EMI DM Filter Volume Minimization for a PFC BoostConverter Including Boost Inductor Variation and MF EMI

Limits

Jonas Wyss, Jurgen BielaHigh Power Electronics Laboratory

ETH ZurichSwitzerland

Email: wyss@hpe.ee.ethz.ch

AcknowledgmentsThe authors would like to thank B&R Industrie-Automation AG very much for their strong financialsupport of the research work.

Keywords<<Power factor correction>>, <<Three-phase system>>, <<EMC/EMI>>

AbstractFor the AC-DC conversion in drive systems, Power Factor Correction (PFC) converters are widely usedas they can ensure a high power factor. The EMI filters that are needed for meeting grid regulationshave a considerable impact on the total converter volume. In this paper, a method to optimize an EMIfilter stage of a PFC converter with respect to volume, is investigated. It includes the optimal choice ofthe boost inductance value, as it has a big impact on both the converter and the EMI filter design. Inaddition, different damping topologies are investigated and compared with each other. It is shown that incomparison to a boost inductance value so that the boost inductor current ripple is set to 15 % of the inputcurrent, an optimal boost inductance value reduces the total volume of EMI filter and boost inductor upto 17 %.

1 IntroductionFor supplying electrical systems from the mains, a three-phase boost PFC converter is often used toensure a high power factor and low harmonics. While the main goal is the power transfer retaining ahigh power factor, the converter has also to comply with standards at the low and high frequency (LF andHF) spectrum [1]. In order to meet the LF standards, a pulse-width modulation (PWM) with a sufficientlyhigh switching frequency is usually employed, with the side-effect of creating HF noise, which has to beattenuated by an EMI filter. The design of the EMI filter has considerable impact on the converter design[2], i.e. volume, losses, cost and system stability.In this paper, the EMI filter design of a bidirectional three-phase boost PFC converter with a three-levelT-type topology (cf. Fig. 1) with the specifications in table I is investigated. In previous works (e.g. [3],[4]), the boost inductor has been determined by a restriction on the maximum allowed current ripple.However, as the boost inductor has a considerable influence on various aspects of the EMI filter (e.g.required attenuation) and the converter itself (e.g. volume, control stability), it should be included in theoptimization of the EMI filter. In [5], the total volume of boost inductor and EMI filter in dependence ofthe ripple factor

kripple =∆ILb,pk−pk,max

IL,avg(1)

has been determined for a 300W single-phase boost PFC converter, showing that for kripple≥ 0.4 the totalvolume is nearly constant, while for kripple < 0.4, the volume is increasing with decreasing ripple factor.

However, in [5] no medium frequency (MF) limits had to be considered, as the switching frequency wasa magnitude higher than in this paper. However, MF limits have a significant influence on the EMI filter,when the switching frequency is lower (see section 2).

EMI FilterLISN EMI

FilterLISN EMI FilterLISN

Phase 1Phase 2

Phase 3

Model

Boost Inductance Lb

Filter Values[Lf, Cf, Ld/Cd, Rd]

Number of Filter Stages nf

FilterVolume Vf

Boost Inductor Volume VLb

Limits met?

a) b)

Figure 1: a) Electrical circuit of the converter. b) Block diagram of the converter model.

Table I: Specifications of the investigated bidirectionalthree-phase PFC converter.

AC Voltage (ph-ph) 400 VDC Voltage 800 VPower 30 kWSwitching Frequency 15 kHz

Table II: Degrees of freedom for the filter optimization.

Boost Inductance LbFilter Inductance L f

Filter Capacitance C f

Damping Impedance Ld/CdDamping Resistance RdNumber of Filter Stages n f

The considered optimization with respect to volume focuses on the differential mode (DM) filter as thisis mainly determining the volume of the EMI filter. The parasitic coupling between the components isneglected. For multi-stage filters, the stages consist of the same components, e.g. L f 1 = L f 2 = ...= L f n,as this leads to a minimal volume [6]. The degrees of freedom for the filter design are listed in table II.In section 2, the model of the converter including the volume of the filter components is described. Insection 3, the optimization procedure is outlined. In section 4, the optimization results are presented.

