SF(t) = 1 SW1 closed and SW2 open. SF(t) = 0 SW1 open and SW2 closed. It follows that the output voltage wave form of the a.c chopper is determined ...
AC Chopping Technique With Phase and Voltage Control Khaled E. Addoweesh
Marzouk S. AI-Khalidi
Elect. Eng. Dept. College of Engineering P.O. Box 800, Riyadh 11421, Saudi Arabia
Saudi Arabian MICT. & Refining
(SAMAREC) P.O. Box 3946 Riyadh 11199, Saudi Arabiia
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Abstract AC Voltage chopping techniques used in AC voltage controllers represent an attmctive alternntive to phase angle ors controlled techniques. Moreover, using m i c r ~ p r ~ ~ e s to determine switching instances makes it passible to generate an output voltage with better characteristics.
TI& paper describes a novel chopping technique in which both the amplitude and the phase angle of the fundamental component of the output voltage can be controlled. Detailed analysis of the proposed technique is presented. results verifying the theoretical results are a b given.
SF(t) = 1 SW1 closed and SW2 open SF(t) = 0 SW1 open and SW2 closed It follows that the output voltage wave form of the a.c chopper is determined according to the switching function SF(t) as shown in Fig. 1. Characteristics of the output wave form depends on both the pure input sine wave and the switching function SF(t). SF(t) could be generated by multiplying two functions F,(t) and F,(t), as shown in Fig. 2. The output voltage could be expressed
as:
I. INTRODUCTION The ac chopper consists of a main switch SW1, connected between the ac supply and the load, along with a fly wheeling switch SW2 as shown in Fig. 1. SW2 is used to provide a path for the energy stored in the inductor when SWl is open.
The input supply voltage is chopped into segments and the output voltage level is decided by the ratio between ON/OFF periods [1]-[6]. Many firing strategies could be practically implemented.
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The n o d i supply voltage is v, ( t )
sin
o,t
(3)
Hence, the output voltage can be mathematicallyexpressed as follows:
The operation of the ac voltage regulator in the chopping mode gives the following features: 1. improved power factor; 2. control range is wide in terms of firing angles regardless of load power factor; 3. the order of the dominant load voltage harmonics can be controlled through changing frequency; 4. Linear control of the fundamental component of the output voltage.
The function F,(t) can be expressed by Fourier series as:
whm
This paper presents a control strategy of the ac chopper, where both the amplitude and phase angle of the output voltage are
kl(dutycydeofF,(t)= ON P e r i o d
controlled. Switching logic is generated by a " p r o c e s s o r system. Theoretical analysis, and experimental results are detailed.
2%
=-
2%-0,
2n
II. PRINCIPLE OF OPERATION AND ANALYSIS The function F$(t) can be exprcscd by F d e x series as follows:
Both the main switch in the a.c chopper circuit SW1 and the fly wheeling one SW2 Fig.1, are controlled by the switching function SF(t) in the following manner: 0-7803-1227-9/93/$3.00@1993 IEEE
684
and
From (3) and (5)
Where
T sin*,
A, =
-
COSS,
n a, =
1 sinancosan (n-1)
-2 sina*,
+
n
2sin%, (n-1)
dl
Irn
=
2
a,
=
(n-1)8, 1
From (6) and 0, the output voltage can be expressed as
where
Y? = 1-
Ftmdamental Component of Output Voltage The first and last terms only contribute to the fundamental component. The last term (V1.2 cc)contributesto the value of the fundamental only when mp2n+ 1 = f 1. Hence the instantaneous value of the fundamental component can be expressed as, vl(t) = hbsino,t +
+
B? =aIt can be r c a l i i that the last term (Ik2c) is small compand with the other terms [71. As a result the fundamental component can be approximated to:
3 sin(o,t - 3 ) 2
+ [E + 34sin
si+,t
-
3-
V, (t) = k , k , s i n o , t + k ? s i n 5 s i n ( o 8 t - 8 1 )
tan-1-l)
x
(for n =
C1
+
ain
3 2
-
9
(for n =
2
2
(10)
equation (10) can be simplified using the following idartitia
si o,t +
yl + 4
= a 4
$1
ZZ+
t.n-1+$
2
c o s ( x - y ) = cosx cosy + sinx s i n y
-2)
h-, (9)
685
,
NAPUNDE
1.1
I
The Fourier coefficients of the fundamental component are,
a,
=
-k’sina8, x 2
b,
=
k,k,+=k, sine,
(12)
The amplitude of the fundamental component is
0
KI-a8
-10
For a fixed value of kl, the term under the square root is constant. Hence, the relation between v, and kzis linear for fixed values of 14. The relation between v, and kland k, is shown in Fig.3.
KI -a1
-20
B 5
K1-0.5
-50
-40
i
I -50
e
The phase angle of the fundamental component of the output voltage is,
V,
=
KI ~ 0 . 3
-60
-1 tanm1 0, xk, cot-+-
sina-021 Control of output pbrsc angle
Fig.4
Equation (14) reveals that q, is a function of k, only , which is a good feature of this switchhg technique. Therefore, k, could be used as a controller for as shown in Fig. 4.
