DC To AC Conversion….
INVERTERS
Inverters
DEFINITION: Converts DC to AC power by switching the DC input voltage (or current) in a pre!eter"ine! se#uence so as to generate AC voltage (or curr current) ent) output$
T%&ICA' A&&'ICATION: A&&'ICATION:
*&+ In!ustrial !rives+ Traction+ ,-DC
.eneral bloc/ !iagra"
Inverters
DEFINITION: Converts DC to AC power by switching the DC input voltage (or current) in a pre!eter"ine! se#uence so as to generate AC voltage (or curr current) ent) output$
T%&ICA' A&&'ICATION: A&&'ICATION:
*&+ In!ustrial !rives+ Traction+ ,-DC
.eneral bloc/ !iagra"
variable DC link
•
DC link voltage is varied by a DC-to DC converter or controlled rectifier.
•
Generate “square wave” output voltage.
•
Output voltage amplitude is varied as DC link is varied.
•
requency of output voltage is varied by c!anging t!e frequency of t!e square wave pulses.
T A!vantages:
•
•
•
si"ple wave0or" generation 1eliable
Disa!vantages:
•
•
•
E2tra conversion stage &oor har"onics
V Iwt
xe
D
n
DC voltage is hel! constant$ Output voltage a"plitu!e an! 0re#uency are varie! si"ultaneously using &34 techni#ue$ .oo! har"onic control+ but at the e2pense o0 co"ple2 wave0or" generation$
Current Source Inverter (CSI) Input (DC) current is 5choppe!6 to obtain AC output current$ 7 Nee! large '$ 7 'ess popular co"pare! to -I$
!ower "ow consieration Assu"e loa! is !rawing lagging &ower Factor$: 7 (8) io and (+) vo: fow (1)
(+) power
7 () io and (-) vo: fow (3)
(+) power
7 (8) io and (-) vo: fow (2)
(-) power
7 () io and (+) vo: fow (4)
(-) power
#our $uarant o%eration Negative power 9ow in!icates that the power is 0e! bac/ 0ro" loa! to source$ 7 ,ence+ inverter "ust have 5 #ua!rant6 capability to cater 0or all possible loa! types$ 7 &ractically+ this can be achieve! by placing an antiparallel !io!e across each switching !evice$
Classifcation According to the nature of input source
-oltage source inverters (-I) Current source inverters (CI) In case o0 -I+ the input to the inverter is provi!e! by ripple 0ree !c voltage source whereas in CI+ the voltage source is ;rst converte! into a current source an! then use! to supply the power to the inverter$
According to the Waveshape of the Output Voltage
#uarewave inverter
T&%es o' inverter
"oltage #ource $nverter %"#$&
Current #ource $nverter %C#$&
Thyristor Inverter Classi;cation According to the Method of Commutation 'ine
co""utate! inverters Force! co""utate! inverters ine Commutated Inverters! In case o0 a$c$ circuits, a$c$ line voltage is available across the !evice$ 3hen the current in the C1 goes through a natural =ero+ the !evice will turne!o>$ This process is /nown as natural co""utation process an! the inverters base! on this principle are /nown as line co""utate! inverters$
"orced Commutated Inverters! In case o0 !$c$ circuits+ since the supply voltage !oes not go through the =ero point+ so"e e2ternal source is re#uire! to co""utate the !evice$ This process is /nown as the 0orce! co""utation process an! the inverters base! on this principle are calle! as 0orce! co""utate! inverters$ As the !evice is to be co""utate! 0orce0ully+ these types o0 inverters re#uire co"plicate! co""utation circuitries$ These inverters are 0urther classi;e! as: (i) Au2iliary co""utate! inverters (ii) Co"ple"entary co""utate! inverters
According to Connections! eries inverters &arallel inverters ?ri!ge inverters #ridge inverters are further classi$ed as!
(i) ,al0bri!ge (ii) Fullbri!ge
IN-E1TE1
witches
@ an! are the gate co""utate! !evices such as power ?BTs+ 4OFETs+ .TO+ I.?T+ 4CT+ etc$$ 3hen close!+ these switches con!ucts an! current
Operation with 1esistive 'oa! The operation o0 the circuit can be !ivi!e! into two perio!s: &erio!I+ where switch @ is con!ucting 0ro" to T/2 &erio!II+ where switch is con!ucting 0ro" T/2 to T where T @0 an! 0 is the 0re#uency o0 the output voltage wave0or"
-oltage an! Current wave0or"s 0or 1esistive loa!
witch
@ is close! 0or hal0ti"e perio! (T/2) o0 the !esire! ac
output It connects point p o0 the !c source to point A an! the output voltage eo beco"es e#ual to +dc/2 At t ! T/2+ gating signal is re"ove! 0ro" @ an! it turnso> For the ne2t hal0ti"e perio! (T t T)+ the gating signal is given to It connects point N o0 the !c source to point A an! the output voltage reverses Thus+ by closing @ an! alternately+ 0or hal0ti"e perio!s+ a s#uarewave ac voltage is obtaine! at the output 3ith resistive loa!+ waveshape o0 loa! current is i!entical to that o0 output voltage ?y controlling the ti"e perio!s o0 the gate!rive signals+ the 0re#uency can be varie!$ ,ere !io!es D@ an! D !o not play any role The voltage across the switch when it is OFF is dc .ating circuit shoul! be !esigne! uch that switches @ an! shoul! not turnon at the sa"e ti"e$
Circuit Anal&sis Average Output -oltage E0 av
1 2
2
e0 ( t )d t
0
0
14 o0 Output -oltage
E0 RMS
2
1 2
2 0
e ( t )d t 0
E dc 2
,ar"onics
#ourier Series 7 tu!y o0 har"onics re#uires un!erstan!ing o0 wave shapes$ Fourier eries is a tool to analyse wave shapes$ Fourier eries:
Inverse Fourier :
aronics o' s$uare*wave
when n is even+ cos nG @ H bn
when n is o!!+ cos nG @
S%ectra o' s$uare wave
pectra (har"onics) characteristics: ,ar"onic !ecreases as n increa"e". It decrea"e" with a 0actor o0 (@ n). Even har"onics are absent Nearest har"onics is the r!$ I0 0un!a"ental is J,=+ then nearest har"onic is @J,=$ Due to the s"all separation between the 0un!a"ental an! har"onics+ output lowpass ;lter !esign can be #uite !iKcult$
Instantaneous Output-oltage The 0ourierseries can be 0oun! out by using the 0ollowing e#uation
There0ore+ There0ore+ the instantaneous output voltage o0 a hal0 hal0 bri!ge inverter can be e2presse! in Fourierseries 0or" as
The nth har"onicco"ponent is given by
e0 ( n)
Cn 2
2 E dc
n
2 E dc
n
2
for
n
14 value o0 0un!a"ental co"ponents is
E1 RMS
2
Edc
0.45 E dc
1, 3, 5....
