Environmental
Communication
Biosci. Biotech. Res. Comm. 10(2): 123-132 (2017)
Damping controller design for wind farms based on
quantum particle swarm to improve power system
stability
Zahra Rahimkhani
Department of Computer Sciences, Sarvestan Branch, Islamic Azad University, Sarvestan, Iran
ABSTRACT
As a results of technological progresses, wind power has appered as one of the most encouraging renewable energy
sources. Due to severe Grid Code requirements, wind power plants (WPPs) should provide ancillaryservices such
as fault ride-through and damping of power system oscillations to resembleconventional generation. Through an
adequate selection of input–output signal pairs, WPPs can be effectivelyused to provide electromechanical oscilla-
tions damping. In this paper, implementation of the damping supplementary controllers of Wind Turbine (WT) based
on Quantum Particle Swarm Optimization(QPSO) to damp low frequency oscillations in a weakly connected system
is consideredd. Also, singular value decomposition (SVD)-based method is used to analysis and assess the control-
lability of the poorly damped electromechanical modes by WT different control channels. The problem of damping
supplementary controller based WT system is formulated as an optimization problem according to the time domain-
based objective function which is solved QPSO. The effectiveness of the proposed controllers on damping low fre-
quency oscillations is checked through eigenvalue analysis.
KEY WORDS: WIND TURBINE,POWER SYSTEM STABILITY, QUANTUM PARTICLE SWARM OPTIMIZATION, SUPPLEMETARY DAMPING
CONTROLLER
123
ARTICLE INFORMATION:
*Corresponding Author: isi.rahimkhani@gmail.com
Received 12
th
March, 2017
Accepted after revision 19
th
June, 2017
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124 DAMPING CONTROLLER DESIGN FOR WIND FARMS BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS
Zahra Rahimkhani
INTRODUCTION
Large interconnected ac systems have many well-known
advantages. However, larger interconnected ac systems
also increase the system complexity from the operation
point of view, and might adversely decrease the system
reliability.Steady state stability, lack of reactive power
supply, voltage stability, electromechanical oscillations
and transient stabilityare common problems that can
happen in power systemsexpanded and transmit large
amount of power over long distance transmission lines.
Increasing power system complexity gives rise to low
frequency oscillations in the range of 0.2–3.0 Hz. If not
well damped, these oscillations may keep growing in
magnitude until loss of synchronism results, (Hsu et al
1988 Shayeghi et al 2009, Zhang et al 2011).
In order to damp these power system oscillations
and increase system oscillations stability, the installa-
tion of power system stabilizer (PSS) is both economi-
cal and effective.However, PSSs may adversely affect
voltage pro le, may result in leading power factor, and
may not be able to suppress oscillations resulting from
severe disturbances, especially those three-phase faults
which may occur at the generator terminals(Banaei et
al (2010).Flexible AC transmission systems devices,such
as Static VAR Compensators (SVC), Thyristor Control
Series Compensators (TCSC), Static Synchronous Com-
pensators (STATCOM), and Uni ed Power Flow Control-
ler (UPFC),are one of the recent propositions to allevi-
ate such situations by controlling the power ow along
the transmission lines and improving power oscillations
damping(Banaei et al 2010, Shayeghi et al 2011).
The renewable energy systems and specially wind
energy have been attracted due to the increasing con-
cern about CO2 emissions. Wind power is rapidly
increasing its presence in the power generation mix
as one of the most promising renewable power source
(WWEA (2011) (Ackermann (2005). For many countries
wind power has already become an important electric-
ity source, e.g., Denmark, Portugal, Spain and Germany.
Due to this increment in wind power generation share,
power systems stability and reliability may be affected
(WWEA 2011 Tsili et al 2008). The characteristics of
wind farms are substantially different from conventional
power plants, such as hydraulic, nuclear or thermal
(WWEA 2011 (Ackermann 2005). These facts have led
to the establishment of grid codes regarding wind farm
connection, and their integration in the grid (Hamdan
1999 MinisteriodeIndustriaTurismoyComercio 2006).
According to these codes wind farms must comply with
requirements including voltage sag ride through capa-
bility (Gomis-Bellmunt et al 2008), frequency regulation
(Chen Blaajberg et al (2009), and active and reactive
power regulation (ChenBlaajberg et al (2009).
