Transient Stability Analysis
of VSC-HVDC Systems
Xiongfei Wang and Heng WuDepartment o f Energy Technology
Aalborg Univers i ty , Denmark
Workshop
DC Gr ids, Technologies
and Appl icat ions
Aachen, 18 Apr i l 2018
Transient Stability Synchronization stability under large disturbance
Power system stability
Rotor angle stability
Voltage stability
Small- signal angle stability
Transient stability
Small-signal voltage stability
Large-signal voltage stability
Frequency stability
Transient stability: Maintain synchronism with the power grid under large disturbance
Transient Stability Synchronous Generator (SG)
Synchronous generator
1E
0gV
Infinite
bus
PCCV Xg1
Xg2
Xf XT
S3 S4
S1 S2
Single-machine infinite-bus power system
Pe
δ
Pm
δ0 δ1 δu
a
b
ce
Aa
Pre-
disturbance
Post-
disturbance
m eP P D H
Swing equation
Power equation
3sin
PCC g
e
g
V VP
X
Transient Stability Critical fault clearing angle/time
Single-machine infinite-bus power system
Synchronous generator
1E
0gV
Infinite
bus
PCCV Xg1
Xg2
Xf XT
Xgnd
S3 S4
S1 S2
Pe
δ
Pm
δ0 δ1 δu
a
b
c e
Pre-fault
During fault
Post-fault
Fault clearing angle: δ1
Critical clearing angle (CCA)
Critical clearing time (CCT)
Transient Stability Voltage-Source Converter (VSC)
Voltage-Source Converter (VSC)
1E
0gV
Infinite
bus
PCCV Xg1
Xg2
Xf XT
Xgnd
S3 S4
S1 S2
Single-VSC infinite-bus power system
Difference between VSC and SG
- No natural “rotor speed” response in VSC - lack of physical link with synchronization
- Synchronization is realized by power control and/or Phase-Locked Loop (PLL)
- Limited overcurrent capability - trigger current-mode control
Control of VSC
ig
VSC
VDC
Xf Pe,Qe Xg
ig_abcvPCCabc
Idref
Iqref
PWM
Modulator
abcdq
θPLL
abcdq
PLLθPLL
+–
+–
id iq
PI
PI
PCCV 0gV
ig
VSC
VDC
Xf
Voltage
Loop
Prefvmod_abc
PWM
Modulator
Pe,Qe
Peωgt
θref δ
VPCC
Xg
vPCC_abc
vPCCref_abc Ki
PCCV 0gV
Voltage
Reference
Grid-Forming Control
Grid-Feeding Control
Transient Stability PSC-VSC within overcurrent limit
PSC-VSC when ig < Ilimit
ig
VSC
VDC
Xf
Voltage
Loop
Prefvmod_abc
PWM
Modulator
Pe,Qe
Peωgt
θref δ
VPCC
Xg
vPCC_abc
vPCCref_abc Ki
PCCV 0gV
Voltage
Reference
Dynamic representation of PSC-VSC as a Voltage Source
- Decoupled timescale: transient stability: 2s ~ 3s, voltage control: 1ms ~ 10ms[1][3]
- Voltage control loop can be simplified as a unity gain
- Only the influence of active power control
Transient Stability First-order nonlinear system
PCC
0gV PCCV
Xg
Pe,Qe
Dynamic equivalent of PSC-VSC when ig < Ilimit
δ Ki∫
Pref
Pe
i ref eK P P
3sin
2
PCC g
e
g
V VP
X
3sin
2
PCC g
i ref
g
V VK P
X
Transient Stability Phase-portrait analysis
SinkSource
Phase portrait of first-order nonlinear systems
First-order nonlinear system with equilibrium points ( )
- For any initial conditions, the system is always stabilized at the closest sink point
- Zero overshoot in the dynamic response
0
Transient Stability Disconnection of Xg2 (ig < Ilimit)
Abrupt disconnection of transmission line Xg2 (ig < Ilimit)
10
0
10
δ
3/4π 1/4π 0 1/2π
a
b
c e
π
δ0 δ1 δu
Pre-disturbance
Post-disturbance
Phase portrait analysis
With equilibrium points after disturbance
- PSC-VSC has no transient stability problem
- Overdamped response (zero overshoot)
- Better performance than SG
0gV
Infinite
bus
PCCV Xg1
Xg2
Xf XT
S3 S4
S1 S2
VSC
VDC
Transient Stability Disconnection of Xg2 (ig < Ilimit)
2 3 4 5 6 7t/s
0
1/2π
π
100
200
0
δ/
rad
Pe/
MW
-400
-2000
200400
i g/
A
Overdamped response
Simulation results
Po: [1 kW/div]
δ: [0.5π/div]
iga: [10A/div]
Overdamped response
[1 s/div]
Experimental results
Simulation and experimental results
Transient Stability High-impedance fault - CCA/CCT
