11-E-PSS-1993
Simultaneous Coordinated Tuning of UPFC and
Multi-Input PSS for Damping of Power System Oscillations
Yashar Hashemi , Javad Morsali , Rasool Kazemzadeh
Mohammad Reza Azizian , Ahmad Sadeghi Yazdankhah
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Sahand University of Technology
Iran
Keywords: Power oscillation damping, Simultaneous coordinated designing,
Unified power flow controller (UPFC), Multi-input power system stabilizer (MPSS)
performance than the conventional single
input PSS and UPFC coordination.
Abstract
The objective of this work is to coordinated
design controllers that will enhance damping
of power system oscillations. With presence
of FACTS device as UPFC Two specific
classes of PSS have been investigated, the
first one is a conventional power system
stabilizer (CPSS) and the second is Multiinput power system stabilizer (MPSS). Since
uncoordinated CPSS (or MPSS) and UPFC
damping controller may cause unwanted
interactions, it is necessary to simultaneous
coordinated tune the controller parameters.
The problem of coordinated design is
formulated as an optimization problem and
particle swarm optimization algorithm is
employed to search for optimal parameters of
controllers. A Multi-input signal PSS is
introduced to maintain the robustness of
control performance in a wide range of
oscillation frequency. Finally in a system
having a UPFC a comparative analysis
between results from application of the MPSS
and CPSS is presented. The eigenvalue
analysis and the time domain simulation
results show that the multi-input PSS and
UPFC coordination provides a better
1. Introduction
Power systems contain many modes of
oscillation as a consequence of interactions of
its components, as for example one generator
rotor swinging relative to another. With the
lack of sufficient damping oscillations
resulting from small signal instability can be
of increasing amplitude which could lead to
power transfer restrictions and in extreme
cases power system collapse. The frequency
of these oscillations is usually in the range of
0.2-3 Hz [1]. There are two electromechanical
modes of oscillations have reported [2]: a)
local mode, with a frequency 0.8-3 Hz, which
is related to oscillation in a single generator or
a group of generators in the same area
oscillate against each other; and b) inter area
mode, with frequency 0.2-0.8 Hz, in which
the units in one area oscillate against those in
other area.
Traditionally, the damping of low frequency
oscillations is provided by installing a Power
System Stabilizer (PSS) which uses local
measurements such as rotor speed or active
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Simultaneous Coordinated Tuning of UPFC and Multi-Input PSS for Damping of Power System Oscillations
26th International Power System Conference
static phase shifting transformer using
stochastic optimal control theory. Edris [9]
proposed a simple control algorithm based on
equal area criterion. Jiang et al [10] proposed
a static phase shifting transformer control
technique based on nonlinear variable
structure control theory. In the literature,
SVCs have been applied of a synchronous
machine. Wang and Swift [11] used damping
torque coefficients approach to investigate the
SVC damping of a SMIB system on the basic
of Phillips-Heffron model. It was shown that
the SVC damping control provides the power
system with negative damping when it
operates at a lower load condition than the
deal point, the point at which SVC control
produces zero damping effect. Robust SVC
controller based on H ∞ , structured singular
value μ , and quantitative feedback theory
QFT also have been presented to enhance
system damping [12-14].
Research on the possible damping effect of
UPFC, the most versatile FACTS devices, has
also been conducted during the recent years.
Besides the works in [15,16]. Dong, Zhang
and Crow [17] proposed a PI based approach
for the dynamic control of UPFC. In [18], a
fuzzy logic based damping controller for
UPFC was developed, and the effectiveness
of this fuzzy controller was demonstrated in
the simulation results of a two area four
machine system.
However, uncoordinated local control of
FACTS devices and PSSs may cause
unwanted interactions that further results in
the system destabilization. To improve overall
system performance, many researches were
made on the coordination among conventional
PSS and FACTS power oscillation damping
(POD) controller [19-22]. Some of these
methods are based on the complex non-linear
simulation [19,20], the others are linear
approaches [21,22].
A comparative analysis between results from
application of the MPSS and CPSS in
coordination with the UPFC as a FACTS
device is presented in this paper. The problem
of robust output feedback controller
coordinated design is formulated as an
power as feedback signals. The PSS method
that is currently widely used is based on the
signal ΔP formula ( ΔP − PSS ) with the
effective power as the input. This method is
applied to suppress the local power
perturbation between generators. For the low
frequency perturbation that occurs between
power systems in wide-area operation,
however there is little system perturbation
information included in the active power, so
ΔP − PSS has little effectiveness. As a
solution to that problem, ΔP + Δω PSS,
which uses the internal frequency or the
rotational speed ( ω ) as well as the active
power is effective for damping low frequency
oscillations, is used. However, ω includes
turbine and generator system axle torsion
fluctuation, so consideration must be given to
the use of a notch filter or other such devices
when this input is used.
Other effective way to damp power system
swings is using Flexible Alternating Current
Transmission Systems (FACTS) which is a
genetic term for a group of technologies that
radically increases the capacity of the
transmission network while maintaining or
improving voltage stability and grid
reliability. This type of damping control is
realized by adding a supplementary
stabilizing signal on the primary control loops
of FACTS devices.
Many approaches have been adopted to
design the FACTS controller. Several
approaches based on modern control theory
have been applied to TCSC controller design.
