j. marcos alonso€¦ · next step is to model the b-h curve and to obtain a valid expression for...

10/12/2018

1

J. Marcos Alonso

Electrical Eng. Dept., Campus Viesques, Ed. 3, Room 3.2.20

33204-Gijon, Asturias, Spain

[email protected]

SPAIN

Introduction to VIs: Why? What? How?

Analytical Modeling of VIs

SPICE-based Modeling of VIs

Examples of Applications

Conclusions

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Why?

• Variable inductors can provide additional control

parameters to improve converter operation:

4

BUCK DC-DC CONVERTER

Duty Cycle

Frequency

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• Variable inductors can provide additional control

parameters to improve converter operation:

5

BUCK DC-DC CONVERTER

Inductance

What?

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Air Core Inductors are non-variable inductors:

B(T)

H(A/m)

L (H)

I (A)

0=B/H is constant

The inductance does not depend on the

current or any other electrical parameter

I

I

7

A

r

Tapped inductors can be used as variable inductors:

8

Discrete variation of the inductance

Difficult implementation of selector switch (bidirectional), especially

at high frequency

Difficult implementation of closed-loop control

Not practical in many applications

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Variable inductors based on moving cores:

9

Continuous variation of the inductance

Mechanical control of the inductance

Difficult implementation of closed-loop control

Not practical in many applications

Magnetic Core Inductors are inherent variable inductors:

B(T)

H(A/m)

L (H)

I (A)

is variable, it depends on the

operating point (B, H)

The inductance depends on the

current circulating through the

winding

It has no independent controlConstant Variable

Constant Variable

4

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Magnetic Core Inductors are inherent variable inductors:

B(T)

H(A/m)

L (H)

I (A)

is variable, it depends on the

operating point (B, H)

The inductance depends on the

current circulating through the

winding

It has no independent controlConstant Variable

Constant Variable

4

Saturation

≠Short Circuit

Magnetic Core Inductors are variable inductors:

L (H)

I (A)

For variable inductor operating in the saturation region the effective

inductance must be considered:

Constant Variable

5

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Magnetic Core Inductors are variable inductors:

L (H)

I (A)

This type of variable inductor can be used in different applications:

Power factor correction, Maximum Power Point Tracking in PV applications,

voltage regulation, etc.[1]

However, application is not flexible due to its inherent dependence of the inductance

versus current

A controllable variable inductor would be much more interesting for general

applications

Constant Variable

[1] W.G. Hurley, W.H. Wölfle; Transformers and Inductors for Power Electronics. Wiley. 2013.6

A controllable variable inductor is a device whose inductance can be varied

by using an electrical magnitude, typically a current:

Icontrol

L (H)

VariableIcontrol

Now, the inductance depends on the control current

The effect of the current circulating through the inductance can be

neglected

The equation that rules the VI operation will be simpler:

7

(A)

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How?

The trick is to superpose a DC flux to the AC flux created by the inductor

main winding

By shifting the DC operating point along the B-H curve the permeability is

modulated

This modifies the inductance seen from the AC winding

DC FluxAC Flux

g

Modulated by DC flux

DC current

DC current

Variable Inductance:

Depends on DC current

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The AC flux generates a voltage across the DC winding

This voltage can be high and could damage the DC current source used to

supply the DC winding.

DC FluxAC Flux

g

DC current

DC current

PROBLEM:

9

Adding a series choke to the DC winding can filter the reflected AC voltage

DC FluxAC Flux

g

DC current

DC current

A POSSIBLE SOLUTION:

Disadvantages: complex, bulky and inefficient

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Adding two auxiliary windings in reverse polarity on the outer legs

Both DC windings generate DC flux in the same direction

The AC flux enters each DC winding with a different polarity

As a consequence, the AC voltages reflected across the DC windings

compensate each other

The DC current source sees almost no AC voltage across its terminals

A BETTER SOLUTION:

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Triple E structure Quadruple U structure

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Introduction to VIs




Conclusions

Main ac winding on the central arm

DC bias windings on the lateral arms

DC bias current modulates material permeability

Goal: Obtain the variation of the inductance as a function of the dc bias

current. It is also important to determine the total inductance seen from the

auxiliary windings because this inductance will strongly affect to the dynamic

behavior of the VI.

22

CONTROLIdc

L

dc

Ndc Ndc

Np

lg

A1 A2

M1

M2

ac

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23

It is assumed that the ac component is small compared to the dc level

Superposition law can be applied to calculate dc and ac components

24

Once solved, the dc winding inductance can be calculated:

Analyzing the circuit:

The following equation must be solved to obtain

the magnetic flux density dc level:

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25

AC reluctances must be considered:

Calculation of AC flux and AC inductance is straightforward:

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27

DC magnetic flux density:

DC winding inductance:

28

AC magnetic flux:

AC winding inductance:

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Introduction to VIs




Conclusions

Importance of modeling of magnetic devices prior to manufacturing

Provide a better understanding of complex magnetic structures

Two typical modeling methods:

Finite Element Analysis (FEA): high accuracy, time consuming.

