Voltaje Source Inverter

8/12/2019 Voltaje Source Inverter

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CURRENT CONTROLLED VOLTAGE SOURCE INVERTER BASED THREE PHASSHUNT ACTIVE POWER FILTER

1NageswaraRao G., 2 Dr. Chandra Sekhar K 3Dr. Sangameswararaju P.,

AbstractIn this paper a three-phase shunt active filter is used to eliminate supply Current harmonics, correct supplypower-factor, for balanced nonlinear load. The active power filter produces equal but opposite harmonic currentsto the point of connection with the nonlinear load. This results in a reduction of the original distortion and correctionof the power factor. A three-phase insulated gate bipolar transistor based current controlled voltage source inverterwith a dc bus capacitor is used as an active filter. The firing pulses to the shunt active filter will be generatedby using sine PWM method. The models for three-phase active power filter controller for balanced and unbalancednon-linear load is made and is simulated using Matlab/simulink software. The proposed active power filter canlargely reduce the total harmonic distortion of current and correct the power factor to unity with balanced andunbalanced nonlinear load

Keywords: Active power filter, Harmonics

I. INTRODUCTIONPower electronic equipment usually introduces

current harmonics. These current harmonics result inproblems such as a low power factor, low efficiency,power system voltage fluctuations and communicationsinterference. Traditional solutions for these problemsare based on passive filters due to their easy design,simple structure, low cost and high efficiency. Theseusually consist of a bank of tuned LC filters to suppresscurrent harmonics generated by nonlinear loads.Passive filters have many disadvantages, such asresonance, large size, fixed compensation characterand possible overload. To overcome thesedisad-vantages, active power filters have beenpresented as a current-harmonic compensator forreducing the total harmonic distortion of the current andcorrecting the power factor of the input source. Fig. 3.1shows the configuration of a three-phase active powerfilter.

A personal computer (PC) based digital controlis used to implement the control scheme. The active

power filter is connected in parallel with a nonlinearload. Its main power circuit is composed of apulse-width- modulation (PWM) converter. The inductorL2is used to perform the voltage boost operation incombination with the DC-link capacitorC 2 and functionsas a low pass filter for the line current of an activepower filter. The principle of operation of an activepower filter is to generate compensating currents intothe power system for canceling the current harmonicscontained in the nonlinear load current. This will thus

result in sinusoidal line currents and unity power factorin the input power system. At present, calculation ofthe magnitude of the compensating currents of anactive power filter is based either on the instantaneousreal and reactive powers of nonlinear loads or theintegrative methods of Fourier analysis Both theseapproaches neglect the delay time caused by low passhigh pass filters when compensating currentcalculations.

The method considered the instantaneous powerdelay caused by the current regulators and DC-linkvoltage feedback circuit and presented a load powerestimation method to improve the dynamic response ofinput power regulatioSn. In this paper, besidesconsidering the current regulator delay and the DC-linkvoltage feedback delay, the low pass filter delay is alsodiscussed. In addition, the design of the cutofffrequency for the low pass filter, current regulators andDC-link voltage regulator are also given. The controlstrategies of the active power filter focus on thecontroller design for both the line current regulators ofthe active power filter and the DC-link voltage regulator.A simplified analytical model of the active power filtersystem is proposed. Using the derived analytical model,analyses of DC-link voltage response and currenttracking capability for the active power filter will beeasier. Applying the proposed control strategy, thecurrent harmonics of a nonlinear load can becompensated quickly and the fluctuations of DC-linkvoltage during transient and steady states areeffectively suppressed. The exclusive features of thispaper are summarised as follows:

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II. ACTIVE POWER FILTER CONTROL

2.1 IntroductionThe active power filter was a recently developed

piece of equipment for simultaneously suppressing the

current harmonics and compensating the reactivepower. Fig 3.1 shows the configuration of a three-phaseactive power filter. A personal computer (PC) baseddigital control is used to implement the control scheme.The active power filter is connected in parallel with anonlinear load. Its main power circuit is composed ofa pulse-width modulation (PWM) converter.

The inductorL2 is used to perform the voltageboost operation in combination with the DC-linkcapacitorC 2 and functions as a low pass filter for theline current of an active power filter. The principle ofoperation of an active power filter is to generatecompensating currents into the power system forcanceling the current harmonics contained in thenonlinear load current. This will thus result in sinusoidalline currents and unity power factor in the input powersystem.

2.2 Principle of OperationThe proposed three-phase active power filter is

shown in Fig. 3.1. It consists of a power converter, aDC-link capacitor and a filter inductor. To eliminatecurrent harmonic Components generated by nonlinear

loads, the active power filter produces equal butopposite harmonic currents to the point of connectionwith the nonlinear load. This results in a reduction ofthe original distortion and correction of the power factor.For the sake of simplicity, in the calculation of reference

currents and description of the control scheme, thereference frame transformation method will be used.

