Open Science Research Excellence

Open Science Index

Commenced in January 2007 Frequency: Monthly Edition: International Paper Count: 31

31
10009974
Validation of Solar PV Inverter Harmonics Behaviour at Different Power Levels in a Test Network
Abstract:

Grid connected solar PV inverters need to be compliant to standard regulations regarding unwanted harmonic generation. This paper gives an introduction to harmonics, solar PV inverter voltage regulation and balancing through compensation and investigates the behaviour of harmonic generation at different power levels. Practical measurements of harmonics and power levels with a power quality data logger were made, on a test network at a university in Germany. The test setup and test results are discussed. The major finding was that between the morning and afternoon load peak windows when the PV inverters operate under low solar insolation and low power levels, more unwanted harmonics are generated. This has a huge impact on the power quality of the grid as well as capital and maintenance costs. The design of a single-tuned harmonic filter towards harmonic mitigation is presented.

30
10009672
Modular Harmonic Cancellation in a Multiplier High Voltage Direct Current Generator
Abstract:

Generation of high DC voltages is necessary for testing the insulation material of high voltage AC transmission lines with long lengths. The harmonic and ripple contents of the output DC voltage supplied by high voltage DC circuits require the use of costly capacitors to smooth the output voltage after rectification. This paper proposes a new modular multiplier high voltage DC generator with embedded Cockcroft-Walton circuits that achieve a negligible harmonic and ripple contents of the output DC voltage without the need for costly filters to produce a nearly constant output voltage. In this new topology, Cockcroft-Walton modules are connected in series to produce a high DC output voltage. The modules are supplied by low input AC voltage sources that have the same magnitude and frequency and shifted from each other by a certain angle to eliminate the harmonics from the output voltage. The small ripple factor is provided by the smoothing column capacitors and the phase shifted input voltages of the cascaded modules. The constituent harmonics within each module are determined using Fourier analysis. The viability of the proposed DC generator for testing purposes and the effectiveness of the cascaded connection are confirmed by numerical simulations using MATLAB/Simulink.

29
10009212
Investigation of Grid Supply Harmonic Effects in Wound Rotor Induction Machines
Abstract:

This paper presents an in-depth investigation of the effects of several grid supply harmonic voltages on the stator currents of an example wound rotor induction machine. The observed effects of higher order grid supply harmonics are identified using a finite element time stepping transient model, as well as a time-stepping electromagnetic model. In addition, a number of analytical equations to calculate the spectral content of the stator currents are presented in the paper. The presented equations are validated through comparison with the obtained spectra predicted using the finite element and electromagnetic models. The presented study provides a better understanding of the origin of supply harmonic effects identified in the stator currents of the example wound rotor induction machine. Furthermore, the study helps to understand the effects of higher order supply harmonics on the harmonic emissions of the wound rotor induction machine.  

28
10006390
Application of Single Tuned Passive Filters in Distribution Networks at the Point of Common Coupling
Abstract:

The harmonic distortion of voltage is important in relation to power quality due to the interaction between the large diffusion of non-linear and time-varying single-phase and three-phase loads with power supply systems. However, harmonic distortion levels can be reduced by improving the design of polluting loads or by applying arrangements and adding filters. The application of passive filters is an effective solution that can be used to achieve harmonic mitigation mainly because filters offer high efficiency, simplicity, and are economical. Additionally, possible different frequency response characteristics can work to achieve certain required harmonic filtering targets. With these ideas in mind, the objective of this paper is to determine what size single tuned passive filters work in distribution networks best, in order to economically limit violations caused at a given point of common coupling (PCC). This article suggests that a single tuned passive filter could be employed in typical industrial power systems. Furthermore, constrained optimization can be used to find the optimal sizing of the passive filter in order to reduce both harmonic voltage and harmonic currents in the power system to an acceptable level, and, thus, improve the load power factor. The optimization technique works to minimize voltage total harmonic distortions (VTHD) and current total harmonic distortions (ITHD), where maintaining a given power factor at a specified range is desired. According to the IEEE Standard 519, both indices are viewed as constraints for the optimal passive filter design problem. The performance of this technique will be discussed using numerical examples taken from previous publications.

