ACTIVE FILTICIIS SIMULATION TO CORRECT TkE POWER FAC1I~OIP
USING PSPICE.
Rtt-r-icioSalmer6n Revuelta
(I'
Juan C. Montan0 Asquerino
(z
Dept. Fisica Aplicada e Ingcni8:ria ElCctrica. University d Huelva,
Escuela Politecnica Superior. Ctra. Palos dc la Frontcra. 21819 La Rabida, Huelva, Spain.
F'hone (+34) 59 350651 Fax (+34) 59 350311 Email: Patricio@uhu.es
IRNA, Consejo Superior de Invcstigaciones Cientiilicas.
AV&. Reina Mcrccdcs s/n. 41012 Scvilla, Spain.
(+34) 54 624711 Fax (+34> 54 624M2 Email: MontarioI@cica.es
Abstract.-The fundamental re:sults of the instantaneom power
theory have been applied to optimize the power factor iii
three-phase systems with nonlinear loads. Compeiisa(ion in
steady and transient state:; is considcred. The mtd& for
PSPICE oE an active poww i[ilter and a control circuit arc
presented. The results of a pr.aclica1case, using these
, A&"
are included.
I. b!TRODUCTION
The current nccd of correcting the power factor in
Three-phase system with iionlinear loads has motivated, UI
the recent years, the appearance of a great i i u " of
projects on static VAr compensators [l]. Sincc the 80's
concrctcly, electrical engineers have bccn investigating tho
utilization of so-called de5,igilatcd active power f i l t e r s for
the compelsation of three-phase nonlinear loads, sucli a!<
rectifiers, AC choppers a d cycloconverters [2-81.
Active power filters ate based on a DC-AC bridge
convertcr, with fed-in voltage or current, constituted by
switching deviccs with practically no energy storagc
componeiits. At present, d-e switching elements are of thc
types BITS, MOSFETS ard IGBTS, tllat switch incrmsetl
currents in very short times with high performance. Pulsc
Width Modulation (P'YM) techniques are generally use to
control the converter [3-51 This permits injection into thc
electrical line of a sequcncc: of current pulses with differctit
objectives, such as optim~zation of the power factor. In
such case, the objectivc is to obtain a line-curmilt
waveform that rcpruduces t h a supply voltage waveform.
This paper approaches the problem of compcnsating
three-phase nonlincar loads in sinusoidal and nonsinusoida I
situations with the objective of developing a i n d e l of
active power filter aid its control circuit, to verify
theoretical predictions and system perfonnancc tlxough
simulated tests, facilitating the coniputcr presentation of the
waveforms of interest. The module analog Deliaviornl
nrodcling provides great wsatility for tlie simulation of
bolck diagrams. These characteristics make PSPICE an
especially interesting tool 1-01the analysis of active powcr
filters.
definition of two orthogonal components of the line current,
i The f i s t is tlie mstc,inkuzeous active current, ip,and die
second the znstatuneous rr'actwe current, i,,; of the two,
oidy the fornicr is necessary for tlic transmission of the
imtantaiieous power p('t).Thus, the current compcment i, is
comlxmable. So, it is possible to speak of a truc process
of ins[anfnneouscoinpensalion for a transient state. This IS
exclusive of systcnis of more rhan one pliasc arid it
represents conccptuall!: a novelty.
Tlic complctc for~tnulatioriof thc problem is I-~rescntcd
in (9-101. If the 3-plxise voltage-sourcc have a refermce
such tlnt xu,= 0, th:: vector corresponding to the load
current is dccomposcd in the fonn
J = J
P
4
where U is the insiantaieous voltage vector; U the
instantaneous norm of U: J= Edn;p(t) the conventional
instantaneous power: p= U'.< and io the instantaneous zcrophase sequence curremivector: io= LE, , where I = [111],
aid 3.b= i,+i2+i3.
For supplying the mstantaneous power to the load,
oiily die current i, is necessary. So, to reduce t!ie line losses
as: much as possible without altcrhg the ltt,tantawous
power (or tlie iilstanta neous active a " u t ) transmission,
that is, without using eiiergy storsge, the instantme ous nonactive current i, should be eliminated. The compensator can
bc built with switching deyiccs without reactive elements,
111 this way its incoming instantaneous power is null arid it
docs not interfere in die process of instantaneous t r a d e r
of energy between source and load.
Figure 1 shows the basic scheme of thc instantaricous
compensation (3),
(3)
11. INSTANTANEOUS AND STEADY STATE
COMP.ZNSATION
In tliree-phxe systemu, for arbitrary voltage ai01
current wavcfonns, the global process of energy exchangc
bctwccn source and load I:, explained satisfactorily by tlic
0-7803-31-09-5/96/$5 00
+ i
Tliey are calculated instantaneously without any time delay
by using the iilstantaneous voltages and currents on the load
sidc .
1906 IEEE
1543
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1
it
el
i3
I
c2
U-
1
U-
J
2
-I
U-
I
I
-I
3
0
Fig. 3. Active power filter.
Fig. 1. Block diagram for the calculation of the instantaneous
compensating current for a three-phase system.
