Fang Zhuo
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Fang Zhuo has a total of 218 co-authors. Here are the top co-authors by number of shared publications:
Hao Yi
State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an, China
33 shared publications- Hao Yi
School of Electrical Engineering, Xian Jiaotong University, Xian, China
33 shared publications Feng Wang
School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, China
32 shared publications- Feng Wang
School of Electrical Engineering, Xian Jiaotong University, Xian, China
30 shared publications Shuhuai Shi
State Key Laboratory of Electrical Insulation and Power Equipment Xi'an Jiaotong University Xi'an People's Republic of China
14 shared publications- Jiachen Tian
Xi'an Jiaotong University Xi'an China
13 shared publications
Latest Publications
- 15 June 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Instrumentation and Measurement
- Vol. 75 (00189456) , 9005219
Single-Phase Grounding Fault Localization for Neutral Noneffectively Grounded Networks With Control-Heterogeneous Distributed Generations
The integration of the distributed generations (DG) stations distorts the conventional single-phase grounding (SPG) fault localization results. Considering the flexibility of DGs, a novel SPG fault localization methodology for the neutral non-effectively grounded distribution networks is proposed in this article. In the proposed method, DGs are controlled to inject the harmonic currents to actively participate in the localization process. Firstly, the SPG fault characteristic at the harmonic frequency is analyzed, and the measured harmonic impedance at the feeder junction is shown to correlate with the fault distance. Subsequently, typical control strategies of the grid-following and grid-forming DGs under the SPG fault are modified to assist the harmonic impedance detection. Then, the coupling effect between DGs at various feeders is studied, and this coupling effect is eliminated by modifying the output impedance of the control-heterogeneous DGs at the special frequency band. Finally, the SPG fault localization can be realized through the coordination operation of the multiple control-heterogeneous DGs, and the simulation model and the hardware-in-loop experimental results verify the effectiveness under various testing conditions.
- 15 June 2026
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Instrumentation and Measurement
- Vol. 75 (00189456) , 9005219
Single-Phase Grounding Fault Localization for Neutral Noneffectively Grounded Networks With Control-Heterogeneous Distributed Generations
The integration of the distributed generations (DG) stations distorts the conventional single-phase grounding (SPG) fault localization results. Considering the flexibility of DGs, a novel SPG fault localization methodology for the neutral non-effectively grounded distribution networks is proposed in this article. In the proposed method, DGs are controlled to inject the harmonic currents to actively participate in the localization process. Firstly, the SPG fault characteristic at the harmonic frequency is analyzed, and the measured harmonic impedance at the feeder junction is shown to correlate with the fault distance. Subsequently, typical control strategies of the grid-following and grid-forming DGs under the SPG fault are modified to assist the harmonic impedance detection. Then, the coupling effect between DGs at various feeders is studied, and this coupling effect is eliminated by modifying the output impedance of the control-heterogeneous DGs at the special frequency band. Finally, the SPG fault localization can be realized through the coordination operation of the multiple control-heterogeneous DGs, and the simulation model and the hardware-in-loop experimental results verify the effectiveness under various testing conditions.
- Open Access
- 10 March 2026
- Published by Elsevier in SSRN Electronic Journal
Stage-based Protection Scheme via Harmonic Undervoltage in Power Electronic Converters Interfaced Distribution Networks
The conventional overcurrent protection fails to isolate the permanent short-circuit fault with the power electronic converters interface, hindering the utilization of various converters for power supply restoration. A novel protection scheme based on the harmonic undervoltage is proposed in this paper to realize accurate and rapid fault isolation. From the system-level perspective, the three-stage harmonic undervoltage protection method is proposed, enabling coordinated operation between primary and backup protection. The operation principle, parameter design, and extension scheme for complex networks of the novel protection method are introduced, enhancing the computational efficiency and adaptability. From the converter-level perspective, the transient overcurrent limited strategy based on voltage feedforward dynamic gain adjustment is presented for avoiding undesired device shutdown during faults. Besides, the active harmonic injection loop is added to the control system, assisting the operation of the proposed protection method. The simulation and the experimental results indicate that the above method can rapidly locate various short-circuit faults in networks with converters, facilitating flexible control of the distribution networks.
