A Digital Control Technique for a single phase PWM inverter.pdf

672

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998

Letters to the Editor

A Digital Control Technique for a

Single-Phase PWM Inverter

K. S. Low

Abstract— This paper describes the closed-loop control of a single-phase

pulsewidth modulated (PWM) inverter using the generalized predictive

control (GPC) algorithm. This approach determines the desired switching

signals by minimizing a cost function that reduces the tracking error

and the control signals. Experimental results have demonstrated that the

prototype system performs well.

Index Terms— Digital control, pulsewidth modulated inverters.

Fig. 1.

The overall experimental setup.

I. I NTRODUCTION

Uninterruptible power supplies (UPS’s) are used in many industrial

systems to reduce power line disturbances and interruption. For

critical loads, such as communication systems in the airport, medical

equipment in the hospital, workstations in the computer centers, etc.,

a highly reliable and stable voltage supply is required. One of the

important mechanisms of the UPS is to convert the dc voltage of the

battery to sinusoidal ac output through an inverter LC lter block.

To achieve the desired dynamic response and attain good robustness

with respect to disturbances or parameter variations, various advanced

control techniques have been applied to control the inverter [1]–[4].

In this letter, we propose a new approach using the generalized

predictive control (GPC) scheme. The main characteristic of the

proposed control scheme is that it employs the receding-horizon

strategy [5]. Based on the system model, the GPC scheme predicts

the output of the plant over a time horizon based on the assumption

about future controller output sequences. An appropriate sequence

of the control signals is then calculated to reduce the tracking error

by minimizing a quadratic cost function. This process is repeated

for every sample interval. Thus, new information can be updated at

every sampling interval. Due to this approach, it gives good rejection

against modeling errors and disturbances.

The GPC scheme has been used successfully in many applications,

especially in the process control industries, such as steel casting,

glass processing, oil renery, pulp and paper industries, etc. In this

letter, we explore its application in the control of the inverter. Some

experimental results of a prototype system are demonstrated.

its derivative, i.e.,

z(t)= V o

(1)

V o

Then, the system in Fig. 1 can be modeled using the following

second-order state-space model:

z(t)=az(t)+bu(t)+h(t)

(2)

y(t)=cz(t)

(3)

where

a =

; b =

;

di o

ri o

h(t)=

;

c =[10]:

In (2), u is the input voltage and i o is the output current. By treating

the disturbance as an unmeasurable variable, the discrete-time state

model of the system can be expressed as

z(kT + t)=Gz(kT)+Hu(kT)

(4)

where T is the sampling time of the system, k is the discrete-time

index, and

G = e a T ;

e a d b:

H =

(5)

is the difference operator, such that

z(kT)=z(kT) z(kT T )

(6)

II. T HE M ODEL OF THE S YSTEM

The block diagram of the system is shown in Fig. 1. It consists of a

single-phase full-bridge inverter with an LC output lter. The inverter

switching sequence is controlled by a digital signal processor (DSP),

such that the output voltage follows the desired sinusoidal waveform.

The resistor r in the circuit is the equivalent series resistor (ESR) of

the inductor. The ESR of the capacitor is neglected in the circuit, as

it is small. Dene the state variables as the output voltage V o and

u(kT)=u(kT) u(kT T ):

(7)

To eliminate steady-state error, the system (4) is augmented to the

following new system:

z(kT + T )

V o (kT)

G 0

z(kT)

V o (kT T )

+ H

u(kT):

(8)

Dene

z(kT)

V o (kT T )

X(kT)=

Manuscript received April 21, 1997; revised September 24, 1997. Abstract

published on the Internet May 1, 1998.

The author is with the School of Electrical and Electronic Engineering,

Nanyang Technological University, Singapore 639798.

Publisher Item Identier S 0278-0046(98)05690-1.

