Virtual Impedance Control

for Grid-Connected Power

Converters

Xiongfei Wang, Frede Blaabjerg

Aalborg University, Denmark

xwa@et.aau.dk

1

2

Introduction

Impedance modeling and analysis

Virtual impedance control

Conclusions

Outline

3

Impact of Power Electronics

Instability – Resonance (zero damping) – Harmonic (under-damping)

Sub-synchronous oscillation f1

2f1 Near synchronous oscillation

Harmonic oscillation fs/2

fs

Sideband oscillation

- multisampling control

f1: Grid fundamental frequency; fs: Switching frequency Grid Syn.: grid synchronization; PF: power factor;

Current Ref.: current reference generation

4

► Offshore wind power plant - burned filters of offshore converter station1

► Electric railway network - tripped locomotive2

1. B. Matthias and T. Gerald, “Knall auf hoher see,” DER SPIEGEL 35/2014.

2. E. Mollerstedt and B. Bernhardsson, ”Out of control because of harmonics - an analysis of the harmonic response of an inverter

locomotive,” IEEE Control Systems, vol. 20, no. 4, pp. 70-81, Aug. 2000.

Real-Life Challenges

More Interactions among Clustered Power Converters

5

Introduction

Impedance modeling and analysis

Virtual impedance control

Conclusions

Outline

6

Impedance Modeling

Circuit-Oriented Analysis Tool

Ideal

Real case

Re{Yo}>0, stable but may be resonant

Re{Yo}=0, resonant, zero damping

Re{Yo}<0, unstable, negative damping

Impedance/admittance predicts grid-

converter interactions

L2

C VgGcl ic

Series resonanceParallel resonance

Vdc

L1 L2

C Vg

Grid-Connected Converter

L2

C VgYoGcl ic

Parallel instability Series instability

7

Impedance-Based Stability Analysis

Example - Current Control of Grid Converter with Long Cable

LCL-Filter

L1

CLg

VSC

Vpcc

Multiple PI-sections cable model

L2

ig

Vdc

i1

Vg

Grid

Zg

► Multiple resonance peaks of power cable

► Not all resonances will cause instability

► Instability region needs to be identified

1) Current control is internally stable

2) External instability is dependent on

the impedance ratio Y2clZg

-50

0

50

100

150

Ma

gn

itu

de

(d

B)

101

102

103

-540

-360

-180

0

Ph

as

e (

de

g)

Frequency (Hz)

T2(s)

sf1

6

8

Impedance-Based Stability Analysis

Example - Current Control of Grid Converter with Long Cable

► Identification of resonance frequency with Bode diagrams

X. Wang, F. Blaabjerg, and M. Liserre, “An active damper for suppressing multiple resonances with unknown frequencies,”

IEEE APEC 2014, 2184-2191.

-150

-100

-50

0

Ma

gn

itu

de

(d

B)

101

102

103

-90

-45

0

45

90

135P

ha

se

(d

eg

)

Frequency (Hz)

Y2cl(s) Yg(s)

Two resonance peaks

Capacitive Y2cl + Inductive Yg

2 2cl g cl gY Z Y Y

2 2cl g cl gY Y Y Y

2 2cl g cl gY Y Y Y

9

Impedance-Based Stability Analysis

Example - Current Control of Grid Converter with Long Cable

► Validation in time-domain simulations

X. Wang, F. Blaabjerg, and M. Liserre, “An active damper for suppressing multiple resonances with unknown frequencies,”

IEEE APEC 2014, 2184-2191.

10

Introduction

Impedance modeling and analysis

Virtual impedance control

Conclusions

Outline

11

Virtual Impedance Control

Basic Idea - Circuit Representation of Multi-Loop Control

Gvo(s):outer virtual impedance controller; Gvi(s): inner virtual impedance controller; Gc(s): current controller

► Modify the reference of modulator (duty cycle) with Gvi(s)

► Adjust the reference of controller reference with Gvo(s)

X. Wang, Y. W. Li, F. Blaabjerg, P. C. Loh, “Virtual-impedance-based control for voltage- and current-source converters,”

IEEE Trans. Power Electron. vol. 30, no. 12, pp. 7019-7037, Dec. 2015.

