Synchronverter-based Operation of STATCOM to Mimic ... - IEEE Xplore

Synchronverter-based Operation of STATCOM to Mimic Synchronous Condensers Phi-Long Nguyen∗, Qing-Chang Zhong∗, Frede Blaabjerg† , and Josep M. Guerrero‡ ∗ Department

of Aeronautical and Automotive Engineering Loughborough University, Leicestershire LE11 3TU, United Kingdom Email: [email protected]., [email protected]. † Institute of Energy Technology, Aalborg University (AAU), Aalborg 9220, Denmark Email: [email protected]. ‡ BarcelonaTech, Department of Automatic Control Systems, 08036 Barcelona, Spain Email: [email protected].

Abstract—The operating principles of static synchronous condenser (STATCOM) are similar to that of a rotating synchronous condenser. However, so far, most controlling methods proposed for STATCOM have not taken into account the internal characteristics of rotational synchronous machines. In this paper, following the idea of synchronverters, the controller for a STATCOM is designed according to the mathematical model of synchronous generators that are operated in the compensator mode. As a result, no phase-locked loop (PLL) is needed. Moreover, a third operation mode, i.e. the droop control mode (or the D-mode in short), is introduced to the operation of STATCOM, in addition to the conventional voltage regulation mode (or the V -mode in short) and the direct Q control mode (or the Q-mode in short). This allows parallel-operated STATCOMs to share reactive power properly. The proposed control strategy is verified with simulations in MATLAB/Simulink/SimPowerSystems. Index Terms—STATCOM, microgrid, voltage droop control, system strength, reactive power compensation, synchronverters, virtual synchronous machines.

I. I NTRODUCTION Synchronous machines have been used since long time ago as synchronous compensators or synchronous condensers to control the voltage profile of power systems, especially in transient states, by consuming or generating reactive power. The use of synchronous compensators is considered to be simple and could maintain high flexibility and reliability [1], [2]. They are nowadays still used in many applications, especially when robust operation is required, e.g. in remote and islanded operation of wind farms [2] and in high voltage direct current (HVDC) transmission systems [3], [4]. Although synchronous compensators have good stable operating characteristics, the loss is usually high and can reach 1 − 2% of the rated power [5], which is mainly due to the rotational loss and the heat caused by high reactive currents. As a result, static synchronous compensators (STATCOM), which are effectively voltage-source inverters (VSI) [6], [7], have been proposed as an alternative option. The operating principles of STATCOM are similar to those of rotational synchronous compensators externally [6], [8]– [10], but most of the controllers proposed to control STATCOM have not taken advantage of the mathematical model

c 978-1-4577-2119-9/12/$26.00 2011 IEEE

of synchronous machines. Very recently, there is an emerging trend to exploit the properties of synchronous machines to facilitate the control of inverters [11] and grid-connected VSIs [11]–[17]. In this paper, STATCOMs are controlled to operate as virtual rotational synchronous condensers, following the idea of the synchronverter proposed in [12], [13]. From the grid side, the power system sees STATCOMs as actual synchronous machines operated in the condenser mode. The proposed controller does not need a PLL to provide the grid frequency and synchronisation. A third operation mode, the droop mode, is also introduced to the operation of STATCOM. This allows parallel-operated STATCOMs to share reactive power according to the voltage drop. The rest of the paper is organised as follows. The conventional control schemes for STATCOM are reviewed in Section II and the major principles of the synchronverter technology are summarised in Section III. The synchronverter-based controller for STATCOM that does not need a PLL is proposed in Section IV and simulation results are shown in Section V, followed by conclusions made in Section VI. II. OVERVIEW

OF THE OPERATING PRINCIPLES OF

STATCOM Figure 1 depicts a STATCOM connected to a power system. The equivalent circuit of the system shown in Figure 1(a)The phase difference between e and vg is δ = θ−θg . Under normal operations, δ is small (and negative). As a result, sin δ ≈ δ and cos δ ≈ 1. The real power P and reactive power Q flowing out of the STATCOM are [7] Vg E Vg E sin δ ≈ 3 δ, XL XL   Vg2 Vg Vg E cos δ − (E − Vg ) . ≈3 Q=3 XL XL XL P =3

