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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 12, NO. 2, MARCH 1997 311

Three-Phase Four-Wire ShuntActive Filter Control Strategies

Maurcio Aredes, Student Member, IEEE Jurgen Hafner, and Klemens Heumann, Member, IEEE

AbstractThis paper describes a three-phase four-wire shuntactive power filter using a conventional three-leg converter,without the need of power supply at dc bus. Two approacheshave been developed to control the active filter. Both controlstrategies consider harmonics and zero sequence components inthe voltage and current simultaneously. The first one providesconstant power and the second one sinusoidal current to thesource, even under unbalanced voltage conditions. Simulationresults from a complete model of shunt active filter are presentedto validate and compare the control strategies.

Index TermsActive power filters, active power line condition-ers, FACTS, instantaneous active and reactive power.

I. INTRODUCTION

ACTIVE power filters for three-phase systems withoutneutral conductor have been successfully developed, andnowadays some commercial products are already available.

Although three-phase four-wire active filters have been intro-

duced in the 1980s [1], the development is still in its infancy

and no experimental prototype has been put in operation

outside the universities.

Some researches appoint the four-leg converter topology as

the best alternative to implement a three-phase four-wire active

power filter [2][4]. Alternatively, the authors present here an

interesting solution that uses a conventional three-leg converter

to implement a three-phase four-wire shunt active filter.

The instantaneous power theory ( theory) has been used

successfully to control active power filters for three-phase

systems [5][7]. This theory was extended in [8] and [9] for

applications in three-phase four-wire systems. Here, a critical

comparison between two control strategies that provide load

current compensation including zero sequence components and

considering distorted system voltage is carried out.

The first one, the constant source instantaneous power

strategy, was introduced in [9]. It compensates the current of

a nonlinear load such that the compensated current shall draw

a constant active power from the network, even if the system

voltage is already distorted. However, its dynamics within acomplete simulation model of shunt active filter has not been

reported so far and there are some difficult aspects that should

be evidenced.

The second approach is the sinusoidal source current strat-

egy. It compensates currents of a nonlinear load to provide

Manuscript received January 26, 1995; revised September 6, 1996.M. Aredes is with Cepel-Centro de Pesquisas de Energia Eletrica.J. Hafner and K. Heumann are with Technische Universitat Berlin, Institut

fur Allgemeine ElektrotechnikSekr. E2, 10587 Berlin, Germany.Publisher Item Identifier S 0885-8993(97)01851-6.

sinusoidal, balanced currents to the source, even when the

system voltage is distorted and/or unbalanced.

The performance of both control strategies will be compared

and discussed in details through simulation results from a

complete model of shunt active filter including the three-

leg converter and its pulse width modulation (PWM) current

control.

II. PWM CONVERTERS FOR

THREE-PHASE FOUR-WIRE SYSTEMS

In this section, two configurations of Voltage Source Invert-

ers (VSI), which can be used in three-phase four-wire systems,will be presented. The fundamental difference between the VSI

of Fig. 1(a) and (b) is the number of power semiconductor

devices. A conventional three-leg converter is used in Fig. 1(a)

and the ac neutral wire is connected directly to the midpoint ofthe dc bus, while in Fig. 1(b) the ac neutral is provided through

a fourth leg. Since the configurations have PWM current

control, they behave as controlled current source. The ac

currents generated by the VSI have some high-order harmonics

at the switching frequency, which can be easily filtered using

a small passive filter ( and in Fig. 1). Ideally, the currents

track accurately their references .

The controllability of the four switch-leg inverter topol-

ogy [Fig. 1(b)] is better than the split-capacitor inverter

topology [Fig. 1(a)] [2], [3]. However, the conventional three-

leg converter is preferred because of its lower number of power

semiconductor devices [10], [11]. The problems related to the

dc capacitor voltage control by using the topology of Fig. 1(a)

will be discussed below and a simple control circuit will be

proposed later.

