Control for PWM ac chopper feeding nonlinear loads

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Control for PWM ac chopper feeding nonlinear loads a

a

L. Rahmani , F. Krim , M. S. Khanniche & A. Bouafia

a

a

Laboratory of Power Electronics and Insdustrial Control, Department of Electrical Engineering, University of Setif, Algeria Version of record first published: 19 Aug 2006.

To cite this article: L. Rahmani , F. Krim , M. S. Khanniche & A. Bouafia (2004): Control for PWM ac chopper feeding nonlinear loads, International Journal of Electronics, 91:3, 149-163 To link to this article: http://dx.doi.org/10.1080/00207210410001672674

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INT. J. ELECTRONICS, VOL.

91, NO. 3, MARCH 2004, 149–163

Control for PWM ac chopper feeding nonlinear loads

Downloaded by [ABDELOUAHAB BOUAFIA] at 09:45 05 April 2013

L. RAHMANIy, F. KRIM*y, M. S. KHANNICHEz and A. BOUAFIAy This paper presents a novel robust control technique for PWM ac choppers with the ability to generate high quality sinusoidal waveforms with adjustable amplitudes over a wide range control. For this purpose a deadbeat-based digital controller has been developed to perform tight closed-loop control of the ac chopper. This controller is based on a generalized predictive control (GPC) approach. A dedicated control algorithm has been developed and implemented. The proposed controller presents the advantages of allowing a very fast transient response and compensating effectively for load disturbance and the effects of nonlinear loads. Computer simulations are performed to investigate the proposed controller performance. The simulation results show that the designed controller has a good dynamic behaviour, a good rejection of impact load disturbance, and is very robust. To evaluate the proposed approach an experimental prototype has been constructed. Experimental results under various loading conditions have demonstrated that the system performs well.

1.

Introduction An ac voltage regulator is used as one of the power electronics systems to control an output ac voltage for a power range from a few watts (as in light dimmers) up to fractions of megawatts (as in starting systems for large induction motors). Phaseangle control (PAC) of thyristors was traditionally used in this type of regulator. Such a technique offers some advantages such as simplicity and the ability to control a large amount of power economically (Shepherd 1965). However, it suffers from inherent disadvantages such as: (1) high low-order harmonic contents in the output, resulting in poor power factor, especially at large firing angles; (2) the load voltage waveform is determined by the load phase angle, which also affects the control range in terms of firing angle (Bidweihy et al. 1980). To improve these defects, several solutions have been proposed and can be classified largely into two. One is the modification of the power circuit by adding a free-wheeling path; this improves the input power factor slightly but cannot control the harmonics (Revenkar and Trasi 1977, Krishanamurthy et al. 1977, Bose 1981). The other is the determination of a proper control scheme. If power switches with self or forced commutation are introduced in the chopper circuit and operate according to the appropriate switching method, then the above problems will be solved (Revenkar and Trasi 1977). Moreover with the development of power semiconductor devices, PWM techniques are being encouraged increasingly and will become more sophisticated. They can be Received 15 August 2003. Accepted 10 February 2004. *Corresponding author. e-mail: [email protected] yLaboratory of Power Electronics and Industrial Control, Department of Electrical Engineering, University of Setif, Algeria. International Journal of Electronics ISSN 0020–7217 print/ISSN 1362–3060 online # 2004 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/00207210410001672674


