Power Factor Compensation in Triac Controlled AC. Chopper Circuits. M. E. Balci and M. H. Hocaoglu. Department ofElectronics Engineering. Gebze Institute ...
IEEE PEDS 2005
Effects of Source Voltage Harmonic Distortion on Power Factor Compensation in Triac Controlled AC Chopper Circuits M. E. Balci and M. H. Hocaoglu
Department of Electronics Engineering Gebze Institute of Technology Gebze, TURKEY
Single-phase loads, composed with triac controlled ac chopper, are frequently used power electronic loads in industrial applications; such as glass melting [7, 8], controlling of ac motor speed [9, 10] and dimming lamps [11]. In general, to achieve effective and proper operation, such applications come with a compensation problem to be solved in a cost efficient manner. The studies, that are presented in [7, 8], demonstrate methods for power factor improvement with ilters proper fisn trlac controlled ac chopper circuits which are employed as the glass melter. It iS shown that significant improvement in the power factor can be achieved by filtering out of the specific harmonics [7, 8]. The energy efficiency of triac controlled ac chopper circuits in the applications of ac motor speed control is the subject of the studies, which are presented in references [9, 10]. In the studies, it is demonstrated that the efficiency of ac motors could be Keywords- Harmonics, ac chopper circuits, power factor, optimized by implementation of chopper circuits. The study [11] experimentally analyses that phase-controlled dimmable reactive power conmensadon, nonsinusoidal condtion electronic ballast for fluorescent lamps taking into account power factor correction and efficiency. In the studies [7-1 1], it I. INTRODUCTION is observed that, although triac controlled ac chopper circuits have poor power factor performance due to its harmonic For the systems, which are contaminated with nonsinusoidal voltages and currents, it is well known that producing nature they are largely employed as an efficiency improvement tool tolaand aarcaproly Power Factor Compensation is an important...problem .. .. . .and . motors, lamnps cheap controllerloerfor acac motors,clamps and heaters. widely discussed in the literature [1-6]. The studies on power..................improvement factor correction in nonsinusoidal condition can be divided into The harmonic limitations are very important issues so that two groups; some of the studies are focused on physical meaning of power in nonsinusoidal conditions and correct power systems are preserved from the effect of harmonic interpretation of compensable power [14]. Other are pollution. Thus, the designs of power electronic devices, the specialized on the effects of harmonic distortion levels on most extensive harmonic sources, must be compatible with the harmonic limiting standards. IEEE and IEC standards of reactive power compensation [5, 6]. In the studies, focused on physical meaning of power, conventional power definitions are harmonic limitations can be grouped into two categories: analyzed in nonsinusoidal condition by giving particular a) Standards based on Customer/System Limits emphasis to the usefulness of active, reactive and distortion * IEEE 519-1992 [12] power components with the aims of not only exploration of the physical essence of the energy and power for the scientific I 1000-2 2 * EC [13] consistency but also provision of engineering tools to achieve * IEC 1000-3-6 maximum power factor. All of these studies demonstrate that [14] reactive power compensation is a challenging problem for b) Standards based on Equipment Limits power systems in nonsinusoidal conditions. I*EC 1000-3-2 (up to
Abstract- In recent years, detailed modeling of power electronic devices and their behavior on different system conditions are a great concern of the power industries and customers. One of the widely proliferated such devices is the triac controlled ac choppers. Although these types of devices have important application areas, their poor power factor performance is the main obstacle for the large scale implementation in power systems. This paper presents an analysis on the behaviour of a single phase load composed with triac controlled ac chopper during reactive power compensation under nonsinusoidal voltage. The results of these analysis shows that for high conduction angle distortion on the source voltage improve the power factor which is contradicting with the previous findings. In addition, it is observed that, performance of power factor compensation systems are heavily affected by source voltage harmonics phase angles which are ignored in existing literature.
This work is supported by State Planning Organization of Turkey (Project no:
2003KI20530).
16A) [15]
IEC 1000-3-4 (16-75A) /16] Standards of customer/systems harmonic limits focus on THD of PCC (point of common coupling) places. On the other
0-7803-9296-5/05/$20.00 C) 2005 IEEE
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hand, standards of equipment harmonic limits consider the levels of individual harmonics. In [EC 1000-3-2 standard, ac chopper circuits are classified as lighting equipments and they are tested with allowed maximum power when firing angle is set to 90'±5'. In EEE 519-1992, reactive power compensation is required to maximize the efficiency of power system and the methods of reactive power compensation for converter circuits are summarized. Moreover, THD index or individual harmonic limits, which are used to limnit injected harmonic, may not be a good indicator for description of power factor performance of such devices owing to fact that the angles at individual harmonics are omitted. In this paper, a complete analytical model of a single phase load composed with triac controlled ac chopper is developed taking into account source voltage distortion and impedance [17]. The model, developed in this paper, is constructed by using differential state equations, which is applied on these type problems in some studies [18, 19]. Usage of a complete and analytical model gives the opportunity to employ extensive parametrical analysis without causing computational burden, which may be present in the case of classic numerical computations [20-22] that is also used for these types of studies [23]. The model, developed in this paper, is used to investigate the effect of source voltage total harmonic distortion and harmonic phase angles on power factor compensation, available with basic capacitance, at different triac conduction angles. POWER FACTOR CHARACTERIZATION IN NONSINUSOIDAL CONDITIONS In general, power factor is characterized as a function of total harmonic distortion of current (THDI) or distortion factor (df) [4, 24-26]. In these characteristic analysis, power factor (pf) is derived in harmonic domain by considering well known total harmonic distortion (THD) and distortion factor (dl) indices as depicted in equation (1) and (2). IL
S
S
,
+(TD,/1 4I+(THD,/
I=
1+ (THD, /100
(1)
where P and S stand for active and apparent powers, respectively. An appropriate estimation of power factor could also be determined by using equation (2) for low level voltage distortions:
21
I
+ f i(am)2 dca i(
2
i (ci) =
iSin(ci)
(5)
RLld
due to resistive load. And rms of current can be defined as vm
I = TNR7
2 (;r - a) + Sin 2;
-d
41 + (THD, /100)2 =pf,
'df
(2W)( a
(6)
Finally, the power factor is formulized as in equation (8) by
substituting equalion (6) into equation (7) pf = P/S= I2R,_dIVI pf = 4(2( -a) + Sin2a)I2zr
(8)
summarized characterizations.
