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, .

MATLAB SIMULINK

AC

MATLAB SIMULINK , Fourier, SimPowerSystems , blocks

(, , , ) R, L, Ed AC

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MATLAB SIMULINK

AC

MATLAB SIMULINK , Fourier, SimPowerSystems , blocks

(, , , ) R, L, Ed AC

MATLAB SIMULINK

AC : , 16, , 27300 email: contact@hws.org.gr (open access) : hws.org.gr (direct link: http://hws.org.gr/books/EHIMXMS.pdf) ISBN 978-618-82223-0-4 Copyright . , 2015 CC-BY 4.0 ( 4.0) http://creativecommons.org/licenses/by/4.0/ http://creativecommons.org/licenses/by/4.0/legalcode CC-BY 4.0 ( 4.0) (Free Cultural Works) http://creativecommons.org/freeworks This work is available under the CC-BY 4.0 license.

. 10 , , MATLAB SIMULINK. , . 1. , , . .

2014-2015 .. 2. , . (Pan-Hellenic Conference on Electronics and Telecommunications - PACET) 20153,4. , , . . , . 90%.

.

1 - http://tinyurl.com/o3vapby. 2 : . , : , , 2014-2015 3 . 4 - (. , . , . ), .

1: MATLAB-, , ... 1 1.1 .. 1 1.2 , ans... 1 1.3 .. 3 1.3.1 , , 3 1.3.2 . 4 1.3.3 . 4 1.3.4 whos.. 5 1.3.5 (complex). 6 1.3.6 ( ), s.... 6 1.3.7 length.7 1.3.8 ( ) - plot... 8 1.3.9 , ... 10 1.4.1 ... 10 1.4.2 ( hold).. 11 1.5 - - trapz11 1.6 . 13 2: Fourier... 14 2.1 14 2.2 Fourier.. 14 2.3.1 Fourier MATLAB fft ... 15 2.3.2 Fourier MATLAB ... 17 2.3.3 Fourier MATLAB (scaling) 20 2.3.4 .. 21 2.3.5 .... 22 2.4 . 23 2.5 . 24 2.6 THD.. 27 2.7 . 28 3: SIMULINK (SimPowerSystems). 29 3.1.1 SIMULINK... 29 3.1.2 , block. 29 3.1.3 . 30 3.1.4 ... 30 3.2.1 SimPowerSystems. 31 3.2.2 powergui block 31 3.3 .. 31 3.3.1 DC ... 32 3.3.2 C RMS 33 3.3.3 C .. 35 3.3.4 (mux), (demux) (multimeter).. 37 3.3.5 C Fourier . 38 3.4 . 40 4: 41 4.1 To block simulink snubber ... 41 4.2 To snubber 41 4.3 .. 42 4.4 measurement port ( ).. 42 4.5 ... 42 4.6 42 4.6.1 (), RMS . 43 4.6.2 (), .. 44 4.6.3 .. 44 4.6.4 / 45 4.6.5 Ed... 45

4.6.6 .......... 46 4.6.7 (L>>R), 48 4.6.8 48 4.7 . 49 5: ( ).. 50 5.1 (controlled rectifiers) 50 5.2 (thyristor) 50 5.3 thyristor block simulink... 50 5.4 pulse generator block.. 50 5.5 scope 51 5.6 scope. 51 5.7 ...52 5.8 MATLAB.. 52 5.9.1 ... 53 5.9.2 . 55 5.9.3 DC . 57 5.9.4 DC ... 58 5.9.5 .. 58 5.10 ... 60 6: ( ).. 61 6.1.1 61 6.1.2 .. 62 6.1.3 RMS dc .. 63 6.2 - ... 63 6.2.2 RMS dc .. 65 6.2.3 - .. 65 6.3 R-L-Ed , FWD.. 67 6.4 . 67 7: 68 7.1 ( ). 68 7.2 Goto From blocks. 69 7.3 70 7.4 RMS dc . 70 7.5 - . 70 7.5.1 - 71 7.5.2 - .. 72 7.6 72 7.7 . 74 8: ... 75 8.1 ... 75 8.2 .. 75 8.3 .. 76 8.4 simulink.. 77 8.5 crest factor ( ) 77 8.6 (Peak Inverse Voltage PIV). 78 8.7 ... 78 8.8 RMS . 80 8.9 .. 80 8.10 add block...81 8.11 ... 82 8.12.1 .. 83 8.12.2 ... 84 8.13 ... 86 9: 87 9.1 ( ). 87 9.2 Synchronized 6-Pulse Generator block 89 9.3 simulink 91 9.4 simulink Universal Bridge block... 91 9.5 Gain block...92 9.6 (Subsystems) 93

9.7.1 - . 94 9.7.2 - ... 95 9.7.3 - 96 9.8.1 - .. 96 9.8.2 - (- ). 97 9.9.1 Controlled Current Source block.. 98 9.9.2 ...99 9.9.3 .. 100 9.10 ... 101 10: AC ... 103 10.1 . 103 10.2 SIMULINK ( ) 103 10.3 ... 105 10.4.1 AC .... 107 10.4.2 AC 108 10.5 Transport Delay block.. 110 10.6.1 1 111 10.6.2 2 112 10.6.3 3 113 10.7 ... 114 : D. Pylarinos, I. Androulidakis, K. Siderakis, E. Drakakis, "A Matlab/SimulinkApproach for a First Course in Power Electronics", 3rd Panhellenic Conference on Electronics andTelecommunications, Ioannina, Greece, May 8-9, 2015... 115

1: MATLAB

MATLAB SIMULINK

- 1 -

1: MATLAB-, ,

1.1 MATLAB : * + - / ^. . ^ ( 32 3^2) sqrt (

2 sqrt(2)). : >> 2^3/(1+3) ans = 2 1.2 , ans , , MATLAB ans ( answer=). : : >> x=2^3 x = 8 ( ) . _ . : >> metabliti_1=2^3 metabliti_1 = 8 MATLAB . disp ( display) ( disp(x) x)

1: MATLAB

MATLAB SIMULINK - 2 -

: >> x1=2^3; >> x2=2*x1; >> x1 x1 = 8 >> x2 x2 = 16 >> disp(x2) 16 1: MATLAB . , . H MATLAB . >> x1=5; >> x1=6; >> disp(x1) 6 2: MATLAB , /, . date . date . . MATLAB, help . : >> help date DATE Current date as date string. S = DATE returns a string containing the date in dd-mmm-yyyy format. See also now, clock, datenum. Reference page in Help browser doc date

1: MATLAB

MATLAB SIMULINK

- 3 -

doc MATLAB. 1.3 MATLAB MATrix LABoratory ( ). . (.. , ). . MATLAB. / / . 1.3.1 , , MATLAB . :

1. 2. 3. 4.