#witc$ (%evice) Volta&e and 'rrent atin&" VCE 0 E DC The current current wave0or" 0or 0or switch is a s#uare wave with a pea/ value o0 E!c1$ ITavg
1
T 2
T
IT RMS
I T Peak
1
T
Edc 2R
0
T 2
0
E dc 2 R
E dc
dt
Edc 2R
4R
2
dt
E dc 2 2R
+%eration with ,- -oa 3ith
an in!uctiveloa!+ the output voltage wave0or" is si"ilar to that with a resistive loa!+ however the loa!current cannot change i""e!iately with the output voltage The operation o0 hal0bri!ge inverter with 1' loa! is !ivi!e! into 0our !istinct "o!es D@ an! D are /nown as the 0ee!bac/ !io!es
oe I (t/ 0 t 0 t1)2 @ is turne!on at instant tl+ the loa! voltage is e#ual to 8E!c an! the positive loa! current increases gra!ually At instant t+ the loa! current reaches the pea/ value witch @ is turne!o> at this instant Due to sa"epolarity o0 loa! voltage an! loa! current+ the energy is store! by the loa! oe II (t1 0 t 0 t3)2 Due to in!uctiveloa!+ the loa! current !irection will be "aintaine! evena0ter @ is turne!o> The sel0in!uce! voltage in the loa! will be negative$ The loa! current 9ows through lower hal0 o0 the supply an! %2 In this "o!e+ the store! energy in loa! is 0e! bac/ to the lower hal0 o0 the source an! the loa! voltage is cla"pe! to dc/2.
oe III (t3 0 t 0 t4)2 At instant t+ the loa!current goes to =ero+ in!icating that a@ the store! energy+ has been returne! bac/ to the lower hal0 o0 supply At instant t3, is turne!on This will pro!uce a negative loa! voltage eo E!c an! a negative loa! current 'oa! current reaches a negative pea/ at the en! o0 this interval Mode IV %to & t & t'(! witch is turne!o> at instant t$ The sel0 in!uce! voltage in the in!uctive loa! will "aintain the loa! current The loa! voltage changes its polarity to beco"e positive E!c+ loa! current re"ains negative an! the store! energy in the loa! is returne! bac/ to the upper hal0 o0 the !c source At t*+ the loa! current goes to an! @ can be turne!on again$ This cycle o operation repeats$
peratin&
Circuit*5$uations Instantaneous Current io: 2 E dc
i0 ( t ) n 1,3,5..
n
Z n
n
tan
R
2
( n L)
n L
1
R
R
2
( n L)
2
2
sin( n t
n
)
Fun!a"ental
Output &ower
Cross Conuction or Shoot through #ault In
the hal0bri!ge inverter circuit+ each switch con!ucts 0or a perio! o0 T/2 secs At any particular instant+ one switch is turne!on an! the other is turne!o> ,owever+ the outgoing switch !oes not turno> instantaneously !ue to its ;nite turno> !elay Due to this+ both switches (inco"ing an! outgoing) con!uct si"ultaneously 0or a shortti"e$ This is /nown as crosscon!uction or shoot through0ault 3hen both switches con!ucts si"ultaneously+ the input DC supply is short circuite! an! with this switches get !a"age!$ Cross con!uction can be avoi!e! by allowing the outgoing switch to turno> co"pletely ;rst an! then applying the gate!rive to the inco"ing !evice A !ea!ban! or !elay is intro!uce! between the trailinge!ge o0 the base!rive o0 outgoing !evice an! the lea!inge!ge o0 the base !rive o0 the inco"ing !evice$ There0ore+ !uring the !ea!ban! interval+ no !evice receives base!rive ,ence+ the !ea!ban! shoul! be longer than the turno> ti"e o0 the power!evices use! in the inverter circuit$
&roble"@$
The singlephase hal0bri!ge inverter has a resistive loa! o0 @Oh"$ an! the centertap DC input voltage is LM -$ Co"pute: (i) 14 value o0 the output voltage$ (ii) Fun!a"ental co"ponent o0 the output voltage wave0or"$ (iii) First ;ve har"onics o0 the outputvoltage wave0or"$ (iv) Fun!a"ental power consu"e! by the loa!$ (v) 14 power consu"e! by the loa!$ (vi) -eri0y that the r"s value !eter"ine! by har"onic su""ation "etho! is nearly e#ual to the value !eter"ine! by integration "etho!$
SI67-5*!AS5 #8--*9,ID75 I6V5,T5,S
inverter
5:8IVA-56T CI,C8IT
#'(#) O*+
#,(# O
for t ' t t )
wave inverter
+ ON H
*
@+
<
OFF
0or
t t t
T
The
inverter uses two pairs o0 controlle! switches (@+ an! +) an! two pairs o0 !io!es (%1,%2 and %3,%4) #witc$ can e #', 0T, #T, I0T etc..
The
!evices o0 one pair operate si"ultaneously
In
or!er to co"pose a positive voltage (8 Eo) across the loa!+ switches @ an! are turne!on si"ultaneously whereas to have a negative voltage ( Eo) across the loa!+ we nee! to turnon the switches an!