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divided into two: programmed PWM techniques have been employed extensively for minimization of either selected harmonics or total harmonic distortion (THD) (choe et al. 1989, Addoweesh and Mohamadein 1990, Jang and Choe 1995, 1998, Jang et al. 1995, Michel et al. 1997, Youm and Kwon 1999). However, these pre-decided (off-line) control techniques have disadvantages: (1) the output voltage is very much distorted by nonlinear loads, e.g. by diode rectifiers with capacitive filters, and this represents a fundamental feature for this kind of load; (2) the response time of the voltage regulation usually takes a few cycles for sudden application or removal of full load. Another approach is real-time waveform feedback control, such as time-optimal response or instantaneous feedback control (IFC) (Kawamura et al. 1984, Khanniche and Lake 1994), which overcomes the above-mentioned demerits and is quite simple to implement. However, this real time-control has other disadvantages: (1) high switching frequency is required for this scheme to achieve low THD; (2) harmonic frequencies are spread over a wide range around the average switching frequency. The need for high dynamic performance and excellent static regulation of the load voltage has stimulated considerable research activity. The latter approach technique (Gokhale et al. 1985, Kawamura et al. 1986, 1988, Kwabata et al. 1990, Hua 1995) has been already used for the PWM inverter. That is why the control principle is well described in Malesani (1999) and Cho et al. (1999). But up to now there has been no publication on this type of control applied to the PWM ac chopper. Thus the principal contribution of this paper is the development of the technique for the PWM ac chopper. For this purpose, a novel deadbeat control technique has been developed. The PWM ac chopper system is converted into a discrete time system, and state feedback output deadbeat control is applied. The PWM is determined at every sampling instant by the microprocessor on the basis of both output measurements and reference. This type of approach has a very fast transient response and compensates effectively for load disturbances. This paper deals with a novel robust deadbeat-based control technique dedicated to PWM ac choppers. Computer simulations are performed to investigate the performance of the proposed technique. Experimental results under various loading conditions have demonstrated that the system performs well. 2.

The chopper-type ac voltage regulator The circuit consists of two ac switches, one connected in series and the other in parallel with the load, as shown in figure 1. When the series switch BS is ON the load voltage is equal to the supply voltage, and when it is OFF the output voltage is equal to zero and the parallel switch BP is turned ON to flywheel the current in the load if it is inductive. Each switch consists of two anti-parallel MOSFETS. When a switching function (figure 2(a)) is applied, the output voltage vL appears in the PWM form at the load terminals (figure 2(b)). The PWM techniques are compared in terms of THDS, L and DFS, L of both input and output sides, of input power factor and control of the fundamental output voltage. These terms are defined as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 THDS, L ¼ IS,2 L IS1, ð1Þ L1 VS1, L1 DFS, L ¼ IS1, L1 IS, L ð2Þ PFS ¼ RL IL2 =VS IS

ð3Þ

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iL

BS

vL

Load

vS

iL

iS

BS

vS

(a) Figure 1.

BP

vL

(b)

Ac chopper circuit. (a) phase angle control; (b) pulse width modulation.


α

a t

0

0.01

vL

0.02

b t

0 0.01

iL

0.02

c t

0

0.01

0.02

iS

d

t

0 0.01

Figure 2.

Load

iS

0.02

Waveforms of (a) switching function; (b) output voltage; (c) load current; (d ) input current.

where: IS, L are the rms values of supply/load current, IS1, L1 are the rms values of fundamental supply/load current, VS is the rms value of supply voltage and RL, LL are load parameters. These PWM waveforms can be obtained by solving vL ðtÞ ¼ !LL

diL þ RL iL ðtÞ dt

ð4Þ

with vL(t) ¼ vS(t) and iS(t) ¼ iL(t).

3.

Control technique

This technique is based on deadbeat control (Gokhale et al. 1985, Kawamura et al. 1986, 1988). The closed loop digital feedback system measures the output and controls the ac chopper switches to generate the required PWM pattern for providing low THDL sinusoidal output voltage. The digital control algorithm is designed to control the pulse width such that the output voltage fits the sinusoidal reference at every sampling instant. Thus, the output voltage is in phase and very close to the sinusoidal reference. Any deviation

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iS BS

vS

iL a

L

v ch BP

a D1

iC vL

C

RL

K

a

RL

b

LF D4

b Continuous-time Discrete -time iC

vS Digital controller Downloaded by [ABDELOUAHAB BOUAFIA] at 09:45 05 April 2013

Figure 3.

D3 CL

RL

D2

b

vL

AC Controller

Rectifier load

A/D Converter

Basic diagram of deadbeat-controlled PWM ac chopper.

of the output voltage from the reference due to load disturbance or nonlinearity is corrected within one sampling interval T. The PWM pattern is determined at each sampling instant by a microprocessorbased system on both output measurements and reference. A low THD sinusoidal output is obtained by using a feedback control technique. A basic block diagram of a deadbeat controller for the PWM ac chopper is shown in figure 3. The chopper, the L-C filter and the load (RL for linear load, ac controller/full-wave rectifier for nonlinear load) are considered as the plant of a closed loop digital feedback system. 4.

