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Power Factor of AC Controllers for
Inductive Loads
E. EL-BIDWEIHY, KADRY AL-BADWAIHY, MOUSTAFA SADEK METWALLY, AND MOHAMMAD EL-BEDWEIHY
Abstract-A general relationship for the input power factor of accontroliers with inductive loads is derived in this paper. Its simplifiedfonn is given for the phase angle, integral cycle, and symmetricalpulsewidth modulated controllers. The latter may or may not have afreewheeling path for the load.The variation of the input power factor and distortion factor versus
the load power are presented for these controllers. These results com-pliment and correct previously published results.
NOMENCLATURE
E rms value of the sinusoidal input voltage.f Supply frequency.
IL rms value of the load current.I, rms value of the supply current.L Load inductance.P Load power.
Pmax Maximum load power.p Normalized load power (PIPmax).Q Load quality factor (2rrfL/R).R Load resistance.Z Time harmonic load impedance at the supply frequency.ae Firing angle.X Input power factor., Distortion factor of the supply current waveform.0 Time harmonic load phase angle at the supply fre-
quency.
INTRODUCTIONT HYRISTORS ARE widely used to control the power flow
from an ac source to an inductive load and the commonlyused circuit is shown in Fig. 1(a). Integral cycle and phase-angle controllers use the same circuit, but with different firingschemes of the thyristors which commute naturally in both
Manuscript received Aprfl 20, 1978; revised December 14, 1978.The authors are with the Department of Electrical Engineering,
Faculty of Engineering, King Abdul-Aziz University, P. 0. Box 1540,Jeddah, Saudi Arabia.
A
B f R
'i E sin wt LoadL
(a)A
B < > R
r E sn wt T LoadL
(b)Fig. 1. AC controllers for inductive loads. (b) Load freewheels in T.
cases. These controllers share a common feature that theinput power factor at 100-percent power is equal to the loadpower factor with sinusoidal current at the supply frequency,and it drops as the load power is decreased.Forced commutation of the thyristors in Fig. 1(a) was pro-
posed recently [1] in an attempt to improve the input powerfactor of the controller. The same approach was also adoptedin another attempt to improve the input power factor [21, butthe load is allowed to freewheel as shown in Fig. 1(b).A general relationship for the input power factor of such
controllers with inductive load is derived in this paper. Sim-plified versions for each controller are also attached.
INPUT POWER FACTORThe power delivered to the load in Fig. I is controlled by the
firing scheme of the thyristors A and B. The maximum powerdelivered to the load Pm,x can be achieved when the firing
EL-BIDWEIHY etai.: POWER FACTORS OF AC CONTROLLERS
scheme is such that the load current is the same as if the loadis connected directly to the supply; thus
Ea2Pmax = FZl Cos 0 (1)
where IZI is the magnitude of the load impedance and is itsphase angle to sinusoidal currents at the supply frequency.As the load power P is decreased below Pmax, the supply and
load currents are no longer sinusoidal. Let Is and IL be therms values of the supply and load currents, respectively. Notethat I, and IL are not generally equal if the load is allowed tofreewheel as in Fig. 1(b).The normalized load power p is the ratio of the load power P
at any firing scheme to the maximum load power; thus
(2)Fig. 2. Input power factor as function of normalized load power for
the integral cycle, phase angle, and SPWM controllers.
The input power factor of the controller is defined asthe ratio of the active input power P to the apparent inputpower [3]. The latter is the product of the rms values of thesupply voltage and supply current; hence
X = PI(EIs) (3)1.0
where E is the rms value of the supply voltage. Substitutingfrom (1) and (2) in (3), we get
PX=' -cos0.
s~R (4)
The above relationship holds true for the controller of Fig. 1
with any firing scheme for both natural or forced commutationof thyristors. It is also true whether the load is allowed tofreewheel or not.
INTEGRAL CYCLE CONTROLLERIn this method complete cycles of supply conduction are
followed by complete cycles of extinction. Therefore, thecurrent contains both subharmonics and higher harmonicsdepending on the conduction pattern. The theory of opera-tion and practical implementation of the controller are illus-trated in [4].An expression for the input power factor of this controller
can be derived from (4). For such controller, the thyristorscommute naturally; hence, the load and supply currents arethe same. Subsequently, (4) simplifies to
= -coss q. (5)The variation of X versus p is shown in Fig. 2 for Q = 1 and
5 where Q = tan 0. It should be noted that p varies in discretesteps but the relationship is shown continuous. The aboverelationship is general for any integral cycle controller withan inductive load contrary to that concluded in [5] .
