Damping of Inter-Area Low Frequency Oscillation Using an Adaptive Wide-Area Damping Controller

J Electr Eng Technol Vol. 8, No. ?: 742-?, 2013
http://dx.doi.org/10.5370/JEET.2013.8.?.742
742
Damping of Inter-Area Low Frequency Oscillation Using
an Adaptive Wide-Area Damping Controller
Wei Yao†
, L. Jiang*, Jiakun Fang**, Jinyu Wen** and Shaorong Wang**
Abstract – This paper presents an adaptive wide-area damping controller (WADC) based on
generalized predictive control (GPC) and model identification for damping the inter-area low
frequency oscillations in large-scale inter-connected power system. A recursive least-squares algorithm
(RLSA) with a varying forgetting factor is applied to identify online the reduced-order linearlized
model which contains dominant inter-area low frequency oscillations. Based on this linearlized model,
the generalized predictive control scheme considering control output constraints is employed to obtain
the optimal control signal in each sampling interval. Case studies are undertaken on a two-area four-
machine power system and the New England 10-machine 39-bus power system, respectively.
Simulation results show that the proposed adaptive WADC not only can damp the inter-area
oscillations effectively under a wide range of operation conditions and different disturbances, but also
has better robustness against to the time delay existing in the remote signals. The comparison studies
with the conventional lead-lag WADC are also provided.
Keywords: Wide-area damping controller, Low frequency oscillation, Generalized predictive control,
Model identification, Time delay
1. Introduction
With the interconnection of regional grids and the
increasing of line power, the inter-area low frequency
oscillation between different control areas is becoming a
more and more serious problem which limits the
enhancement of the transmission capacity of power grids
or even breaks up of whole power system [1].
Conventionally, the power system stabilizers (PSSs) are
used to damp inter-area mode oscillations. However, the
PSSs, which use local measurement as the input, can not
always damp inter-area mode oscillations effectively
because inter-area modes are not always observable from
the local signals [2, 3].
With the technological advancements and increasing
deployments of wide-area measurement system (WAMS)
in power system, remote signals from WAMS become
available for the design of wide-area damping controller
(WADC) to solve the above problem [2-5]. Many classical
control approaches, such as residue method [2, 3], robust
control approach [4, 5], have been adopted for design of
WADC which require a reasonably accurate model of the
system at a nominal operating condition. However, lack of
availability of accurate and updated information about each
and every dynamic component of a large-scale inter-
connected system and especial the model variations caused
by the change of operation conditions and unavoidable
faults put a fundamental limitation on such classical
control design approaches. To overcome the inherent
shortcomings of classical method based damping
controllers, adaptive control method had been adopted to
design an adaptive damping controller for power systems
[6-11]. These controllers use a linear model with online
updated parameters to design an adaptive controller to cope
the model variation and uncertainty of large-scale power
system. In addition, for a wide-area damp control system,
the impact of the time delay existing in remote signals
must be considered [12], 13]. As the delay can typically
vary from tens to several hundred milliseconds and is
comparable to the period of some critical inter-area modes,
it should be taken into account at the design stage for a
satisfactory damp performance [14], 15].
Model predictive control (MPC) is one of the major
adaptive control strategies which has attracted many
attentions and has been applied in process control
successfully. Although there are several formulations of the
MPC strategy, they explicitly use a model of system to
obtain the control input signal by minimizing an object
function [16]. The generalized predictive control (GPC) is
one of the most popular control methods of MPC. The
GPC approach can not only deal with variable dead-time,
but also cope with over-parameterization as it is a
predictive method [17]. The GPC has been applied
successfully to power system such as design of controllers
for flexible AC transmission systems (FACTS) and the
† Corresponding Author: The State Key Laboratory of Advanced
Electromagnetic Engineering and Technology, Huazhong University
of Science and Technology, China. (yao_wei@163.com)
* Department of Electrical Engineering & Electronics, The University
of Liverpool, Liverpool, UK.
** The State Key Laboratory of Advanced Electromagnetic Engin-
eering and Technology, Huazhong University of Science and
Technology, Wuhan, China.
Received: January 3, 2013; Accepted: August 23, 2013
ISSN(Print) 1975-0102
ISSN(Online) 2093-7423