27
10005825
Single Phase 13-Level D-STATCOM Inverter with Distributed System
Abstract:
The global energy consumption is increasing persistently and need for distributed power generation through renewable energy is essential. To meet the power requirements for consumers without any voltage fluctuations and losses, modeling and design of multilevel inverter with Flexible AC Transmission System (FACTS) capability is presented. The presented inverter is provided with 13-level cascaded H-bridge topology of Insulated Gate Bipolar Transistor (IGBTs) connected along with inbuilt Distributed Static Synchronous Compensators (DSTATCOM). The DSTATCOM device provides control of power factor stability at local feeder lines and the inverter eliminates Total Harmonic Distortion (THD). The 13-level inverter utilizes 52 switches of each H-bridge is fed with single DC sources separately and the Pulse Width Modulation (PWM) technique is used for switching IGBTs. The control strategy implemented for inverter transmits active power to grid as well as it maintains power factor to be stable with achievement of steady state power transmission. Significant outcome of this project is improvement of output voltage quality with steady state power transmission with low THD. Simulation of inverter with DSTATCOM is performed using MATLAB/Simulink environment. The scaled prototype model of proposed inverter is built and its results were validated with simulated results.
26
10003517
Impact of Harmonic Resonance and V-THD in Sohar Industrial Port–C Substation
Abstract:
This paper presents an analysis study on the impacts of the changes of the capacitor banks, the loss of a transformer, and the installation of distributed generation on the voltage total harmonic distortion and harmonic resonance. The study is applied in a real system in Oman, Sohar Industrial Port–C Substation Network. Frequency scan method and Fourier series analysis method are used with the help of EDSA software. Moreover, the results are compared with limits specified by national Oman distribution code.
25
10003180
Evaluation of Methodologies for Measuring Harmonics and Inter-Harmonics in Photovoltaic Facilities
Abstract:
The increase in electric power demand in face of environmental issues has intensified the participation of renewable energy sources such as photovoltaics, in the energy matrix of various countries. Due to their operational characteristics, they can generate time-varying harmonic and inter-harmonic distortions. For this reason, the application of methods of measurement based on traditional Fourier analysis, as proposed by IEC 61000-4-7, can provide inaccurate results. Considering the aspects mentioned herein, came the idea of the development of this work which aims to present the results of a comparative evaluation between a methodology arising from the combination of the Prony method with the Kalman filter and another method based on the IEC 61000-4-30 and IEC 61000-4-7 standards. Employed in this study were synthetic signals and data acquired through measurements in a 50kWp photovoltaic installation.
24
9998759
A Research on DC Voltage Offsets Generated by PWM-Controlled Inverters
Abstract:

The increasing penetration of Distributed Generation and storage connected to the distribution network via PWM converters increases the possibility of a DC-component (offset) in voltage or current flowing into the grid. This occurs when even harmonics are present in the network voltage. DC-components can affect the operation and safety of several grid components. Therefore, an investigation of the way they are produced is important in order to take appropriate measures for their elimination. Further research on DC-components that appear on output voltage of converters is performed for different parameters of PWM technique and characteristics of even harmonics.

23
9998882
Design of Active Power Filters for Harmonics on Power System and Reducing Harmonic Currents
Abstract:

In the last few years, harmonics have been occurred with the increasing use of nonlinear loads, and these harmonics have been an ever increasing problem for the line systems. This situation importantly affects the quality of power and gives large losses to the network. An efficient way to solve these problems is providing harmonic compensation through parallel active power filters. Many methods can be used in the control systems of the parallel active power filters which provide the compensation. These methods efficiently affect the performance of the active power filters. For this reason, the chosen control method is significant. In this study, Fourier analysis (FA) control method and synchronous reference frame (SRF) control method are discussed. These control methods are designed for both eliminate harmonics and perform reactive power compensation in MATLAB/Simulink pack program and are tested. The results have been compared for each two methods.

