International Journal of Engineering & Technology, 7 (4.

10) (2018) 206-211

International Journal of Engineering & Technology

Website: www.sciencepubco.com/index.php/IJET

Research paper

Stability Enhancement of STATCOM using Flower Pollination

Algorithm
Srikanth Velpula1, Thirumalaivasan R1*, Janaki M1
1
School of Electrical Engineering, Vellore Institute of Technology, Vellore-632014, Tamilnadu, India.
*Corresponding author E-mail: thirumalai22@gmail.com

Abstract

The Static Synchronous Compensator (STATCOM) is a Voltage Source Converter (VSC) based shunt connected FACTS device. The
key roles of STATCOM are to control the voltage at midpoint of transmission line, enhance power transfer capability and control reac-
tive power at load end. However, the performance of STATCOM depends upon the parameters of the controller. In this paper, we present
the tuning of Type-1 controller parameters for STATCOM based on a systematic method using Flower Pollination Algorithm (FPA). The
margins for the Type-1 controller parameters are estimated from the movement of eigenvalues for the variation in controller parameters
during inductive and capacitive modes of STATCOM. The performance of the STATCOM with FPA optimized Type-1 controller pa-
rameters is evaluated by transient simulation. The eigenvalue analysis and transient simulation are done based on D-Q model of STAT-
COM. It is noticed that, the response of STATCOM follows the step change in reactive current reference with least error.

Keywords: FACTS; Flower Pollination Algorithm (FPA); Static Synchronous Compensator (STATCOM); Voltage Source Converter (VSC).

[11] - [12], the application of Genetic Algorithm (GA) to tune the

controller parameters ensures D-stable of eigenvalues and the
1. Introduction results show an excellent transient response of STATCOM under
the considered range of operation and system conditions.
The Flexible AC Transmission Systems Controllers facilitate the A biologically inspired meta-heuristic optimization technique
fast and reliable control of the power system. The integration of called Flower Pollination Algorithm (FPA) was proposed by X-S.
FACTS controllers can alleviate the problem of under loading of Yang in, 2012 [13], [14]. The inspiration for this algorithm is from
transmission lines and improve system stability. The VSC based the process of flower pollination in the plants. This is a very sim-
STATCOM is a shunt connected FACTS device which can supply ple algorithm with only two operators, and a few of the parameters
a controlled reactive power to regulate the bus voltage where it is needs to set. The FPA is especially applied to many different dis-
connected. The reactive power supply of STATCOM is regulated ciplines in engineering, such as economic load dispatch problems
through controlling the output voltage of converter. The active [15], neural network training [16], machining process planning
power control of STATCOM is very small as the voltage on DC [17], and controller design [18].
side is held by the capacitor. However, the use of energy storage In this paper, FPA is adopted to tune the controller parameters of
across the DC capacitor enables the active power control capabil- STATCOM. A 24-pulse voltage source converter (VSC) and
ity of STATCOM. The noteworthy fact that the performance of Type-1 controller are considered for STATCOM configuration
the STATCOM and thereby the power system completely depends [11], [19]. The Type-1 controller modulates the magnitude and
on the parameters of controller [1], [2]. phase angle of the converter output voltage relative to the supply
In [3], a PI controller based STATCOM with varying DC capaci- voltage [1]. The performance of the STATCOM with FPA opti-
tor voltage is presented to reduce the harmonics in current and mized controller parameters is evaluated through eigenvalue anal-
voltage by fixing a modulation index. In [4], it is reported that ysis and transient simulation. The results show the better transient
Particle Swarm Optimization (PSO) based self tuning PI controller performance and the system is stable under various operating con-
performs fast calculation of gains under varying load conditions. ditions of STATCOM.
The tuning of PI controller parameters of STATCOM using Back The structure of the paper as follows: Modeling of the STATCOM
Propagation Algorithm (BPA) and improvement in low conver- is described in Section 2. The design of current controller and
gence speed of BPA using the Bats Echolocation Algorithm are application of FPA to optimize the controller parameters is report-
presented in [5]. In comparison to fixed gain and PSO based self ed in Section 3. The Section 4 presents results and discussions
tuned PI controller, the BPA based PI controller shows effective followed by conclusions in Section 5.
dynamic response of the STATCOM. The reactive current control
of STATCOM using Fuzzy Logic PI controller eliminates the
oscillatory instability in comparison to PI control [6]. The tuning 2. STATCOM Model
of STATCOM controller gains using Artificial Neural Network
(ANN) is presented in [7]-[10], which report that, the use of Fuzzy The functional block diagram of STATCOM is shown in Fig.1.
Logic improves the controller performance under various system The coupling transformer having resistance (Rs) and reactance
conditions and consequently reduce the size of STATCOM. In

