نمذجة ومحاكاة نظام الكتروني قابل للبرمجة يعمل على ربط ... - جامعة دمشق

.. ..2009 !.. 1 3 $ " % "- -$ - - . -4$ & " "'( 2 ! " #" - , $ " ) * "+/Utility Grid (Photovoltaic Module) PVM - - "+ 3 0( 1 2 " /3 * 6 . 4 DC-DC Boost Converter " 8 + "7 /DC-AC Inverter;-( " 8 2 (Sliding Mode Control) SMC 9: "( "" + ) * !$ . (" " < "7 6=- - " < Mathematica - 8 Symbolic Analysis : @- "" ABB : 1 8 ? (Low Pass Filter) LPF 7>( "" +8- A- " 1 < 2 /" " 1- -4 -$ < 3% 160Hz% + (Total Harmonic Distortion) THD. !" # $ %$ &' &( # )* +$ , -# ./(0. ! 1 # $ .)# – $2 4 – $2 ".)# – $2 4 – $2 " %$.)# , – -# 5 6 4 -#1234201

"* 5 * :( " $7 8 9# % 4 - - 4 $ $( :B 8 + ) ! 1 :- 9+ C C"" 9> # %" + A* " / - -*:4 - - #+ . % .. 9> A* :D 2"- 87% + 4 $ " "" 1% 4 8 " + "-: A" * /Inverter + " 8 Boost + " " "(- @ " 6 * ) F7 3 E> 1.(Photovoltaic Systems) PV's 202

.. ..2009 !.. "+ -1 ; *?

"* 5 * :( " $7 8 9# % 4 .4 #$ " ! 4 67 .4 * $ 8 $2 ** .! )# ! $2 8 5* $ $ % -1-2E , )H E# 5$ < 8 * N$! # 6$$ K8 $ 8 P% S?$ [2] A5 :( * $ 8 >$#$ 2 -# . * G( *" T $ < $ :( B" , $2 88 E % AE 6$ :7 ! U .= 5*# " 9? $ *# # +%G , , G >, 8 G < * $ 8 * 7 " A (*$ *" ( :( >$# 6 %M$ $ >% (1)6 # $ .220V 1K < * $ $ DC/AC "* IJ D 5( , *" 6; "*6; "* CE , # $ A :7 *" 9 J4K.4 J A * $ >K 8 % 5 7B$ B8 A ; B( J$ $ *" G A-# %G #$ " A ; 4 "* $ ? 6$ 9 A(220V,50Hz) )$ :7 (12-24V) $ $A4 , )$ < *" ( V$ )$ ; ) G$2 , ?$$ $ (*$2 ? B6 B(-# ( 8 !K # 96 (# :7 :7204

.. ..2009 !..A * $ >6 8 ( -# ( .)*J24 "* $ $, A%G E# * T G A(2) , WJ8 %G >$# -# .K$ ( :7 J "* # , ( 8 !K # 96

"* 5 * :( " $7 8 9# % 4 9 4 (R,S,T) E;E * ! P% )*$ -#, #J ? * *$ A)"$ B J#$A :7 B 9 T : K 9C? (3) , $ $E$ $7 9D :( [[Z8Y 9? ?# SW1~3 * E;E *? ;H7 % (/,ƒ,1) *L1~3 W ! < $ ( P% A4 :7 9 4 . 9 , : 9CJ H (3) , 4 $ 0 : " $ G2G2! $ 6 " 8 !$ -# # +%G , $*?$ # J$ :( P% $ -# S 4 :7 ? *"

.. ..2009 !..5 J J @8$ T :( *$ $ PV's 8:BE .9# D 9 5M$ ) T $$# , 5% DC/AC Inverter ? 8 C ", V$ THD ?,$ +$ #$ " B .B( 8 +%G $. 4 :7 ! $ T+ " 3" 8 "" 7 1-2-2W$K $ $

