description and design of ejector transducers with extension nozzles for linear measurements

8/12/2019 Description and Design of Ejector Transducers With Extension Nozzles for Linear Measurements

1/5

Damping of Transient Oscillations on the Output LC Filter ofPWM. Inverters by Using a Virtual Resistor .

Pekik Argo Dahono', Yogi Rizkian Bahar',Yukihiko S ato2, and Te ruo Kataoka3(' Department of Electrical Engineering, Bandung Institute of Technology, Indon esiaEmail :[email protected]

(* Departmentof Electrical and Electronic Engineering, Tokyo Institute ofTechno logy, JapanEmail :[email protected](3 Department of Electrical Engineering, okyoDenki University, JapanEmail : [email protected]

Abstract-This paper presents a method to damptransient oscillations on the output LC ilter of PWMinverters by using a virtual resistor. A virtual resistor isan additional control algorithm that simulates the rolesof a resistor in the output LC ilters. Because no realresistor is used, the oscillations can be dampedeffectively without sacrificing the power efficiency. Theimplementation of the virtual resistor is determined byhow the resistor is connected to the LC filter.Experimental results are included to verify the proposedmethod.1 Introduction

An output LC filter is commonly used in PWMinverters to reduce the prod uced output harmonics. Inorder to minimize the output harmonics, the LC filteris usually designed to have a resonant frequency thatis much lower than the lowest harmonic frequencyand is also designed to hav e a high qua lity factor (Q-factor). With such a design, however, the LC filterwill be large and expensive. Moreover, a large LCfilter that has a high quality factor will result in anoscillatory transient response. Because the damping isvery low, the oscillations may exist continuously andthe output waveforms of the inverters will be badlydistorted instead of improved. Several methods toimprove the performance of PWM inverters havingan output LC filter were proposed in the literature[11-[5]. Though these methods may produce excellentresults, the methods are usually quite complicated toimplement.Damping a transient oscillation in an LCcircuit by u sing a resistor is well understood by an yelectrical engineers. Because of excessive power lossin the resistor, however, this method is impracticalespecially in high-power applications. In this paper, amethod to damp the transient oscillations on theoutput LC filter of PWM inverters by using a v irtual

0-7803-7233-6/01/$10.0002001 IEEE.

resistor is proposed. A virtual resistor is n additionalcontrol algorithm that simulates the roles of a resistorin an LC filters. Because no real resistor is used, theefficiency of the converters is not sacrificed. Theadditional control algorithm that is used to simulatethe resistor is determined by how the resistor isconnected to the LC filter. The resistor can beconnected either in series to or in parallel with theinductor or capacitor of the filter. A comparisonamong several possible connections is presented inthis paper. Experimental results are included to showthe validity of the proposed concept.

2 Damping of Transient Oscillations by Usinga Resistor

Fig. l (a) show s a schematic diagram of single-phasePWM inverter having an output LC filter. It isassumed that the output voltage of the inverter(voltage across the capacitor) is controlled by using asimple PI voltage controller. The load is treated as adisturbance and represented as a current source. Thedc voltage source is assumed constant and no ripple.Fig. l( b) show s the associated block diagram .,Fig. 2 shows how a resistor can be connected tothe LC filter to damp the transient oscillations. Theblock diagrams those showing the effects of res istorin the LC filter are also shown in this figure. Theeffectiveness of a resistor in damping a transientoscillation is well understood and do not need anyadditional explanations. The power loss in theresistor, however, prevents the use of this approach inpractices especially in large power applications. Howto replace the resistor by using a virtual resistor isdiscussed in the n ext section.

403
mailto:[email protected]:[email protected]:[email protected]


2/5

Modulator&Gate SignalGenerator

( 4 (b)Fig.1 (a) Schematic diagram of PWM inverter having n output LC filter. (b) Block diagram.

R

Fig 2. Four possible connections of resistor in the LC filter nd the associatedblock diagrams.