: >> x1=[1 2] x1 = 1 2 >> x2=[3; 4] x2 = 3 4 >> x1' ans = 1 2

1: MATLAB

MATLAB SIMULINK - 4 -

. , MATLAB : >> x1=[1 2]; >> x2=[3; 4]; >> x3=x1*x2 x3 = 11 >> >> x4=x1'*x2 ??? Error using ==> mtimes Inner matrix dimensions must agree. 1.3.2 MATLAB . . x1. x1^2 MATLAB 1x2 ( 1x2) . . : >> x1=[1 2]; >> x1^2 ??? Error using ==> mpower Matrix must be square. >> x1.^2 ans = 1 4 . , ( ). 1.3.3 , : .

1: MATLAB

MATLAB SIMULINK

- 5 -

MATLAB . , : >> x(1:3)=1; x(4:6)=2; >> disp(x) 1 1 1 2 2 2 , : >> pin1=1:6 pin1 = 1 2 3 4 5 6 6 1 6 . . , :

= :: . , MATLAB 1 ( ). ( ). : >> pin2=1:2:6; >> disp(pin2) 1 3 5 >> pin3=9:-1:7; >> disp(pin3) 9 8 7 >> pin4=0:0.01:0.05 >> disp(pin4) 0 0.0100 0.0200 0.0300 0.0400 0.0500 : . 1.3.4 whos .

1: MATLAB

MATLAB SIMULINK - 6 -

GUI MATLAB (workspace) . whos. ( whos) whos. whos metabliti1 metabliti2 ... . : >> t=1/5000:1/5000:1; >> whos t Name Size Bytes Class Attributes t 1x5000 40000 double 1.3.5 (complex) MATLAB . i j. , whos complex. : >> x=3+5j >> disp(x) 3.0000 + 5.0000i >> x=3+5j >> disp(x) 3.0000 + 5.0000i >> y= [x 2-j] >> disp(y) 3.0000 + 5.0000i 2.0000 - 1.0000i >> whos x y Name Size Bytes Class Attributes x 1x1 16 double complex y 1x2 32 double complex 1.3.6 ( ), s 1.2.3 () . / .. 50Hz. 50

1: MATLAB

MATLAB SIMULINK

- 7 -

100 ( ), 5000 . : >> t=1/5000:1/5000:1; 1: t 1/5000 0. 1. t=0:1/5000:1; 5001 5000. 50 + 1 . t=1/5000:1/5000:1; t=0:1/5000:1-1/5000; 2: (DAQ) (.. ). Fs Ts, Fs=1/Ts. Fourier. Fs=5000 s=1/5000. , 0, , 2 ... . , ( t1 t2 ): : >> Fs=5000; >> Ts=1/Fs; >> t1=Ts:Ts:1; >> whos t1 Name Size Bytes Class Attributes t 1x5000 40000 double >> t2=0:Ts:1-Ts; >> whos t2 Name Size Bytes Class Attributes t2 1x5000 40000 double 1.3.7 length . pin2(2) pin2.

1: MATLAB

MATLAB SIMULINK - 8 -

: >> pin2=1:2:6; >> disp(pin2) 1 3 5 >> pin2(2) ans = 3 , ... 1: . length. : >> x=[1 2;3 4] x = 1 2 3 4 >> x2=x(:,2) x2 = 2 4 >> x2=x(1,:) x2 =

1 2 >> length(x2) ans = 2 1.3.8 ( ) - plot () () plot. .. plot(pin4) pin4.

1: MATLAB

MATLAB SIMULINK

- 9 -

( ) ( ) . plot . plot(x,y) x y . . MATLAB . plot (>> help plot). plot : >> x=[1 5];y=[4 2]; >> plot(x,y) (, ). Export Setup ( File) . . plot help MATLAB . : (a+bj) (a,b)

1: MATLAB

MATLAB SIMULINK - 10 -

1.3.9 , . (x) ( sin(x) ) . H MATLAB , . MATLAB pi. : >> pi ans = 3.1416 >> x=0:pi/180:2*pi; >> plot(sin(x)) 1: whos x x 361 ( 360). ; ; 2: MATLAB deg2rad. : >> x=0:360; >> plot(sin(deg2rad(x))) 1.4.1 (.. ) (). :

o o o o2A A sin A sin( t) A sin(2 f t) A sin( t)pj w p= = = = T

, f . :

0( ) sin( ) 2 sin( ) 2 230 sin(100 )rmsv t V t V t tw w p= = = . 50 Hz, 1/50 0.02 sec. . 10kHz 0.0001. : >> Ts=0.0001; >> t=0:Ts:0.02-Ts; >> v=230*sqrt(2)*sin(100*pi*t); >> plot(t,v)

1: MATLAB

MATLAB SIMULINK

- 11 -

1.4.2 ( hold) , . 2 . : >> Ts=0.0001; >> t=0:Ts:0.02-Ts; >> f=50; >> R=2; >> Vo=230*sqrt(2); >> w=2*pi*f; >> v=Vo*sin(w*t); >> i=v/R; >> plot(t,v);hold on;plot(t,i) Current plot held 1: ( ) ( ) 2: hold (>> plot(t,v);hold on;plot(t,i)) . plot (Figure) hold on MATLAB ( hold) . hold on plot . 1.5 - - trapz ( 2o rmsX X ) . . : : .

2

0

1 ( )T

rmsX x t dtT=

1: MATLAB

MATLAB SIMULINK - 12 -

: . 0

1 ( )T

avX X x t dtT= =

MATLAB. MATLAB /, trapz. . : AC (.. 230 V) (.. R=10 ). ;

. . , . Ts=0.0001 (0.02 sec). 200 100 100 . . RMS (>> disp(max(v1)/2) ). 1: Vrms=Vo/2 Vo/. 2: , Ohm. 3: 4 16.26346 MATLAB 16.2635. format (.. format long)

1: MATLAB

MATLAB SIMULINK

- 13 -

4: . >> Ts=0.0001; >> t=0:Ts:0.02-Ts; >> f=50; >> R=10; >> w=2*pi*f; >> v1(1:100)=230*sqrt(2)*sin(w*t(1:100)); >> v1(101:200)=0; >> v1rms=sqrt(1/200*trapz(v1.^2)) v1rms = 162.6346 >> disp(max(v1)/2) 162.6346 > i1=v1/R; >> i1rms=sqrt(1/200*trapz(i1.^2)) i1rms = 16.2635 1.6 , : plot, subplot, hold

, (

t) trapz

2: Fourier

MATLAB SIMULINK

- 14 -

2: Fourier 2.1 ( ). 50Hz 100Hz, 150Hz ... - :

1

2 2 1 2 2 2 1 2 1

3 3 1 2 3 3 1 3 1

1 1 1

sin( )sin(2 ) sin( ), 2 2sin(3 ) sin( ), 3 3

...sin( ) sin( ),

1 1m

m m

m m

m m

A = A tA A t A t f fA A t A t f f

A A t A t f fk k k k k k

ww w projan V w ww w ant stoicaw w

k w w ant stoicaw kw k

= = = == = = =

= = = =

2.2 Fourier Fourier ( ). ( Fourier, ). , x(t) , x() :

1

( ) { cos( ) sin( )}h hh

x x a h t b h tw w w

== + + ,

2

0

1 ( ) sin( ) ( )hb x t h t d tp

w wp= , 2

0

1 ( ) cos( ) ( )ha x t h t d tp

w wp= , 1, 2,...,h= () ( DC ) ( ) . 1: / . 2: Fourier (.. f(t)) (.. F()) ( Fourier). Fourier. Fourier : 2( ) ( ) i f hF f f t e dfp