Deadbeat control algorithms for a PWM ac chopper

A real-time deadbeat control law has been proposed by Gokhale et al. 1985 for a PWM inverter, in which an output voltage inverter Vin can take three values þE, E and 0 in a three levels scheme (Kawamura et al. 1986) or two values þE and E in a two levels scheme (Hua 1995). But, in the case of the ac chopper, the output voltage vch can take any value, depending on sampling time of VSM sin (!t) or 0 as shown in figure 4. To overcome these disadvantages a new method has been developed. The system equation for the PWM ac chopper and ac filter is: 0 1 0 vL v_L ð5Þ ¼ þ v !2p 2p !p v_L !2p ch v€L pffiffiffiffiffiffiffi 1=ffiffiffiffiffiffiffiffiffi LC where !p ¼p ffi is the angular resonance frequency of the second-order filter, p ¼ ð1=2RÞ L=C , vch is the input filter voltage, vL is the capacitor voltage and v_L its derivative. Defining: 0 1 0 T _ x ¼ ½vL , vL , A ¼ , B¼ ð6Þ !2p 2p !2p !2p the continuous-time domain state (5) can be written as x_ ¼ Ax þ Bvch

ð7Þ

where x is the state variable, A the non-singular state transition matrix and B the input vector. Then the closed-form solution is Zt xðtÞ ¼ exp½Aðt t0 Þxðt0 Þ þ exp ½Aðt ÞBvch ðÞ d ð8Þ t0

153


iC

v ch

iL vL

C

Figure 4.

State model of overall circuit.

T

N=40 k+1

k


Load

L

0

10

Figure 5.

20

30

Sampled reference signal, vref (k) ¼ VrefM sin (2pk / N). T

BP

t0

N 40

BS

T BP

t2

t1

KT

BP

t3

BS

t1

t0

(K+1)T

t2

t3

(K+1)T

KT

∆T(K)

Figure 6.

BP

∆ T(K)

Top: pulse pattern; bottom: filter input voltage.

where x(t0) is the initial state at t ¼ t0. One period of a 50 Hz reference sine wave is divided into N equal intervals of duration T (figure 5). As shown in figure 6, the power switches are turned ON and OFF once during each interval T, such that the filter input vch is VSM sin (!t) and the width T is centred in the interval T. The discrete time system equation with input of figure 6 is derived as follows: Z ðKþ1ÞT XðK þ 1Þ ¼ exp ½ATXðKÞ þ exp½AððK þ 1ÞT Þ Bvch ðÞ d ð9Þ KT

where t0 ¼ KT, t1 ¼ KT þ ðT TðKÞÞ=2, t3 ¼ ðK þ 1ÞT

t2 ¼ KT þ ðT þ TðKÞÞ=2,

For t1 t t2, vch (t) ¼ VSM sin (!t), (9) becomes Z XðK þ 1Þ ¼ expðATÞXðKÞ þ

KTþ TþTðKÞ 2 KTþ TTðKÞ 2

exp½AððK þ 1ÞT Þ Bvch ðÞ d

ð10Þ

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To simplify the integral of equation (10), we can approximate VSM sin (!t) in the interval [t0, t3] by its average value as follows: vch ðtÞ ¼

VSM sinð2pKT=NÞ þ VSM sinð2pðK þ 1ÞT=NÞ ¼ VSM 2

ð11Þ

Where sinð2pKT=NÞ þ sinð2pðK þ 1ÞT=NÞ ¼ 2


Equation (10) becomes T TðKÞ XðK þ 1Þ ¼ exp½ATXðKÞ þ A1 exp A ½exp½ATðKÞ IVSM B 2 ð12Þ pffiffiffiffiffiffiffi Under the assumptions T 2RC, T 2p LC ; ðATÞ2 ðATÞ3 exp ½A:T ffi I þ AT þ þ 3! 2! T TðKÞ T 1 A exp A ½exp½ATðKÞ I ffi exp A TðKÞ 2 2

ð13Þ

After a short calculation equation (12) becomes: XðK þ 1Þ ¼ exp½ATXðKÞ þ VSM exp½AðT=2ÞBTðKÞ

