Mathematical Modeling and Fault Tolerance Control for a Three-Phase Soft-Switching Mode Rectifier

Table 1

𝑣_𝐶𝑟(𝑡), 𝑖_𝐷(𝑡), and 𝑖_𝐷𝑎(𝑡) solutions for SSMR in the seven operation modes.

Time period	Variable
	𝑣𝐶𝑟(𝑡)	𝑖𝐷(𝑡)	𝑖𝐷𝑎(𝑡)
𝑇1∶[𝑡0~𝑡1]	𝑣𝐶𝑜(𝑡)	𝑖𝐿𝑚(𝑡)−[𝑣𝐶𝑜(𝑡)/𝐿𝑟](𝑡−𝑡0)	0
𝑇2∶[𝑡1~𝑡2]	𝑣𝐶𝑜(𝑡)cos𝜔𝑜(𝑡−𝑡1)	0	0
𝑇3∶[𝑡2~𝑡3]	0	0	0
𝑇4∶[𝑡3~𝑡4]	0	0	𝑖𝐿𝑚(𝑡)+𝑣𝐶𝑜(𝑡)/𝑍𝑜+[𝑣𝐶𝑜(𝑡)/𝐿𝑟](𝑡−𝑡3)
𝑇5∶[𝑡4~𝑡5]	0	0	0
𝑇6∶[𝑡5~𝑡6]	[𝑖𝐿𝑚(𝑡)/𝐶𝑟](𝑡−𝑡5)	0	0
𝑇7∶[𝑡6~𝑡0]	𝑣𝐶𝑜(𝑡)	𝑖𝐿𝑚(𝑡)	0