-

-=

2: Fourier

MATLAB SIMULINK

- 15 -

3: . , ( ) Fourier ( Fourier ) . Fourier (fast Fourier transform fft) 4: (.. ) , ( Fourier ), . 5: Fourier . 6: Fourier ( ) 7: MATLA fft. . 8: , wikepedia: http://en.wikipedia.org/wiki/Fourier_series 2.3.1 Fourier MATLAB fft MATLAB fft Fourier. help MATLAB. 1: , , . , ( ) ( Fourier ) , :

230 2 (2 50 ) 100 (2 150 )y t thm p hm p= + 0.1 sec, 2 kHz

2: Fourier

MATLAB SIMULINK

- 16 -

50 Hz 325.2 100 150 Hz. >> Fs=2000; >> Ts=1/Fs; >> tmax=0.1; >> t=0:Ts:tmax-Ts; >> y1=230*sqrt(2)*sin(2*pi*50*t); >> y2=100*sin(2*pi*150*t); >> y=y1+y2; 2: Fourier . (.. ) 50Hz ( y(t)). .. / ( ). , .. . .

3: / ( ) . 325.3 50 Hz 100 150 Hz. Fourier , .

>> disp(230*sqrt(2)) 325.2691

2: Fourier

MATLAB SIMULINK

- 17 -

4: , . MATLAB ( ) . . ( ) , 5: . ( ) , fft: >> Y=fft(y); >> whos Y Name Size Bytes Class Attributes Y 1x200 3200 double complex , complex . fft 200 (). 6: H fft . , . 2.3.2 Fourier MATLAB plot ( plot(Y)) default plot.

!

2: Fourier

MATLAB SIMULINK

- 18 -

200 : >> plot(Y)

, . abs angle. . : >> plot(abs(Y))

:

>> plot(abs(Y))

2: Fourier

MATLAB SIMULINK

- 19 -

1: x. , Nyquist ( Nyquist-Shannon), ( Nyquist FN=0.5FS, FN Nyquist FS ). 2: Hz. frequency bins ( ) 3: (.. Nyquist ). . ( scaling) 4: , 1. 0 MATLAB ( 1). default MATLAB.

zoom

2: Fourier

MATLAB SIMULINK

- 20 -

2.3.3 Fourier MATLAB (scaling) , . ( fb frequency bin) 0, 1 ... : >> fb(1:100)=0:99; >> plot(fb,abs(Y(1:100)))

:

1. ( 5 frequency bins 15 frequency bins)

2. 3.25 3. (2000Hz)

Nyquist (1000 Hz), frequency bin 5 50 Hz frequency bin 15 150 Hz

4. ( 100)

fhz hz frequency bins hz () : >> fhz=fb*Fs/

(, ) . plot . .

2: Fourier

MATLAB SIMULINK

- 21 -

fb . Hz : >> N=length(y); >> fhz=0:Fs/N:((N/2)-1)*(Fs/N); >> plot(fhz, abs(Y(1:N/2)/(N/2))) 1: Hz 2: /2 plot . Fourier MATLAB. . 2.3.4 y, Fs : >> N=length(y); >> Y=fft(y)/(N/2); >> fhz=0:Fs/N:((N/2)-1)*(Fs/N); >> plot(fhz, abs(Y(1:N/2))) : : Fourier y=230*sqrt(2)sin(250t)+100sin(2150t) >> Fs=2000; >> Ts=1/Fs; >> tmax=0.1; >> t=0:Ts:tmax-Ts; >> y1=230*sqrt(2)*sin(2*pi*50*t); >> y2=100*sin(2*pi*150*t); >> y=y1+y2; >> N=length(y); >> Y=fft(y)/(N/2); >> fhz=0:Fs/N:((N/2)-1)*(Fs/N); >> plot(fhz, abs(Y(1:N/2)))

2: Fourier

MATLAB SIMULINK

- 22 -

1: (/2) fft plot. , ( ) 2: (.. ) 2.3.5 (scaling) . ( Hz) ( fhz ). : >> [y1,x1]=max(abs(Y(1:N/2))) >> disp(y1) 325.2691 >> disp(x1) 6 >> fhz(x1) ans = 50

2: Fourier

MATLAB SIMULINK

- 23 -

1: N/2 , fft ( plot), ( ). frequency bins Hz. Hz (fhz) 2.4 . ( 2o rmsX X= ) , . . , :

2

1rms hrms

h

I I

==

( AC ) : ( 10 ) (.. 15% ). : >> Ts=0.0001; >> t= Ts:Ts:0.02; >> f=50; >> w=2*pi*f; >> Io=10; >> i1=Io*sin(w*t); >> i3=0.15*Io*sin(3*w*t); i1 i3. i4; : >> i4=i1+i3; >> i1rms=10/sqrt(2); ( : (10 / 2 )=7.0711) >> i3rms=1.5/sqrt(2); ( : (1.5 / 2 )=1.0607) >> i4rms=sqrt(i1rms^2+i3rms^2) i4rms = 7.1502

2: Fourier

MATLAB SIMULINK

- 24 -

i4 . :

2

0

1 ( )T

rmsX x t dtT=

. trapz . : >> whos i4 Name Size Bytes Class Attributes i4 1x200 1600 double >> i4rms=sqrt(1/200*trapz(i4.^2)) i4rms = 7.1501 (, , ) 1: RMS RMS (true RMS). 2 RMS , . . ( SIMULINK). 2.5 . ; : :

0

1 ( ) ( )TWP v t i t dt

T T= =

2: Fourier

MATLAB SIMULINK

- 25 -

0 01 10

1 ( cos( )) ( sin( ))T

h Vh h Ihh h

P V V h t I I h t dtT

w j w j

= = = + - + -

:

0 01 10

( cos( )) ( sin( ))T

n Vn m Imn m

V V n t I I m tw j w j

= =+ - + - =

0,

cos( )2n n

Vn n

n mV I j jI

-

. : . p11 1 1 , p13 1 3 p . . >> Ts=0.000001; >> t=0:Ts:0.02-Ts; >> f=50; >> w=2*pi*f; >> Io=10; >> Vo=230*sqrt(2); >> v=Vo*sin(w*t); >> i3=0.15*Io*sin(3*w*t); >> i1=Io*sin(w*t); >> i4=i1+i3; >> p11=(1/length(v))*trapz(v.*i1) p11 = 1.6263e+003 >> p13=(1/length(v))*trapz(v.*i3) p13 = -3.6116e-009 >> p=(1/length(v))*trapz(v.*i4) p = 1.6263e+03 p11, p13 p.