Dio!es
D@+ D+ D an! D are /nown as the 0ee!bac/ !io!es 0unctional only with reactive loa!s$
+%eration with ,esistive -oa The bri!geinverter operates in two"o!es in onecycle o0 the output$ Mode)I %* & t & T+,(! In this "o!e+ switches @ an! con!ucts si"ultaneously$ The loa! voltage is 8E!c an! loa! current 9ows 0ro" & to <$ At t T+ @ an! are turne!o> an! an! are turne!on Mode)II %T+, & t & T(2 At t T+ switches an! are turne!on an! @ an! are turne!o> The loa! voltage is E!c an! loa! current 9ows 0ro" < to & At t T+ an! are turne!o> an! @ an! are turne!on again As the loa! is resistive+ it !oes not store any energy$ There0ore+ 0ee!bac/ !io!es are not e>ective here$
E#uivalent Circuit
CircuitAnalysis The analysis o0 the 0ullbri!ge inverter with resistive loa! can be carrie!out on si"ilar lines o0 hal0bri!ge inverter with resistiveloa! ,ence all e#uations o0 hal0bri!ge are vali! with E!c replace! by E!c Average Output -oltage: E0 av
1 2
2
e0 ( t )d t
0
0
14 o0 Output -oltage E0 RMS
2
1 2
e02 ( t )d t 0
E dc
4 E dc
Fourier Series : e0 ( t ) n 1,3,5..
Fundamental Outut Voltage
t!
n
sin(n t )
E 0 ( fund .)
n "armonic comonent E0 ( n )
2 2 E dc
E0 ( fund .) n
#witc$ (%evice) Volta&e and 'rrent atin&" V E CE 0
DC
The current wave0or" 0or switch is a s#uare wave with a pea/ value o0 E!c1$ ITavg
IT RMS
I T Peak
1
T
T 2
0
1
T
E dc R
Edc 2R
T 2
0
E dc
dt
Edc 2R
2R
2
dt
E dc 2R
&roble" A singlephase 0ullbri!ge inverter is operate! 0ro" a - battery an! is supplying power to a pure resistive loa! o0 @ Oh"$ Deter"ine: (i) the 0un!a"ental output voltage an! the ;rst ;ve har"onics$ (ii) 14 value by !irect integration "etho! an! har"onic su""ation "etho!$ (ill) Output r"s power an! output 0un!a"ental power$ (iv) Transistor switch ratings$
Operation -ith R oad Mode)I %t' & t & t,(! At instant t@+ the switch @ an! are turne!on$ &oint & gets connecte! to positive point o0 !$c$ ource E!c through @ &oint < gets connecte! to negative point o0 input supply$ The output voltage+ eo 8 E!c The loa! current starts increasing e2ponentially !ue to the in!uctive nature o0 the loa!$ The instantaneous current through @ an! is e#ual to the instantaneous loa! current$ During this interval+ energy is store! in in!uctive loa!$ Mode)II %t, & t & t.(! ?oth the switches <@ an! < are turne!o> at instant t$ Due to the in!uctive nature o0 the loa!+ the loa! current !oes not re!uce to =ero instantaneously There is a sel0in!uce! voltage across the loa! which "aintains the 9ow o0 current in the sa"e!irection$ The polarity o0 this voltage is e2actly opposite to that in "o!eI The output voltage beco"es E!c but the loa! current continues to 9ow in the sa"e !irection+ through D an! D Thus+ in this "o!e+ the store! energy in the loa! in!uctance is returne! bac/ to the source$ 'oa! current !ecreases e2ponentially an! goes to at instant t when all the energy store! in the loa! is returne! bac/ to supply D an! D are turne!o> at t
Mode III %t. & t & t/(! witches an! are turne!on si"ultaneously at instant t 'oa! voltage re"ains negative ( E!c) but the !irection o0 loa! current will reverse The current increases e2ponentially in the other !irection an! the loa! again stores the energy Mode IV %to & t & t'(! witches an! are turne!o> at instant to (or t) The loa! in!uctance tries to "aintain the loa! current in the sa"e !irection by in!ucing the positiveloa! voltage$ This will 0orwar!bias the !io!es D@ an! D The loa! energy is returne! bac/ to the input !c supply$ The loa! voltage beco"es eo 8E!c but the loa! current re"ains negative an! !ecreases e2ponentially towar!s =ero$ At t@ (or tJ)+ the loa! current goes to =ero an! switches @ an! can be turne!on again$ The con!uction perio! with a very highly in!uctive loa!+ will be T or L 0or all the switches as well as the !io!es$ The con!uction perio! o0 switches will increase towar!s T or @
CircuitAnalysis Average Output -oltage: E0 av
1
T
T 0
e0 ( t )d t
0
14 o0 Output -oltage
E0 RMS
1
T 2
T 2
E 2 dt 0
E dc
4 E dc
Fourier Series : e0 ( t )
n
n 1,3,5..
Fundamental comonent
sin(n t )
2 2 E dc
E 1 RMS
t!
n "armonic comonent E0 ( n )
0.9E dc
E0 ( fund .) n
For 1' loa!+ the e#uation 0or the instantaneous current io can be 0oun! as 4 E dc i0 ( t )
n 1,3,5..