Wei Yao, L. Jiang, Jiakun Fang, Jinyu Wen and Shaorong Wang
743
generator excitation system [18], 19].
In this paper, the GPC integrating model identification is
proposed for the synthesis of an adaptive WADC, which
can cope with variation of operating conditions, model
uncertainties and robustness against time delay existing in
wide-area signals feedback. Simulation studies are carried
out based on the two-area four-machine power system and
the New England 10-machine 39-bus power system,
respectively. Comparison results with the conventional
WADC are also given. The results demonstrate that the
proposed adaptive WADC can provide effective damping
of inter-area mode oscillations under various operation
conditions and different disturbances. Moreover, it has
much better performance than conventional WADC with
time delay existing in the wide-area signals.
The rest of the paper is organized as follows. Section 2
presents a general architecture of wide-area damping
control system. An adaptive GPC strategy and the
procedure of the proposed adaptive WADC based on this
GPC are described briefly in Section 3. Section 4 designs
an adaptive WADC for a two-area four-machine
benchmark power system and verifies its effectiveness by
detailed simulation. Then, the proposed adaptive WADC is
employed to design a WADC for the New England 10-
machine 39-bus power system in Section 5. Finally, some
conclusions are drawn in Section 6.
2. Architecture of Wide-Area Damping Control
The wide-area stabilizing control structure shown in Fig.
1, so-called “decentralized/hierarchical” architecture, is
used in this paper. In the local decentralized control level,
including automatic voltage regulator and PSS (AVR-PSS)
at generators, main controls of FACTS or high voltage
direct current (HVDC) transmission system, provides
damping for local modes. Thus, the local mode will be very
highly damped. However, these local controllers are not
capable of damping inter-area modes under stressed
operating conditions because of the local signals lack of
good observability of some critical inter-area natural modes.
Therefore, additional damping is required particularly for
the these inter-area modes. As shown in Fig. 1, in the wide-
area control level, the control signal of the WADCs are to
provide damping for the inter-area modes, controlled from
the selected generator, FACT or HVDC using a global
input signal from the WAMS. As few global signals are
required only for some critical inter-area modes and under
specific network configurations, no more than the few
WADCs sites with the highest controllability of these inter-
area modes need be involved in the wide-area control level.
The above specific architecture was first discussed in [3]
where it was preferred for its higher operational flexibility
and reliability, especially in the event of loss of
communication links or a failure that makes the wide-area
control signal unavailable. Under such circumstances,
the controlled power system is still viable (although with
a reduced performance level), owing to the fact that a
fully autonomous and decentralized layer without any
communication link is always present to maintain a
standard performance level [2].
3. Adaptive Generalized Predictive Control
The structure of the adaptive generalized predictive
controller is shown in Fig. 2. It is an indirect type
controller and mainly composes of two parts: system
identification and controller synthesis based on generalized
predictive control scheme.
3.1 General system model
Although a real power system is a complex, nonlinear
and high-order dynamic system, it can be represented by a
relatively simple linear model with fixed structure but
whose parameters vary with the operating conditions. This
linear model is accurate enough for the purpose of design a
damping controller [8]. In the application of designing an
adaptive WADC, the following controlled auto-regressive
and moving average (CARMA) linear model is utilized to
avoid the off-set of the control signal [19].
1 1 1
( ) ( ) ( ) ( 1) ( ) ( )A B Cz y t z u t z e t− − −
= − + (1)
Fig. 1. General architecture of the wide-area damping
control system
ˆ( )tθ
Fig. 2. Overview of an adaptive generalized predictive
controller