- 10 March 2026
- Published by Elsevier in SSRN Electronic Journal
Open AccessStage-based Protection Scheme via Harmonic Undervoltage in Power Electronic Converters Interfaced Distribution Networks
The conventional overcurrent protection fails to isolate the permanent short-circuit fault with the power electronic converters interface, hindering the utilization of various converters for power supply restoration. A novel protection scheme based on the harmonic undervoltage is proposed in this paper to realize accurate and rapid fault isolation. From the system-level perspective, the three-stage harmonic undervoltage protection method is proposed, enabling coordinated operation between primary and backup protection. The operation principle, parameter design, and extension scheme for complex networks of the novel protection method are introduced, enhancing the computational efficiency and adaptability. From the converter-level perspective, the transient overcurrent limited strategy based on voltage feedforward dynamic gain adjustment is presented for avoiding undesired device shutdown during faults. Besides, the active harmonic injection loop is added to the control system, assisting the operation of the proposed protection method. The simulation and the experimental results indicate that the above method can rapidly locate various short-circuit faults in networks with converters, facilitating flexible control of the distribution networks.
- 23 December 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 14 (3) , 3099-3115
Lightweight DC-Link Capacitance Design Scheme for Back-to-Back Converters in Soft Open Point
The DC-link capacitors in back-to-back (BTB) converters perform as a necessary DC-link voltage supporter and power buffer for both sides. However, the DC-link capacitor is normally over-designed due to performance considerations, causing a larger volume and higher cost. This article proposes a more comprehensive and accurate design scheme of the DC-link capacitance for the BTB three-level neutral point clamped converter, achieving the DC bus lightweight design. Multidimensional aspects are considered when quantifying the capacitance constraints, including small-signal interactive stability, DC-link voltage fluctuation facing a given power step change from both AC sides, and switching ripple filtering performances. Corresponding to the above multidimensional aspects, the stability constraint, response speed constraint, and filtering performance constraint of the DC-link capacitance and the control parameter value are analyzed. Additionally, the active capacitor is adopted to suppress the neutral point voltage low-frequency oscillation and to avoid the unfavorable boundary reduction of the DC-link capacitance selection. The effectiveness of the proposed lightweight DC-link capacitance design scheme is validated through simulations and experimental results. Experimental results indicate that the DC-link capacitance of each converter can be reduced to 10μF in the 2kW experimental BTB converter, realizing over 60% volume reduction of the DC bus compared with conventional designs.
- 23 December 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 14 (3) , 3099-3115
Lightweight DC-Link Capacitance Design Scheme for Back-to-Back Converters in Soft Open Point
The DC-link capacitors in back-to-back (BTB) converters perform as a necessary DC-link voltage supporter and power buffer for both sides. However, the DC-link capacitor is normally over-designed due to performance considerations, causing a larger volume and higher cost. This article proposes a more comprehensive and accurate design scheme of the DC-link capacitance for the BTB three-level neutral point clamped converter, achieving the DC bus lightweight design. Multidimensional aspects are considered when quantifying the capacitance constraints, including small-signal interactive stability, DC-link voltage fluctuation facing a given power step change from both AC sides, and switching ripple filtering performances. Corresponding to the above multidimensional aspects, the stability constraint, response speed constraint, and filtering performance constraint of the DC-link capacitance and the control parameter value are analyzed. Additionally, the active capacitor is adopted to suppress the neutral point voltage low-frequency oscillation and to avoid the unfavorable boundary reduction of the DC-link capacitance selection. The effectiveness of the proposed lightweight DC-link capacitance design scheme is validated through simulations and experimental results. Experimental results indicate that the DC-link capacitance of each converter can be reduced to 10μF in the 2kW experimental BTB converter, realizing over 60% volume reduction of the DC bus compared with conventional designs.
