The power grid with large proportion of hydropower may engage the ultra-low frequency oscillation (ULFO),which threatening the operation of system.To the NY Power Grid system,whose dimension is over thousands,this pap...The power grid with large proportion of hydropower may engage the ultra-low frequency oscillation (ULFO),which threatening the operation of system.To the NY Power Grid system,whose dimension is over thousands,this paper reveals the cause of ULFO with the phase portrait method,i.e.,lies in the saturation of the different limits of the governor system of the generators,in other words,the occurrence of limit cycle is due to the non-smooth bifurcation.And furthermore,it proposes two methods to suppress ULFO with the philosophy of destroying the condition of non-smooth bifurcation.In detail,first,the phenomenon of ULFO in NY Power Grid,the damping characteristics and the limits in the governor system of the hydropower units are presented.Second,based on the non-smooth bifurcation theory,the mathematical basis of the oscillation in the non-smooth system caused by the saturation of limits is introduced.And then,the non-oscillation and oscillation dynamic of the system corresponding to without/with limits in the governor system are analyzed.Furthermore,it discusses the influence of the saturation of single limit on the characteristics of ULFO with the phase portraits.Moreover,the phase portraits of the ULFO under different faults is analyzed,and it shows that the limiting saturation occurs with a large enough disturbance.Thus,the ULFO is resulting from the negative damping of generation and the saturation of multiple limits under a large enough disturbance.In addition,according to the above mechanism,two strategies to suppress the ULFO,i.e.,the governor parameters tuning and the fault strength relief are designed.The simulation shows the effectiveness of proposed strategies.展开更多
A master-slave configuration used to control the nonlinear behaviors arising in a vertical cavity surface emitting laser (VCSEL) with strong external optical feedback is established. In terms of bifurcation diagram, t...A master-slave configuration used to control the nonlinear behaviors arising in a vertical cavity surface emitting laser (VCSEL) with strong external optical feedback is established. In terms of bifurcation diagram, time and frequency domain, the influence of the continuous optical injection from the master VCSEL on the nonlinear characteristics of the slave is investigated theoretically. For relatively weak injection, the slave still keeps its intrinsic nonlinear state. With increasing the injection strength, these nonlinear behaviors evolve to periodic fluctuation, and at last are replaced by the steady-state (e.g. the critical injection parameter for steady-state is 1.2 when external cavity's reflectivity and length are 4% and 4 cm, respectively). During this evolution the bifurcation-contraction phenomena are also observed.展开更多
通过多尺度法对Duffing-van der Pol系统的幅频响应特性进行研究,多频激励改变了单频激励条件下系统的振动状态。与Duffing系统相比,Duffing-van der Pol系统不但使系统主共振曲线发生了偏移,而且系统的振幅也发生了变化。经过分析得出...通过多尺度法对Duffing-van der Pol系统的幅频响应特性进行研究,多频激励改变了单频激励条件下系统的振动状态。与Duffing系统相比,Duffing-van der Pol系统不但使系统主共振曲线发生了偏移,而且系统的振幅也发生了变化。经过分析得出了Duffing-van der Pol系统主共振幅频特性曲线的偏移和振幅的改变与加入的多频激励的幅度和频率有关。利用Matlab对Duffing-van der Pol进行了数值仿真,仿真结果得出多频外激励改变了原有单频激励的振动状态,并且随着多频激励的幅值和频率的改变,系统的振动状态出现了一定规律的变化。对比研究了解析分析与数值仿真结果,得出的结论比较一致。展开更多
A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Pe...A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Periodic solutions are obtained through harmonic balance method with alternating frequency/time domain(HB-AFT) technique, and then compared with the results of numerical simulation. Good agreement confirms the feasibility of HB-AFT scheme. Moreover, the Floquet theory is adopted to analyze motion stability of the system when rotor runs at different speed intervals. A simple strategy to determine the monodromy matrix is introduced and two ways towards unstability are found for periodic solutions: the period doubling bifurcation and the secondary Hopf bifurcation. The results obtained will contribute to the global response analysis and dynamic optimal design of rotor systems.展开更多
基金National Natural Science Foundation of China (Nos. 51477050, 50707035) and 111 plan (No. B08013).