In the future more wind farm contribution will be
required by the system operators. The capability to damp
power system oscillations will play an important role.
There is a draft of the new Spanish grid code for wind
power in which reference as already been made to inertia
emulation and power oscillation damping (Gomis-Bell-
munt et al (2008) (Chen,Blaajberg et al (2009).Different
methods to select the best feedback signal to damp power
oscillations have been discussed in (Hamdan (1999), but
the case for WPPs has not been yet well covered. Recent
research focuses on the best input–output signal pairs
coupling based controllability and observability analy-
ses such using singula value decomposition(SVD) (Li
et al (2012).
Also a lead lag based QPSO controller is designed to
damp low frequency oscillations. It is well known that
traditional lead-lag damping controller structure is pre-
ferred by the power system utilities because of the ease of
on-line tuning and also lack of assurance of the stability
by some adaptive or variable structure methods (Panda
et al(2008) (H Shayeghi et al (2009). Having several local
optimum parameters for a lead-lag controller, using of
traditional optimization approach is not suitable for
such a problem. Thus, the heuristic methods as solution
for nding global optimization are developed (Panda et
al (2010) (Panda S (2009).Particle swarm optimization
(PSO) is a novel population based metaheuristic, which
utilize the swarm intelligence generated by the coopera-
tion and competition between the particle in a swarm
and has emerged as a useful tool for engineering optimi-
zation (Shayeghi et al 2008).This new approach features
many advantages; it is simple, exible, fast and can be
coded in few lines. Also, its storage requirement is mini-
mal. However, the main disadvantage is that the PSO
algorithm is not guaranteed to be global convergent. In
order to overcome this drawback and improve optimiza-
tion synthesis, in this paper, a quantum-behaved PSO
technique is proposed for optimal tuning of wind tur-
bine based damping controller for enhancing of power
systems low frequency oscillations damping.
In this paper a novel approach is presented to model
power system supplied by wind turbine namely
Phillips-
Heffronmodel based d-q algorithm in order to studying
system dynamical stability.In addition, a block diagram
representation is formed to analyze the systemstability
characteristics.Also, singular value decomposition (SVD)
is used to choose damping control signal which has most
effect on damping the electromechanical (EM) mode
oscillations. A very powerful tool commonly used for
this purpose is Popov-Belevitch_Hautus(PBH) which can
be used to evaluate the EM mode controllability of the
PSS and the different inputs of system.A single machine
in nite bus (SMIB) system equipped with a PSS and a
wind turbine as a negative load. The problem of damp-
BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS DAMPING CONTROLLER DESIGN FOR WIND FARMS 125
Zahra Rahimkhani
ing controllers design is formulated as an optimization
problem to be solved using QPSO. The aim of the optimi-
zation is to search for the optimum controller parameter
settings that maximize the minimum damping ratio of
the system.
Fig.1shows a SMIB system equipped with a wind tur-
bine. As it can be seen the in nite bus is supplied by AC
transmission system. The wind turbine is modeled as a
negative load which can tune active and reactive power.
Wind turbines tune the active power transferred
to the network through an appropriate control of the
generator-side converter. The purpose is to deliver the
most active power from the wind turbine following an
optimum wind power extraction [3-9]. Also, reactive
power regulation is done through the control of the grid
side converter. Because of the obtainability of active
and reactive power measurements for converter control,
these could be utilized potentially as control signals for
damping controllers. For reaching goals of paper, the
systeminputs (or control signals) could be the active and
the reactive power transferred by wind turbine. Also, the
outputs could be considered as the voltage magnitude
and the voltage phase angle (Domı´nguez-Garcı´a JL
et al (2012)).
POWER SYSTEM NONLINEAR MODEL
The non-linear model of the SMIB system of Fig.1 is:
Where:
where P
m
and P
e
are
the input and output power, respectively;
M
and
D
the
inertia constant and damping coef cient, respectively;
b
the synchronous speed; and
the rotor angle and
speed, respectively; E
q
, E
fd
´
and V
t
the generator internal,
eld and terminal voltages, respectively; T
do
´
the open
circuit eld time constant;
x
d,
x
d
´ and x
q
the d-axis, d-axis
transient reactance, and q-axis reactance, respectively;
K
A
and T
A
the exciter gain and time constant, respec-
tively; V
ref
the reference voltage.