Fig. 2 shows a typical motion of the -phase VSI current

controlled by a hysteresis-based PWM current controller. If the

current references are assumed to be composed from zero

sequence component, the line currents will

return through the ac neutral wire. This forces, in the split-

capacitor inverter topology, the current of each phase to floweither through or through and to return through the ac

neutral wire. The currents can flow in both directions through

the switches and capacitors. Table I summarizes the conditions

that cause voltage variations in the capacitors and

for a zero sequence current reference in the split-capacitor

inverter topology.

When rises and decreases, but not with

equal ratio because the positive and negative values of

are different and depend on the instantaneous values of the ac

phase voltages. The inverse occurs when . The dc

08858993/97$10.00 1997 IEEE


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312 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 12, NO. 2, MARCH 1997

(a)

(b)

Fig. 1. Three-phase four-wire PWM converters: (a) three-leg converter(split-capacitor inverter topology) and (b) four-leg converter (fourswitch-leg inverter topology).

Fig. 2. Hysteresis-band PWM current control.

TABLE IVARIATION CONDITIONS FOR THE C APACITOR VOLTAGES

AND

voltage variation depends also on the shape of the current

reference and the hysteresis bandwidth. Therefore, the total dc

Fig. 3. Three-phase four-wire shunt active power filter using a conventionalthree-leg converter.

voltage, as well as the voltage difference ( ) will

oscillate not only at the switching frequency, but also at thecorresponding frequency of that is being generated by the

VSI.

In the example given in Fig. 2, the phase current causes

voltage variations such that at the end of the period the voltage

is higher and lower. If a dynamic offset level is

added to both limits of the hysteresis-band, it is possible to

control the capacitor voltagedifferenceand to keep it within an

acceptable tolerance margin. For instance, a negative offset in

Fig. 2 counteracts the above voltage variation. Later, a simple

control scheme will be proposed to do it.

III. SHUNTTHREE-PHASE FOUR-WIRE ACTIVE FILTER

The shunt three-phase four-wire active power filter con-

figuration that will be explored in this paper is presented

in Fig. 3. It is composed from a conventional three-leg VSI

with a dynamic hysteresis-band PWM current control and an

active filter controller that realizes an instantaneous control

algorithm. The inputs of this controller are the instantaneous

phase voltages and line currents of the load. Its outputs are

the instantaneous three-phase current references and

. The voltage regulator supervises the dc capacitor voltages

and provides two control signals, and , as shown in

Fig. 3. The signal compensates for losses in the PWM

converter, which tends to discharge the dc capacitors and

. The signal is the dynamic offset level used to controlthe capacitor voltage difference, as will be seen later.

IV. SHUNT ACTIVE FILTER CONTROL

To control the active filter, two approaches are consid-

ered: 1) the constant source instantaneous power strategy

that provides constant real power to the source, even under

unbalanced voltage source, and 2) the sinusoidal source cur-

rents strategy that provides sinusoidal currents to the source,

even under unbalanced voltage source. In both strategies the

whole zero-sequence current of the load is compensated, but

it is impossible to satisfy simultaneously both conditions:


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AREDES et al.: THREE-PHASE FOUR-WIRE SHUNT ACTIVE FILTER CONTROL STRATEGIES 313

sinusoidal currents and constant power at the source if the

system voltage is unbalanced and/or distorted.

A. Constant Source Instantaneous Power Strategy

The physical meaning of the instantaneous active and re-

active power ( - theory) will be briefly summarized below

for better understanding the optimal load flow conditions that

guides the realization of this control strategy.The active filter controller of Fig. 3 uses the - - transfor-

mation and the instantaneous power defined in this reference

frame [5][7]. The instantaneous voltages and currents of a

nonlinear load are transformed into the - - axis by

(1)

(2)

where and are phase voltages and and are

line currents.

The real power , the imaginary power and the zero

sequence power are defined as

(3)

The physical meaning of these instantaneous powers is

detailed in [8] and [9], and Fig. 4 summarizes those concepts.Three points should be remarked.

The total instantaneous energy flow per time unit, that

is, the instantaneous active three-phase power is always

equal to the sum of the real power and the zero-sequence

power.

The zero-sequence components of voltages and currents

do not contribute to the instantaneous powers and .

The imaginary power represents an energy that can

be constant or not and is being exchanged between

the phases of the system. This means that does not

contribute to the energy transfer between source and loadat any time.

