Three-Level Inverter Performance Using Adaptive Neuro- Fuzzy Based Space Vector Modulation

Transcription

1 Three-Level Iverter Performace Usig Adaptive Neuro- Fuzzy Based Space Vector Modulatio G.. Durgasukumar (Correspodig author) Research scholar, Departmet of Electrical Egg, IIT Roorkee Roorkee, Idia Tel: M.K.Pathak Departmet of Electrical Egg, IIT Roorkee Roorkee, Idia Abstract Space vector modulatio is a optimal pulse width modulatio techique i variable speed drive applicatio. This paper presets Adaptive Neuro-fuzzy based space vector modulatio techique for a three level iverter. It uses uses hybrid learig algorithm (combiatio of back propagatio ad least square methods) for traiig due to this the required traiig error is obtaied with less umber of epoches compared to other techiques like Neural, fuzzy etc. The proposed scheme uses the d-axis ad q-axis voltages iformatio at the iput side ad the corrected two-level duty ratios for switchig pulses, two-level idex are geerated as output. The performace measure i-terms of the total harmoic distortio (THD) of iverter lie-lie voltage has bee evaluated with Adaptive Neuro-fuzzy based system is compared with the covetioal based SVM method. Keywords: Adaptive Neuro-Fuzzy iferece system (ANFIS), three-level iverter. Two-level iverter, Space vector modulatio (SVM), Total harmoic distortio (THD). Itroductio Iverter is a electrical device that produces AC output voltage from a DC supply voltage. The coverted AC ca be at ay required voltage ad frequecy with the use of appropriate switchig ad cotrol circuits. The performace of iverter is maily depeds o the switchig operatio. As a result, umber of pulse width modulatio strategies has bee developed ad studied (Attaiese.et.al.007, Kwasiski. et.al.003 ad Wexi et.al. 008). I all these strategies, space-vector modulatio (SVM) stads out because it reduces the harmoic cotet ad offers sigificat flexibility to optimize switchig waveforms. But the disadvatage of SVM is it requires complex olie computatio that limits the switchig frequecy of iverter. I order to use high switchig frequecy power semicoductor devices (IGBTs) effectively, the operatig frequecy of SVM has to be icreased. But practically DSP based covetioal SVM fails whe the switchig frequecy icreases. This problem ca be overcome by usig techiques like eural, fuzzy, Neuro- fuzzy etc (Ashuma. et.al. 005). A eural etwork based SVM is implemeted ad compared with the covetioal DSP based SVM (Pito. et.al.000 ad Modal. et.al.00). I this, ANN based SVM performace is deteriorated whe compared to the covetioal SVM. A eural etwork based SVM for differet architectures ad differet switchig frequecies have bee studied ( Muthuramaligam. et.al. 005). These discussed SVM techiques takes much time to trai ad total harmoic distortios (THD) obtaied are more compared to the covetioal method. The ANFIS method takes less time to trai ad gives better performace compared to other artificial itelligece methods due to its hybrid learig algorithm (Jyh-Shig Roger Jag.et.al.993). 0

2 This paper describes ANFIS based SVM implemetatio of a two level voltage fed iverter. I Sectio, SVM theory of two-level iverter ad three-level iverter is preseted. ANFIS priciple, architecture ad ANFIS based SVM procedure is described I Sectio 3. Results of ANFIS based SVM ad its compariso with covetioal based SVM is preseted i the Sectio 4. Cocludig remarks are stated i sectio 5. Simulatio studies are carried out usig 3-Phase, 3hp, 400V, 50Hz, ad 480RPM iductio motor.. Space vector modulatio for three-level iverter A three-level space-vector diagram ca be decomposed ito six space-vector diagrams of two-level. The space vector diagram three-level iverter ad its correspodig two level hexagos are show i Figure (a) ad (b). A three-level space-vector plae is trasformed to the two-level space-vector plae by usig the two steps ) From the locatio of a give referece voltage ad selected hexago make a traslatio of the referece vector towards the cetre of the hexago. ) The origial referece voltage vector has to be subtracted by the amout of the ceter voltage vector of the selected hexago. From the locatio of a referece voltage ad selected hexago, if the referece voltage vector is i the regios that are overlapped by adjacet small hexagos the the space vector diagram ca have multiple values. Oce the value is obtaied, the origi of a referece voltage vector is chaged to the ceter of selected hexago. This is obtaied by subtractig the vector of the selected hexago from the origial referece vector of the three-level space vector diagram. Figure represets the chage of origial referece voltage vector (V ref ) from three-level to two-level (V * ). After chagig the referece vector the effective times are calculated i a similar maer of two-level iverter as T = () T =, () T 0 = T s -T -T (3) Where V * is the corrected referece voltage of two level. The d ad q compoets of the referece voltage V * is give i Table. I order to geerate two-level duty ratios idepedet of samplig time (T s ) for the Adaptive Neuro-Fuzzy system the above equatios are cosidered as D = M. (4) D = M. (5) D 0 =-(D +D ) (6) Where D is the duty cycle of switchig vector that lags V ref D is the duty cycle of switchig vector that leads V ref