Also, from Fig.1we have:
Also, we have:
FIGURE 1. a SMIB system supplied by wind turbine
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
126 DAMPING CONTROLLER DESIGN FOR WIND FARMS BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS
Zahra Rahimkhani
For the in nite bus:
POWER SYSTEM LINEARIZED MODEL
By linearizing Eq (1)-(4):
Where:
Using above equation we can obtain the state variable
of the power system installed with the wind turbine to
be(state space model):
And
Where P
w,
Q
w
and u
PSS
are the linearization of the
input control signals of the wind turbine and PSS out-
put respectively.
PSO VERSUS QPSO
In a PSO system (H Shayeghi et al (2008)) (A. Awami
et al (2007)) (H. Shayeghi et al (2010)), multiple can-
didate solutions coexist and cooperate simultaneously.
Each solution candidate, called a “particle”, ies in the
problem space (similar to the search process for food of
a bird swarm) looking for the optimal position. A parti-
cle with time adjusts its position to its own experience,
while adjusting to the experience of neighboring parti-
cles. If a particle discovers a promising new solution, all
the other particles will move closer to it, exploring the
region more thoroughly in the process.
PSO starts (Panda S et al (2008)) with a population of
random solutions ‘particles’ in a D-dimension space. The
ith particle is represented by X
i
= (x
i1
,
x
i2
,..., x
iD
). Each par-
ticle keeps track of its coordinates in hyperspace, which
are associated with the ttest solution it has achieved so
far. The value of the tness for particle i(pbest) is also
stored as P
i
= (p
i1
,
p
i2
,..., p
iD
). The global version of the
PSOkeeps track of the overall best value (gbest), and its
location, obtained thus far by any particle in the pop-
ulation (Li Y et al (2012)) (Panda S et al (2008)). PSO
consists of, at each step, changing the velocity of each
particle toward its pbest and gbest according to follow-
ing equations:
Where, p
id
= pbest and p
gd
= gbest
PSO algorithm is as follow:
Step. 1: Initialize an array of particles with random
positions and their associated velocities to
satisfy the inequality constraints.
Step. 2: Check for the satisfaction of the equal-
ity constraints and modify the solution if
required.
Step. 3: Evaluate the tness function of each par-
ticle.
Step. 4: Compare the current value of the tness
function with the particles’ previous best
value (pbest). If the current tness value is
less, then assign the current tness value
to pbest and assign the current coordi-
nates (positions) to pbestx.
Step. 5: Determine the current global minimum
tness value among the current positions.
Step. 6: Compare the current global minimum with
the previous global minimum (gbest). If
the current global minimum is better than
gbest, then assign the current global mini-
mum to gbest and assign the current coor-
dinates (positions) to gbestx.
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
Zahra Rahimkhani
BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS DAMPING CONTROLLER DESIGN FOR WIND FARMS 127
Step. 7: Change the velocities according to eq. (20).
Step. 8: Move each particle to the new position
according to eq. (21) and return to Step 2.
Step. 9: Repeat Step 2–8 until a stopping crite-
rion is satis edor the maximum number
of iterations is reached.
The main disadvantage is that the PSO algorithm is
not guaranteed to be global convergent (H. Shayeghi
et al (2010)). The dynamic behavior of the particle is
widely divergent form that of that the particle in the
PSO systems in that the exact values of x
i
and v
i
cannot
be determined simultaneously. In quantum world, the
term trajectory is meaningless, because x
i
and v
i
of a
particle cannot be determined simultaneously according
to uncertainty principle. Therefore, if individual parti-
cles in a PSO system have quantum behavior, the PSO
algorithm is bound to work in a different fashion. In the
quantum model of a PSO called here QPSO, the state of
a particle is depicted by wave function W(x, t) instead of
position and velocity (Coelho LS (2008)) (H.Shayeghi et
al(2010)). Employing the Monte Carlo method, the parti-
cles move according to the following iterative equation:
Where u and k are values generated according to a
uniform probability distribution in range (Coelho LS
(2008)), the parameter
is called contraction expansion
coef cient, which can be tuned to control the conver-
gence speed of the particle. In the QPSO, the parameter
must be set as
< 1.782 to guarantee convergence of the
particle (H. Shayeghi et al (2010)).Where Mbest called
mean best position is de ned as the mean of the pbest
positions of all particles. i.e.:
The procedure for implementing the QPSO is given by
the following steps (Coelho 2008 and Shayeghi et al
(2010):
Step 1: Initialization of swarm positions: Initial-
ize a population (array) of particles with
random positions in the n-dimensional
problem space using a uniform probability
distribution function.