Chen at al. [3] presented a state feedback
controller for TCSC by using a pole
placement technique. Chang and Chow [4]
developed a time optimal control strategy for
the TCSC where a performance index of time
was minimized. A fuzzy logic controller for a
TCSC was proposed in [5]. Heuristic
optimization
techniques
have
been
implemented to search for the optimum TCSC
based stabilizer parameters for the purpose of
enhancing SMIB system stability [6,7].
A considerable attention has been directed to
realization of various TCPS schemes. Baker
et al [8] developed a control algorithm for
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Simultaneous Coordinated Tuning of UPFC and Multi-Input PSS for Damping of Power System Oscillations
26th International Power System Conference
optimization problem and PSO algorithm is
employed to search for optimal controllers
parameters. Firstly, the system eigenvalues
without controllers and the second with
proposed coordinating is investigated. It is
quite evident that the system stability is
greatly enhanced with the coordinated design
of UPFC and MPSS, as the damping ratio of
the electromechanical mode eigenvalue has
been greatly improved. In this study the
nonlinear time-domain simulation is carried
out to validate the effectiveness of the
proposed controllers. The controllers are
simulated and tested under different operating
conditions.
⎡ mE cos δ EVdc ⎤
− xE ⎤ ⎡iEd ⎤ ⎢
⎥
2
⎢i ⎥ + ⎢ m sin δ V ⎥
⎥
0 ⎦ ⎣ Eq ⎦ ⎢ E
E dc
⎥
2
⎣
⎦
cos
m
δ
V
⎡ B
B dc ⎤
− xB ⎤ ⎡iBd ⎤ ⎢
⎥
2
⎢i ⎥ + ⎢ m sin δ V ⎥
⎥
0 ⎦ ⎣ Bq ⎦ ⎢ B
B dc
⎥
2
⎣
⎦
⎡VEtd ⎤ ⎡ 0
⎢V ⎥ = ⎢
⎣ Etq ⎦ ⎣ xE
⎡VBtd ⎤ ⎡ 0
⎢V ⎥ = ⎢
⎣ Btq ⎦ ⎣ xB
⎡iEd ⎤
sin δ E ]⎢ ⎥ +
⎣iEq ⎦
⎡iBd ⎤
sin δ B ]⎢ ⎥
⎣iBq ⎦
dVdc 3mE
=
[cos δ E
dt
4Cdc
3mB
[cosδ B
4Cdc
(1)
(2)
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The dynamic model of the power system
presented in Fig. 1 is [23]:
δ& = ω0ω
(3)
2.Model of Power System Including UPFC
In this section a power system consisting of a
UPFC is described. Fig. 1 shows a singlemachine infinite-bus (SMIB) system with
UPFC. It is assumed that the UPFC
performance is based on pulse width
modulation (PWM) converter. In Fig.
1 mE , mB and δ E , δ B are the amplitude
modulation ratio and phase angle of reference
voltage of each voltage source converter
respectively. These values are input control
signals of the UPFC. A linearised model of
the power system is used in studying dynamic
studies of power system. In order to consider
the effect of UPFC in damping of low
frequency oscillation (LFO), the dynamic
model of the UPFC is employed, in the
resistance and transient of the transformers of
the UPFC can be ignored. The equations
describing the dynamic performance of the
UPFC can be written as [23]:
Vt it
Pe
Qe
VEt
iB
_
VBt
ω& =
E& q′ =
VSC-E
+
xE
_
Vdc
mE δE
− Eq + E fd
′
Tdo
(5)
(6)
pe = Vtd itd + Vtq itq
(7)
Vt 2 = Vtd2 + Vtq2
(8)
xBB
m sin δ EVdc xBd xdE
(Vb cos δ
Eq′ − E
+
2 xdΣ
xdΣ
xdΣ
mB sin δ BVdc
)
2
m cos δ EVdc xBq xqE
(Vb sin δ +
iEq = E
+
2 xqΣ
xqΣ
+
mB cos δ BVdc
)
2
x
m sin δ BVdc
)+
iBd = − dt (Vb cos δ + B
2
xdΣ
Vb
xBV
iE
(4)
k
−1
E& fd =
E fd + A (Vt 0 − Vt )
TA
TA
iEd =
xB +
xtE
pm − pe − Dω
M
VSC-B
mE sin δ EVdc xdE
x
+ E Eq′
2 xdΣ
xdΣ
iBq = −
mB δB
mE cos δ EVdc xqE
2 xqΣ
mB cos δ BVdc
)
2
Fig. 1: A single machine connected
to infinite bus with UPFC
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−
xqt
xqΣ
(Vb sin δ +
(9)
Simultaneous Coordinated Tuning of UPFC and Multi-Input PSS for Damping of Power System Oscillations
26th International Power System Conference
ΔQe = 2 xq itq Δitq − ΔEq′ itd − Eq′ Δitd + 2 xd′ itd Δitd (17)
By combining and linearising Equations (19), the state variable equations of the power
system equipped with the UPFC can be
represented as :
Thus we can have:
x& = Ax + Bu
+ k14 Δδ E + k15ΔmB + k16 Δδ B
[
u = [Δu
x = Δδ
(10)
ΔVdc ]T
Δω ΔEq′ ΔE fd
ΔmE
pss
⎡ 0
⎢ k
⎢ − 1
⎢ M
⎢ k4
A=⎢ −
M
⎢
⎢ − k A k5
⎢ TA
⎢ k
⎣ 7
ΔQe = k10 Δδ + k11ΔEq′ + k12 Δvdc + k13ΔmE
Δδ E
ωb
D
M
−
2.1 UPFC Damping Controller
ΔmB Δδ B ]
0
k
− 2
M
k
− 3
′
Tdo
k k