Damping of Inter-Area Low Frequency Oscillation Using an Adaptive Wide-Area Damping Controller
744
where, y(t) and u(t) are the output and input of the system,
respectively, and e(t) is a discrete white-noise sequence.
A(z-1
), B(z-1
) and C(z-1
) are na, nb and nc order polynomial,
respectively. They are given as follows
1 1
1( ) ...A a
a
n
nz = 1+a z a z−− −
+ + (2)
1 1
0 1( ) ...B b
b
n
nz = b +b z b z−− −
+ + (3)
1 1
1( ) ...C c
c
n
nz = 1+c z c z−− −
+ + (4)
The polynomial C(z-1
) may either represent the external
noise components affecting the output (in which case its
coefficients have to be estimated) or a design polynomial
interpreted as a fixed observer for the prediction of future
outputs. For simplicity, the C(z-1
) polynomial is usually
chosen to be 1.
3.2 Model identification algorithm
In this paper, a recursive least-squares algorithm (RLSA)
with a varying forgetting factor is used to track the power
system model parameters ai and bi shown in Eq. (1) [6].
As the RLSA is a well known method, only a general
formulation is presented in the following, without
demonstration.
Given the vector ˆ( )θ t of parameter estimates by:
1 0 1
ˆ( ) [ ,..., , , ,..., ]θ a b
T
n nt a a b b b= (5)
and the measurement vector φ(t) by:
( ) [ ( 1),..., ( ), ( 1),..., ( 1)]φ T
a bt y t y t n u t u t n= − − − − − − − (6)
The update of the estimates is obtained by:
2
0
ˆ( ) ( ) ( ) ( 1)
( ) ( 1) ( ) [1 ( ) ( 1) ( )]
ˆ ˆ( ) ( 1) ( ) ( )
( ) 1 [1 ( ) ( )] ( )
( ) [ ( ) ( )] ( 1) ( )
φ θ
K P φ φ P φ
θ θ K
φ K
P I K φ P
T
T
T
T
t y t t t
t t t t t t
t t t t
t t t t
t t t t t
η
η
λ η
λ
 = − −

= − + −

= − +
 = − − ∑
 = − −
(7)
where, P(t) is the covariance matrix, I is an identity matrix,
K(t) is the vector of adjustment gains, λ is the forgetting
factor used to progressively reduce the effects of old
measurements, and Σ0 are the preselected constants. The
initial value 2
(0)P Iα= , 2 5 10
10 ~ 10α = .
In addition, moving boundaries are introduced for every
parameter to protect the parameters from large modeling
errors which are caused by a variety of sudden disturbances
in the power system [11]. The mean values of the estimated
parameters at the sampling instant t are of the form:
1
1
( ) ( ) 1,2,...,( 1)
T
i i a b
k
t t k i n n
T
ϕ θ
=
= − = + +∑ (8)
where θi(t) is the element in ˆ( )θ t , and T>1, with a value
chosen to ensure stability of the parameters. The larger the
value of T, the more stable and less adaptable the
parameter boundaries become.
The high and low boundaries for each parameter are
defined as follows:
( ) ( ) ( )
( ) ( ) ( )
iH i i
iL i i
t t t
t t t
ϕ ϕ γ ϕ
ϕ ϕ γ ϕ
 = +

= −
(9)
where 0< γ <1, the larger the value γ, the more likely it is
for the parameters to vary. At each sampling instant, each
estimated parameter is bounded by its corresponding high
and low boundaries.
3.3 Generalized predictive control
The GPC is a long range predictive control approach that
adopts an explicit parameterized system model to predict
the process future output, which depends on both currently
available input/output data and present/future control
values. The latter are determined by minimizing a cost
function, which is chosen in such a way that satisfying the
controlled system dynamics and constraints, penalize
system output deviation from the desired trajectory and
minimize control efforts [17].
As the design of WADC is a positional control problem,
the cost function to be minimized is defined as follows:
2 2
1 1
ˆ( , ) { ( ) ( 1) }
uNN
GPC u j
j j
J N N E y t j r u t j
= =
= + + + −∑ ∑ (10)
where E{.} is the expectation operator, ˆ( )y t j+ is an
optimal j-step ahead prediction of the system output up to
time t. N is the prediction horizon, u(t+j-1) is an optimal j-
step ahead prediction of the system input, Nu is the control
horizon, rj is a control weighting sequence and usually
defined as a constant value, rj=r, for j=1, 2, ... Nu.
In order to obtain ˆ( )y t j+ , the following Diophantine
equations are used:
1 1 1
1 1 1 1
1 ( ) ( ) ( )
( ) ( ) ( ) ( )
E A F
E B G H
j
j j
j
j j j
z z z z
z z z z z
− − − −
− − − − −
 = +

