Ijetr021124
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This paper presents a hybrid power compensator (HPC) designed to address power quality issues in electrified railway systems caused by nonlinear loads. The HPC utilizes a back-to-back converter with a shared DC link and employs a hysteresis harmonic current controller for efficient compensation of harmonic currents, power factor correction, and voltage unbalance. Simulation results demonstrate the HPC's effectiveness in enhancing power quality compared to systems without compensation.
![International Journal of Engineering and Technical Research (IJETR)
ISSN: 2321-0869, Volume-2, Issue-1, January 2014
53 www.erpublication.org
Abstract— A power quality problems in power systems have
been increased due to nonlinear loads. To compensate these
problems hybrid power compensator was proposed in this
paper. A hybrid power compensator (HPC) is proposed in this
paper to eliminate the harmonic currents, compensate power
factor and voltage unbalance problems created by the
nonlinear loads present in three phase systems. A HPC
contains back to back converter by sharing the same dc link
power and v/v transformer to provide a voltage balance in
transmission line. Hysteresis harmonic current controller is
used to produce pulse for back to back converter. A controller
maintains the dc-link voltage and compensates the power
factor, harmonic currents. A comparative analysis for traction
system with and without HPC was performed using
MATLAB-Simulink. Simulation results are provided to
eliminate power quality problems effectively.
Index Terms—HPC, traction power, harmonic elimination,
power factor correction, non-linear loads, cophase system
I. INTRODUCTION
Highlight a section that you want to designate with a certain
style, and then select the appropriate name on the style menu.
The style will adjust your fonts and line spacing. Do not
change the font sizes or line spacing to squeeze more text into
a limited number of pages. Use italics for emphasis; do not
underline.
Electrified Railway Systems are very complex systems in
which a variety of components (or subsystems) cooperate to
realize the transport service for which the system has been
designed.
A railway system is perhaps one of the most critical real
systems, from the safety and reliability viewpoint, because it
must satisfy numerous requirements and presents complex
architectural links among its various subsystems [3]. In fact,
a lot of safety requirements are strongly dependent on correct
interaction operation.
The performance of this kind of systems strictly depends
on the capability of the system to be correctly integrated. A
correct approach to the analysis of traction systems is the
fundamental starting point for the right design and
functionality of this complex reality.
The amount of negative-sequence currents depends on
the topology of the traction power system, in particular, the
type of traction transformers used [14]. Typical
Manuscript received January 09, 2014.
Natesan.P, Power System Engineering, Valliammai Engineering College,
Chennai, India, 8148483654.
Madhusudanan.G, Electrical and Electronics Engineering, Valliammai
Engineering College, Chennai, India.
transformers used include Scott transformers, Woodbridge
transformers, three- phase V/V transformers,
impedance-matching balance trans- formers, etc., [15].
Scott transformers, Woodbridge transformers are balanced
transformers but three-phase V/V transformers are
unbalanced. When balanced transformers are used, no
negative-sequence current is injected into the public grid
when two feeder sections consume the same power.
However, for the traction systems with three-phase V/V
transformers, the negative-sequence current injected into
the public grid is half of the positive- sequence current even
when two feeder sections consume the same power. The
problem with this topology is that a strategy to effectively
compensate the negative-sequence and harmonic currents
needs to be developed.
In this paper, a hybrid device combining active and
passive compensators, named as the hybrid power
compensator (HPC), is proposed for compensation in
cophase traction power supply. The parameter design
procedure for minimum HPC voltage operation as well as the
minimum voltage rating achievable is discussed.
II. V/V TRANSFORMER
The structure of RPC with three-phase V/V transformers
is depicted in Fig. 2. The 220-kV three-phase high-voltage
source is converted into two 27.5-kV single-phase voltage
sources, which are connected to the two feeder sections, via
a three-phase V/V traction transformer. The turns ratio of
the V/V traction transformer is KV [7]. The HPC consist of
back to back coverter through a common dc capacitor with
a stable dc-link voltage, is connected to the two feeder
sections via two step- down transformers with a turns ratio
of KD . The two converters are connected to the
single-phase step-down transformers via two output
inductor La and Lb respectively.