P1=Vrms*I1rms= >> disp(230*Io/sqrt(2)) 1.6263e+003

(0)

2: Fourier

MATLAB SIMULINK

- 26 -

1: (.. 50 Hz) ( ) . VIcos , . cos - ( (displacement) ), ( (distortion) ). , (pfdisp) (pfdist) :

1

1,

cosdisprms true disp dist

distrms

pfI pf pf pf

pfI

j = = =

(true power factor pftrue) . ( ), , cos . cos , . 2:

2: Fourier

MATLAB SIMULINK

- 27 -

, DPF PFdisp pfdisp, DF PFdist pfdisp ... 3: , 2.6 THD . (Total Harmonic Distortion Ratio) THD. . , :

2 2

2 2

1 1

hrms hh h

Irms

I ITHD

I I

= == =

THD ( ) . . (THD=0). THD . 1: ( ) :

2 2

2 2

1 1

hrms hh h

Irms

I ITHD

I I

= == =

2 21

2hrms I

h

I I THD

==

2 2 2

1 12

1 ( )rms hrms rms rms Ih

I I I I I THD

== + = +

2

11 ( )

dist

I

pfTHD

=+

: :

100 sin(100 ) 30 sin(500 ) 40 sin(300 )I t t tp p p= + + RMS ,

2: Fourier

MATLAB SIMULINK

- 28 -

>> I1rms=100/sqrt(2); >> I3rms=40/sqrt(2); >> I5rms=30/sqrt(2); >> Irms=sqrt(I1rms^2+I3rms^2+I5rms^2) Irms = 79.0569 >> thd=sqrt(I3rms^2+I5rms^2)/I1rms thd = 0.5000 >> pfdist=I1rms/Irms pfdist = 0.8944 >> pfdist=1/(sqrt(1+thd^2)) pfdist = 0.8944 2.7 , : ()

Fourier Fourier MATLAB

fft .

, Nyquist

(true RMS)

( , )

(THD)

>> disp(I1rms) 70.7107

3: SIMULINK

MATLAB SIMULINK

- 29 -

3: SIMULINK (SimPowerSystems) 3.1.1 SIMULINK

To SIMULINK block . SIMULINK MATLAB 6.5 (2002), simulink MATLAB ( ). (MATLAB SIMULINK) . , blocks, ( ), (play) (). 1: , (.. , , ). 2: / . 3: SIMULINK ( MATLAB) , , / . 3.1.2 , block

SIMULINK blocks (), // .

1: , , . 2: SIMULINK blocks . search block . 3: block , help ( documentation

3: SIMULINK

MATLAB SIMULINK - 30 -

block help doc MATLAB). 4: block ( ) . block . block blocks ( ). 5: block, block block , .

3.1.3 , . SIMULINK , . , (*). 1: / . 2: () MATLAB / . . ( ) ( ). 3: , ( , block ) ( MATLAB). 3.1.4 ( block ) mdl. mdl (Save as) (Export). slx ( ,

3: SIMULINK

MATLAB SIMULINK

- 31 -

) . 1: / mdl SIMULINK . mdl / . 3.2.1 SimPowerSystems SimPowerSystems MATLAB Simscape. ( ) - (Power Electronics). blocks, , . , DC ( .. ) Ohm. blocks, . . . 3.2.2 powergui block blocks SimPowerSystems, block powergui. To block ( gui graphical user interface), ( Fourier). MATLAB, block ( ) , . block . block . , . 3.3 . , .

3: SIMULINK

MATLAB SIMULINK - 32 -

, ... , , . , , . 3.3.1 DC - , DC 100 V R=10. DC . 1: H DC Electrical Sources ( block: DC Voltage Source) block Series RLC Branch Elements ( 2 SimPowerSystems). 2: block Simulink drag & drop . 3: blocks . block block. (Amplitude) DC Series RLC Branch block 10 . , .

4: play () ( powergui block). . , . 5: block Current Measurement Measurements SimPowerSystems. block , (+) (-) () . ( i).

3: SIMULINK

MATLAB SIMULINK

- 33 -

6: . block Display. . blocks , Display block .

7: blocks Rotate Block block 8: (.. R) (.. Series RLC Branch R=10 Ohm). . , . . 9: ( , blocks ). R=10 Ohm R=10. 3.3.2 C RMS , AC (AC Voltage Source) DC . block (peak), (phase) (frequency). 230 2 , 50 Hz 0. 1: Simulink MATLAB .. 230 2 230*sqrt(2)

3: SIMULINK

MATLAB SIMULINK - 34 -

2: display . ; ( ) (play). 10 . display, 10 . 3: RMS block. : 50Hz block ( ) ( ). (0.02 sec). 4: RMS block . true RMS RMS .

5: (Scope). 6: Scope ( ). 7: , Scope.

3: SIMULINK

MATLAB SIMULINK

- 35 -

3.3.3 C , AC . Scope . 1: ( default 10 sec), Scope ( ) ( zoom out) (zoom in) . . Configuration Parameters ( Simulation / ). Solver , : o (start time) (stop time)

o

(.. ode45) o (Variable-step)

(Fixed-step) 2: , . 3: . ( ). 4: . . (auto) . 5: ( ) . . () // .

3: SIMULINK

MATLAB SIMULINK - 36 -

6: ( MATLAB) 7: , Scope, Data history - () Limit data points to last Save data to workspace. Array Format. Scope () MATLAB. 8: , 10 . 9: , 1 (0.02 sec). 0.001 ( 1/10 ) Scope 21 . , 20 1 ( 0) .

10: .

- : 0~10 sec - - =auto - 51

- : 0~0.02 sec - - =0.001 - 21

- : 0.001~0.02 sec - - =0.001 - 20

3: SIMULINK

MATLAB SIMULINK

- 37 -

3.3.4 (mux), (demux) (multimeter) . 2 . , block mux ( ) . mux . 1: . 2: (legend) MATLAB.

. (multimeter) . . 3: , Measurements. . 4: . 5: , Plot selected measurements. 6: .

3: SIMULINK

MATLAB SIMULINK - 38 -

7: (demux)

3.3.5 C Fourier , AC (, ) Fourier powergui. , 300 V 50 Hz 30 V, 150 Hz 10. . 1: Fourier powergui Scope workspace MATLAB (Structure with time).

3: SIMULINK

MATLAB SIMULINK

- 39 -

2: Fourier FFT Analysis powergui. ( , , ) FFT . 3: . simulink . 4: ( , % ) Display style List (relative to specified base) Base value . 5: 5 0.0001. FF , (0.0001 s), / (200), DC (0), (300), THD (10%), (30) (10). 6: simulink (), . 7: 1/0.0001=10000 THD Fourier . .

3: SIMULINK

MATLAB SIMULINK - 40 -

3.4 , : simulink , blocks,

simulink blocks SimPowerSystems powergui block simulink (, , ) powergui block Fourier ,

(THD)

4:

MATLAB SIMULINK

- 41 -

4: 4.1 To block simulink snubber MATLAB , block . : blocks . , block SimPowerSystems. 4.2 To snubber block SimPowerSystems . snubber ( ) . (, , /). snubber , . snubber . 1: R-C snubber. 2: (R-C) snubber block. simulink (R=500 , Cs=25010-9 F). 3: snubber , (inf) . 4: snubber (.. - , ), simulink 5: snubber .

