Transient Stability Analysis

of VSC-HVDC Systems

Xiongfei Wang and Heng WuDepartment o f Energy Technology

Aalborg Univers i ty , Denmark

xwa@et.aau.dk

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.”