= +
(11)
where Ej(z-1
) and Fj(z-1
) are unique polynomials of order j-
1 and na, respectively. Gj(z-1
) is an unique polynomials of
order j-1. Hence,
1ˆ( | ) ( ) ( 1| )G j jy t j t z u t j t f−
+ = + − + (12)

745
where 1 1
( ) ( ) ( ) ( 1)F Hj j jf z y t z u t− −
= + −
The N steps j-ahead predictions can be represented by
the following matrix equation:
ˆY GU f= + (13)
where
ˆ ˆ ˆ ˆ[ ( 1) ( 2) ( )]Y T
y t y t y t N= + + +⋯ ，
[ ( ) ( 1) ( 1)]U T
uu t u t u t N= + + −⋯ ，
1 2[ ]f T
Nf f f= ⋯ ，
0
1 0
1 2 0
1 2
0 0
0
G
u u
u
N N
N N N N
g
g g
g g S
g g S
− −
− − −
 
 
 
 
 =
 
 
 
 
 
⋯
⋯
⋮ ⋮ ⋱ ⋮
⋯
⋮ ⋮ ⋱ ⋮
⋯
，
0
i
i j
j
S g
=
= ∑ （ 0,1,2....( )ui N N= − ）
The elements gi of the matrix G, with dimensions
uN N× , are points of the plant's step response and can be
computed recursively from the model. The elements fi of
the matrix f can be computed similarly.
One of the major advantages of GPC is its ability to
handle constraints online in a systematic way. The
algorithm does this by optimizing predicted performance
subject to constraint satisfaction. In practice, the
constraints of the control signal should be considered and
can be expressed as follows:
min maxI U IU U≤ ≤ (14)
where Umin and Umax denote the lower limit and upper limit
of the control signal. I denotes the Nu identity vector.
According to the Eqs. (10), (13) and (14), the
implementation of GPC with bounded signals can be
represented as a inequality constrained quadratic
programming (QP) problem, which can be stated as:
0
1
( )
2
U U HU b U f
A U b
T T
qp c
min: J
s.t.:
= + +
≤
(15)
where P=2(GT
G+R), 1 2[ ]R uNdiag r r r= ⋯ , b= -2fT
G,
f0=fT
f, Aqp=[T, -T ]T
, and bc=[IUmax, - IUmin ]T
. T is the
identity matrix.
The future control input sequence U can be obtained by
solving the QP problem shown as Eq. (15). Because GPC
is a receding-horizon control method, only the first element
of U is actually applied. Therefore, it is only necessary to
calculate the first row of U at each sampling interval.
3.4 Procedure of WADC based on adaptive GPC
In order to implement the control algorithms of the
proposed adaptive WADC based on GPC, the essential
procedure may be followed:
(1) Initialize the system out Y0, system input U0,
covariance matrix P(0), and choose the prediction
horizon N, the control horizon Nu, weighting sequence
r, the order of the prediction model na and nb.
(2) At the sampling interval t, obtain the system out y(t)
and system input u(t-1), update the measurement φ(t).
(3) Update the parameters of the prediction model
according to Eqs. (7-9).
(4) Predict the output ˆY using Eq. (13) and the new
model parameters updated in Step (3), over the
prediction horizon N.
(5) Solve the QP problem shown as Eq. (15) with respect
to control input sequence U over the control horizon
Nu, satisfying the constraints.
(6) Apply the first element of the future control input
sequence U obtained from the optimization procedure
as the control input u(t) until new measurements are
available.
(7) Let t=t+1, fetch the next sampling data, then go back to
Step (2) again.
4. Case Study I: Two-Area Four-Machine System
At first, case study is carried out based on the two-area
four-machine system, as shown in Fig. 2., to illustrate the
principle and effectiveness of the proposed adaptive
WADC using the MATLAB/Simulink software. The
subtransient generator model and the IEEE-type DC1
excitation system are used for each generator. All of the
loads are used the impedance model. In addition, in order
to damp the local low frequency oscillations, G1 and G3
are equipped with a PSS respectively with local rotor speed
as input and its transfer function is shown in Appendix.
The output of PSS is limited as [-0.15~0.15]pu. Details of
the system data are given in Ref. [1]. The proposed
adaptive WADC is compared with the conventional WADC
Fig. 3. The two-area four-machine power system