4:

MATLAB SIMULINK - 42 -

4.3 snubber , : (Ron) (Lon) , (Vf) (Ic). 1: 2: Ic . , . 4.4 measurement port ( ) block Show measurement port. block 4.5 . , (continuous), (.. ode23t). 4.6 (AC DC). . :

1. dV Vavg Vdc 2. RMS dV Vrms 3. ( ) dI avg dc 4. RMS Id Irms 5. dc Pdc= Vdc dc = dV dI 6. ac Pac= Vrms Irms= dV Id 7. (efficiency) dc

ac

PnP

=

4:

MATLAB SIMULINK

- 43 -

8. (form factor) rms ddc d

V VFFV V

= =

9. (ripple factor) 2 1,acdc

VRF FFV

= = -

22 2 2 dac rms dc dV V V V V= - = - 10. (transformer utilization

factor) dcs s

PTUFV I

= , Vs Is RMS / ( )

11. (crest factor) ( )s peaks

ICF

I= ,

Is . 12. pftrue 13. THD

1: . 4.6.1 (), RMS R. : V=100/sqrt(2) V, Vf=0, Ron=0.00001 , Lon=0 , Ic=0 A, Rs=inf , Cs=0 F, : 0.02 s 1: block mean value mean ( MATLAB). block ( , block) 2: VRrms=Vo/2 Vo/. 3: 50 V RMS 31.83 4: snubber simulink (R=500 , Cs=25010-9 F)

4:

MATLAB SIMULINK - 44 -

4.6.2 (), , . . . 4.6.3 . simulink, :

1: . 2V0/ ( VRmean=63.66 V) 2: snubber . default . 3: ( )

4:

MATLAB SIMULINK

- 45 -

4.6.4 / / , . / simulink block Linear Transformer ( /) (inf).

1: . / ; 3: OFF

4.6.5 Ed DC d .

4:

MATLAB SIMULINK - 46 -

Ed (VAK=vs(t)-Ed) AC DC , :

( ) sin( ) sin( ) ds d sm dsm

Ev t E V t E tV

w w> > > 1 1sin ( ) 180 sin ( )d d

sm sm

E EtV V

w- - - 1: (Peak Inverse Voltage PIV) PIV=-Vsm- Ed. 2: Vsm=100 V Ed=50 V 30 180-30. 30 0.001666666666667 sec.

3: . 1 (2 cos 2 )

2dc mI V a E a E

Rpp= + - ( )

4.6.6 , . , Lenz, . ( ). :

-R ts L

d2Vi (t)= [sin(t-)+sin() e ]Z

( ) R, L

Vd

VAK

2 2 -1 L = R +( L) , =tan ( )R

4:

MATLAB SIMULINK

- 47 -

simulink (R=1 , L=0.001 ), Vspeak=100 V ( snubber default ). . 1: (0.02/360) 2: 1/100 (0.0002/360)

1 2

1: :

1-R L

1sin( -)+sin() e 0 = ()

2: R=1 , =30=/6, => tan= 0.5774 => L=0.5774R => L= 0.0018 H. 1=210.

4:

MATLAB SIMULINK - 48 -

:

4.6.7 (L>>R), ( ) ( 90) 360, .

4.6.8 snubber . snubber . ; simulink ( ). powergui (configure parameters).

0.01161 360/0.02=208.98 209 0.0117 360/0.02 210.6

R=1 , L=1

4:

MATLAB SIMULINK

- 49 -

=30=/6 : L=tan(pi/6)*1/(100*pi) H variable step solver ode23t max step size= 0.00002/360

4.7 , : block SimPowerSystems (snubber)

DC ( )

powergui

1=0.01164360/0.02=210.06

5:

MATLAB SIMULINK

- 50 -

5: ( ) 5.1 (controlled rectifiers) ( -) . (Silicon Controlled Rectifier SCR) . 5.2 (thyristor) : (), () (G). . ( ). . , ( ). , . ( ) ( ) . . , , , () 5.3 thyristor block simulink simulink thyristor blocks (.. detailed thyristor block ). , thyristor block. block 3 : (a), (k) (g). block , block (snubber) (m) 5.4 pulse generator block . , block (pulse generator). , : , . . phase delay secs (sec=0.02*deg/360). (: Use simulation time).

5:

MATLAB SIMULINK

- 51 -

5.5 scope scope block number of axes (default) . scope ( ). scope, ( ) . 5.6 scope scope . .

scope . , scope. Signal Properties. (Signal name)

scope scope % (default) scope

5:

MATLAB SIMULINK

- 52 -

5.7 blocks RMS . .. (.. Pdc=Vdc*Idc, n=Pdc/Pac) / MATLAB blocks simulink. block product block Divide. block constant .

Divide block . 5.8 MATLAB MATLAB . To Workspace block. block , . , .. RMS ( ) array

5:

MATLAB SIMULINK

- 53 -

5.9.1 . . ( ) , . . : , , (). Vspeak=100 V, f=50 Hz, R=2 , , 30, 50 V. .

[cos 1]2

Sdc

VV ap= +

[cos 1]2

Sdc

VI aRp= +

,

1 sin(2 )2

2d rms Sa

V Vp a

p- +

=

5:

MATLAB SIMULINK

- 54 -

1: Vdc Vac (Pdc, Pac, n, FF, RF ). ( ) 2: Vdc=IdcR Vrms=IrmsR

3: d measurement port thyristor block. 4: simulink . workspace MATLAB .

5:

MATLAB SIMULINK

- 55 -

5.9.2 , . 1, 1=+. =1-. :

( )2( ) [sin( ) sin( ) ]R t as L

dVi t t a e

Zwww j j

- -= - - - () :

1( )

1sin( ) sin( )RLe

b awb j a j- -- = - .

:

1: 2: () =0 =90. , , . : , , (). Vspeak=100 V, f=50 Hz, R=2 , L=0.005 H, , 30,

5:

MATLAB SIMULINK

- 56 -

50 V. . ( )

1: Vdc=IdcR Vrms=IrmsR

1[cos cos ]2S

dcVI a

Rbp= -

1[cos cos ]2S

dcVV a bp= -

1 1

,

1 [sin(2 ) sin(2 )]2

2d rms Sa

V Vb a b

p- + +

=

5:

MATLAB SIMULINK

- 57 -

5.9.3 DC . : vs(t)=vAK(t)+vR(t)+Ed. vAK(t)=vS(t)-Ed. : (OFF) d : , , (). Vspeak=100 V, f=50 Hz, R=2 , , 30, 50 V, d=50 V. . ( )

12 ( )[cos 1]2 2

mdc d

VV a p b ap p - - = + + E ,

dc ddc

V EIR

1 11 2 sin sind d

m m

E EaV V

a a a p- - -

5:

MATLAB SIMULINK

- 58 -

5.9.3 DC . , R block R-L L=0.001 H L=0.005 H

L=0.001 H L=0.005 H

5.9.4 (freewheeling diode FWD) . , . 1=+, , . .

