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Hung-Cheng Chen
Department of Electrical Engineering National Chin‐Yi University of Technology No.57, Sec. 2, Zhongshan Rd., Taiping Dist. Taichung 41170 Taiwan

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Original research paper
Published: 04 August 2021 in IET Renewable Power Generation
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Due to the negative impact of a highly stochastic wind power fluctuation on the power quality and stability during high penetration of wind power in power systems, there is growing interest in power smoothing and energy redistribution in wind power systems by using large-scale energy storage technologies. The aim of this work is to use a vanadium redox flow battery as an energy storage system (ESS) to smooth wind power fluctuation with two system configurations and corresponding control strategies. As the first step, a vanadium redox flow battery (VRFB) mathematical model, underlain by electrochemical theories, is built to describe the battery behaviours in charge/discharge cycles. Accordingly, the aforementioned system configuration and power fluctuation smoothing schemes are proposed. At the end of this work, simulations are conducted on a 3.6 MW doubly-fed induction generator (DFIG) at a diversity of wind speeds for an assessment of feasibility that this work can be applied to a high penetration of wind power in practice. Simulation results reveal that power fluctuations can be improved by power smoothing. The root mean square deviation (RMSD) percentage can be reduced to less than 1%.

ACS Style

Feng‐Chang Gu; Hung‐Cheng Chen. Modelling and control of vanadium redox flow battery for smoothing wind power fluctuation. IET Renewable Power Generation 2021, 1 .

AMA Style

Feng‐Chang Gu, Hung‐Cheng Chen. Modelling and control of vanadium redox flow battery for smoothing wind power fluctuation. IET Renewable Power Generation. 2021; ():1.

Chicago/Turabian Style

Feng‐Chang Gu; Hung‐Cheng Chen. 2021. "Modelling and control of vanadium redox flow battery for smoothing wind power fluctuation." IET Renewable Power Generation , no. : 1.

Journal article
Published: 14 June 2021 in Energies
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This paper proposes a modular battery management system for an electric motorcycle. The system not only can accurately measure battery voltage, charging current, discharging current, and temperature but also can transmit the data to the mixed-signal processor for battery module monitoring. Moreover, the system can control the battery balancing circuit and battery protection switch to protect the battery module charging and discharging process safety. The modular battery management system is mainly composed of a mixed-signal processor, voltage measurement, current measurement, temperature measurement, battery balancing, and protection switch module. The testing results show that the errors between the voltage value measured by the voltage measurement module and the actual value are less than 0.5%, about 1% under the conditions of different charging and discharging currents of 9 A and 18 A for the current measuring module, less than 1% for the temperature measurement module; and the battery balancing in the battery management system during the charging process. When the module is charged at 4.5 A for about 805 s, each cell of the battery has reached the balancing state. Finally, the testing results validate that the modular battery management system proposed in this paper can effectively manage the battery balancing of each cell in the battery module, battery module overcharge, over-discharge, temperature protection, and control.

ACS Style

Hung-Cheng Chen; Shin-Shiuan Li; Shing-Lih Wu; Chung-Yu Lee. Design of a Modular Battery Management System for Electric Motorcycle. Energies 2021, 14, 3532 .

AMA Style

Hung-Cheng Chen, Shin-Shiuan Li, Shing-Lih Wu, Chung-Yu Lee. Design of a Modular Battery Management System for Electric Motorcycle. Energies. 2021; 14 (12):3532.

Chicago/Turabian Style

Hung-Cheng Chen; Shin-Shiuan Li; Shing-Lih Wu; Chung-Yu Lee. 2021. "Design of a Modular Battery Management System for Electric Motorcycle." Energies 14, no. 12: 3532.