746
proposed in [3], whose parameters can be found in
Appendix.
4.1 Design of adaptive WADC
For the test system, the generator G1 is selected to locate
the proposed adaptive WADC in order to damp the only
inter-area oscillation mode. The detailed structure of the
proposed adaptive WADC is illustrated in Fig. 4. The linear
model of the power system shown as Eq. (1) is used as the
prediction model for GPC. The output of the WADC ug is
used as the input u(t) of the linear model, while the wide-
area signal ω13 (per unit) is used as the output signal y(t).
Moreover, in order to form a well-conditioned optimization
problem for GPC, keeping identified system model
parameters at the same order of magnitude is important.
Proper scaling of the output signals will help to improve
the identification accuracy. Due to the wide-area signal ω13
used in this paper, 100 is the suitable scaling number
according to the value used in the simulation. It should be
noted that, for a relatively large scale power system, the
geometric measures of observability and controllability are
used to select the most effective wide-area input signals
and WADC locations [20].
For the estimation, the order of the linear model is
chosen as: na=4, nb=5. The following parameters need to be
specified for the proposed adaptive WADC: the prediction
horizon N, the control horizon Nu, the weighting sequence r,
and the sampling period Ts. Although their values are
normally guided by heuristics, there are some general
guideline for choosing these parameters to ensure the
optimization is well proposed in [8]. For the proposed
adaptive WADC, desired response can be achieved by
setting N=7, Nu=2, r=0.6, Ts=40ms, Σ0=0.02, T=10, γ=0.04.
To avoid the excessive interference of the adaptive WADC
on the local control, ±0.05pu is limited to the output of
the proposed adaptive WADC.
4.2 Simulation and analysis
When a three-phase-to-ground fault occurs on bus 8 at
t=1s and lasts for 0.1s, the system responses are shown in
Fig. 5. The results show that the proposed adaptive WADC
is able to achieve slightly better performances than those of
conventional WADC. Note that the conventional WADC is
tuned and tested under similar operation point. In addition,
the identified parameters of the prediction model (1) are
shown in Fig. 6. The identified parameters are updated fast
enough to track the change of operation condition and
gu
lu
Fig. 4. Configuration of generator equipped with an
adaptive WADC
0 2 4 6 8 10
22
24
26
28
30
Time (sec)
Rotorangleδ
13
(deg)
Without WADC
Conventional WADC
Adaptive WADC
0 2 4 6 8 10
-1
-0.5
0
0.5
1
x 10
-3
Time (sec)
Rotorspeedω
13
(pu)
Without WADC
Conventional WADC
Adaptive WADC
Fig. 5. Responses to three-phase-to-ground fault under
nominal operating condition
0 2 4 6 8 10
-3
-2
-1
0
1
2
3
Time (sec)
a
a1
a2
a3
a4
0 2 4 6 8 10
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Time (sec)
b
b0
b1
b2
b3
b4
b5
Fig. 6. The variation of the identified parameters of the
prediction model

