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8/11/2019 Factor de Potencia Ingles

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~

2. 7

Reacti ve power consi derati ons

Due to the phase- angl e cont r ol w th del ay angl e i n t he case

of 1i ne- commutated conver tors the di spl acement to be seen i n

Fi g. 23 of t he phase cur rent s r esul t i ng f r om t he val ve currents

w t h r espect t o t he phase vol t age i n t he suppl y syst em gi ves r i se

to cont rol react i ve power .

I n addi t i on, as descr i bed i n 2. 3,

the reactances i n the cornmutat i ngci r cui t cause over l aps between

the consecut i ve cur rent bl ocks of the i ndi vi dual phases whereby

the f undamental osci l l at i ons of the phase cur rents are f urt her

r etarded. The react i ve power caused by thi s i s the cornmutat i ng

reacti ve power .

The cont r ol r eact i ve power i s consi der ed f i r st .

2. 7. 1 Contr ol react i ve power

I n Fi g. 23 t he vol t age and cur rent of one phase are separat el y

pl ot ted i n accordance w th t he r epresent at i on i n Fi g. 12 f or two

del ay angl es a = 0

and a =

~5.

I t was assumed f or t hi s t hat t he

commutat i ng ci rcui t contai ns no react ances ( L

K

= O) , t he di r ect

cur r ent I d i s compl etel y smoothed and the phase vol t age curve i s

si nusoi dal .

wt

Fi g. 23 Cur ves of phase cur r ent i R and phase vol t age u

R

pl ot ted agai nst t i me for a si x-pul se conver tor when

f ree- f i r i ng = 0

and w th phase shi f t cont r ol


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I n t he f r ee- f i r i ng condi t i on t he f undament al osci l l at i on i

1R

of t he

cur r ent i R i s i n phase w t h t he si nusoi dal phase vol t age ~ due t o

i t s ~h order symnet r y. Wt h phase shi f t cont r ol t he cur r ent bl ocks

ar e di spl aced backwar ds t hr ough

t hus di spl aci ng i t s f undament al

osci l l at i on by ~1. Because of t he ~h order syr nmet r y of t he bl ock

wavef orm resul t i ng f rom t he assumed omssi ons,

= ~ as can be

1

seen f r om Fi g. 23b. Hence

cos ~1 = cos a

2. 30

The r eal power Pl i n t he t hree- phase syst em i s t hen

U

rms

I

1rms

3

U

rms

I

1rms

cos

a

2. 31

The r . m s. val ue of t he f undamental osci l l at i on of t he squar e- wave

cur r ent i s obt ai ned by Four i er anal ysi s:

I

1rms

~

I d

30

J

72

cos

2

.f3

J

. [ 2 .

I d

Usi ng equat i on 2. 3 and i nsert i ng val ues f or U

rms

and I

1rms

:

3 J

2

Udi o cos

2. 33

I gnor i ng t he conver t or l osses, t he r eal power of t he f undament al

osci l l at i on on t he a. c. si de i s i dent i cal t o t he power on t he d. c.

si de.

The appar ent power of t he f undament al osci l l at i on i s gi ven by

The t ot al apparent power S becomes

S

=

3 Urms

I

rms 2. 35


3/5

- ~6 -

Thus t he

power

f actor

A .

i s

def i ned by

Pl

3

U

I

1rms

cos

rms

A .

S

3

U

1

ms

rms

Taki ng 9

I

1rms

rms

as t he f undament al osci l l at i on cont ent ,

9 cos

For t he cur r ent wavef orm i l l ust r at ed i n Fi g. 23 ( e. g. i n t he

t hree- phase br i dge connect i on) , accordi ng to equat i on 2. 32

I

1rms

2

.f3

I d

and moreover

= ; i

. J 2

2

I d

2. 37

rms

.f3

whence

9

0 955

From equat i on~ 2. 30 and 2. 36 the r el at i onshi p between a and cos ~1

i s obt ai ned f r om

A . =g cos = 9 cos

1

I t can be seen t hat , due t o t he cur rent wavef orm bei ng burdened

w t h harmoni cs, t he power f act or A i s l ess t han 1 even i n

t he f r ee- f i r i ng condi t i on ( cos = cos

fJ J

1

= 1) .

The react i ve power Q1 of t he f undament al osci l l at i on i s gi ven by

Ql

S

2

P

1

2

2

3

U I

1rms

cos

rms

3 U I 1rms

.

si n

2. 39rms

Ql

U

di o

I d

si n

2.~


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I f t he f undament al osci l l at i on r eact i vepower i s r ef erred t o t he

f undament al osci l l at i on apparent power Si = U

di

I d equat i ons

2. 39 and 2. ~1 produce t he expressi on

1 ( cos e x . _ d ) 2

x

Wth t he rel at i ve di rect vol t age

cos e x . d

x

t he equat i on f or an el l i pse i s obt ai ned, whi ch t ur ns i nt o a

ci r cl e when bot h r adi i ar e made t he same.

d e x .

2

U

di

1

2. ~~

pos i t i ve, i s r epresented by a semci rc l e.

The capaci t i ve r ange

I n Fi g. 25 t he i nducti ve r ange, i n whi ch t he react i ve power i s

w t h negat i ve r eact i ve power cannot be obtai ned w th t he

l i ne- commutat ed conver t or s di scussed here w t hout addi t i onal sel f com

mutat i ng devi ces. Wt h const ant rel at i ve i nduct i ve di r ect vol t age

drop d

x

i . e. constant suppl y syst em shor t - ci rcui t vol t age u

k

t he del ay angl e e x . i s t he paramet er of t hi s ci r cl e. The si ze of

t he angl e depends upon t he magni t ude of d

x

I n Fi g. 25 t he react i ve

power consumpt i on at e x = O and e x = 160

0

i s pl ot t ed f or

5

val ues of

d

x

i n accordance w t h t he rel at i onshi p uo

=

ar c cos ( 1 2 dx) .

_

-

_ . _

Wth posi t i ve r el at i ve di r ect vol t age oper at i on i s i n t he r ect i f i er

mode and w th negat i ve r el at i ve di r ect vol t age i n the i nver ter mode.

Fi g. 25 Var i at i on of r eact i ve power i n mai ns w t h

di r ect vol t age at constant di r ect cur r ent output

Paramet er: Overl ap angl e u

Margi n of commut at i on 20

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