n
tan
1
n
n L R
R
2
( n L)
2
sin( n t
Z n
R
2
n
)
( n L)
2
The
single phase 0ullbri!ge inverter has a source voltage dc ! 22 -$ The inverter supplies an 1'C loa! with ! 1 o$5, 6 ! 1 57 and ' ! *2 8. T$e inverter 0re#uency is ,=$ Deter"ine: (a) the r"s loa! current at 0un!a"ental 0re#uency (b) the r"s value o0 loa! current (c) the power output (!) the average supply current
0ER"ORMANCE 0ARAMETERS O" INVERTERS I!eally+ an inverter shoul! give a sinusoi!al voltage at its output$ ,owever+
outputs o0 practical inverters are non sinusoi!al an! "ay be resolve! into 0un!a"ental an! har"onic co"ponents$
&er0or"ance
o0 an inverter is usually evaluate! in ter"s o0 the 0ollowing per0or"ance para"eters$
1armonic "actor of nth 1armonic %1"n( The har"onic 0actor is a "easure o0 the in!ivi!ual har"onic contribution in the output voltage o0 an inverter$ It is !e;ne! as the ratio o0 the r"s voltage o0 a particular har"onic co"ponent to the r"s value o0 0un!a"ental co"ponent "F n
E nRMS E 1 RMS
Total aronic Distortion (TD) A total har"onic !istortion is a "easure o0 closeness in a shape between the output voltage wave0or" an! its 0un!a"ental co"ponent It is !e;ne! as the ratio o0 the r"s value o0 its total har"onic co"ponent o0 the output voltage an! the r"s value o0 the 0un!a"ental co"ponent 4athe"atically+ 2 E nRMS
T"D n 2,3,4...
E02 RMS
E12 E 1
E1 RMS
2istortion "actor %2"(! A
!istortion 0actor in!icates the a"ount o0 har"onics that re"ain in the output voltage wave0or"+ a0ter the wave0or" has been subPecte! to secon!or!er attenuation (i$e$ !ivi!e! by n )$ It is !e;ne! as E nRMS
DF n 2,3,4...
n
2
2
E 1 RMS
o-est)Order 1armonics %O1( ! The lowest 0re#uency har"onic+ with a "agnitu!e greater than or e#ual to threeper cent o0 the "agnitu!e o0 the 0un!a"ental co"ponent o0 the output voltage+ is /nown as lowe"t-order $ar5onic. ,igher the 0re#uency o0 the 'O1+ lower will be the !istortion in the
A
singlephase hal0bri!ge inverter has a resistive loa! o0 !! 3 $5 an! the !e input voltage dc ! 24 Volt". %eter5ine: (a) I.?T ratings (b) Total har"onic !istortion T,D (c) The !istortion 0actor DF (!) The har"onic 0actor an! the !istortion 0actor o0 the lowest or!er har"onic
A
singlephase transistori=e! bri!ge inverter has a resistive loa! o0 ! 3 $5 and t$e dc inpt volta&e o dc ! 49 Volt. Volt. %eter5ine : (a) Transistor ratings (b) Total har"onic !istortion (c) Distortion 0actor DF (!) ,ar"onic 0actor an! !istortion 0actor at the lowest or!er har"onic
V+-T V+-TA75 C+6T,+ C +6T,+- +# SI67-5*!AS SI67- 5*!AS5 5 I6V5,T5,S I6 V5,T5,S In "any in!ustrial applications+ it is o0ten re#uire! to vary the output voltage o0 the inverter !ue to the 0ollowing reasons: to co"pensate 0or the variations in the input voltage$ to co"pensate 0or the regulation o0 inverters$ to supply so"e special loa!s which nee! variation o0 voltage with 0re#uency+ such su ch as an in!uction "otor$ "otor$ The various "etho!s 0or the control o0 output voltage o0 inverters are as un!er: E2ternal control o0 a$c$ output voltage$ E2ternal control o0 !$c$ input voltage$ Internal control o0 inverter$ The ;rst two "etho!s re#uire re#uire the use o0 peripheral co"ponents+ whereas the thir! "etho! re#uires no peripheral co"ponents. co"ponents .
5xternal Control o' A.C. +ut%ut Voltage In this type o0 control+ an a$c$ voltage controller is inserte! between the output ter"inals o0 inverter an! the loa! ter"inals Through the ;ring angle control o0 a$c$ voltage controller+ the voltage input to the a$c$ loa! is regulate! This "etho! gives rise to higher har"onic content in the output voltage+ particularly when the output voltage 0ro" the a$c$ voltage controller is at low level There0ore+ this "etho! is rarely e"ploye! e2cept 0or low power applications$
5xternal Control o' D.C. In%ut Voltage 3hen the available voltage source is a$c$+ then !$c$ voltage input to the inverter is controlle! through a 0ullycontrolle! recti;er through an uncontrolle! recti;er an! a chopper or through an a$c$ voltage controller an! an uncontrolle! recti;er $ In case the available voltage source is !$c$+ then !$c$ voltage input to the inverter is controlle! by "eans o0 a chopper T$e 5ain advantages o volta&e control "c$e5e" are: As the inverter output voltage is controlle! through the a!Pust"ent o0 !$c$ input voltage to the inverter+ output voltage wave0or" an! its har"onic contents are not a>ecte! appreciably$ I0 the !$c$ input to the inverter is varie! to co"pensate 0or source voltage 9uctuations+ the inverter can be !esigne! 0or a very li"ite! voltage range$ uch an inverter is "ost eKcient+ both in ter"s o0 power loss an! co"ponent