− A 6
TA
k8
T
0
0
(18)
The damping controller is designed to
produce an electrical torque in phase with the
speed deviation according to phase
compensation method. The four control
parameters of the UPFC ( mE , mB and δ E ,
δ B ) can be modulated in order to produce the
0 ⎤
k pd ⎥
−
⎥
M ⎥
kqd ⎥
−
′ ⎥
Tdo
⎥
k Ak pd ⎥
−
TA ⎥
− k9 ⎥⎦
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⎡0
⎢
⎢0
⎢
B=⎢ 0
⎢
⎢k
⎢ A
⎢ TA
⎣⎢ 0
−
0
0
0
0
k qe
M
k qe
−
′
Tdo
k A kve
−
TA
kce
−
0
k qδe
M
k qδe
−
′
Tdo
k A kvδe
−
TA
kcδe
1
′
Tdo
1
−
TA
0
−
0
k pb
M
k qb
−
′
Tdo
k A kvb
−
TA
kcb
damping torque. the structure of UPFC based
damping controller, as shown in Fig. 2, is
similar to the PSS controllers. It consists of
gain block with gain G, a signal washout
block and two-stage phase compensation
block with time constant T1, T2, T3 and T4.
The time constant Td represents the finite
delay caused by the firing controls and the
natural response of the UPFC.
0 ⎤
k pδb ⎥
−
M ⎥
k qδd ⎥
⎥
−
′ ⎥
Tdo
k k ⎥
− A vδb ⎥
TA ⎥
kcδb ⎦⎥
Δpe = k1Δδ + k 2 ΔEq′ + k qd ΔVdc + k qe ΔmE
speed
deviation
(11)
+ k qδe Δδ E + k qb ΔmB + k qδb Δδ B
ΔVt = k5 Δδ + k6 ΔEq′ + kvd ΔVdc + kve ΔmE
⎛ sTω
G⎜⎜
⎝ 1 + sTω
Also in power system of Fig. 1 can be
written:
(14)
Vtd = xqitq
(15)
Substituting (14) and (15) into (13) we obtain:
Qe = ( xq itq )itq − ( Eq′ − xd′ itd )itd
⎞⎛ 1 + sT1
⎟⎜
⎟⎜ 1 + sT
2
⎠⎝
⎞⎛ 1 + sT3
⎟⎟⎜⎜
⎠⎝ 1 + sT4
⎞
⎟⎟
⎠
+
3.Multi-Input Power System Stabilizer
The dynamic stability of a system can be
improved by providing suitably tuned power
system stabilizers on selected generators to
provide damping to critical oscillatory modes.
Suitably tuned power system stabilizers
(PSS), will introduce a component of
electrical torque in phase with generator rotor
speed deviations resulting in damping of low
frequency power oscillations in which the
generators are participating. The input to
stabilizer signal may be one of the locally
available signals such as changes in rotor
speed, rotor frequency, accelerating power or
any other suitable signal. This stabilizing
signal is compensated for phase and gain to
result in adequate component of electrical
And ΔmE , ΔmB , Δδ E and
Δδ B are
the
deviation of input control signals of the UPFC
and explained previously.
Reactive power of system expressed in d-q
coordinates are obtained as:
Qe = Vtd itq − Vtq itd
(13)
Vtq = Eq′ − xd′ itd
⎞⎛ 1
⎟⎜
⎟⎜ 1 + sT
d
⎠⎝
U
Fig. 2: structure of UPFC based
damping controller
(12)
+ kvδE Δδ E + kvb ΔmB + kvδb Δδ B
Uref
ks
1 + sTs
+
(16)
Linearising the equation above we have:
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Simultaneous Coordinated Tuning of UPFC and Multi-Input PSS for Damping of Power System Oscillations
26th International Power System Conference
torque that results in damping of rotor
oscillations and thereby enhance power
transmission and generation capabilities.
As a generator exciter control method for
increasing power stability, ΔP − PSS
is
widely used. This method is applied to
suppress the local power perturbation between
generators.
For
the
low
frequency
perturbation that occurs between power
systems in wide-area operation, however there
is little system perturbation information
included in the active power, so ΔP − PSS
has little effectiveness. As a solution to that
problem, ΔP + Δω PSS, which uses the
internal frequency or the rotational speed ( ω )
as well as the active power is effective for low
frequencies, is used [24,25]. In multi input
PSS, a circuit for improving transitional
stability is added to achieve an excellent
effect for both transitional stability and
operating stability. In addition we were able
to confirm that almost the same effect can
included if voltage of the generator is used in
place of the ω signal. The frequency signal
can be detected directly by calculation from
the voltage and current. Thus there is no need
for equipment that has an electromagnetic
sensor, and multi-input PSS can be
implemented even in hydroelectric generators,
where the installation of an exciter pick-up is
difficult.
