a current control method for phase-controlled rectifier

8/8/2019 A Current Control Method for Phase-controlled Rectifier

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A CURRENT C ONTROL METHOD for PHASE-CONTROLLED RECTIFIER

THAT HAS AN LCLFILTER

Burhanuddin Halimi' and Pekik Argo Dahono*

Department of Electrical Engineering

Bandung Institute of Technology

J1. Ganesa No. 10, Bandung 40132Telp. 62-22-25033 16 Fax.62-22-2508132

' [email protected] tb. ac.d

[email protected]

'

Abstract - A new current control method for three-phase phase-eontrolled thyristor rectifier that hasan LCL filter is proposed in this paper. Theproposed method is based on state feedback an dtracking system. By using this method, the loadcurrent can be controlled with a minimum sensorand the load current state can track the referencewell. Experimen tal results are included to verify theproposed method.

Index Term - Current control, observer, optimalcontrol, tracking system

I. Introduction

In some rectifier applications, such as in the

electrochemical industries and magnet power supplies,a rectifier is usually operated as a dc current sourcewith very low ripple requirement [11-[6]. Because an Lfilter which meets this requirement can become verylarge and impractical, it is often desirable to use a high-order filter, such as an LCL filter [2]-[7].Unfortunately, a high-order filter can make the systemunstable if improperly designed [SI. Various currentcontrol methods for three-phase phase-controlledthyristor rectifiers were published [9]-[ 101. These

methods are usually concentrated on how to design thePI current controller

In this paper, a new current control method for

three-phase phase-controlled thyristor rectifier that hasan LCL filter is proposed. The proposed method isbased on state feedback. In state feedback, there are

some variables that have to be measured. Hence, itneeds sensors as many as the state variables that aremeasured. Therefore, it can make the reliability of thesystem decrease. To solve this problem, the proposedmethod uses an observer to observe the unmeasuredstates. By using an observer, the load current can becontrolled with a minimum sensor, i.e. just one currentsensor. In some specific applications, due to some

environmental constrains, such as high temperature,wet condition, long distance between the rectifier andload, placing the current sensor on the load side isimpractical. In the proposed method, the current sensoris placed directly on the output of the rectifier side

instead of on the load side. Because the sensor is placedon the output of the rectifier, the effect of noise anddelay time on the control signal can be reduced.

Experimental results are included to show the validityof the proposed current control method.

11. Filter .Analysis

In this section, rectifier with an L filter andrectifier with an LCL ilter are analyzed. The analysisrefers to Fig. 1. In this analysis, it is assumed that theload is resistive.

-T u

Rectifier L Filter

(b)

Fig. 1 Rectifier with (a) an L ilter(b) an LCL ilter

0-7803-7233-6/01/$10.00 02001 IEEE. 20



The output voltage of the rectifier in Fig. l (a) can bewritten as :

diov, = rf o+L - RLio

dt

wherer /

Lfi0 : load current

v,

RLIf the current is separated into the average and ripple

component, i.e. io = io + o, 1) can bewritten as :

: resistance of the filter inductor: inductance of the filter inductor

:output voltage of the rectifier: resistanceof the load

- -

v, = r f ( t + s )+ L f ( ~ o + ~ ) + R L b + ~ )

di0At steady stale, he value of L f- s equal to zero.

Therefore, (2) can be witten as :

v, =F,+Lf -+(rfi + R L k

dt

dt

(3)

where V,= (rf +R~Fo.he 1 0 4 current ripple transfer

function can be obtained by using (3), i.e.:

v, L f s + ( r f + R L)(4)

1lo ---

where V, = v, - , is the rectifier output voltage ripple.

By using a similarmanner, the load current rippletransfer function for the case of rectifier with an LCLfilter canbe written as :

-1

LfLoCs3+ {L fC(ro+R L)+L O G fs2+'0 -v,

- _

(5 ){ L f + r f C k o+ % ) + L o b + ( r f + ro+&I

where

r /

L,ro

LOCIf the f d and the second inductor are identical (L, =

Lo = L and r / = ro = r), hen (4)canbe witten as

: resistance of the fmt filter inductor: inductanceof the frst filter inductor: resistance of the second filter inductor: inductance of the second filter inductor: capacitance of the filter capacitor

w i m e r , = 2 r + R LThe bode plots of load current ripple transfer

functionsbased on the same energy stored in the filterare depicted in Fig. 2 . Fig. 2 shows that an LCL filteris better than an L filter on suppressing the high

frequency harmonics . Moreover, itmeans hat to meetthe very low ripple requirement, the LCL filter ismorepractical than the L filter. However, Fig. 2 (b) shows

that the outer LC filter give up to 1SO" additional phasedelay in the system transfer function, and it often giverise to stability problems.