SPICE based behavioral models: quicker implementation and

simulation.

Previous works:

Ben-Yaakov 2005

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Relatively complex structures

Several windings in different arms

AC and DC excitation

Different applications

31

CONTROLIdc

L

dc

Ndc Ndc

Np

lg

A1 A2

M1

M2

ac

L ( H)

0 0.1 0.2 0.3 0.4 0.51

2

3

4

5

IDC (A)

Required elements:

Constant reluctance elements: air gap, non magnetic materials

Variable reluctance elements: depend on magnetic flux density (B)

Windings: magnetic – electrical interaction

32

CONTROLIdc

L

dc

Ndc Ndc

Np

lg

A1 A2

M1

M2

ac

+- +

-Ndc Idc Ndc IdcNpIp

Rl RrRc

Rg

() () ()

fcfl fr

Fdc Fp Fdc+-

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33

In SPICE simulator:

Voltage Magnetomotive Force

Current Magnetic Flux

Resistance Reluctance

34

ℜ𝑚 =𝑙𝑚

𝜇 𝐴𝑚

But can only be considered as a

constant when the material operates in

linear region!

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In a general case the material has to be

modeled in the whole range:

35

Material

B-H Curve

𝜇(𝐵) =𝑑𝐵

𝑑𝐻

ℜ𝑚(𝐵) =𝑙𝑚

𝜇(𝐵) 𝐴𝑚

Reluctance depends on

Magnetic Flux density B:

Next step is to model the B-H Curve and to obtain a valid expression for 𝜇(𝐵)

Neglecting hysteresis effects

Simple relationship to avoid SPICE convergence problems

36

Hyperbolic model:

𝐻 𝐵 =𝑘1

𝑘2𝐵+ 1

Brauer’s model:

𝐻 𝐵 = 𝑘1𝑒𝑘2𝐵

2+ 𝑘3 𝐵

𝜇 𝐵 = 𝑘1 1 + 2𝑘2𝐵2 𝑒𝑘2𝐵

2+ 𝑘3

−1 Direct expression of non-linear

material permeability:

𝑑

𝑑𝐵

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TDK-EPCOS N87 MATERIAl

37

N87 Datasheet

TDK-EPCOS N87 MATERIAl

38

𝜇 𝐵 = 𝑘1 1 + 2𝑘2𝐵2 𝑒𝑘2𝐵

2+ 𝑘3

−1

Maximum relative error 26% @ 0.3 T

0 0.1 0.2 0.3 0.4 0.5

B (T)

H (

A/m

)

0

500

1000

1500

Datasheet

Brauer’s Model

TDK-EPCOS N87 @ 25 ºC

𝐻 𝐵 = 𝑘1𝑒𝑘2𝐵

2+ 𝑘3 𝐵

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39

+-

value={(lm/(V(um)*Am))*I(Em)}

Em Gmb

value={I(Em)/Am}

Bm

Gmu1 1

value={ud(V(Bm))}

um

.func ud(B) { 1/( (1+2*k2*B*B)*exp(k2*B*B) + k3 ) } ; differential permeability

+

-

FR

fR

Resistance emulation Bm calculation d calculation

Can be implemented as an isolated component

40

Electric Variables

Magnetic Variables

Geometric

Parameters

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41

+-EFw

value={ Nw*I(EVw) }value={ -I(EFw) }

GVw

1m

{Nw}

Lw

Magnetic Part

(MMF)

Electric Part

(Winding)

+-

+-

EVw

1

+

-

vw

iw

+

-

Fw

fw+

-

fwddt

Nw

Implementation of M.M.F.Implementation electric-magnetic interaction

Airgap Linear Reluctor

Non Linear Reluctor Winding

Available for evaluation at: http://www.unioviedo.net/ate/marcosaa

B

OutputL

Output

http://www.unioviedo.net/ate/marcosaa

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43

OUTER ARMS

21.74

(*) Dimensions in mm. Not to scale.

9.10

10.92

3.15

CENTRAL ARM

5.20

0.60

12.20 gap

EFD25 CORE*

CONTROLIdc

L

dc

Ndc Ndc

Np

lg

A1 A2

M1

M2

ac

44

AirgapMain Winding

Non-linear

Reluctors

Auxiliary

Windings

Inductance

Calculation

Parameters

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45

LTspice circuit for the simulation of the VI, including the calculation of the ac

winding inductance:

46

DC magnetic flux density in the outer

arms: theoretical results (blue solid line)

and simulation results (blue squares).

AC winding inductance: theoretical

results (blue solid line) and

simulation results (blue squares).

theoretical

simulation

theoretical

simulation

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47

LTspice circuit for the simulation of the VI including the calculation of the dc bias

winding inductance.

48

DC bias winding inductance

DC bias winding inductance theoretical results (blue solid) and

simulation results (red triangles).