2 Converter ModelIn this section the converter model, which is the paramount part of the filter optimization (cf. Fig.8), is described. In section 2.1 the used standards a filter has to fulfill are introduced and it is shownhow the control stability is ensured. In section 2.2 the volume estimation of the passive components isexplained. Finally, in section 2.3 the different passive damping topologies are described and an analyticalconsideration of what to expect out of the optimization is done.

2.1 Standards and StabilityIn the converter model a space vector modulation (SVM) and the resulting currents and voltages ofthe converter including the filter stage are calculated. Fig. 1 shows the electrical circuit and the blockdiagram of the model. The switches and voltage sources are assumed as ideal. In order to check if theHF limits are met, a line impedance stabilizing network (LISN) is inserted to get the estimation of a realmeasurement device, which is measuring the voltage over the LISN resistor with a quasi-peak detector[7]. For the LF, MF and THD limits, the fourier transformation of the input current without the LISN iscompared with the limits. The stability criterion is checked for a line impedance of 50µH.The LF and THD limits are taken from the EN 61000-3-12 standard and the HF limits from the CISPR 11standard class A. In between, i.e. between 700Hz and 150kHz, there is no well suited limit for modernswitched converters. However, in the future a standard must be expected [8].In Fig. 2 the fourier transformation of the input current of a converter with the specifications of tableI is shown where the optimization of the EMI filter does not include any MF limits. The peak at theswitching frequency is nearly as high as some of the LF limits. To prevent this and fill the gap betweenLF and HF limits, a logarithmic linear function from the LF to the HF limit is used in this work. All usedlimits are shown in Fig. 2.

Frequency (Hz)102 103 104 105 106 107 108

Cur

rent

s (%

I fund

)

10-10

10-8

10-6

10-4

10-2

100

102

Input Current

LF Limits (EN 61000-3)

MF Limits

HF Limits (CISPR 11 class B)

Figure 2: Input current spectrum of a converter with the specifications of table I with an optimized EMI filter notconsidering the MF limits. The LF, MF and HF limits used in this paper are also shown.

Another consideration when designing an EMI filter is the control stability, as the inclusion of a filter cansignificantly affect the converter behaviour. Middlebrook’s stability criterion [9],[10] states that if thefilter output impedance is lower over all frequencies than the converter input impedance, then the filterdoes not affect the system control stability. In [11] the criterion has been extended to 3-phase systemsand is used in this work.If a filter design meets all limits and the stability criterion, it is considered to be a valid design and theperformance with respect to volume can be evaluated. The volume estimation of the passive componentsis described in the following section.

2.2 Volume of Passive ElementsIn order to evaluate the performance of a filter with respect to volume the volume of the passive com-ponents has to be estimated. The components of the filters can be seen in Fig. 5 for different dampingtopologies. The volume of the damping resistors is negligible in comparison to the capacitor and inductorvolumes. For the capacitor volume, the approximation formula

VC = k1 ·CV 2 + k2(V ). (2)

from [6] is used which estimates the capacitor volume on the basis of X2 capacitors. This is based onthe fact that the capacitance and the breakdown voltage of a plate capacitor depends on its geometric andmaterial parameters [7]:

C =εA f

d(3)

where A f is the plate surface area and d is the distance between the plates and

V = Ebr ·d (4)

where Ebr is the breakdown electric field. This results in

VC = A f ·d =CV 2

εE2br

∝ CV 2. (5)

The factor k2 in (2) depends on the manufacturing process.The volume estimation of the inductors is based on an E-Core of the core material 2605SA1 and variablegeometry parameters according to Fig. 3a). The volume is minimized while ensuring that the inductorcooling is sufficient.For the core losses, the improved generalized Steinmetz equations from [12] are used. For the windinglosses, the skin and proximity effects are included, for the calculation of the magnetic field the mirror

method is used [13]. Regarding the cooling of the inductor, it is assumed that the inductor is placedin the air duct of the heat sink for the semiconductors, which leads to a better heat transfer coefficientfor the surface αsur f ace than in free convection (αsur f ace = 5−15Wm−2 K−1 [14]). In this optimization,αsur f ace = 20Wm−2 K−1 and an ambient temperature of 55 ◦C are assumed and the maximum allowedtemperature is set to 80 ◦C.The inductor volume optimization procedure, visualized in Fig. 3b), is divided in three steps:

1. The inductor is optimized with a genetic algorithm (GA) which leads to a local minimum. How-ever, the GA cannot guarantee to find the global minimum. The randomness of the local minimumfound by the GA is undesired in the filter optimization.

