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Frede Blaabjerg and Xiongfei Wang Department of Energy Technology Aalborg University, Denmark [email protected], [email protected] Harmonic Stability in Renewable Energy Systems: An Overview

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Page 1: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

Frede Blaabjerg and Xiongfe i WangDepar tment o f Energy Technology

Aalborg Univers i ty , Denmarkfb l@et .aau.dk, [email protected]

Harmonic Stability in Renewable Energy Systems: An Overview

Page 2: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 2 | 1 7 . 0 9 . 2 0 1 4

Outline

Introduction• State-of-the-art

• Harmonic stability concept

Modeling and Analysis of Harmonic Stability• Modeling of power system components

• Harmonic stability analysis

Mitigation of Harmonic Instability• Passive damping of filters

• Active damper

Conclusions

Page 3: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 3 | 1 7 . 0 9 . 2 0 1 4

State-of-the-Art

Power Electronics Enabling Sustainable and Flexible Power Grids

Page 4: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 4 | 1 7 . 0 9 . 2 0 1 4

State-of-the-Art

Larg

e W

ind

Gen

erat

orLa

rge

Win

d G

ener

ator

Turbine P & ω ControlTurbine P & ω Control

Grid Q &V ControlDC-Link Control

Grid Q &V ControlDC-Link Control

Grid SynchronizationGrid Synchronization

Current Control Current Control

Semiconductor Switching Semiconductor Switching

Trad

ition

al G

ener

ator

Trad

ition

al G

ener

ator

Prime MoverPrime Mover

Excitation ControlExcitation Control

0.1Hz

1Hz

100Hz

0.1Hz

10Hz

500Hz

2500Hz

Traditional Generator Output Voltage

Wind Generator Output Voltage

Harmonic Spectrum

Wideband harmonics will be aggravated

Page 5: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 5 | 1 7 . 0 9 . 2 0 1 4

State-of-the-Art

GRID

Power Converter

Power Cable Power TransformerWind Power Plant

LCL Filter

Wideband controller interactions of converters – harmonic stability

Page 6: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 6 | 1 7 . 0 9 . 2 0 1 4

Harmonic Stability ConceptHarmonic Instability v.s. Harmonic Resonance

Ideal

Real

General

Re{Yo}>0, stable but may be still resonate Re{Yo}=0, critically stable (resonance) Re{Yo}<0, unstable with amplified resonance

Re{Zg} + Re{Yo} ?

Page 7: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 7 | 1 7 . 0 9 . 2 0 1 4

Modeling and Analysis of Harmonic Stability• Modeling of power system components

• Harmonic stability analysis

Page 8: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 8 | 1 7 . 0 9 . 2 0 1 4

Modeling of Power System ComponentsTraditionally Sine Wave → Currently Square Wave

Power Electronics

Power Lines & Cables

Passive Filters

Transformers

Sinusoidal

Square

Page 9: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 9 | 1 7 . 0 9 . 2 0 1 4

Switch-Mode ConvertersSwitch-Mode Converters

Modeling methodsModeling methods

Small-signal modelingSmall-signal modeling

State-space averaging (High pulse ratio, LTI)State-space averaging (High pulse ratio, LTI)

Harmonic state-space (Low pulse ratio, LTP)

Harmonic linearization

Large-signal modeling Feedback linearization

Control BandwidthControl Bandwidth

Current & voltage control Current & voltage control Harmonic instabilityHarmonic instability

Power control & PLLPower control & PLL Sub-harmonic instabilitySub-harmonic instability

Nonlinear phenomenaNonlinear phenomena

Dead-timeDead-timeLow-order harmonicsLow-order harmonics

Damping of resonance

Impedance of power switch Parasitic capacitors

Modeling of Power System ComponentsPower Electronics Based Sources and Loads

Power Electronics

Page 10: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 1 0 | 1 7 . 0 9 . 2 0 1 4

Modeling of Power System ComponentsSmall-Signal Modeling of Power Electronics Converters

Page 11: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 1 1 | 1 7 . 0 9 . 2 0 1 4

Harmonic State Space Modeling of Converters

Modeling of Power System Components

Page 12: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 1 2 | 1 7 . 0 9 . 2 0 1 4

Modeling of Power System Components

∈ ∈, 0, fixed periodic signal , 0, dynamically time

varying signals

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-100

0

100

200Time domain signal with transient

time(sec)

Mag

(vol

t)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-50

0

501st order signal

time(sec)

Mag

(vol

t)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-2

0

2x 10

-15 3rd order signal

time(sec)

Mag

(vol

t)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-5

0

55th order signal

time(sec)

Mag

(vol

t)

Harmonic Domain Harmonic State-Space

Page 13: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 1 3 | 1 7 . 0 9 . 2 0 1 4