(1)

(2)

From Eq. (2), the reactive power Q can be controlled via changing the voltage difference E − Vg . When the reactive power Q is changed, the voltage vg changes slightly as well. This can be used to regulate the voltage at the PCC. Hence,

942

v g = Vg θ g

Z eq

jX L

ig

PCC

veq

~

~

hence the mechanical speed of the machine is the same as the electrical speed. Similarly to the control of a synchronous generator, there are two control channels: one for the real power and the other for the reactive power. The real power is controlled by a frequency droop control loop, using the (imaginary) mechanical friction coefficient Dp as the feedback gain. This loop regulates the (imaginary) speed θ˙ of the synchronous machine and creates the phase angle θ for the generated voltage e. The reactive power is controlled by a voltage droop control loop, using a voltage droop coefficient Dq . This loop regulates the field excitation Mf if , which is proportional to the amplitude of the voltage generated. More details about the synchronverter technology, including experimental results, can be found in [13].

e=E θ

(a) Single-phase equivalent circuit Transmission line

PCC

vg

ig CB

XL

Coupling transformer

+

C

e

Vdc -

STATCOM

(b) Sketch of the physical connection Figure 1.

a STATCOM mainly have two different operation modes: one is to provide the desired amount of Q, which is called the direct Q control mode (or the Q-mode in short), and the other is to regulate the PCC voltage, which is called the voltage regulation mode (or the V -mode in short). Equation (1) shows the relationship between the real power P and the phase difference δ. The real power flowing in or out forces the DC-bus voltage Vdc to increase or decrease. As a result, Vdc can be regulated via controlling δ or the phase angle θ of the voltage e generated by the STATCOM. III. OVERVIEW

OF THE

.

Dp

STATCOM connected to a power distribution system

S YNCHRONVERTER T ECHNOLOGY

A synchronverter is an inverter that mimics a conventional synchronous generator [13] or a virtual synchronous machine. Figure 2 shows the control scheme of a synchronverter, which includes the mathematical model of a three-phase round rotor synchronous machine described by 1 ˙ θ¨ = (Tm − Te − Dp θ), J    , Te = Mf if i, sinθ

(4)

˙ f if sinθ,  e = θM

(5)

˙ f if i, cosθ  , Q = −θM

(6)

(3)

where Tm , Te , e, θ and Q are the mechanical torque applied, the electromagnetic torque, the generated voltage, the rotor angle and the reactive power, respectively. if is the field excitation current and i is the stator current vector. Mf is the maximum mutual inductance between the stator windings  = and cosθ and the field winding.  2π are  sinθ 

T defined as  = sin θ + , cosθ  = sinθ sin θ sin θ − 2π   3 T 3 2π 2π cos θ cos θ − 3 cos θ + 3 . Here, it is assumed that the number of pairs of poles for each phase is 1 and

Pset

−

Tm

1

θ&n

− Te Q

Qset

1 Js

−

1 Ks

− θr .

θ

1 s

Formulas of e, Q, Te

θ

e

Mfif

i Dq

−

Vr

Vg Figure 2.

IV. D ESIGN

The synchronverter control strategy [12], [13]

OF A

S YNCHRONVERTER - BASED STATCOM C ONTROLLER

The synchronverter is able to control real power and reactive power independently with a compact control structure, in which the model of a synchronous machine is embedded. Hence, it could be applied to implement STATCOM if the synchronous machine is operated in the condenser mode, i.e. when P = 0. This leads to the proposed controller for a STATCOM shown in Figure 3, after dealing with some special aspects and making some necessary changes. Similarly, the controller has two control channels. The upper channel regulates the real power to control the internal frequency θ˙ and the phase θ so that the DC-bus voltage Vdc is maintained constant and that the STATCOM tracks the phase of the grid voltage. The lower channel regulates the reactive power and/or the voltage. A particular property of the proposed STATCOM is that it can be operated in an extra mode, called the droop mode or the D-mode, in addition to the conventional Q-mode and V -mode, so that parallel-operated STATCOMs can share the reactive power properly. The D-mode is the combination of the conventional Q-mode and V -mode, by operating the two switches SQ and SV shown in the lower part of Figure 3. The positions of the switches SQ and SV , together

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)

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in the time domain. The time constant Td can be chosen as 5 times of the system period, as a rule of thumb.

