Lecture 5: DC-DC Conversion

Transcription

1 1 / 31 Lecure 5: DC-DC Conversion ELEC-E845 Elecric Drives (5 ECTS) Mikko Rouimo (lecurer), Marko Hinkkanen (slides) Auumn 217

2 2 / 31 Learning Oucomes Afer his lecure and exercises you will be able o: Explain basic operaing principles of swiched DC-DC conversion Draw he equivalen circui of a 4-quadran DC-DC converer Implemen a simple pulse-widh modulaor in he Simulink sofware

3 3 / 31 Ouline Inroducion Buck Converer 4-Quadran DC-DC Converer Unipolar Pulse-Widh Modulaion Synchronous Sampling

4 4 / 31 Symbol Used for he DC Moor L a R a e a =

5 Inroducion DC source volage is ypically a baery or a diode bridge Armaure volage has o be adjused in order o be able o conrol he speed and orque Topologies and conrol of DC-DC converers are very similar o hose of hree-phase inverers Grid Baery Recifier DC-DC converer DC-DC converer Thyrisor bridges could be used o feed he DC moors, bu hey are no considered in his course. 5 / 31

6 6 / 31 DC-DC Converers Are Similar o 3-Phase Inverers 4-quadran DC-DC converer DC moor 3-phase inverer AC moor

7 7 / 31 Why No Linear Volage Regulaion? In principle, could be adjused using a rheosa or a ransisor in he linear region Wha would be he efficiency if = 1 V and = 5 V? Wha would be he losses in he ransisor if = 1 A? Why linear volage regulaion does no work in pracice (excep in very low-power drives)? Rheosa u CE Transisor in he linear region

8 8 / 31 Ouline Inroducion Buck Converer 4-Quadran DC-DC Converer Unipolar Pulse-Widh Modulaion Synchronous Sampling

9 9 / 31 Swiched-Mode DC-DC Conversion To avoid high losses, he ransisor is swiched periodically on and off Typical power semiconducors: IGBT, MOSFET, hyrisor, GTO We will assume ideal swiches Typical swiching frequencies f sw = khz Figure shows a buck converer (sep-down converer) gae u CE

10 1 / 31 Buck Converer i C Low power loss u CE i C in he ransisor On-sae: u CE Off-sae: i C = Moor is an inducive load Curren ia mus flow even when he ransisor is swiched off Freewheeling diode is needed Nex we will consider shor ime periods ea = consan and R a = can be assumed On-sae i C u CE = Freewheeling diode = Off-sae

11 11 / 31 i C + On-sae ( + ) = i C i C = T sw Off-sae ( )

12 Duy cycle + d = + T sw d 1 + is he on-ime T sw is he swiching period Average of he volage i C T sw = 1 Tsw d T sw = d over he period T sw 12 / 31

13 Curren Ripple Volage equaion L a d d On-sae: = = e a = 1 + ( e a )d L a Off-sae: = = ( e a ) + L a = 1 L a ( e a )d = e a L a + T sw Duy raio in seady sae D = + T sw = U a = E a Curren ripple in seady sae = D(1 D) f sw L a 13 / 31

14 14 / 31 Maximum Curren Ripple Maximum ripple for D = 1/2 (a abou half base speed),max = 4f sw L a Example parameer values for a 1-kW DC moor L a = 5 mh = 1 V f sw = 5 khz,max =.1 A If he raed curren is 1 A, he curren ripple is only 1% (5 khz is no a high swiching frequency a 1-kW power level) Curren ripple and orque ripple T M = k f are ypically insignifican

15 15 / 31 Ouline Inroducion Buck Converer 4-Quadran DC-DC Converer Unipolar Pulse-Widh Modulaion Synchronous Sampling

16 16 / 31 Four Quadrans Back-emf e a = k f ω M Torque T M = k f Mechanical power p M = ω M T M = e a Converer should allow boh is oupu volage e a and curren o reverse in 4-quadran operaion Generaing e a < > Mooring e a < < T M Mooring e a > > Generaing e a > < ω M