Modeling of Power System ComponentsPower Lines and Cables

L u m p e d p a r a m e t e r – Π m o d e l (Γ m o d e l , T m o d e l )

D i s t r i b u t e d p a r a m e t e r ( t r a v e l i n g w a v e m o d e l s )

o B e r g e r o n m o d e l – s i n g l e f r e q u e n c y m o d e l

- o n l y m e a n i n g f u l a t t h e s p e c i f i e d s t e a d y - s t a t e f r e q u e n c y

o F r e q u e n c y d e p e n d e n t ( m o d e ) – d i s t r i b u t e d r e s i s t a n c e

- o n l y a c c u r a t e f o r m o d e l i n g b a l a n c e d s y s t e m s

o F r e q u e n c y d e p e n d e n t ( p h a s e ) – m o s t a c c u r a t e m o d e l

sinh( )

tanh( 2)2

c

c

Z Z

Y Y

Long line correction

Page 14: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 1 4 | 1 7 . 0 9 . 2 0 1 4

Harmonic Stability AnalysisAC Power-Electronics-Based Power System

Cable

1

Cable 2

Cable 3

Lf,1

Cf,1

Lf,3

Cf,3

Lg,3

Lf,2

Cf,2

Lg,2

RL load 2

L2 R2

RL load 1

L1 R1Bus 1 (V1)

Bus 2 (V2)Bus 3 (V3)

Voltage-controlled inverter – system voltage and frequency regulation Current-controlled inverter – unity power factor operation Harmonic instability – current/voltage controller interactions of inverters

Page 15: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 1 5 | 1 7 . 0 9 . 2 0 1 4

Impedance-Based Analysis and Control

Inverter output currents

Bus voltages

Voltage-controlled inverter 1 Current-controlled inverter 2 Current-controlled inverter 3

Bus 1 Bus 2 Bus 3

Experimental results – unstable case

Harmonic Stability of Small-Scale System

Page 16: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 1 6 | 1 7 . 0 9 . 2 0 1 4

** *

Component Connection Method (CCM) – state-space matrix and eigenvalues Generalized to multi-bus power system

Impedance-based analytical approach – frequency-domain analysis Balanced three-phase system – SISO transfer functions Generalized Nyquist stability criterion is required for MIMO systems

Harmonic Stability Analysis Tools

Harmonic Stability Analysis

Page 17: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 1 7 | 1 7 . 0 9 . 2 0 1 4

Harmonic Stability Analysis

*

*

1 1 11

1

1( ) ( ) ( ) ( )1

( )

*clv,

ov,

lv,

V s = G s V s Z s+

Z s

Minor-loop gain Tmv (s)

1( ) ( ) ( ) ( )1

( )

*gm cli,m gm

oi,m

li,m

i s = G s i s Y s+

Y s

Minor-loop gain Tmc (s)

Impedance-Based Analysis and Control

Identify the effect of each inverter by impedance-based modeling

Minor-loop gain composed by the impedance ratio

Page 18: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 1 8 | 1 7 . 0 9 . 2 0 1 4

Harmonic Stability AnalysisImpedance-Based Analysis and Control

Unstable closed-loop response caused by voltage-controlled inverter

Stable closed-loop response with the reduced bandwidth of voltage-controlled inverter

Page 19: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 1 9 | 1 7 . 0 9 . 2 0 1 4

Harmonic Stability AnalysisImpedance-Based Analysis and Control

Inverter output currents

Bus voltages

Voltage-controlled inverter 1 Current-controlled inverter 2 Current-controlled inverter 3

Bus 1 Bus 2 Bus 3

Experimental results – stable case

Page 20: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 2 0 | 1 7 . 0 9 . 2 0 1 4

Mitigation of Harmonic Instability• Passive damping of filters

• Active damper

Page 21: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 2 1 | 1 7 . 0 9 . 2 0 1 4

Mitigation of Harmonic InstabilityPassive Damping for Output Filters of Converters

10 kW10 kHz switching/control freq.2.1kHz resonance freq. LCL4.5 kHz res. for LCL+trap

Page 22: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 2 2 | 1 7 . 0 9 . 2 0 1 4

Mitigation of Harmonic Instability

Experimental results

Series R Parallel R-C LC trap + parallel R-C

Single Converter

Parallel Converters

Passive Damping for Output Filters of Converters

Page 23: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 2 3 | 1 7 . 0 9 . 2 0 1 4

Damping of harmonic instability, no low-order harmonic filtering Low-power, high-frequency, high-bandwidth, plug-and-play Same hardware topology with APF High-frequency output current needs new design of output filters

Active Damper

Mitigation of Harmonic Instability

Page 24: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 2 4 | 1 7 . 0 9 . 2 0 1 4

Harmonic Instability MitigationExperimental Results

PCC voltage VSC currents

VSC currentsPCC voltage

Without active damper

With active damper

Stabilizing interactions of harmonic resonant current controllers

Page 25: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 2 5 | 1 7 . 0 9 . 2 0 1 4

