Virtual Impedance Control for Grid-Connected Power...
Transcript of Virtual Impedance Control for Grid-Connected Power...
Virtual Impedance Control
for Grid-Connected Power
Converters
Xiongfei Wang, Frede Blaabjerg
Aalborg University, Denmark
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2
Introduction
Impedance modeling and analysis
Virtual impedance control
Conclusions
Outline
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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
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► 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
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Introduction
Impedance modeling and analysis
Virtual impedance control
Conclusions
Outline
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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
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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
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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
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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.
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Introduction
Impedance modeling and analysis
Virtual impedance control
Conclusions
Outline
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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.
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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
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Virtual Impedance Control
Case I - Inner Virtual Impedance for Current Control Stability
System description
Control diagram Equivalent circuit
► Example - Virtual damper
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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]
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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.
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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˚
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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
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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
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Virtual Impedance Control
Example - Passivity-Based Impedance Shaping
► Experimental verification
#1 current
PCC voltage
#2 current
#3 current
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Introduction
Impedance modeling and analysis
Virtual impedance control
Conclusions
Outline
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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