12

Virtual Impedance Control

Case I - Inner Virtual Impedance for Current Control Stability

sLf Zvi,2L sLg

VpccsCf

1VM

sLf sLg

VM VpccsCf

1Zvi,2Ci

or Zvi,2Cv

sLf sLg

VM VpccsCf

1Zvi,2g

Converter current feedback Capacitor current/voltage feedback Grid current feedback

,2 ,2( ) ( ) ( )vi L vi dZ s G s G s,2

,2

( )( ) ( )

f

vi ci

vi d f

LZ s

G s G s C

,2

,2

( )( ) ( )

f

vi cv

vi d f

L sZ s

G s G s C

2

,2

,2

( )( ) ( )

f g

vi g

vi d

L L sZ s

G s G s

Grid current control loop

13

Virtual Impedance Control

Case I - Inner Virtual Impedance for Current Control Stability

System description

Control diagram Equivalent circuit

► Example - Virtual damper

14

Virtual Impedance Control

Case I - Inner Virtual Impedance for Current Control Stability

► Example - Virtual damper

Lg = 0 mH

[4 ms/div]

i2: [5A/div]

Vpcc: [250 V/div]

[4 ms/div]

i2: [5A/div]

Vpcc: [250 V/div]

[4 ms/div]i2: [5A/div]

Vpcc: [250 V/div]

w/o damper

Lg = 4.5 mH Lg = 9 mH

w/ virtual damper

[4 ms/div]

i2: [5A/div]

Vpcc: [250 V/div]

[4 ms/div]

i2: [5A/div]

Vpcc: [250 V/div]

[4 ms/div]

i2: [5A/div]

Vpcc: [250 V/div]

15

Virtual Impedance Control

Case II - Outer Virtual Impedance for Grid Synchronization Stability

K. M. Alawasa, Y. A.-R. I. Mohamed, and W. Xu, “Active mitigation of subsynchronous interactions between PWM voltage-

source converters and power networks,” IEEE Trans. Power Electron., vol. 29, no. 1, pp. 121–134, Jan., 2014.

16

Virtual Impedance Control

Passivity-Based Impedance Shaping

► A linear, continuous system G(s) is passive if

• G(s) is stable, no right half-plane poles

• Re{G(jω)} ≥ 0, -90˚ ≤ arg{G(jω)} ≤ 90˚

L. Harnefors, L. Zhang, and M. Bongiorno, “Frequency-domain passivity-based current controller design,” IET Power

Electron. vol. 1, no. 4, pp. 455-465, 2008.

Re

Im G(jω)

► For a cascaded dynamic system, the closed-loop response is passive if

• All subsystems G(s), H(s) are passive

rG(s)

H(s)

y

-180˚ ≤ arg{G(jω)H(jω))} ≤ 180˚

17

Virtual Impedance Control

Example - Passivity-Based Impedance Shaping

► Multi-paralleled grid converters in renewable power plants

X. Wang, F. Blaabjerg, et al., “Proportional derivative based stabilizing control of paralleled grid converters with cables

in renewable power plants,” IEEE ECCE 2014, pp. 4917-4924.

Lg

Grid

Vg

Four Π-sections cable model (1km/Π-section)

LcCc

2

Cc

2

LcCc

2

Cc

2

LcCc

2

Cc

2

L1

L2

Cf

L1

L2

Cf

L1

L2

Cf

L1

L2

Cf

LcCc

2

Cc

2

Π-section

Vd

c

Vd

c

Vd

c

Vd

c

18

Virtual Impedance Control

Example - Passivity-Based Impedance Shaping

► Experimental verification

• Six paralleled three-phase voltage-source converters (50 kVA in total) with LCL-filters

• Flexible and intelligent control platform with three DS1007 dSPACE systems

• Reconfigurable for different operating scenarios of distribution power systems

19

Virtual Impedance Control

Example - Passivity-Based Impedance Shaping

► Experimental verification

#1 current

PCC voltage

#2 current

#3 current

20

Introduction

Impedance modeling and analysis

Virtual impedance control

Conclusions

Outline

21

Conclusions

Impedance modeling and analysis - intuitive and efficient tool

Virtual impedance control - circuit representation of multiple-loop

control

Passivity-based impedance shaping provides a robust control design

against grid impedance variation