Then, (8) can be expressed as

X(kT + T)=GX(kT)+Hu(kT)

(9)

0278–0046/98$10.00

1998 IEEE

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998

673

(a)

(b)

Fig. 2. Experimental result under rated load. (a) Output voltage (vertical:

25 V/div; horizontal: 5 ms/div). (b) Harmonic spectrum of (a) (vertical: 1

percent/div; horizontal: 100 Hz/div).

(b)

Fig. 3. Experimental result under triac load. (a) Output voltage (vertical:

25 V/div; horizontal: 5 ms/div). (b) Harmonic spectrum of (a) (vertical: 1

percent/div; horizontal: 100 Hz/div).

where

Denoting V o (kT + jTjkT) as the prediction of V o (kT + jT) at

time kT; the controller gains can be obtained by minimizing the

following cost function:

G = G 0

and H = H

The output variable now becomes

u(kT)=CX(kT)=V o (kT)

kV o (kT + jT) V o (kT + jTjkT)k 2 + ku(kT)k 2

J c =

(10)

j=1

(12)

where

C =[101]:

with respect to u: The parameter N y in (12) is known as the

prediction horizon. It is dened as the interval over which the

tracking error is minimized. The control weighting factor is used

to penalize excessive control activity and to ensure a numerically

well-conditioned algorithm. In this paper, N y and are chosen as 25

and 1, respectively. Their choices affect the dynamics and robustness

of the system. The selection criteria are beyond the present scope of

this letter.

III. C ONTROLLER D ESIGN

To develop the GPC controller for the inverter, we employ the

receding-horizon control strategy. In this strategy, a sequence of

future control signals is calculated by minimizing a cost function

dened over a prediction horizon. However, only the rst element

of the future control signals is applied to the system. At the next

sampling interval, the control calculation is repeated again. In this

letter, we dene the control law as

u(kT)=K 1 V o (kT)+K 2 X(kT)

IV. E XPERIMENTAL R ESULTS

To investigate the effectiveness of the proposed scheme in con-

trolling the inverter, a DSP board (TMS320C31) is used to realize

the controller in real time. The DSP board uses a slave processor

TMS320P14, which is capable of generating a 10-b pulsewidth modu-

(11)

where K 1 and K 2 are the controller gains, and V o

is the reference

output voltage.

674

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45, NO. 4, AUGUST 1998

On the ZVT-PWM C uk Converter

lated (PWM) waveform with a switching frequency of 25 kHz. As the

controller requires approximately 50 s for execution, the sampling

period is set to 80 s, resulting in two PWM pulses per controller

output. The lter is designed to have a cutoff frequency of 1.8 kHz.

The inverter is designed to produce a sinusoidal voltage of 100 V

(pp) at 50 Hz with a rated current of 5 A (pp). In the experiment,

the dc-link voltage is 60 V. Fig. 2(a) shows the experimental results

of the output voltage under rated load. The corresponding harmonic

spectrum is depicted in Fig. 2(b). The results show that the harmonic

distortion is less than 1%. To study the transient response of the

proposed scheme, a nonlinear load using a triac with rated load is

connected. Experimental results are demonstrated in Fig. 3. In this

case, a ring angle of 60 has been used. Thus, no load is connected

from 0 to 60 and a full load is connected from 60 to 180 .

Similarly, the same loading condition is applied in the negative cycle.

In spite of the rough load condition, the results show that the harmonic

distortion is still less than 2%, and the performance remains good.

Ching-Jung Tseng and Chern-Lin Chen

Abstract— A modied zero-voltage-transition pulsewidth modulation

(ZVT-PWM) C uk converter is proposed in this letter. Better robustness,

smaller minimum duty ratio, and lower turn-on loss are obtained in

this converter. No additional component is needed compared with the

conventional ZVT-PWM C uk converter.

Index Terms— Converters, pulsewidth modulation, switching circuits.