Journal article
Published: 24 November 2019 in Energies
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A novel, active cell balancing circuit and charging strategy in lithium battery pack is proposed in this paper. The active cell balancing circuit mainly consists of a battery voltage measurement circuit and switch control circuit. First, all individual cell voltages are measured by an MSP430 microcontroller equipped with an isolation circuit and a filter circuit. Then, the maximum cell voltage difference is calculated by subtracting the minimum cell voltage from the maximum cell voltage. When the maximum cell voltage difference exceeds 0.05 V, the balancing action starts to carry on. The MSP430 microcontroller output controls signals to close the switches corresponding to the battery cell with the maximum voltage. At this time, the balancing charge power performs a balancing charge for other batteries, except for the one that is switched on. In addition, a three-stage balancing charge strategy is also proposed in this paper to achieve the goal of speedy charging with balancing action. In the first stage, a 0.5 C balancing current is used to perform pre-balanced charging on all battery cells until the maximum cell voltage difference is less than 0.05 V, which is required for entry to the second stage of charging. In the second stage, constant current charging of 1 C, coupled with 0.2 C balancing current charging is carried out, until the maximum battery cell voltage reaches 4.2 V, which is required for entry into the third stage of charging. In the third stage, a constant voltage charging is coupled with 0.2 C balancing current charging, until the maximum battery cell voltage reaches 4.25 V, which is required to complete the balancing charge. The imbalance of power between the battery cells during battery pack charging, which reduces battery charging efficiency and battery life, is thus effectively improved. In this paper, a six-cells-in-series and two-in parallel lithium battery pack is used to perform a balancing charge test. Test results show that the battery cells in the battery pack are capable of quickly completing a balancing charge under different initial voltages, the maximum voltage difference is reduced to within the range of 0.05 V, and the total time required for each balancing charge is approximately 3600 s.

ACS Style

Shing-Lih Wu; Hung-Cheng Chen; Chih-Hsuan Chien. A Novel Active Cell Balancing Circuit and Charging Strategy in Lithium Battery Pack. Energies 2019, 12, 4473 .

AMA Style

Shing-Lih Wu, Hung-Cheng Chen, Chih-Hsuan Chien. A Novel Active Cell Balancing Circuit and Charging Strategy in Lithium Battery Pack. Energies. 2019; 12 (23):4473.

Chicago/Turabian Style

Shing-Lih Wu; Hung-Cheng Chen; Chih-Hsuan Chien. 2019. "A Novel Active Cell Balancing Circuit and Charging Strategy in Lithium Battery Pack." Energies 12, no. 23: 4473.

Original article
Published: 08 July 2019 in Journal of Electrical Engineering & Technology
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Partial discharge (PD) is very likely to deteriorate the insulating materials in power facilities. For this sake, PD detection and pattern recognition are treated as an effective approach to diagnosing the high-voltage insulation of power systems. A novel PD feature extraction approach for defect pattern recognition of a gas-insulated switchgear (GIS) is developed and then presented in this paper, using fractional Fourier transform (FrFT). A PD detector is utilized to measure the PD signal of the GIS using an ultra high frequency sensor, which is first transformed to its FrFT as the order ranges from 0 to 1. A 3D characteristic spectrum is then constructed, according to which the fractal parameters are extracted as the constituents of the cluster domains of defect types. Extension matter-element models of the PD defect types are then established according to the experimentally derived PD features. Subsequently, the PD defect type can be directly identified using the correlation degree between a tested pattern and the matter-element models. The pattern recognition performance is investigated on 80 sets of PD patterns, and the performance of the proposed approach is demonstrated accordingly. High accuracy, accompanied with high tolerance, was reached in the presence of noise interference using FrFT.

ACS Style

Feng-Chang Gu; Hung-Cheng Chen; Bo-Yan Chen. A Fractional Fourier Transform-Based Approach for Gas-Insulated Switchgear Partial Discharge Recognition. Journal of Electrical Engineering & Technology 2019, 14, 2073 -2084.

AMA Style

Feng-Chang Gu, Hung-Cheng Chen, Bo-Yan Chen. A Fractional Fourier Transform-Based Approach for Gas-Insulated Switchgear Partial Discharge Recognition. Journal of Electrical Engineering & Technology. 2019; 14 (5):2073-2084.

Chicago/Turabian Style

Feng-Chang Gu; Hung-Cheng Chen; Bo-Yan Chen. 2019. "A Fractional Fourier Transform-Based Approach for Gas-Insulated Switchgear Partial Discharge Recognition." Journal of Electrical Engineering & Technology 14, no. 5: 2073-2084.