•

θn •

Vrdc − Vdc

•

Δθ −

PI

θ

Td s + 1 s

θ

v g , ig Calculate e and Q

e

PWM generation

M f if 1 s

Q Qset

− ΔQ

Figure 3.

1 KQ

SQ

SV

Vr 1 ΔV Kv − Vg

B. Regulation of the reactive power (the Q-mode) In the Q-mode, the reactive power Q generated/absorbed by the STATCOM is regulated to be the set-point Qset . To select this operation mode, SQ is on and SV is off, i.e. the voltage control channel in the lower part of Figure 3 is not in operation. Therefore, Mf if is controlled according to the reactive power error Q = Qset − Q.

(7)

Since Mf if is proportional to the RMS value E = √12 Mf if θ˙ of e, and E is proportional to the generated reactive power Q, the control effect can be explained as

A synchronverter-based STATCOM controller

Qset > Q ⇒ Q > 0 ⇒ Mf if ↑⇒ Q ↑ to Qset ,

(8)

Qset < Q ⇒ Q < 0 ⇒ Mf if ↓⇒ Q ↓ to Qset .

(9)

Table I O PERATION MODES OF THE PROPOSED STATCOM SQ ON OFF ON

SV OFF ON ON

Operation Mode Q-mode: Direct Q control V -mode: Voltage regulation D-mode: Droop control

with the corresponding operational modes of the STATCOM, are shown in Table I. A. Regulation of the DC-bus voltage and locking with the grid phase As discussed in the previous section, the DC bus voltage can be regulated by controlling the phase θ of the voltage e. Tracking the grid frequency is also able to regulate θ, which eventually regulates Vdc . In Figure 3, Δθ˙ is the output of the PID controller used to regulate the DC-bus voltage and θ˙n is ˙ the the rated system frequency. Noting that θ˙ = θ˙n − Δθ, regulating mechanism can be described as Vdc ↓⇒ θ˙ ↑⇒ θ˙ ↓⇒ θ ↓⇒ δ ↓⇒ Vdc ↑ to Vrdc and Vdc ↑⇒ θ˙ ↓⇒ θ˙ ↑⇒ θ ↑⇒ δ ↑⇒ Vdc ↓ to Vrdc . As a result, there is no need to add an extra PLL to obtain θ˙g as the reference frequency for the STATCOM. This considerably improves the performance of the STATCOM. In order to speed up the effect of any change in the frequency θ˙ on the phase angle θ so that it can quickly lock with the grid phase instead of via a pure θg , the phase angle is obtained via Td s+1 s integrator 1s from the frequency θ˙ as normally done, e.g., in the case of the synchronverter in [13]. That is, a proportionalderivative (PD) unit with the time constant Td is cascaded with the integrator to speed up the dynamic response of the integrator. The PD unit only plays a role in the transient state and does not affect the steady-state response of the integrator, which is still θ=

944

t 0

˙ θdt

and

Because of the integrator in the loop, the error Q is eliminated and the reactive power Q tracks the set-point Qset accurately in the steady state. C. Regulation of the grid voltage (the V -mode) The system strength Zeq of a power system, as shown in Figure 1(a), changes with every load change on the grid, which causes Vg to drop or increase accordingly. The fluctuation of Vg reduces system stability and directly affects the normal operation of other equipment on the grid. It may also increase the grid loss. Therefore, regulating the voltage Vg at the PCC is an essential function of a STATCOM and the V -mode is the most common operation mode of STATCOMs. In this mode, the voltage Vg at the PCC is regulated to be the set-point Vr , which is usually the nominal value of the system. In order to operate the STATCOM in this mode, SQ is off and SV is on, i.e. the reactive power control channel in the lower part of Figure 3 is not in operation. Therefore, Mf if is controlled according to the voltage error V = Vr − Vg .

(10)

The control effect can be explained as Vg < Vr ⇒ V > 0 ⇒ Mf if ↑⇒ E ↑⇒ Vg ↑ to Vr , (11) and Vg > Vr ⇒ V < 0 ⇒ Mf if ↓⇒ E ↓⇒ Vg ↓ to Vr . (12) In the steady state, Vg = Vr because of the integrator in the loop.