This "etho! o0 voltage control+ however+ su>ers 0ro" the 0ollowing disadvantages: Filter circuit increases the cost+ weight an! si=e+ an! at the sa"e ti"e re!uces eKciency an! "a/es the transient response sluggish$ For re!ucing the ripple content o0 !$c$ voltage input to the inverter+ a ;lter circuit is re#uire! in all type o0 sche"es$ In these sche"es+ the nu"ber o0 power converters use! 0or the control o0 inverter output voltage varies 0ro" two to three$ 4ore power han!ling converter stages results in "ore losses an! re!uce! eKciency o0 the entire sche"e$
The
co""utating capacitor voltage !ecreases as the !$c$ input voltage is re!uce!$ This has the e>ect o0 re!ucing the circuit turno> ti"e 0or the C1 0or a constant loa! current$
There0ore+
0or a large variation o0 output voltage 0or a constant loa! current+ control o0 !$c$ input voltage is not !esirable$
This
li"itation can+ however+ be overco"e by a separate! ;2e! !$c$ source 0or charging the co""utating capacitor+ but this "a/es the sche"e costly an! co"plicate!$
Internal Control of Inverter Inverter
output voltage can also be a!Puste! by e2ercising a control within the inverter itsel0$
The two possible ways o0 !oing this are: eries
inverter control &ulsewi!th "o!ulation control
Series Inverter Control
Series Inverter Control This "etho! o0 voltage control involves the use o0 two or "ore inverters in series The output voltage o0 two inverters can be su""e! up with the help o0 trans0or"ers to obtain an a!Pustable output voltage The inverter output is 0e! to two trans0or"ers whose secon!aries are connecte! in series &hasor su" o0 the two voltages 61 and 62 &ive" t$e re"ltant volta&e 6 The voltage 6 ! 61 2+ 62 2+ 2 61 62 co" Q ;1/2 It is essential that the 0re#uency o0 output voltages 61 62 0ro" the two inverters are the sa"e 3hen Q is =ero+ 6 ! 61 + 62 an! 0or Q G E' In case E '@ E' +The angle Q can be varie! by the ;ring angle control o0 two inverters$ The series connection o0 inverters+ calle! "ultiple inverter control+ !oes not aug"ent the har"onic content even at low output voltage levels$
!ulse*with oulation Control The
"ost eKcient "etho! o0 controlling the output voltage is to incorporate pulse wi!th "o!ulation control(&34 control) within the inverters In this "etho!+ a ;2e! !$c$ input voltage is supplie! to the inverter an! a controlle! a$c$ output voltage is obtaine! by a!Pusting the onan!o> perio!s o0 the inverter !evices$ The &34 control has the 0ollowing a!vantages: The output voltage control can be obtaine! without any a!!itional co"ponents 3ith this type o0 control+ lower or!er har"onics can be eli"inate! or "ini"ise! along with its output voltage control The ;ltering re#uire"ents are "ini"ise! as higher or!er har"onics can be ;ltere! easily The "ain !rawbac/ o0 this "etho! is that the C1s use! in this "etho! "ust have very low turnon an! turno> ti"es (invertergra!e C1s)+ there0ore+ they are very e2pensive$ The co""only use! &34 control techni#ues are: inglepulse wi!th "o!ulation (&34) 4ultiplepulse wi!th "o!ulation (4&34) inusoi!al pulse wi!th "o!ulation (sin &34)
T
-ow*%ass flters 7 In s#uare wave inverters+ "a2i"u" output voltage is achievable$ ,owever there in NO control in har"onics an! output voltage "agnitu!e$ 7 The har"onics are always at three+ ;ve+ seven etc$ ti"es the 0un!a"ental 0re#uency$ 7 ,ence the cuto> 0re#uency o0 the low pass ;lter is so"ewhat ;2e!$ The ;lter si=e is !ictate! by the -A ratings o0 the inverter$ 7 To re!uce ;lter si=e+ the <= "witc$in& "c$e5e can be utilise!$ 7 In this techni#ue+ the har"onics are 5pushe!6 to higher 0re#uencies$ Thus the cuto> 0re#uency o0 the ;lter is increase!$ ,ence the ;lter co"ponents (I$e$ ' an! C) si=es are re!uce!$
=6otching>o' s$uare wave
Notching results in controllable output voltage "agnitu!e
!ulse*with oulation (!;) A better s#uare wave notching is shown below this is /nown as &34 techni#ue$ 7 ?oth a"plitu!e an! 0re#uency can be controlle! in!epen!ently$ -ery 9e2ible$
T &34 output voltage an! 0re#uency control
Single*%ulse ;ith oulation In singlepulse wi!th "o!ulation control+ there is only one pulse per hal0cycle an! the wi!th o0 the pulse is varie! to control the inverter output voltage$ ?y co"paring a rectangular re0erence signal o0 a"plitu!e+ E1 with a triangular carrier wave o0 a"plitu!e E C $ The
0un!a"ental 0re#uency o0 output voltage is !eter"ine! by the 0re#uency o0 the re0erence signal$ The pulsewi!th+ &+ can be varie! 0ro" to @ by varying E 1 0ro" to E C $ The
ratio o0 E 1 to Ec is the control variable an! is !e;ne! as the a"plitu!e "o!ulation in!e2$ The a"plitu!e "o!ulation in!e2+ or si"ply modulation inde3 is M
E R
E C
<
The Fourier series o0 E ' is
4 E dc
E L n 1,3,5,....