2. A brute force method would solve the problem, but the mirror method needed to calculate theHF losses uses too much computing the time. However, the losses neglecting the HF losses can becalculated much faster. Using this fact, in a reasonable amount of time a brute-force routine createsa database of cores where the cooling constraints neglecting HF losses are met, and, in order tolimit the size of the database in reasonable bounds, the volume is smaller than the minimum foundwith the genetic algorithm.

3. The database is sorted with respect to volume and in this order, the losses are calculated includingthe HF losses. The best core geometry with respect to volume which meets the cooling constraintsincluding HF losses is chosen.

N: Number of Turns

a

a

b

c

d

Inductor Specification: L, i(t), Core Material, Cooling Constraints

Minimal Volume

Find Local Minimum (incl. HF Losses) Vmin,ga with GA

Create Database (neglecting HF Losses) with V < Vmin,ga

Sort Database in Respect of Volume

Find Smallest Design which Meets Cooling Constraints incl. HF Losses

a) b)

Figure 3: a) Geometric parameters of an E-core inductor. b) 3-step procedure of minimizing the inductor volume.

2.2.1 Approximation of the Inductor VolumeThe optimization in section 3 is performed with the described procedure. However, most of the comput-ing time is used for the estimation of the inductor volume. Therefore, an approximation formula wouldaccelerate the computing time tremendously, which is done in this section out of the gained results fromthe optimization in section 3.In [6], the approximation formula

VL = k1 ·LI2 + k2 ·L+ k3 · I (6)

has been proposed. However, in comparison with the data gained of the inductor optimization the curvedoes not fit very well as can be seen in Fig. 4. Therefore, a more suitable approximation formulais derived. To design an inductor there are 2 key parameters. First, the core area Ac depends on thesaturation flux Bs:

L · I = N ·Bs ·Ac (7)

where N is the number of turns. Second, the window area Aw depends on the maximal allowed currentdensity Srms:

Aw =Irms ·NSrms · kw

(8)

where kw is the copper filling factor (typically 0.4...0.7). The combined equations lead to

L · I · Irms = kw ·Srms ·Bs ·Aw ·Ac. (9)

Neglecting the ripple of the current, the energy stored in the inductor is proportional to the area product[15] AcAw of the inductor, i.e. LI2 ∝ AcAw or in units, J ∝ m4. Therefore, a curve fit of the form

VL = k1 ·(LI2) 3

4 + k2 (10)

is evaluated. It fits better than (6). In order to improve the fitting further

VL = k1 ·(LI2) 3

4 + k2 ·LI2, (11)

is used. The three formulas (6), (10) and (11) are compared with the data points gained from the inductoroptimization in Fig. 4. The parameters k1 and k2 are determined using a pattern search optimization.Equation (11) shows the best results and is used for the analytical considerations in section 2.3.1.

Inductance (mH)0 0.25 0.5 0.75 1

Vol

ume

(dm

3 )

0

100

200

300

400

500

Optimized Inductors

k1∙LI2+k2

k1·(LI2)(3/4)+k2

k1∙(LI2)(3/4)+k2∙LI2

I = 43 A

I = 29 A

Figure 4: Different approximations for the inductor volume.

2.3 Filter TopologiesIn the optimization, the 4 standard passive damping filter topologies, depicted in Fig. 5, are investigated.In a) the damping capacitor Cd does not have to be rated for the full input voltage, but is on the otherhand reducing the HF attenuation as it connected in series to the filter capacitor C f . Similarly, in b)the damping inductor Ld does not have to be rated for the full input current, but is reducing the HFattenuation. The damping capacitor Cd in c) has to be rated for the full input voltage, but is not reducingthe HF attenuation. On the other hand, it is increasing the reactive power consumption. The dampinginductor Ld in d) has to be rated for the full input current, but is not reducing the HF attenuation [7].

