This document describes a fuzzy logic controller that is proposed to improve the stability of an AC/DC power system using a Voltage Source Converter based HVDC (VSC-HVDC) transmission system. The controller monitors oscillations on the AC line parallel to the VSC-HVDC line and uses fuzzy logic rules to adaptively adjust the active power output of the VSC-HVDC in a way that dampens the oscillations. Simulation results on an IEEE 4-generator test system showed the controller effectively enhances the dynamic stability of interconnected power systems and is robust to different system operating conditions and oscillation modes.

1. A VSC-HVDC Fuzzy Controller for Improving the
Stability of AC/DC Power System
Sheng Li, Jianhua Zhang, Jingfu Shang, Ziping WU,Mingxia Zhou
Key Laboratory of Power System Protection and Dynamic Security Monitoring and Control under Ministry of Education, North
China Electric Power University, Changping District, Beijing 102206, China
Abstract —This paper puts forward an auxiliary fuzzy logic
controller for the Voltage Source Converter based HVDC
transmission system, VSC-HVDC, to improve the stability of the
AC/ DC system by damping the oscillation effectively after
disturbance. The fast control capability of the VSC-HVDC and the
process of area mode oscillations are analyzed. No detailed model
of the system is required for the design of the proposed control
scheme. The controller judges the operation states and the control
effect and accordingly adjusts its active power order in an adaptive
way by using fuzzy rules, so as to damp out the area mode
oscillation. Simulation results on the IEEE 4-generator AC/DC
power systems have shown that the controller can enhance the
dynamic stability of interconnected power systems effectively and
is robust to the variation of system operating conditions and
oscillation modes.
Keywords: VSC-HVDC; fuzzy logic control; tie-line oscillation
I.
INTRODUCTION
Compared with traditional HVDC, voltage source converter
based HVDC ，(VSC-HVDC) has a series of advantages and
adds fast control capability to power transmission.
There are dozens of VSC-HVDC project in operation
worldwide for different purpose, such as transporting power by
wind, connecting asynchronous power systems, deregulated
electricity market manipulating, improving power quality,
feeding remote passive network and etc. Nowadays,
VSC-HVDC has been reported to have the ability to deal with
power level as much as 300 kV, 1000MW, which means that
VSC-HVDC can be used in not only distribution system but also
transmission system. At the same time, with the development of
VSC-HVDC operation practice, a lot of research interests have
been put on the study of modeling, controller design and
influence to the grid connected of VSC-HVDC.
There are three kinds of control strategy for VSC-HVDC. The
three control strategy deal with the different state of system.
First is basic steady state control when power system is
normal. In [1], the approximately decoupled relationship
between the two controlling variables and the two controlled
variables of VSC is proposed. An inverse steady state model
controller for VSC-HVDC system is proposed. In [2], traditional
proportional integral (PI) controllers of VSC-HVDC in
conventional a-b-c coordinates are proposed. In [3], an
equivalent continuous-time state space model of VSC-HVDC in
the synchronous dq reference frame is presented. The d- and
q-axis of VSC model are decoupled using the feed forward
compensation method. In [12], an adaptive control strategy to
improve dynamic performances of VSC-HVDC systems is
presented. The adaptive controller considers parameters
uncertainties, which was based on back stepping method.
Second is stability control when power system is interfered by
some fault. Power system stability is very important, especially
for a large-scale system. In year 2003, a record number of total
blackouts happened in North America as well as in large portion
of Europe, which affected 50million people and caused huge
economy losses. In [5,6] ,controller of VSC is considered to add
the damping ability of system
Third is restore control or black start control when the power
system connecting the one terminal of VSC-HVDC is dead. In
[7,8] ,some restore operation by VSC-HVDC are researched
Further study is needed to explore the benefit the VSC-HVDC
technology can bring to power system.
Fuzzy logic control strategy doesn’t depend on the detailed
system model and is robust to different operating conditions. In
this paper a fuzzy logic controller is developed to damp the
oscillation of AC line parallel with VSC-HVDC transmission
line.
The rest of the paper is organized as follows. In Section 2, the
modeling and main feature of HVDC Light system is presented.
In section 3, the mode of area oscillation is discussed and proper
input signal for fuzzy damping control is recommended. In
section 4, the ancillary damping fuzzy controller is designed.
Simulation system and case study results are presented and
illustrated in Section 5. At last, Conclusions are drawn in
Section 6.
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II.