DC bias winding effective inductance (L_(dc_eff)): theoretical results

(green solid) and simulation results (blue squares)

theoretical

simulation

theoretical

simulation

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49

AC winding inductance

AC winding inductance: theoretical results (blue solid line) and

experimental measurements (red triangles).

theoretical

experimental

50

VI Current

VI Voltage

Right Arm Induction

Left Arm Induction

Center Arm InductionVI Inherent Time

Response

0.5 V

1.0 V

0.0 V 0.0 mA

50 mA

100 mA

350 mV

-350 mV

0.0 mV

0.2 us 0.6 us 1.0 us 1.4 us

V(out) I(R5)

V(bc) V(bd) V(bi)

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51

VI Model

52

-10V

-5V

0.0us 0.5us 1.0us 1.5us 2.0us 2.5us 3.0us 3.5us 4.0us 4.5us

0V

5V

-15V

10V

-10V

-5V

0V

5V

10V

15V

5.0us

V(lt1,mid)

V(lt2,mid)

SIMULATION EXPERIMENTAL

Input and Output

Voltage

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53

-5V

0.5us 1.0us 1.5us 2.0us 2.5us 3.0us 3.5us 4.0us 4.5us

0V

5V

-20V

10V

-10V

0V

10V

20V

5.0us

-10V

0.0us

V(lt1,lt2)

V(lt2,mid)


Inductor and

Output Voltage

54


-50V


0V

50V

-150V

100V

5.0us

100V

-100V

-50V

0V

50V

-100V

100V

-50V

0V

50V

100V

0.0us-100V

V(fc)

-V(auxl-)

V(fc, auxl-)

Voltage across

bias windings

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55

2uV


-400mV

3uV

5.0us

-200mV

0.0us

1uV

0mV

200mV

400mV V(bc) V(br) V(bl)

V(l_spice)

Magnetic Flux Density B (mT)

Middle arm Right arm

Left arm

Inductance (uH)

56

RMS Output Voltage (V)

DC Bias Current (A)

0

0

0.1 0.2 0.3 0.4

RM

S O

utp

ut V

olta

ge

(V

)

5

6

7

8

9

RL

=0.5

W

RL

=1.0W

0 0.1 0.2 0.3 0.4

5

6

7

8

9

Vo_exp

Vo_sim

Ibiask

Experimental

Simulation (LTspice model)

0.5

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Introduction to VIs




Conclusions

Use of Magnetic Regulators to Improve Power Converter Performance

2222222

22

441 LfLCfR

RV

R

VP

LA

LAE

LA

LALA

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Universal Ballast with Variable Inductance and Digital Control

Variable

Inductance

Resonant TankRectifier

Low Pass

Filter

R

LoadVCC

+

-

Vo

VCC L CS

CO

R

+

-

VOS

+

-

+

-

VCC /2

VCC /2

VCC L

CP CO R

LO

+

-

VOP

+

-

VCC /2

+

-

VCC /2

Resonant converter

LC series resonant converter

LC parallel resonant converter

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L

CP

REP

8

2

RV1

IREP

+

-

VREP

VCC L

CP CO R

LO

+

-

VOP

+

-

VCC /2

+

-

VCC /2

INDUCTANCE

R=

DC

OU

TP

UT

VO

LT

AG

E

R1

R2

R3

R4

Inductance

excursion

Lmin Lmax

R1< R2 R3< <R4

Target value

VCC

L

CP CF R

LF

+

-

Vo

Current

Source Current

Reference

Voltage

Reference

ZF

Zi

Variable

Inductor

Idc

Error

Amplifier

e

1

n

n

Magnetic Control of PRCEquivalent circuit

Can be used to control other resonant converters at constant frequency

Forward converter

with demag.

winding.

One output for each

LED branch.

Variable inductor

w/ auxiliary

windings. Output current sensing and regulation

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VDC

M1

M2

CB2

D12

D22

Co2

Vg

Rg

LED Lamp #2

1

1

D11

D21

Co1

Vg

Rg

LED Lamp #1

1

1

CB1

L1

L2

n1

n2

To other arrangements

To other arrangements

Application to several LED arrays

Each branch can be controlled independently

Multi-array LED lamp

380 V

VDC

M1

M2

CB

L

D1

D2

Co

+-

VDC

2Vg

Rg

LED

Lamp

n

1

1

i

+

-

vg

+

-

v1

is

+

-

Vo

Io

L

VDC+- 2

nVo+-

i

jvg v1

Equivalent Circuit

t

-

nVo

j

VDC

2

VDC

2

-nVo

t

2

TS TS

vg

v1

t

(t)

(t)

i(t)Ip

-Ip

t

nIp

IO

iS (t)

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Variable inductors can be used to provide additional control

parameters in power electronics converters.

Analytical modeling of VI is useful for the first design and

evaluation of the variable inductor.

SPICE based models can be used to simulate the complete converter

under VI control.

VI have been tested successfully to perform control of power

converters in different applications

New ideas and applications are expected in the near future. There

are possibilities to develop new ideas using VI for the control of

power converters.

18

Gijón, Asturias, Spain

j. marcos alonso€¦ · next step is to model the b-h curve and to obtain a valid expression for...

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