Fig. 1 Construction diagram of V/V Transformer
The two converters can be controlled as current
sources to shift a certain amount of active power from one
feeder section to the other. These two converters can also
provide harmonic suppression and reactive power
Analysis of Hybrid Power Compensator for
Non-linear Traction Loads
Natesan P, Madhusudanan G](https://image.slidesharecdn.com/ijetr021124-171120162513/85/Ijetr021124-1-320.jpg)
![Analysis of Hybrid Power Compensator for Non-linear Traction Loads
54 www.erpublication.org
compensation [9]. Hence, the system can achieve
integrated compensation of negative sequence currents,
harmonic currents and reactive power.
III. CONTROLLER
The The control block of the system is
Fig. 2 Hysteresis Controller
The instantaneous load active and reactive power is
computed using the modified instantaneous pq theory .The
mathematical expression, in which vac and are the load
voltage and current rms, while vacd and iLd are 90◦delay of
load voltage and current, respectively. and refer to the
instantaneous load active (real) and reactive
(imaginary)power
(3.1)
The active power part can be split into dc part
which corresponds to the fundamental average active
load power; [12] and oscillating part which corresponds
to the oscillating active power between system source and
load and contributes as part of harmonics and reactive power
(which need to be compensated). The mathematical
expression is shown in
(3.2)
The required compensation power is then computed
according to the power quality requirement, where and
are the required active and reactive compensation power.
(3.3)
The reference of Vac and phase compensation
current, and , can then be computed ,where and
are the phase voltage and its 90◦ delay value
(3.4)
(3.5)
The computed reference current signal is then sent
to the hysteresis current controller, which pulse width
modulated signals are generated for the electronic switches
of and phase converters.
The HPC balances the grid-side current by
transferring active power from the phase to the
phase.Concerning the design of the LC filter parameter,
it is selected so as to reduce the harmonics compensation
capacity of the compensator [14]. Although the highest load
harmonic contents are located at the third harmonic
frequency, the LC filter is tuned at the second highest load
harmonics (fifth harmonic) for smaller physical size of the
components.
IV. SIMULATION RESULTS
Simulations using MATLAB done to verify the before
mentioned theoretical studies. The circuit schematic of the
system used in simulations is provided in Fig. 12. The
parameters are selected as close to practical applications as
possible [16], [19]. The substation V/V transformer is
composed of two 20 MVA single-phase transformers, with
turning ratios of 110 kV/27.5 kV and 110 kV/13.75 kV.
Traction loads are simulated using rectifier RL load, with
linear capacity of 15 MVA. The compensation device is then
connected across the two single-phase outputs of V/V
transformer to provide power quality compensation of the
system. [19] Notice that the LCL filter is included here to
filter the ripples introduced by the compensator.
A. Cophase Traction Power Without Compensation
The system performance without compensation is
investigated first. Shown in Fig. 4 is the three-phase source,
secondary voltage, and current waveforms for cophase
traction power without compensation [6]. It could be
observed that the system suffers from unbalance, reactive
power and harmonics problem. A traction load of 25MVA is
connected to 110 KVA grid through step down transformer
(110/25KV).
Fig. 3 Cophase Traction Power Without Compensation
Traction load is a time varying load which is
represented by rectified with RL-load (non-linear load). In
general the non-linear load generates harmonics, voltage
unbalance, power factor variation and other power quality
problems. The load we used on the test system generated a
THD of 33.8% and power factor of the system was decreased
to 0.77.
Fig. 4 Vac side voltage and current without compensation](https://image.slidesharecdn.com/ijetr021124-171120162513/85/Ijetr021124-2-320.jpg)
![International Journal of Engineering and Technical Research (IJETR)
ISSN: 2321-0869, Volume-2, Issue-1, January 2014
55 www.erpublication.org
Rectifier with RL load will be the best example of
traction load. Traction loads are changes with time [14].
Traction power system connected to any one of the phase of
three phase supply. It will cause voltage unbalance among
other phases.
Fig. 5 Unbalanced voltage and current in transmission line
The single-phase back to-back converter is adopted in the
power conditioner, which could balance the active currents
between the transformer’s two secondary windings. One
phase at the secondary side of the traction transformer
directly supplies the traction loads. The other phase supplies
the loads indirectly via a power conditioner.