ANALYTICAL MODEL OF TRIAC CONTROLLED AC CHOPPER CIRCUIT
The system, given in Figure 1, has a triac controlled ac chopper circuit, a distribution line and a load, which is modeled as constant impedance and a compensation capacitance, is placed on the load terminal.
.I Vt
)
(2)
(pf&,) and distortion factor
Vst? I Ia1i
(3) df=I,ll On the other hand, in some studies on the triac controlled circuits, power factor is characterized as a function of conduction angle (a) [4, 27]. Power factor formula is derived
LT
where displacement power factor (df) are defined as
(7)
Due to the fact that source distortion are not considered in the analysis, these characteristic formulations may not be accurate enough to predict power factor and reactive power compensation characteristic of the triac controlled ac chopper circuit at the conditions, where source side distortions are considerably high, and/or an impedance between source and load is present. Moreover, THD of voltage and current may not be a good indicator for the characterization of power factor compensation owing to the fact that the angles of current and voltage harmonics are not considered in THD indices. Thus, the effects of harmonics are not properly accounted in
6qw 9de TW
Pf = fP
(4)
I
where the current Is
III.
pP, + P Pf
by the process which is detailed here for the consistency of the paper: Determining the rns value of current
Pf.. = PI /S.
Figure
1200
i.
The expenmemental system
The system can be analyzed into two operating modes as triac conduction and triac cut off. During triac cut off mode, current and voltages are calculated by using super position theorem. During triac conduction mode, equations of current and voltage in the circuit are found by solving the system of equations given below.
V.(t) = Vm, Sin(to, t+,&
(9)
,in
(t)+L
dt
+
(t)=v(t)
(10)
d *~ . (=0 ddiL RL_sd 'iL.d (t) + LLOdO VLdt ,d
(11)
dv
(12) Lotd = 0 dt Equations (9-12) are solved for the initial conditions line current, load voltage and load current. The solution of the system for line current iine(t), load voltage vL,.d(t) and load current iL,d(t) is
iDn(t) -iL_d(t) -C
i4; 0'() =X[A,, Sin(o, t+)+BCos(o..t + gn)] + C3 eDktl +nX L
n=l. (13)
[k= eD']
VLt-d(t)=
A +LO B. w.) Sin(w,,t+t)+ R,[AVm .R , ,e[(..Line RLjne n D;) ]} i .,t
CD
.
+ AL.,, C L,=
C
ANALYSIS
To show the effects of total harmonic distortion and
harmonic phase angles of source voltage over reactive power compensation, available with a basic capacitance, power factor and distortion factor, in the condition of maximum power factor, are calculated by using proposed analytical model at different triac conduction angle and source voltage distortion. Two different parametrical analyses are considered in the
system. In the first case, for each triac conduction angle, varied from 45' to 135', maximum power factor is calculated. Effect of source voltage distortion is also taken into account considering various THD values, which is changed from 1% to 14%. For each case of obtained maximum power factor, current distortion factors are also calculated. In the second case, effects of source voltage harmonic angles on the maximum power factor, available with a basic capacitance, and current distortion factor, in the condition of maximum power factor, are analyzed by varying harmonic angles for source voltage THD of 10%.
A. Case 1
In this case, the effect of source voltage THD on reactive compensation, power factor and distortion factor are analyzed in the systems with triac controlled ac chopper loads. The RMS value of source voltage is kept constant while adjusting the magnitudes of harmonic voltages namely 3rd, 5th, 7 harmonics of fundamentals. Source voltage waveforms and harmonic magnitudes at 1% and 14% of THD are given in Figure 2. power
\..
kL, XW2. i(*te,)+,' ]]
os)co, t
(14)
4
where An, B9 and ck3, are coeffficients for nth harmonic of source voltage. These coefficients and initial values of line current, load voltage and current are given in Appendix of the reference [17] and they are not repeated here for lack of space. Triac cut-offtime is the solution of equation (16)g
(tC9t.Off)
iLo3,d(t7 _tf
IV.
+L~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 91-mTa
iLS()=S,(A-CRb,. BT W-D, ) +S2[(IRLjnT C, D,kLL '=1-R
ATP version of EMTP [20], the analytical computation and EMTP results are in very close agreement [17].
*
.
b2
' ,
-
l,8"t
for interval tCfldU n