Journal article
Published: 19 April 2018 in IEEE Transactions on Dielectrics and Electrical Insulation
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As a key concern in a power system, a deteriorated insulation will cause a partial discharge phenomenon and hence degrades the power supply quality. Thus, a partial discharge test has been turned into an approach of significance to protect a power system from an unexpected fault. As the first step in this work, a defect cast resin transformer is treated as a test object, and the detected partial discharge data are then transformed into a time-frequency-energy distribution through the Hilbert-Huang-Transform (HTT). The distribution is capable of providing both time-domain and frequency-domain information. It is a highly promising approach to pattern identification of a partial discharge and fault diagnosis. There is an excellent adaptability when applied to a nonlinear as well as nonstationary signal analysis for HHT, but with two major concerns, that is, the determination of optimal shifting number and the identification of unintended illusive components. For this sake, a combination of Kolmogorov-Smirnov (K-S test) and a sorting by signal energy ratio is proposed in the determination of the optimal shifting number. Subsequently, illusive components are ridded through a cumulative K-S test, such that an intrinsic mode function (IMF) is precisely extracted, intrinsic physical meaning contained over each spectral band is well preserved, and a mode confusion problem is removed as well.

ACS Style

Feng-Chang Gu; Hung-Cheng Chen; Meng-Hung Chao. Application of improved Hilbert-Huang transform to partial discharge signal analysis. IEEE Transactions on Dielectrics and Electrical Insulation 2018, 25, 668 -677.

AMA Style

Feng-Chang Gu, Hung-Cheng Chen, Meng-Hung Chao. Application of improved Hilbert-Huang transform to partial discharge signal analysis. IEEE Transactions on Dielectrics and Electrical Insulation. 2018; 25 (2):668-677.

Chicago/Turabian Style

Feng-Chang Gu; Hung-Cheng Chen; Meng-Hung Chao. 2018. "Application of improved Hilbert-Huang transform to partial discharge signal analysis." IEEE Transactions on Dielectrics and Electrical Insulation 25, no. 2: 668-677.

Journal article
Published: 01 January 2018 in Sensors and Materials
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ACS Style

Shing-Lih Wu; Hung-Cheng Chen; Ming-Yang Tsai. AC Impedance-based Online State-of-charge Estimation for Li-ion Batteries. Sensors and Materials 2018, 539 .

AMA Style

Shing-Lih Wu, Hung-Cheng Chen, Ming-Yang Tsai. AC Impedance-based Online State-of-charge Estimation for Li-ion Batteries. Sensors and Materials. 2018; ():539.

Chicago/Turabian Style

Shing-Lih Wu; Hung-Cheng Chen; Ming-Yang Tsai. 2018. "AC Impedance-based Online State-of-charge Estimation for Li-ion Batteries." Sensors and Materials , no. : 539.

Journal article
Published: 04 October 2017 in Applied Sciences
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As a key concern in a power system, a deteriorated insulation is likely to bring about a partial discharge phenomenon and hence degrades the power supply quality. Thus, a partial discharge test has been turned into an approach of significance to protect a power system from an unexpected malfunction. An improved Hilbert–Huang Transformation (HHT) is proposed in this work as an effective way to address the issues of an optimal shifting number and illusive components, both suffered in a conventional HHT approach, and is then applied to a defect mode recognition for a partial discharge signal analysis in the case of a cross-linked polyethylene insulated power cable. As the first step, the partial discharge signal detected is converted through the proposed improved HHT to a time-frequency-energy 3D spectrum. Then as the second step, the fractal features contained therein are extracted by way of a fractal theory, and in the end the defect modes are recognized as intended by use of an extension method.

ACS Style

Fengchang Gu; Hungcheng Chen; MengHung Chao. Application of Improved Hilbert–Huang Transform to Partial Discharge Defect Model Recognition of Power Cables. Applied Sciences 2017, 7, 1021 .

AMA Style

Fengchang Gu, Hungcheng Chen, MengHung Chao. Application of Improved Hilbert–Huang Transform to Partial Discharge Defect Model Recognition of Power Cables. Applied Sciences. 2017; 7 (10):1021.

Chicago/Turabian Style

Fengchang Gu; Hungcheng Chen; MengHung Chao. 2017. "Application of Improved Hilbert–Huang Transform to Partial Discharge Defect Model Recognition of Power Cables." Applied Sciences 7, no. 10: 1021.