"* 5 * :( " $7 8 9# % 4 iL = ton*Vi/L; % p-p Inductorcurrent rippleILmin = Ii - iL/2; % Min inductorcurrentILrms = sqrt(Ii.^2 + iL.^2/12); %RMS inductor currentIqrms = sqrt(ILrms.^2 * D); %RMS switch currentIdrms = sqrt(ILrms.^2 * (1-D)); %RMS diode currentICi = iL / sqrt(12); % RMS inputcapICo = sqrt(Idrms.^2 - Io.^2); %RMS output cap currentPl_L = ILrms.^2 * RL; % InductorlossPl_Qc = Iqrms.^2 * Rs; % Switchloss (conduction)Pl_Qs = 0.5 * Ii * Vo * tsw * f; %Switch loss (switching)Pl_Qg = Qg * Vgg * f .* Pones; %Switch loss (gate drive)Pl_D = Vf .* Ii * (1-D); % DiodelossPl_Ci = ICi.^2 * Rcin .* Pones; %Cin lossPl_Co = ICo.^2 * Rcout; % CoutlossPl_misc = Pl_misc .* Pones; %miscellaneous const lossPl_tot= Pl_L+ Pl_Qc + Pl_Qs +Pl_Qg + Pl_D + Pl_Ci + Pl_Co +Pl_misc; % total load powerEff= Pones / Pl_tot; % Efficiencyvs. input power+ " 3" 8 "" 7 MATLAB ; (4) 208

.. ..2009 !..8 + " (" 8 1 + " $ (5) ;(" 8 + 3" 8 9: + 2-2-2H *?$ 52 #$ 9 ?* , -# # +%G $. [7] PV's 8 , $ $ , 6?* G $( $ (Sliding Mode Control) SMC 6 #$ :($ :( 8,# M A(Pulse Width Modulation) PWM ?* ( 5M$ ) , *" 5M$ ( ?$ 5 E T5M$ D 9 5M$ ) $ 5 J 9# 6 #$ * $ *?$ 52 #$ ?* WJ$ .# " $ 946 9" ?$ 27 AB ?$ @K PWM 9 ?$ SMC)# !$ $ .M$ 5 J J 8 T F$ (Boost $ , *?$ 9 E $2 8 5 E.(6) , G SMC 6 * , , #$ X Converter $2 5** (7) , #J 9# V4$ 5 " 5 E 8# -# M$ # ? M$ ( T 9 56% ? # M$ 31% ? M$ ( 40V ? :7 T[8]. ?* +%G , $ #$ GK #! . \E 209

"* 5 * :( " $7 8 9# % 4 "( " @8 + " +< + ; (6) 9: ; 8 (" " < + < " ;( " 3 (7) SMC9: " 8 + " $ 3-2-2 6 #$ *P &! , J % GK :( [/^$_(/V # , L$ J T% 52 E AJ , *?$ #$ " ?#$ AVR6* M! #$5CD ( #$ BASCOM Z5[/Z^$_/ .(18V ~ 40V) $&[9]HexDec.>( 5 :7 J T% 9 M! #$ V # J + $ V #$C7 E A !$ 9# . \E Proteus , B ,210

.. ..2009 !..:( ? V4$ < 9# V4$ ? 8 %K$5 .Protues 9# 4 , , 9 (8) .8P% C , ( $2 A ? 9# V4$#$ 31% :$# ( $ ) 52#$ , )*J C7 ( D M$ 1.5Sec 9" ( 6 56% :$# (# $) T9" !$ ; U %G .$ E$ 8$ ) 40V ? :7 T" V4$ (9) WJ .*?$ ( :( 9* , SMC %G , 8#; A 5M$ 2 T $(*$ M$ 9 ; 95.6% ? ( , *?$ 9 5 E.$( :( 6$ !$Protues 8 4.c - @Boost Converter 8 " " (8) 211

"* 5 * :( " $7 8 9# % 4 "" # . ;( (" C" # . (9) DC/AC " > $ 4-2-2DC/AC )$ :7 $ " 8 !$ # +%G ?$8 H-Bridge Inverter " 9 8 +%G $$ .Inverter` 8 "F #$ :( $ Microcontroller M! #$ V$ 220V :( 8,# 8 +%G , $ .4 " ( B;J,Sine-wave Pulse ) SPWM #$ $ P% T $ E 50Hz[10]V4$ 5 . J 1 $ > (Width Modulation, O100W +" # ( 91% a " #$? 8 :7 ?212

.. ..2009 !..A ># ?$ < *?, 5?,$ -;E :7 T , 5?,$ 5JK ## %M$ 8 +%G $ ) %G SPWM * $ ( P%[11]T &* (10) WJ .4 :7 ! 6SX-6* " 97 * A8 :(T 979 ( J#$#! (P%A! )# :7 ! ? 2000(11) .SPWM * , 100W (*$ # (-# A? " < ? 8 $2 **.8 :( 5? 1 V4$ (12,13,14) WJ$ 98 100W $ " ;( 4 ;( ! (10) SPWM213

