harmonic stability in renewable energy systemsieee-ecce.org/2014/images/documents/ss3a - harmonic...

Frede Blaabjerg and Xiongfe i WangDepar tment o f Energy Technology

Aalborg Univers i ty , Denmarkfb l@et .aau.dk, xwa@et.aau.dk

Harmonic Stability in Renewable Energy Systems: An Overview

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

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

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

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

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} ?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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