RIGIDITY CHARACTERIZATION OF COMPACT RICCI SOLITONS

Li, Fengjiang,Zhou, Jian Korean Mathematical Society 2019 대한수학회지 Vol.56 No.6

In this paper, we firstly define the Ricci mean value along the gradient vector field of the Ricci potential function and show that it is non-negative on a compact Ricci soliton. Furthermore a Ricci soliton is Einstein if and only if its Ricci mean value is vanishing. Finally, we obtain a compact Ricci soliton $(M^n,g)(n{\geq}3)$ is Einstein if its Weyl curvature tensor and the Kulkarni-Nomizu product of Ricci curvature are orthogonal.

Rigidity characterization of compact Ricci solitons

Fengjiang Li,Jian Zhou 대한수학회 2019 대한수학회지 Vol.56 No.6

In this paper, we firstly define the Ricci mean value along the gradient vector field of the Ricci potential function and show that it is non-negative on a compact Ricci soliton. Furthermore a Ricci soliton is Einstein if and only if its Ricci mean value is vanishing. Finally, we obtain a compact Ricci soliton $(M^{n},g) (n \geq 3)$ is Einstein if its Weyl curvature tensor and the Kulkarni-Nomizu product of Ricci curvature are orthogonal.

Half-Cycle-Waveform-Inversed Single-Carrier Seven-level Sinusoidal Modulation

Fengjiang Wu,Bo Sun,Lujie Zhang,Li Sun 전력전자학회 2013 JOURNAL OF POWER ELECTRONICS Vol.13 No.1

A half-cycle-waveform inversion based three reference modulations seven-level SPWM (TRM-SPWM) scheme with one carrier is proposed in this paper. To keep the same comparison logics for the modulations and carrier during the negative half cycle and the positive one for the modulations, in the negative half cycle of the modulations, the DC offsets related to the amplitude of the carrier are set on the three modulations, respectively. The seven-level SPWM waveform with dead time thereby is implemented with only one Digital Signal Processor (DSP) without any other attached logic circuit. The basis principle of the proposed TRM-SPWM is analyzed in detail, and the frequency spectrums of the conventional and the proposed schemes are derived and compared with each other through simulation. The DSP based implementation is presented and detailed experimental waveforms verify the accuracy and feasibility of the proposed TRM-SPWM scheme.

Interfacial behaviors in Cu/molten Sn–58Bi/Cu solder joints under coupling with thermal and current stressing

Fengjiang Wang,Hong Chen,Dongyang Li,Zhijie Zhang,Xiaojing Wang 대한금속·재료학회 2019 ELECTRONIC MATERIALS LETTERS Vol.15 No.1

The interfacial behaviors of Cu/molten Sn–58Bi/Cu solder joints under the coupling eff ect of a temperature gradient and thecurrent stressing have been investigated. The most obvious change of the interfacial behaviors under the individual electromigration(EM) and thermomigration (TM) in molten solder was the asymmetrical growth of interfacial Cu–Sn intermetalliccompounds (IMCs), which grew rapidly as the stressing time prolonged. The growth rates of the interfacial IMCs inducedby TM under a temperature gradient of 40 °C/cm were slightly faster than EM under the current density of 0.5 × 10 4 A/cm 2 . However, the microstructure evolution and interfacial behaviors changed obviously when the thermal was distributedunevenly across the entire solder stripe under current stressing. It was found that there was a Bi-rich layer adhered to theanode side and a distributed Cu 6 Sn 5 phase existed in the solder matrix when the anode and the cold end were at the sameend. Additionally, a large number of Bi-blocks and Cu–Sn IMCs were dramatically observed in the solder matrix when theanode and the hot end were on the same side. The main reason for this result may be attributed to the signifi cant change ofthe diff usion of Bi atoms under the thermo-electric coupling conditions. In the initial melting stage of solder, the Bi atomsin molten Sn–58Bi solder rapidly diff used to the anode and then began to be reversely dissolved into the solder matrix. Theexperimental results proved the additional temperature gradient played a positive or negative role on the reverse dissolutionof Bi atoms in the heat preservation process.

Dual-Side Circulating Currents Free TPS Control for Dual Active Bridge DC-DC Converter and Its Implementation

Fengjiang Wu,Guizhong Wang,Xiaoguang Li 전력전자학회 2019 ICPE(ISPE)논문집 Vol.2019 No.5

In this paper, a novel triple phase-shift (NTPS) modulation is proposed first to eliminate the dual-side circulating currents of isolated dual-active bridge DC-DC converter. Furthermore, the current stress of the proposed NTPS control when the phase shift is tuned in two regions is derived and compared with each other and the best tuning region of the phase shift is determined to achieve the optimal current characteristics. The steady-state and transient performance of two implementation methods of NTPS control are discussed and the better one is determined. The corresponding experimental results of the proposed NTPS control validate its accuracy and validity.