5:

MATLAB SIMULINK

- 59 -

: , , (). Vspeak=100 V, f=50 Hz, R=2 , L=0.005 H, 30, 50 V. Vf=0 Ron ( ). . ( , , (Continuous) powergui, ode23t)

1: Vdc=IdcR Vrms=IrmsR

[cos 1]2

Sdc

VV ap= +

[cos 1]2

Sdc

VI aRp= +

,

1 sin(2 )2

2d rms Sa

V Vp a

p- +

=

5:

MATLAB SIMULINK

- 60 -

2: . . 5.10 , : simulink simulink matlab

RMS

Pdc Pac

6:

MATLAB SIMULINK

- 61 -

6: ( ) 6.1.1 ( ) . /. 4.6.4. 1: / . : ) / ) 180. TH1 , 2 (+) . ( + 2) 2: / .

3: , simulink

6:

MATLAB SIMULINK

- 62 -

4: / . powergui / ( ). 5: AC peak 100 V / 1:2 6: . OFF vs2. OFF ON, 2vs2

6.1.2 2 Vs,peak=Vs2,peak=100V, f=50Hz, R=2 =30. 1: ( ) 2: (OFF) (ON)

6:

MATLAB SIMULINK

- 63 -

6.1.3 RMS dc 2 Vs,peak=Vs2,peak=100V, f=50Hz, 2 30 ( ). :

22 [cos 1]SdcVV ap= +

, 2

1 sin(2 )2

d rms S

aV V

p ap

- + =

( Vdc59.4 Vd,rms69.68) 6.2.1 - 2 Vs,peak=Vs2,peak=100V, f=50Hz, R=1 , L=0.001 H =30 ( ). . 1: . 2: - ( ) . 3: simulink 0 , .

6:

MATLAB SIMULINK

- 64 -

4: . 1. , ( 0.02 0.04). .

: + TH2 1 OFF. 1 2vs2. 2 OFF 1 vs2. 60 V 30 V : 1 180 ( 180+). OFF, vs20 ( vs2=Vs2peaksin(1) . 180+ 2 1 2vs2 ( -50 V -100V) vak2 5: ( ).

6:

MATLAB SIMULINK

- 65 -

6.2.2 RMS dc RMS dc : simulink . display RMS block RMS . , . 2 Vs,peak=Vs2,peak=100V, f=50 Hz, R=2 , L=0.002 H =30. blocks RMS (dc) . . 1: dc dcV I R= , ,d rms d rmsV I R= 6.2.3 - , = => 1=+ 2 1 OFF ( ). ( =). 1: ( ). 2: 3: , ( )

R=2 , L=0.0035 H R=2 , L= 0.01 H

6:

MATLAB SIMULINK

- 66 -

4: , .

R=2 , L=0.01 H R=2 , L=0.05 H

R=2 , L=0.1 H

R=2 , L=0.1 H (zoom-in)

R=2 , L=1 H

R=2 , L=1 H (zoom-in)

6:

MATLAB SIMULINK

- 67 -

5: , . DC 6: : ) (L>>R) )

7: 4

MATLAB SIMULINK

- 68 -

7: 7.1 ( ) ( 4.6.3) . , 2 . 2 (180) . , , , .

1: OFF vs/2. vs.

7: 4

MATLAB SIMULINK

- 69 -

7.2 Goto From blocks simulink , . 1 2 3 4 +. 4 2 pulse generator blocks. 2 / , 4 . simulink Goto From blocks. blocks Goto block From block (tags). , .

7: 4

MATLAB SIMULINK

- 70 -

7.3 4 Vs,peak=Vs2,peak=100V, f=50Hz, R=2 =30. 1: ( ) 2: (OFF) (ON) 3: 2 , Vspeak 7.4 RMS dc 4 Vs,peak=100V, f=50Hz, 2 30 ( ). :

2 [cos 1]SdcVV ap= +

,

1 sin(2 )2

d rms S

aV V

p ap

- + =

( Vdc59.4 Vd,rms69.68) 7.5 - 4 : (>) (

7: 4

MATLAB SIMULINK

- 71 -

7.5.1 - 4 Vs,peak=100V, f=50Hz, R=1 , L=0.001 H =30 ( ). . 1: . 2: - ( ). 3: simulink 0 , . . 4: 1 2. 2 . 0.5 1.

7: 4

MATLAB SIMULINK

- 72 -

5: . =17.4406 >. 6: =10 . . 7.5.2 - R-L Vs,peak=100 V, R=1 , L=0.1 , =30 1: :

2 2 (cos )SdcVV

( Vdc=55.132)

7.6 . . , is .

7: 4

MATLAB SIMULINK

- 73 -

iak1,2 & iak3,4

1: , DC AC 2: 3,4 (0, ) (+, 2) 1,2 (, +). . 45 ( 0.9 0.92 sec). = 0.0016666666666 sec

3: . (Ls). Ls=0.001 H. 1: , u 2:

+ 3,4 1,2

3,4 2

7: 4

MATLAB SIMULINK

- 74 -

7.7 , :

- Goto From blocks simulink

8: 3

MATLAB SIMULINK

- 75 -

S2V

T H 1

T H 2

S3V

S1V

T H 3

8: 8.1 , . . 8.2 . . :

S1 peak

S2 peak

S3 peak peak

V =V sin(t)V =V sin(t-120)

V =V sin(t-240)=V sin(t+120)

MATLAB : >> f=50; >> w=2*pi*f; >> t=0:0.00001:0.02; >> gonia=t*360/0.02; >> Vs1=100*sin(w*t); >> Vs2=100*sin(w*t-deg2rad(120)); >> Vs3=100*sin(w*t-deg2rad(240)); >> plot(gonia, Vs1); hold on; plot(gonia,Vs2);hold on; plot (gonia,Vs3) :

8: 3

MATLAB SIMULINK

- 76 -

8.3 . 120. 1: 120 1 2 3 2: OFF 3: 1 , 3 1 vs1-vs3 vs1>vs3 30. 2 150 3 270 4: 1 30, 2 150o vs3 270o 5: 30

6: =20 : 1 30+20=50 (1==20) 2 30+120+20=170 (2=120+) 3 30+240+20=290 (2=240+)

7: 150+ 2 1 vak1=v1-v230 2 150+>180 ( 180 150+ 1 OFF 180) 11: 150 (.. =150 1 180 )

8: 3

MATLAB SIMULINK

- 77 -

12: (30) :

0~60 60~30+ 30+~180 180~150+ 150+~300 300~270+ 270+~3601 OFF OFF OFF OFF OFF OFF 2 OFF OFF OFF OFF OFF OFF 3 ON OFF OFF OFF OFF OFF ON

8.4 simulink . R=2 . VS1peak= VS2peak= VS3peak=100 V f=50Hz. =20 8.5 crest factor ( ) 4 . , . peak , crest factor. 1: ( - crest factor) 4 :

( )s peak

s

ICF

I= , Is .