- 4 December 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Power Electronics
- Vol. 41 (5) , 8559-8578
Topology and Control Method for Reconstructable Hybrid Distribution Transformer to Enhance the Compensation Capability
The traditional hybrid distribution transformer (HDT), comprising a three-phase main transformer and power electronic converters, is widely used to address voltage sag and reactive loads in distribution networks. However, its compensation performance is constrained by the limited capacity of the converters. In scenarios involving severe voltage sags or excessive reactive loads, the HDT may fail to provide complete compensation. To address this limitation, this article introduces a reconstructable hybrid distribution transformer (REC-HDT) with multiple operating modes, designed to enhance current and voltage compensation capabilities without significantly increasing costs. The topology and three operating modes of the REC-HDT are meticulously designed and analyzed. The compensation mechanisms for voltage and current are elucidated through a detailed examination of power flow between the converter and the transformer. Furthermore, an enhanced control strategy is proposed to support smooth mode transitions across various operating conditions. Simulation studies and experimental validation demonstrate the feasibility and effectiveness of the REC-HDT topology and control strategy.
- 4 December 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Power Electronics
- Vol. 41 (5) , 8559-8578
Topology and Control Method for Reconstructable Hybrid Distribution Transformer to Enhance the Compensation Capability
The traditional hybrid distribution transformer (HDT), comprising a three-phase main transformer and power electronic converters, is widely used to address voltage sag and reactive loads in distribution networks. However, its compensation performance is constrained by the limited capacity of the converters. In scenarios involving severe voltage sags or excessive reactive loads, the HDT may fail to provide complete compensation. To address this limitation, this article introduces a reconstructable hybrid distribution transformer (REC-HDT) with multiple operating modes, designed to enhance current and voltage compensation capabilities without significantly increasing costs. The topology and three operating modes of the REC-HDT are meticulously designed and analyzed. The compensation mechanisms for voltage and current are elucidated through a detailed examination of power flow between the converter and the transformer. Furthermore, an enhanced control strategy is proposed to support smooth mode transitions across various operating conditions. Simulation studies and experimental validation demonstrate the feasibility and effectiveness of the REC-HDT topology and control strategy.
- 21 August 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Industry Applications
- Vol. 62 (1) , 1539-1550
An Improved Virtual DC Machine Control for Inertia Enhancement in DC Microgrid
Virtual DC Machine (VDCM) control is a promising approach for providing inertia support in DC microgrids, thus enhancing voltage stability. However, it suffers from a complex model and difficult parameter tuning. For this issue, an improved VDCM (IVDCM) control strategy is proposed, offering several advantages over the conventional VDCM (CVDCM) control. Specifically, compared to CVDCM, the voltage recovery control in IVDCM is moved after the VDCM loop, and a capacitor current feedback is adopted in the current inner loop. The improved control structure enables the IVDCM to provide more inertial power and mitigate the DC bus voltage fluctuations. Furthermore, the small-signal output impedance of the IVDCM can be simplified into a second-order model. The time-domain expressions for the DC output voltage are then derived, and the dynamic performance indices and constraints of the IVDCM are established, defining the feasible region for IVDCM control parameters. Consequently, an intuitive approach for control parameter design is achievable. Simulation and experimental results demonstrate the effectiveness of the proposed IVDCM control strategy and the associated parameter design method.
- 21 August 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Industry Applications
- Vol. 62 (1) , 1539-1550
An Improved Virtual DC Machine Control for Inertia Enhancement in DC Microgrid
Virtual DC Machine (VDCM) control is a promising approach for providing inertia support in DC microgrids, thus enhancing voltage stability. However, it suffers from a complex model and difficult parameter tuning. For this issue, an improved VDCM (IVDCM) control strategy is proposed, offering several advantages over the conventional VDCM (CVDCM) control. Specifically, compared to CVDCM, the voltage recovery control in IVDCM is moved after the VDCM loop, and a capacitor current feedback is adopted in the current inner loop. The improved control structure enables the IVDCM to provide more inertial power and mitigate the DC bus voltage fluctuations. Furthermore, the small-signal output impedance of the IVDCM can be simplified into a second-order model. The time-domain expressions for the DC output voltage are then derived, and the dynamic performance indices and constraints of the IVDCM are established, defining the feasible region for IVDCM control parameters. Consequently, an intuitive approach for control parameter design is achievable. Simulation and experimental results demonstrate the effectiveness of the proposed IVDCM control strategy and the associated parameter design method.