Fig. 3 shows the load current ripple of the systemwith an L filter and with an LCL filter. By using the

same energy storage in the filter, the load current rippleof the systm with an LCL filter is better than of thesystem with an L filter.

kT1111111 I 1 1 1 1 1 1 1 1 II 1 1 1 1 I 1 1 1 1 1 1 1 1 I 11111111 I

111111 I 1 1 1 1 1 1 1 1 I I 1 1 1 1 1 1 1 Id o - r i ~ r - i ~ n n r - ~ i i n n i r - i i i r i n

I 11111111 I I 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 I

10' Id Id 10

I 1 1 1 1 1 1

I I I 11 1

I I 1 1 1 1

I I 1111

I I 1 1 1 1

I I IIIII

I I OIII

I I 11111

I I 1111

I I 1111

J- IL IU- t runj.-+...++m,I 1 1 1 11111

I I 1111

18

Frequency (rad/sec)

(b)

Fig. 2 Bode plot of the load current ripple transferfunction

Fig. 3 Load current ripple ( 2ms/Div, lA/Div)

21



111. A C urrent Control Method For Phase-

Controlled Rectifier That Has An LCL Filter

There are two ways to place the current sensor incurrent control for phase-controlled rectifier that having

an LCL ilter, i.e. on the load side and on the output ofrectifier side. In some specific applications, due to

some environmental constrains, such as hightemperature, wet condition, long distance between therectifier and load, placing of current sensor on the loadside is impractical. In these cases, placing of the currentsensor on the output of the rectifier side directly as

shown in Fig. 4(b) is more practical. Because thesensor is placed on the output of the rectifier, the effectof noise and delay time on the control signal can bereduced.

In control system design, first, it is assumed thatall of states are observable. Therefore, the commonmethod of states feedback analysis can be used in thiscase.

The system of Fig.4 can be expressed in state

space equation as :

x = A , X + B , U + G , X ~ (7)

Y = c,x (8)

where U the output voltage rectifier v,.

t

x = [ iJ vcand the disturbance vector, respectively.WhereiJ :output current of the rectifiervc :voltage of the filter capacitorVO :voltage of the load

io 1 and x d = [ vo 3 are the state vector

In this system, we require that the state x track areference state x, To formulate this problem in term ofstate variables, it is expedient to assume that xd and x,

satisfy following equation:

i d = AdXd (9 )

x r = A J , (10)I--(b)

Fig. 4 Schemes of load current control methods(a) without and (b) with proposed method.

For this case, the state reference is a step reference. So ,matricesAd and A, are equal to zero. At steady state thecurrents on the all of inductors are equal. Therefore, thecurrent reference IR,f. can be used as state reference oni, and io .

The error can be defined as

e = x - x ,

By using (7) and (lo), it can be obtain :

e=f- f , = A , e + E x , + B , u

where

E = [ A , - A , f G ]

and

22



Now, the system can be expressed as :

X =Ax +Bu

y = Ce =Cx

where

I I

l o 01 Fig. 5 Scheme of the observer

In control system design, the problem is to determinethe gain matrixK n a associated feedback law

One of methods that can be used to solve this problemis quadratic optimum control method. In this method,an appropriate performance integral is used to obtainthe optimum gain matrix. The performance is expressedthe integral of quadratic form, i.e.,

For this case, it is desired that the error of all of statevariables is minimum. So, the weighting matrix is ofthe form

By this performance, the normalized state feedbackgain K s given as

K = [K KO] (17)

K = k , K2 K 3l (18)

where

KO [K; K; K; K d ] (19)

For the system under consideration, one of thesystem states is measurable, i.e. the output current of

the rectifier is. Therefore, it must be designed an

observer to estimate the capacitor voltage vc , he load

current io ,and the load voltage v,,.The design of the observer can be based on (7).