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)

B1

Transmission line 50 km

Feeder 1 km

B2

CB3

Xs

25 kV 100 MVA Power source

Load 4 P = 2 MW Q = 1 MVar (capacitive)

Rs

Vs

1.5/25 kV 5 MVA

C

~

25/5 kV 10 MVA

B3 (PCC)

25/0.6 kV 3 MVA Coupling transformer

B5

CB2

B4 Load 3 P = 2 MW (Floating)

Load 2 P = 0.8 MW Q = 0.3 MVar (capacitive)

CB1 Load 1 P = 2.5 MW Q = 1.5 MVar (inductive)

+ STATCOM ± 5 MVar 1.5 kV

Figure 4.

Single-line diagram of the power system used in simulations

D. Droop control (the D-mode) The STATCOM is operated in this mode when both SQ and SV are turned on. In the steady state, the input to the integrator to generate the Mf if is 0, i.e., Q V + = 0. KQ Kv

C

(13)

In practice, the parameters KQ and Kv can be tuned as follows. The droop coefficient Dq can be determined at first with the specification of the STATCOM. For example, if it is required to generate the rated reactive power when the voltage drops by 10%, then Qn , 10%Vn

(15)

where Vn is the amplitude of the nominal phase voltage of the grid and Qn is the rated capacity. According to [13], the time constant of the voltage regulation loop is τv =

Kv Kv , ≈ θ˙ θ˙n

XL

Cf

(16)

from which the gain Kv can be determined after the time constant τv is chosen. Normally, it can be chosen as a couple of system periods. Then, the parameter KQ can be obtained from (14) as (17) K Q = K v Dq . Since K1v = KQq , which is often much larger than K1Q , the voltage loop is much faster than the reactive power loop. This is expected. D

V. S IMULATION R ESULTS To verify the control strategy, a power system model shown in Figure 4 was built in MATLAB/Simulink/SimPower Systems. The detailed model of the STATCOM is shown in

vga vgb vgc

Ls , Rs

Q Hence, the voltage droop coefficient Dq = − V defined in [13] becomes KQ Q Dq = − . (14) = V Kv

Dq =

Ls , Rs i a ib ic

Figure 5.

iga igb igc

Cf

Detailed model of the STATCOM used in the simulations

Figure 5. The STATCOM was connected to the grid via a 1.5/25 kV transformer. For the real power control loop, the PI control gains were chosen as KP = 0.005 and KI = 0.1 and the time constant of the PD unit was chosen as Td = 0.1s. For the reactive power control loop, Dq was chosen so that 100% nominal reactive power increment corresponds to 10% of voltage drop, Qn i.e. Dq = 10%V = 2449.5 where Qn = 5 MVar is the n  rated power of the STATCOM and Vn = 25 23 kV. The time constant of the voltage loop was chosen as τv = 0.058s and, as a result, Kv = 18.37 and KQ = 45000. The simulation step size was chosen as Ts = 50μs, with the IGBT models running in the average mode. A. Under different normal operation modes The normal operation of the STATCOM was tested under different operation modes. After connecting the STATCOM to the grid, the simulation was conducted in the following sequence of events: 1) Change Qset from 0 to −3 MVar at t = 2s (in the Qmode); 2) Switch to the V -mode at t = 3s to regulate Vg to be 1 pu; 3) Switch to the D-mode at t = 4s; 4) Stop the simulation at t = 4.5s.

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)

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Vdc [kV]

3 2.5 2 1.5

2

2.5

3 3.5 Time [s] (a) DC-bus voltage Vdc

4

4.5

4

4.5

P [MW]

1 0 −1 1.5

2

2.5

3 3.5 Time [s] (b) Real power

Q [MVar]

6 2 −2

Vg [pu]

−6 1.5

2

1.1 1 0.9 0.8 0.7 1.5

2.5

3 3.5 Time [s] (c) Reactive power

4.5

δ[°]

θg, θ [ ° ]

3 3.5 4 Time [s] (d) Vg with the STATCOM connected

0 −5 −10 −15 −20 1.5

2.5

θg

2

2.5

3 3.5 Time [s] (e) Voltage phase tracking

2

2.5

4.5

θ

4

4.5

3 3.5 4 Time [s] (f) Phase difference δ = θ − θg

4.5

1 0.5 0 −0.5 −1 1.5

Figure 6.