- 25 December 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 13 (1) , 747-758
Light-Load Optimization Strategy for CLLC Resonant Converters Based on Asymmetric Variable Duty-Cycle Modulation Control
The CLLC resonant converter is a bidirectional isolated DC/DC converter with excellent soft-switching characteristics. However, the CLLC resonant converter exhibits poor voltage regulation and low operating efficiency under light-load conditions. Therefore, to optimize the light-load voltage regulation performance and enhance the operating efficiency of the CLLC resonant converter under light-load conditions, this paper proposes an asymmetric variable duty-cycle modulation (AVDM) control method. AVDM control regulates the output voltage under light-load conditions by varying the duty-cycle of the asymmetric square waves in the primary and secondary circuits. Additionally, this paper adopts a multi-frequency modeling strategy based on a feedforward neural network (FNN) to indirectly analyze the time-domain characteristics of the CLLC resonant converter when using AVDM control. Based on the converter’s time-domain characteristics, the optimal operating points that ensure zero-voltage-switching (ZVS) operation in the CLLC resonant converter under various light-load conditions can be determined. Furthermore, a closed-loop control system utilizing AVDM control can be designed based on the optimal operating points. Finally, the feasibility of the proposed AVDM control is verified by a 2kW rated power CLLC resonant converter experimental prototype.
- 25 December 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 13 (1) , 747-758
Light-Load Optimization Strategy for CLLC Resonant Converters Based on Asymmetric Variable Duty-Cycle Modulation Control
The CLLC resonant converter is a bidirectional isolated DC/DC converter with excellent soft-switching characteristics. However, the CLLC resonant converter exhibits poor voltage regulation and low operating efficiency under light-load conditions. Therefore, to optimize the light-load voltage regulation performance and enhance the operating efficiency of the CLLC resonant converter under light-load conditions, this paper proposes an asymmetric variable duty-cycle modulation (AVDM) control method. AVDM control regulates the output voltage under light-load conditions by varying the duty-cycle of the asymmetric square waves in the primary and secondary circuits. Additionally, this paper adopts a multi-frequency modeling strategy based on a feedforward neural network (FNN) to indirectly analyze the time-domain characteristics of the CLLC resonant converter when using AVDM control. Based on the converter’s time-domain characteristics, the optimal operating points that ensure zero-voltage-switching (ZVS) operation in the CLLC resonant converter under various light-load conditions can be determined. Furthermore, a closed-loop control system utilizing AVDM control can be designed based on the optimal operating points. Finally, the feasibility of the proposed AVDM control is verified by a 2kW rated power CLLC resonant converter experimental prototype.