747
external disturbance. After the disturbance, the parameters
move to the new steady values.
Moreover, the response of the adaptive WADC under a
new operation point (i.e. the tie-line power changes to
Ptie=50MW), is shown in Fig. 7. The results show that the
adaptive WADC has better damping ability than the
conventional WADC. That is because the conventional
WADC is tuned based on a nominal operating condition
and its performance will be degrades when the operating
condition changes.
Finally, the results about the wide-area signals with the
time delay are shown in Fig. 8 and Fig. 9. The results show
that the proposed adaptive WADC has much better
performances than those of conventional WADC. The
proposed adaptive WADC can keep the stability of the
power system when the time delay existing in the wide-
area signal reaches 120ms. However, the conventional
WADC can not keep the stability of the power system
when the time delay of wide-area signal reaches 80ms.
This is because the proposed adaptive WADC can absorb
the change of the time delay into the prediction model and
is more effective to retain the stability of power system
considering wide-area signal delays.
5. Case Study II: New England 10-Machine
39-Bus System
To investigate the feasibility of the proposed WADC for
a large-scale power system, a case study is undertaken
based on the New England 10-machine 39-bus system, as
shown in Fig. 10. This test system consists of 10 generators,
39 buses, and 46 transmission lines. Each generator is
modeled as a fourth-order model and equipped with a IEEE
ST1A excitation system. The mechanical power of each
generator is assumed as constants for simplicity. The
detailed parameters and operating conditions are given in
[21].
5.1 Design of adaptive WADC
The modal analysis results of this test system has a
critical poor damping inter-area mode, which has lowest
damping ratio 0.0442 and oscillation frequency 0.6273Hz.
Therefore, the WADC should be designed for providing
damping for this critical inter-area mode. To determine
WADC location and wide-area feedback signals, geometric
measures of modal controllability/observability is employed
to evaluate the relative strength of candidate signals and
the performance of controllers at different locations with
respect to a given inter-area mode in [5, 20]. WADC should
be located on the generator which has larger geometric
0 2 4 6 8 10
-5
0
5
10
Time (sec)
Rotorangleδ
13
(deg)
Without WADC
Conventional WADC
Adaptive WADC
0 2 4 6 8 10
-1
-0.5
0
0.5
1
x 10
-3
Time (sec)
Rotorspeedω
13
(pu)
Without WADC
Conventional WADC
Adaptive WADC
Fig. 7. Responses to three-phase-to-ground (Ptie=50MW)
0 2 4 6 8 10
15
20
25
30
Time (sec)
Rotorangleδ
13
(deg)
Without WADC
Conventional WADC
Adaptive WADC
0 2 4 6 8 10
-1
-0.5
0
0.5
1
1.5
x 10
-3
Time (sec)
Rotorspeedω
13
(pu)
Without WADC
Conventional WADC
Adaptive WADC
Fig. 8. Responses to three-phase-to-ground with 80ms time
delay
0 2 4 6 8 10
20
22
24
26
28
30
Time (sec)
Rotorangleδ
13
(deg)
Without WADC
Adaptive WADC
0 2 4 6 8 10
-1
-0.5
0
0.5
1
x 10
-3
Time (sec)
Rotorspeedω
13
(pu)
Without WADC
Adaptive WADC
Fig. 9. Responses to three-phase-to-ground fault with 120
ms time delay

