The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-har...The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.展开更多
针对一种新型并联全桥子模块构成的模块化多电平换流器（paralleled full bridge sub-module MMC,PFB-MMC）拓扑,提出一种适用于任意新型双端口MMC的电磁暂态通用等效建模方法。传统单端口子模块MMC的等效算法要求全部子模块流过相同的...针对一种新型并联全桥子模块构成的模块化多电平换流器（paralleled full bridge sub-module MMC,PFB-MMC）拓扑,提出一种适用于任意新型双端口MMC的电磁暂态通用等效建模方法。传统单端口子模块MMC的等效算法要求全部子模块流过相同的桥臂电流,这对双端口MMC不再适用。针对这一问题,适用于双端口MMC的迭代求解算法被提出。MMC桥臂中全部子模块的内部节点和模块间的互联节点均被迭代消去,整个桥臂在电磁暂态解算器中被等效成仅含4个外部节点,尽管在这一过程中求解的步骤有所增加,但依然能够完整保留各桥臂全部的内部信息。对降阶导纳矩阵进行求解后,即可完成之前被等效消去的节点信息例如电容电压、连接节点电流的更新。因此,该文提出的建模方法,能够在精确仿真系统内、外部动态特性的同时,大幅提高其电磁暂态仿真速度。在PSCAD/EMTDC环境中验证所提出模型的精度和加速比。展开更多
基金Project supported by the National Natural Science Foundation of China (No.50275024)
文摘The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.
文摘针对一种新型并联全桥子模块构成的模块化多电平换流器（paralleled full bridge sub-module MMC,PFB-MMC）拓扑,提出一种适用于任意新型双端口MMC的电磁暂态通用等效建模方法。传统单端口子模块MMC的等效算法要求全部子模块流过相同的桥臂电流,这对双端口MMC不再适用。针对这一问题,适用于双端口MMC的迭代求解算法被提出。MMC桥臂中全部子模块的内部节点和模块间的互联节点均被迭代消去,整个桥臂在电磁暂态解算器中被等效成仅含4个外部节点,尽管在这一过程中求解的步骤有所增加,但依然能够完整保留各桥臂全部的内部信息。对降阶导纳矩阵进行求解后,即可完成之前被等效消去的节点信息例如电容电压、连接节点电流的更新。因此,该文提出的建模方法,能够在精确仿真系统内、外部动态特性的同时,大幅提高其电磁暂态仿真速度。在PSCAD/EMTDC环境中验证所提出模型的精度和加速比。