B. Cophase Traction Power With HPC Compensation
Fig. 6 Cophase Traction Power With HPC Compensation
HPQC is connected with a traction load of 25MVA
which is connected to 110 KVA grid through step down
transformer (110/25KV), to mitigate the THD and to
increase the power factor. Traction load is a time varying
load which is represented by rectified with RL-load
(non-linear load).
Fig. 7 Vac side voltage and current with HPC
phase side traction load and side HPC is is
connected. side traction loads are cause voltage
unbalance and it will reduced by compensating voltage by
using side transformer.Rectifier with RL load will be the
best example of traction load [19]. Traction loads are
changes with time. Traction power system connected to any
one of the phase of three phase supply with Hybrid Power
Quality Compensator.
Fig. 8 balanced voltage and current in transmission line with HPC
V. CONCLUSION
A strategy to improve the power factor and eliminate
harmonic currents in high-speed traction systems using
co-phase hybrid power quality compensator (HPQC) was
designed. The current references for the RPC converters are
generated according to the load currents on both sections of
the traction power supply system and current controllers are
designed to track the current references.A comparative
analysis for traction system with and without HPQC was
performed using MATLAB-Simulink.
TABLE I. OUTPUT COMPARISON
Without compensation HPC compensation
Power factor Harmonics ( %) Power factor Harmonics (%)
0.77 33.8 0.90 12.54
REFERENCES
[1] H. Y. Kuo and T. H. Chen, “Rigorous evaluation of the voltage
unbalance due to high-speed railway demands,” IEEE Trans. Veh.
Technol., vol. 47, no. 4, pp. 1385–1389, Nov. 1998.
[2] D. C. Howroyd, “Public-supply-system distortion and unbalance from
single-phase a.c. traction,” Proc. Inst. Electr. Eng., vol. 124, no. 10, pp.
853–859, 1977.
[3] S. T. Senini and P. J.Wolfs, “Novel topology for correction of
unbalanced load in single phase electric traction systems,” in Proc. IEEE
33rd Annu. Power Electron. Spec. Conf., Jun. 2002, vol. 3, pp.
1208–1212.
[4] Z. Zhang, B. Wu, J. Kang, and L. Luo, “A multi-purpose balanced
transformer for railway traction applications,” IEEE Trans. Power
Delivery, vol. 24, no. 2, pp. 711–718, Apr. 2009.
[5] H. Wang, Y. Tian, and Q. Gui, “Evaluation of negative sequence
current injection into the public grid from different traction substation in
electrical railways,” in Proc. 20th Int. Conf. Exhib. Electr.
Distrib.—Part 1, 2009, pp. 1–4.
[6] C. Dai and Y. Sun, “Investigation of the imbalance current
compensation for transformers used in electric railways,” in Proc.
Asia-Pacific Power Energy Eng. Conf., 2010, pp. 1–4.](https://image.slidesharecdn.com/ijetr021124-171120162513/85/Ijetr021124-3-320.jpg)
![Analysis of Hybrid Power Compensator for Non-linear Traction Loads
56 www.erpublication.org
[7] Z. Sun, X. Jiang, D. Zhu, and G. Zhang, “A novel active power quality
compensator topology for electrified railway,” IEEE Trans. Power
Electron., vol. 19, no. 4, pp. 1036–1042, Jul. 2004.
[8] P. C. Tan, R. E. Morrison, and D. G. Holmes, “Voltage form factor
control and reactive power compensation in a 25-kV electrified railway
system using a shunt active filter based on voltage detection,” IEEE
Trans. Ind. Appl., vol. 39, no. 2, pp. 575–581, Mar./Apr. 2003..
[9] M. Chen, Q. Li, and G. Wei, “Optimized design and performance
evaluation of new cophase traction power supply system,” in Proc.
Asia-Pacific Power Energy Eng. Conf., 2009, pp. 1–6.
[10] G. Zeng and R. Hao, “Analysis and design of an active power filter for
three-phase balanced electrified railway power supply system,” in Proc.
5th Int. Conf. Power Electron. Drive Syst., 2003, vol. 2, pp. 1510–
1513.
[11] F. Zhou, Q. Li, and D. Qiu, “Co-phased traction power system based on
balanced transformer and hybrid compensation,” in Proc. Asia-Pacific
Power Energy Eng. Conf., 2009, pp. 1–4.