748
controllability with respect to the mode concerned, while
smaller geometric controllability with respect to other
modes in order to reduce the effect on other modes.
Therefore, G4 is selected as controller location and
deviation of P3-18 is chosen as the wide-area feedback
signal for the proposed WADC. In this case, 0.1 is the
suitable scaling number according to the value used in the
simulation. Moreover, a washout filter is added to
eliminate constant deviation of P3-18 when the operating
condition of system is changed.
The order of the linear model is chosen as: na=7, nb=7.
The following parameters need to be specified for the
proposed adaptive WADC: the prediction horizon N, the
control horizon Nu, the weighting sequence r, and the
sampling period Ts. As similar with the two-area test
system, the proposed adaptive WADC of the New England
test system, desired response can be achieved by setting
N=25, Nu=12, r=0.3, Ts=100ms, Σ0=0. 2, T=10, γ=0.04. For
comparison purpose, the performances of the conventional
WADC proposed in [3], whose parameters can be found in
Appendix, are also provided.
5.2 Simulation and analysis
Simulation studies are carried out based on detailed
nonlinear model to verify the effectiveness of the proposed
adaptive WADC under a wide range of operating
conditions. However, only a few typical case results are
given in this paper due to the space restriction.
A three-phase-to-ground fault occurs at the end terminal
of line 3-4 near bus 3 at t = 0.5s, followed by outage of
faulty transmission line 3-4 at t = 0.6s, the responses of the
active power P16-17 and P3-18 are shown in Fig. 11. It reveals
that the proposed adaptive WADC provides slightly better
damping performances than the conventional WADC under
this situation.
For a larger disturbances, a three-phase-to-ground fault
occurs at the end terminal of line 15-16 near bus 15 at t =
0.5s, followed by outage of faulty tie-line 15-16 at t = 0.6s,
the responses of the active power P16-17 and P3-18 are shown
in Fig. 12. It is observed that the proposed adaptive WADC
effectively damps the power oscillations, while the
conventional WADC cannot maintain the whole system
stability due to the large change of operation condition
caused by the outage of tie-line 15-16. Moreover, the
identified parameters of the prediction model (1) are shown
Fig. 10. The New England 10-machine 39-bus system
0 5 10 15 20
-100
0
100
200
300
400
Time (sec)
ActivePowerP16-17
(MW)
Without WADC
Conventional WADC
Adaptive WADC
0 5 10 15 20
-200
-100
0
100
200
300
Time (sec)ActivePowerP3-18
(MW)
Without WADC
Conventional WADC
Adaptive WADC
Fig. 11. System responses to three-fault-to-ground fault
under Scenario I (Outage of fault line 3-4)
0 5 10 15 20
0
200
400
600
800
Time (sec)
ActivePowerP16-17
(MW)
Without WADC
Conventional WADC
Adaptive WADC
0 5 10 15 20
-400
-200
0
200
Time (sec)
ActivePowerP3-18
(MW)
Without WADC
Conventional WADC
Adaptive WADC
under Scenario II (Outage of fault tie-line 15-16)