"* 5 * :( " $7 8 9# % 4 #+ @ + 3 ( (11) (13) A# 5M$ 2 $ " V4$ (12) B .# 5M$ 2 T $(*$ " V4$214

.. ..2009 !..30 9" 6 ; 33ºC :7 9# 6$ :7 (14) , WJ :#?$2 > 5( 3 :( 6$ M$ 9 ; 35ºC ( P% 5 E ?".8 ># < 3" " # . (12) 3" 3 "" # . (13) 215

"* 5 * :( " $7 8 9# % 4 SPWM 98 100W " " # . (14) Boost Converter 8 " Inverter + $ 5-2-2# , 9% ? 8 *$ C7 # +%G , $*? , $ $ , *?$ J$$ -# A+;(SMC 6 #$ * X , A *";P m8( (*$2$ E T $ :( 8,# !$ %G , $ .B? P% % ? 9 SPWM * , 9 SMC * $, $# V4$ 8 +% $2 ** (15) .#$ " G . ? :( G67 $ $ ? V4$ 8$ .Proteus) A! ( # , @( A , *?$ ! ( 3% ?# , O94% :7 ? ! > A40V :$# 18V 96) 87% ? :7 (*?$ 5% ?) 1K9 9( < A ? *?$ , 5(J216

.. ..2009 !..', *?$ 7 ) ? 9 T , 5E# $ 8$.B ? 217

"* 5 * :( " $7 8 9# % 4 Proteus 8 . 8 " + 3 ( (15) 8 " + 8 +8 A 1 6-2-2T Pspice , #$ $ (16) ? &E ! (15) , ? 9 9# ( P% AV OUT9# $ WJ$ .T W ! # < >6$ :( +K (K$-# 220V±10% ? ( T 9D B B?$ (16) , . B )" ( 50Hz G 9D +%G $8#; G A+K &E ! # T &* (16) ?97 , ) # H %G A50Hz $ ? 5?,$ [12] . 8 +%G =%M$ $ 56$ 1 J ) @ T( P% AT #$ $ , (17) ?WJ$ .EE T T% LPF JK 5$ $ W !218

.. ..2009 !..? ( T 9D B B?$ (17) , 9# $ . B ?$ ( 50Hz G 9D +%G $ -# 220V±5%G AT T% W ! # T &* (17) ? A EE ?,$ , WJ &J < E ?,$ ;#J 8#;+%G =%M$ $ 56$ 1 -# " >% J &K %GTDH :( W*! * T , 5?,$ =$# # .8[13] 5?,$ @$ ( >% (Total Harmonic Distortion)$ ! K ? V 1 -# .(1) &b.h 5?,$ ( K ? V h A(50Hz) T 12 2 Vh2h1Vh% THD = 100= 100(1)V1h=2 V1# %M$ $$ $ 5 ? , 10% " THD #$ 9( # %M$ ( P% :( ? # , J#$[14], $#J T $ , THD ? )# ( . ,!5JK " T W $ ( ?,$ @$ . 8#; + :# :( A+K (K$ &E $ # , ( &! :7% THD = %15.54; output with C only & % THD = %7. 9;8output with T Filter" A"> > !6 $ 8 + ;( ! 4 (16) ;(219

"* 5 * :( " $7 8 9# % 4 " 1LPF = $ 8 + ;( ! 4 (17) ;( " 66J, B N T 6* LPF W ? !$ ', . \E +K (K$ &E $ # , AE :( 6 # %M$.T ([15]@ $ 96 THD #$ @` ) , :$# 5 % $ 96 " % A,%# ?,$ 5K(J +%G * L?7 :7 = >% C (EE ?,$ 5K(J $) 3KHz2 9M! ) EE 5?,$ " * 96 63% ?,$Total ) THD ?,$ +$ #$ :7 = >% A11% 6$$96 " P% .6.45% ? :7 7.89% ? (Harmonic Distortion, G 3KHz :( " :7 SPWM T% , 5 % $6KHz $ :7 B2! BE #$$ THD H A+ (1) $ , # $( @J >% 8( $ G(! 9 :( &$ JK -# A# 9 # G ? ,G7 % . ) B#$ %G A5K 9 " A3KHz $ ( M$ :( ( (6KHz)