Lf

Cf

Rd

a) b) c) d)

CfRdLd

Ld

Rd

Rd

Cd

CfCf

Lf LfLf

Cd

Figure 5: Standard passive damping filter structures: a) Serial-RC damping b) Parallel-RL damping c) Parallel-RCdamping d) Serial-RL damping.

For all 4 damping topologies, there is an optimal damping resistor Rd in order to achieve a low maximalfilter output impedance over the whole frequency range [16]. As the serial-RC damping network of Fig.5a) was not included in [16], the same method has been applied to this filter structure which results in

Rd,opt =

√L f

C f·

√(4n+3) · (2n+1)

2 · (4n+1) · (n+1)3 with n =Ld

L f. (12)

In section 3 all 4 filter topologies are investigated and in section 4 compared with each other. In thenext section, with the help of the approximation formulas for the volume of the passive components ananalytical consideration comparing the filter topologies is performed.

2.3.1 Analytical ConsiderationsComparing filter topologies a) and c) of Fig. 5, the filter components C f , Cd and Rd can be transformedinto each other with

C f ,s =C f ,p +Cd,p Cd,s =C f ,p +C2

f ,p

Cd,pRd,s = Rd,p ·

C2d,p

(C f ,p +Cd,p)2 (13)

where C f ,s, Cd,s and Rd,s are the components of the serial-RC damping and C f ,p, Cd,p and Rd,p thecomponents of the parallel-RC damping topology. In a reasonable filter design, the voltage across thecapacitor Cd,s is low (as otherwise the losses in the damping resistor would be high) and the volume ofthis capacitor is negligible in comparison to the volume of C f ,s. Neglecting the volume of the dampingresistors, the total volume of C f ,p, Cd,p and Rd,p is (using equation 2)

Vs = kC1 ·C f ,sU2 + kC2 ·UVp = kC1 ·C f ,pU2 + kC2 ·U + kC1 ·Cd,pU2 + kC2 ·U

= kC1 ·C f ,sU2 +2kC2 ·U(14)

As kC2 · U is much smaller than kC1 ·CU2, the two volumes are almost equal. Therefore it is expectedthat the total volumes of the filter stages a) and c) of Fig. 5 do not differ significantly.Comparing filter structures b) and d) of Fig. 5, the filter components of L f , Ld and Rd can be transformedto each other with

L f ,p = L f ,s +Ld,s Ld,p = L f ,s +L2

f ,s

Ld ,sRd,p = Rd,s ·

(L f ,s +Ld,s)2

L2d,s

(15)

where L f ,s, Ld,s and Rd,s are the components of the serial-RL damping and L f ,p, Ld,p and Rd,p the com-ponents of the parallel-RL damping topology. In a reasonable filter design, the current through Ld,p islow (as otherwise the losses in the damping resistor would be high) and the volume of this inductor isnegligible in comparison to the volume of L f ,p. Neglecting the volume of the damping resistors, the totalvolume of the inductive part of the filter is (using (11))

Vp = kL1 ·(L f ,pI2) 3

4 + kL2 ·L f ,pI2

Vs = kL1 ·(L f ,sI2) 3

4 + kL2 ·L f ,sI2 + kL1 ·(Ld,sI2) 3

4 + kL2 ·Ld,sI2.(16)

Using (15), The difference between the two volumes is

Vp−Vs = kL1 · I64 ·(

L34f ,p−

(L

34f ,s +L

34d,s

))Vs−Vp

kL1 · I64= (L f ,s +Ld,s)

34 −(

L34f ,s +L

34d,s

) (17)

Considering the right hand side of (17), multiplying with (L f ,s +Ld,s)14 results in

L f ,s +Ld,s−(

L34f ,s · (L f ,s +Ld,s)

14 +L

34d,s · (L f ,s +Ld,s)

14

). (18)

Using the fact that L34f ,s · (L f ,s +Ld,s)

14 > L f ,s and L

34d,s · (L f ,s +Ld,s)

14 > Ld,s, the term on the right hand

side of (17) is negative and therefore the volume of the parallel-RL structure is in general supposed to besmaller than the volume of the serial-RL structure.The two considerations of this section are approved in section 4.