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2

4

Simulation results under different operation modes

The results are shown in Figure 6. The Vdc was successfully maintained at the set-point Vrdc = 2.5 kV with some dynamics, while the real power P remained at nearly zero and the phase difference δ was kept very small all the time. Although the system frequency was kept constant, the phase of the grid voltage (the constant part) did change when the events happened and the proposed STATCOM successfully tracked the grid phase without the need of a PLL, as shown in the Figure 6(e). The transitions between the three operation modes of the STATCOM were very smooth with fast responses and small overshoots. Vg was about 0.92 pu before the STATCOM started regulating the reactive power. The STATCOM quickly responded to the change of Qset = −3 MVar at t = 2s, which caused Vg to reduce to about 0.8 pu. When the mode was changed to the voltage regulation mode at t = 3s, Vg was quickly regulated to 1 pu with about Q = +3.5 MVar provided. When the STATCOM was switched to the D-mode at t = 4s, the reactive power generated was reduced to about 0.42 MVar, which caused the Vg to settle down at about 0.932 pu, i.e. with the voltage error of V = 6.8%Vn . The change of the reactive power is Q = 3.42 MVar from the set-point Qset = −3 MVar. This is in line with (14) because 5 × 106 3.42 × 106 Q ≈ = Dq . = V 6.8%Vn 10%Vn B. With a variable grid frequency The purpose of this simulation is to demonstrate the voltage phase tracking performance of the STATCOM under extreme conditions with grid frequency variations. The grid frequency was set to be at nominal frequency fn = 50 Hz at the beginning. After connecting the STATCOM to the grid, the simulation was conducted in the following sequence of events: 1) Switch to the V -mode at t = 2s and, at the same time, change the grid frequency to f = 52 Hz; 2) Change the grid frequency back to the nominal value fn = 50 Hz at t = 3s; 3) Drop the grid frequency to f = 48 Hz at t = 4s; 4) Change the grid frequency back to nominal value fn = 50 Hz at t = 5s; 5) Stop the simulation at t = 6s. The results are shown in Figure 7. The DC-bus voltage shown in Figure 7(b) reflected the extreme frequency change but was successfully driven back to the set-point without any problem. At t = 2s, although the operation mode and the frequency were changed at the same time, the system still responded very well. The phase tracking performance was excellent under the large grid frequency variations, as can be seen from Figure 7(e). It is worth emphasising that no PLL was used in the case. The voltage Vg with the STATCOM connected is shown in Figure 7(f). Since the STATCOM was operated in the V mode from t = 2s, the voltage Vg was maintained very well at 1pu for the whole process. The STATCOM has rejected the effect of the extreme frequency change and has demonstrated excellent self-synchronisation ability without the need of an additional PLL.

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)

VI. C ONCLUSIONS

fg [Hz]

53 50 47 1.5

3.5 4 4.5 5 5.5 Time [s] (a) Change of the grid frequency

Q [MVar]

P [MW]

Vdc [kV]

3.5 3 2.5 2 1.5 1.5

2.5

3

6

R EFERENCES

2 2.5

3 3.5 4 4.5 Time [s] (b) DC-bus voltage Vdc

2 1 0 −1 −2 1.5

2

2.5

6 3 0 −3 −6 1.5

2

2.5

θg, θ [ ° ] Vg [pu]

2

5 5.5

6

3

5

5.5

6

3

5

5.5

6

3.5 4 4.5 Time [s] (c) Real power

3.5 4 4.5 Time [s] (d) Reactive power

300 θg θ 200 100 0 −100 −200 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [s] (e) Voltage phase tracking 1.15 1 0.85 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Time [s] (f) Vg with the STATCOM connected

Figure 7.