22
9998338
Adaptive Hysteresis Based SHAF Using PI and FLC Controller for Current Harmonics Mitigation
Abstract:

Due to the increased use of the power electronic equipment, harmonics in the power system has increased to a greater extent. These harmonics results a poor power quality causing a major effect on the customers. Shunt active filters (SHAF) are used for the mitigations of the current harmonics and to maintain constant DC link voltage. PI and Fuzzy logic controllers (FLC) were used to control the performance of the shunt active filter under both balance and unbalance source voltage condition. The results found were not satisfying the IEEE-519 standards of THD to be less than 5%. Hysteresis band current control was used to obtain the gating signals for SHAF, though it has some drawbacks and thus to obtain a better performance of the SHAF to mitigate the harmonics, adaptive hysteresis band current control scheme is implemented. Adaptive hysteresis based SHAF is used to obtain better compensation of current harmonics and to regulate the DC link voltage in a better way.

21
9997969
Power Quality Improvement Using PI and Fuzzy Logic Controllers Based Shunt Active Filter
Abstract:

In recent years the large scale use of the power electronic equipment has led to an increase of harmonics in the power system. The harmonics results into a poor power quality and have great adverse economical impact on the utilities and customers. Current harmonics are one of the most common power quality problems and are usually resolved by using shunt active filter (SHAF). The main objective of this work is to develop PI and Fuzzy logic controllers (FLC) to analyze the performance of Shunt Active Filter for mitigating current harmonics under balanced and unbalanced sinusoidal source voltage conditions for normal load and increased load. When the supply voltages are ideal (balanced), both PI and FLC are converging to the same compensation characteristics. However, the supply voltages are non-ideal (unbalanced), FLC offers outstanding results. Simulation results validate the superiority of FLC with triangular membership function over the PI controller.

20
9998235
Fuzzy Logic Controller Based Shunt Active Filter with Different MFs for Current Harmonics Elimination
Abstract:

One of the major power quality concerns in modern times is the problem of current harmonics. The current harmonics is caused due to the increase in non-linear loads which is largely dominated by power electronics devices. The Shunt active filtering is one of the best solutions for mitigating current harmonics. This paper describes a fuzzy logic controller based (FLC) based three Phase Shunt active Filter to achieve low current harmonic distortion (THD) and Reactive power compensation. The performance of fuzzy logic controller is analysed under both balanced sinusoidal and unbalanced sinusoidal source condition. The above controller serves the purpose of maintaining DC Capacitor Voltage constant. The proposed shunt active filter uses hysteresis current controller for current control of IGBT based PWM inverter. The simulation results of model in Simulink MATLAB reveals satisfying results.

19
16559
Repetitive Control and Feedback Dithering Modulation of a DC/AC Converter
Abstract:

Repetitive control and feedback dithering modulation are applied to a single-phase voltage source inverter, with an aim to eliminate harmonics and stabilize the inverter under load variations. The proposed control and modulation scheme comprise multiple loops of feedback, which helps improve inverter performance and robustness. Experimental results show that the designed inverter exhibits very low distortion at its output with THD of about 0.3% under different load variations.

18
3812
The Effect of Dynamic Eccentricity on Induction Machine Stator Currents (Part A)
Abstract:

Current spectrums of a high power induction machine was calculated for the cases of full symmetry, static and dynamic eccentricity. The calculations involve integration of 93 electrical plus four mechanical ordinary differential equations. Electrical equations account for variable inductances affected by slotting and eccentricities. The calculations were followed by Fourier analysis of the stator currents in steady state operation. The paper presents the stator current spectrums in full symmetry, static and dynamic eccentricity cases, and demonstrates the harmonics present in each case. The effect of dynamic eccentricity is demonstrating via comparing the current spectrums related to dynamic eccentricity cases with the full symmetry one. The paper includes one case study, refers to dynamic eccentricity, to present the spectrum of the measured current and demonstrate the existence of the harmonics related to dynamic eccentricity. The zooms of current spectrums around the main slot harmonic zone are included to simplify the comparison and prove the existence of the dynamic eccentricity harmonics in both calculated and measured current spectrums.