2.3 Compensating Current CalaulationsConsider Fig 1 where and

e a , e b , e c and v af , v bf , v cf represent the phase voltagesof a power system and the input voltages of a powerconverter, i af , i bf , i cf and v dc 2 denote the input currentsof the active power filter and the DC-link voltage,respectively. Neglecting the reactorsLs of the inputpower system, the differential equations of the

three-phase active Power filter in Fig.1 can bedescribed as follows.

L2d dt i af = e a R 2i af v af

... (1)

L2d dt i bf = e b R 2i bf v bf

... (2)

L2d dt i cf = e c R 2i cf v cf

... (3)

C 2 d dt v dc 2 = f a i af + f b i bf +f c i cf ... (4)

Fig. 1. Configuration of active power filter

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Where C 2 is the capacitance of the DC-linkcapacitor,R 2 and L2 are the resistance and inductanceof the active power filter line reactors, respectively,f a , f b , f c are Switching functions, and the possible

values are 0, 13 and

23. For model analysis and

controller design, the three-phase voltages, currentsand switching functions can be transformed to ad-q-o rotating frame. This yields,

x d x q x n

=23

sin c

cos c 12

sin c

23

cos c

23

12

sin c +

23

cos c +

23

12

x a x b x c

... (5)

Where c is the transformation angle of therotating frame andx denotes currents, voltages orswitching functions. From equations(3.1) (3.5), thestate model in the rotating frame Can be written as.

L2d dt i df = e d R 2i df +e L2i qf v df

... (6)

L2d dt i qf = e q R 2i qf e L2i df v df

... (7)

C 2d dt

v dc 2 =32 (f d i df + f q i qf )

... (8)

where

v df = f d v dc 2 ... (9)

v qf = f q v dc 2 ... (10)

e is the frequency of the power system and thesubscripts d and q are used to denote thecomponents of thed - and q -axis in the rotating frame,respectively. Equations.(3.6) (3.8) will be used to

derive the block diagram of the active power fitter andcalculate the input voltage commands of powerconverter.

Let transformation anglee be equal to the angleof phase voltage. Assume that the three-phase voltagesare balanced. This yields the voltage components:

e d = V m ... (11)

e q =0 ... (12)

Where V m is the peak value of the phase voltageof the input power system. Under the above balancedthree-phase voltage condition, the instantaneous realpower p L and reactive powerq L on the load side canbe expressed as:

P L =32 V m i dL... (13)

q L =0 ... (14)

Equations. (3.13) and (3.14) are suitable for bothbalanced and unbalanced loads. When the phasevoltages of power system are balanced,p Land q Ldepend only on i dLand i qL, respectively. For a fullyharmonic-current compensated active power filter

system, the instantaneous real powerp s and reactivepowerq s from the power system can be expressed as:

p s =32 V m i 1... (15)

q s =0 ... (16)

Where the fundamental component of the loadcurrent i 1 can be obtained from thed -axis currenti dLby means of a low pass filter. The corresponding

reference currents, i df

and i qf

of the active power filterin the rotating filter are.

i df = i 1 i dl ... (17)

i qf = i ql ... (18)

Equations (3.17) and (3.18) are obtained from theproposed novel calculation method for referencecurrents of the active power filter by using the loadcurrent feedback, reference frame transformation and adigital low pass filter. It is noted that the referencecurrents can be obtained simply by subtracting thefundamental component from the measured loadcurrents regardless of whether the load is balanced ornot.

2.4 Power Converter Control:To reduce the DC-link capacitor fluctuation

voltages and compensate the system loss, aproportional-integral controllerG DC (S ) is used in theDC-link voltage control loop. As a result, the d-axis

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reference current of the active power filter has to bemodified to:

I df = I 1 I dl +I dc ... (19)

I dc = G dc (S ) (V dc 2

V dc 2)... (20)

Where I dc is the current command of the DC-link

voltage regulator,V dc 2 and V dc 2

are the command andfeedback of the DC-link voltage, respectively. Thevariables in capitals represent the Laplace transformsof the corresponding variables in the time domain. Theblock diagram ofd- and q -axis reference currents of anactive power filter are shown in Fig. 3.2, where thevoltage detection represents the Dclink voltagedetecting circuits.

The input voltage commands,V df and V af of thepower converter can be obtained by using equations.

This yields: nV df = V m R 2I df + e L2 I af U df

... (21)

V df = R 2 I qf e L2I df U qf ... (22)

Where U df and U qf are the voltage commands ofcurrent regulators of an active power filter

Fig. 2 Block diagram of d- and q-axis referencecurrent of active power filter.