The circuit operates without the aid of energy storage
elements. The coinpcnsating current is obtained by
hysteresis control. The width of the hysteresis band is
preset when the reference current is calculated. The discrete
output levels of die hysteresis comparator determine die
gating sequence of the switching devices, fig. 4.
In the steady state one may be interested in studying
the possibility of full compensation, i.e., the elimination of
the non-active terms of the current to obtain unity PF.
Under this condition, the voltage source supplies the active
current dcfiicd by Fryze [ 1I], which means that the current
source waveform reproduces the voltage source waveform.
Fig.2 shows the block diagram for the calculation of
reference waveforms for full compensation.. Two LPF are
included for determination of die average power P and the
average norm squared of the voltage (U') respectively. The
quotient of both quantities constitutes the equivalent
conductance (GJ
.p
I'
Fig. 4. Hysteresis Control for one Phase.
The converter output follows the reference waveform of the
instantaneous reactive current, within the band imposed by
the control operation. Several models of generalized power
converters were simulated in a computer by using their
transfer functions [12]. Thus, given the switching function
matrix of the inverter (fig.5) and the voltage vector on the
DC and AC sides defined respcctively by
Fig. 2. Block diagram for calculating the full-compensating
current.
v,
= [
v.,
v4
;
v, = [ v v.,
Sl
. . .
v.4]
(4
and the respcctive current vectors,
111. ACTIVE POWER FILTERS: MODELS FOR
COMPUTER-AIDED SIMULATION.
The proposed type of compensator is the DC-AC
converter which is shown in fig. 3 . It works as an active
power filter that delivers the compensating current vector.
The gating pulses switch the transistors of the three-phase
bridge as usual and the output pulse amplitudes reach the
voltage value of the DC side.
the input-output rclatioilships are given by
where A is the switching function matrix whose terms A,
define the closed state "I", or the open state " 0 of the
1544
I
LOAD
I
Fig. 7. Compcnsalcd three-phase bridgc controllld
rectifier.
Fig. 5. Switching matrix for multiphasc invcrter.
switching element. Thus, it is vcrified
It is assumed that this nodinear load is fed by a
balanced sinusoidal SUI ply voltage. The switching elcmcnts
SCRS of the rectifier are switched by a gating wip:lc of 60
dcg referred to the zero-crossing instant of the phase
volt age.
Fig. 8 shows significant waveforms of plase 11: source
c m c n t before compensation, instantaneous compensating
current and the compensatcd supply current. The last two
prcscnt deviations with respect to thc rcfcrence signal (the
shading region) due to the hysteresis band.
and for the three-phase invccrtcr
which enables establishmtnt of the equivalent circuit of
dcpcndent sources (fig. 6), [12-13].
U A A :
. .
. . . . .
:.
...........
.!
t
+
t
Fig. 6 . Model for Computt:r-Aided Simulation of a ThreePhase Inverter.
Each one of the elcmcnts of AV(') represents
waveforms d c f i c d accoiding to two discrete levclls
obtained on the output side of the hystcrcsis comparatoL,
one per plase. This procedm constitutes the usual control
of current by pulse widtli incldulation (PWM).
a
1m. .................
,...................
.+..
IV. SIMULATION OF A PRACTICAL CASE.
Thc principles set OUI in thc previous paragraphs on
instantaneous and steady s t m compensation, as well as the
methodology presented -01 obtaining computer-aided
modcls of active jmwcr filters, are applied for the analysis
of a practical case, 1141.
Fig.7 shows a three-phase bridge rectifier with
mductive load.
b
1545
..................
*.......................
-.*
LOA
,.................
+.....................
..
delay equivalent to several fundTmenta1 periods of the
supply voltage. Both can be implemented by using a static
compensator built with the coilfiguration of a power
inverter. The control system and the powcr circuit have
been studied by using efficient computer models. These
provide great versatility for the simulation of block
......
diagrams for control circuits using PSPICE. The simulation
process makes it possible to confirm thc results on
compensating load in different practical cases.
torr;
OR.
-I(YXI
TlCW
REFERENCES
C
Fig 8 Waveforms Correspondmg to Phase 1 in the System
Shown in fig 7 a) Current in Load, b) Instantaneous
Compensating Current, c) Source Current after Compensation
(11 T.J.E. Miller, "Reactive Power Control in Electric Systems"
Fig. 9 shows the compensatiiig current and the source
current after steady state compensation.
.....:............ .-......... *
i.L(,&
2ifl
i.
. . . . . . . . . . . . ..: . . . . . . . . .
............. ........5.......................
.f
+
~
.....
,. .
. . . . . .~
?(XI I
en<
-,ru1 >
<".r
1 lh.3
I',*%
ili,i%
xi-
b
Fig 9. a) Full Coinpcnsatmng Current b) Source Current after
Compensation
V. CONCLUSIONS
For thrcc-phase systems and nonlinear loads, two
different procedures of load compensation were considered:
the instantaneous compensation, for eliminating the
instantaneous reactive current, and the full conipensatzon,
for eliminating all the non-active current components
circulating through tlie load. The fist procedure is able to
operate in the transient states. The second procedure is
conceived only in steady shtes, the compensator suffers a
John Wiley, 1982.
[2] H. Akagi, Y . Kanazawa, and A. Nabae, "Instantanous Reactive
Power Compensators Comprising Switching Devices Without
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