17
829
Firing Angle Range Control For Minimising Harmonics in TCR Employed in SVC-s
Abstract:
Most electrical distribution systems are incurring large losses as the loads are wide spread, inadequate reactive power compensation facilities and their improper control. A typical static VAR compensator consists of capacitor bank in binary sequential steps operated in conjunction with a thyristor controlled reactor of the smallest step size. This SVC facilitates stepless control of reactive power closely matching with load requirements so as to maintain power factor nearer to unity. This type of SVC-s requiring a appropriately controlled TCR. This paper deals with an air cored reactor suitable for distribution transformer of 3phase, 50Hz, Dy11, 11KV/433V, 125 KVA capacity. Air cored reactors are designed, built, tested and operated in conjunction with capacitor bank in five binary sequential steps. It is established how the delta connected TCR minimizes the harmonic components and the operating range for various electrical quantities as a function of firing angle is investigated. In particular firing angle v/s line & phase currents, D.C. components, THD-s, active and reactive powers, odd and even triplen harmonics, dominant characteristic harmonics are all investigated and range of firing angle is fixed for satisfactory operation. The harmonic spectra for phase and line quantities at specified firing angles are given. In case the TCR is operated within the bound specified in this paper established through simulation studies are yielding the best possible operating condition particularly free from all dominant harmonics.
16
6158
Rotor Flow Analysis using Animplicit Harmonic Balance Method
Abstract:

This paper is an extension of a previous work where a diagonally implicit harmonic balance method was developed and applied to simulate oscillatory motions of pitching airfoil and wing. A more detailed study on the accuracy, convergence, and the efficiency of the method is carried out in the current paperby varying the number of harmonics in the solution approximation. As the main advantage of the method is itsusage for the design optimization of the unsteady problems, its application to more practical case of rotor flow analysis during forward flight is carried out and compared with flight test data and time-accurate computation results.

15
6880
An Innovative Transient Free Adaptive SVC in Stepless Mode of Control
Abstract:

Electrical distribution systems are incurring large losses as the loads are wide spread, inadequate reactive power compensation facilities and their improper control. A comprehensive static VAR compensator consisting of capacitor bank in five binary sequential steps in conjunction with a thyristor controlled reactor of smallest step size is employed in the investigative work. The work deals with the performance evaluation through analytical studies and practical implementation on an existing system. A fast acting error adaptive controller is developed suitable both for contactor and thyristor switched capacitors. The switching operations achieved are transient free, practically no need to provide inrush current limiting reactors, TCR size minimum providing small percentages of nontriplen harmonics, facilitates stepless variation of reactive power depending on load requirement so as maintain power factor near unity always. It is elegant, closed loop microcontroller system having the features of self regulation in adaptive mode for automatic adjustment. It is successfully tested on a distribution transformer of three phase 50 Hz, Dy11, 11KV/440V, 125 KVA capacity and the functional feasibility and technical soundness are established. The controller developed is new, adaptable to both LT & HT systems and practically established to be giving reliable performance.

14
15328
Stability of Electrical Motor Supplied by a Five Level Inverter
Abstract:
The development of the power electronics has allowed increasing the precision and reliability of the electrical trainings, thanks to the adjustable inverters, as the Pulse Wide Modulation (PWM) five level inverters, which is the object of study in this article.The authors treat the relation between the law order adopted for a given system and the oscillations of the electrical and mechanical parameters of which the tolerance depends on the process with which they are integrated (paper factory, lifting of the heavy loads, etc.).Thus the best choice of the regulation indexes allows us to achieve stability and safety training without investment (management of existing equipment).
13
200
A Control Strategy Based on UTT and ISCT for 3P4W UPQC
Abstract:
This paper presents a novel control strategy of a threephase four-wire Unified Power Quality (UPQC) for an improvement in power quality. The UPQC is realized by integration of series and shunt active power filters (APFs) sharing a common dc bus capacitor. The shunt APF is realized using a thee-phase, four leg voltage source inverter (VSI) and the series APF is realized using a three-phase, three leg VSI. A control technique based on unit vector template technique (UTT) is used to get the reference signals for series APF, while instantaneous sequence component theory (ISCT) is used for the control of Shunt APF. The performance of the implemented control algorithm is evaluated in terms of power-factor correction, load balancing, neutral source current mitigation and mitigation of voltage and current harmonics, voltage sag and swell in a three-phase four-wire distribution system for different combination of linear and non-linear loads. In this proposed control scheme of UPQC, the current/voltage control is applied over the fundamental supply currents/voltages instead of fast changing APFs currents/voltages, there by reducing the computational delay and the required sensors. MATLAB/Simulink based simulations are obtained, which support the functionality of the UPQC. MATLAB/Simulink based simulations are obtained, which support the functionality of the UPQC.
12
13464
Star-Hexagon Transformer Supported UPQC
Abstract:
A new topology of unified power quality conditioner (UPQC) is proposed for different power quality (PQ) improvement in a three-phase four-wire (3P-4W) distribution system. For neutral current mitigation, a star-hexagon transformer is connected in shunt near the load along with three-leg voltage source inverters (VSIs) based UPQC. For the mitigation of source neutral current, the uses of passive elements are advantageous over the active compensation due to ruggedness and less complexity of control. In addition to this, by connecting a star-hexagon transformer for neutral current mitigation the over all rating of the UPQC is reduced. The performance of the proposed topology of 3P-4W UPQC is evaluated for power-factor correction, load balancing, neutral current mitigation and mitigation of voltage and currents harmonics. A simple control algorithm based on Unit Vector Template (UVT) technique is used as a control strategy of UPQC for mitigation of different PQ problems. In this control scheme, the current/voltage control is applied over the fundamental supply currents/voltages instead of fast changing APFs currents/voltages, thereby reducing the computational delay. Moreover, no extra control is required for neutral source current compensation; hence the numbers of current sensors are reduced. The performance of the proposed topology of UPQC is analyzed through simulations results using MATLAB software with its Simulink and Power System Block set toolboxes.
11
14237
Analytical Estimation of Rotor Loss Due to Stator Slotting of Synchronous PM Machines
Abstract:

In this paper, we analyze the rotor eddy currents losses provoqued by the stator slot harmonics developed in the permanent magnets or pole pieces of synchronous machines. An analytical approach is presented to evaluate the effect of slot ripples on rotor field and losses calculation. This analysis is then tested on a model by 2D/3D finite element (FE) calculation. The results show a good agreement on loss calculations when skin effect is negligible and the magnet is considered.

10
3192
Harmonics Elimination in Multilevel Inverter Using Linear Fuzzy Regression
Abstract:
Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.
9
9322
Testing the Accuracy of ML-ANN for Harmonic Estimation in Balanced Industrial Distribution Power System
Abstract:
In this paper, we analyze and test a scheme for the estimation of electrical fundamental frequency signals from the harmonic load current and voltage signals. The scheme was based on using two different Multi Layer Artificial Neural Networks (ML-ANN) one for the current and the other for the voltage. This study also analyzes and tests the effect of choosing the optimum artificial neural networks- sizes which determine the quality and accuracy of the estimation of electrical fundamental frequency signals. The simulink tool box of the Matlab program for the simulation of the test system and the test of the neural networks has been used.
8
5898
Artificial Neural Networks Application to Improve Shunt Active Power Filter
Abstract:
Active Power Filters (APFs) are today the most widely used systems to eliminate harmonics compensate power factor and correct unbalanced problems in industrial power plants. We propose to improve the performances of conventional APFs by using artificial neural networks (ANNs) for harmonics estimation. This new method combines both the strategies for extracting the three-phase reference currents for active power filters and DC link voltage control method. The ANNs learning capabilities to adaptively choose the power system parameters for both to compute the reference currents and to recharge the capacitor value requested by VDC voltage in order to ensure suitable transit of powers to supply the inverter. To investigate the performance of this identification method, the study has been accomplished using simulation with the MATLAB Simulink Power System Toolbox. The simulation study results of the new (SAPF) identification technique compared to other similar methods are found quite satisfactory by assuring good filtering characteristics and high system stability.
7
14006
Extraction of Fetal Heart Rate and Fetal Heart Rate Variability from Mother's ECG Signal
Abstract:

This paper describes a new method for extracting the fetal heart rate (fHR) and the fetal heart rate variability (fHRV) signal non-invasively using abdominal maternal electrocardiogram (mECG) recordings. The extraction is based on the fundamental frequency (Fourier-s) theorem. The fundamental frequency of the mother-s electrocardiogram signal (fo-m) is calculated directly from the abdominal signal. The heart rate of the fetus is usually higher than that of the mother; as a result, the fundamental frequency of the fetal-s electrocardiogram signal (fo-f) is higher than that of the mother-s (fo-f > fo-m). Notch filters to suppress mother-s higher harmonics were designed; then a bandpass filter to target fo-f and reject fo-m is implemented. Although the bandpass filter will pass some other frequencies (harmonics), we have shown in this study that those harmonics are actually carried on fo-f, and thus have no impact on the evaluation of the beat-to-beat changes (RR intervals). The oscillations of the time-domain extracted signal represent the RR intervals. We have also shown in this study that zero-to-zero evaluation of the periods is more accurate than the peak-to-peak evaluation. This method is evaluated both on simulated signals and on different abdominal recordings obtained at different gestational ages.