VSC-HVDC MODELING AND ITS CHARACTERISTIC
DC LINE
2Cd
T
1
AC system1
2Cd
T
Ud
Xf
Xf
2Cd
VSC1
AC system2
2Cd
VSC2
Fig.1. Topology of 2-level converter VSC-HVDC Transmission system

2. Figure 1 shows the topology of a Six pulse two level two
terminal VSC-HVDC Transmission system. VSC1 and VSC2
have the same structure. Xf stands for a high order filter with
small capacity. Transformer T provides a interface for power
exchanging between the AC system and VSC-HVDC
transmission line.
⎡usa ⎤
⎡ia ⎤
⎡ia ⎤ ⎡uca ⎤
d ⎢ ⎥
⎢u ⎥ = L
ib + R ⎢ib ⎥ + ⎢ucb ⎥
⎢ sb ⎥
⎢ ⎥ ⎢ ⎥
dt ⎢ ⎥
⎢usc ⎥
⎢ic ⎥
⎢ic ⎥ ⎢ucc ⎥
⎣ ⎦
⎣ ⎦
⎣ ⎦ ⎣ ⎦
id
P , Qc
c
Ps , Qs
approximation of the power flowing between the converter and
the AC network in steady state neglecting the losses.
Suppose three phases are balanced, based on Kirchhoff’s law
the following equation indicating the relationships among
different variables of the system is obtained.
2Cd
U s ∠δ s
R
Uc∠δ s − δ
X
Ud
The equation (3) in vector form is as follows ：
Is
AC system
u Sabc = L
Xf
2Cd
DC system
In Fig2, Us is the fundamental component of bus voltage in
AC system side and Uc is the fundamental component of bus
voltage of AC side of VSC. δ is the phase angle difference
between Us and Uc. X is the equivalent inductance of converter
filter and R is the resistance of equivalent loss of VSC. Pc and Qc
are active and reactive power respectively transferred from the
network to the rectifier. Ud is the DC bus voltage and Id is the
current of DC lines.
The following equations indicate the relationships among
different variables of the system without loss being considered.
U sU c
sin δ
Xc
(1)
U s (U s − U c cos δ )
Q=
Xc
Udcmax=1
Udcmax=1.4
(2)
Udcmax=1.8
P
Pmax=0.9
Smax=0.6
Smax=0.9
Pmax=0.6
Smax=0.3
A
B
Us=1
D
C
diabc
+ Riabc + uCabc
dt
(4)
where
Fig.2. typical VSC diagram
P=
(3)
Pmax=0.3
uCabc
⎡ sin( wt + δ )
mU d ⎢
=
sin( wt + δ − 120
2 ⎢
⎢sin( wt + δ + 120
⎣
⎤
)⎥
⎥
)⎥
⎦
(5)
M and δ are respectively the modulation index and the initial
phase angle of modulation wave.
Following equation (6) is obtained by transform equation (4)
L
diabc
= − Riabc + (u Sabc − uCabc )
dt
(6)
AC voltage and AC current are transformed to voltage and
current in the synchronous dq0 reference frame through Park
transformation .with the transformation matrix P and P-1
⎡
⎤
⎢coswt cos(wt − 2π / 3) cos(wt + 2π / 3)⎥
2
P = ⎢sinwt sin(wt − 2π / 3) sin(wt + 2π / 3) ⎥ (7)
⎥
3⎢ 1
1
1
⎢
⎥
⎣ 2
2
2
⎦
− sin wt
cos wt
1⎤
⎡
P −1 = ⎢cos( wt − 2π / 3) − sin( wt − 2π / 3) 1⎥ (8)
⎢
⎥
⎢cos( wt + 2π / 3) − sin( wt + 2π / 3) 1⎥
⎣
⎦
where ω is the angular frequency of system.
After Park transformation, equation (9) in vector form is
obtained
Q
Pmax=0.3
didq0
R
1
dP−1
= − idq0 + (uSdq0 − uCdq0 ) − P
I dq0 (9)
dt
L
L
dt
Pmax=0.6
It is supposed that system operates symmetrically in the
steady-state condition. So there is no zero sequence component
when 3 phase are balanced, So equation (10)is obtained
from(9)its relationship of balance of voltage [13] is:
Pmax=0.9
Fig.3. operation range of VSC
The operation range in function of the capacity of VSC,
Smax the DC cable capacity, Pmax, and the rated DC voltage,
Udcmax is shown in the PQ-diagram in Fig.3, Where P and Q
expressed in per unit. The formulas (1) and (2) give an
⎡id ⎤ 1 ⎡ − R wL⎤⎡id ⎤ 1 ⎡usd ⎤ 1 ⎡ucd ⎤
s⎢ ⎥ = ⎢
⎥⎢ ⎥ + ⎢ ⎥ − ⎢ ⎥
⎣iq ⎦ L ⎣− wL − R⎦⎣iq ⎦ L ⎣usq ⎦ L ⎣ucq ⎦
(10)
where s is a differential operator, in the synchronous frame,
usd and usq are source voltages, the d and q axis components of
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3. the respective AC bus voltage in the synchronous frame. id and iq
are line currents, ucd and ucq are converter input voltages.