PHASE ANGLE CONTROLLERThis is the most widely used method in power control and
it employs the same circuit of Fig. 1(a). The thyristorsA andB are fired symmetrically at firing angles a and a + a, res-
pectively. The thyristors commute naturally when the loadcurrent reaches zero.For this controller the load and supply currents are the same
and P = ILR. Hence the input power factor of the phase angle
0.5
Phase controllerQ =5
SPWM controller5
//
0.5 p 1.0
Fig. 3. Variation of the distortion factor with normalized load powerfor phase angle and SPWM controllers.
controller is simplyX = N/ cos4f. (6)
It is clear that the phase angle controller has the same inputpower factor as the integral cycle controller. Fig. 2 shows thevariation of X as function of p.The phase angle controller has the advantage of continuous
power control from zero to 100 percent. Also integrated cir-cuits for gating the thyristors of this controller are now com-mercially available. However, it has the disadvantages of dis-torting the supply and load currents, and having a low inputpower factor at low normalized load power.The distortion factor , of a current waveform is defined as
the ratio of the fundamental component to the rms value ofthe current waveform. The distortion factor of this controllerwas computed and the results are shown in Fig. 3 for Q = 1and Q = 5.
CONTROLLERS WITH FORCED COMMUTATEDTHYRISTORS
Two independent attempts were made to improve the inputpower factor of the phase angle controller using forced com-mutation. One method [1] uses the circuit of Fig. 1(a), while
P = PIPmax.
21
212 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS AND CONTROL INSTRUMENTATION, VOL. IECI-27, NO. 3, AUGUST 1980
Fig. 4. Input power factor and controller efficiency versus firing angle.
the second method [21 uses the circuit of Fig. 1(b). The latterallows the load to freewheel after switching off the thyristorsto make use of the magnetic energy stored in the load induc-tance at the switching off instant.
In both methods, it was found that the highest input powerfactor is attained when thyristor A is turned ON and OFF atangles a and rr- a of the positive half cycle of the supply volt-age, respectively. Similarly, thyristor B is turned ON and OFFat angles nr + a and 27r - ca, respectively. The controller is thusnamed symmetrical pulsewidth modulated controller (SPWMC).In the following we derive relationships for the input powerfactor of both controllers.
SPWM Controller ofFig. 1 a)Let I, be the value of the load current at the instant of com-
mutation of thyristor A. The input power in this case is notequal to I2R, but is given by
P=I2 R + fLI2 (7)
where the second term is due to the magnetic energy stored inthe load inductance at the switching off instants of thyristors.This energy is assumed dissipated somehow since the circuitdoes not allow the load to freewheel. Equation (7) can bewritten as
p=I2 R/i (8)
where 7t is the controller efficiency defined as the ratio ofload power to the input power. Note that all other controllersdiscussed in this paper have approximately 100-percent effi-ciency.Substituting from (8) into (4), we arrive at the following
expression for the input power factor:= cos q5. (9)
The variations of the input power factor and efficiencyversus the firing angle a are shown in Fig. 4 for Q = 5. It isclear that a significant improvement in the input power factoris achieved at the expense of poor controller efficiency.As an example, consider a load whose cos 0.1. The input
power factor has a maximum value of 0.82 at an efficiency of2 percent. We conclude that this controller is impractical.
SPWM Controller with Freewheeling LoadThis SPWM controller can be considered the first practical
attempt to improve the input power factor to values greater-than the load power factor to sinusoidal currents using forcedcommutation of thyristors. The load is allowed to freewheelafter the thyristors are turned off and thus the load and supplycurrents are not the same. Substituting ILR for P in (4), theinput power factor is
(10)ILX N I-cos 0.Is
It is clear from (10) and (6) that the SPWM controller withfreewheeling load gives higher power factor than the phaseangle controller since IL of this controller is greater than orequal to I,The variation of the input power factor versus p is shown in
Fig. 2 for Q = 1 and 5. Fig. 2 shows that the input powerfactor of this controller is greater than that of the phase anglecontroller for the same normalized power. For example, theinput power factor of the SPWMC for Q = 5 equals 0.2, 0.3,and 0.24 at p = 100 percent,50 percent,and 1O percent, respec-tively. The phase controller has an input power factor of 0.2,0.14, and 0.06 at the same respective values of p and the samevalue of Q.The improvement in the input power factor is not as high as
given in [2]. This is because the number of terms retained inthe Fourier expansion of the supply current were not enoughfor the computation of the rms value.The supply distortion factor of the SPWM controller is also
calculated and is shown in Fig. 3 along with the correspondingvalues for the phase controller. Figs. 2 and 3 illustrate that theimprovement in the input power factor of the SPWM over thephase controller is achieved at the expense of an increased dis-tortion in its supply current. Therefore, it is concluded thatthe increase of the input power factor of the SPWM controllermay not pay back for the cumbersome and costly circuitryneeded for forced commutation and the increase in supplycurrent harmonic content.
CONCLUSIONSExpressions and results for the input power factor of differ-
ent controllers with inductive load were derived and presented.The controllers considered in this paper are the SPWMC withor without freewheeling path for the load and the integralcycle controller. The results for the phase angle controller arealso included for completeness and ease of comparison be-tween different types of controllers.
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