Copyright © 2018 Authors. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original work is properly cited.
International Journal of Engineering & Technology 207

(Xs) is connected between the STATCOM and bus (with voltage 2.2. STATCOM Current Control
Vs) to provide the isolation.
The block diagram of Type-1 controller for controlling the cur-
rents of STATCOM is shown in Fig.2. In Type-1 controller, the
phase angle α and dead angle β modulate the STATCOM currents.
The phase angle α controls the real current of STATCOM. It is
noted that, the conduction period of the converter depends on the
dead angle β. Hence, by modulating dead angle β, the magnitude
of converter output voltage is controlled, thereby controlling reac-
tive current. While modulating the dead angle β, the DC voltage is
held constant. In this work, the STATCOM reactive current is held
constant to the value corresponding to the magnitude of the bus
voltage.

Fig. 1: STATCOM configuration.

The converter of STATCOM is usually a multilevel or multi-pulse

configuration. In a three-level converter with fundamental switch-
ing frequency, the magnitude of converter output voltage can be
controlled by modulating the dead angle β [20], [21]. Also, the
three-level configuration of converter minimizes the harmonic
distortion on the ac side [2], [19], [21] and [22]. Fig. 2: Type-1 Controller.
In this paper, the phase angle and magnitude of the STATCOM
converter output voltage are modulated using the Type-1 control- The real and reactive current components of STATCOM in D-Q
ler. The transient performance is validated through D-Q model of variables are represented as:
STATCOM. In the modelling of STATCOM, the realization of
three level is not considered. I P  I sDsin(θ s )  I sQcos(θ s )
(4)
2.1. Mathematical Model of STATCOM in D-Q Refer- I R  I sDcos(θ s )  I sQsin(θ s )
ence Frame
while the α, β are obtained from the equations:
The transformation of three-phase variables into D-Q frame is
done with the Kron's transformation [23]. The output voltage of
converter in D-Q reference frame is represented as: V 
α  tan 1  R(ord) 
2 2  VP(ord) 
Vsi  VsD
i
 VsQ
i (5)
 VR(ord)  VP(ord) 
i
VsD  k m Vdcsin(θs  α) (1) β  cos 1  
 k1Vdc 
i
VsQ  k m Vdccos(θs  α)

The STATCOM equations in D-Q variables are described as: The IP and IR values are positive if the STATCOM absorbs real
and reactive power.
dIsD R ω
  s B IsD  ω0IsQ  B VsD  VsD
i 
dt Xs Xs   3. Design of Current Controller
dIsQ R ω ω (2)
  s B IsQ  ω0IsD  B VsQ  VsQ
i 
This section presents the design of current controller for STAT-
dt Xs Xs  
COM. To simplify the controller design procedure, the voltage of
dVdc ω ω the STATCOM at the bus is assumed constant (the dynamics of
  B Idc  B Vdc
dt bc bc R p the network are not considered).

Where Idc=-km[sin(θs+α)IsD + cos(θs+α) IsQ], IsD and IsQ are the D- 3.1. Trajectories of Eigenvalues
Q variables of the STATCOM current, θs is the phase angle of bus
voltage, and α is the phase angle difference between fundamental The locus of eigenvalues are plotted with the variation in control-
component of the converter output voltage and STATCOM bus ler parameters for the range of ‘0’ to ‘20’ for the reactive current
voltage Vs. Reference of -1, -0.5, 0.5 and 1 as shown in Fig.3. In Fig.3, the
Here, km is the modulation index of a three-level converter which locus of eigenvalues are shown upto the range of ‘-200’ on real
is a function of dead angle β and given by km =k1 cosβ, where k1 = axis, for the range beyond the ‘-200’ the eigenvalues are far away
kρ. k =4√6/π for a 24-pulse converter and ρ is transformation ratio from the imaginary axis and considered to be stable.
of the STATCOM interfacing transformer.
208 International Journal of Engineering & Technology

Fig. 3: Locus of the eigenvalues with the variation in control parameters for capacitive and inductive modes of STATCOM.