Journal article
Published: 13 August 2014 in Entropy
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The work is aimed at using the chaos synchronization error dynamics (CSED) technique for defect pattern recognition in gas insulated switchgear (GIS). The radiated electromagnetic waves generated due to internal defects were measured by the self-made ultrahigh frequency (UHF) micro-strip antenna, so as to determine whether partial discharge will occur. Firstly, a data pretreatment is performed on the measured raw data for the purpose of computational burden reduction. A characteristic matrix is then constructed according to dynamic error trajectories in a chaos synchronization system, subsequent to which characteristics are extracted. A comparison with the existing Hilbert-Huang Transform (HHT) method reveals that the two characteristics extracted from the CSED results presented herein using the fractal theory were recognized at a higher rate pattern.

ACS Style

Hung-Cheng Chen; Her-Terng Yau; Po-Yan Chen. Chaos Synchronization Error Technique-Based Defect Pattern Recognition for GIS through Partial Discharge Signal Analysis. Entropy 2014, 16, 4566 -4582.

AMA Style

Hung-Cheng Chen, Her-Terng Yau, Po-Yan Chen. Chaos Synchronization Error Technique-Based Defect Pattern Recognition for GIS through Partial Discharge Signal Analysis. Entropy. 2014; 16 (8):4566-4582.

Chicago/Turabian Style

Hung-Cheng Chen; Her-Terng Yau; Po-Yan Chen. 2014. "Chaos Synchronization Error Technique-Based Defect Pattern Recognition for GIS through Partial Discharge Signal Analysis." Entropy 16, no. 8: 4566-4582.

Journal article
Published: 22 May 2014 in Energies
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This paper presents a novel impedance-based approach to efficiently estimate the state of charge (SOC) of a Li-ion battery. By using an AC impedance analyzer, a database is constructed, containing records of AC impedance versus SOC. In practical applications, the SOC values can be found instantly once the contents of the database are referenced. For validation purposes, AC impedance comparisons are conducted using AC impedance analyzer as a benchmark at SOC of 0%, 50% and 100%, which indicate errors of 8.636%, 2.604% and 0.600%, respectively.

ACS Style

Shing-Lih Wu; Hung-Cheng Chen; Shuo-Rong Chou. Fast Estimation of State of Charge for Lithium-Ion Batteries. Energies 2014, 7, 3438 -3452.

AMA Style

Shing-Lih Wu, Hung-Cheng Chen, Shuo-Rong Chou. Fast Estimation of State of Charge for Lithium-Ion Batteries. Energies. 2014; 7 (5):3438-3452.

Chicago/Turabian Style

Shing-Lih Wu; Hung-Cheng Chen; Shuo-Rong Chou. 2014. "Fast Estimation of State of Charge for Lithium-Ion Batteries." Energies 7, no. 5: 3438-3452.

Research article
Published: 24 April 2014 in Mathematical Problems in Engineering
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The purpose of the paper is to analyze and improve the transient stability of an industrial combined heat and power (CHP) system in a high-tech science park in Taiwan. The CHP system installed two 161kV/161kV high-impendence transformers to connect with Taipower System (TPS) for both decreasing the short-circuit fault current and increasing the fault critical clearing time. The transient stabilities of three types of operation modes in CHP units, 3G1S, 2G1S, and 1G1S, are analyzed. Under the 3G1S operation mode, the system frequency is immediately restored to 60Hz after tie line tripping with the TPS. Under the 1G1S and 2G1S operation modes, the system frequencies will continuously decrease and eventually become unstable. A novel transient stability improvement approach using load shedding technique based on the change in frequency is proposed to improve the transient stability.

ACS Style

Hung-Cheng Chen; Long-Yi Chang; Li-Qun Shang. Transient Stability Improvement for Combined Heat and Power System Using Load Shedding. Mathematical Problems in Engineering 2014, 2014, 1 -8.

AMA Style

Hung-Cheng Chen, Long-Yi Chang, Li-Qun Shang. Transient Stability Improvement for Combined Heat and Power System Using Load Shedding. Mathematical Problems in Engineering. 2014; 2014 ():1-8.

Chicago/Turabian Style

Hung-Cheng Chen; Long-Yi Chang; Li-Qun Shang. 2014. "Transient Stability Improvement for Combined Heat and Power System Using Load Shedding." Mathematical Problems in Engineering 2014, no. : 1-8.