.. ..2009 !..Frequency Harmonics 3 rd % 5 th % 7 th % 9 th %2KHzC-only 14.12 2.5 0.4 0.05T-filter 7.8 1.2 0.22 0.033KHzC-only 6.1 8.2 1.64 0.1T-filter 3.9 5.06 0.92 0.054.5KHzC-only 4.7 10.8 3.6 0.7T-filter 2.1 5.9 1.2 0.086KHzC-only 3.1 11.2 3.9 0.85T-filter 0.41 5.93 1.16 0.05SPWM VWJXY? ZT[HK?@ AABC D?E=F GHI@JK?@ LJMK?@ DNOP QRSRTU (1) ;?@THD %14.347.8910.356.4512.336.3712.286.05 $ 9 :4 -3-2UG < * ( PV 52 , 4 :( # +%G $$IEEE519 & * ?#$ 5b$ -# .4 +%G 67[16]Sandia 5 $ V4$ 9K$2 5$ P% A IEEE929 , 6$ *? #$ -# V4$ ? , National Laboratories 8# ( :7 ! 8#) :7 ? ? (*( -# A=$ 1K) 4 $$ 5 *J2.( &8 5M$) KIEEE929 9+ 1-3-2:( PV ! # , U;$ #$ J 5 IEEE929 ?56$ # ! ?$ ( 4 < K$$ -# .$ * " $$ 5 ( B;J, .5)$ $ :7 $ B ? T ( :7 !:7 B ! 8# * , ) A*?, 0.5Hz 9" 8([16] :7 B ? T ) P% . K!? 6 1K , Z%/7 A";$ 8# P% AB;" @221

"* 5 * :( " $7 8 9# % 4 (18) ." :( G A 9? $ %G 10%. $2 8 "! ** " :( Microcontroller M! #$ V 8 +%G , SMC X ,

.. ..2009 !..C"" 9> # " 1-1-3-2>$ T6 ?* G >$ K " , $ * G .7V 2< E (U PV ,F PV ) ? T 97 *$ .(19) , #J 97 *$ OAD835 6* 5% U1)J 9 X (8$ AU1 9 Y ( V 3 )$ < E (U G ,F G ) & (F PV -F G ) 5$ 5% 57 ()J 9) >$ T6 T , Butterworth 6* K JK 5$ W ? .(F PV +F G ) :( !# K 97 ?$ P% $ -# AK $ $ E Uc M! #$ V ADC # ( @" $V m2$# $ :7 @$ >$ K ? #$ $ % A(18) , P% $ -# .IEEE929 * * ?#$ M K!:( 8,# B? % SPWM T% , M$ $ M$ ;" 9 9# #$ V4$ (20,21) $ .3KHz $ KG" $D >$ K 96 < B* M$ ?$ 9 T.1Hz +" >$ &;$ 0.25VC"" 9> # " B ( (19) 223

"* 5 * :( " $7 8 9# % 4 > + ;( 4 (20) "" + = C"" ;: " ;( 4 (21) C 9> # " 2-1-3-2K :( $(2 >* K ? J :( &K $ $ $$ $ A(Random Processes) 4 59D . 1K Z%/7 .(Correlation Function) * $2 < $ (Mean) *$$ [A] +" * 5% 97 G A$2 8 9 (Uniform Distribution) 8

.. ..2009 !..X ( t)= A Sin( t)Rf1X ( t)= ASin( t ± )2( ) = E 1( ) = 20[ X ( t).X ( t)]12;;=+ + X( ) dx dx2AR( ) = Cos (2f )2G < 5?# $ >* K " 9 !$ " % , G J $ :( $ $ (22) , $ [Y] 1 %G " * , K ? < J( )$ (23)>* K ? #$ $ (18) , Uc M! #$ V ? :( ? * SPWM 5J ?$ F$ ; -# @$ .(15) , 1X2 elsewheref12;(2)C 9> # " 3 ( (22) 225

"* 5 * :( " $7 8 9# % 4 9> # " 3-1-3-2J $$ $$ $ P$ G * K " 4* G .7 ?$ $ (24) , Instrumentation Amplifier >6 ";( J %G #$ ( .f( CF (JK$) ]* J4 8( ? V 1 E -# (3) :*$ T 5% ? 9 T 8( ?Vout VR13=R + Rout1213 6103RR119( V11 R22 R + R21V) ; R822R(1 +R97= R , R105)( V1= RV)112, R5= R , R62V 2E ., *?$(3)= R , R41= R, 96 6mV ? 6 T . A9 :( ? 1$ ? B # :7 ? * ? +%G O1V +? * K# ( * K " $ .(25) :( WJ T :##$ $ % A(18) , Uc M! #$ V ADC B ?$ K! # $ :7 SPWM ?$ , @$ * K ?.IEEE929 * ?#$ M3 9> # " 3 ( (24) 226