Grid fault with high short-circuit impedance Xgnd (ig < Ilimit)
0gV
Infinite
bus
PCCV Xg1
Xg2
Xf XT
Xgnd
S3 S4
S1 S2
DC/AC Converter
VDC
Phase portrait analysis
00 3sin
2
CCT CCA
mref g
i ref
g
dCCT dt
V VK P
X
3/4π 1/4π 0 1/2π π 5
0
5
10
15
δ
δu
a
b
c e
fault clear
Pre-fault During fault Post-fault
uCCA
No equilibrium points during fault
Constant CCA and CCT
Transient Stability High impedance fault - self-restoration
0−5
0
5
10
15
20
25
30
δ
1/2π π 3/2π 2π 5/2π
a
b
c e c1
fault clear
Lose synchronism,
around one cycle
of swing
re-synchronization
δu
pre-fault
duringfault post-fault
Phase portrait analysis when the fault is cleared beyond the CCA
Self-restoration with PSC-VSC
- The system will be re-synchronized (point c1) if the fault is cleared beyond the CCA (point e)
- Reduce the risk of the system being collapsed due to the delayed fault clearance
Transient Stability High impedance fault - simulations
Fault is not cleared - no equilibrium points
Fault clearing time < CCT
Fault clearing time > CCT
3 4 5 6 7t/s
2
−200−100
100200
0
01/2π
π 3/2π
2π
0
−500
500
δ/r
adP
e/M
Wi g
/A
fault
3 4 5 6 72
100
200
0
−500
0
5000
1/2π
π
fault fault cleared
δ/r
adP
e/kW
i g/A
3 4 5 6 72−500
0
500
−200−100
100200
0
01/2π
π 3/2π
2π
δ/r
adP
e/M
Wi g
/A
fault fault cleared
Around one cycle of
oscillation
Re-synchronization
fault fault cleared
Po: [1 kW/div]
δ: [π/div]
iga: [20A/div]
vpcca: [250V/div]
[1 s/div]
Transient Stability High impedance fault - experiments
Fault is not cleared - no equilibrium points
Fault clearing time < CCT
Fault clearing time > CCT
fault fault cleared
Po: [1 kW/div]
δ: [π/div]
iga: [20A/div]
vpcca: [250V/div]
[1 s/div]
One cycle of oscillation
Re-synchronized
Po: [1 kW/div]
δ: [π/div]
iga: [20A/div]
vpcca: [250V/div]
[1 s/div]
fault
Transient Stability PSC-VSC reaching overcurrent limit
Dynamic representation of PSC-VSC as a Current Source
- Decoupled timescale: transient stability: 2s ~ 3s, current control: 1ms ~ 10ms[1][3]
- Current control loop can be simplified as a unity gain
- Only the influence of PLL
PSC-VSC when ig = Ilimit
ig
VSC
VDC
Xf Pe,Qe Xg
ig_abcvPCCabc
Idref
Iqref
PWM
Modulator
abcdq
θPLL
abcdq
PLLθPLL
+–
+–
id iq
PI
PI
PCCV 0gV
Transient Stability Dynamic model of PLL effect
Dynamic equivalent of PSC-VSC when ig = Ilimit Block diagram of PLL
PLL gn p i PCCqK K V , zq d g PCCq gq zqV I X V V V
singq g PLLV V PLL PLL g
PCC
Id+jIq VPCCd+jVPCCq Vgd+jVgq
jXg
abcdq
vPCCabcvPCCd
vPCCqPI
1
s
Δω
ωgn
θPLL ωPLL
sinPLL p i zq g PLLK K V V
Transient Stability Second-order nonlinear system
Dynamic model of PLL for transient stability analysis
sinPLL p i zq g PLLK K V V
Kp+Ki/s VgsinδPLL
Vzq 1
s
Δω δ δPLL
sinzq g PLL eq PLL eq PLLV V D H
1 p gd g
eq
i
K I LH
K
Governing equation of PLL dynamics
cosp g PLL
eq
i
K VD
K
Swing equation of SG
3sin
PCC g
m
g
V VP D H
X
Transient Stability Voltage-angle curve of PLL
Voltage-angle curve of PLL
Vgsinδ
δ
Vzq
δ0 δ1 δu
a
b
ce
Pre-
disturbance
Post-
disturbanceSimilarly to SG
- Before point c, Vzq>Vgsinδ, ωPLL increases
- After point c, Vzq<Vgsinδ, ωPLL decreases
- Loss of synchronization if ωPLL> ωg at point e
sinzq g PLL eq PLL eq PLLV V D H
Governing equation of PLL
Transient Stability Design-oriented analysis
Damping ratio: Kp+Ki/s VgsinδPLL
Vzq 1
s
Δω δ δPLL 2
p g
i
K V
K
9.2s
g p
tV K
−10
0
10
20
30
40
3/4π π 1/4π 0 1/2π
δPLL (rad)
c d
δm
H
zP
LL
ζ =0.4 ts=0.1s
ζ =0.4 ts=0.5s
ζ =0.4 ts=1s
20
0
20
40
60
80
100
3/4π π 1/4π 0 1/2π δPLL (rad)
c d
δm
Hz
PL
L
ζ =0.1 ts=0.2s
ζ =0.5 ts=0.2sζ =1 ts=0.2s
Dynamic model of PLL for transient stability analysis
Settling time:
- Large damping ratio and settling time lead to better transient behavior.