[12] A. Luo, C. Wu, J. Shen, Z. Shuai, and F. Ma, “Railway static power
conditioners for high-speed train traction power supply systems using
three-phase V/V transformers,” IEEE Trans. Power Electron., vol. 26,
no. 10, pp. 2844–2856, Oct. 2011.
[13] A. Luo, F. Ma, C. Wu, S. Q. Ding, Q.-C. Zhong, and Z. Shuai, “dualloop
control strategy of railway static power regulator under V/V electric
traction system,” IEEE Trans. Power Electron., vol. 26, no. 7, pp.
2079– 2091, Jul. 2011.
[14] Z. Shu, S. Xie, and Q. Li, “Single-phase back-to-back converter for
active power balancing, reactive power compensation, and harmonic
filtering in traction power system,” IEEE Trans. Power Electron., vol.
26, no. 2, pp. 334–343, Feb. 2011.
[15] W. Y. Dong, “Research on control of comprehensive compensation for
traction substations based on the STATCOM technology,” Ph.D.
dissertation, Tsinghua Univ., Beijing, China, 2009.
[16] V. , B. Corasaniti, M. B. Barbieri, P. L. Arnera, and M. I. Valla, “Hybrid
active filter for reactive and harmonics compensation in distribution
network,” IEEE Trans. Ind. Electron., vol. 56, no. 3, pp. 670–677, Mar.
2009.
[17] H. Akagi and K. Isozaki, “A hybrid active filter for a three-phase 12
pulse diode rectifier used as the front end of a medium-voltage motor
drive,” IEEE Trans. Power Electron., vol. 27, no. 1, pp. 69–77, Jan.
2012.
[18] Z. Shuai, A. Luo, J. Shen, and X. Wang, “Double closed-loop control
method for injection-type hybrid active power filter,” IEEE Trans.
Power Electron., vol. 26, no. 9, pp. 2393–2403, Sep. 20
[19] P. E. Sutherland, M. Waclawiak, and M. F. McGranaghan, “System
impacts evaluation of a single-phase traction load on a 115-kV
transmission system,” IEEE Trans. Power Delivery, vol. 21, no. 2, pp.
837–844, Apr. 2006.
[20] Keng-Weng Lao,NingYi Dai,,Wei-Gang Liu,and Man-Chung Wong,
“Hybrid Power Quality Compensator With Minimum DC Operation
Voltage Design for High-Speed Traction Power Systems” IEEE Trans.
power electronics, vol. 28, no. 4, april 2013.
Natesan.P, Power System Engineering, Valliammai Engineering College,
Chennai, India, 8148483654.
Madhusudanan.G, Electrical and Electronics Engineering, Valliammai
Engineering College, Chennai, India.](https://image.slidesharecdn.com/ijetr021124-171120162513/85/Ijetr021124-4-320.jpg)
Ijetr021124
- 1. International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869, Volume-2, Issue-1, January 2014 53 www.erpublication.org Abstract— A power quality problems in power systems have been increased due to nonlinear loads. To compensate these problems hybrid power compensator was proposed in this paper. A hybrid power compensator (HPC) is proposed in this paper to eliminate the harmonic currents, compensate power factor and voltage unbalance problems created by the nonlinear loads present in three phase systems. A HPC contains back to back converter by sharing the same dc link power and v/v transformer to provide a voltage balance in transmission line. Hysteresis harmonic current controller is used to produce pulse for back to back converter. A controller maintains the dc-link voltage and compensates the power factor, harmonic currents. A comparative analysis for traction system with and without HPC was performed using MATLAB-Simulink. Simulation results are provided to eliminate power quality problems effectively. Index Terms—HPC, traction power, harmonic elimination, power factor correction, non-linear loads, cophase system I. INTRODUCTION Highlight a section that you want to designate with a certain style, and then select the appropriate name on the style menu. The style will adjust your fonts and line spacing. Do not change the font sizes or line spacing to squeeze more text into a limited number of pages. Use italics for emphasis; do not underline. Electrified Railway Systems are very complex systems in which a variety of components (or subsystems) cooperate to realize the transport service for which the system has been designed. A railway system is perhaps one of the most critical real systems, from the safety and reliability viewpoint, because it must satisfy numerous requirements and presents complex architectural links among its various subsystems [3]. In fact, a lot of safety requirements are strongly dependent on correct interaction operation. The performance of this kind of systems strictly depends on the capability of the system to be correctly integrated. A correct approach to the analysis of traction systems is the fundamental starting point for the right design and functionality of this complex reality. The amount of negative-sequence currents depends on the topology of the traction power system, in particular, the type of traction transformers used [14]. Typical Manuscript received