17 4-Quadran DC-DC-Converer S 1 and S 4 swiched ON: = S 2 and S 3 swiched ON: = S 1 and S 3 swiched ON: = S 2 and S 4 swiched ON: = S 1 S 2 S 3 S 4 This circui opology is also known as a 1-phase inverer, full bridge, and H-bridge. 17 / 31

18 18 / 31 Operaion Modes Only Nonzero Volage Swiching Saes Are Shown =, > =, > =, < =, <

19 19 / 31 Noaion of Poenials and Volages Leg A Leg B Legs can be modelled as bi-posiional swiches A B Negaive DC-bus poenial N u AN is he volage beween poenials A and N N Circui diagram u BN is he volage beween poenials B and N Converer oupu volage A = u AN u BN N B Equivalen circui

20 2 / 31 Swiching Saes of he Bi-Posiional Swiches Swiching sae q q = if he swich is conneced o N q = 1 if he swich is conneced o P Pole volages P A u AN = q A Converer oupu volage u BN = q B N B = (q A q B ) Figure: q A = 1 and q B =, giving = q A q B

21 Swiching-Cycle Averaged Quaniies u AN d A T sw u AN Average pole volage over T sw u AN = 1 Tsw u AN d = d A T sw u BN d B T sw Average volage u BN is obained similarly Average oupu volage u BN = (d A d B ) T sw 21 / 31

22 22 / 31 Ouline Inroducion Buck Converer 4-Quadran DC-DC Converer Unipolar Pulse-Widh Modulaion Synchronous Sampling

23 23 / 31 Pulse-Widh Modulaion PWM generaes he conrol signals q A and q B for he power swiches Goal: swiching-cycle averaged volage equals he reference volage,ref Various PWM mehods exis: hey all give =,ref bu produce differen pulse paerns Unipolar PWM will be considered in he following,ref N PWM q A A B q B

24 24 / 31 Duy Cycles Condiions =,ref and d A + d B = 1 lead o he duy cycles d A = 1 ( 1 + u ) a,ref 2 d B = 1 ( 1 u ) a,ref 2 Example in he figure:,ref =.5 Wha are he duy cycles d A and d B? How o generae he conrol signals q A and q B? q A 1 q B 1 d A T sw d B T sw T sw d A d B,ref

25 Carrier Comparison q A 1 Carrier comparison is ofen used for generaing he conrol signals Triangular carrier wih he period Tsw Magniude varies beween and 1 If d is higher han he carrier, hen q = 1 (oherwise q = ) Same carrier for boh d A and d B Nex slide: sep change in he volage reference (.5.75 ) q B 1 carrier d A d B,ref There are various ways o scale he carrier waveform and he reference quaniies. Using he carrier varying beween and 1 ogeher wih he duy cycle references is convenien in digial implemenaion. T sw 25 / 31

26 q A d A = 1 2 ( 1 + u ) a,ref 1 q B d A d B = 1 2 ( 1 u ) a,ref 1 d B,ref = (d A d B ) 26 / 31

27 27 / 31 Ouline Inroducion Buck Converer 4-Quadran DC-DC Converer Unipolar Pulse-Widh Modulaion Synchronous Sampling

28 28 / 31 Digial Conroller Curren is measured for he feedback of he curren conroller Digial conrollers are used nowadays Sampling of he curren is ypically synchronized wih he PWM Synchronised sampling effecively removes he curren ripple from he samples q A, q B PWM Sampling,ref (k) (k) Curren conroller,ref (k)

29 Synchronous Sampling Volage reference,ref can be updaed in he beginning and in he middle of he carrier (marked wih he circles) Curren samples (circles) can be aken a hese same ime insans Nex slide: Curren response is governed by L a d d = e a where R a = is assumed carrier T s T s Differen varians of sampling synchronized wih he PWM exis, while only one is presened here. Furhermore, i can be noiced ha acually four curren samples per carrier period could be aken wihou he curren ripple in he case of he unipolar PWM. 29 / 31 1 T sw,ref

30 e a,ref T s T s T sw 3 / 31

31 When considering he curren conroller, = and = can be assumed. 31 / 31