The P+ω input PSS is shown in Fig. 3. P and
ω are generator local signals which are
selected as the PSS input ( Δu PSS in Fig. 3). If
P input PSS and ω input PSS are optimized
independently and are combined for use as
P+ω input PSS, an unexpected unstable
oscillation mode may occur. In this paper, the
parameters of the P+ω input PSS with
parameters of the UPFC controller are
optimized all together.
4.Function Optimization
Optimization is defined as finding the best
possible solution to a problem given a set of
constraints. Numerous applications of
evolutionary algorithms can be found
especially in electric power systems [26]. The
flexibility of evolutionary algorithms to
address optimization problem using any
reasonable representation and objective
functions gives an advantage over classical
optimization procedures. A control structure
with a number of adjustable gains and time
constants, mathematical model of the system
and objective functions is required, while the
aim is to obtain the best values of controllers
gains and time constants that optimize
objective function subject to system
constraints.
Optimization
problem
is
formulated as follow:
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ΔP
G
1 + sTd
sTω
1 + sTω
1 + sT1
1 + sT2
1 + sT3
1 + sT4
+
Δω
G
1 + sTd
sTω
1 + sTω
1 + sT1
1 + sT2
Min f (Gm , Tn ) = af1 + bf 2
(19)
Gm min ≤ Gm ≤ Gm max
s.t
Tn min ≤ Tn ≤ Tn max
Where
f1 =
N
∑ ∑ (ξ0 − ξi, j )2 and
j =1 ξ i ≤ξ 0
f2 =
N
∑ ∑ (σ 0 − σ i, j )2
(20)
j =1 σ i ≥σ 0
Where σ i, j , ξi, j are the real part and damping
ratio of the ith eigenvalue of the jth operating
point. σ 0 , ξ 0 are the desired minimum real
part and damping ratio which is to be
achieved. Gm , Tn are the optimization
parameter and f (Gm , Tn ) is objective function
where m,n are the total number of gains and
time constants. The values of a and b are the
weight factors for f1, f2 with regard to optimal
point. In this article σ 0 , ξ 0 , a and b is chosen 2, 1, 5 and 10 sequentially. N is the total
number of operating points for which the
optimization is carried out.
Evolutionary algorithm can be applied to any
problem that can be formulated as function
optimization (19). It requires data structure to
represents solutions, performance index to
evaluate the solutions, and variations operator
to provide new solutions from the old ones.
Advantage of the evolutionary algorithm
comes from the ability in automating and
Δu PSS
1 + sT3
1 + sT4
Fig. 3: Multi-input PSS
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Simultaneous Coordinated Tuning of UPFC and Multi-Input PSS for Damping of Power System Oscillations
26th International Power System Conference
problem solving routines. Genetic algorithm
(GA) and PSO are both considered as
evolutionary algorithm. Genetic algorithm is a
search technique to find approximate solution
to optimization technique. The algorithm uses
techniques inspired by evolutionary biology
such as mutation, cross over, natural
selection. Despite obtaining good solutions in
hard search spaces, still have some
disadvantages such as tendency to converge
toward local optima rather than global
optimum of the problem, and hard to
implement on dynamic data sets. PSO is
another evolutionary technique that is not
largely affected by nonlinearity and the size
of the problem. The technique can easily
converge to optimal solution that can be
executed in search in solution space for
solving multi-objective optimization problems
as formulated in (19). Large number of
evolutionary
algorithms
applications,
especially for parameter estimation and tuning
of control gains can be found in electric
power system literature [27], [28]. Among all
these techniques PSO has gained increased
attention. Some advantages of PSO over other
optimization techniques are:
4.1 Particle Swarm Optimization Algorithm
Particle Swarm Optimization is an
evolutionary algorithm developed by James
Kennedy and Russell Eberhart [31]. The
original objective of their research was to
mathematically simulate behavior of bird
flocks. The search algorithm is based on
cooperation and competition among the
population members. The objective is to find
optimal regions of a complex search space
through interaction of individuals in a
population of particles. Each individual of the
population has an adaptable velocity (position
change), according to which it moves in the
search space. Moreover, each individual has a
memory remembering the best position of the
search space it has ever visited. Its movement
is an aggregated acceleration toward its best
previously visited position. Another best
value that is tracked by PSO is the best value
obtained so far by any particle in the
neighborhood of the particle. The main idea is
to change the position and velocity of each
particle toward global best (gbest) location at
each time step. As a result, after number of
iterations the particles among populations are
found to have accumulated around one or
more of the optima and tends to find the
global optima among all. Given the size of the
problem and the system complexities, the
solution is assumed to lie in the range of an
N-dimensional space, where each potential
solution is called a particle. Particle has a
position and a velocity and moves in the
search space toward an optimal solution.
Steps for PSO algorithm is given in following
as shown in Fig. 4:
1. Initialize each particle with random
solution in problem domain (initialization)
2. For each particle evaluate the objective
function
3. For each particle, calculate the objective
function and compare it with its best
particle (Pbest). If the current value of the
objective function is better than the Pbest
then set the value as the Pbest and the
current position of the particle.