n
sin
n 2
sin n t
3hen pulsewi!th p is e#ual to its "a2i"u" value o0 G ra!ians+ then the 0un!a"ental co"ponent o0 output voltage E ' has the pea/ value o0 E L1 m
4 E dc
The 14 output voltage can be 0oun! 0ro" E L RMS
E dc
The pea/ value o0 the nth har"onic co"ponent is given b E Lnm
4 E dc
n
sin
n 2
E Lnm E L1
sin
n 2
n
,ar"onic content in &34
&ole -oltage 3ave0or" 3ith A Dc 4o!ulating ignal
The co%arator out%ut (:) an the %ole voltage (V
)
?y
using si"ple "athe"atics the high!uration o0 the pulses (t $ ), drin& w$ic$ t$e pole volta&e 5a&nitde i" .*dc, can e ond to e
where
Tc is the ti"e perio! o0 the triangular carrier wave0or"+ V5 is the "agnitu!e o0 the "o!ulating signal an! Vc('ap) i" t$e pea> (po"itive) 5a&nitde o t$e carrier "i&nal. The low!uration ( t l) o0 pulses !uring which the pole voltage "agnitu!e is $JE dc, can e ond a":
The
!c co"ponent o0 the pole voltage (-) can be 0oun! to be
ulti%le
In
!ulse*with oulation
this "etho! o0 pulsewi!th "o!ulation+ the har"onic content can be re!uce! using several pulses in each hal0cycle o0 output voltage$ ?y co"paring a re0erence signal with a triangular carrier wave+ the gating signals are generate! 0or turning on an! turningo> o0 a thyristor$ The carrier 0re#uency+ 0c+ !eter"ines the nu"ber o0 pulses per hal0cycle+ Np+ whereas the 0re#uency o0 re0erence signal sets the output 0re#uency+ 0o$ The "o!ulation in!e2 controls the output voltage$ This type o0 "o!ulation is also /nown as sy""etrical pulse wi!th "o!ulation$
4ultiplepulse wi!th "o!ulation
The
nu"ber o0 pulses Np per hal0cycle is 0oun! 0ro" the e2pression+ m f f c # P
where
m f
f c
2 f 0
2
is the 0re#uency "o!ulation ratio$
f 0
The
variation o0 "o!ulation in!e2 (4) 0ro" to @ varies the pulse wi!th 0ro" to GNp an! the output voltage 0ro" to dc I0 & is the wi!th o0 each pulse+ the 14 output voltage can be obtaine! 0ro" the 0ollowing e2pression E L( RMS )
E dc
# P P
4o!ulation In!e2 4o!ulation
in!e2 is the ratio o0 pea/ "agnitu!es o0 the "o!ulating wave0or" an! the carrier wave0or"$ It relates the inverterRs !clin/ voltage an! the "agnitu!e o0 pole voltage (0un!a"ental co"ponent) output by the inverter$ Now let SV5 sin(?t ) e t$e 5odlatin& "i&nal and let t$e 5a&nitde o trian&lar carrier "i&nal var@ etween t$e pea> 5a&nitde" o +Vc and -Vc. T$e ratio o t$e pea> 5a&nitde" o 5odlatin& wave (V5) and t$e carrier wave (Vc) i" dened V m (5). a" 5odlation-indeB m V c
4o!ulation In!e2 Nor"ally
the "agnitu!e o0 "o!ulation in!e2 is li"ite! below one (i$e$+ " @)$ For " @+ the instantaneous "agnitu!e o0 0un!a"ental pole voltage (- A,1 ) will e &iven @: -AO+@
$J E!c 5 sin(?t)
where
SR is the angular 0re#uency o0 the "o!ulating wave0or"$ For " @ the pole output 1 E voltage (0un!a"ental co"ponent) will have a r"s 2 2 ). "agnitu!e o0 $JE dc (
dc
T$i"
5a&nitde, a" can e ond ot ro5 i" onl@ C9.*D o t$e nda5ental pole volta&e 5a&nitde otpt @ a "Eare wave inverter operatin& ro5 t$e "a5e dc lin> volta&e.
Over4o!ulation 3hen
the pea/ "agnitu!e o0 "o!ulating signal e2cee!s the pea/ "agnitu!e o0 carrier signal (resulting in " U @)+ the &34 inverter operates un!er over"o!ulation$ During over"o!ulation the 0un!a"ental co"ponent o0 the pole voltage increases slightly with increase in "o!ulation in!e2 but the linear relation between the"+)+ no longer continues$ Also+ lower 0re#uency har"onics crop up in the poleoutput wave0or"$ It "ay easily be seen that 0or S"R very high (say " in;nity)+ the pole voltage shape will be i!entical to the s#uare wave shape$ Over "o!ulation is generally not pre0erre!
The
general e2pression 0or various har"onics in the output voltage is obtaine! by !eriving an e2pression 0or a general pair o0 pulses+ such that the &ositive pulse o0 !uration & starts at t V an! the negative one o0 the sa"e wi!th starts at t G8 V The e>ects o0 all &ulses can be co"bine! together to obtain the e>ective output voltage$ Thus 0or this pair o0 pulses+
$nm
2 E dc
m
sin( n t ) d ( t ) m
2 E dc
n
2
cos n(
2
m
2) cos n(
m
2)
2 E dc
%nm
2
m
cos( n t ) d ( t ) 2
m
2 E dc
n
sin n(
m
2) sin n(
m
2)
I0
there are / pulses situate! at V@, V+ V W$+ VX t$en
$n
4 Edc
n
sin n
2
k
sin n m 1
m
%n
4 E dc
n
cos n
2
k
sin n m 1
m
,ar"onic content o0 4&34
For
X an! X @+ a"plitu!e o0 ;rst+ thir!+ ;0th an! seventh har"onics as a ratio o0 the "a2i"u" value o0 0un!a"ental are plotte! against the pulse wi!th e2presse! as a ratio o0 !istance between two a!Pacent pulses$ As the nu"ber o0 pulses per hal0cycle (i$e$ /) is increase!+ the consi!erable re!uction in lower or!er har"onics is achieve!$ 3ith X @+ substantial re!uction in thir!+ ;0th an! seventh har"onics is achieve! in the co"plete range o0 the output voltage$ 3ith larger values o0 Np+ the a"plitu!es o0 lower or!er har"onics woul! be lower+ but the a"plitu!es o0 so"e higher or!er har"onics woul! increase$ ,owever+ such higher or!er har"onics pro!uce negligible ripple or can easily be ;ltere! out
3ith