Journal article
Published: 27 January 2014 in Energies
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This paper presents a nonlinear control strategy utilizing the linearization and input-output decoupling approach for a nonlinear dynamic model of proton exchange membrane fuel cells (PEMFCs). The multiple-input single-output (MISO) nonlinear model of the PEMFC is derived first. The dynamic model is then transformed into a multiple-input multiple-output (MIMO) square system by adding additional states and outputs so that the linearization and input-output decoupling approach can be directly applied. A PI tracking control is also introduced to the state feedback control law in order to reduce the steady-state errors due to parameter uncertainty. This paper also proposes an adaptive genetic algorithm (AGA) for the multi-objective optimization design of the tracking controller. The comprehensive results of simulation demonstrate that the PEMFC with nonlinear control has better transient and steady-state performance compared to conventional linear techniques.

ACS Style

Long-Yi Chang; Hung-Cheng Chen. Linearization and Input-Output Decoupling for Nonlinear Control of Proton Exchange Membrane Fuel Cells. Energies 2014, 7, 591 -606.

AMA Style

Long-Yi Chang, Hung-Cheng Chen. Linearization and Input-Output Decoupling for Nonlinear Control of Proton Exchange Membrane Fuel Cells. Energies. 2014; 7 (2):591-606.

Chicago/Turabian Style

Long-Yi Chang; Hung-Cheng Chen. 2014. "Linearization and Input-Output Decoupling for Nonlinear Control of Proton Exchange Membrane Fuel Cells." Energies 7, no. 2: 591-606.

Article
Published: 01 March 2013 in IET Science, Measurement & Technology
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Partial discharge (PD) pattern identification is an important tool in high-voltage (HV) insulation diagnosis of power systems. Based on an extension method, a PD identification system for HV power transformers is proposed in this paper. A PD detector is used to measure the raw three-dimensional (3D) PD patterns of epoxy resin power transformers using an L sensor, according to which two fractal features (the fractal dimension and the lacunarity) and the mean discharge are extracted as critical PD features that form the cluster domains of defect types. The matter–element models of the PD defect types are then built according to the PD features derived from practical experimental results. The PD defect type can be directly identified by the correlation degrees between a tested pattern and the matter–element models. To demonstrate the effectiveness of the PD features extraction and the extension method, the identification ability is investigated on 144 sets of field-test PD patterns of epoxy resin power transformers. Compared with a multilayer neural network and K-means methods, the results show that a high accuracy together with a high tolerance in the presence of noise interference is reached by use of the extension method.

ACS Style

Hung‐Cheng Chen. Partial discharge identification system for high‐voltage power transformers using fractal feature‐based extension method. IET Science, Measurement & Technology 2013, 7, 77 -84.

AMA Style

Hung‐Cheng Chen. Partial discharge identification system for high‐voltage power transformers using fractal feature‐based extension method. IET Science, Measurement & Technology. 2013; 7 (2):77-84.

Chicago/Turabian Style

Hung‐Cheng Chen. 2013. "Partial discharge identification system for high‐voltage power transformers using fractal feature‐based extension method." IET Science, Measurement & Technology 7, no. 2: 77-84.

Journal article
Published: 01 January 2013 in International Journal of Environmental Science and Development
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ACS Style

Po-Hung Chen; Hung-Cheng Chen; Feng-Jih Wu; Li-Ming Chen; An Liu. Environmental Protection Power Dispatch for Modern Power System. International Journal of Environmental Science and Development 2013, 501 -508.

AMA Style

Po-Hung Chen, Hung-Cheng Chen, Feng-Jih Wu, Li-Ming Chen, An Liu. Environmental Protection Power Dispatch for Modern Power System. International Journal of Environmental Science and Development. 2013; ():501-508.

Chicago/Turabian Style

Po-Hung Chen; Hung-Cheng Chen; Feng-Jih Wu; Li-Ming Chen; An Liu. 2013. "Environmental Protection Power Dispatch for Modern Power System." International Journal of Environmental Science and Development , no. : 501-508.

Book chapter
Published: 25 November 2012 in Lecture Notes in Electrical Engineering
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As a key concern in a power system, a deteriorated insulation will cause a partial discharge phenomenon and hence degrades the power supply quality. Thus, a partial discharge test has been turned into an approach of significance to protect a power system from an unexpected fault. As the first step in this work, a defect cast resin transformer is treated as a test object, and the detected partial discharge data are then transformed into a time–frequency–energy distribution through the Hilbert–Huang Transform. The distribution is capable of providing both time-domain and frequency-domain information. It is a highly promising approach to pattern identification of a partial discharge and fault diagnosis.