ð14Þ

This is the discrete-time system of (7). Rewriting (14) gives XðK þ 1Þ ¼

11 21

12 g ðKÞ TðKÞ XðKÞ þ 1 g2 ðKÞ 22

ð15Þ

where exp½A:T ¼ ¼

11 21

12 22

T 0 g1 ðKÞ ¼ VSM exp A 2 g2 ðKÞ 2 !p

Taking the first element of (15), the output voltage VL ðk þ 1Þ ¼ 11 VL ðkÞ þ 12 V_ L ðkÞ þ g1 ðkÞTðkÞ

ð16Þ

where v_L ðkÞ ¼ ð1=CÞiC ðkÞ. Equation (16) becomes VL ðk þ 1Þ ¼ 11 VL ðkÞ þ 12 ð1=CÞiC ðkÞ þ g1 ðkÞTðkÞ

ð17Þ

155


The required pulse width T(K ) can be computed to make the output voltage VL[(K þ 1)T ] equal to the desired reference voltage Vref[(K þ 1)T ] at t ¼ (K þ 1)T. Replacing VL (K þ 1) with Vref (K þ 1) in (17) and solving for T (K ) gives TðkÞ ¼ ð1=g1 ðkÞÞðVref ðK þ 1Þ 11 VL ðkÞ 12 ð1=CÞiC ðkÞÞ

ð18Þ

This is the deadbeat control rule for the ac chopper.


5.

Computer simulations

The state equation (5) and the deadbeat control rule (18), derived in } 4, are used for the development of computer simulations. For this purpose the SIMULINK program is used. This technique does not require the input voltage E to be greater or equal to the maximum reference voltage vrefM, as for the inverter. This condition is not necessary for the ac chopper. Since, for this type of converter, the source voltage is sinusoidal similarly to the reference voltage. This feature constitutes an advantage for the ac chopper in comparison with the inverter.

5.1. Linear load The following circuit parameters are used for computing the pulse width T (K ): VSM ¼ 100 V, L ¼ 0.5 mH, C ¼ 800 mF, N ¼ 40, T ¼ 500 ms, VrefM ¼ 60 V, RL ¼ 5 , LL ¼ 10 mH. Figure 7 shows the normalized pulse widths based on real-time computation during a period of time T. It is observed that the value of T/T is always less than unity, and ranges from 0.543 to 0.788. Figure 8(a–d ) shows the steady-state output voltage vch and the input current waveforms and their corresponding spectra. The output voltage vch of figure 8(a) and the ac input current of figure 8(c) present discontinuities during repetitive periods even if the load current becomes roughly sinusoidal as in figure 8(g). This causes the generation of larger harmonics than those of the load current. For any sampling frequency fm, it is observed that the dominant harmonics are around fm ( ¼ 2 kHz) with the orders (N 1) and (N þ 1) as shown in figure 8(b, d ). It means that the harmonic generation in the ac line current depends mainly upon the control variable and not on the load phase angle. In a PWM ac chopper it is required to attach the input filter. Figure 8(e, h) shows the load voltage (THDL ¼ 1.23%), the load current and their corresponding spectra. The simulated output waveforms are very close to sinusoidal waveforms, as shown in figure 8(e, g). From the spectra of figure 8( f, h) it is observed that the loworder harmonics are completely suppressed because they are much lower than those of the input current and voltage. 1

0

U(K) = ∆T(K)/T

t(S) 0

Figure 7.

0.005

0.01

0.015

0.02

Normalized pulse widths during an output cycle.

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24

vch V

a

50

-12

t(S) 80

c

0

0

-50 -100

iS A

12

0.005

0

0.01

0.015

0.02

b

t(S)

- 24

0

12

0.005

0.01

0.015

0.02

d

60

8

40

4


20

N

0 0

10

60

vL V

20

30

40

50

60

70

80

e

20 0 -20

t(S)

-60 80

0

0.005

0.01

0.015

N 0

90

0.02

0

10

20

30

40

60

70

12 iL A 8 4 0 -4 -8 -12 0 12

80

90

g

t(S)

0.005

0.01

0.015

0.02

h

f

60

50

8

40 4

20 0 0

N 4

0

80

N 0

0

40

80

Figure 8. (a, b) Input voltage: waveform and spectrum; (c, d ) input current: waveform and spectrum; (e, f ) load voltage: waveform and spectrum, (g, h) load current: waveform and spectrum.