404


3/5

3 Implementation f Virtual ResistorBy using the block diagrams in Fig. 2 we knowwhat is the role of a resistor in damping the transient

oscillations. The block diagrams in Fig. 2 can bemanipulated without changing the behavior of thesystem. Manipulating the block diagrams in Fig. 2into the ones as shown in Fig. 3can derive therequired virtual resistors. Because the system in Fig.3 is just manipulation of the system in Fig. 2, thetransient behaviors of both systems are the same.Though the transient behaviors of both systems arethe same, the system in Fig. 3has no power lossproblem because no real resistor is used. The requiredadditional algorithm can be called a s a virtual resistoror a los sless resistor.Virtual Rcsislor

I

(a)Virtual Resistor

r

(c)Virtual Resistor

rI4

Fig 3. Virtual resistor simulating the roles of resistorin Fig. 2.

Fig. 3shows that implementations of a virtualresistor that is connected in series to the inductor orcapacitor of the filter needs an additional currentsensor. Implementations of a virtual resistor that isconnected in parallel with the inductor or capacitor ofthe filter needs a voltage sensor. Because a voltagesensor is already exist, an additional voltage sensor isnot required if the resistor is connected in parallelwith the capacitor. The voltage across the inductorcan be measured as the inverter output voltage minusthe capacitor voltage. The inverter output voltage canbe estimated from the inverter output voltagemodulator (the output of the PI controller). Thus,additional voltage sensor is also not required if theresistor is connected in parallel with filter inductor.However, implementations of a resistor that isconnected in parallel with the filter inductor orcapacitor need a differentiator that may bring a noiseproblem. Implementation of a resistor that isconnected in serie s to the filter inductor or capacitordoes not need a differentiator and, therefore, thedesign is simpler. Moreover, a current sensor on thefilter inductor may be required for protection purpose.

4 Experimental ResultsIn order to verify the proposed concept, a smallexperimental single-phase PWM inverter system wasconstructed. Bipolar junction transistor m odules wereused as the inverter switching devices. The switchin gfrequency was fixed at 1.3 kHz. The dc voltagesource is fixed at 100 Vdc. The hndamental outputvoltage frequency is fixed at 50 Hz The filterinductance and capacitance are 12 mH and 200 pF.respectively. For the PI voltage controller, theproportional constant is unity and the integral timeconstan t 0.032 s.Fig. 4 shows the experimental result when aresistive load is used .This figure show s the outputvoltage waveform of the inverter V and load currentwaveform I without using the proposed virtualresistor. It can be seen that the output voltagewaveform is distorted due to the continuousoscillation on the output LC filter. The oscillation isslightly damped by the load resistance and powerlasses in the inverter and the LC filter.Fig. 5 shows the results when a virtual resistor thatis connected in series to the filter inductor is used.Fig. 6 shows the results when a virtual resistor isconnected in parallel with the filter capacitor. Theseresults show that the oscillation is damped effectivelyby the virtual resistor. By using the virtual resistor ,the output voltage waveform is improvedsignificantly. The output voltage THD (totalharmonic distortion) is reduced from 10 to 2 .

405


4/5

. . . . .. .

. . . . . .i

Fig.4. Output voltage and load current withoutvirtual resistor.(Upper : Output voltage : 50 V/div ; mddiv)(Lower :Load current : 5 N d iv ;5mddiv)

Fig.5 Outp ut voltage and load cu rrent with a vi1 tualresistor connected in series to the filter inductor.(Upper :Output voltage : 5 V/div ; mddiv)(Lower :Load current : 5 Ndiv ; mddiv)

Fig. 7 shows the result when the load is replacedby a single-phase diode rectifier with a capacitivefilter. Because the input current of the rectifier isdiscontinuous, transient conditions on the LC filterare generated continuously. Fig. 7 shows that theoutput voltage of the inv erter is badly distorted.Fig. 8 shows the result when a virtual resistor isconnected in series to the filter inductor.Fig.9is theresult when a v irtual resistor is connected in parallelwith the filter capacitor. The proposed virtual resistoreffectively damped the oscillation on the output LCfilter of the inverter. The o utput voltage waveform issignificantly improved by the virtual resistor. TheTHD is reduced significantly from 22 to 6 .