- With Ki = 0, the PLL is a first-order nonlinear system - small Ki is preferred!
Transient Stability Simulations - low-impedance fault
High damping ratio PLL
- Switch to current control
- Remain synchronization
- Switch back to PSC when
the fault is cleared
Transient Stability Simulations - low-impedance fault
Low damping ratio PLL
- Switch to current control
- Loss of synchronization
- Switch back to PSC after
the fault is cleared, and the
system is resynchronized
Operating Scenarios PSC-VSC SG
With Equilibrium Points No transient stability problem May lose synchronization
No Equilibrium
Points during
the fault
High-impedance
fault
- Fixed CCA and CCT
- Re-synchronize with the grid even if
the fault is cleared beyond CCA
- CCA and CCT are dependent on
the fault condition
- May lead to system collapse if the
fault is cleared beyond CCA
Low-impedance
fault
- Switching to current-limit control, and
the stability is depended on the PLL
- Re-synchronize with the grid after the
fault is cleared
- Same as high impedance fault
Highlights
- The first-order nonlinear system with equilibrium points has no transient stability problem
- For higher-order systems, the controller can be tuned for first-order dynamic during transients
- Control flexibility can bring better stability in power electronic based power systems
Conclusions
[1] P. Kundur, Power System Stability and Control. New York, NY, USA: McGraw-Hill, 1994
[2] L. Zhang, L. Harnefors, and H. –P. Nee. “Power-synchronization control of grid-connected voltage-source converters”. IEEE Trans. Power
Syst.,. 25, no. 2, pp. 809−820, May. 2010.
[3] L. Harnefors, X. Wang, A. G. Yepes, and F. Blaabjerg, “Passivity-based stability assessment of grid-connected VSCs – an overview,” IEEE
J. Emerg. Sel. Topics Power Electron., vol. 4, no. 1, pp. 116-125, Mar. 2016.
[4] H. Wu and X. Wang, “Transient angle stability analysis of grid-connected converters with the first-order active power Loop,” IEEE
Applied Power Electronics Conference and Exposition (APEC), 2018.
[5] H. Wu and X. Wang, “Transient stability impact of the phase-locked loop on grid-connected voltage source converters,”
International Power Electronics Conference (IPEC-ECCE Asia), 2018, accepted.
[6] S. Ma, H. Geng, L. Liu, G. Yang, and B. C. Pal, “Grid-synchronization stability improvement of large scale wind farm during severe grid
fault,” IEEE Transactions on Power Systems, vol. 33, pp. 216–226, Jan 2018.
[7] H. Geng, L. Liu, and R. Li, “Synchronization and reactive current support of pmsg based wind farm during severe grid fault,” IEEE
Transactions on Sustainable Energy, vol. PP, no. 99, pp. 1–1, 2018.
Thank you! Questions?
Transient Stability Analysis of VSC-HVDC Systems
Xiongfei Wang, Aalborg University
Voltage-Source Converters (VSCs) are critical components in modern dc systems. The VSC-grid interactions pose new challenges on the system stability and power quality. Many research efforts have been made to address the small-signal stability of grid-connected VSC systems. Yet, less attention was given to the transient dynamics of VSCs with large grid disturbances. Very few works were reported on the transient stability of grid-connected VSCs, i.e. the ability to maintain synchronism with the power grid under severe transient disturbance. This presentation will give a comprehensive discussion on the transient stability of VSC-HVDC systems. The influences of synchronization control schemes based on active power control and phase-locked loop are analyzed by using the phase portrait. A number of superior features of the VSC over synchronous generators are revealed, and verified by simulations and down-scale experiments.”