1.2

VL1/VS

1 0.8 0.6 0.4 0.2

X0

0 0

Figure 9.

0.3

0.6

0.9

1

RMS values of load voltage.

5.1.1. Output characteristics. To investigate the output characteristics of the PWM ac chopper, the variation of rms values of fundamental load voltage VL1, THDL and DFL is shown in figures 9 to 11. Control range of figure 9: the fundamental output voltage VL1 is varied linearly to Vref/VS ¼ X0 through the full control range. Total harmonic distortion (1) (Jang et al. 1995): figure 10 represents the variation of load voltage THDL values with X0. We observe clearly that THDL is very low and approaches zero through the full control range. This confirms the results obtained in figure 8 (e, f ). Distortion factor (2), defined as the ratio of the fundamental current to the total current (Jang et al. 1995), is shown in figure 11. With the proposed deadbeat

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Control for PWM ac choppers 0.1

THDL

X0 0

0

0.2

0.4

0.6

1

0.8

Figure 10. Variation of THDL with X0. 1

DFL


0.5

X0 0 0

0.2

0.4

0.6

0.8

1

Figure 11. Variation of DFL with X0.

VL1 (peak) (V) Phase shift ( ) THDL (%) Tmax (ms) Table 1.

No load

RL ¼ 10

LL ¼ 20 mH

RL ¼ 5 , LL ¼ 10 mH

RL ¼ 5 , CL ¼ 500 mF

60.17 1.041 1.26 355

60.18 1.384 1.72 453

59.72 1.043 0.86 408

59.86 1.418 1.1 394

60.53 1.316 2 467

VL1, phase shift, THDL and Tmax with different linear loads. DF S

1 0.6 0.2 0

X0 0

0.3

0.6

0.9

1

Figure 12. Variation of DFS with X0.

PWM method the load DFL is unity through the full control range. This constitutes the main objective of the control technique. Table 1 illustrates VL1, phase shift, THDL and T(K )max for different linear loads, where the phase shift means the phase angle of fundamental load voltage. 5.1.2. Input characteristics. Figure 12 represents the variation of DFS (2) (Jang et al. 1995). It is observed that this factor rises steeply with X0. Figures 13 and 14 represent the variation of THDS (2) and that of input power factor (3). From figures 13 and 14, there is observed a significant improvement of both THDS and PFS values for X0 in the range [0.6, 1], but on the contrary, for low values of X0, THDS and PFS are significantly worse. That is why an input filter should be installed at the supply source. Figures 15 and 16 show the variation of THDL with L and C filter parameters.

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THDs

0.8

0.4

X0 0 0.1

0.3

Figure 13.

0.7

0.9

Variation of THDS with X0.

PFs

0.8


0.5

0.4

X0

0 0

0.2

0.4

0.6

0.8

1

Figure 14. Variation of PFS with X0. 20

THDL%

15 10 5 L(mH)

0 0.8 L

0.2 L

1.4 L

2L

Figure 15. Variation of THDL with L. 35 THDL% 25 15 5 0

C(µF) 0.1C

0.4C

0.8C

1.2C

1.6C

2C

Figure 16. Variation of THDL with C.

5.2. Nonlinear load 5.2.1. Ac controller load. Simulation parameters are VSM ¼ 100 V, L ¼ 0.5 mH, C ¼ 800 mF, fm ¼ 3 kHz and 6 kHz, VrefM ¼ 60 V, RL ¼ 3.5 . The transient response of the system can be demonstrated by using a triac with rated load. Figures 17 and 18 show the simulated output waveforms for a nonlinear load with firing angles of 45 , 90 and a switching frequency of 3 kHz, 6 kHz. The pure resistive load is replaced with a phase-controlled resistor. A triac, in series with a resistor, is triggered at the firing angles of 45 , 90 every half cycle. In this

159

Control for PWM ac choppers 80 60 V 40 20 0 -20 -40 -60 -80

0

vL

iL

0.005

0.01

N=60, α=45° A 60 THDL=1,5% 40 VLMAX=59,84V 20 0 -20 -40 -60 t[S] 0.015

0.02

80 V 60 40 20

vL

iL

N=60,a =90° THDL=3.25% VLMAX=59,26V

0 -20 -40 -60 -80

A

60 40 20 0 -20 -40 -60

0

0.005

0.01

0.015

t[S] 0.02


Figure 17. Output voltage and load current waveforms.