The trajectories of eigenvalues for the variation in controller pa- The flexibility of the FPA in comparison to other algorithms is
rameters are shown in Fig.3. We can observe that for the low val- simple and can be applicable to single as well as multi objective
ue of proportional controller gains, the location of eigenvalues are functions. Concern to biological point of view, the ultimate objec-
close to the imaginary axis with low damping, whereas unstable tive of the flower pollination is the surviving of best fittest and
for low values of proportional gain of real current controller (kp2). optimal reproduction of plant species. With regard to the optimiz-
In general, the damping of the eigenvalues increases with increase ing process in plants species, the FPA has four rules and summa-
in the gain of controller parameters. We tune the gains of control- rized as [13], [14] and [24]:
ler to enhance the transient performance of STATCOM while Rule-1: Biotic and cross-pollination are considered as global pol-
maintaining the stability of STATCOM. Hence, from the trajecto- lination process. The pollinators which are carrying pollens obey
ries of eigenvalues and the realistic values of controller parame- the Lévy flights.
ters, we choose the upper and lower boundaries for controller Rule-2: Self or Abiotic-pollination is treated to be a local pollina-
parameters. The Flower Pollination Algorithm is used to find the tion.
optimal controller parameters for the stable operation of STAT- Rule-3: The pollinator constancy is regarded as the reproduction
COM under capacitive and inductive mode of operation. probability, which is proportional to the similarity of the two
flowers involved.
3.2. Application of Flower Pollination Algorithm (FPA) Rule-4: The switching between the local and global pollination is
For Controller Parameter Optimization controlled by the probability p ɛ [0 1].

3.2.1. Introduction to FPA 3.2.1. Formulation of Objective Function

The Flower Pollination Algorithm (FPA) is a population based The damping ratio ζ of around 10% to 20% is considered as ac-
meta-heuristic optimization technique, inspired by the flower pol- ceptable to damp the oscillations. In most of the utilities, the al-
lination of plants. This optimization procedure imitates the flower lowable damping ratio is 10%, which is considered to be the min-
pollination. The natural phenomenon of pollination plays an im- imum requirement. As well as, real part of the eigenvalue is con-
portant role for the reproduction of flowering plants. The basic fined to be below a specific boundary, say α, which ensures the
advantage of FPA is that the pollinators can travel for a long dis- less decay rate α. The boundary of real part α= -0.5 is considered
tances to enhance the algorithm to avoid local landscape and ex- as sufficient to ensure the settling time which should be an ac-
plores a larger search space. Also, the flower consistency of the ceptable value. To ensure the acceptable controlled system, the
algorithm promises that the flowers are chosen from the similar closed loop pole location must simultaneously meet either condi-
species which guarantees the fast convergence [13], [14] and [24].
International Journal of Engineering & Technology 209

tions with an acceptable response for small disturbance under f(z)  Re(z)  min Im(z), α  0 (6)
specified range of operating conditions.
Where z ɛ C, represents a point of the D-contour on the complex
plane C.

