# FILTER DESIGN FOR MULTILEVEL CONVERTERS

Rip V n n n 2 . 1. 0 % % ... For the same amount of energy, magnetic components are (2 to 10 times??) bigger, heavier and more expensive than capacito...

FILTER DESIGN FOR MULTILEVEL CONVERTERS

1

Series-Parallel MultiLevel Cell with Filters

I chop

I LHV

LHV D

D

I LLV / 2 VHV

CHV

f

HV 0

VCHV

1  2 LHV CHV

I LV

D

D

1 D

1 D

1 D

1 D

LLV LLV

CLV VCLV

f sw 2

AC-equivalent circuit of Series-Parallel MultiLevel Cell

I LHV

LHV CHV VCHV

VHV

f

HV 0

1  2 LHV CHV

I LV np n p f sw

I LV

I LLV VHV ns .n p ns n p f sw

LLV / n p

CLV f 0LV 

VCLV 1

2 LLV n p .CLV 3

Steady state, time domain : worst case ripples Pulsation on the Low Voltage side (2nd order filter)

LV ripple%

V

 2 1  f     VHV  n p ns  n p ns f sw  1 f 0LV  2 LLV n p .CLV V

LV pk  ripple

LV 0

2

  1   L n C   LV p LV  LV  2 ( n p ns )1.5 f sw Vripple%  2 

Pulsation on the High Voltage side (2nd order filter)

I

HV ripple%

 I 2 1  f    I LVmax  n p  n p f sw  1 HV f0  2 LHV .CHV HV pk  ripple

HV 0

2

  1    LHV CHV   HV  2 .n1p.5 f sw I ripple%  2 

4

Ripples : from time domain to frequency domain

-20bB/dcd

200dB

+

-40dB/dcd

=

-60dB/dcd

fswitching B1≈ripple

Ripple requirement

100dB

f0

0dB

1kHz

10kHz

100kHz

1MHz

=>Conclusion : the ripple requirement allows increasing f0 when increasing fswitching

10MHz

5

EMC standards : frequency domain formulation

-20bB/dcd

200dB

+

-40dB/dcd

=

-60dB/dcd

fswitching B1≈ripple

100dB

0dB

Ripple requirement

f0

EN55022A

1kHz

10kHz

100kHz

1MHz

10MHz

6 =>Conclusion : salient point of EMC standards imposes decreasing f0 when increasing fswitching

EMC standards : frequency domain formulation fswitching

200dB

fswitching B1≈ripple

Ripple requirement 100dB

f0

EN55022A 7

Steady state : ripples and standards combined Required cut-off frequency vs switching frequency

4

2

1

3

2

1

4

3 8

Steady state : ripples and standards combined Required cut-off frequency vs switching frequency for MultiCell converters 10

Simplified EN55022A Filter for multiCell Chopper

5

nCell nCell nCell nCell

4

10

10

[email protected]

cutoff frequency [Hz]

10

=10 =2 =5 =1 = =15 =2 =12 = =1

3

2

10

3

10

4

10 switching frequency [Hz]

5

6

10 9

Steady state : ripples and standards combined

10

10

Required cut-off frequency • for ≠ standards, • for ≠ switching frequencies • for ≠ number of cells

4

3 Some standards

Simplified 5 HVDC Filter for multiCell Chopper; Pnom=100 10

cutoff frequency [Hz]

cutoff frequency [Hz]

Simplified EN55022A Filter for multiCell Chopper 5 10

10

10

4

3

180 EN55022A [dBuV] EN55022B [dBuV] HVDCA: P=100kW [dBuA] HVDCB: P=1kW [dBuA]

10

10

3

4

5

10 10 switching frequency [Hz]

10

maximum ripple [dBuX]

160

2

6

140

10

120

2

10

3

100

4

5

10 10 switching frequency [Hz]

10

6

80 60 40 20

10

10

10

4

3

2

10

0 3 10

10

4

5

10 10 switching frequency [Hz]

6

10

7

Simplified HVDC Filter for multiCell Chopper; Pnom=1k 5 10

cutoff frequency [Hz]

cutoff frequency [Hz]

