Switching Flow Graph Model

Transcription

1 Switching Flow Graph Model Keyue Smedley Power Electronics Laboratory University of California Irvine

2 Switching flow graph model Modeling of single phase active power filter 2

3 Switching flow graph model 3

4 Switching FlowGraph Nonlinear Model A unified graphic modeling tool Tool provides: Largesignal model Smallsignal model Steadystate model 4

5 Switching converters are time variant systems. When the switches are in one position (e.g. transistors are on), the converter equivalents to a subcircuit. When the switches are in the other position (e.g. transistors are off), the converters equivalents to another subcircuit. ) Both subcircuits are linear time invariant systems, we can therefore use FlowGraph Method to model them. 2) Introduce switching branches to combine the flowgraphs of the subcircuits into a SWITCHING FLOW GRAPH! 5

6 Bucboost ig S vg v il L ic ir C R vo vrl RL (a) vg il ic ir il ic L C R vo vg ir L C R vo RL ON circuit (b) RL OFF circuit 6

7 On and OFF flow graphs GON LS CS vg vl il ic vo RL R (a) vrl ig ir GOFF LS CS vg il ic vo vl RL R vrl ig ir 7

8 Switch branch definition Ts t Switch branches TON TOFF t Switch functions < t < TON TON < t < Ts 8

9 Switching flow graph of bucboost G vg il ic vo vl LS RL CS R vrl ig ir 9

10 Simplified switching flow graph U C I P E L LS + RL vg il io vo vl R RCS + ig

11 Signal flow in switch branches x(t) x(t) t t (t) (t) TON TOFF t TON TOFF t Ts Ts y(t) = x(t)(t) y(t) = x(t)(t) t t (a) (b)

12 Switch branch large signal model U C I P E L x(t) x(t) x x d(t) d'(t) (a) (b) where x is a multiplier 2

13 Switch branch steadystate model U C I P E L X D Y X D' Y (a) (b) 3

14 Switch branch small signal model U C I P E L x(t) ^ x(t) ^ D y(t) ^ D' y(t) ^ d(t) ^ X d(t) ^ X (a) (b) 4

15 Steadystate model vg il io vo vl LS + RL R RCS + ig D' Vg D VL Ig RL D IL D' Io R Vo 5

16 Large signal model vg il io vo vl LS + RL R RCS + ig d'(t) x vg x Ls + RL il x io R RCs + vo vl x d(t) ig d(t) d'(t) 6

17 Small signal model vg il io vo vl LS + RL ig Vo R RCS + ^d(t) ^vg D Ls + RL ^ il D' ^io D' R RCs + ^vo ^d(t) Vg IL v^ ^ ig D ^d(t) IL 7

18 Simplified small signal model D' ^vg (Vg + Vo (Ls + RL) IL) D' ^d(t) D IL ^ vl ^ ig Ls + RL D ^il D' ^io R RCs + ^vo 8

19 Steady state relationship 9

20 Smallsignal model 2

21 Modeling of OCC Active Power Filter 2

22 Single phase APF Nonlinear load iload M S + + M4 S ig L 2 iapf Vg C Vo M2 + S2 + M3 S3 + + _ 22

23 Unipolar Operation i g i Load iapf ig i Load iapf S S 4 S S 4 i g L apf V o i g L apf V o i Load i Load i apf S 2 S 3 i apf S2 S 3 > and t < d T s < and t < d T s i g i Load iapf S S 4 ig i Load iapf S S 4 i g i Load i apf L apf S 2 S 3 V o i g i Load i apf L apf S 2 S 3 V o > and d T s t < T s < and d T s t < T s 23

24 Power stage model i Load ( d) sgnvg i g v L i APF i C /Ls /Cs v C ( d ) sgnvg 24

25 APF Inputoutput relation e = V o d ( ) e = > < Control ey equation Lossfree resistor = R e i g i ge = i g > i g < e = R e i ge V m d = V m R s i ge V m = R s V o R e 25

26 OCC APF controller Nonlinear load iload M S + + M4 S4 + + ig L 2 Vg iapf C Vo M2 S2 + + M3 S3 + + ig* Rs + Phasedetector OUT M M2 M3 M4 L o g i c Q Q R S CLK OUT + O R w/reset I Vm Voltage loop PI compensator Vc Vref Integrator with reset APF OCC controller 26

27 OCC APF controller Nonlinear load iload M S + + M4 S4 + + ig L 2 Vg iapf C Vo M2 S2 + + M3 S3 + + ig* Rs + Phasedetector OUT M M2 M3 M4 L o g i c Q Q R S CLK OUT + O R w/reset I Vm Voltage loop PI compensator Vc Vref Integrator with reset APF OCC controller 27

28 OCC controller model Vm i g C R2 OUT + R Vc Vref Slow loop ( ) V m = V ref + V ref V c Fast loop R s i ge /V m = d R 2 Cs+ R Cs R s V o R Cs + RCs 2 V m * d V ref 28

29 MATLAB model 29

30 Load: current, Z load = ( j25.85) Ω. Waveforms from Pspice (left) and from the model (right). From top to bottom: Load Current, APF

31 Waveforms from Pspice (left) and from the model (right). From top to bottom: Load Current, line current.

32 Waveforms from Pspice and from the model together. On the left the waveforms are shown over two switching cycles. On the right in detail. From top to bottom: APF current, line current.