Suppose that the fundamental component of AC bus voltage
us is in q-axis. Therefore, usd is equal to 0 while the magnitude of
usq is equal to that of us, which will simplify the model (10) as.
⎡id ⎤ 1 ⎡ − R wL⎤⎡id ⎤ 1 ⎡ 0 ⎤ 1 ⎡ucd ⎤
s⎢ ⎥ = ⎢
+
−
iq ⎦ L ⎣− wL − R⎥⎢iq ⎥ L ⎢usq ⎥ L ⎢ucq ⎥
⎦⎣ ⎦ ⎣ ⎦ ⎣ ⎦
⎣
system is outage.
In this paper, the research interest is mainly put on the
VSC-HVDC control function for enhance power system
stability .
III.
AREA MODE OSCILLATION SIGNAL CHOOSING
(11)
VSC1
Equation (1) and (2) show that the VSC can act as a
synchronous machine with almost no inertia and therefore, it can
control active and reactive power almost instantaneously [9],
and almost independently [10]. Also, since it has virtually no
inertia, it does not contribute to the short circuit current [9]. By
means of Phase Width Modulation (PWM) technology,
especially Sinusoidal PWM (SPWM),two degrees of freedom,
i.e. phase and amplitude can be acquired. Phase and Amplitude
Control (PAC) technology is developed for VSC-HVDC
applications [2,11].The VSC can easily interchange active and
reactive power with an AC network as well as a synchronous
machine.
Deferent basic steady state control is applied in VSC
dependent on its role in VSC-HVDC .Usually every terminal of
VSC-HVDC has two aspects of control task. For the AC side
,VSC can take AC bus voltage or reactive power as control
object. For the DC side , VSC can take DC voltage or active
power or DC current as control object. At least one VSC in the
VSC-HVDC acts to keep DC voltage stable for providing an
normal operation point for the whole VSC-HVDC. To the VSC
connected to passive network , Controlling AC bus voltage will
be the only object . Basic VSC-HVDC Control mode is shown
in and Fig 5
Qsref 1
M1
U DCref 1
δ1
Fig.4 Basic VSC-HVDC Controller for Terminal 1
Qsref 2
δ2
A1
PAD
B1
VSC-HVDC brings power system many advantages,
including [ 12-16]: (i) IGBT valve can switch off and on
immediately. there is no worry about commutation failure
problem, (ii) no telecommunication required between two
stations of HVDC Light system, (iii) active and reactive power
controlled independently. reactive power compensation not
required, (iv)only small filter is required to filter high frequency
signal from PWM. (v)proper ancillary stability controller of
VSC-HVDC design improve the stability level of power system
(vi) VSC-HVDC can work as black start source after power
PA
AC LINE
PBD
PB
AREA B
ΔPAC
ΔΔPAD
B2
Fig. 6. Two-area power system with AC and VSC-HVDC tie lines
Figure 6 shows Two-area power system with AC and
VSC-HVDC tie lines. The controllability of VSC-HVDC can
not only adjust the power flow between the two area in normal
steady state , but also damping the oscillation by some
disturbance, if proper ancillary damping policy has been made
in advance.
There are some phenomena can be observed and taken as
evidence to determine that area oscillation happens. For
example , the angle and angle speed between the centre of inertia
of the two area will change during area oscillation and be taken
as input signal of controller in [17], But the two variables are not
ideal options to identify area oscillation because they have to
depend on some costly communication means to be acquired,
and the reliability has to be ensured.
Actually the active power flow of the AC tie line which can be
measured locally is a ideal signal and sensitive enough for
detecting the oscillation. In Fig 6 , it is assumed VSC2 works in
the mode of controlling the power flow of the VSC-HVDC line
Under this circumstance , the power of AC tie line to be
measured is chosen at the end near Area B because of short
distance. To damping oscillation, the change of active power, △
PAC and the change speed of active power,△△PAC need to be
sent to the ancillary damping controller of VSC2.
IV.