Step 2: Evaluation of particle’s tness: Evaluate
the tness value of each particle.
Step 3: Comparison to pbest (personal best): Com-
pare each particle’s tness with the par-
ticle’s pbest. If the current value is better
than pbest, then set the pbest value equal
to the current value and the pbest location
equal to the current location in ndimen-
sional space.
Step 4: Comparison to gbest (global best): Compare
the tness with the population’s overall
previous best. If the current value is better
than gbest, then reset gbest to the current
particle’s array index and value.
Step 5: Updating of global point: Calculate the
Mbest using eq.(24).
Step 6: Updating of particles’ position: Change
the position of the particles according to
Eq. (23), where c1 and c2 are two random
numbers generated using a uniform prob-
ability distribution in the range [0, 1].
Step 7: Repeating the evolutionary cycle: Loop to
step 2 until a stop criterion is met, usually
a suf ciently good
PSS AND WIND TURBINE DAMPING
CONTROLLER
The damping controller is designed to produce an elec-
trical torque in-phase with the speed deviation accord-
ing to phase compensation method. The PSS structure to
be considered is the very widely used lead-lag controller,
whose transfer function is [28]:
The wind turbine damping controllers are of the struc-
ture shown in Fig. 2 which u can be U = [P
w
, Q
w
]
T
. It
includes gain block, signal-washout block and lead–lag
compensator. The parameters of the damping controller
are obtained using QPSO algorithm.
(22)
(23)
(24)
(25)
FIGURE 2. Wind turbine lead-lag
controller
WIND TURBINEDAMPING CONTROLLER
DESIGN USING QPSO
To obtain optimal parameters, this paper employs QPSO
(Coelho LS (2008)) to enhance optimization synthesis
and nd the global optimum value of tness function.
Zahra Rahimkhani
128 DAMPING CONTROLLER DESIGN FOR WIND FARMS BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS
The objective function (which must be minimized) is
de ned as follows (Shayeghi et al 2006):
Where t is the time range of simulation and N is the total
number of operating points for which the optimization
is carried out. The design problem can be formulated as
the following constrained optimization problem, where
the constraints are the controller parameters bounds
(Awami et al (2007):
Typical ranges of the optimized parameters are [0.01–
100] for K and [0.01–1] for T
1
, T
2
, T
3
and T
4
. The pro-
posed approach employs QPSO algorithm to solve this
optimization problem and search for an optimal or near
optimal set of controller parameters.
CONTROLLABILITY MEASUREMENT
BASED ON SVD
Controllability shows how the state variables describing
the behavior of a system can be in uenced by its inputs.
More accurately, the dynamical system x = Ax + Bu
•
or
the pair (A,B) is said to be state controllable if, for any
initial state x(0) = x
0
any time t
1
> 0 and any nal state
x
1
there exist an input u(t) such that x(t
1
) = x
1
. Otherwise
the system is said to be state uncontrollable.
In damping of power oscillations, it is necessary to
detemine controllability for speci c eigenvalues (elec-
tromechanical mode). A very powerful tool commonly
used for this purpose is Popov-Belevitch_Hautus(PBH)
test which is described as below.It includes in evaluating
the rank of matrices:
Which
k
is the kth eigenvalue of the matrix A, I is the
identity matrix, b
k
is the column of B corresponding to
ith input u
i
. The mode
k
of linear system in state space
form is controllable if matrix C(
k
) has full row rank.
The rank of matrices can be evaluated by their singular
values. The singular values are de ned as below:
If is a m n complex matrix, then there exist unitary
matrices U and V with dimensions of m m and n n,
respectively, such that:
(29)
Where
With
1
≥
r
≥ 0 where r = min{m,n} and
1
,...,
r
are the
singular values of G.