3 D 0 is the duty cycle of zero switchig vector. The geerated duty cycles are multiplied with the respective six sectors switchig states, depedig upo the sector umber. The duty cycles obtaied for the sector- is give by equatios (7) ad (8). For other sectors the values are calculated i similar method. As the ull state is shared equally betwee V 0 ad V 7 switchig states, the value of each switchig state is cosidered as 0.5. A two-level iverter space vector diagram with eight differet switchig states (V 0 -V 7 ) represeted i Figure 3. Sector : Tur o duty cycles (7) Tur off duty cycles (8) I Figure 4, the relatioship betwee the effective duty cycles ad the actual gatig patter is preseted whe the referece vector is located i the Sector-. I this case, the V vector is applied to the iverter durig D iterval ad V vector is applied durig D iterval. I the three phase symmetrical modulatio method, the zero sequece voltage vectors is distributed symmetrically i oe samplig period to reduce the ripple. Thus, i geeral, the switchig sequece is give by withi two samplig periods. With the poit of view of the upper switchig devices of oe iverter leg, the former sequece ( sequece) is called ON sequece, ad the latter (7---0) is called OFF sequece. The geerated duty cycles are compared with the up/dow couter that is geerated by the required samplig period. From the obtaied time iterval values switchig pulses are geerated usig the relay circuit. The desired corrected equalet two-level switchig states are coverted to three-level switchig states by comparig the three-level switchig states with covetioal two-level switchig states of selected hexago ad usig the two-level idex. A two-level idex gives the hexago umber i which hexago the referece vector is located. The coversio of two-level switchig states ito three level switchig states are show i Figure ANFIS based space vector modulatio 3. Model of Adaptive euro fuzzy cotroller for two-level switchig pulses ad Two-level idex The algorithm of proposed ANFIS cotroller that geerates switchig pulses ad Two-level idex is based o d-axis voltage V ds ad q-axis voltage V qs. The correspodig typical Adaptive Neuro-fuzzy structure is show i Figure 6. From the first order Sugeo Fuzzy model, a typical rule set with two iputs V ds ad V qs with resposes f,f,,f ca be give i geeralized form as Rule: if (V ds is M i )ad (V qs is M j ) the f = p V ds +q V qs +r (9) where =,,.. ad i,j=,,..respectively Where p, q, r are the liear parameters ad M i ad M j are o liear parameters.

4 The system architecture cosists of five layers amely Fuzzy layer, product layer, ormalized layer, defuzzificatio layer ad total output layer. Layer : It is fuzzy layer i which V ds ad V qs are the iputs for each set of odes M to M 5 respectively. Where M to M 5 are the liguistic labels used i fuzzy theory to defie membership fuctios. The membership fuctios take are bell shaped with maximum equal to ad miimum equal to 0. Every ode i this layer is called as adoptive ode ad the parameters i this layer are called premise (Precoditio) parameters. The membership relatio betwee the output ad the iput fuctios of this layer is expressed as Where ad deote the output of the odes i the first layer µmi ad µmj deote the membership fuctios of the layer i=,, 5 (0) j=,,...5 () Bell shape membership fuctio ca be expressed usig three parameters ad ca give as F(x; a,b,c) () Where the parameter a ad b vary the width of curve ad the parameter c locates the ceter of the curve. The parameter b should be positive. Layer : The output of every ode i layer is the product of all the icomig sigals. Each ode output represets the firig stregth of a rule. A fuzzy rule euro receives iputs from the previous layer that represet fuzzy sets i the rule atecedets. If there are multiple iputs to a euro i this layer, the cojuctio of the rule atecedets is evaluated by the fuzzy operatio, itersectio. This operatio ca also be used to combie multiple iputs to a fuzzy rule euro. The total umber of rules is 5 i this layer. Layer 3: It is a fixed ode ad it calculates the ratio of the i th rule activatio level to that of all activatio levels. Neuros i this layer represet fuzzy sets used i the cosequet of the fuzzy rules. A output membership euro receives iputs from the previous layer euros ad combies them usig the fuzzy operatio, uio. Therefore, the ormalized firig stregth computed ca be give as (3) i=,,.. (4) Layer 4: It is a adaptive ode ad calculates the cotributio of i th rule towards the overall output. i.e., defuzzificatio process of fuzzy system (usig weighted average method) is obtaied. The output of a Neuro-fuzzy system is crisp, ad thus, a combied output fuzzy set must be defuzzified. The ode fuctio ca be expressed as i=,, p (5) Where parameters p,p,...,p p, q,q,..q p ad r,r,...,r p, i this layer are referred to as the cosequet parameters. Layer 5: It is a sigle fixed ode ad produces the overall output as the summatio of cotributio from each rule. This euro calculates the sum of outputs of all defuzzificatio euros ad produces the overall ANFIS output (6) 3

