Analysis of VSC-HVDC System Stability with

Protective Reactors

Hui Li1, Jun Liang

2, Ming Xiong

1, and Li Zhang

1

1School of Automation, Beijing Information Science & Technology University, Beijing, China

2School of Engineering, Cardiff University, Cardiff, UK

Email: lhbxy@bistu.edu.cn, LiangJ1@cardiff.ac.uk, {xiong54ming, zzrzl}@163.com

Abstract—The use of Voltage Source Converter based High

Voltage Direct Current (VSC-HVDC) links is considered a

major step in facilitating long distance power transfer and

integrating renewable energy sources. The introduction of

protective reactors throughout such systems can have

significant impact on their stable operations. Therefore, a

stability study in VSC-HVDC systems is necessary. This

paper proposes a method to analytically describe a two-

terminal VSC-HVDC link with respect to its eigenvalues.

The results from dynamic simulations using PSCAD show

that large protective reactors can result in system stability

problem, and the suggestion is provided to develop a novel

variable dc reactor in the summary.

Index Terms—VSC-HVDC, dc-network stability, protective

reactor

I. INTRODUCTION

Over last decade, the power engineering society is

showing an increasing interest in Voltage Source

Converter based High Voltage Direct Current (VSC-

HVDC) technology because of its specific controllability

feature [1]. Development of Modular Multilevel

Converter (MMC) has made VSC-HVDC more

competitive in large power transmission due to its

advantages of modular design, low switching frequency,

high efficiency, and excellent output voltage waveforms

[2]. Meantime, the VSC technology makes the extension

to multi-terminal HVDC connections (MTDC) relatively

easy. MTDC grids could form the backbone of a pan-

European interconnected system in future [3] because it

can offer more additional controllability compared to the

two-terminal VSC-HVDC system [4].

However, the development of VSC-HVDC networks is

constrained by the lack of operational experience, the

immaturity of appropriate protective devices, and the lack

of appropriate fault analysis techniques [5]. DC fault

protection and dc circuit breakers (DCCBs) are the major

challenge for developing a dc grid. An ac-side switchgear

is not considered fast enough to cope with the rapid rise

of fault current characteristic of freewheel diode

condition which can damage power-electronic devices in

several milliseconds.

Manuscript received June 1, 2015; revised January 25, 2016.

In fact, dc reactor is preferable to limit dc fault current

[6]. The minimum size of the dc reactor depends on the

breaking time of the DCCB, and its maximum current

breaking rating, which is directly linked with the cost of

the breaker. On the other hand, the dc reactor size is also

limited by its cost, and possibly, the extra conduction loss

and stability requirement of the dc grid. Reference [7]

proposes a 6.5mH protective inductor design for the

onshore and offshore converters, but only analyzes the

transient characteristic of the transmission system under

the cable-to-ground fault. Values in the order of 100mH

per pole for ±320kV systems are typically used in

previous published work [8]. Reference [9] proposes the

design of a 400mH 400A toroid-type high temperature

superconductor dc reactor magnet which has some

advantages such as high current density, low electrical

loss, and so on. However, large dc reactors require large

footprint which is particularly difficult for offshore

application. Presence of large inductance extends the

electrical distance between converter stations, which has

a detrimental effect on the dc voltage control, and the

stability of HVDC grids.

The aim of this paper is to propose a method to

analysis dc-network stability in a two-terminal VSC-

HVDC system because of large protective reactors. The

presented method acts on the state space description of

the system and derives the eigenvalues of the system in

fully symbolic expressions. Mathematical analysis and

dynamic simulations testify that large inductance of

protective reactor results in significant impact on the

VSC-HVDC system steady operation.

II. STABILITY ANALYSIS IN A VSC-HVDC SYSTEM

WITH PROTECTIVE REACTOR

A. Mathematical Description of a VSC-HVDC System

The system under consideration is a two-terminal

symmetrical monopole VSC-HVDC link, as in Fig. 1(a).

The connection is comprised of two VSC stations, as well

as ac and dc side components. Each station is assumed to

be connected to a strong ac grid, which can therefore be

modeled as a voltage source. The connection of a VSC

converter to its respective ac grid is normally performed

via a coupling inductor and step-up transformer.

Assuming that these components are lossless, they can be

represented by a single inductor combining their

International Journal of Electronics and Electrical Engineering Vol. 4, No. 5, October 2016

©2016 Int. J. Electron. Electr. Eng. 408doi: 10.18178/ijeee.4.5.408-411

inductances. In Fig. 1(a), if power is transmitted from

Station 1 to Station 2, Station 1 is a dc-voltage controlled

station and Station 2 is active-power controlled.

The dc terminals of each station are connected to dc

capacitors whose middle point is ground. For simplifying

the analysis, each dc cable is modeled as a series

connection of a resistance and an inductance, with values

that are proportional to the length of the cable. Given the

physical characteristic of the symmetrical monopole

configuration and considering balanced conditions, the

model in Fig. 1(a) can be equated to the asymmetrical

monopole model in Fig. 1(b).