.. ..2009 !.. 9> # " . (25) IEEE519 9+ 2-3-2( 3% ? 6$$ 2 ) -# THD IEEE 519 #84.1C 8 )# P% A :7 !8 T , EE W $ $ ) % .1995 ANSI

"* 5 * :( " $7 8 9# % 4 ABB : LPF = $ 8 + ;( ! 4 (27) B$ ; 8#; $ ABB W 4 9 (26) & AE EE $ T 6* LPF 5# 9 B$ P% A@*" 5$ " , ABB W J T% 7 :(; K$ )$ 5# #$ ABCD ? 5 E &8$ ;>6 J #$ $ * :7 ? )*" ( ?$ E * , # :( Mathematica ,5$A V? < $ M! CD %G ; -# .(28)F$ #K! * 5** W 9# :( E A

.. ..2009 !..98 / " 1 T F LPF = 7 (28) Mathematica " 1 T F LPF = >$ (MATLAB 98(29) 3 ( -4-2(30) , G )#(15) , $2 ** igh(9? IR2111 $ 9 $ %K$ 5 *$ [17]9 $ 9# " APower MOSFET 5$6$[18]+" T * A B* 9# # E$ $ LM35 $229

"* 5 * :( " $7 8 9# % 4 9 A150ºC :$# -40ºC J 9# 5M$ 1mV/ºC5 ? < , # G ARS232 %K ( PC )# < ! C;[19]$ -# A(30) )# 58 :7 ! $[20]9 ', P% ( B;J, . Pony-Prog 2000 V $ V #$)# 8 5* $ W$$ +%G C;.! )# :( 8 +%G C " ( !8 $ )*$$ )# :7 ! ?#$ 7 :7 G 9D )$#$ V $ )*$ %G A< Port ! %, >% #$ V :7#$ V (15) , B? @7 AT90S4433M!( #$ V 6$ .(30) , G AT90S4414/8535 Flash Memory 9% 8Bit 1 ,J7 %K @? [21]*"2 < (31) , $2 8 %G $ . 12KByte ?A*" :7 @! -# (80~140W) (*$ *" 9( Standby 8$2 * B# ! C 8# B2!K 8 T (*$2 ? $ A * $ ? 8 ? G .Mode8 ( # J ? +%G 5 # , :7 *" 9.(2) , 8$2 * :7 -# X * $ " 8 ?@K !K 8 ? & > A , *? )*J -# # ,? :7 B, C* 9( :$# 8$2 * , ( 8 9 (31) , ! WJ$ ., ] W* :( A , *" A T .-# ! !230

.. ..2009 !..8 " + B ( (30) 231

"* 5 * :( " $7 8 9# % 4 40mWATT2×36Cell100Watt16~24Volt-40Cº ÷85CºP S 203PV 0 >$W DC 3 3V DC (" "TMP "220V±5%49.5~50.6 Hz87%> 0.98< 3%V AC ;( "F o ;( ""_ "" ` 3 THD " A @ $ 3 >$ (2) "? :7 ! " T &* (32) PC ! )# :7 ! ? SX-2000 6* " 97 *.B? % B ;( 4 SX-2000: 0 PH2SY48 4 $ * $ & (31) SX- : 4 / ;( 4 ;( ! (32) PC 4 $ 2000232

.. ..2009 !..$( L $ 3 1 " " -5-2E ?* G ((K$ $) K$ )# %, =#7 $ N, G APC ! )# 9M! 5 8 * , B(4 :7 (16~24VDC) 4 "* IJ ? (33) .(220VAC-50Hz)5# A 8 $2 ** , WJ G 8 [gh6$ ! $$ -# .B # @$ " 8 %G C COM1 $ * ( $ 5* ? RS232D C* " 1( ; $ PC ! )# COM2 , WJ G )# GH 6 5 6 A(*$2 @ @ , 8 )$ $ 5" A(34).*" 9# :7 ?PC$( L 4 $ * "$ ( (33) 233

"* 5 * :( " $7 8 9# % 4 & ) * 8 > GUI "( M"4 (34) " 3 " FB E;3 -3:7 $ Inverter " 8 $ ?$ -# %G , $ (1 , Boost Converter *?$ J$ ASine-wave )$ D 5 *J J 5 E T :( 8,# M $ ? 9 , T 97 * $ #$ $ -# .9# $ *?$ #$ $ , ASPWM J 1 $ ;.SMC 6 #$ X, T 97 5K! ( , 8 +%G G :$$ (2:7 !