It is seen from equations. (3.21) and (3.22) thatthe cross coupling termse L2I df , and e L2I qf exist inthe d-q current control loops. To decouple thed-q current loops and simplify the control scheme, thevoltage de couplers can be designed as follows:

U df = G df (S ) (I df I df ) ... (23)

U qf = G af (S ) (I qf I qf ) ... (24)

Where G df and G qf are the proportional-integralcontrollers gain ofd- and q -axis current control loopsof the active power filter, respectively. The blockdiagram of thed-q current control loops can be derivedfrom equations. (3.6)-(3.8) and (3.21)-(3.24) as shown

in Fig 3.3. Applying the inverse transformation of therotating frame, the three-phase input voltage commandsand of the power converter can be obtained as

Fig. 3 Control block diagram ofd and q axiscurrent controllers of active Power filter.

v af

v bf

v cf

=23

sine

sin e

23

sin e +23

cos e

cos e 23

cos

e +23

1

1

1

v df

v qf 0

... (25)

The output for three-phase input voltagecommands V af

, V bf and V cf

can be_obtained throughthe input/output (o/p ) interfaces of a personal computer.These commands are then compared with a 10khztriangular-wave carrier to produce the switching patternfor the IGBT devices.

III. MODEL ESTABLISHMENT AND STABILITYANALYSIS:

The analytical model for the active power filtercan be established as shown in Fig.4. It consists of acalculation circuit for the reference currents, a DC-linkvoltage regulator and a simplified model for the relationbetween reference and real currents of the activepower filter. Based on the analytical model, thefollowing design of the proportional-integral controllerparameters, K Pdc and K Idc and of the DC-link voltageregulator and analysis of the DC-link voltage responseare given. From Fig.4.5, the closed-loop transferfunctions can be derived as:

)( sG df

2 R

2 Le

2 Le

2 R

22

1sL R +

)( sGqf

d F 2

3

qF

2

3

2

1sC

2 Le

2 L

e

22

1sL R +

*

df i

df i

qf i

*

qf i

+

+

+

+

E d= Vm E d= V m

E q = 0 E q = 0

+

*

df V

df V

*

qf V qf V

2dcV

A c t i v e p o w e r fi l t erM o de l

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Fig. 4. Analytic model for active power filter

I df (S )I dL (S ) =

2 (1 +sT dc )C 2T 2s 2(1 +sT a ) (S )

... (26)

V dc 2 (S )I dL (S )

= 3 (1 +s T dc )F d T a s 2

(1 + sT a ) (S )... (27)

I qf (S ) = 11 + sT f

... (28)

V dc 2 (S )I qL (S )

= 3 (1 +sI dc ) F q s

(S )... (29)

Where F d

and F q are the Laplace transforms of

f d and f q respectively, while the symbol (S ) is thecharacteristic polynomial which can be expressed as

(s ) =2C 2T f T dc s 4+2C 2 (T f +T dc ) s 3 +

2C 2s 2 +3 F d Pdc s +3F d K Idc ... (30)

The DC-link voltage variation is imposed basicallyby i df because the switching function in the d-axiscomponent is much greater than that of the q-axis, i.e.f d >> fsubq in addition, since the voltage drop acrossthe inductors L2 of an active power filter is small ascompared to the phase voltage magnitudeV m theinductor voltage ofL2 can be neglected. This yieldse d = V df and from equations. (3.9) and (3.11)F d isobtained a

F d = V m V dc 2... (31)

Substitution of equation. (4.13) in to equations.(4.8), (4.9) and (4.12), the closed-loop transferfunctions and the characteristic polynomial can bewritten, respectively, as

I df (S )I dL (S ) =

2 (1 + sT dc ) C 2 V dc 2T a S 3(1 + sT a ) (S )

... (32)

V dc 2 (S )I dl (S ) =

3 (1 + s T dc ) V m T a S 2(1 + sT a ) (S )

... (33)

(S )=2 C 2V dc 2T f T dc s 4 +2C 2 V dc 2 (T f + T dc ) s 3

+2C 2V dc 2s 2 +3C m K pdc s +32C 2V m K Idc ... (34)

Assume that the steady-state value of the DC-linkvoltage is equal to the DC-link voltage command,V dc 2 = V dc 2. By using Routh-Hurwitz criterion, it iseasy to find that the DC-link voltage regulatorparameters, an K Idc must satisfy the following relationsfor stable operation.

d csT +11

sK

K Idc p dc +

2d cV

*2d cV

'2d cV

+ d c I

asT +11

1

f sT +11

f sT +11

d F 23

qF 23

2

1sC

*d f I

*

q f I

d f I

q f I

+

+

2d cV

d L I

q L I

+

+

+

1 I

L ow p ass fil te r

R e fe re nc e c ur re nt c al cu la to r

C u r r e n t r e g u l at o r & a c t i v e p o w e rF ilt er m od el

Fig. 5. Total control block of proposed system

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K Pdc

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