- 8 November 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Transportation Electrification
- Vol. 11 (2) , 5912-5926
A Novel Dual-Input Split-Source Multilevel Inverter With Single-Stage-Integrated Dynamic Voltage-Boosting Feature for Hybrid Energy Storage in Transportation Systems
Advanced and reliable power converter solutions are fundamental to advancing future transportation systems and facilitating the ongoing transition towards environmentally sustainable technologies. Transportation systems can employ multiple sources to improve their reliability and economic operation. Therefore, a novel dual-input multilevel inverter configuration is proposed and designed in this paper for multi-source transportation applications. The proposed topology synthesizes the dual-input split source multilevel inverter and switching capacitor (SC-DSSMLI) units, resulting in a high voltage boosting ratio due to its integrated boost converter stage. Additionally, the layout is compact and cost-effective, leveraging a modular switched capacitor (SC) structure to produce multiple output levels without increasing the number of DC sources. Furthermore, the topology’s scalability is enhanced by stacking additional SC stages. The inductor duty cycle and SC unit performance can be adjusted to achieve the desired boosting factor. A modified level-shifted pulse width modulation technique ensures efficient operation of the proposed SC-DSSMLI topology, eliminating the complexity of the modulation schemes or additional calculations. The SC-DSSMLI’s capability to operate efficiently with single or dual-input sources offers significant flexibility over existing dual-input topologies. The continuous input inductor current is another key feature, along with a method to mitigate inrush current, which can damage SCs. Experimental results, alongside topological comparisons and various performance criteria, are presented in the paper, confirming the benefits of reduced component count, high operational efficiency. Furthermore, the paper provides a comprehensive analysis of the stress experienced by all switches, along with a count of passive elements, offering a detailed comparison with other existing topologies.
- 8 November 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Transportation Electrification
- Vol. 11 (2) , 5912-5926
A Novel Dual-Input Split-Source Multilevel Inverter With Single-Stage-Integrated Dynamic Voltage-Boosting Feature for Hybrid Energy Storage in Transportation Systems
Advanced and reliable power converter solutions are fundamental to advancing future transportation systems and facilitating the ongoing transition towards environmentally sustainable technologies. Transportation systems can employ multiple sources to improve their reliability and economic operation. Therefore, a novel dual-input multilevel inverter configuration is proposed and designed in this paper for multi-source transportation applications. The proposed topology synthesizes the dual-input split source multilevel inverter and switching capacitor (SC-DSSMLI) units, resulting in a high voltage boosting ratio due to its integrated boost converter stage. Additionally, the layout is compact and cost-effective, leveraging a modular switched capacitor (SC) structure to produce multiple output levels without increasing the number of DC sources. Furthermore, the topology’s scalability is enhanced by stacking additional SC stages. The inductor duty cycle and SC unit performance can be adjusted to achieve the desired boosting factor. A modified level-shifted pulse width modulation technique ensures efficient operation of the proposed SC-DSSMLI topology, eliminating the complexity of the modulation schemes or additional calculations. The SC-DSSMLI’s capability to operate efficiently with single or dual-input sources offers significant flexibility over existing dual-input topologies. The continuous input inductor current is another key feature, along with a method to mitigate inrush current, which can damage SCs. Experimental results, alongside topological comparisons and various performance criteria, are presented in the paper, confirming the benefits of reduced component count, high operational efficiency. Furthermore, the paper provides a comprehensive analysis of the stress experienced by all switches, along with a count of passive elements, offering a detailed comparison with other existing topologies.
- 24 October 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Power Electronics
- Vol. 40 (2) , 2860-2873
Low-Frequency Oscillation Damping of Grid-Forming STATCOMs With Phase-Compensated DC-Link Voltage Synchronization
The dc-link voltage synchronization (DCVS) can be applied in the grid-forming static synchronous compensator (STATCOM) to realize dc-link voltage regulation and synchronization with the grid simultaneously. However, DCVS may lead to low frequency oscillation (LFO) of grid-forming STATCOM. To analyze and resolve the LFO issues of grid-forming STATCOM, this article built the small signal model of grid-forming STATCOM with consideration of DCVS, ac voltage and current dual close loop control (VCDC) and reactive power control (RPC). It is revealed that the LFO is mainly caused by the −180° phase characteristic of DCVS and phase lag introduced by VCDC. Besides, RPC may bring right half plan poles to the close loop and lead to subsynchronous oscillation. Based on the analysis, a lead-lag compensator is utilized and designed in this article to compensate phase lag in the close loop, which is simple but can effectively damp the LFO of grid-forming STATCOM. Besides, the proposed strategy is compared with the existing methods and shows the advantage of inertia provision to decrease the rate of change of frequency in the synchronization. Simulation and Experimental results validate the stability analysis and effectiveness of the proposed method.