January 09, 2014. Natesan.P, Power System Engineering, Valliammai Engineering College, Chennai, India, 8148483654. Madhusudanan.G, Electrical and Electronics Engineering, Valliammai Engineering College, Chennai, India. transformers used include Scott transformers, Woodbridge transformers, three- phase V/V transformers, impedance-matching balance trans- formers, etc., [15]. Scott transformers, Woodbridge transformers are balanced transformers but three-phase V/V transformers are unbalanced. When balanced transformers are used, no negative-sequence current is injected into the public grid when two feeder sections consume the same power. However, for the traction systems with three-phase V/V transformers, the negative-sequence current injected into the public grid is half of the positive- sequence current even when two feeder sections consume the same power. The problem with this topology is that a strategy to effectively compensate the negative-sequence and harmonic currents needs to be developed. In this paper, a hybrid device combining active and passive compensators, named as the hybrid power compensator (HPC), is proposed for compensation in cophase traction power supply. The parameter design procedure for minimum HPC voltage operation as well as the minimum voltage rating achievable is discussed. II. V/V TRANSFORMER The structure of RPC with three-phase V/V transformers is depicted in Fig. 2. The 220-kV three-phase high-voltage source is converted into two 27.5-kV single-phase voltage sources, which are connected to the two feeder sections, via a three-phase V/V traction transformer. The turns ratio of the V/V traction transformer is KV [7]. The HPC consist of back to back coverter through a common dc capacitor with a stable dc-link voltage, is connected to the two feeder sections via two step- down transformers with a turns ratio of KD . The two converters are connected to the single-phase step-down transformers via two output inductor La and Lb respectively. Fig. 1 Construction diagram of V/V Transformer The two converters can be controlled as current sources to shift a certain amount of active power from one feeder section to the other. These two converters can also provide harmonic suppression and reactive power Analysis of Hybrid Power Compensator for Non-linear Traction Loads Natesan P, Madhusudanan G
- 2. Analysis of Hybrid Power Compensator for Non-linear Traction Loads 54 www.erpublication.org compensation [9]. Hence, the system can achieve integrated compensation of negative sequence currents, harmonic currents and reactive power. III. CONTROLLER The The control block of the system is Fig. 2 Hysteresis Controller The instantaneous load active and reactive power is computed using the modified instantaneous pq theory .The mathematical expression, in which vac and are the load voltage and current rms, while vacd and iLd are 90◦delay of load voltage and current, respectively. and refer to the instantaneous load active (real) and reactive (imaginary)power (3.1) The active power part can be split into dc part which corresponds to the fundamental average active load power; [12] and oscillating part which corresponds to the oscillating active power between system source and load and contributes as part of harmonics and reactive power (which need to be compensated). The mathematical expression is shown in (3.2) The required compensation power is then computed according to the power quality requirement, where and are the required active and reactive compensation power. (3.3) The reference of Vac and phase compensation current, and , can then be computed ,where and are the phase voltage and its 90◦ delay value (3.4) (3.5) The computed reference current signal is then sent to the hysteresis current controller, which pulse width modulated signals are generated for the electronic switches of and phase converters. The HPC balances the grid-side current by transferring active power from the phase to the phase.Concerning the design of the LC filter parameter, it is selected so as to reduce the harmonics compensation capacity of the compensator [14]. Although the highest load harmonic contents are located at the third harmonic frequency, the LC filter is tuned at the second highest load harmonics (fifth harmonic) for smaller physical size of the components. IV. SIMULATION RESULTS Simulations using MATLAB done to verify the before mentioned theoretical studies. The circuit schematic of the system used in simulations is provided in Fig. 12. The parameters are selected as close to practical applications as possible [16], [19]. The substation V/V transformer is composed of two 20 MVA single-phase transformers, with turning ratios of 110 kV/27.5 kV and 110 kV/13.75 kV. Traction