Conclusions

Renewab le energy sys tems – power e lec t ron ics based power sys tems Pulse w id th modu la t ion o f power conver te rs – h igh-order harmon ics Cont ro l le rs in te rac t ions o f power conver te rs – harmon ic ins tab i l i t y Impedance-based method – con t ro l le r -des ign-or ien ted ana lys is too l Act ive damper – a p romis ing power sys tem s tab i l i ze r

Fu tu re t rends Advanced mode l ing o f w ind power conver te rs – L inear Time-Per iod ic

(LTP) mode ls Sys tem- leve l harmon ic s tab i l i t y ana lys is – complex renewab le power

p lan ts s t ruc tu re Resonance de tec t ion i s the key fo r ac t i ve damper

Page 26: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

H A R M O N I C S T A B I L I T Y I N R E N E W A B L E E N E R G Y S Y S T E M – F R E D E B L A A B J E R G 2 6 | 1 7 . 0 9 . 2 0 1 4

References

[1] X. Wang, F. Blaabjerg, and W. Wu, “Modeling and analysis of harmonic stability in an AC power-electronics-based power system,” IEEE Trans. Power Electron., vol. 29, no. 12, pp. 6421-6432, Dec. 2014.

[2] X. Wang, F. Blaabjerg, M. Liserre, Z. Chen, J. Li, and Y. W. Li “An active damper for stabilizing power electronics based AC systems,” IEEE Trans. Power Electron., vol. 29, no. 7, pp. 3318-3329, Jul. 2014.

[3] X. Wang, F. Blaabjerg, and M. Liserre, “An active damper to suppress multiple resonances with unknown frequencies,” in Proc. APEC 2014, pp. 2184-2191, 2014.

[4] X. Wang, F. Blaabjerg, and P. C. Loh, “Design-oriented analysis of resonance damping and harmonic compensation for LCL-filtered voltage source converters,” in Proc. IPEC 2014, 216-223, 2014.

[5] X. Wang, F. Blaabjerg, and P. C. Loh, “An impedance-based stability analysis method for paralleled voltage source converters,” in Proc. IPEC 2014, 1529-1535, 2014.

[6] X. Wang, F. Blaabjerg, and P. C. Loh, “Analysis and design of grid-current-feedback active damping for LCL resonance in grid-connected voltage source converters,” in Proc. ECCE 2014, 373-380, 2014.

[7] X. Wang, F. Blaabjerg, and P. C. Loh, “Proportional derivative based stabilizing control of paralleled grid converters with cables in renewable power plants,” in Proc. ECCE 2014, 4917-4924, 2014.

[8] X. Wang, F. Blaabjerg, Z. Chen, and W. Wu, “Resonance analysis in parallel voltage-controlled distributed generation inverters,” in Proc. APEC 2013, 2977-2983, 2013.

[9] X. Wang, F. Blaabjerg, Z. Chen, and W. Wu, “Modeling and analysis of harmonic resonance in a power electronics based AC power system,” in Proc. ECCE 2013, 5229-5236, 2013.

[10] R. Beres, X. Wang, F. Blaabjerg, C. L. Bak, and M. Liserre, “A review of passive filters for grid-connected voltage source converters,” in Proc. IEEE APEC 2014, pp. 2208-2215, 2014

[11] R. Beres, X. Wang, F. Blaabjerg, C. L. Bak, and M. Liserre, “Comparative evaluation of passive damping topologies for parallel grid-connected converters with LCL filters,” in Proc. IPEC 2014, pp.3320-3327, 2014.

[12] R. Beres, X. Wang, F. Blaabjerg, C. L. Bak, and M. Liserre, “Comparative analysis of the selective resonant LCL and LCL plus trap filters,” in Proc. OPTIM 2014, pp.740-747, 2014.

[13] R. Beres, X. Wang, F. Blaabjerg, C. L. Bak, and M. Liserre, “New optimal design method for trap damping sections in grid-connected LCL filters,” in Proc. ECCE 2014, pp. 3620-3627, 2014.

[14] J. Kwong, X. Wang, and F. Blaabjerg, “Impedance-based analysis and design of harmonic resonant controller for a wide range of grid impedance,” in Proc. PEDG 2014, pp.1-8, 2014.

[15] J. Kwong, X. Wang, C. L. Bak, and F. Blaabjerg, “Modeling and grid impedance variation analysis of parallel connected grid-connected inverter based on impedance-based harmonic analysis ,” in Proc. IECON 2014, in press, 2014.

Page 27: Harmonic Stability in Renewable Energy Systemsieee-ecce.org/2014/images/documents/SS3A - Harmonic RStability.pdf · Harmonic Stability in Renewable Energy Systems: ... Harmonic Stability

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