~ ~

Station 1 Station 2

Vdc control Active power

control

Power flow direction

L Rdc Ldc L

L LRdc Ldc

2Cdc

2Cdc

2Cdc

2Cdc

(a) Symmetrical model

~ ~

Station 1 Station 2

2L 2Rdc 2Ldc 2L

Cdc Cdcvdc1 vdc2

idc Pout

(b) Equivalent asymmetrical model

Figure 1. Two-Terminal monopole VSC-HVDC system

the active-power controlled VSC acts as an ideal power

source delivered power Pout to the ac side. We only

consider the dynamic of the active-power controller in

Station 2 when delivered power Pout is changed. The dc-

cable dynamics are provided as in (1):

d(2 4 ) 2

ddc dc dc1 dc2 dc dc

L L i v v R it

d 1(- 2 )

d (2 4 )dc dc2 dc dc

dc

i v R it L L

(1)

While the dynamics of the dc capacitor located at the

terminals of the power controlled station will be written

in (2):

d

d

out

dc dc2 dc

dc2

PC v i

t v

2

2,0 2,0

d 1 1( )

d

out,0

dc2 dc dc2 out

dc dc dc

Pv i u P

t C v v (2)

Considering the state 1 dc

x i , 2 dc2

x u , as well as

inputs 1 out

u P , the state matrix A of the resulting state-

space model is described by expressed in (3):

2

2,0 t,0

2 1

2 4 2 4

1 1

/

dc

dc dc

dc dc dc ou

R

L L L LA

C C v P

(3)

B. Analysis of a Simplified System

The rated parameters of the VSC-HVDC link are

presented in Table I. Substituting the nominal values of

Table I, in matrix A Rdc=3.84Ω, Ldc=0.048H, Cdc=50μF,

Vdc2,0=320kV, Pout,0=240MW. When the value of reactor

L is changed, the eigenvalues of the state-space model are

followed, as shown in Fig. 2.

TABLE I. RATED PARAMETERS OF THE VSC-HVDC LINK IN FIG. 1

Pout,0 Rated active power 240WM

Vdc2,0 Rated dc voltage 320kV

Cdc Shunt capacitor 50μF

r Dc cable resistance per km 0.0192Ω/km

l Dc cable inductance per km 0.24mH/km

length Cable line length 200km

-25 -20 -15 -10 -5 0 5100

150

200

250

300

350

400

10mH

20mH

40mH

60mH

80mH

100mH

120mH

150mH

200mH

Figure 2. Comparison of eigenvalues in the instance of different L

As shown in Fig. 2, when the value of L is less than

150mH, the system is still steady. But when the value of

L is more than 150mH, the system is not steady. Along

with the value of L from small to large, the real part of

eigenvalue is changed from negative to positive. This

means the system losses steady if reactance is increased

to some large value.

International Journal of Electronics and Electrical Engineering Vol. 4, No. 5, October 2016

©2016 Int. J. Electron. Electr. Eng. 409

Assuming the dc voltage in Station 1 is constant, and

If the reactance is constant, we change Pout,0 and check

the system dynamics performance. Fig. 3(a) is the

eigenvalue result when L=60mH, and Fig. 3(b) is the

eigenvalue result when L=100mH.

-10 -8 -6 -4 -2 0 2242.8

242.9

243

243.1

243.2

243.3

243.4

243.5

243.6

243.7

100MW

200MW

240MW

300MW

350MW

400MW

450MW

500MW

(a) L=60mH

-6 -4 -2 0 2 4 6199.8

199.9

200

200.1

200.2

200.3

200.4

200.5

200.6

200.7

100MW

200MW

240MW

300MW

350MW

400MW

450MW

500MW

(b) L=100mH

Figure 3. Comparison of eigenvalues at different delivered active powers

As shown in Fig. 3(a), when the delivered active power

is more than 450MW, the system losses steady and the

eigenvalue is positive. But in Fig. 3(b), when the

delivered active power is more than 350MW, the system

losses steady. This shows that the reactor decides the

dynamic performance of VSC-HVDC systems when

delivered active power is changed. Once the delivered

active power is large, small reactance is needed to keep

the system stability.

III. DYNAMIC SIMULATION IN A VSC-HVDC SYSTEM

WITH PROTECTIVE REACTORS

In this section, the tests of dynamic simulations using

PSCAD/EMTDC are done by changing delivered active

power increasing 20% to check the pole current transient

performance at different inductance values.

If the delivered active power at station 2 is added from

400MW to 480MW, we can get the pole current figures

when the reactors are changed, as shown in Fig. 4(a) and

Fig. 4(b). Fig. 4(a) expresses that the pole current arrives

at a new stable value after the delivered active power is

changed, and the larger reactance will result in the longer

steady time. For example, when the reactance is 100mH,

the time consumption to a new steady state is about 1s.

(a) The pole current curves in 2s

(b) The pole current curves in 30ms

Figure 4. The results after power changed from 400MW to 480MW

Fig. 4(b) is the pole current curve of Fig. 4(a) from

2.498s to 2.535s. As shown in Fig. 4(b), the larger

reactance will produce the smaller di/dt value. Large

reactance can limit the current rising, but the maximum

value of pole current would be large. For example, when

the reactance is 100mH, the maximum value of pole

current is 1.4 times of 0.65kA (original value).

