Sample-Data Modeling of a Zero Voltage Transition DC-DC Converter for On-Board Battery Charger in EV

Table 5

Definition of matrix for each mode of operation.

Mode I	𝐴1	𝑖^′𝐿𝑆𝑖^′𝐿𝑓𝑉^′𝑜=100000−𝐿𝑓01𝐶𝑓−1𝑅𝐶𝑓𝑖𝐿𝑆𝑖𝐿𝑓𝑉𝑜+1𝐿𝑆00100𝐶𝑓𝑉𝑠𝐼𝑍
	𝐵1	𝑖sec𝑖𝐷1𝑖𝐷2𝑖sum=1𝑁10012𝑁20−1112𝑁2000𝑖𝐿𝑆𝑖𝐿𝑓𝑉𝑜+𝑉000000^𝑠𝐼𝑍
Mode II	𝐴2	𝑖^′𝐿𝑆𝑖^′𝐿𝑓𝑉^′𝑜=𝑁00−𝑁^2𝐿𝑆+𝐿𝑓100−𝑁^2𝐿𝑆+𝐿𝑓01𝐶𝑓−1𝑅𝐶𝑓𝑖𝐿𝑆𝑖𝐿𝑓𝑉𝑜+𝑁^2𝑁^2𝐿𝑆+𝐿𝑓0𝑁𝑁^2𝐿𝑆+𝐿𝑓001𝐶𝑓𝑉𝑠𝐼𝑍
	𝐵2	𝑖sec𝑖𝐷1𝑖𝐷2𝑖sum=010𝑁00𝑖010010^𝐿𝑆𝑖𝐿𝑓𝑉𝑜+𝑉000000^𝑠𝐼𝑍
Mode III	𝐴3	𝑖^′𝐿𝑆𝑖^′𝐿𝑓𝑉^′𝑜=𝑁00−𝑁^2𝐿𝑆+𝐿𝑓100−𝑁^2𝐿𝑆+𝐿𝑓01𝐶𝑓−1𝑅𝐶𝑓𝑖𝐿𝑆𝑖𝐿𝑓𝑉𝑜+010000𝐶𝑓𝑉𝑠𝐼𝑍
	𝐵3	𝑖sec𝑖𝐷1𝑖𝐷2𝑖sum=000000𝑖010010^𝐿𝑆𝑖𝐿𝑓𝑉𝑜+𝑉000000^𝑠𝐼𝑍
Mode IV	𝐴4	𝑖^′𝐿𝑆𝑖^′𝐿𝑓𝑉^′𝑜=100000−𝐿𝑓01𝐶𝑓−1𝑅𝐶𝑓𝑖𝐿𝑆𝑖𝐿𝑓𝑉𝑜+−1𝐿𝑆00100𝐶𝑓𝑉𝑠𝐼𝑍
	𝐵4	𝑖sec𝑖𝐷1𝑖𝐷2𝑖sum=1𝑁10012𝑁20−112𝑁−12000𝑖𝐿𝑆𝑖𝐿𝑓𝑉𝑜+𝑉000000^𝑠𝐼𝑍
Mode V	𝐴5	𝑖^′𝐿𝑆𝑖^′𝐿𝑓𝑉^′𝑜=𝑁00𝑁^2𝐿𝑆+𝐿𝑓100−𝑁^2𝐿𝑆+𝐿𝑓01𝐶𝑓−1𝑅𝐶𝑓𝑖𝐿𝑆𝑖𝐿𝑓𝑉𝑜+−𝑁^2𝑁^2𝐿𝑆+𝐿𝑓0𝑁𝑁^2𝐿𝑆+𝐿𝑓001𝐶𝑓𝑉𝑠𝐼𝑍
	𝐵5	𝑖sec𝑖𝐷1𝑖𝐷2𝑖sum=01𝑁00𝑖0−10000−1^𝐿𝑆𝑖𝐿𝑓𝑉𝑜+𝑉000000^𝑠𝐼𝑍
Mode VI	𝐴6	𝑖^′𝐿𝑆𝑖^′𝐿𝑓𝑉^′𝑜=𝑁00𝑁^2𝐿𝑆+𝐿𝑓100−𝑁^2𝐿𝑆+𝐿𝑓01𝐶𝑓−1𝑅𝐶𝑓𝑖𝐿𝑆𝑖𝐿𝑓𝑉𝑜+010000𝐶𝑓𝑉𝑠𝐼𝑍
	𝐵6	𝑖sec𝑖𝐷1𝑖𝐷2𝑖sum=001000𝑖0−10000^𝐿𝑆𝑖𝐿𝑓𝑉𝑜+𝑉000000^𝑠𝐼𝑍