Fig. 5 General VSC-HVDC Controller for Terminal 2
A2
AREA A
M2
PDCref 2
VSC 2
DC LINE
VSC-HVDC FUZZY CONTROLLER DESIGN
The design of steady state controller for VSC-HVDC system
is mainly based on its mathematical model. However, the
ancillary damping controller for VSC-HVDC is easy to be
influenced by the external interference of the uncertainty, such
as the random fluctuation of the load and disturbance of
different faults in the two area. It is important to design the
VSC-HVDC controllers to be adaptive for different conditions
the system. This paper presents a fuzzy logic ancillary damping
control added to a normal steady state controller of
VSC-HVDC.
The knowledge based on fuzzy control [18], outperform the
linear control in many of the cases exposed before, a reason of
this is that the human knowledge adds several types of
information and can mix different control strategies that can not
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4. be added in an analytical control law and do not need an accurate
mathematical model.
The Knowledge-based fuzzy control uses the experience and
the knowledge of an expert about the system behavior. A kind of
Knowledge-based fuzzy control is the rule-based fuzzy control,
where the human knowledge is approximated by means of
linguistic fuzzy rules in the form if-then, which describes the
control action that would be made for a human operator. Due to
the nonlinear behavior showed by the converter, to the failed
attempt of design a linear control, and supported in the
advantage of the fuzzy control exposed before, a nonlinear fuzzy
control might be desirable to effectively damping area
oscillation, by dynamically adjust the active power reference of
the normal steady state controller. The control proposed for the
ancillary fuzzy logic controllers is a Mamdani controller,
because of it is usually used as feedback controller .The rule
base represents a static mapping between the antecedent and the
consequent variables.
Qsref 2
Pdcref 2
ΔPAC
ΔΔPAC
Ancillary damping
Fuzzy
logic controller
+
+
Basic VSC-HVDC
Controller
for Terminal 2
The membership functions in Fig 8 were tuned searching the
minimum error in steady state and the minimum oscillation in
steady transitory by trial and error method, by using the toolbox
FIS of Matlab. The rule base that represents the knowledge
obtained from the behavior of the system is summarized in table
I, which was proposed after getting a knowledge about the
dynamic and steady state behavior of the system.
Table I
Rule base of ADFC
△PAC,
△△PAC
NB
NS
Z
PS
PB
NB
NS
NS
NS
Z
NS
NS
NS
NS
NS
Z
Z
NS
Z
Z
Z
PS
NB
PS
Z
PS
PS
PS
PS
PB
Z
PS
PS
PS
PB
V.
M2
δ2
ΔPdcref 2
Fig.7 Structure of the controller with the ancillary damping control for
Terminal 2
Fuzzy sets must be defined for each input and output variable,
as shown in Fig.5. Five fuzzy subsets are needed for the
antecedent error ,For both △PAC and △△PAC, the subsets are:
negative big (NB), negative small (NS), zero error(Z), positive
small (PS), and positive big (PB). Fig.6. The fuzzy subsets used
in the consequent were just like the antecedent
CASE STUDIES
To validate the established ancillary damping fuzzy control
strategy, simulation studies of the test system shown in Fig. 9
have been done with digital simulation software package
PSCAD/EMTDC. The test simulation system is a 4 machine
system whose parameter is obtained from [19]. At the steady
state, about 700MW power is generated from each of the
generators. L7 and L9 stand for two loads on buses 7 and which
are 967 MW and 1700MW respectively, and G3 a immense
source. A two terminal VSC-HVDC transmission line with
rated power 400MW is append to connect bus 7 and bus 9 as tie
line. Basic control mode is that VSC1 controls DC active power
voltage transmitted and its AC voltage, and VSC2 controls DC
voltage and its AC voltage .The ancillary damping fuzzy control
function is added to the controller of VSC1. The active power of
the lines between bus7 and bus8 is measured as input signal for
the ancillary damping fuzzy control to dynamically modulate
the DC power reference of VSC1 to damping the oscillation
cause by disturbance.
In the simulation test, a three-phase to earth fault at one line
between bus 8 and bus 9 is applied at 1s from the beginning and
last 80ms, then the fault is cut off. The processes of simulation
with and without ancillary fuzzy control are shown below.
5
G1 1
6
7
9 10
VSC1
G2
2
L7
8
11
3 G3
VSC2
4
G4
L9
Fig. 9 The IEEE 4-generator AC/DC system
Fig.8. Member fuction of △PAC ,△△PAC and △PDCref
Fig10 shows the change process of the active power of lines
between bus 7 and bus8.
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5. Fig11 shows the curves of the G1 power angle taking the
angle of G3 as reference .
Fig12 shows the curves of the G4 power angle taking the
angle of G3 as reference .