ACS Style

Hung-Cheng Chen. Hilbert–Huang Transform Based Partial Discharge Signal Analysis. Lecture Notes in Electrical Engineering 2012, 206, 49 -55.

AMA Style

Hung-Cheng Chen. Hilbert–Huang Transform Based Partial Discharge Signal Analysis. Lecture Notes in Electrical Engineering. 2012; 206 ():49-55.

Chicago/Turabian Style

Hung-Cheng Chen. 2012. "Hilbert–Huang Transform Based Partial Discharge Signal Analysis." Lecture Notes in Electrical Engineering 206, no. : 49-55.

Journal article
Published: 01 June 2012 in Expert Systems with Applications
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This paper presents a new partial discharge (PD) pattern recognition method based on the cerebellar model articulation controller (CMAC). CMAC is an adaptive system by which defect types for partial discharge can be identified by referring to a table rather than by mathematical solution of simultaneous equations. CMAC maps input features of partial discharge into an input vector which is used to address a memory where the appropriate defect types are stored. Five types of defect models are well-designed on the base of investigation of many power apparatus failures. A PD detector is used to measure the raw three-dimension (3D) PD patterns, from which the fractal dimension, the lacunarity, and the mean discharges of phase windows are extracted as PD features. These critical features form the cluster domains of defect types. Using the characteristics of self-learning, association, and generalization, like the cerebellum of human being, the proposed CMAC-based pattern recognition scheme enables a powerful, straightforward, and efficient pattern recognition method. Moreover, the CMAC has the advantages of higher accuracy, shorter learning times, and noise tolerance, which are useful in recognizing the PD patterns of electrical apparatus. To demonstrate the effectiveness of the proposed method, comparative studies using a multilayer neural network (MNN) and K-means method are conducted on 200 sets of field-test PD patterns with high accuracy and high tolerance in noise interference.

ACS Style

Hung-Cheng Chen; Feng-Chang Gu. Pattern recognition with cerebellar model articulation controller and fractal features on partial discharges. Expert Systems with Applications 2012, 39, 6575 -6584.

AMA Style

Hung-Cheng Chen, Feng-Chang Gu. Pattern recognition with cerebellar model articulation controller and fractal features on partial discharges. Expert Systems with Applications. 2012; 39 (7):6575-6584.

Chicago/Turabian Style

Hung-Cheng Chen; Feng-Chang Gu. 2012. "Pattern recognition with cerebellar model articulation controller and fractal features on partial discharges." Expert Systems with Applications 39, no. 7: 6575-6584.

Journal article
Published: 01 February 2012 in Expert Systems with Applications
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ACS Style

Hung-Cheng Chen; Feng-Chang Gu; Meng-Hui Wang. A novel extension neural network based partial discharge pattern recognition method for high-voltage power apparatus. Expert Systems with Applications 2012, 39, 3423 -3431.

AMA Style

Hung-Cheng Chen, Feng-Chang Gu, Meng-Hui Wang. A novel extension neural network based partial discharge pattern recognition method for high-voltage power apparatus. Expert Systems with Applications. 2012; 39 (3):3423-3431.

Chicago/Turabian Style

Hung-Cheng Chen; Feng-Chang Gu; Meng-Hui Wang. 2012. "A novel extension neural network based partial discharge pattern recognition method for high-voltage power apparatus." Expert Systems with Applications 39, no. 3: 3423-3431.

Journal article
Published: 16 December 2008 in International Journal of Applied Electromagnetics and Mechanics
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ACS Style

Hung-Cheng Chen; Kuo-Hua Huang. Finite element analysis of coupled electromagnetic and thermal fields within a practical induction heating cooker. International Journal of Applied Electromagnetics and Mechanics 2008, 28, 413 -427.

AMA Style

Hung-Cheng Chen, Kuo-Hua Huang. Finite element analysis of coupled electromagnetic and thermal fields within a practical induction heating cooker. International Journal of Applied Electromagnetics and Mechanics. 2008; 28 (4):413-427.

Chicago/Turabian Style

Hung-Cheng Chen; Kuo-Hua Huang. 2008. "Finite element analysis of coupled electromagnetic and thermal fields within a practical induction heating cooker." International Journal of Applied Electromagnetics and Mechanics 28, no. 4: 413-427.