Holistic control of three-phase bidirectional rectiﬁers

Holistic controlof three-phase bidirectional rectifiers

Alexei V Nikitin

Nonlinear LLC

Wamego, KS, USA

[email protected]

NAECON 2018

Dayton, OH

24 July 2018

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mailto:[email protected]

Acknowledgments

I would like to thank

Arlie Stonestreet II and Kyle D. Tidball

of Ultra Electronics ICE, Manhattan, KS, USA,

Ian Stothers of Ultra Electronics Controls, Cambridge, UK, and

Ruslan L. Davidchack of the University of Leicester, UK,

for their valuable suggestions and critical comments

Special thanks to Arlie and Kyle for providing the high-fidelity

LTspice models for the SiC MOSFETs and the SiC Schottky

diodes used in the simulations

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Why “analog” or “e↵ectively analog” control?

“Bare” ICM-based 3-phase 6-switch rectifier

EMI filtering with non-dissipative resonance damping

Illustrative performance examples

“E↵ectively analog” oversampled digital ICM implementation

Control and management of ICM switching behavior

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Why “analog” or “e↵ectively analog” control for switching converters?

1 Voltage and current relations in switching power converter

would be best described by system of continuous-time

di↵erential equations

2 Di↵erential equation can be easily solved, in real time, by

simple analog feedback circuit comprising integrator

3 This o↵ers various advantages over digital alternatives

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Example: ICM controller for 2-level H-bridge inverter

2-level H-bridge inverter with basic ICM controller

ICM ⌘ Inductor Current Mapping

1 Integrator

2 Two Schmitt triggers (inverting and non-

inverting) with slight o↵set in reference voltage

For controller: V?= �V ref

µ� ⌧ V out

For power stage:

V?= V out + 2LI load + 2LC V out

overlines denote averaging over time interval between any

pair of rising/falling edges of Q1 or Q2

with such idealizations as e↵ectively ideal behavior of

controller circuit, negligible voltage drops across

components, and e↵ectively constant L and C

with practical choice of T and hysteresis gap �h that

ensures su�ciently high switching frequencies

V out=

�V ref

µ� 2LI load

!�⌧ V out � 2LC V out

– 2nd order lowpass with !n = 1p2LC

and Q =p

2LC⌧

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ICM-controlled 3-phase 6-switch bridge rectifier

ICM controller per each “leg”

For “bare” configuration:8>>>>>><

>>>>>>:

I a = � ⌧L V 0

a � 1LRdt�VCM�V N

�

I b = � ⌧L V 0

b � 1LRdt�VCM�V N

�

I c = � ⌧L V 0

c � 1LRdt�VCM�V N

�

Ia + Ib + Ic = 0

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“Bare” configuration (w/o EMI filtering and ICM damping inputs)

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“Spread-spectrum” switching

“Fundamental” switching range mainly confined to [fmin, fmax]:

fmin ⇡1

4TµVDC

�h

1 �

8hV 02a i

V 2DC

!, fmax ⇡

1

4TµVDC

�h

Can be “pivoted” around fmax by injecting FCS inputs with fsw = fmax

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Flexible regulation options

� is “power setting” parameter

Steady-state AC power drawn from or supplied to 3-phase AC source:

PAC = �⌧

L�⌦

V 02a↵+⌦V 02

b↵+⌦V 02

c↵�

E.g. to output Vref :

� =V 2

ref⌦|V 0

a |↵2

+⌦|V 0

b |↵2

+⌦|V 0

c |↵2

8L⇡2⌘⌧

IloadVDC

✓Vref

hVDCi

◆n

All quantities are positive, no trigonometric function evaluations

only first-quadrant multiplications/divisions

all variables except Iload are either constants or slowly varying

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Steady-state “benchmark”LTspice simulations for C2M0025120D SiC MOSFETs and the C4D20120A SiC Schottky diodes

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“Wild” frequency compatibility

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Transients under mains voltage imbalance

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Phase loss/return transients

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60%–40% load sharing by two paralleled rectifiers

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Startup/overload management

Multiple ways to modify basic regulation equation:

� =V 2

ref⌦|V 0

a |↵2

+⌦|V 0

b |↵2

+⌦|V 0

c |↵2

8L⇡2⌘⌧

IloadVDC

✓Vref

hVDCi

◆n

For example, for Pout 12 kW, Vref = 400V, and n = 2:

� =1, 600V2

⌦|V 0

a |↵2

+ h|V 0b|i

2 +⌦|V 0

c |↵2

8L0.975⇡2⌧

min (Iload, 30A)

max (VDC, 380V)

1, 600V2

max (hVDCi, 380V)2

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Startup/overload management

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Operation under “sub-boost” conversion ratios

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Steady-state operation under normal and overload conditions

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Analog and digital ICM implementations

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Analog and digital ICM implementations

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Summary

Analog ICM controllers o↵er1 Many overall advantages over respective digital controller architectures

2 Simplicity without sacrificing performance

3 Adaptivity to various power converter topologies

4 Multiple ways to optimize cost-size-weight-performance tradespace

Some particular features includeHigh-quality power under wide range of load conditions & changes

unity power factor & low THD

Flexible regulation optionsincluding voltage, current, power, or combination

Only DC-side current sensing needed

“Wild” frequency compatibility & EMI filtering with non-dissipative resonance damping

Easy load sharing & N + 1 redundancy Simple start-up & overload management

Tolerance to mains voltage imbalance & phase loss Inherent bidirectionality

Intrinsic spread-spectrum switching Can be “pivoted” on injected FCS inputs

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Appendix: Control and management of ICM switching behavior







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Appendix: “Pivoting” switching spectrum by injecting FCS inputs

Inject triangle wave FCS with fsw = fmax (forces synchronous switching):

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Appendix: “Pivoting” switching spectrum by injecting FCS inputs

Inject triangle wave FCS with fsw = fmax (forces synchronous switching):

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“Analog” Inductor Current Mapping (ICM) control approach

Analog ICM vs digital controllers

“Holistic” high-bandwidth real-time control

incorporating flexible regulation options, startup, EMI, and overload management,

“wild” frequency compatibility, tolerance to mains voltage imbalance and/or phase loss

No analysis of various topological stages during switching cycle needed

No coordinate transformations and PLLs

No phase currents sensing

Low computational intensity for “e↵ectively analog” digital implementation

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Holistic control of three-phase bidirectional rectiﬁers

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