0 V by steppg volts for each step. Clearly, our proposed techque s better tha the fxed-durato pulse techque terms of lower THD. Fg.7 THD of the AC voltage cotrollers cotrolled by usg the covetoal PWM, GA-ANN [0], the proposed PWM at load R = 40 Ω, L = 300 mh reduced. ACKNOWLEDGMENT Ths research work s supported by the research fud from Kg Mogkut's Isttute of Techology Ladkrabag. REFERENCES [] RASHID M.H.: Power electrocs crcut devces ad applcatos (Pretce-Hall, 993, d ed.) [] HASHEM M., DARWISH K.: Geeralzed symmetrcal agle PWM techque for AC voltage cotroller. Power Egeerg Cof., UPEC 004, September 004, vol., pp [3] FEDYCZAK Z., JAHKOWSKI M., SZCZESNIAK P.: Comparso of basc propertes of sgle phase seral AC voltage cotroller usg bpolar PWM chopper, Power Electro Appl., 005,, pp. -0 [4] KAITWANIDVILAI S., KANPRACHAR S.: Harmoc reducto AC cyclo-coverter usg a geetc algorthms. ICEMC, Thalad, 005 [5] AL-OTHMAN A.K., AHMED N.A., AL-KANDARI A.M., EBRAHEEM H.K.: Selectve harmoc elmato of PWM AC/AC voltage cotroller usg hybrd RGAPS approach, It. J. Electr. Coput. Syst. Egg., 007,, (4), pp [6] HWANG W.R., THOMPSON W.E.: A tellget cotroller desg based o geetc algorthms. Proc. 3 d IEEE Cof. o Decso ad Cotrol, December 993, vol. 5, (7), pp [7] RAO S.S., SHAILAJA N.: Improvg voltage regulato ad harmoc elmato usg geetc algorthms PWM choppers. INTELEC, 005, pp [8] NEGNEVITSKY M.: Artfcal tellgece, a gude to tellget systems (Addso Wesley, 005, d ed.) [9] TENG C., GEORGE C.S.: Neural fuzzy systems (Pretce-Hall, 999) [0] KAITWANIDVILAI, S. ad PIYARUNGSAN, P.: Low-cost mcroprocessor-based alteratg curret voltage cotroller usg geetc algorthms ad eural etwork. IET Power Electro., 00, Vol.3, Iss. 4, pp Table shows the comparso betwee the proposed ad the covetoal techques. As see ths table, the umber of odes ad the trag tme of the proposed techque are lower tha the covetoal ANN [0]; however, the %error of voltage from the proposed techque s creased. Table Number of odes, tme ad mea of voltage error of the proposed techque ad the covetoal PWM Descrpto Dstrbuted ANN ANN [0] Number of odes 6 the hdde layer Tme (secod) Mea of Voltage error (%) V. CONCLUSIONS As see the smulato results, the proposed GA ad the dstrbuted artfcal eural etwork ca be appled to the AC voltage cotroller, ad the performace obtaed from the proposed techque s better tha that of the covetoal fxed-durato pulse PWM. The proposed techque uses the low order voltage harmoc cotet to calculate the THD v for the ftess fucto. Thus, the load value s ot ecessary for our proposed techque. I addto, based o the cocept of dstrbuted ANN, the trag tme ad the umber of odes the etwork are

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