this "etho!+ since voltage control is achieve! with a si"ultaneous re!uction o0 lower or!er har"onics+ this sche"e is co"paratively a!vantageous over singlepulse "o!ulation$ ,owever+ !ue to larger nu"ber o0 pulses per hal0cycle+ 0re#uent turningon an! turningo> o0 thyristors is re#uire! which increases the switching losses$ Also+ 0or this sche"e invertergra!e thyristors are re#uire! which are costly$
Sinusoidal 0ulse Width Modulation In
this "etho! o0 "o!ulation+ several pulses per hal0cycle are use! as in the case o0 "ultiple pulse wi!th "o!ulation Instea! o0 "aintaining the wi!th o0 all pulses the sa"e as in the case o0 "ultiplepulse "o!ulation+ the wi!th o0 each pulse is varie! proportional to the a"plitu!e o0 a sinewave evaluate! at the centre o0 the sa"e pulse ?y co"paring a sinusoi!al re0erence signal with a triangular carrier wave o0 0re#uency+ 0c+ the gating signals are generate! The 0re#uency o0 re0erence signal+ 0 r + !eter"ine the inverter output 0re#uency an! its pea/ a"plitu!e+ controls the "o!ulation in!e2+ 4+ an! then in turn the 14 output voltage+ E ' The nu"ber o0 pulses per hal0cycle !epen!s on the carrier 0re#uency 3ithin the constraint that two thyristors o0 the sa"e ar" (T@+ T) cannot con!uct at the sa"e ti"e+ the instantaneous output voltage is shown in 0ollowing ;gure The sa"e gating signals can be generate! using uni!irectional triangular carrierwave
inusoi!al pulsewi!th "o!ulation
inusoi!al pulsewi!th "o!ulation
?y
varying the "o!ulation in!e2 4+ the 14 output voltage can be varie!$ It can be observe! that the area o0 each pulse correspon!s appro2i"ately to the area un!er the sinewave between the a!Pacent "i!points o0 OFF perio!s on the gating signals$ I0 &" is the wi!th o0 the " th pulse+ the r"s output voltage$ 1/ 2 #
E L
E dc m 1
P m
,ar"onic analysis o0 the output "o!ulate! voltage wave reveals that &34 has the 0ollowing i"portant 0eatures: For
"o!ulation in!e2 less than one+ the largest har"onic a"plitu!es in the output voltage are associate! with har"onics o0 or!er 0 c 0 r$ Y @ or Np Y @+ where Np is the nu"ber o0 pulses per hal0cycle ?y increasing the nu"ber o0 pulses per hal0cycle+ the or!er o0 !o"inant har"onic 0re#uency can be raise!+ which can then be ;ltere! out easily$ For Np J+ har"onics o0 the or!er o0 L an! @@ beco"e signi;cant in the output voltage$ It "ay be note! that the highest or!er o0 signi;cant har"onic o0 "o!ulate! voltage wave is centre! aroun! the carrier 0re#uency For "o!ulation in!e2 greater than one+ lower or!er har"onics appear since 0or "o!ulation in!e2 greater than one+ pulse wi!th is no longer a sinusoi!al 0unction o0 the angular position o0 the pulse$
&*'E3IDT, 4OD*'ATED(&34) IN-E1TE1 #uarewave inverters su>ers 0ro" two "aPor !rawbac/s: The output voltage o0 the inverter cannot be controlle! 0or a ;2e!source voltage$ To achieve voltage control+ the inverter "ust be 0e! either 0ro" a controlle! ac!c or 0ro" a !c!c converter$ The output voltage contains appreciable har"onics (low0re#uency range)$ Also+ T,D is very high$ Due to these !rawbac/s+ s#uarewave inverter is rarely use! in practice$ To achieve voltage control within the inverter an! to re!uce the har"onic contents in the output voltage+ &34 inverters are use!$ In &34 inverters+ wi!th o0 the output pulses are "o!ulate! to achieve the voltage control$
&34 techni#ue allows: -ariation o0 output voltage within the inverter by varying the gain o0 the inverter$ This allows the input !$c$ voltage to be o0 ;2e! a"plitu!e -ariation o0 output 0re#uency either by varying the nu"ber o0 pulses per hal0 cycle o0 the output or by varying the perio! 0or each hal0cycle with ;2e! nu"ber o0 pulses in each hal0cycle i"ultaneous variation o0 output voltage an! 0re#uency is also possible o that -0 ratio can be /ept constant$ This 0eature is re#uire! in in!uction "otor!rives$ Control o0 har"onics at the output o0 the inverter$
&ulse3i!th 4o!ulate! ,al0?ri!ge Inverters
3ith
a hal0bri!ge inverter+ an output voltage o0 =ero is not possiblethe output -oltage can be only positive or negative$ There0ore+ the output voltage is allowe! to reverse instea! o0 being =ero$ 3e can control the output -oltage by controlling the wi!th Z$ inusoi!al &34 a recti;e! sinusoi!al re0erence signal is co"pare! with a triangular carrierwave$ For the ti"e !uring which the re0erence signal is higher than the carrierwave+ the switches are operate! to pro!uce positivegoing pulsesH otherwise+ negativegoing pulses are pro!uce!$
E1 U EC + @ is ON an! e 8E!c$ E1 EC + is ON an! e E!c
carrier
reEenc@ ratio M f
Fre&uenc' of t!e carrier signal
f c
Fre&uenc' of t!e modulating signal
f
1
Circuit Anal&sis: Fun!a"ental Output -oltage The 0un!a"ental output voltage can be very easily 0oun! by assu"ing that the carrier ratio is #uite high Fun!a"ental output voltage is proportional to the instantaneous "o!ulation in!e2 an! to the pea/ value o0 the output voltage (dc/2)
Eo( fund )
M
(!ere
M
E dc
sin
2 E m
E c
m
t;
M 1
4a2i"u"
value o0 0un!a"ental output voltage occurs at ! 1, E 0( fund )
Inverter
)ain
)ain
Edc 2 2
0.707
E dc 2
4ain
Fundamental outut voltage
0.707 M E dc 2
DC inut voltage
E dc 2
E)
E) (max)
0.707 M
0.707,
*!en M
1
14 Output -oltage 14 output voltage is given by E dc
E oRMS
2 2
EoRMS
Eo ( fund )
2
2
Eo ( 2)
Eo ( 3)
......