5 Where output of layer4 3. Adaptive Neuro-Fuzzy priciple ad leasrig algorithm Basically, ANFIS takes the iitial fuzzy model ad tues it by meas of a hybrid techique combiig gradiet descet back-propagatio ad mea least-squares optimizatio algorithms which are show i Figure 7. The gradiet descet algorithm is maily implemeted to tue the o-liear premise parameters ad the least-square method is used to optimize or adjust the liear cosequet parameters. At each epoch a error measured that defies the sum of the squared differece betwee actual ad desired output. Traiig stops whe either the predefied epoch umber or error rate is obtaied. 3.. Forward pass I the forward pass, a traiig set of iput patters [as iput vectors i.e V ds ad V qs ] is preseted to the ANFIS, ode outputs are calculated o layer by layer basis, ad rule cosequet parameters are idetified by the least-squares estimator. I the Takagi Sugeo type fuzzy iferece, a output vector, duty ratio, is a liear fuctio. Thus, give the values of the membership parameters (for example triagular MF which has 3 parameters a, b ad c ) ad a traiig set of 0000 iput [V ds ad V qs ] ad output [ duty ratio] patters, oe ca form 0000 liear equatios i terms of the cosequet parameters ( p, q ad r) as: D ()= w () pv ds() qv qs () r w () pv ds() qvqs () r... w () pv ds() qvqs () r D P ()= w () pv ds() qv qs () r w () pv ds() qvqs () r... w () pv ds() qvqs () r... D (m)= w (m) pv ds( m) qv qs ( m) r w (m) pv ds( m) qvqs ( m) r... w (m) pv ds( m) qvqs ( m) r Where m = iput/output patters; = umber of odes i the rule layer = 5 D -P the predicted duty ratio of the ANFIS whe iputs V ds ad V qs are preseted to it. Equatio (4) ca be writte i a matrix form, such as (8) Where D -P D -P A k m = 0000 predicted duty ratio vector (7) 4

6 (9) A is a m (+ umber of iput variables) = matrix, w () w () V ds() w () V qs().. w () w () V ds() w () V () qs w () w () V ds() w () V qs().. w () w () V ds() w () V qs() A= (0) w (m) w (m) V ds( m) w (m) V qs( m).. w (m) w () V ds( m) w () V qs( m) I this case, the umber of iput-output patters m=0000 used i traiig is greater tha the umber of cosequet parameters (+ umber of iput variables) = 75. It meas that we are dealig with a overdetermied problem, ad thus a exact solutio to Equatio (9) may ot eve exist. Istead, oe should fid a least-square estimate of k, k *, that miimizes the squared error medullas of. This is achieved usig the pseudo-iverse techique: k * = (A T A) - A T D -P () where A T is the traspose of A, ad (A T A) - A T is the pseudo-iverse of A if (A T A) is o-sigular. As soo as the rule cosequet parameters are established, we ca compute a actual etwork output vector D e, ca be determied as, e = D -P - D () 3.. Backward pass I the backward pass, the back-propagatio algorithm is applied. The error sigals are propagated back, ad the atecedet parameters are updated accordig to the chai rule. For istace, cosider a correctio applied to parameter a of the bell-shaped membership fuctio used i ode A. The chai rule ca be expressed from Equatio (6) as, E E e D ( w f ) w w i i i i A a a e D ( wifi ) wi wi wa a w (3) Where η is the learig rate, ad E is the istataeous value of the squared error for the ANFIS output euro, i.e., Where (4) E e ( D P D ) w ( w ) w w i i i Ai a ( D P D)( ) fi wi wai a b b b ds b( V ) ( ) b ds a wai b wai V a a V c c c ds a c 5 (5) (6)