4. Among all best particles, identify the
particle that has the best objective function
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• It has the ability to escape local minima
• It has less parameter to adjust, unlike
many others
• It is easy for computer implementation
and coding
• It is easy to implement and program
with mathematical and logic operations
• It does not require a good initial
solution to start the iteration
• It can be used with almost any realistic
objective functions i.e. continuous or
noncontinuous, convex or non-convex
• It has more effective memory capability
(local and neighboring best)
A detailed survey on PSO applications to
large scale power systems is covered by
Alrashidi and El-Hawary [29]. Recently a
comprehensive overview of PSO techniques
and different applications in electric power
systems are covered by del Valle et. al [30].
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Simultaneous Coordinated Tuning of UPFC and Multi-Input PSS for Damping of Power System Oscillations
26th International Power System Conference
global searches and hence requiring less
iteration for the algorithm to converge.
6. Repeat steps 2−5 until stopping criteria are
met. These criteria are maximum iteration and
minimum error criteria.
value. The value of the objective function
is assigned as gbest with its new position.
start
Select parameters of PSO: N, C1, C2, C, w
5.Controllability Measure
SVD is employed to measure the
controllability of the EM mode from each of
the five inputs: u pss , m E , δ E , m B , and δ B .
Generate the randomly positions and velocities of particles
Initialize Pbest with a copy of the position for particle, determine gbest
The minimum singular value, σ min is
estimated over a wide range of operating
conditions. For SVD analysis, Pe ranges from
0.05 to 1.4 pu and Qe = [-0.4, 0, 0.4]. At each
loading condition, the system model is
linearised, the EM mode is identified, and the
SVD-based controllability measure is
implemented.
For comparison purposes, the minimum
singular value for all inputs at Qe = -0.4, 0.0
and 0.4 pu is shown in Figs. 5–7, respectively.
From these figures, the following can be
noticed:
Update velocities and positions according to (21), (22)
Evaluate the fitness of each particle
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Update Pbest and gbest
No
Satisfystoping criterion
Yes
Optimal value of the controller parameters
End
Fig. 4: Flowchart of the PSO technique
5. For each particle update the velocity vector
and then the position vector according to:
(
)
vik +1 = ωvik + c1r1 Pidk − xidk +
(
c2 r2 Pgdk
−
k
xgd
)
xidk +1 = xidk + cvidk +
•
(21)
•
(22)
•
The
ith
particle
is
represented
by X i = ( xi1 , xi 2 ,K, xiD ) , value of the fitness
for particle i (Pbest) is stored as
Pi = ( pi1 , pi 2 ,K, piD ) and velocity of particle i
is presented as Vi = (vi1, vi 2 ,K, viD ) . Where,
Pid and Pgd are pbest and gbest . The positive
constants c1 and c2 are the cognitive and
social components that are the acceleration
constants responsible for varying the particle
velocity towards pbest and gbest , respectively.
Variables r1(.) and r2(.) are two random
functions based on uniform probability
distribution functions in the range. The inertia
weight ω is responsible for dynamically
adjusting the velocity of the particles, so it is
responsible for balancing between local and
•
EM mode controllability via δ E is
always higher than that of any other
input.
The capabilities of δ E and m B to
control the EM mode is higher than
that of PSS.
The EM mode is more controllable
with PSS than with either m E or δ B .
All control signals except m B and δ E
at Qe = 0 suffer from low
controllability to EM mode at low
loading conditions.
Fig. 4: Minimum singular value
with all stabilizers at Qe = -0.4
7
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Simultaneous Coordinated Tuning of UPFC and Multi-Input PSS for Damping of Power System Oscillations
26th International Power System Conference
Pole-Zero Map
6
Imaginary Axis
4
0.998
0.996
0.993
0.986
0.965
0.86
0.999
2 1
100
0 1
80
60
40
20
-2 1
-4
0.999
0.998
-6
-120
-100
0.996
-80
0.993
-60
Real Axis
0.986
-40
0.965
0.86
-20
0
Fig. 7: Dominant eigenvalues of the power
system in nominal loading condition
with UPFC & MPSS controllers
Fig. 5: Minimum singular value
with all stabilizers at Qe = 0.0
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Pole-Zero Map
10
0.996
0.99
0.98
0.96
0.91
0.7
0.998
Imaginary Axis
5
1
100
0
80
60
40
20
1
-5
0.998
0.996
-10
-120
0.99
-100
Fig. 6: Minimum singular value
with all stabilizers at Qe = 0.4
-80
0.98
-60
Real Axis
0.96
-40
0.91
0.7
-20
0
Fig. 8: Dominant eigenvalues of the power
system in heavy loading condition
with UPFC & MPSS controllers
6. Simulation Results
6.1 Dominant Eigenvalues
The dominant eigenvalues of the test system
with UPFC & MPSS controllers are shown in
Figures 7-9. The system data and detailed
controllers parameters are given in the
Appendix and Table 2 sequentially. Also The
system eigenvalues without and with the
proposed stabilizers with ξ ⟨1 are given in
Table 3 at the three operating points, nominal,
light, heavy given in Table 1. This table
clearly demonstrates the effectiveness of the
MPSS coordination with UPFC in enhancing
system stability. After the coordinated tuning
of
UPFC
and
MPSS
controllers,
electromechanical modes of oscillations are
well damped. The results show the
improvement in damping of overall power
oscillations in the system as all the damping
ratios are more than 50%.