*,
In case (a) the Fouriex coefficients of the fundamental waveform are giving by
T““’
a, = A -- cos20 e¶,=
I
2
le,,,
1 where
Fig.2
Switching function SF(t).
Leading - b g g i n g Phase Angle Control: The phase angle could be controlled according to the wave form of the output voltage. Fig. 5 shows two cases of chopped wave forms.
In case @) starting with a pulse a,, bl can be expressed as follow,
I
Input K1 and K2 I
lnitilize
and save in a
pointer
Send value to
Send first
value to CHI
Initialize CHO Initialize CH1
and send second
value to CHI
f L\ \ I
Fig3
Enable INT
Fig.7
Flow chrt of the miaoprocrsll~rp p m .
Fig.8
Gate drive circuit of the MOSFETs.
I
Chopped Hnvefom.
Harmonic contents of the output voltage for kl = 0.8 and p = 12 is shown in Fig. 9. Dominant harmonics are of the order pf 1. Fig. 10 shows an oscillogram of output voltage. Harmonic contents of the supply current for kl = 0.9 are shown in Fig. 11. The fundamental component is not linear with V, due to the discontinuity. Relation between the displacement angle of supply current, which is the phase angle of the fundamental component, and the time ratios is shown in Fig. 12. The displacement angle is almost constant for constant values of Kl.The relation between PF as seen from the supply side and kland k2is shown in Fig. 13.
m.PERFORMANCE OF THE AC CHOPPER Firing signals controlling the ac chopper are generated using a microprocessor system as shown in Fig. 6. Pulse and gap widths for a specifiedvalues of k, and k2are calculated and s t o d in a look-up table in the memory. CHO of the CTC is programmed to operate as a counter with a time constant = 1, while CHI is programmed to operate as a timer. Both Channel interrupts are enables and are served by the interrupt service routines. ISRl, ISR2 respectively. The flow charts of the main program and the ISRs are shown in Fig.7.
1.001
Synchronization is maintained by CHO, which is triggered by the rising and falling edges of the zero-crossing detector. Power semiconductor switches used in the ac chopper circuit are MOSFETs. Gate drive circuit for one switch is shown in Fig. 8.
k2 Fig.6
Fig.9
AC chopper and the interface with tha microprocessor
687
Harmonic oontaats of output voltago.
K1=.9 K1=.7
LL
K1=.5
o_ 0.50
K1=.3
0.00 1 0.00
0.50
1 .oo
k2 Fig.13 Power factor 0.
IV. CONCLUSIONS
Fig.10 Output voltage (a) simulated (b) experimental.
A control strategy of the ac chopper, in which both the phase and amplitude of the fundamental component of the output voltage are controlled has been proposed in this paper. Mathematical model of this chopper has shown that the phase angle ($,) is mainly dependent on k,, while vI is dependent on k2. The relation between v1 and k, is linear for fixed values of k,.
IS 1
ACKNOWLEDGMENT The authors are grateful to king Abdulaziz City for Science and Technology, Saudi Arabia for supporting this work. REFERENCES
0.00
111
K.E. Addoweesh and A.L. Mohamadein, "Microprocessor based harmonic elimination in Chopper Type AC voltage regulators", IEEE Trans. on Power Electronics, Vo1.5, N0.2, April 1992.
121
A. Mozdzer and B.K. Bose, "Three-phase ac power control using power transistors", IEEE Trans. Ind. Appl., Vol. 1A-12, pp.499-505. Sqt./Oct. 1976.
131
A.L. Mohamadein and K.E. Addoweesh, "Evaluation of the performance of the chopper type ac voltage controllers", accepted in Intern. Joum. of Electronics, UK. vol. 67, pp. 669-683, Oct. 1989.
141
Bhat, "Digitally controlled multiple-pulse width modulated ac chopper for power control", Intern. Journ. of Electronics, UK. vol. 51, no.1, pp.45-56, July 1981.
151
G. Roy, P. Poitevin and G. Olivier, "A comparative study of single-phase modulated ac choppers", IEEETrans. Ind. Appl., vol. 1A-20, no.6, pp. 1498-1506, NovJDec. 1984.
[61
B. Wiliams, "Asymmetrically-modulatedac chopper" IFEE Trans. Ind. Eelctron., vol.1E-29, no.3, pp.181-189, Aug. 1982.
173
M. Al-Khalidi, "AC Voltage Chopper as a Phase Controller", M.Sc. dissertation, King Saud University,1993.
1 .oo
0.50
k2 Fig.11 Hprmonic contents of supply cumnt.
a -
-20.00
Y
c
-60.00 e,
0 a In
.n
K1=.9
I
1-
K1=.7
-40.00
Q
V -
3 .
-80.00
1
/ K1=.5 / K1=.3
k2 Fig. 12 Displlctmnt angle of supply current.
688
S.