3 Optimization ProcedureIn this section the filter optimization is described. First the optimization parameters are described, thenthe optimization sequence is explained.The filter design is characterised by three key parameters ω0, ωm and Zm. The resonance frequency ω0describes the HF damping of the filter, i.e. the resonance frequency of a filter structure using f → ∞ isevaluated. Generally, the higher ω0, the lower the filter volume, but if it is chosen too high the MF andHF limits cannot be met anymore. The second main constraint is Middlebrook’s stability criterion. Thekey parameters ωm defines the frequency and Zm the maximal value of the filter output impedance. Fig.6 illustrate the filter parameters.

Frequency (kHz)103 104 105 106

Tran

sfer

Fun

ctio

n (1

)

10-4

10-2

100

102

ω0 ωm

Frequency (kHz)103 105 106

Out

put I

mpe

danc

e (Ω

)10-2

100

102

Zm

Figure 6: Transfer function and output impedance of a filter illustrating the filter parameters.

The optimization is cascaded as can be seen in Fig. 8a). In the outer loops the parameters which have abigger influence on the converters than the inner loops are varied.

1. The main part of the optimization procedure is the converter model presented in section 2, whichchecks the EMI limits and estimates the volume for a given filter stage.

2. In the most inner loop the maximal value of the filter output impedance Zm (cf. Fig. 6) is optimized,i.e. mainly the ratio L f/C f is adjusted, which is a trade-off between inductor and capacitor volume.

3. In the next loop, the second key parameter regarding Middlebrook’s stability criterion, i.e. thefrequency location of the maximum filter output impedance ωm (cf. Fig. 6), is optimized, i.e.mainly the ratio n = Ld/L f or Cd/C f is adjusted, which is a trade-off between damping capability (inorder to fulfill Middlebrook’s stability criterion) and volume of the damping element.

4. In the next loop, the resonance frequency ω0 (cf. Fig. 6), i.e. the key parameter of the filterregarding the attenuation in the high frequency region, is adjusted. The higher ω0, the lower arethe capacitances and inductances, but it also lowers the attenuation. A higher ω0 is desirable, butit cannot exceed a certain value in order to fulfill the attenuation requirements.

5. In the main loop, the boost inductance Lb is varied, which affects the required attenuation as well asthe converter input impedance. It is a trade-off between boost inductor volume and filter volume.

For the reasons stated above, it is assumed that for all loops the volume function is convex, which isconfirmed in section 4.The optimization algorithm is implemented as follows: For a given lower and upper bound (LB and UB),the algorithm evaluates the results of LB+ 1/4 ·(UB−LB), LB+ 2/4 ·(UB−LB) and LB+ 3/4 ·(UB−LB).The adjacent points of the minimal result form the new lower and upper bound. The algorithm repeatsthis until a minimal difference between lower and upper bound is reached. Fig. 7 illustrates the algorithm.

UBLB+2/4·(UB-LB) LB+3/4·(UB-LB)LB+1/4·(UB-LB)

Minimum

ParameterLB

Res

ult New LB New UB

Figure 7: Illustration of the optimization algorithm.

System Specification:P, Vdc, Vac, fn, fs

5. Boost Inductance Lb

4. Filter Cut-Off Frequency ω0

3. Filter Output Impedance Maximum Frequency ωm

2. Filter Output Impedance Maximum Zm

Calculate Volumes

Volume for one Filter Design

Volume as f(Zm)

Volume as f(ωm)

Volume as f(ωc)

Volume as f(Lb)

Calculate Filter Component Values

Calculate Currentsand Voltages

Limits met?

yes

no

vary Zm

vary ωm

vary ω0

vary Lb

1. System Model

(Fig. 1a)

VLb

VLb

VLb

VLb

VLf

VLf

VLf

VLf

VCf

VCf

VCf

VCf

VCd

VLd

Parallel-RL

Serial-RL

Parallel-RC

Serial-RC

a) b)

Minimal Volume

Vtot = 2.38 dm3

Vtot = 2.43 dm3

Vtot = 2.39 dm3

Vtot = 2.39 dm3

Figure 8: a) Block diagram of the cascaded filter optimization. b) Volume distribution of the filter components ofthe smallest filter for different damping topologies.