A STATCOM is operated as a virtual synchronous condenser has been proposed without the need to use a PLL. The proposed STATCOM controller also introduces a third operational mode, i.e. the droop control mode or the Dmode in short, to the operation of STATCOM, in addition to the conventional direct Q control mode (the Q-mode) and the voltage regulation mode (the V -mode). This allows parallel-operated STATCOMs to share reactive power properly. Simulation results are presented to demonstrate the excellent performance of the proposed control strategy.

[1] P. Rush and I. Smith, “Run-up and synchronisation of a large synchronous compensator,” IEE Proc. Electric Power Appli., vol. 1, no. 3, pp. 91–99, Aug. 1978. [2] V. Akhmatov and P. Eriksen, “A large wind power system in almost island operation: A danish case study,” IEEE Trans. Power Syst., vol. 22, no. 3, pp. 937–943, Aug. 2007. [3] N. Kirby, M. Luckett, L. Xu, and W. Siepmann, “HVDC transmission for large offshore windfarms,” in Proc. of the 7th Conf. on AC-DC Power Transmission, 2001, pp. 162–168. [4] O. Nayak, A. Gole, D. Chapman, and J. Davies, “Dynamic performance of static and synchronous compensators at an HVDC inverter bus in a very weak AC system,” IEEE Trans. Power Syst., vol. 9, no. 3, pp. 1350–1358, Aug. 1994. [5] E. Luiz da Silva, J. Hedgecock, J. Mello, and J. Ferreira da Luz, “Practical cost-based approach for the voltage ancillary service,” IEEE Trans. Power Syst., vol. 16, no. 4, pp. 806–812, Nov. 2001. [6] N. Hingorani and L. Gyugyi, Understanding FACTS: Concepts and Technology of Flexible AC Transmission Systems. Wiley-IEEE Press, 1999. [7] B. Singh, R. Saha, A. Chandra, and K. Al-Haddad, “Static synchronous compensators (STATCOM): A review,” IET Proc. Power Electron., vol. 2, no. 4, pp. 297–324, Jul. 2009. [8] T. Wildi, Electrical Machines, Drives and Power Systems, 6th ed. Prentice-Hall, 2005. [9] S. Mori, K. Matsuno, T. Hasegawa, S. Ohnishi, M. Takeda, M. Seto, S. Murakami, and F. Ishiguro, “Development of a large static VAR generator using self-commutated inverters for improving power system stability,” IEEE Trans. Power Syst., vol. 8, no. 1, pp. 371–377, Feb. 1993. [10] L. Gyugyi, “Power electronics in electric utilities: Static VAR compensators,” in Proc. of IEEE, 1988, pp. 483–494. [11] L. Zhang, L. Harnefors, and H.-P. Nee, “Power-synchronization control of grid-connected voltage-source converters,” IEEE Trans. Power Syst., vol. 25, no. 2, pp. 809–820, May 2010. [12] Q.-C. Zhong and G. Weiss, “Static synchronous generators for distributed generation and renewable energy,” in Proc. of IEEE PES Power Systems Conference & Exhibition (PSCE), 2009. [13] ——, “Synchronverters: Inverters that mimic synchronous generators,” IEEE Trans. Ind. Electron., vol. 58, no. 4, pp. 1259–1267, Apr. 2011. [14] H.-P. Beck and R. Hesse, “Virtual synchronous machine,” in Proc. of the 9th International Conference on Electrical Power Quality and Utilisation (EPQU), 2007, pp. 1–6. [15] J. Driesen and K. Visscher, “Virtual synchronous generators,” in Proc. of IEEE Power and Energy Society General Meeting, 2008, pp. 1–3. [16] Y. Chen, R. Hesse, D. Turschner, and H.-P. Beck, “Improving the grid power quality using virtual synchronous machines,” in 2011 International Conference on Power Engineering, Energy and Electrical Drives (POWERENG), 2011, pp. 1–6. [17] M. Torres and L. A. C. Lopes, “Frequency control improvement in an autonomous power system: An application of virtual synchronous machines,” in 2011 IEEE 8th International Conference on Power Electronics and ECCE Asia (ICPE & ECCE), 2011, pp. 2188–2195.

Simulation results with a variable grid frequency

2012 7th IEEE Conference on Industrial Electronics and Applications (ICIEA)

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