Fig. 5 shows the scheme of the observer. In this case,both of inductors are assumed to be identical Becauseaverage output voltage of the rectifier has a linearrelationshipwith the output signal of the controller

(input of the trigger circuit), the signal v, does not needto be measured directly. Thus,only one current sensoris required. The current sensor is used to measure thefirst inductor current i, (output current of the rectifier).The results of the observer are filter capacitor voltage,

load current, and. load voltage

IV.Experimental Results

In order to verify the proposed control method, asmall experimental system was constructed. A three-phase thyristor bridge module was used as the rectifier.The firing signals for the thyristors were generated byusing a dedicated firing signal generator that has alinear relationship between the input signal and outputvoltage of rectifier. The PI controller and the proposedobserver were implemented by using analog IC circuits.These control circuits can be made simple if a powerfulmicrocontroller or DSP s used. The experimental datais shown in the appendix. A variable resistor was used

as the load.The experimental result of the load current control

without the proposed control method is shown in Fig. 6. The current sensor is placed on the load side. Fig.6shows that the system overshoot is quite large when thereference stepped-up and the system tends to divergewhen the reference stepped-down. A large oscillationcan be observed on the load current when the referenceis suddenly changed. The oscillation can only be

reduced by reducing the gain of PI controllers and,therefore, the speed of current controller should bereduced.

The experimental results of the proposed methodare shown in Fig. 7 nd Fig. 8. Fig. 7 shows that whena step reference is used, the proposed method canimprove the system response significantly. The outputcurrent oscillation is significantly damped by theproposed control method. Thus, the speed (bandwidth)of current controller can be increased. For the casewhen a ramp reference is used, the proposed methodcan still maintain the load current to follow the currentreference very well such asshown in Fig. 8.

23



OA

(a) Current reference (a) Current reference (1AiDiv.)

(b) Load current @) Load current (lA/Div.)

Fig 6 Experimental result without the proposedcontroller. (Kp = 0.8, Ki = 0.6,40ms/Div, lA/Div)

V.Conclusion

In this paper, a new current control method forthree-phase phase-controlled thyristor rectifier that hasan LCL filter has been proposed and verified by

experimental results. By using this method, the loadcurrent can be controlled with minimum sensor, i.e. onesensor that placed on the rectifier output directly. Byusing the proposed control method, a large oscillationon the LCL ilter can be damped significantly. In this

method, the system load current state can track thecurrent reference very well. Accuracy of the proposed

observer due to the inaccuracy of filter parameters isunder investigation. .

APPENDIX

Experimental data :

v!,0 l h= 60Voltf =50Hz

L,= Lo = 38 mH

r / = r, = 0.5 ohmc = 1ooouF

I . 1

( c ) Capacitor voltage (lOV/Div.)

I , - I

(d) Load voltage (10 V/Div.)

Fig. 7 Experimentalresultsof the proposed method(Kp = 0.8, Ki = 0.6, ..uhns/Div.)

24



I I

OAi(a) Current reference (1 m i v )

I I

(b) Load current (1Ndiv)

Fig. 8 Experimental result with the proposed method.(Kp= 0.8, Ki= 0.6,40 ms/Div.)

REFERENCES

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[9] R. J. Hill, F. L. Luo, “Stability Analysis of

Thyristor Current Controller”, IEEE TransactionIndustry Application, Vol. 1A-23 No. 4 January-February 1987.

[101F. L. Luo and R. J. Hill, “Fast Response and

Optimum Regulation in Digitally ControlledThyristor Converter”, IEEE Transaction IndustryApplication, Vol. 22, No. 1, JanuaryFebruary1986, pp. 10-17

Raymond J. Yarema, “Subhannonic Ripple

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Precision Programmable Magnet Power Supplyfo r A Wide Range of Magnet Time Constants”,EEE Transaction on Nuclear Science,Vol. NS-28,No. 3, June 1981J. A. Pomilio et al, “A Novel Topology fo r TheBending Magnets Power Supply at LNLS”, IEEETransaction on Nuclear Science, Vol. 39, No.5,October 1992Heinrich et al, “Design and Operation of A 40-

Mw . Highly Stabilized Power Supply”, IEEETransaction on Industry Application, Vol. 32, No.5 , Sept./Oct. 1996Jonathan M. S. Kim and Shashi B. Dewan,“Closed-Loop Voltage Regulation of DualConverters with Circulating-Current Mode, Usedin Four-Quadrant dc Magnet Power Supply”,EEE Transaction on Industry Application, Vol. 27

No.6, Nov./Dec. 1991

B.H.Kwon, “Highly Stable Power Supply UsingDigitally Controlled Phase-Controlled Rectifierand Active Filter”,IEEProc.-Electr. Power Appl.,Vol. 141, No. 5 , Sept. 1994

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a current control method for phase-controlled rectifier

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