Pole-Zero Map
10
0.996
0.99
0.98
0.96
0.91
0.7
0.998
Imaginary Axis
5
1
100
0
80
60
40
20
1
-5
0.998
0.996
-10
-120
0.99
-100
-80
0.98
-60
Real Axis
0.96
-40
0.91
0.7
-20
0
Fig. 9: Dominant eigenvalues of the power
system in light loading condition
with UPFC & MPSS controllers
Table II: the optimal parameter and
settings of the proposed controllers
controller
parameters
Table I: Loading conditions
Loading
Pe (pu)
Qe (pu)
Nominal
0.8
0.167
Heavy
1.2
0.4
Light
0.2
0.01
G
T1
T2
T3
T4
8
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coordinated
design
CPSS
UPFC
100
1.5
1.0073
1.3639
1.5
7.1440
1.5
0.8183
1.5
1.0924
coordinated design
MPSS
( ω input and P
input sequential)
0.2690
0.1505
0.0646
1.5
0.05
1.5
1.5
1.5
0.05
1.5
UPFC
-17.5212
0.05
1.0568
1.5
0.9054
Simultaneous Coordinated Tuning of UPFC and Multi-Input PSS for Damping of Power System Oscillations
26th International Power System Conference
Table III: eigenvalues and damping ratios of power system
before and after the coordinated tuning with ξ ⟨1
without PSS,MPSS
and UPFC
CPSS & UPFC
nominal
eigenvalue
damping
ratio
0.0773±i6.5648
-0.0118
-.1795±i0.6643
0.2609
-2±i2.65
0.6019
-1.87±i2.13
0.6596
-1.77±i1.37
0.7922
-1.264±i5.25
-6.6±i1.55
-0.95±i0.11
MPSS & UPFC
0.9234
0.9736
0.9936
heavy
eigenvalue
damping
ratio
0.0775±i6.3711
-0.0122
-.3113±i0.8209
0.3546
-2.74±i4.06
0.5593
-1.5±i0.84
0.8715
-1.18±i0.53
0.9115
-1.07±i0.36
0.9477
-9.45±i6.54
0.8221
-3.15±i1.70
0.8804
-11.93±i3.41
0.9614
-0.95±i0.11
0.9936
light
eigenvalue
0.0713±i6.5243
damping
ratio
-0.0109
-1.99±i5.73
-1.59±i1.1
0.3277
0.8223
-5.35±i5.62
-4.63±i3.05
0.79±i0.49
0.6896
0.8355
0.8512
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Speed deviation
Speed deviation
-3
0.02
20
Speed deviation
0.03
(b)
(a)
CPSS & UPFC
x 10
15
0.01
(c)
CPSS & UPFC
10
MPSS & UPFC
MPSS & UPFC
5
0
2
4
6
-5
10 0
8
MPSS & UPFC
0.01
0
0
-0.01
0
CPSS & UPFC
0.02
2
Time (sec)
4
6
-0.01
10
0
8
2
4
Time (sec)
6
8
10
Time (sec)
Fig. 10: Dynamic responses for speed deviatin at
(a) nominal (b) heavy (c) light loading condition; Solid (MPSS & UPFC), Dashed (CPSS & UPFC)
Power deviation
0.2
0.4
CPSS & UPFC
0.2
CPSS & UPFC
(a)
0.2
MPSS & UPFC
0.1
0
-0.1
0
Power deviation
Power deviation
0.3
2
4
6
8
10
CPSS & UPFC
(b)
0.1
MPSS & UPFC
0
0
-0.2
-0.1
-0.4
0
2
Time (sec)
4
6
8
10
-0.2
0
(c)
MPSS & UPFC
2
4
6
8
10
Time (sec)
Time (sec)
Fig. 11: Dynamic responses for power deviation at
(a) nominal (b) heavy (c) light loading condition; Solid (MPSS & UPFC), Dashed (CPSS & UPFC)
6.3 Non-Linear Simulation Results
Conclusion
The power system stability enhancement via
multi-input PSS and FACTS-based stabilizers
when applied simultaneous coordinated is
discussed and investigated for a SMIB
system. Also a comparative performance
study of a single input CPSS and a multiinput PSS coordination with UPFC is carried
out to appreciate the effectiveness of MPSS in
contrast to CPSS. The multi-input uses two
state-space variables, rotor speed deviation
and active power deviation. For the proposed
controllers design problem, an objective
function to minimize the power system
In order to illustrate the performance of the
coordinated tuning result, simulation studies
are carried out as shown in Fig. 12 and a
three-phase short circuit of 100 ms duration is
simulated at infinite bus in the test system.
While the fault occurs at the infinite bus, the
original system is restored upon the clearance
of the fault. Figures 10, 11 show the speed
deviation and power deviation for three
loading conditions. It can be readily seen that
the coordinated designing of the MPSS and
UPFC are more effective than the coordinated
designing of the CPSS and UPFC in terms of
reduction of overshoot and setting time.
9
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Simultaneous Coordinated Tuning of UPFC and Multi-Input PSS for Damping of Power System Oscillations
26th International Power System Conference
oscillation is used. Then, particle swarm
optimization is employed to optimally and
coordinately tune the controller parameters.