An optimal power flow can be provided to the source,

even under unbalanced and nonsinusoidal voltage conditions.

This occurs when the active filter compensates the powers

(alternating part of the real power), and of

the load. Fig. 5 shows the optimal power flow in terms of

- - coordinates. It shows that the source supplies only the

averagereal power to the load and the averagereal power

to the active filter. The additional power is equal to the

sum of , to cover the converter losses and , to provide

energy balance inside the active filter. If an active filter is

Fig. 4. Physical meaning of the instantaneous powers defined in the - - reference frame.

Fig. 5. Optimal power flow related to the - - reference frame.

used for compensating , it has to compensatefullythe power

, because it is impossible to produce separately

from [9]. The zero sequence power that the active filter

supplies to the load can be taken as a balanced real power

from the source, since it is always possible to generate

with , even under nonsinusoidal conditions.

The entire control block diagram of the three-phase four-

wire shunt active filter is presented in Fig. 6. The control

circuit as shown in this figure realizes the constant source

instantaneous power strategy. There are two shaded areasinvolving the 800-Hz cutoff frequency low-pass filters and the

low-pass filter for the power . These areas will be changed

in the next section to adapt the circuit to the sinusoidal source

current strategy.

Unfortunately, the phase voltages could not be used directly

in the control because of instability problems. It was verified

that resonance between the source impedance and the small

passive filter ( and in Fig. 3) can appear. Therefore, low-

pass filters were used with a relatively high cutoff frequency

(800 Hz) to attenuate voltage harmonics at the resonance

frequency, which is higher than 800 Hz. These filters turn


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Fig. 6. Control block diagram of the shunt active filter.

the system stable, but also degenerate the compensation char-

acteristics of the shunt active filter, as will be shown later.

The - - transformation box of Fig. 6 realizes (1)(3).

Two filters with 50-Hz cutoff frequency separate the powers

and from and , respectively. These signals are used

in the - current reference box, which realizes the following

equations:

(4)

where

(5)

Finally, the - - inverse transformation box calculates the

instantaneous current references to the PWM current control

as

(6)

With this approach the active filter supplies the whole of

the load. If zero sequence voltage is not present in the system,

the zero sequence power is always zero. In this case, the

zero sequence current of the load is compensated without

the need of energy balance inside the active filter ( ).

The signal is used in (5) as anaverage real powerand

is obtained from the voltage regulator, as shown in Fig. 6. The

sum of and is compared to a dc bus voltage reference

( ) and the deviation is filtered and multiplied by , to

match the desired amplitude for the ac current component

that neutralizes the dc bus voltage variations. Low-pass filters

with a cutoff frequency at 20 Hz are inserted in the voltage

regulator to render it insensitive to the fundamental frequency

(50-Hz) voltage variations, which appear when the active filter

compensates the fundamental zero sequence current of the

load, even when , as explained in Fig. 2. Note that

the compensation of and of the load also causes voltage

variation (see Fig. 5). Further, this slower feedback loop is also

useful to correct voltage variations due to compensation errors

that occur during transient response of the shunt active filter.

Due to the same reasons above, another low-pass filter is

applied in the circuit that generates the signal . In this case,the filtered voltage difference produces

according to the following limit function:

(7)

where is the dc bus voltage reference. The signal

actuates as a dynamic offset level that is added to both

hysteresis-band limits in the PWM current control, as shown

in Fig. 6, which is

upper hysteresis band limit

lower hysteresis band limit(8)

where is the instantaneous current reference

given by (6) and is a fixed semi-bandwidth of the hysteresis

control. Thus, the signal shifts the hysteresis-band to change

the switching times such that

rises and lowers

rises and lowers(9)


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Fig. 7. Block diagram of the fundamental positive-sequence voltage detector.

B. Sinusoidal Source Current Strategy

The active filter can compensate load currents under unbal-

anced system voltages to provide sinusoidal, balanced currents

to the source but now, disregarding the optimal power flow

proposed in Fig. 5. For this purpose, a positive sequencedetector must replace the 800-Hz cutoff frequency low-pass

filters (shaded area in Fig. 6). The phase angle and frequency

of the fundamental positive sequence voltage component ( )

must be accurately determined by the detector, in order to

allow the active filter to compensate the fundamental reactive

power of the load. The active filter must produce ac currents

( ) orthogonal to the voltage component . Otherwise it

would also produce active power.

