dc to dc 2.pdf

Two Quadrant Converers -Second-Quadrant Chopper -First and Second Quadrant Chopper -First and Fourth Quadrant Chopper Second Quadrant Chopper The second quadrant chopper Vo,dc produces a positive voltage and negative current...

Two Quadrant Converers -Second-Quadrant Chopper -First and Second Quadrant Chopper -First and Fourth Quadrant Chopper Second Quadrant Chopper The second quadrant chopper Vo,dc produces a positive voltage and negative current ii io Io,dc D2 iS2 R Vi S2 vo L E  io ii iD2 io Output voltage R R iS2 vo L Vi vo L Tsw d2Tsw E E (a) (b) 𝑣𝑜 = 1 − 𝑥2 𝑉𝑖 vo Vi 𝑉𝑜,𝑑𝑐 = 1 − 𝑑2 𝑉𝑖 𝑀 = 1 − 𝑑2 𝑉𝑜,𝑑𝑐 − 𝐸 𝐼𝑜,𝑑𝑐 = 𝑅 to maintain negative current.. Io,dc 𝑉𝑜,𝑑𝑐 < 𝐸 io 𝐸 1 − 𝑑2 < 𝑉𝑖 𝐸 1− < 𝑑2 < 1 𝑉𝑖 Example 1 analysis of a second quadrant chopper with the following parameters: Vi=100V, E=80V, d2= 0.25 , R=10Ω, L=20mH and fsw=2kHz. Example 2 for the dc chopper described in Example 1, determine the duty ratio to produce a load current of -3A. 𝐼𝑜,𝑑𝑐 = −3 → 𝑉𝑜,𝑑𝑐 = 𝐸 + 𝐼𝑜,𝑑𝑐 𝑅 = 80 + −3 ∗ 10 = 50𝑉 50 𝑀= = 0.25 → 𝑑2 = 0.75 200  First and Second Quadrant Chopper The first and second quadrant chopper produces output bidirectional current. The chopper is a combination of the first- and second quadrant choppers. x1 and x2 are the switching variables of switches S1 and S2. The chopper can be operated as two independent choppers by keeping the inactive switch off.  First and fourth quadrant chopper The first-and-fourth-quadrant chopper can produce positive and negative output voltage with positive output current. The load emf (E) must be positive for the first- quadrant operation and negative when the chopper is to operate in the fourth quadrant. The state of the chopper is designated as (x1x4)2, where x1 and x4 denote switching variables of switches S1 and S4, respectively. For the first-quadrant operation, switch S4 must remain on to provide a path for the output current. Switch S1 performs the chopping, with the duty ratio d1, so the chopper operates alternatively in states 1 (01) and 3 (11). In the fourth quadrant, switch S1 is off, S4 operates with the duty ratio d4, and the chopper alternates between states 0 (00) and 1 (01).  4 th Quadrant Operation 𝑣𝑜 = −𝑥4 𝑉𝑖 𝑉𝑜,𝑑𝑐 = −𝑑4 𝑉𝑖 𝑀 = −𝑑4 Since 𝑖𝑜 > 0 → 𝐼𝑜,𝑑𝑐 > 0 → 𝑉𝑜,𝑑𝑐 > 𝐸 𝐸 −𝑑4 > 𝑉𝑖 In fourth quadrant E