I. I NTRODUCTION

Various soft-switching techniques have been proposed to reduce

switching losses and EMI noises of pulsewidth modulation (PWM)

converters in recent years. Zero-voltage-transition (ZVT)-PWM con-

verters [1], [2], which achieve zero-voltage switching (ZVS) for both

the transistors and the diodes, while minimizing their voltage and

current stresses, are deemed desirable. However, circuit operations

are easily interfered with by the nonidealities of circuit components.

The minimum duty ratio is also limited by the discharging time of the

resonant inductor. A modied ZVT-PWM Cuk converter is proposed

to improve these disadvantages of the conventional ZVT-PWM Cuk

converter [1], shown in Fig. 1.

V. C ONCLUSIONS

A GPC algorithm has been developed to control a single-phase

inverter. The approach uses the receding-horizon strategy. The gains

are obtained by minimizing a cost function, which can be adjusted by

changing the prediction horizon and the control weighting factor. The

experimental results have demonstrated that the proposed controller

performs well under various loading conditions.

II. T HE M ODIFIED ZVT-PWM C UK C ONVERTER

The circuit diagram and key waveforms of the modied ZVT-

PWM Cuk converter are shown in Fig. 2. The modied converter

differs from the conventional one by connecting the D)2 anode to the

output terminal instead of to the D 1 anode. The following benets

are obtained.

R EFERENCES

[1]

S. L. Jung and Y. Y. Tzou, “Discrete sliding-mode control of a PWM

inverter for sinusoidal output waveform synthesis with optimal sliding

curve,” IEEE Trans. Power Electron. , vol. 11, pp. 567–577, July 1996.

[2]

M. Carpita and M. Mar.esoni, “Experimental study of a power condition-

ing system using sliding mode control,” IEEE Trans. Power Electron. ,

vol. 11, pp. 731–742, Sept. 1996.

Better robustness : In the conventional converter, voltage across

the auxiliary diode D 2 is zero when the main diode D 1 is

conducting. D 1 and D 2 are essentially in parallel. D 2 may

be easily turned on by small disturbances and, thus, a certain

percentage of current will ow through it. This phenomenon

may generate serious reverse-recovery loss when the auxiliary

switch S 2 turns on unless an additional saturable reactor is

placed in series with the resonant inductor. In the modied

ZVT-PWM Cuk converter, D 2 is reverse biased by the output

voltage when D 1 is conducting. It prevents D 2 and L r from

conducting and, thus, avoids the reverse-recovery loss.

[3]

A. Kawamura, R. Chuarayapratip, and T. Haneyoshi, “Deadbeat control

of PWM inverter with modied pulse patterns for uninterruptible power

supply,” IEEE Trans. Ind. Electron. , vol. 35, pp. 295–300, May 1988.

[4]

A. V. Jouanne, P. N. Enjeti, and D. J. Lucas, “DSP control of high-power

UPS systems feeding nonlinear loads,” IEEE Trans. Ind. Electron. , vol.

43, pp. 121–125, Feb. 1996.

[5]

H. Demircioglu and D. W. Clarke, “Generalized predictive control with

end-point state weighting,” Proc. Inst. Elect. Eng. , vol. 140, pt. D, no.

4, pp. 275–282, 1993.

Smaller minimum duty ratio: In ZVT-PWM converters, the

minimum duty ratio can be dened as the minimum time ratio

that either S 1 or S 2 is on. In the conventional ZVT-PWM Cuk

converter, I Lr has to discharge to zero before S 1 turns off to

prevent D 2 and L r from conducting for the entire switching

period. Otherwise, the same switching loss as mentioned above

will be generated. The minimum duty ratio of the conventional

Manuscript received May 26, 1997; revised February 11, 1998. Abstract

published on the Internet May 1, 1998.

The authors are with the Power Electronics Laboratory, Department of

Electrical Engineering, National Taiwan University, Taipei, 10764 Taiwan,

R.O.C.

Publisher Item Identier S 0278-0046(98)05691-3.

0278–0046/98$10.00

1998 IEEE

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