The positive sequence voltage detector as presented in Fig. 7

not only satisfies the above constraints, but also determines

correctly the amplitude from . First, an integrated circuit

with a VCO chip (PLL circuit) should determine accurately

the fundamental frequency ( ) of the system voltage,which may be unbalanced and contain harmonics. Afterwards,

the fundamental frequency is used as input to a sine-wave

generator that produces three auxiliary signals ( ) to

be used as fundamental positive sequence currents along

the detector of Fig. 7. The phase angle and the amplitude of

these sine signals are not important,except that they must keep

120 among themselves and have equal amplitudes.

Again, the voltage detector uses an algorithm based on the

instantaneous powers defined in the - - reference frame.

However, the average values of the real ( ) and imaginary

( ) powers are considered here. The average powers

and are composed only from the fundamental positive

sequence voltage , since the auxiliary currentsare also composed only from a fundamental positive sequence

component. In this case, the influence of the fundamental

negative sequence voltage and harmonics will appear in the

high-frequency components of and .

The - voltage reference box of Fig. 7 calculates

(10)

Finally, the - - instantaneous values ( ) of the

fundamental positive sequence voltage, are determined in

the - - inverse transformation box, without errors in the

amplitude or phase angle, as

(11)

If the voltages calculated in (11) are considered as input

to the main control circuit (Fig. 6), instead of the filtered

voltages used previously, now the compensating powers

and will include the fundamental negative sequence power,

the fundamental reactive power, and the harmonic power.

Thus, the active filter controller handles the load currents as

connected to a sinusoidal, balanced voltage source. In this

case, if , and are compensated by the shunt

active filter, the source currents become sinusoidal, balanced,

and composed only from the active portion of the fundamental

positive sequence current of the load that is in phase with .Therefore, the sinusoidal source current strategy is realizeddoing the following changes in Fig. 6:

1) to replace the 800-Hz low-pass filters of Fig. 6 with the

circuit of Fig. 7;

2) to remove the 50-Hz low-pass filter that obtains in

Fig. 6, because the new input voltages and

do not contain any zero-sequence voltage component

( ) and is always zero.

At this point, it should be remarked that the voltage regulator

of Fig. 3 now has an additional task besides those described

previously, that is, it should correct errors in power compen-

sation. This errors arise because the feedforward control in

the main circuit is now unable to supervise the zero sequencepower. Another kind of error will also appear. To understand

this point, a simple example follows.

Suppose that the system voltages and load currents are

composed only from fundamental positive and negative se-

quence components. As expected, the active filter will supply

the whole negative sequence current ( ) to the load. How-

ever, the ac voltage at the shunt active filter contains also

negative sequence component at same frequency. So if it is

not orthogonal to , the active filter will supply/absorb a

nonzero average negative-sequence power. Since the power

compensation error causes voltage variation at the dc bus,


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TABLE IIMAIN PARAMETERS OF THE SIMULATED SYSTEM BASED ON FIG. 3

the slower feedback control loop of the voltage regulator willsense it and will change the signal to make the active

filter to absorb/supply a positive-sequence power from the ac

network to neutralize the above voltage variation. This occurs

because the active filter current references are calculated only

from [ of (11)].

V. SIMULATED RESULTS

A complete model of the shunt active filter was implemented

in a digital simulator and the most important results will be

presented to compare both control strategies. The fundamental

frequency of the system is 50 Hz. The source voltages are

composed from arbitrarily chosen phasors in terms of sym-metrical components. The rms amplitude and phase angle of

these phasors are

V

V

The other main system parameters based on Fig. 3 are sum-

marized in Table II.

Two simulations that use the same system parameters, but

realize different control strategy, will be shown. The phasevoltages at the load were almost the same for both simulation

cases and Fig. 8 shows the voltages for the constant sourceinstantaneous powercase. The load current was the same for

both simulations (Fig. 9). The diode bridge was connected

at ms and the controlled (thyristor) bridges were

connected after ms, according to their firing angles

(see Table II). Then, at ms, the firing pulses of the

three-phase thyristor bridge were blocked, as shown in Fig. 9.