80 V

60 40 20 0 -20 -40 -60 -80

vL

iL

0

0.005

0.01

A 60 N=120,a =45˚ THDL =1,40% 40 VLMAX=59,78V 20 0 -20 -40 -60 t[S] 0.015

0.02

80 V 60

vL

40 20 0 -20 -40 -60 -80

iL

N=120,a =90˚ THDL = 1,91% VLMAX=59,66

A 60 40 20 0 -20 -40 -60

0

0.005

0.01

0.015

t[S] 0.02

Figure 18. Output voltage and load current waveforms.

N ¼ 60 45 90

N ¼ 120

VL1 peak (V)

THDL (%)

Phase shift ( )

VL1peak (V)

THDL (%)

Phase shift ( )

59.88 59.41

1.51 3.25

1.09 0.85

59.78 59.66

1.41 1.91

0.83 0.66

Table 2.

THDL, VL1 and phase shift for the ac controller.

experiment, a step change from no load to full load occurs at firing instants. As can be seen, the output voltage waveform exhibits only small deviation from the ideal sinusoidal form. The output voltage drops after the firing instant. The worst waveform at the output for a nonlinear load occurred when the firing angle was near the peak, ¼ 90 , of the output. The dynamic performance remained reasonably good. Table 2 illustrates THDL, VL1 and the phase shift with ac controller load under different firing angles. Decreasing the inductance and increasing the capacitance of the output filter can improve the voltage drop at the output (table 3). 5.2.2. Rectifier load. Simulation parameters are VSM ¼ 100 V, L ¼ 0.5 mH, C ¼ 800 mF, fm ¼ 6 kHz, VrefM ¼ 60 V, RL ¼ 3 , LF ¼ 14 mH. Next, we investigate the performance of the ac chopper with a capacitive load. In this experiment, the output of the ac chopper is connected to a bridge rectifier with a capacitor and a resistor as load, connected in parallel to the output. In the simulation, a large capacitor (900 mF, 1800 mF) is used. The output load resistor is adjusted until the output current of the ac power source reaches 37 A and 43 A (peak).

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Filter 1 mH, 400 mF 0.5 mH, 800 mF 0.25 mH, 950 mF


Table 3.

VL1 (peak) (V)

THDL (%)

59.10 59.41 49.49

7.67 2.73 2.58

THDL and VL1 for ac controller with different L-C filters, N ¼ 60, ¼ 90 , RL ¼ 3.5 .

Figure 19. Output voltage and load current waveforms under rectifier load.

Figure 19 summarizes the simulation results when the ac chopper output is connected to a 50 Hz rated bridge rectifier RLCL load with current crest factor CF of 2 and 2.5. This figure indicates that the output voltage waveforms can still maintain a sinusoidal output under a rectifier RLCL load. The result shows that the tracking performance remains satisfactory.

6. 6.1.

Experimental measurements System implementation

The controller discussed so far has been implemented and tested experimentally on a single-phase ac chopper for various types of load. The circuit configuration for a single-phase PWM ac chopper is shown in figure 3. Two measurements are required at each sampling instant (vL, iL). Using these data, the pulse width is computed in real time. The digital controller consists of a microcomputer with a 1 GHz Intel microprocessor and a PCI card interfaced to the microcomputer bus which contains a 16 bit multiplier, an accumulator NCR 45CM16, a programmable interval timer (PIT) 8254, a programmable interrupt controller (PIC) 8259A, a programmable I/O port 8255A, and two 12-bits A/D converters with 2.5 ms time conversion. To execute the control rule, equation (18), a finite computation time CT is required. For instance, at the instant KT, the voltage vL(K ) and iL(K ) are sampled, then the analogue values are converted to digital numbers. Next, the two multiplications and two additions in (18) take another time delay, followed by the execution time of the routine program to compute the pulse width T; defining the computation time as a delay Td, the maximum pulse width tmax in figure 6 is tmax T 2Td. In other words, the duty ratio D1 of figure 6 is 0 D1 (T 2Td )/T. Thus, using this pulse pattern, the maximum output amplitude is limited by D1. The computation time (CT ¼ Td ) of T is approximately