Simplified EN55022B Filter for multiCell Chopper 5 10

3

4

5

10 10 switching frequency [Hz]

10

6

10

10

10

4

3

2

10

3

4

5

10 10 switching frequency [Hz]

10

10

6

Influence of the discrete nature of the spectrum (mainly for choppers…)

10

10

10

HVDC Filter for multiCell Chopper; Pnom=100kW

5

nCell = 1 nCell = 2 nCell = 3 nCell = 4 nCell = 5 nCell = 6 nCell = 7 nCell = 8 nCell = 9 nCell =10 nCell =11 nCell =12 randomcheck

4

3

2

10

3

10

4

10

5

10

6

switching frequency [Hz] random check for EN550222B: swF=120kHz; nCell =1; duty =0.51 180 EN55022B vHdBuV(duty) envdBuV envdBuVFB

160

maximum ripple [dBuV]

cutoff frequency [Hz]

10

140 120 100 80 60 40 20 0 4 10

5

10 switching frequency [Hz]

10

6

11

Steady state : ripples and standards combined

10

10

5

HVDC Filter for multiCell Chopper; Pnom=100kW 5 10

EN55022A Filter for multiCell Chopper

Accounting for the discrete nature of the spectrum (mainly for choppers…)

4

3 Some standards

cutoff frequency [Hz]

cutoff frequency [Hz]

10

10

10

4

3

180 EN55022A [dBuV] EN55022B [dBuV] HVDCA: P=100kW [dBuA] HVDCB: P=1kW [dBuA]

10

10

3

4

5

10 10 switching frequency [Hz]

10

maximum ripple [dBuX]

160

2

6

140

10

120

2

10

3

100

4

5

10 10 switching frequency [Hz]

10

6

80 60 40 20

10

10

10

5

EN55022B Filter for multiCell Chopper

0 3 10

4

3

2

10

10

4

5

10 10 switching frequency [Hz]

6

10

HVDC Filter for multiCell Chopper; Pnom=1kW 5 10

7

cutoff frequency [Hz]

cutoff frequency [Hz]

10

3

4

5

10 10 switching frequency [Hz]

10

6

10

10

10

4

3

2

10

3

4

5

10 10 switching frequency [Hz]

12

10

6

Step response, average model : full load => no load Worst Case :

D  100%; I

( t 0 ) LHV

 I LVmax Voltage overshoots

I LVmax

LHV 0.ILV

VHV

I L( tLV0 )  I LVmax

CHV VCHV

0

LLV / n p 0.VHV

CLV VCLV

Best response of the control to limit overshoot on LV side : impose D=0 13

Step response, state plane analysis full load => no load High Voltage Side

Low Voltage Side

VCHV

VCLV

Worst Case

VHV

VHV

I LHV 0

I LVmax

LHV CHV

LHV CHV

I LLV 0

I LVmax

LLV CLV

LLV CLV 14

Limit the voltage overshoot on the High Voltage Side

I LV . HV Vovrsht % 

LHV CHV

VHV

HV LHV VHV .Vovrsht % ...........  ...............  CHV I LV max 15

D  100%; I

Worst Case :

( t 0 ) LHV

0 Voltage dips

I LVmax

LHV I L( tLV0 )  0 VHV

CHV VCHV

0

LLV / n p

CLV VCLV Best response of the control to limit voltage dip on LV side : maintain D=100% 16

Step response, state plane analysis no load => full load High Voltage Side

Low Voltage Side

VCHV

VCLV

VHV

VHV Worst Case

I LHV 0

I LVmax

LHV CHV

LHV CHV

I LLV 0

I LVmax

LLV n p CLV

LLV n p CLV 17

Limit the voltage dip on the Low Voltage Side

I LV . LV Vdip 

LLV n pCLV VHV

...........  ...............