7 Similarly, the correctios applied to parameters b ad c ca also be obtaied. 4. Results ad Discussio As explaied i the previous sectio ANFIS based SVM is traied i uder modulatio regio for equalet two-level duty ratios ad two-level idex. From the obtaied two-level duty ratios switchig pulses S a, S b, S c are geerated usig the switchig frequecy 3 khz. The traiig data for ANFIS is geerated by simulatig the covetioal SVM. The traiig time for oe epoch is typically 5-0 miutes with 60GHz Petium dual core PC ad traiig error obtaied is less tha The umber membership fuctios for the iput variables d-axis-v ds ad q-axis-v qs is 5 ad 5 respectively. Therefore the umber of rules is 5(5*5=5). Bell shape membership fuctios are used for two iput variables V ds ad V qs. Usually Bell shape membership fuctio is specified by three parameters. Therefor ANFIS used here cotais a total of 05 fittig parameters, of which 30(5*3+5*3=30) are premise parametrs ad 75(3*5=75) are coscequet parametrs. From the obtaied two-level switchig pulses ad two-level idex, three-level switchig pulses are geerated by comparig two-level pulses with thre-level switchig pulses. These three-level switchig pulses are fed to the iverter circuit. 4. Performace of Iductio motor at 3KHz iverter switchig frequecy The performace of iductio motor durig startig ad steady state with covetioal ad ANFIS based SVM methods at 3KHz iverter switchig frequecy ad 400V DC lik voltage is show i Figure 8. it is observed the the speed repose reaches the steady state earlier with ANFIS based SVM method compared to covetioal based SVM method. The %THD of phase currets with covetioal ad ANFIS are show i Figure 9. The dyamic performace of iductio motor drive for the step chage i the load torque (5N-m) is show i Figure 0. The torque ripple is less with ANFIS based SVM compared to eural ad covetioal based SVM methods. Due to this smooth speed respose is obtaied with ANFIS based SVM 4. % THD of iverter Lie voltages at 3 KHz switchig frequecy The % THD of iverter lie-lie voltage with iverter DC voltage 50V ad at switchig frequecy 3 KHz is as show i the Figure. The %THD is less with ANFIS based SVM method compared to covetioal SVM method. 4.3 Compariso of THD at various switchig frequecies: The %THD values of three-level iverter lie-lie voltages (V ab, V bc ad V ca ) at 3 khz up to 50- harmoic order rage with Covetioal ad ANFIS based SVM methods is as give i Table. 5. Coclusio A Adaptive Neuro- fuzzy based space vector modulatio techique for a three-level iverter has bee preseted that operates i the uder modulatio regio. The proposed Adaptive Neuro-Fuzzy based SVM method ca be applied at ay switchig frequecy. The duty ratios are geerated idepedet of switchig frequecy. The Adaptive Neuro-fuzzy based SVM is simulated with the iductio motor drive ad evaluated thoroughly for steady state ad dyamic performace with a covetioal SVM. The performace of ANFIS based SVM is foud to be excellet compare to the covetioal based SVM method. The torque ripple is less with ANFIS based space vector modulatio techique. Due to this smooth speed respose obtaied compared to covetioal SVM method. The THD reduced by 40% with Adaptive Nero Fuzzy based SVM method compare to covetioal SVM. Appedix Machie ratig= 3 hp 6