Half-Cycle-Waveform-Inversed Single-Carrier Seven-level Sinusoidal Modulation

Wu, Fengjiang,Sun, Bo,Zhang, Lujie,Sun, Li The Korean Institute of Power Electronics 2013 JOURNAL OF POWER ELECTRONICS Vol.13 No.1

A half-cycle-waveform inversion based three reference modulations seven-level SPWM (TRM-SPWM) scheme with one carrier is proposed in this paper. To keep the same comparison logics for the modulations and carrier during the negative half cycle and the positive one for the modulations, in the negative half cycle of the modulations, the DC offsets related to the amplitude of the carrier are set on the three modulations, respectively. The seven-level SPWM waveform with dead time thereby is implemented with only one Digital Signal Processor (DSP) without any other attached logic circuit. The basis principle of the proposed TRM-SPWM is analyzed in detail, and the frequency spectrums of the conventional and the proposed schemes are derived and compared with each other through simulation. The DSP based implementation is presented and detailed experimental waveforms verify the accuracy and feasibility of the proposed TRM-SPWM scheme.

LAGUERRE CHARACTERIZATION OF SOME HYPERSURFACES

Fang, Jianbo,Li, Fengjiang Korean Mathematical Society 2016 대한수학회보 Vol.53 No.3

Let x : $^{Mn-1}{\rightarrow}{\mathbb{R}}^n$ ($n{\geq}4$) be an umbilical free hyper-surface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. We denote the Laguerre scalar curvature by R and the trace-free Laguerre tensor by ${\tilde{L}}:=L-{\frac{1}{n-1}}tr(L)g$. In this paper, we prove a local classification result under the assumption of parallel Laguerre form and an inequality of the type $${\parallel}{\tilde{L}}{\parallel}{\leq}cR$$ where $c={\frac{1}{(n-3){\sqrt{(n-2)(n-1)}}}$ is appropriate real constant, depending on the dimension.

Elimination of the State-of-Charge Errors for Distributed Battery Energy Storage Devices in Islanded Droop-controlled Microgrids

Weixin Wang,Fengjiang Wu,Ke Zhao,Li Sun,Jiandong Duan,Dongyang Sun 전력전자학회 2015 JOURNAL OF POWER ELECTRONICS Vol.15 No.4

Battery energy storage devices (ESDs) have become more and more commonplace to maintain the stability of islanded power systems. Considering the limitation in inverter capacity and the requirement of flexibility in the ESD, the droop control was implemented in paralleled ESDs for higher capacity and autonomous operation. Under the conventional droop control, state-of-charge (SoC) errors between paralleled ESDs is inevitable in the discharging operation. Thus, some ESDs cease operation earlier than expected. This paper proposes an adaptive accelerating parameter to improve the performance of the SoC error eliminating droop controller under the constraints of a microgrid. The SoC of a battery ESD is employed in the active power droop coefficient, which could eliminate the SoC error during the discharging process. In addition, to expedite the process of SoC error elimination, an adaptive accelerating parameter is dedicated to weaken the adverse effect of the constraints due to the requirement of the system running. Moreover, the stability and feasibility of the proposed control strategy are confirmed by small-signal analysis. The effectiveness of the control scheme is validated by simulation and experiment results.

Laguerre characterization of some hypersurfaces

Jianbo Fang,Fengjiang Li 대한수학회 2016 대한수학회보 Vol.53 No.3

Let $x$ : ${M}^{n-1}\rightarrow{\mathbb R}^{n}$ $(n\geq4)$ be an umbilical free hypersurface with non-zero principal curvatures. Then $x$ is associated with a Laguerre metric $\mathbf{g}$, a Laguerre tensor $\mathbf{L}$, a Laguerre form $\mathbf{C}$, and a Laguerre second fundamental form $\mathbf{B}$, which are invariants of $x$ under Laguerre transformation group. We denote the Laguerre scalar curvature by $R$ and the trace-free Laguerre tensor by $\tilde{\mathbf{L}}:={\mathbf{L}}-\frac{1}{n-1}tr({\mathbf{L}})\mathbf{g}$. In this paper, we prove a local classification result under the assumption of parallel Laguerre form and an inequality of the type $$\|\tilde{\mathbf{L}}\|\leq cR,$$ where $c=\frac{1}{(n-3)\sqrt{(n-2)(n-1)}}$ is appropriate real constant, depending on the dimension.

Elimination of the State-of-Charge Errors for Distributed Battery Energy Storage Devices in Islanded Droop-controlled Microgrids

Wang, Weixin,Wu, Fengjiang,Zhao, Ke,Sun, Li,Duan, Jiandong,Sun, Dongyang The Korean Institute of Power Electronics 2015 JOURNAL OF POWER ELECTRONICS Vol.15 No.4

Battery energy storage devices (ESDs) have become more and more commonplace to maintain the stability of islanded power systems. Considering the limitation in inverter capacity and the requirement of flexibility in the ESD, the droop control was implemented in paralleled ESDs for higher capacity and autonomous operation. Under the conventional droop control, state-of-charge (SoC) errors between paralleled ESDs is inevitable in the discharging operation. Thus, some ESDs cease operation earlier than expected. This paper proposes an adaptive accelerating parameter to improve the performance of the SoC error eliminating droop controller under the constraints of a microgrid. The SoC of a battery ESD is employed in the active power droop coefficient, which could eliminate the SoC error during the discharging process. In addition, to expedite the process of SoC error elimination, an adaptive accelerating parameter is dedicated to weaken the adverse effect of the constraints due to the requirement of the system running. Moreover, the stability and feasibility of the proposed control strategy are confirmed by small-signal analysis. The effectiveness of the control scheme is validated by simulation and experiment results.