The active filter was connected at ms. Fig. 10 shows

the filtered (no switching frequency) line currents of the active

filter for the sinusoidal source current case. For the constant

Fig. 8. System voltages.

Fig. 9. Load currents.

source instantaneous powercase, the current of the active

filter is presented in Fig. 11. These figures show that both

control strategies have the same dynamic behavior.

The compensated currents that flow through the source are

shown in Fig. 12(a) for the constant source instantaneouspowercase and in Fig. 12(b) for the sinusoidal source current

case. Although both approaches provide fast response and

equally compensate the neutral current of the load, they cannot

avoid the harmonic currents that are excited by the harmonic

voltages of the source and are flowing to the passive filter

( F ). Nevertheless, from a harmonic point

of view, the sinusoidal source current strategy offers a better

compensation for the source currents. Due to this reason, this

control strategy has been preferred and experimental results

from a laboratory prototype using this control strategy were

reported in [11].


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Fig. 10. Active filter currents when the sinusoidal source current strategyis applied.

Fig. 11. Active filter current when theconstant source instantaneous powerstrategy is applied.

(a)

(b)

Fig. 12. Currents of the power supply compensated by (a) the constantsource instantaneous power strategy and (b) the sinusoidal source currentstrategy.

Fig. 13 compares the three-phase instantaneous power (

) of the load with the powers from the compensated line

currents, for both control strategies. The constant source

instantaneous power strategy (pconst curve) should present a

perfectly smoothed instantaneous power at source side. Unfor-

tunately, it presented a poor performance due to the presence

Fig. 13. Three-phase instantaneous powers.

Fig. 14. Imaginary powers.

Fig. 15. Capacitor voltages at the dc bus.

of the 800-Hz cutoff frequency low-pass filters (Butterworth

Filter fifth order), applied in the measured system voltages to

solve problems of instability. For the level of voltage distortion

considered, the need of low-pass filter in the measured voltagesin case of using the constant source instantaneous power

strategycauses power compensation errors at the same order

of magnitude as the sinusoidal source current strategy. The

average switching frequency of the PWM inverter is about 13

kHz, and the losses in the snubber circuits are so high as the

average load power.

The imaginary powers illustrated in Fig. 14 were calculated

from the same voltages and currents used in Fig. 13. The

curve for the constant power strategy contains a small negative

average value because the 800-Hz cutoff frequency filters

delay the measured system voltages. This does not occur in the

sinusoidal source current strategy and confirms the efficiency

of the positive sequence voltage detector (Fig. 7).The dc capacitor voltage variations were almost similar in

both cases, as shown in Fig. 15. It is possible to see a 50-

Hz component that is caused by the zero-sequence current

compensation, as explained early. A discharge of the dc

capacitors occurred when the loads is connected. Contrarily,

an overvoltage occurred when the three-phase thyristor bridge

is disconnected.

VI. CONCLUSIONS

Two control schemes for a shunt three-phase four-wire

active power filter employing a conventional three-leg con-


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verter were developed and a critical comparison between both

approaches was carried out. The three-leg converter topology

was preferred due to its lower number of power semiconductor

devices, and a dynamic hysteresis current control was devel-

oped to overcome the problems related with the dc voltage

difference between dc capacitors.

A three-phase active filter without neutral wire could be

realized using a two-leg converter if the split-capacitor

inverter topology and the dynamic hysteresis current controlare applied, or generally use ( )-leg converter in -wire

systems.

Although the constant source instantaneous power strategy

is easier to realize, all simulation results indicated that thesinu-

soidal source current strategy should be the best alternative to

control a shunt active power filter. Experimental results using

this control strategy were successfully obtained and already

reported in [11].

REFERENCES

[1] G. Dinykel and R. Gretsch, Kompensator fur oberschwingungen und

blindleistung,ETZ Archiv., vol. 9, no. 1, pp. 914, 1987.[2] C. A. Quinn and N. Mohan, Active filtering of harmonic currentsin three-phase, four-wire systems with three-phase and single-phasenonlinear loads, in APEC92Applied Power Elec. Conf., 1992, pp.829836.