loads are simulated using rectifier RL load, with linear capacity of 15 MVA. The compensation device is then connected across the two single-phase outputs of V/V transformer to provide power quality compensation of the system. [19] Notice that the LCL filter is included here to filter the ripples introduced by the compensator. A. Cophase Traction Power Without Compensation The system performance without compensation is investigated first. Shown in Fig. 4 is the three-phase source, secondary voltage, and current waveforms for cophase traction power without compensation [6]. It could be observed that the system suffers from unbalance, reactive power and harmonics problem. A traction load of 25MVA is connected to 110 KVA grid through step down transformer (110/25KV). Fig. 3 Cophase Traction Power Without Compensation Traction load is a time varying load which is represented by rectified with RL-load (non-linear load). In general the non-linear load generates harmonics, voltage unbalance, power factor variation and other power quality problems. The load we used on the test system generated a THD of 33.8% and power factor of the system was decreased to 0.77. Fig. 4 Vac side voltage and current without compensation
- 3. International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869, Volume-2, Issue-1, January 2014 55 www.erpublication.org Rectifier with RL load will be the best example of traction load. Traction loads are changes with time [14]. Traction power system connected to any one of the phase of three phase supply. It will cause voltage unbalance among other phases. Fig. 5 Unbalanced voltage and current in transmission line The single-phase back to-back converter is adopted in the power conditioner, which could balance the active currents between the transformer’s two secondary windings. One phase at the secondary side of the traction transformer directly supplies the traction loads. The other phase supplies the loads indirectly via a power conditioner. B. Cophase Traction Power With HPC Compensation Fig. 6 Cophase Traction Power With HPC Compensation HPQC is connected with a traction load of 25MVA which is connected to 110 KVA grid through step down transformer (110/25KV), to mitigate the THD and to increase the power factor. Traction load is a time varying load which is represented by rectified with RL-load (non-linear load). Fig. 7 Vac side voltage and current with HPC phase side traction load and side HPC is is connected. side traction loads are cause voltage unbalance and it will reduced by compensating voltage by using side transformer.Rectifier with RL load will be the best example of traction load [19]. Traction loads are changes with time. Traction power system connected to any one of the phase of three phase supply with Hybrid Power Quality Compensator. Fig. 8 balanced voltage and current in transmission line with HPC V. CONCLUSION A strategy to improve the power factor and eliminate harmonic currents in high-speed traction systems using co-phase hybrid power quality compensator (HPQC) was designed. The current references for the RPC converters are generated according to the load currents on both sections of the traction power supply system and current controllers are designed to track the current references.A comparative analysis for traction system with and without HPQC was performed using MATLAB-Simulink. TABLE I. OUTPUT COMPARISON Without compensation HPC compensation Power factor Harmonics ( %) Power factor Harmonics (%) 0.77 33.8 0.90 12.54 REFERENCES [1] H. Y. Kuo and T. H. Chen, “Rigorous evaluation of the voltage unbalance due to high-speed railway demands,” IEEE Trans. Veh. Technol., vol. 47, no. 4, pp. 1385–1389, Nov. 1998. [2] D. C. Howroyd, “Public-supply-system distortion and unbalance from single-phase a.c. traction,” Proc. Inst. Electr. Eng., vol. 124, no. 10, pp. 853–859, 1977. [3] S. T. Senini and P. J.Wolfs, “Novel topology for correction of unbalanced load in single phase electric traction systems,” in Proc. IEEE 33rd Annu. Power Electron. Spec. Conf., Jun. 2002, vol. 3, pp. 1208–1212. [4] Z. Zhang, B. Wu, J. Kang, and L. Luo, “A multi-purpose balanced transformer for railway traction applications,” IEEE Trans. Power Delivery, vol. 24, no. 2, pp. 711–718, Apr. 2009. [5] H. Wang, Y. Tian, and Q. Gui, “Evaluation of negative sequence current injection into the public grid from different traction substation in electrical railways,” in Proc. 20th Int. Conf. Exhib. Electr. Distrib.—Part 1, 2009, pp. 1–4. [6] C. Dai and Y. Sun, “Investigation of the imbalance current compensation for transformers used in electric railways,” in Proc. Asia-Pacific Power Energy Eng. Conf., 2010, pp. 1–4.
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