2
2
Eo ( fund )
E 0( n ) n 2
2
2
E0( n )
Eo ( rms )
2
Eo( fund )
E n
n 2
En E n
sum of all t!e !armonics e+cet fundamental . E dc 2
2
M 2 2
Distortion
an! ,ar"onic Factor
E o ( fund )
Distortion Factor
DF
DF (max)
*!en M
0.707,
"armonic Factor "Fmax
100%,
"F *!en
0.707 M
E o ( RMS ) 1 1
DF M
1
2
1
2 2
M
1
,ar"onics at the Output The carrier ratio as !e;ne! earlier is given by M F
fc fm
2
where
p is the nu"ber o0 pulses per hal0cycle The har"onic 0re#uencies present at the output can be e2presse! as where
The
as
0n 0re#uency o0 the nth har"onic
or!er o0 the har"onic [n[ can be written
The
carrier ratio is usually chosen as o!! nu"ber The wave0or" then will have a #uarterwave sy""etry an! only o!! har"onics are present$ This is one o0 the re#uire"ents o0 a &34 signal Now only o!! har"onics are present hence i0 /+ is o!! then / is even an! vice versa There0ore+ the har"onic present at the output are
Fre#uencyspectru" 0or bipolar sinusoi!al &34output in hal0bri!geinverter
0WM "ull)#ridge Inverters In
a &34 inverter+ the output voltage wave0or" has a constant a"plitu!e whose polarity reverses perio!ically to provi!e the output 0un!a"ental 0re#uency The source voltage is switche! at regular intervals to pro!uce a variable output voltage The output voltage o0 the inverter is controlle! by varying the pulsewi!th o0 each cycle o0 the output voltage The bri!ge inverter can be consi!ere! to be a co"bination o0 two hal0 bri!ge circuits The ;rst hal0bri!ge consists o0 two switches @ an! whereas the secon!one consists o0 the switches an! The loa! voltage E &< is the !i>erence between the output voltage /0O and /1O o0 the in!ivi!ual hal0bri!ge circuits
Fullbri!ge inverter
&34 with ?ipolar -oltage witching The &34 bipolar switching sche"e use! with hal0 bri!ge inverter can be use! "ore eKciently with the 0ullbri!ge inverter A triangular wave o0 pea/a"plitu!e[ Ec[ is co"pare! with a sinewave o0 pea/ a"plitu!e SE"[ to generate the base!rives 0or the two !evices in the hal0bri!ge circuit (@ an! ) ?ase!rives 0or an! are e2actly @ out o0 phase to those o0 an! @ respectively Thus+ @ an! con!uct si"ultaneously to "a/e the instantaneous loa! voltage 8 E!c an! then con!uct si"ultaneously to "a/e the instantaneous loa! voltage+ E!c The loa! voltage wave0or" is a bipolar &34 wave0or" with a pea/ voltage o0 YE!c volts
&34 with ?ipolarvoltage switching
*5:+
Circuit Anal5sis I0 the loa! voltage wave0or" 0or hal0bri!ge an! 0ullbri!ge &34 inverters are co"pare!+ then it will be observe! that they are i!entical e2cept 0or the 0act that pea/voltage 0or 0ullbri!ge inverter is 8E!c volts instea! o0 (E!c) There0ore+ the analysis will procee! on the sa"e lines as that 0or the hal0bri!ge inverter to yiel! the 0ollowing results$ 14
value o0 output
EO (r"s) E!c
14
value o0 the 0un!a"ental EO (0un!) $\\ 4]E!c
Distortion
Factor+
DF $\\ $ 4
,ar"onic0actor+
,F 2 %)34) - '&'3) .ain o0 inverter+ . $\\] 4 Do"inant har"onics: Do"inant har"onics 0or 40 o!! are again si"ilar to hal0bri!ge inverter an! are
!; with 8ni%olar !; Switching In unipolar &34 switching+ the polarity o0 the &34 output voltage re"ains positive or negative For positive hal0cycle the output voltage polarity is either (8E!c) or =ero For negative hal0cycle+ the output polarity is either (E!c) or =ero This is calle! as threelevel &34+ since output ta/es three voltage levels+ 8E!c+ + E!c
3ave0or"s 0or unipolar &34 bri!ge inverter
*nipolar &34 wave0or" is generate! as 0ollows: In 0ullbri!ge unipolar &34inverter+ the two hal0 ha l0bri!ges bri!ges are given two separate control signals$ ?ipolar triangular wave o0 pea/ a"plitu!e is co"pare! with two sinusoi!al "o!ulating signals which are @ out o0 phase$ The base!riving wave0or"s 0or the switches @ an! + which 0or"s the ;rsthal0bri!ge inverter are generate! by co"paring the triangular wave0or" with the ;rst sinusoi!al "o!ulating signal Due to this+ a bipolar &34 wave0or" wave0 or" is generate! at the ). output o0 the ;rst hal0bri!ge hal0bri!ge (V < < The base!riving signals 0or switches an! which 0or"s the secon! hal0bri!ge inverter are generate! by co"paring the triangular wave0or" with secon! "o!ulating signal (out o0 phase "o!ulating signal) Due to this a bipolar &34 signal is generate! at the output o0 secon! hal0bri!ge inverter (F ).
The
output voltage o0 the bri!ge inverter inverte r < F !
The output voltage is generate! by using usin g the 0ollowing logic: I0 switches @ an! #2 are G,
switch an! are ON+
I0
@ an! are ON+
I0
an! are ON+
,ar"onic pectru" an! Fun!a"ental Output In unipolar &34 Due to the @ phaseshi0t between two re0erence signals+ the carrier 0re#uency at the output is e>ectively !ouble! The "ost signi;cant har"onic is twice that o0 bipolar &34 The "ost signi;cant har"onics selecting 4 0 as even are given by
n
2 M f
E0 fund
1
, 4M f
1
, 6 M f 1
0.707 M Edc ,
for 0
M
1
T Output o0 the inverter is 5choppe! AC voltage with =ero DC co"ponent6$ In so"e applications such as *&+ 5 $i&$ prit@H "ine wave output is re#uire!$ 7 An 'C section lowpass ;lter is nor"ally ;tte! at the inverter output to re!uce the high 0re#uency har"onics$ 7 In so"e applications such as AC "otor !rive+ ;ltering is not re#uire!$
+ut%ut voltage haronics 7 3hy nee! to consi!er har"onics^ 3ave0or" #uality "ust "atch TN? supply$ 5&ower
where SnR s the har"onics nu"ber$