8 Parameters: Stator resistace R s =0.55Ω, Stator iductace L s =93.38mH Rotor resistace R r =0.78Ω, Rotor iductace L r =93.36mH Magetisig iductace L m =90.5mH Momet of iertia J=0.09Kg-m, Dampig coefficiet B= Refereces Ashuma, Tripathi., Ashwi M. Khambadkoe., ad Sajib K. Pada., (005). Torque Ripple Aalysis ad Dyamic Performace of a Space Vector Modulatio Based Cotrol Method for AC-Drives. IEEE Tras. Power. Electro., 0(), Attaiese.C, Nardi.V, ad Tomasso.G., (007 ).Space vector modulatio algorithm for power losses ad THD reductio i VSI based drives. Electrical power compoets ad systems, 35(), Jyh-Shig Roger Jag.,(993). ANFIS : Adaptive-Network-Based Fuzzy Iferece System. IEEE Tras. Systems, ma, ad Cyberet. 3( ), Kwasiski. A, Krei P. T., ad Chapma P. L., (003). Time domai compariso of pulse-width modulatio schemes. IEEE Power Electro Lett., ( 3), Modal, K., Pito, O.P., ad Bimal K.Bose, (00). A eural etwork based space vector PWM cotroller for a three level voltage-fed iverter iductio motor drive. IEEE Tras. Id. Applicat., 38(3), Muthuramaligam, A., Sivarajai, D.,ad S.Himavathi, S., (005). Space vector modulatio of a voltage fed iverter usig artificial eural etworks. i proc. Cof IEEE Idico, Pito, J. O. P., Bose, B. K., L. Silva, L. E. B., ad Kazmierkowski, M. P., (000). A eural etwork based space vector PWM cotroller for voltage-fed iverter iductio motor drive. IEEE Tras. Id. Applicat., 36(6), Wexi, Yao., Haibig Hu., ad Zhegyu Lu., (008). Comparisos of space-vector modulatio ad carrierbased modulatio of multilevel iverter. IEEE Tras. Power. Electro., 3(),45-5. G.Durgasukumar received Bachelor s ad Master s degrees i Electrical Egieerig from J.N.T.U, Hyderabad (Idia) ad pursuig his Ph.D.degree i the Electrical Egieerig Dept, Idia Istitute of Techology, Roorkee, Idia. His research iterests iclude power electroics ad electric drives, machies. He is presetly pursuig Ph.D uder the guidace of M.K.Pathak. Mukesh Kumar Pathak was bor i Hamirpur (HP), Idia, i 966. He did his graduatio i Electrical Egieerig from L.D. Egieerig College, Ahmedabad (Gujarat), Idia, i 986. He joied Electrical Egieerig Departmet of NIT, Kurukshetra (Haryaa), Idia, as a Lecturer i 987. I 989 he joied Electrical Egieerig Departmet of NIT, Hamirpur (HP), Idia, where he served till 007. Presetly, he is workig as a Assistat Professor i Electrical Egieerig Departmet of IIT Roorkee, Idia, where he joied i 007. He obtaied both his M.Tech (Power Electroics, Electrical Machies ad Drives) ad Ph.D. degrees from IIT Delhi, Idia. He has co-authored a book o Electric Machies. He is a member of IEEE, Life Fellow of Istitutio of Egieers (Idia), Life member of Idia Society for Techical Educatio (ISTE) ad Systems Society of Idia (SSI). 7

9 Table. d ad q compoets of the referece voltage V * S V * d V * q V * d -V.cos(0) V * d -V.si(0) V * d -V.cos(π/3) V * d -V.si(π/3) 3 V * d -V.cos(π/3) V * d -V.si(π/) 4 V * d -V.cos(π) V * d -V.si(π) 5 V * d -V.cos(4π/3) V * d -V.si(4π/3) 6 V * d -V.cos(5π/3) V * d -V.si(5π/3) Table. THD values of iverter Lie lie Voltages Switchig frequecy parameter Simulatio Covetioal ANFIS 3 khz V ab V bc V ca

10 (a) (b) Figure. Space vector diagram of three-level iverter ad six two-level hexagos Figure. Chage of origial referece voltage vector Figure 3. Two-level iverter Space vector diagram with active vectors 9

11 Ts Ts 0.5D0 D D 0.5D0 0.5D0 D D 0.5D0 S S3 S5 S4 S6 S V0 V V V7 V7 V V V0 Figure 4. Actual gatig sigal patter of the space vector PWM (i the case of the sector -) Figure 5. Coversio of Two-Level Switchig States to Three Level Switchig States 0

12 Layer Layer Layer3 Layer4 Fuzzificatio Defuzzificatio iput M Vds M 0 M0 Layer5 Output M 0 Vqs M Duty ratio M Tuig X={X=Vds,X=Vqs} Up-dow couter Two-level switchig pulses Sa Three-level switchig pulses Duty ratio Duty ratio3 + - Relay Sb Sc Covertio of Two-Level Pulses to Three-level Pulses Sa Sb Sc Three-Level Iverter Layer Layer Layer3 Layer4 Fuzzificatio Defuzzificatio iput M Vds M 0 M0 Layer5 Output -Level Idex M 0 Vqs M M Tuig X={X=Vds,X=Vqs} Figure 6. Structure of ANFIS for SVM

13 Figure 7. Afis Hybrid learig algorithm (a) (b) Figure 8. Performace of iductio motor at 3KHz with a)covetioal SVM b) ANFIS SVM (a) (b) Figure 9. %THD of phase currets at 3KHz with a)covetioal SVM b) ANFIS SVM

14 (a) (b) Figure 0. Performace durig step chage i load torque witha) Covetioal SVM b)anfis SVM (a) (b) Figure. %THD of lie-lie at 3KHz iverter switchig frequecy with a)covetioal SVM b)anfis SVM 3

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