8: 3

MATLAB SIMULINK

- 78 -

2: ( peak rms ). peak DC MinMax Running Resettable block. :

3: MinMax Running Resettable block (max) 4: peak AC Abs block 8.6 (Peak Inverse Voltage PIV) MinMax Running Resettable (min) . . PIV peak, peak,PIV=V = 3V ( Vspeak=100 V, PIV=173.2 V) 8.7 scope : . . 1: . .

8: 3

MATLAB SIMULINK

- 79 -

=20 (30 )

=90 (>30 )

8: 3

MATLAB SIMULINK

- 80 -

=150 (vd=0)

8.8 RMS sdc 3 6VV = cosa2

d,rms s1 3V = 6V [ cos(2 )]6 8

ap+ . ( Vdc=77.71 V Vd,rms=81.14 V) =40 sdc 3 2VV = [1+cos(a+30)]2 ( Vdc= 64.07 V) 8.9 1 . 1 . . : 1 . 1 OFF 3 [ 0 (30+) (240+30+) 360] 1 vak1=vs1-vs3. 1 FF TH2 [ (120+30+) (240+30+)] 1 vak1=vs1-vs2 1: TH1 . peak, peak,PIV=V = 3 V 2: scope .

8: 3

MATLAB SIMULINK

- 81 -

8.10 add block (.. vs1 vs2 vs1-vs2) . add block. To add block divide, . . (+ -) block

8: 3

MATLAB SIMULINK

- 82 -

8.11 , scope . . scope (=20)

8: 3

MATLAB SIMULINK

- 83 -

8.12.1 . L , ( ) R=2 , L=0.01 H (=20). .

R=2 , L=0.05 H 0.4 sec ( )

:

8: 3

MATLAB SIMULINK

- 84 -

8.12.2 . =90, R=1 , L=0.01 H . 1: , : OFF , OFF : H vak1 (=90) .

90+30=120 1 230. vak1=0 To TH2 120+90+30=240 350 3 240+90+30=360=0 110. 1 vs1

8: 3

MATLAB SIMULINK

- 85 -

2: >30 . =60, R=1 , L=0.01 H

8: 3

MATLAB SIMULINK

- 86 -

8.13 , : MinMax Running Resettable block peak

MinMax Running Resettable block

PIV

9: 6

MATLAB SIMULINK

- 87 -

9: 9.1 ( ) 4 . 6 . , (TH1, TH3, TH5) (4, 6, 2). +180 . 30.

1 4 +180 3 +120 6 +120+180 5 +240 2 +240+180=+60

:

: : 1 30+ 4 30++180=210+ 3 30++120=150+ 6 30++20+180=330+ 5 30++240=270+ 2 30++240+180=90+

: 30+ ~+60 +60~+120 +120~+180 +180~+240 +240~+300 +300~+360

=+300~0+ 1 OFF OFF OFF OFF 2 OFF OFF OFF OFF 3 OFF OFF OFF OFF 4 OFF OFF OFF OFF 5 OFF OFF OFF OFF 6 OFF OFF OFF OFF

1: 120 60 ( 60) 2: 6 . .

1 3 5

4 6 2

9: 6

MATLAB SIMULINK

- 88 -

3: , : 30+ ~+60 +60~+120 +120~+180 +180~+240 +240~+300 +300~+360

=+300~0+ 1 OFF OFF OFF OFF 2 OFF OFF OFF OFF 3 OFF OFF OFF OFF 4 OFF OFF OFF OFF 5 OFF OFF OFF OFF 6 OFF OFF OFF OFF

vd v1-v2 v1-v3 v2-v3 v2-v1 v3-v1 v3-v2 4: , ( ) :

d AK1

L1 d AK4

i (t)=i (t), 1i (t)= -i (t)=-i (t), 4

0, 1 4

d AK3

L2 d AK6

i (t)=i (t), 3i (t)= -i (t)=-i (t), 6

0, 3 6

d AK5

L3 d AK2

i (t)=i (t), 5i (t)= -i (t)=-i (t), 2

0, 5 2

5: =60 6: =120

7: 90o ( 60

9: 6

MATLAB SIMULINK

- 89 -

9.2 Synchronized 6-Pulse Generator block 6 ( ). Simulink block , Synchronized 6-Pulse Generator block. 1: MATLAB Pulse Generator (Thyristor, 6-Pulse) block . . 2: block MATLAB : workspace MATLAB : >> power_sixpulses MATLAB (), , Synchronized 6-Pulse Generator.

3: Synchronized 6-Pulse Generator 50 Hz 4: Synchronized 6-Pulse Generator block block 6

9: 6

MATLAB SIMULINK

- 90 -

, 1, 2 ... =0:

5: ( ) block 0, . 6: MATLAB ( =0 10) ( )

7: power_sixpulses . add blocks

P1 P2 P3 P4 P5 P6 P1 P2 P3 P4 P5 P6

9: 6

MATLAB SIMULINK

- 91 -

9.3 simulink - . .

9.4 simulink Universal Bridge block To simulink Universal Bridge block. block ( pulse generator) 1: block , . . 2: Configure Parameters powergui, Universal Bridge block.

9: 6

MATLAB SIMULINK

- 92 -

9.5 Gain block , . AB=vs1-vs2, BC=vs2-vs3 CA=vs3-vs1 :

BA=vs2-vs1=-(vs1-vs2)=-AB CB=vs3-vs2=-(vs2-vs3)=-C C=vs1-vs3=-(vs3-vs1)=-CA

Gain block, () (Gain) .

9: 6

MATLAB SIMULINK

- 93 -

9.6 (Subsystems) SIMULINK , block ( block) . , block : . , Create Subsystem. 1: .

2: in out blocks Conn block. SIMULINK . ( In2 Conn1) .

9: 6

MATLAB SIMULINK

- 94 -

9.7.1 - , . , MATLAB ( ).

v1-v2 v1-v3 v2-v3 v2-v1 v3-v1 v3-v2 v3-v2

=60

=70

=10

9: 6

MATLAB SIMULINK

- 95 -

9.7.2 - Universal Bridge Block . sw (switch) . Isw1 1, Isw2 2 ... (Usw1 1, Usw2 2 ...). (Uab, Ubc, Uca). =20, R=2 Vpeak,=100 V

9: 6

MATLAB SIMULINK

- 96 -

9.7.3 - . , AC. (=20,R=2 , Vpeak,=100 V)

d AK1

L1 d AK4

i (t)=i (t), 1i (t)= -i (t)=-i (t), 4

0, 1 4

d AK3

L2 d AK6

i (t)=i (t), 3i (t)= -i (t)=-i (t), 6

0, 3 6

d AK5

L3 d AK2

i (t)=i (t), 5i (t)= -i (t)=-i (t), 2

0, 5 2

30+ 20

80

80 140

140 200

200 260

260 320

320

380 (20) 1 OFF OFF OFF OFF 2 OFF OFF OFF OFF 3 OFF OFF OFF OFF 4 OFF OFF OFF OFF 5 OFF OFF OFF OFF 6 OFF OFF OFF OFF iL1 id id 0 -id -id 0 iL2 -id 0 id id 0 -id iL3 0 -id -id 0 id id

9.8.1 - snubber . , Configure parameters powergui block snubber . R,C snubber Universal Bridge block

9: 6

MATLAB SIMULINK

- 97 -

9.8.2 - (- ) . =20, Vpeak,=100 V, R=2 L=0.001 H

1: 60 . =70, Vpeak,=100 V, R=2 L=0.01 H

2:

9: 6

MATLAB SIMULINK

- 98 -

=70, Vpeak,=100 V, R=2 L=0.001 H

9.9.1 Controlled Current Source block . . Controlled Current Source block. 1: To block s. 2: (.. ) 3: AC Current Source block 0. R14SP2 MATLAB bug.