. . . . . . . .. . . .. . . . : : : :. I . . . . .,,, ...,. , . , , . . . , .

Fig.6 Output voltage and load current with a virtualresistor that is connected in parallel with the filtercapacitor.(Upper :Output voltage : 50 V/div ; mddiv)(Lower :Load current : 5 N d iv ; mddiv)

Fig. 7. Output voltage and load current of the inverterwithout virtual resistor.Upper :Output voltage :5 V/div ; mddiv)(Lower :Load current : N d i v ; d d i v )

_. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -c : 7 . . . . _L...;. , I , . . ,,.,, ,,,.:~.,(.;. . . . , . . I . . . JFig. 8. Output voltage and load current with a virtualresistor connected in series to the filter inductor.(Upper :Output voltage : 50 V/div ; d d i v )(Lower :Load current : 5 N d iv ; mddiv)

406


5/5

. . . . . . . . . . . . . . .

. . . . . . . . .

Fig. 9. Output voltage and load current with a virtualresistor connected in parallel with the filter capacitor.(Upper :Output voltage : 50 V/div ; ms/div)(Lower :Load current : 5 A/div ; mddiv)Figs. 10 1 show the experimental results whenthe output voltage reference is suddenly changed. Arectifier with a capacitive filter is used as the load.Figs. I 1 and 12 show that by using the proposed. virtual resistor, no significant oscillations areobserved.

5. ConclusionA new approach to damp transient oscillations on theoutput LC filter of PW M inverters has been proposedin this paper. The proposed method is based on anovel virtual resistor concept. The validity of theproposed concept is verified by experimental results.Applications of the proposed method to other types ofconverters are left for future investigation.References[ I ] T. Haneyoshi, A. Kawarnura, and R. G. Hoe,Waveform compensation of PWM inverter withcyclic fluctuating loads, IEEE Trans. Ind. Appl.,[2] S. Singer, The app lication of loss-free resistors inpower processing circuits, IEEE Trans. PowerElectr., Vol. 6, No. 4 Oct. 1991 pp. 595-600.[3] T. Yokoyama and A. Kawamura, Disturbanceobserver based fully digital controlled PWMinverter for CVCF operation, IEEE Trans. PowerElectr., Vol. 9 No. 5 Sept. 1994 pp. 473-480.[4] M. . Ryan and R. D. Lorenze, A synchronousframe controller for a single-phase sine waveinverter, Conf. Rec. IEEE Pow er Electr. Soc. Ann.

Meet., 1997 pp. 813-819.[5] Y. Y. Tzou, S L. Jung, and H. C. Yeh, AdaptiveRepetitive control of PWM inverters for very low

Vol. 24 NO. 4 July/August 1988 pp. 582-589.

. . . . I . . . . , . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I

I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

. . . . . . . . . . . . . . . . . . . . . . . . . .Fig. 10 Reference (upper) and actual output voltagewaveforms when the reference is suddenlychanged and with a virtual resistor connected inseries to the filter inductor.

30V/div. 20 mddiv.). . . . . . . . . .. . . . . . . . . . . . . .

t 1. . . . . . . . .

t . . . . . . . 1 . . . . . . . . I . . . I . . . . . . . . . . . I . . . . . . .Fig. 1. Reference (upper) and actual output voltage

waveforms when the reference is suddenlychanged and with a virtual resistor connected inparallel with the filter capacitor.30 V/div. 20 msldiv.)

THD AC-voltage regulation with unknown loads,IEEE Trans. Power Electr., Vol. 14 No. 5 Sept. ~1999 pp. 973-981.

407

description and design of ejector transducers with extension nozzles for linear measurements

Documents