6
265
Estimation of Load Impedance in Presence of Harmonics
Abstract:

This paper presents a fast and efficient on-line technique for estimating impedance of unbalanced loads in power systems. The proposed technique is an application of a discrete timedynamic filter based on stochastic estimation theory which is suitable for estimating parameters in noisy environment. The algorithm uses sets of digital samples of the distorted voltage and current waveforms of the non-linear load to estimate the harmonic contents of these two signal. The non-linear load impedance is then calculated from these contents. The method is tested using practical data. Results are reported and compared with those obtained using the conventional least error squares technique. In addition to the very accurate results obtained, the method can detect and reject bad measurements. This can be considered as a very important advantage over the conventional static estimation methods such as the least error square method.

5
2097
Induction Motor Design with Limited Harmonic Currents Using Particle Swarm Optimization
Abstract:

This paper presents an optimal design of poly-phase induction motor using Quadratic Interpolation based Particle Swarm Optimization (QI-PSO). The optimization algorithm considers the efficiency, starting torque and temperature rise as objective function (which are considered separately) and ten performance related items including harmonic current as constraints. The QI-PSO algorithm was implemented on a test motor and the results are compared with the Simulated Annealing (SA) technique, Standard Particle Swarm Optimization (SPSO), and normal design. Some benchmark problems are used for validating QI-PSO. From the test results QI-PSO gave better results and more suitable to motor-s design optimization. Cµ code is used for implementing entire algorithms.

4
9508
Stability of Electrical Drives Supplied by a Three Level Inverter
Abstract:
The development of the power electronics has allowed increasing the precision and reliability of the electrical devices, thanks to the adjustable inverters, as the Pulse Wide Modulation (PWM) applied to the three level inverters, which is the object of this study. The authors treat the relation between the law order adopted for a given system and the oscillations of the electrical and mechanical parameters of which the tolerance depends on the process with which they are integrated (paper factory, lifting of the heavy loads, etc.).Thus, the best choice of the regulation indexes allows us to achieve stability and safety training without investment (management of existing equipment). The optimal behavior of any electric device can be achieved by the minimization of the stored electrical and mechanical energy.
3
5822
3D Shape Modelling of Left Ventricle: Towards Correlation of Myocardial Scintigraphy Data and Coronarography Result
Abstract:

The myocardial sintigraphy is an imaging modality which provides functional informations. Whereas, coronarography modality gives useful informations about coronary arteries anatomy. In case of coronary artery disease (CAD), the coronarography can not determine precisely which moderate lesions (artery reduction between 50% and 70%), known as the “gray zone", are haemodynamicaly significant. In this paper, we aim to define the relationship between the location and the degree of the stenosis in coronary arteries and the observed perfusion on the myocardial scintigraphy. This allows us to model the impact evolution of these stenoses in order to justify a coronarography or to avoid it for patients suspected being in the gray zone. Our approach is decomposed in two steps. The first step consists in modelling a coronary artery bed and stenoses of different location and degree. The second step consists in modelling the left ventricle at stress and at rest using the sphercical harmonics model and myocardial scintigraphic data. We use the spherical harmonics descriptors to analyse left ventricle model deformation between stress and rest which permits us to conclude if ever an ischemia exists and to quantify it.

2
12572
Simple and Advanced Models for Calculating Single-Phase Diode Rectifier Line-Side Harmonics
Abstract:
This paper proposes different methods for estimation of the harmonic currents of the single-phase diode bridge rectifier. Both simple and advanced methods are compared and the models are put into a context of practical use for calculating the harmonic distortion in a typical application. Finally, the different models are compared to measurements of a real application and convincing results are achieved.
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