9: 6

MATLAB SIMULINK

- 99 -

9.9.2 =20, Vpeak,=100 V, d=10 , R=0.000001

1: 90 2: :

peak,dc

3VV = cos

cos >90o Vdc90. (.. ) .

9: 6

MATLAB SIMULINK

- 100 -

Vpeak,=100 V, d=10 , R=0.000001 (>90)

=100 =120

9.9.3 Ls . 1: ( ) 2:

9: 6

MATLAB SIMULINK

- 101 -

3: u

2: . . 3: . (vab, vbc, vca) multimeter Universal Bridge block. 9.10 , : Universal Bridge block Gain block (subsystems)

9: 6

MATLAB SIMULINK

- 102 -

Controlled Current Source block DC

10: C

MATLAB SIMULINK

- 103 -

10: AC 10.1 AC AC (, ). . . . 1: AC . 2: . 3: 180 (1: 2:+). 4: . 10.2 SIMULINK ( ) SIMULINK AC .

10: C

MATLAB SIMULINK

- 104 -

C Vs,peak=100 V, R=2 =30. .

. :

d,rms s

1-+ sin(2 )2V =V p

d,rms

d,rms

V =R

( Vd,rms=69,68 V Id=34.84 A, Pin=2464 W Pout=Pd=2428 W pf=Pout/Pin=0.9855)

10: C

MATLAB SIMULINK

- 105 -

10.3 - : - >.

10: C

MATLAB SIMULINK

- 106 -

2: > AC R=2 , L=0.01 H (57,5) =90. .

1: . :

1 1

d,rms s

1 -+ [sin(2)-sin(2 )]2V =V , 1

10: C

MATLAB SIMULINK

- 107 -

10.4.1 AC - AC . - :

1: . - 2: 3 6 , . 1, 3 5 , 120+ 240+ 180 4, 6, 2 180+, 300+, 420+=60+

1 4 +180 3 +120 6 +120+180 5 +240 2 +240+180=+60

3: - 3 . 1, 2, 3 () . :

1 1 4 1 3 2 6 2 5 3 2 3

10: C

MATLAB SIMULINK

- 108 -

10.4.2 AC 4 : 1: 060 2 3 ( ). (180-) 1 180 2 60+ 240 3 120+ 300 4 180+ 360 5 240+ 420 240 360 0 60 6 300+ 480 300+ 360 0 120

0 ~

~ 60

60 ~

60+ 60+

~ 120

120 ~

120+ 120+

~ 180

180 ~

180+ 180+

~ 240

240 ~

240+ 240+

~ 300

300 ~

300+ 300+

~ 360 (0)

1 2 3 4 5 6

2: 6090 2 ( ). 120 2: 120 1 120+ 2 60+ 180+ 3 120+ 240+ 4 180+ 300+ 5 240+ 360+ 6 300+ 420+ 300+ 60+

360+ ~

60+ 60+

~ 120+

120+~

180+ 180+

~ 240+

240+~

300+ 300+

~ 360+

1 2 3 4 5 6

10: C

MATLAB SIMULINK

- 109 -

3: 90150 2 0.5*V 3: 0.5*V

1 150 60+ 150+60=210 2 60+ 210 120+ 270 3 120+ 270 180+ 330 4 180+ 330 240+ 390=30 5 240+ 390=30 300+ 90 6 300+ 90 360+ 150

240+ ~ 30

30 ~

300+ 300+

~ 90

90 ~

360+ 360+

~ 150

150 ~

60+ 60+

~ 210

210 ~

120+ 120+

~ 270

270 ~

180+ 180+

~ 330

330 ~

240+ 1 2 3 4 5 6

1: ( ) 2: ( ) 3: ( )

0.5*(v1-v2) 0.5*(v1-v3) 0.5*(v2-v3) 0.5*(v2-v1) 0.5*(v3-v1) 0.5*(v3-v2) 0.5(v3-v2) v1 v2 v3

10: C

MATLAB SIMULINK

- 110 -

10.5 Transport Delay block AC . Transport Delay block. To block . 1: sec. 120 120*0.02/360 2: AC ( 30 ), Synchronized 6-Pulse Generator . 3: Transport Delay . 10.6 SIMULINK Transport Delay block . , .

10: C

MATLAB SIMULINK

- 111 -

10.6.1 1 AC R=2 , Vs,peak=100 V =30.

1: 10.4 ( )

a

0.5Vab/R 0.5Vac/R

Van/R

10: C

MATLAB SIMULINK

- 112 -

10.6.2 2 AC R=2 , Vs,peak=100 V =60. .

Ia 0.5*Vab/R

0.5*Vac/R

10: C

MATLAB SIMULINK

- 113 -

10.6.3 3 AC R=2 , Vs,peak=100 V =120.

1: .

Ia

0.5*Vab/R

0.5*Vac/R

10: C

MATLAB SIMULINK

- 114 -

10.7 , : AC ( ) Transport Delay block :

: D. Pylarinos, I. Androulidakis, K. Siderakis, E. Drakakis, "A Matlab/Simulink Approach for a First Course in Power Electronics", 3rd Panhellenic Conference on Electronics and Telecommunications, Ioannina, Greece, May 8-9, 2015

MATLAB SIMULINK

- 115 -

: D. Pylarinos, I. Androulidakis, K. Siderakis, E. Drakakis, "A Matlab/Simulink Approach for a First Course in Power Electronics", 3rd Panhellenic Conference on Electronics and Telecommunications, Ioannina, Greece, May 8-9, 2015

MATLAB SIMULINK

- 116 -

: D. Pylarinos, I. Androulidakis, K. Siderakis, E. Drakakis, "A Matlab/Simulink Approach for a First Course in Power Electronics", 3rd Panhellenic Conference on Electronics and Telecommunications, Ioannina, Greece, May 8-9, 2015

MATLAB SIMULINK

- 117 -

: D. Pylarinos, I. Androulidakis, K. Siderakis, E. Drakakis, "A Matlab/Simulink Approach for a First Course in Power Electronics", 3rd Panhellenic Conference on Electronics and Telecommunications, Ioannina, Greece, May 8-9, 2015

MATLAB SIMULINK

- 118 -

ISBN 978-618-82223-0-4