J is defined as:
J  max [Re(λi )  max (ζ | Im(λi ) |, α] (7)
i i 1,2,3...n

Where ‘λi’ is the ith eigenvalue of the system, ‘n’ is the number of
eigenvalues.
The negative value of all the elements of ‘J’ indicate that all the
eigenvalues lie on left side of the D-contour, the system is said to
be D-stable. Conversely, the eigenvalues to the right side of the D-
contour result in one or more elements of ‘J’ to the positive value.
From the facts discussed above, the objective function ‘E’ is de-
fined as:

Sum Squared Error (E) = e 2

p 1, 2,...m
(8)

Where e =IRref -IR, and m=size of IRref array with transient simula-
tion carried out for 1.5 sec, IRref is the reactive current reference
and IR is the reactive current of STATCOM.
For the satisfactory operation of STATCOM, the difference be-
tween reactive current reference IRref and reactive current IR (i.e.,
error ‘e’) should be minimum. Hence, the problem of optimization
can be written as:
Minimize E
subjected to J≤ 0
Also, the boundaries for the controller parameters are described
as:
kp1min ≤ kp1 ≤ kp1max ki1min ≤ ki1 ≤ ki1max
kp2min ≤ kp2 ≤ kp2max ki2min ≤ ki2 ≤ ki2max
kp3min ≤ kp3 ≤ kp3max ki3min ≤ ki3 ≤ ki3max

4. Results and Discussions

Fig. 4: Flower Pollination Algorithm Flow Chart. In the FPA optimization process, the minimum value of the objec-
tive function is found for various number of iterations and popula-
tion sizes.
The best minimum value of objective function versus number of
iterations with different population sizes are plotted in Fig.6. The
best minimum value of objective function occurs at less number of
iterations for the increase in population as shown in Fig.6. At this
point of minimal objective function the controller parameters are
considered to be optimal values.
The optimized parameters obtained by FPA are:
kp1=0.71585, kp2=0.2518, kp3=0.21367,
ki1=5.1226, ki2=0.14777, ki3=4.5134.
The location of eigenvalues in complex plane for the entire range
of capacitive and inductive modes of STATCOM with optimal
Fig. 5: D-contour specified with ζ= 10% and α = - 0.5. Type-1 controller parameters is plotted in Fig.7. The correspond-
ing eigenvalues for the capacitive and inductive mode of operation
When the location of all the eigenvalues are in the left side of the
of the STATCOM are shown in Table 1.
contour shown in Fig.5, the conditions on ζ and α are met and also
In Fig.7, the eigenvalues are lying on left side of the D-contour
guarantees a well damped response for small disturbance. The
with the optimal controller parameters. Thus, the optimization of
contour which is shown in Fig.5 is referred as the D-contour [2],
controller parameters using FPA shows the D-stable system under
[25].
various operating conditions considered.
According to this, a system is said to be D-stable, if all the eigen-
The performance of the STATCOM with FPA optimized parame-
values lie to the left side of the D-contour. The controller which
ters for Type-1 is determined by transient simulation and eigen-
ensures the D-stability of a closed loop system under a wide range
value analysis. In transient simulation, the step change in the ref-
of system operating conditions is said to be a `robust' controller.
erence value of reactive current reference is applied from 0.5sec to
Therefore a system said to be `robust', if, for all the range of sys-
1 sec. During the step change, the STATCOM operation is
tem operating conditions the eigenvalues lie on left side of the D-
changed from maximum capacitive to maximum inductive and
contour.
vice versa. The step response of STATCOM with optimized con-
The D-contour shown in Fig.5 can be mathematically described
troller para meters is plotted in Fig.8, which shows the smooth
as:
transition between capacitive and inductive mode of STATCOM.
210 International Journal of Engineering & Technology

Fig. 6: Best Minimum Value of Objective function versus Number of iterations with different Population sizes.

Table1: Eigenvalues with optimal controller parameters based on FPA.

Capacitive Region Inductive Region
iR = -1 iR = 1
-328.68± j 263.28 -328.63 ± j 362.85
-541.18 -541.18
-20.96 -20.96
-7.1212 -7.1304
-0.58691 -0.58691

Fig.8: Step response of STATCOM with optimal controller parameters.

5. Conclusion
In this paper, the optimization of controller parameters for STAT-
COM current control using Flower Pollination Algorithm is pre-
sented. The range of controller parameters is selected from the
eigenvalue analysis. The results show that the eigenvalues of
STATCOM with optimized controller parameters are D-Stable for
the capacitive and inductive mode of operation. The step response
of STATCOM with optimized controller parameters is tested and
it is observed that the STATCOM shows an excellent transient
response.

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