Simulation results are presented for various
loading conditions and disturbances to show
the effectiveness of the proposed coordinated
design approach. The proposed controllers are
found to be robust to fault in operating
conditions
and
generate
appropriate
stabilizing output control signals to improve
stability.
ω ω ωdt δ
0∫
itq
xq itq
Eq′
itd
Vtd
Pm
Vtq
Eq′ − xd′ itd
Vtq
itq
Vtd
itd
Vtq itq + Vtd itd
+
Pe -
ω
∫
+
−
D
M
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Eq′
Vb
Vdc
mE
δE
Eqn. 9
mB
iEd
iBd
iEq
iBq
iEd + iBd
iEq + iBq
itd
Eq′
itd
itq
Vtq
Vtd
δB
iEd
iEq
iBd
iBq
mE
δE
mB
δB
Vtd2
E fd
Eq′ + (xd − xd′ )itd
+ Vtq2
Vt 0
Vt
Eq
∫
kA
(Vt 0 − Vt )
TA
− Eq + E fd
′
Tdo
∫
+
−
3mE
[cos δ E
4Cdc
+
3mB
[cosδ B
4Cdc
⎡iEd ⎤
sin δ E ]⎢ ⎥
⎣iEq ⎦
⎡iBd ⎤
sin δ B ]⎢ ⎥
⎣iBq ⎦
∫
dt
Eq′
E fd
1
TA
Vdc
Fig. 12: nonlinear simulation of test system
Appendix
SMIB system data:
′ : 8.0 sec ; D = 0;
Machine: H = 6.5; Tdo
xd′ = 0.3 ; xq = 0.6 ; xd = 1.8 ; freq = 60; v =
References
1.05;
Exciter: KA = 50; TA = 0.05; Efd-max = 7.3; Efdmin = -7.3;
PSS: uPSS-max = 0.2; uPSS-min = -0.2; Tw = 5; Td
= 0.01; Ti-min = 0.05; Ti-max = 1.5; Kmin = -100;
Kmax = 100; i = 1,2,3,4;
Transmission Line: xtE = 0.1; xBV = 0.6;
UPFC: xE = 0.1; xB = 0.1; Ks = 1; Ts = 0.05;
CDC = 3; Vdc = 2; mE-min = 0; mE-max = 2; mBmin = 0; mB-min = 0; Tw = 5; Td = 0.01; Ti-min =
0.05; Ti-max = 1.5; Kmin = -100; Kmax = 100; i =
1,2,3,4;
[3] Chen. X, Pahalawaththa. N, Annakkage. U and Kumble.
C, “Controlled Series Compensation for Improving the
Stability of Multimachine Power Systems," IEE Proc.,
Pt. C, Vol. 142, 1995, pp. 361-366
[1] Kundur. P, “Power System Stability and Control,” New
York: McGraw Hill; 1994.
[2] Rogers. G, “Power System Oscillations,” Kluwer
Academic Publishers, 2000.
[4] Chang. J and Chow. J, "Time Optimal Series Capacitor
Control for Damping Inter-Area Modes in
Interconnected Power Systems," IEEE Trans. PWRS,
Vol. 12, No. 1, 1997, pp. 215-221.
[5] Lie. T, Shrestha. G, and Ghosh. A, "Design and
Application of Fuzzy Logic Control Scheme for
Transient Stability Enhancement in Power System",
Electric Power System Research. 1995, pp, 17-23.
[6] Abido. M. A, “Genetic-Based TCSC Damping
Controller Design for Power System Stability
Enhancement,” Electric Power Engineering, 1999.
10
MatlabSite.com ‫ﻣﺘﻠﺐ ﺳﺎﯾﺖ‬
Simultaneous Coordinated Tuning of UPFC and Multi-Input PSS for Damping of Power System Oscillations
26th International Power System Conference
[20] Lei. X, Lerch. E. N and Povh. D, “Optimization and
Coordination of Damping Controls for Improving
System Dynamic Performance”, IEEE Trans. Power
Systems, vol. 16, August 2001, pp. 473-480
Power Tech Budapest 99. International Conference on ,
29 Aug.-2 Sept. 1999, Page(s): 165
[7] Abido. M. A, “Pole Placement Technique For PSS And
TCSC-Based Stabilizer Design Using Simulated
Annealing,” Electric Power System Research, 22, 2000,
Page(s) 543-554.
[21] Cai. Li-Jun, Erlich. I, “Simultaneous Coordinated
Tuning of PSS and FACTS Damping Controllers in
Large Power Systems,” IEEE Trans on Power Systems,
vol. 20, no. 1, 2005, pp. 294 - 300.
[8] Baker. R, Guth. G, Egli. W and Eglin. O, "Control
Algorithm for a Static Phase Shifting Transformer to
Enhance Transient and Dynamic Stability of Large
Power Systems," IEEE Trans. PAS, Vol. 101, No. 9,
1982, pp. 3532-3542.
[22] Pourbeik. P and Gibbard. M. J, “Simultaneous
Coordination of Power System Stabilizers And FACTS
Device Stabilizers In a Multi-Machine Power System for
Enhancing Dynamic Performance,” IEEE Trans. Power
Systems, vol. 13, no. 2, 1998, pp. 473–479.