LLV n p CLV

LV VHV .Vdip

I LVmax 18

Calculation of the components High Voltage side

Low Voltage side

  nCell  n p  HV I pk   ripple HV Rip  I   % ripple% I LV max  1  f  0  2 LHV .CHV 

 1.5  f 0  min  nCell f sw Rip %  2 

;

  nCell  n p .ns  LV V  pk  ripple LV  Rip %  Vripple%  VHV  1  f   0 2 L n .C LV p LV 

gabmax  f salient, nCell . f sw 

Valid for uncoupled AND coupled magnetic components

 . max  f salient, nCell . f sw 3  2VHV . f sw

 

19

Calculation of the components High Voltage side

Low Voltage side

HV  LHV VHV .Vovrsht %    CHV I LVmax  1  LHV .CHV   2 . f 0HV

HV  VHV .Vovrsht %  LHV  2 . f HV I  0 LVmax  I LVmax C  HV  HV 2 . f 0HVVHV .Vovrsht %

LV  LLV n p VHV .Vdip %    CLV I LVmax  1  L n .C   LV p LV 2 . f 0LV

LV  VHV .Vdip %  LLV n p  2 . f 0LV I LVmax   I LVmax C  LV  LV 2 . f 0LVVHV .Vdip %

Valid for uncoupled AND coupled magnetic components

20

Calculation of the components Example #1 : 2-level converter => from 10 to 150kHz, the tendancy is an increase of passive components MultiCell -2 Chopper with: nS=1; VHV=800; ILVmax=250; IHVmax=125; relativeOutRipple=0.01; VHVovershoot=0.1; VLVdip=0.05;standardHV=HVDCA;standardLV=EN55022A 10 LHV CHV LLV CLV

-3

L and C values [H or F]

10

10

-4

10

3

10

4

10 switching frequency [Hz]

5

10

6

21

Calculation of the components Example #2 : series 2-cell converter => the HV filter is unchanged, LLV and CLV are reduced if fsw > 80kHz MultiCell -2 Chopper with: nS=2; VHV=800; ILVmax=250; IHVmax=125; relativeOutRipple=0.01; VHVovershoot=0.1; VLVdip=0.05;standardHV=HVDCA;standardLV=EN55022A 10 LHV @nS=1 CHV @nS=1 LLV/[email protected]=1 CLV @nS=1 LHV @nS=2 CHV @nS=2 LLV/[email protected]=2 CLV @nS=2 -3

L and C values [H or F]

10

10

-4

10

3

10

4

10 switching frequency [Hz]

5

10

6

22

Calculation of the components Example #3 : parallel 2-cell converter => all passive components are reduced if fsw > 80kHz MultiCell -2 Chopper with: nS=1; VHV=800; ILVmax=250; IHVmax=125; relativeOutRipple=0.01; VHVovershoot=0.1; VLVdip=0.05;standardHV=HVDCA;standardLV=EN55022A 10 LHV @nP=1 CHV @nP=1 LLV/[email protected]=1 CLV @nP=1 LHV @nP=2 CHV @nP=2 LLV/[email protected]=2 CLV @nP=2 -3

L and C values [H or F]

10

10

-4

10

3

10

4

10 switching frequency [Hz]

5

10

6

23

Calculation of the components Example #4 : parallel multiCell converter => with 10 // cells, all passive components start decreasing at fsw > 15kHz MultiCell -2 Chopper with: nS=1; VHV=800; ILVmax=250; IHVmax=125; relativeOutRipple=0.01; VHVovershoot=0.1; VLVdip=0.05;standardHV=HVDCA;standardLV=EN55022A 10 LHV @nP=1 CHV @nP=1 LLV/[email protected]=1 CLV @nP=1 LHV @nP=2 CHV @nP=2 LLV/[email protected]=2 CLV @nP=2 -3

L and C values [H or F]

10

10

-4

10

3

10

4

10 switching frequency [Hz]

5

10

6

24

Combined requirements High Voltage side

Low Voltage side

LHV

LLV Current design Current design Candidates for volume reduction

0

CHV

Candidates for volume reduction

0

CLV

For the same amount of energy, magnetic components are (2 to 10 times??) bigger, heavier and more expensive than capacitor => Reducing the inductances and increasing the capacitance leaves room for25 optimization… (and increasing the inductance must not be rejected a priori!)