The simulation result verifies that the ancillary damping fuzzy
controller developed in this paper can effectively damp the
oscillation caused by disturbance and enhance the stability of
the system.
VI.
CONCLUSION
VSC-HVDC is an advanced and hopeful transmission
technology and fuzzy control is an effective method used to
control nonlinear system without the need to resort to
complicated mathematical models. In this paper, an ancillary
damping fuzzy control is proposed to change the active power
reference dynamically. System stability is improved with the
proposed ancillary damping fuzzy control are verified in
EMTDC/PSCAD simulation test.
REFERENCES
Fig.10 the active power of lines between bus 7 and bus8
Fig. 11 power angle of G1 taking the angle of G3 as reference图4-5
Fig. 12 power angle of G4 taking the angle of G3 as reference
[1] G.B. Zhang, Z. Xu, and G.Z. Wang, “Steady-state model and its nonlinear
control of VSC-HVDC system,” Proceedings of CSEE, vol.22, pp. 17-22,
Jan. 2002.
[2] G.B. Zhang and Z. Xu, “Steady-state model for VSC based HVDC and its
controller design,” in Proc.2001 IEEE Power Engineering Society Winter
Meeting, vol. 3, pp. 1085–1090.
[3] M. Yin, G.Y. Li, T.Y. Niu, G.K. Li, H.F. Liang, and M. Zhou,
“Continuous-time state-space model of VSC-HVDC and its control
strategy,”Proceedings of the CSEE, vol. 25, pp. 34-39, Sept. 2005.
[4] L. Xu, B.R. Andersen and P. Cartwright, “Control of VSC transmission
systems under unbalanced network conditions,” in Proc. 2003 IEEE PES
Transmission and Distribution Conference and Exposition Conf.,
pp.626–632.
[5] Corsi, S., A. Danelli, et al. (2002). Emergency-stability controls through
HVDC links. Power Engineering Society Summer Meeting, 2002 IEEE.
[6] Ying, J.-H., H. Duchen, et al. (2002). Improvement of subsynchronous
torsional damping using VSC HVDC. Power System Technology, 2002.
Proceedings. PowerCon 2002. International Conference on.
[7] Ying, J.-H., H. Duchen, et al. (2008). HVDC with voltage source
converters - a powerful standby black start facility. Transmission and
Distribution Conference and Exposition, 2008. T&D.
[8] Guangkai, L., Z. Chengyong, et al. (2007). Research on "Soft Start-up" of
VSC-HVDC in Power System Restoration after Blackouts. Industrial
Electronics and Applications, 2007. ICIEA 2007. 2nd IEEE Conference
on.
[9] Vijay, K. Sood “HVDC and FACTS Controllers” Kluwer power
electronics and power editions series, 2004.
[10] Padiyar, K. R., Prabhu, N., “ Modeling, Control desing and Analysis of
VSC based HVDC transmission” Paper published in POWERCOM 2004,
21-24 November, Singapore.
[11] Ooi, B.-T.; Wang, X.; “Boost-type PWM HVDC transmission system”,
IEEE Transactions on Power Delivery, Vol. 6, Oct. 1991, pp.1557 - 1563
[12] B.R. Andersen, L. Xu, P.J. Horton, P. Cartwright, “Topologies for VSC
transmission”, Power Engineering Journal, Vol. 16, June 2002, pp.142 –
150.
[13] G. Venkataramanan, B.K. Johnson, “A Superconducting DC Transmission
System Based on VSC Transmission Technologies”, IEEE Transactions on
Applied Superconductivity, Vol.13, June 2003, pp.1922 – 1925.
[14] F.A.R. Al Jowder; B.T. Ooi, “HVDC LIGHT Station With SSSC
Characteristics”, IEEE Transactions on Power Electronics, Vol. 19, July
2004, pp.1053 – 1059.
[15] L. Weimers, “HVDC Light: A New Technology for a Better
Environment,” IEEE Power Engineering Review, Vol. 8, Aug. 1998,
pp.19-20.
[16] G. Asplund, “Application of HVDC Light to power system enhancement”,
IEEE Power Engineering Society Winter Meeting, Vol. 4, Jan. 2000, pp.
2498-2503.
[17] YANG Xiao-dong, “AN ADAPTIVE SVC FUZZY CONTROLLER FOR
DAMPING TIE-LINK LOW FREQUENCY OSCILLATION”
Proceedings of the CSEE Vol.23 No.1 Jan. 2003
[18] BABUSKA, R. “Fuzzy and Neuronal Control” Delft University of
technology, October 2001.
[19] Kundur P. Power System Stability and Control. New York: MC Graw
-Hill, 1994
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