[9] Edris. A, "Enhancement of First-Swing Stability Using a
High-Speed Phase Shifter," IEEE Trans. PWRS, Vol. 6,
No. 3, 1991, pp. 1113-1118.
[23] Wang. H.F, “Damping Function of Unified Power Flow
Controller,” IEE Proceedings-Generation, Transmission
and Distribution, Vol. 146, no. 1, Jan 1999, pp. 81 – 87.
[10] Jiang. F, Choi. S. S and Shrestha. G, "Power System
Stability Enhancement Using Static Phase Shifter," IEEE
Trans. PWRS, Vol. 12, No. 1, 1997, pp. 207-214.
‫ﻣ‬
‫ﺘ‬
‫ﻠ‬
‫ﺐ‬
‫ﺳ‬
‫ﺎ‬
‫ﯾ‬
‫ﺖ‬
m
o
c
.
e
t
i
S
b
a
l
t
a
M
[24] Kamva. I, Grondin. R, Trudel. G, “IEEE PSS2B versus
PSS4B: The Limits of Performance of Modern Power
System Stabilizers,” IEEE Transactions on Power
Systems, Vol. 20, No. 2, MAY 2005, pp 1360-1366.
[11] Wang. H. F and Swift. F. J, "Capability of the Static VAr
Compensator in Damping Power System Oscillations,"
IEE Proc. Genet. Transm. Distrib, Vol. 143, No. 4, 1996,
pp. 353-358.
[25] Yoshomira. K, Uchida. N, “Multi input PSS
Optimization Method For Practical Use By Considering
Several Operating Conditions,”
[12] Wang. Li, Tsai. Ming-Hsin, “Design of A H∞ Static
VAR Controller for the Damping of Generator
Oscillations,” Power System Technology, 1998.
Proceedings. POWERCON '98. 1998 International
Conference on, Volume: 2, 18-21 Aug. 1998, Page(s):
785 -789. vol. 2.
[26] Alves da Silva. A. P, Abr˜ao. P. J, “Applications of
Evolutionary Computation in Electric Power Systems,”
Proceedings of the 2002 Congress on Evolutionary
Computation CEC, Vol. 2, 2002, pp. 1057-1062.
[13] Parviani. M and Iravani. M. R, “Optimal Robust Control
Design of Static VAR Compensators,” IEEE Proc –
Gener. Trtans. Distrib, Volume 145, No. 3, 1998, pp:
301-307.
[27] Abdel-Magid. Y. L, Abido. M. A and Mantaway, A. H,
“Robust Tuning of Power System Stabilizers in
Multimachine Power Systems,” IEEE Transaction on
Power Systems, Vol. 15, No. 2, 2000, pp. 735-740.
[14] Rao. S. P and Sen. I, “A QTF-Based Robust SVC
Controller For Improving the Dynamic Stability of
Power Systems,” Electric Power System Research, 46,
1998, pp: 213-219.
[28] Abdel-Magid. Y. L, Abido. M. A, Al-Baiyat. S and
Mantaway. A. H, “Simultaneous Stabilization of Multimachine Power Systems via Genetic Algorithms,” IEEE
Transaction on Power Systems, Vol. 14, No. 4, 1999,
pp. 1428-1439.
[15] Jalilvand. A, Safari. A, “Design of an Immune-Genetic
Algorithm-Based Optimal State Feedback Controller as
UPFC”, Electrical Engineering/Electronics, computer,
Telecommunications and information technology,
(ECTI-CON), 2009.
[29] Alrashidi. M. R, El-Hawary. M. E, “A Survey of Particle
Swarm Optimization Application in Electric Power
Systems,” Journal of Electric Power Components and
systems, Vol. 34, 2006, pp. 1349-1357.
[16] Dash. P.K, Mishra. S and Panda. G, “Damping
Multimodal Power System Oscillation Using a Hybrid
Fuzzy Controller for Series Connected FACTS
Devices”, IEEE Transactions on Power Systems, Vol.
15, 2000, pp 1360-1366.
[30] Del Valle. Y, Venayagamoorthy. G. K, Mohagheghi. S,
Hernandez. J. C, Harley. R. G, “Particle Swarm
Optimization:
Basic
Concepts,
Variants
and
Applications in Power Systems,” IEEE Transaction on
Evolutionary Computation, Februuary 2007.
[17] Dong. L.Y, Zhang. L and Crow. M.L, “A New Control
Strategy for the Unified Power Flow Controller”, Power
Engineering Society Winter Meeting, 2002. IEEE, Vol.
1, pp 27-31.
[31] Kennedy. J, Eberhart. R, “Particle Swarm
Optimization,” Proceeding of IEEE international
conference on Neural Networks (ICNN’95), Perth,
Australia, Vol. IV, 1995, pp. 1942-1948.
[18] Schoder. K, Hasanovic. A and Feliachi. A, “Fuzzy
Damping Controller for the Unified Power Flow
Controller”, North American Power Symposium,
Canada, 2000, pp 5-21– 5-27.
[19] Cai. L.J and Erlich. I, “Fuzzy coordination of FACTS
controllers for damping power system oscillations,”
Modern Electric Power Systems Proc. of the
International Symposium Wroclaw, September 11-13,
2002, pp. 251-256.
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