文摘The power grid with large proportion of hydropower may engage the ultra-low frequency oscillation (ULFO),which threatening the operation of system.To the NY Power Grid system,whose dimension is over thousands,this paper reveals the cause of ULFO with the phase portrait method,i.e.,lies in the saturation of the different limits of the governor system of the generators,in other words,the occurrence of limit cycle is due to the non-smooth bifurcation.And furthermore,it proposes two methods to suppress ULFO with the philosophy of destroying the condition of non-smooth bifurcation.In detail,first,the phenomenon of ULFO in NY Power Grid,the damping characteristics and the limits in the governor system of the hydropower units are presented.Second,based on the non-smooth bifurcation theory,the mathematical basis of the oscillation in the non-smooth system caused by the saturation of limits is introduced.And then,the non-oscillation and oscillation dynamic of the system corresponding to without/with limits in the governor system are analyzed.Furthermore,it discusses the influence of the saturation of single limit on the characteristics of ULFO with the phase portraits.Moreover,the phase portraits of the ULFO under different faults is analyzed,and it shows that the limiting saturation occurs with a large enough disturbance.Thus,the ULFO is resulting from the negative damping of generation and the saturation of multiple limits under a large enough disturbance.In addition,according to the above mechanism,two strategies to suppress the ULFO,i.e.,the governor parameters tuning and the fault strength relief are designed.The simulation shows the effectiveness of proposed strategies.
文摘A master-slave configuration used to control the nonlinear behaviors arising in a vertical cavity surface emitting laser (VCSEL) with strong external optical feedback is established. In terms of bifurcation diagram, time and frequency domain, the influence of the continuous optical injection from the master VCSEL on the nonlinear characteristics of the slave is investigated theoretically. For relatively weak injection, the slave still keeps its intrinsic nonlinear state. With increasing the injection strength, these nonlinear behaviors evolve to periodic fluctuation, and at last are replaced by the steady-state (e.g. the critical injection parameter for steady-state is 1.2 when external cavity's reflectivity and length are 4% and 4 cm, respectively). During this evolution the bifurcation-contraction phenomena are also observed.
文摘通过多尺度法对Duffing-van der Pol系统的幅频响应特性进行研究,多频激励改变了单频激励条件下系统的振动状态。与Duffing系统相比,Duffing-van der Pol系统不但使系统主共振曲线发生了偏移,而且系统的振幅也发生了变化。经过分析得出了Duffing-van der Pol系统主共振幅频特性曲线的偏移和振幅的改变与加入的多频激励的幅度和频率有关。利用Matlab对Duffing-van der Pol进行了数值仿真,仿真结果得出多频外激励改变了原有单频激励的振动状态,并且随着多频激励的幅值和频率的改变,系统的振动状态出现了一定规律的变化。对比研究了解析分析与数值仿真结果,得出的结论比较一致。
基金supported by the National Basic Research Program of China("973" Project)(Grant No.2015CB057400)the National Natural Science Foundation of China(Grant No.11302058)
文摘A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Periodic solutions are obtained through harmonic balance method with alternating frequency/time domain(HB-AFT) technique, and then compared with the results of numerical simulation. Good agreement confirms the feasibility of HB-AFT scheme. Moreover, the Floquet theory is adopted to analyze motion stability of the system when rotor runs at different speed intervals. A simple strategy to determine the monodromy matrix is introduced and two ways towards unstability are found for periodic solutions: the period doubling bifurcation and the secondary Hopf bifurcation. The results obtained will contribute to the global response analysis and dynamic optimal design of rotor systems.