If the delivered active power at station 2 is increased

from 200MW to 240MW, we can obtain the pole current

figures when the reactors are changed, as shown in Fig.

5(a) and Fig. 5(b). Comparing Fig. 4(a) and Fig. 5(a), the

smaller delivered active power needs the shorter time to

reach a new stable state at the same inductance when

power is changed. For example, when the reactance is

100mH, the time consumption of new stability is about

0.4s in Fig. 5(a).

(a) The pole current curves in 2s

(b) The pole current curves in 30ms

Figure 5. The results after power changed from 200MW to 240MW

As shown in Fig. 5(b), when the delivered active

power is changed from 200MW to 240MW, the

maximum value of pole current is only 1.35 times of

original value 0.355kA if the inductance is 100mH.

Comparing Fig. 4(b) and Fig. 5(b), this result shows that

the more transmission power needs the smaller reactance

International Journal of Electronics and Electrical Engineering Vol. 4, No. 5, October 2016

©2016 Int. J. Electron. Electr. Eng. 410

to keep the system normal operation. Although large

inductance can limit the di/dt value, it can make the

system dynamic process longer and the overcurrent

phenomenon can be produced too.

IV. SUMMARY

This paper provides an analytical method to describe a

simplified two-terminal VSC-HVDC connection in terms

of purely symbolic eigenvalue expressions. This method

is used to analyses the stability problem in VSC-HVDC

system with large protective reactors. The results show

that the dc system can loss steady when large dc reactors

are used, although large reactance can limit di/dt when

delivered power is increased.

Further work is to design a novel variable dc reactor

for DCCBs to limit fault current and reduce the impact to

dc system stability. Based on the electro-magnetic

characteristics, the dc reactor has very low inductance

during normal operation, which minimizes the adverse

impact on the dc system stability. During a dc fault, the

inductor increases automatically to oppose the current

rising.

ACKNOWLEDGMENT

This work is supported by the Importation and

Development of High-Caliber Talents Project of Beijing

Municipal Institutions (CIT&TCD201304113) and China

Scholarship Council (201408110027).

REFERENCES

[1] A. Fuchs, et al., “Stabilization of large power system using VSC-

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432-443, Feb. 2014.

[5] J. Yang, J. E. Fletcher, and J. O’Reilly, “Short-Circuit and ground

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[6] C. M. Franck, “HVDC circuit breakers: A review identifying future research needs,” IEEE Trans. Power Del., vol. 26, no. 2, pp.

998-1007, Apr. 2011.

[7] F. J. Deng and Z. Chen, “Design of protective inductors for HVDC transmission line within dc grid offshore wind farms,”

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Hui Li received the B.Sc. degree from China Agriculture University in 2000, and the Ph.D.

degree from College of Information and

Electric Engineering, China Agriculture University, Beijing, China, in 2005.

She is currently an Associate Professor in College of Automation, Beijing Information

Science & Technology University. From 2012

to 2013, she was a visiting scholar in Department of Electrical Engineering,

Tsinghua University. From 2014 to 2015, she is a visiting scholar in School of Engineering, Cardiff University, Cardiff, U.K. She is a peer

reviewer for IEEE Journals & Magazines. Her research interests include

stability and dc protection in HVDC transmission, renewable power generation and microgrid energy management system.

Jun Liang (M’02–SM’12) received the B.Sc.

degree from Huazhong University of Science and Technology, Wuhan, China, in 1992 and

the M.Sc. and Ph.D. degrees from China Electric Power Research Institute, Beijing,

China, in 1995 and 1998, respectively.

From 1998 to 2001, he was a Senior Engineer with China Electric Power Research Institute.

From 2001 to 2005, he was a Research Associate at Imperial College, London, U.K.

From 2005 to 2007, he was a Senior Lecturer at the University of

Glamorgan, Wales, U.K. Currently he is a Reader at the School of Engineering, Cardiff University, Wales, U.K. His research interests

include FACTS devices/HVDC, power system stability and control, power electronics, and renewable power generation.

Ming Xiong received the B.Sc. degree from

Beijing Institute of Machinery in 2000, and the M.Sc. degree from Beijing Institute of

Machinery in 2003, and the Ph.D. degree from

School of Automation Science and Electrical Engineering, Beihang University, Beijing,

China, in 2015. He is currently a Lecturer in College of

Automation, Beijing Information Science &

Technology University. His research interests include Artificial Neural Networks, Echo State Networks and

Embedded system.

Li Zhang received the B.Sc. degree from North China Electric Power University in 2000,

and the Ph.D. degree from School of Electrical & Electronic Engineering, North China

Electric Power University, Beijing, China, in

2009. She is currently an Associate Professor in

College of Automation, Beijing Information Science & Technology University. From 2013

to 2014, she was a visiting scholar in

Department of Electrical Engineering, Tsinghua University. Her research interests include renewable power generation and microgrid

energy management system.

International Journal of Electronics and Electrical Engineering Vol. 4, No. 5, October 2016

©2016 Int. J. Electron. Electr. Eng. 411