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