749
in Fig. 13. It shows that the identified parameters update
fast enough to track the dynamic of the power system and
then converge to a new operating condition.
To test the robustness of the proposed WADC to time
delays, system responses to fault scenario I (Outage of
fault line 3-4) with 100ms are shown in Fig. 14. It can be
observed that the conventional WADC can not maintain the
stability of the whole system when the time delay reaches
100ms, while the proposed adaptive WADC can provide
satisfactory damping performance. However, in
comparison with the situation without time delay, the
damping performances provided by adaptive WADC under
100ms time delay decreases slightly.
6. Conclusion
An adaptive wide-area damping controller based on
generalized predictive control and model identification is
proposed in this paper. A parameter identification
algorithm based on recursive least-squares algorithm with a
varying forgetting factor is applied to identify system
prediction model online. The validity and effectiveness
of the proposed adaptive WADC is evaluated by simulation
studies on a two-area four-machine power system and
the New England 10-machine 39-bus power system,
respectively. Simulation results are compared with those of
the conventional WADC and without WADC. The
comparison results show that the performances of the
adaptive WADC to damp the inter-area oscillation is
better than those of the conventional WADC under a wide
range of operating conditions and different disturbances.
Moreover, when the time delay existing in wide-area signal
is considered, the proposed adaptive WADC is more
effective to retain the stability of power system than the
conventional WADC.
Acknowledgements
This work was supported by the National Natural
Science Foundation of China (51177057, 51207063), and
the National High Technology Research and Development
of China (863 Program) (2011AA05A119).
Appendix
The transfer functions of the PSSs of G1 and G3 of two-
area four-machine power system:
1 3
10 1 0.05 1 3.0
( ) ( ) 30
1 10 1 0.03 1 5.4
PSS PSS
s s s
H s H s
s s s
+ +  
= =   + + +  
The transfer function of the conventional WADC for
two-area four-machine power system:
2
10 1 0.324
( ) 26
1 10 1 0.212
WADC
s s
H s
s s
+ 
=  + + 
The transfer function of the conventional WADC for the
0 2 4 6 8 10
-1
-0.5
0
0.5
Time (sec)
a
a1
a2
a3
a4
a5
a6
a7
0 2 4 6 8 10
-0.2
-0.1
0
0.1
0.2
Time (sec)
b
b0
b1
b2
b3
b4
b5
b6
b7
Fig. 13. The Variations of the identified parameters
0 5 10 15 20
-100
0
100
200
300
400
Time (sec)
ActivePowerP16-17
(MW)
Without WADC
Conventional WADC
Adaptive WADC
0 5 10 15 20
-200
-100
0
100
200
Time (sec)
ActivePowerP3-18
(MW)
Without WADC
Conventional WADC
Adaptive WADC
with 100ms time delays under Scenario I (Outage
of fault line 3-4)

750
New England 10-machine 39-bus power system:
10 1 0.
( )
1 10 1 0.
3
WADC
s 6280s
H s 0.1
s 1025s
+ 
=  + + 
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Wei Yao He received the B.Sc. degree
and the Ph.D. degree in electrical
engineering from Huazhong University
of Science and Technology (HUST),
Wuhan, China, in 2004 and 2010,
respectively. Subsequently, he worked
as a Postdoctoral Researcher in De-
partment of Electrical Engineering,
HUST, from 2010 to 2012. He was a Visiting Student in the
Department of Electrical Engineering & Electronics, The
University of Liverpool, UK, from June 2008 to May 2009.
Currently, he is a Lecturer in the College of Electrical and

751
Electronics Engineering, HUST. His research interests
include power system stability analysis and control.
L. Jiang He received the B.Sc. and
M.Sc. degrees in electrical engineering
from Huazhong University of Science
and Technology (HUST), China, in
1992 and 1996, respectively; and the
Ph.D. degree from The University of
Liverpool, UK, in 2001. Currently, he
is a Senior Lecturer in the Department
of Electrical Engineering & Electronics, The University of
Liverpool, UK. His current research interests are control
and analysis of power system, smart grid and renewable
energy.
Jiakun Fang He received the Ph.D.
degree in electrical engineering from
Huazhong University of Science and
Technology (HUST), Wuhan, China in
2012. Currently, he is working as a
Postdoctoral Researcher in Department
of Energy Technology, Aalborg Uni-
versity, Denmark. His research in-
terests include power system dynamic stability control and
power grid complexity analysis.
Jinyu Wen He received his B.Eng. and
Ph.D. degrees in electrical engineering
from Huazhong University of Science
and Technology (HUST), Wuhan,
China, in 1992 and 1998, respectively.
He was a visiting student from 1996 to
1997, and Research Fellow from 2002
to 2003 at the University of Liverpool,
UK. In 2003, he joined the HUST, where he presently
serves as professor. His current research interests include
smart grid, renewable energy, energy storage, FACTS,
HVDC, and power system operation and control.
Shaorong Wang He graduated from
the Zhejiang University, Hangzhou,
China in 1984 and received his Master
of Engineering Degree from the North
China Electric Power University,
Baoding, China in 1990. He earned his
Ph.D. from the Huazhong University of
Science and Technology (HUST),
Wuhan, China in 2004. All three degrees are in the field of
Electrical Engineering. Currently, he is a full professor at
the HUST. His research interests are power system control
and stability analysis.

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