The minimum singular value
r
represents the distance
of the matrix G from all the matrices with a rank of r – 1
[32]. This property can be used to quantify modal control-
lability and observability [32, 33]. The matrix H (and J)
can be written as H = [h
1
h
2
h
3
h
4
] where h
i
is a column vec-
tor corresponding to the ith input. The minimum singular
value,
min
of the matrix [
– A, h
i
] indicates the capabil-
ity of the ith input to control the mode associated with
the eigenvalue
. Actually, the higher
min
, the higher the
controllability of this mode by the input considered. As
such, the controllability of the EM mode can be examined
with all inputs in order to identify the most effective one
to control the mode. Thus, the choice of input through the
PBH test is done by selecting those with the largest of the
minimum singular values of matrices C(
k
).
SIMULATION RESULTS
Power system information is given in appendix A. Con-
stant coef cients in modelling are calcuated according
informations which given in appendix B. In this paper, we
consider
(rotor speed deviation) asoutputs andthree
inputs which are U = [P
w
, Q
w
, u
PSS
]
T
i.e. active power
and reactive power of wind turbine and nally PSS input.
Selecting an affective coupling between inputs-ouput for
damping oscillation of the power system is one of the
most imporatant goals of this paper. Following section
consider this topic.
CONTROLLABILITY AND OBSERVABILITY
MEASURE BY USING PBH TEST
SVD based on PBH is employed to measure the con-
trollability of the electromechanical mode (EM) mode
from each of the three inputs: U = [P
w
, Q
w
, u
PSS
]
T
.
The minimum singular value
min
is estimated over a
wide range of operating conditions. For SVD analysis,
P
e
ranges from 0.01 to 1.5Pu and Q
e
= [-0.4,0,0.4]. At
each loading condition, the system model is linearized,
the EM mode is identi ed, and the SVD-based control-
lability and observability measure is implemented. For
comparison purposes, the minimum singular value for
all inputs at Q
e
= 0.4Pu is shown in Fig. 3. From these
gures, the following can be noticed:
• EM mode controllability via P
w
, Q
w
is almost
higher than the u
PSS
.
(26)
(27)
(28)
Zahra Rahimkhani
BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS DAMPING CONTROLLER DESIGN FOR WIND FARMS 129
USING QPSO TO OBTAIN PARAMETERS OF
SUPPLEMENTARY CONTROLLERS
The QPSO algorithm is used to obtain the optimal param-
eter settings of each of the supplementary controllers so
that the objective function is optimized.The nal param-
eters are given in table 1.
These supplementary controllers are used by wind
turbine system in different loading condition (Table 2).
FIGURE 3. (a) Controllability of oscillation mode by inputs (b) Observability of oscillation model in the
outputs
Table1. Parameters of supplemetary
controller designed by QPSO
PSS P
w
Q
w
k -0.3572 3.23 -30.33
T
1
0.32 2.01 0.042
T
2
0.012 0.027 0.041
T
3
5.1 9.1 0.1
T
4
0.22 3.2 0.073
• The capabilities of P
w
, Q
w
to control the EM
mode is almost equal.
• EM mode observability via V
w
,
w
is almost
higher than the
.
Table 2. System condition
Q
e
P
e
V
t
Q
e
P
e
Operating Condition
00.210.0151
1
(Nominal)
0.10.410.41.2
2
(Heavy)
FIGURE 4. system response in
Zahra Rahimkhani
130 DAMPING CONTROLLER DESIGN FOR WIND FARMS BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS
Responses of system to a mechanical power change
(P
m
= 0.05) in synchronous generator as a disturbance
for system are shown in Fig.4.5.
CONCLUSION
In this paper, SVD has been employed to evaluate the
electromechanical mode controllability to PSS and the
wind turbine control signals. It has been shown that the
electromechanical mode is most powerfully controlled
via P
e
for a wide range of loading conditions. Also,
the quantum-behaved particle swarm optimization
algorithm has been successfully applied to the robust
design of wind turbine based damping controllers. The
effectiveness of the proposed wind turbine controllers
for improving transient stability performance of a power
system are demonstrated by a weakly connected power
system subjected to disturbance.
APPENDIX A
The test system parameters are (all in pu):
FIGURE 5. System response in
Machine and Exciter:
Transmission line and
transformer reactance:
APPENDIX B
Coef cients are:
Zahra Rahimkhani
BIOSCIENCE BIOTECHNOLOGY RESEARCH COMMUNICATIONS DAMPING CONTROLLER DESIGN FOR WIND FARMS 131
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