4 ResultsFig. 9 shows the total filter volume as a function of the boost inductance for all damping topologies (cf.Fig. 5). The analytical considerations of section 2.3.1 (i.e. the volume of the two capacitive dampingtopologies are almost equal and the parallel-RL damping topology has a lower volume than the serial-RL damping topology) are confirmed. Comparing the capacitive damping topology and the parallel-RLdamping topology, only a marginal difference can be identified. Considering the number of filter stagesn f , a single stage clearly outperforms a filter with two stages. The choice of the boost inductance affectsthe filter volume considerably. For example the volume of the parallel-RC damping topology for a boostinductance of 650µH, which corresponds to a peak ripple of 15% of the nominal current, is 21% biggerthan the volume with the optimal choice of 900µH. Fig. 8b) shows the volume distribution of the smallestfilter for each damping topology.Fig. 10 shows exemplarily the dependence of the filter volume with a parallel-RL damping topologydepending on ω0, ωm and Zm, confirming the assumption that the volume functions are convex.

Boost Inductance (μH)600 700 800 900 1000 1100 1200 1300

Vol

ume

(dm

3 )

2.3

2.4

2.5

2.6

2.7

2.8

Parallel-RL(nf = 2)

Serial-RC / Parallel-RC(nf = 1)

Serial-RL(nf = 1)

Parallel-RL(nf = 1)

Figure 9: Minimal volume of the filter including the boost inductor in dependence of the boost inductance fordifferent damping topologies and filter stages.

Lb = 850 μHω0 = 17.75 kHz

Lb = 850 μH

ω0 (kHz)15 16 17 18

Vol

ume

(dm

3 )

2.3

2.4

2.5

2.6

2.7

ωm (kHz)10 12

2

2.5

3

3.5

Lb = 850 μHω0 = 17.75 kHzωm = 12.00 kHz

Zm (Ω)6 6.25 6.5

2.44

2.45

2.46

Figure 10: Minimal volume of the filter with a one-stage parallel-RL damping topology in dependence of ω0, ωmand Zm.

Volume (dm3)2 4 6 8 10 12 14 16 18

Loss

es (W

)

50

100

150

200

250

300

350

400

Figure 11: Filter losses in dependence of the volume for a filter with a one-stage parallel-RL damping topology.Filters with different Lb, ωc, ωm and Zm are considered. The minimal volume is marked with a red circle, thepareto-optimal point is marked with a green circle.

Regarding the losses, the inductive damping topologies show a better performance (101W / 99.63 %efficiency) than the capacitive damping topologies (114W / 99.62 % efficiency). Especially the dampingresistor losses of the capacitive damping topologies are quite high (10.5W) and are more difficult to coolin contrast to the inductive damping topologies (2.3W for serial-RL and 4.9W for parallel-RL damping).

Fig. 11 shows the volumes and losses of the examined filters of the parallel-RL damping configuration.Note that for each filter the inductors are optimized to have minimal volume, otherwise the plot wouldlook different. Also the capacitor losses have been neglected. The losses of the filter with smallestvolume (marked with a red circle in Fig. 11) are not optimal, a better volume-to-loss trade-off could bechosen (i.e. the pareto-optimal point, marked with a green circle in Fig. 11) and may be the focus of afurther improvement of the optimization.

5 ConclusionAn optimization algorithm is proposed, which optimizes the EMI filter and boost inductor regardingvarious limits, including a MF EMI limit. A comparison of different damping topologies is performed.The advantage of including the boost inductor in the optimization of the EMI filter is shown in this paper,as the volume savings between an optimized boost inductance and one set by a ripple current limit of 15% of the nominal current can be up to 17 %.

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