.. ..2009 !..` ! $2 8 " 9# % +%G 5 (3:7 ? * V4$ 5 A 4 *" !. ? V4$ #, 5(J 5 # ? H J T% (' %G , " (4 $ " A -# ) $ . \E ADC/DC *?$ 52 :( *MJ 1K$ -# ) N$ ABoost Converter , ( B;J, %G ABJ , ? 8 , , #.52 " < ? $ K " ?* +%G $$ AK ? B;J, AV K +%G 6' P% 6$ ?#$ * >*8 5* $ ; B # 8 C " (. 8 %G E$ ( ! )# -# %G J $2235

"* 5 * :( " $7 8 9# % 4 References[1] Scientific Studies and Research Center (SSRC), http://www.syrianpv.com[2] S. R. Wenham, M. A. Green, M. E. Watt; "Applied Photovoltaics",Centet for Photovoltaic Devices and System, University of NSW,1999.[3] West R., Mauch K., Michigan T., Mohan N., Bonn R.; "Status andNeeds of Power Electronics for Photovoltaic Inverters", Sandia NationalLaboratories, Albuquerque, Australian National University, 185 pages,2002.[4] V.F. Pires, J. Fernando, A. Silva; "Teaching Nonlinear Modeling,Simulation, and Control of Electronic Power Converters Using MATLAB/ SIMULINK", IEEE Transactions on Education, vol. 45, no. 3, August2002.[5] T. Esram, L. P. Chapman; "Comparison of Photovoltaic ArrayMaximum Power Pint Tracking Techiques", University of Illinois,Urbana, 2004.[6] J.Mahdavi, A.Emadi, H.A.Toliyat; "Application of State SpaceAveraging Method to Sliding Mode Control of DC/DC Converters",IEEE Industry Applications Society, October 2003.[7] F. Bilalovic, O. Music, A. Sabanovic; "Buck Converter RegulatorOperating in the Sliding Mode Control", Proc. Seventh InternationalPCI83" Conference, PP. 331-340, 2004.[8] Ahmed, M., Kuisma, M., Silventoinen, P., Pyrhönen, O.: "SlidingMode Control For Boost Converter Using Control Desk dSPACE". TheFifth International Conference on Power Electronics and Drive Systems,PEDS 2003. Singapore, November 2003.[9] BASCOM-AVR Compiler: Version 1.11.7.4, Copyrigt 2003, MCEElectronics http://www.mcselec.com[10] RASHID M. H., "Power Electronics Circuits, Devices andApplications", Prentice- Hall International Inc., 537 pages, 1993.236

.. ..2009 !..[11] Pitt R., "Improving Inverter Quality". IEEE Industry ApplicationsSociety Conference, pp: 19-20, 2000.[12] T. E. Company, Inc.; "A Review of Inverter Designs and Topologiesby Trace Engineering", http:// www.traceengineering.com[13] MOHAN N., UNDELAND T. M., ROBBINS W. P.; "PowerElectronics, Converter & Inverter, Applications and Design"; John Wileyand Sons, INC., 2 nd ed, New York, 802 pages, 1995.[14] E. caama`o, E. Lorenzo; "On-Site Characterization of Grid-Connected PV Systems", Instituto de Energia Solar, Madrid, 2002.[15] BHAT K. S., DEWAN S. B., "A generalized approach for the steadystate analysis of resonant inverters", IEEE Industry Applications SocietyConference, pp: 664-671, 1998.[16] A.Engler, O. Haas, B. Kansteinner, F. Raptis; "Control of ParallelWorking Power Units in Expandable Grids", 14 th European PhotovoltaicSolar Energy Conference, Spain 2001.[17] Power MOSFET Deriver type IR2111; Datasheet.[18] Liner Temperature Sensor LM35; Datasheet.[19] Sakutaro Nonaka, Fukuoka; "A Utility-Connected Residential PVSystem Adapted a Novel Single-Phase Composite PWM Voltage SourceInverter", Kinki University,820 Japan, 2004.[20] PonyProg, Version 2.06c Beta 2003 ; http://www.lancos.com[21] AVR – Microcontroller AT90S4433, AT- Mega 8535; Datasheet..2007/10/17 : :7 -# I$237