- 24 October 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Power Electronics
- Vol. 40 (2) , 2860-2873
Low-Frequency Oscillation Damping of Grid-Forming STATCOMs With Phase-Compensated DC-Link Voltage Synchronization
The dc-link voltage synchronization (DCVS) can be applied in the grid-forming static synchronous compensator (STATCOM) to realize dc-link voltage regulation and synchronization with the grid simultaneously. However, DCVS may lead to low frequency oscillation (LFO) of grid-forming STATCOM. To analyze and resolve the LFO issues of grid-forming STATCOM, this article built the small signal model of grid-forming STATCOM with consideration of DCVS, ac voltage and current dual close loop control (VCDC) and reactive power control (RPC). It is revealed that the LFO is mainly caused by the −180° phase characteristic of DCVS and phase lag introduced by VCDC. Besides, RPC may bring right half plan poles to the close loop and lead to subsynchronous oscillation. Based on the analysis, a lead-lag compensator is utilized and designed in this article to compensate phase lag in the close loop, which is simple but can effectively damp the LFO of grid-forming STATCOM. Besides, the proposed strategy is compared with the existing methods and shows the advantage of inertia provision to decrease the rate of change of frequency in the synchronization. Simulation and Experimental results validate the stability analysis and effectiveness of the proposed method.
- 10 October 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 13 (1) , 542-552
An In-Field Eigenvalue-Based Stability Assessment Method for Low-Frequency Dynamic Interaction Between Voltage Source Converters and the Grid
Voltage-source converters (VSCs) are essential for renewable energy. However, the oscillatory behavior generated by dynamic interaction between VSCs and the grid is a challenging issue due to the interaction’s intricacy and unknown system details. After introducing VSCs into the power system, stability assessment is often wanted. “Perturbation-based impedance measuring + Middle-Brook criterion” is a well-known approach. However, this approach is rarely adopted due to the need for perturbation devices (PDs). So this paper proposes a stability assessment method to obtain the system eigenvalue map. This method does not need PDs, so is in-field adaptive. The eigenvalue map is evaluated from closed-loop frequency responses (FRs) by vector fitting (VF), and the FRs are measured by the VSC itself. To support the method theoretically, a modularized model of the VSC-grid system is derived. The model indicates how each closed loop FR of the VSC(s) reflects all the eigenvalues of the VSC-grid system. Because the transfer zeros of some FRs reduce the observability of some eigenvalues, weighted combination of VF results from multiple FRs is adopted in the proposed method to guarantee the precision. The accuracy of proposed assessment method and investigation results are verified by both simulations and experiments.
- 10 October 2024
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Journal of Emerging and Selected Topics in Power Electronics
- Vol. 13 (1) , 542-552
An In-Field Eigenvalue-Based Stability Assessment Method for Low-Frequency Dynamic Interaction Between Voltage Source Converters and the Grid
Voltage-source converters (VSCs) are essential for renewable energy. However, the oscillatory behavior generated by dynamic interaction between VSCs and the grid is a challenging issue due to the interaction’s intricacy and unknown system details. After introducing VSCs into the power system, stability assessment is often wanted. “Perturbation-based impedance measuring + Middle-Brook criterion” is a well-known approach. However, this approach is rarely adopted due to the need for perturbation devices (PDs). So this paper proposes a stability assessment method to obtain the system eigenvalue map. This method does not need PDs, so is in-field adaptive. The eigenvalue map is evaluated from closed-loop frequency responses (FRs) by vector fitting (VF), and the FRs are measured by the VSC itself. To support the method theoretically, a modularized model of the VSC-grid system is derived. The model indicates how each closed loop FR of the VSC(s) reflects all the eigenvalues of the VSC-grid system. Because the transfer zeros of some FRs reduce the observability of some eigenvalues, weighted combination of VF results from multiple FRs is adopted in the proposed method to guarantee the precision. The accuracy of proposed assessment method and investigation results are verified by both simulations and experiments.