161

Control for PWM ac choppers 55 ms ¼ (T T )/2, 390 ms ¼ T 2CT.

and

therefore

the

maximum

pulse

width

T

is

6.2. Results


To evaluate the performance of the proposed controller, a low-power prototype was constructed and tested. Experiments were carried out for linear and nonlinear loads. 6.2.1. Linear load. The circuit parameters are the same as those in simulation. Figures 20 and 21 show the output voltage vL and the filter input vch, respectively, for a rated resistive load. The voltage waveform vL is nearly sinusoidal as shown in figure 8(e), and vch shows the two-levels PWM pattern. 6.2.2. Non-linear load. To check the transient response of the proposed controller scheme for a non-linear load, the pure resistive load was replaced with a phase – controlled resistor and a rectifier RC load. Figure 22 shows the output voltage and the load current waveforms with a triac firing angle respectively of 45 and 90 . Figure 23 shows the corresponding input filter voltage vch waveform for ¼ 90 . These pictures show the dip in the output voltage at the firing instant, corresponding to an increase in pulse width in vch as shown in figure 23 and the recovery of vL to follow the reference wave. These waveforms indicate that the transient response of the proposed control technique for

Figure 20. Load voltage; N ¼ 40, RL ¼ 5 .

Figure 21. Input filter voltage; N ¼ 40, RL ¼ 5 .

Figure 22. Output voltage and load current waveform for ac controller; N ¼ 40, RL ¼ 3.5 .

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Figure 23. Input filter voltage waveform; N ¼ 40, RL ¼ 3.5 .

Figure 24. Output waveforms under rectifier load at a CF of 2; RL ¼ 3 , CL ¼ 900 mF.

nonlinear load is only about three sampling intervals. Thus very fast response is achieved. A different situation is shown in figure 24, where the plant behaviour in the presence of a distorting load (diode bridge) is considered. Again, the results show a good agreement with the theoretical analysis. 7.

Conclusions

A deadbeat controller for a single-phase PWM ac chopper feeding nonlinear loads has been successfully developed. The GPC approach has been developed to control the ac chopper for tight closed-loop control. Computer simulations are performed to investigate the performance of the proposed deadbeat controller. To verify the proposed scheme, various experiments have been conducted using a prototype system constructed for this study. The results have demonstrated that the system performs well. This control scheme can be easily extended to a three-phase ac chopper. References ADDOWEESH, K. E., and MOHAMADEIN, A. L., 1990, Microprocessor based harmonic elimination in chopper type ac voltage regulators. IEEE Transactions on Power Electronics, 5, 191–200. BOSE, B. K., 1981, Adjustable speed ac drive systems. IEEE Press, 51–57. CHO, J. S., LEE, Y. S., and CHOE, G. H., 1999, Analysis and design of modified dead beat controller for three phase interruptible power supply. International Conference on Power Electronics and Drive Systems. IEEE, UK, pp. 1003–1009. CHOE, G. H., WALLACE, H., and PARK, A. K., 1989, An improved pwm technique for ac chopper. IEEE Transactions on Power Electronics, 4, 496–505. EL-BIDWEIHY, E., EL-BADWAIHY, K., METWALLY, M. S., and EL-EEDWEIHY, M., 1980, Power factor of ac controllers for inductive loads. IEEE Transactions on Industrial Electronics Control and Instrumentation, 27, 39–44. GOKHALE, K. P., KAWAMURA, A., and HOFT, R. G., 1985, Deadbeat microprocessor control of PWM inverter for sinusoidal output waveform synthesis. IEEE PESC, 28–36. HUA, C., 1995, Two-level switching pattern dead beat DSP controlled PWM inverter. IEEE Transactions on power Electronics, 10, 310–317.



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