[3] C. A. Quinn, N. Mohan, and H. Mehta, A four-wire, current-controlledconverter provides harmonic neutralization in three-phase, four-wiresystems, in APEC93Applied Power Elec. Conf., 1993, pp. 841846.

[4] D. Sutanto and M. Bou-Rabee, Active power filters with reactive powercompensation capability, in Int. Power Eng. Conf., Singapore, Mar.1993, pp. 7378.

[5] H. Akagi, Y. Kanazawa, and A. Nabae, Generalized theory of theinstantaneous reactive power in three-phase circuits, in IPEC83Int.Power Elec. Conf., Tokyo, Japan, 1983, pp. 13751386.

[6] H. Akagi, Y. Kanazawa, and A. Nabae, Instantaneous reactive powercompensator comprising switching devices without energy storage com-ponents, IEEE Trans. Ind. Appl., vol. IA-20, no. 3, pp. 625630,1984.

[7] H. Akagi, A. Nabae, and S. Atoh, Control strategy of active powerfilter using multiple voltage-source PWM converters, IEEE Trans. Ind.

Appl., vol. IA-22, no. 3, pp. 460465, 1986.[8] E. H. Watanabe, R. M. Stephan, and M. Aredes, New concepts of

instantaneous active and reactive powers in electrical systems withgeneric loads, IEEE Trans. Power Delivery, vol. 8, pp. 697703, Apr.1993.

[9] M. Aredes and E. H. Watanabe, New control algorithms for series andshunt three-phase four-wire active power filters, IEEE Trans. Power

Delivery, vol. 10, pp. 16491656, July 1995.[10] G. Superti-Furga, E. Tironi, and G. Ubezio, General purpose low-

voltage power conditioning equipment, in IPEC95Int. Power Elec.Conf., Yokohama, Japan, Apr. 1995, pp. 400405.

[11] M. Aredes, J. Hafner, and K. Heumann, A three-phase four-wire shuntactive filter using six IGBTs, in EPE95Eur. Conf. Power Elec.

Appl., Sevilla, Spain, Sept. 1995, vol. 1, pp. 1.8741.879.

Maurcio Aredes was born in Sao Paulo State,Brazil, on August 14, 1961. He received the B.Sc.degree from Fluminense Federal University, Rio deJaneiro State in 1984, the M.Sc. degree in electri-cal engineering from Federal University of Rio deJaneiro in 1991, and the Dr.-Ing. degree (honors)from Technische Universitat Berlin in 1996.

From 1985 to 1988, he worked as a Commission-ing and Project Engineer at the Itaipu HVDC Trans-mission System, and from 1988 to 1991 he workedas Management Engineer in the Itaipu Power Plant

SCADA Project. At present, he is working within CEPELCentro dePesquisas de Energia Eletrica, Rio de Janeiro, and his main research areaincludes HVDC systems, active power filters, and FACTS technology.

Jurgen Hafner was born in Grobottwar, Germany, on August 7, 1964.He received the diploma degree in electrical engineering in 1991 from theTechnical University, Berlin.

Currently, he is working as an Assistant at the Technical University, Berlin.His research area includes active power filters, control, and simulation.

Klemens R. Heumann was born in Lunen, Germany, on May 15, 1931.He received the Dipl.-Ing. degree from Rheinisch-Westfalische TechnischeHochschule, Aachen, Germany, in 1956, and the Dr.-Ing. degree from Tech-nische Universitat Berlin, in 1961.

He was a Research Engineer from 1956 to 1968 and a General Manager

from 1969 to 1978 in the AEG Research Institute, Berlin. He became aProfessor of Power Electronics at the Universitat Hannover in 1978, andin 1983 he joined the Technische Universitat Berlin, where he is presentlya Professor. He has worked as a Consultant in various industries and is theauthor of four books and author and co-author of more than 100 papers.

Dr. Heumann is the recipient of the 1985 IEEE Power Electronics SocietyWilliam E. Newell Award.

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