Improved dynamic response of dstatcom using genetic algorithm

Network and Complex Systems www.iiste.org
ISSN 2224-610X (Paper) ISSN 2225-0603 (Online)
Vol.3, No.2, 2013-National Conference on Emerging Trends in Electrical, Instrumentation & Communication Engineering
16
Improved Dynamic Response of DSTATCOM using Genetic
Algorithm
Madhusmita Das
Department of Electrical Engineering,National Institute of Technology, Raipur, India
Tel:91-9406052851 E-mail: madhusmita_bsnl@yahoo.co.in
Mrs. Varsha Singh, Dr. Swapnajit Pattnaik
Department of Electrical Engineering,National Institute of Technology, Raipur, India
Tel:91-9425524731 E-mail: varsha_x_singh@yahoo.co.in
Tel:91-9691059463 E-mail: swapnajit.pattnaik@gmail.com
Abstract
The performance of D-STATCOM depends on capacitor voltage regulation. In D-STATCOM, the nonlinear
controller is preferred to linear controller. Regulating and fixing the capacitor DC voltage in DSTATCOM can
improve the system dynamic such as capacitor voltage response, current response and modulation index. The
regulation of DC capacitor voltage based on optimal PI co-efficient. In conventional scheme, the trial and error
method is used to determine PI values. In this paper genetic algorithm is applied for exact calculation of
optimized PI co-efficient, to reduce disturbances in DC link voltage. Optimization and simulations are worked
out in MATLAB environment
Keywords: D-STATCOM, Non linear controller, Optimized PI co-efficient, Genetic Algorithm
1. INTRODUCTION
Static compensator is the static counterpart of the rotating synchronous condenser, but it generates or absorbs
reactive power at a faster rate because no moving parts are involved. In principle, it performs the voltage
regulation function .STATCOM is the voltage-source converter, which converts a DC input voltage into AC
output voltage in order to compensate the active &reactive needed by the system[N.G.Hingorani]. It is a device
connected in derivation, basically composed of a coupling transformer that serves of link between the electrical
power system (EPS) and the voltage synchronous controller (VSC),that generates the voltage wave comparing it
to the one of the electric system to realize the exchange of reactive power.
A STATCOM consists of a three phase inverter (generally a PWM inverter) using SCRs, MOSFETs or
IGBTs, a D.C capacitor which provides the D.C voltage for the inverter, a link reactor which links the inverter
output to the a.c supply side, filter components to filter out the high frequency components due to the PWM
inverter [S.Iyer]. From the d.c. side capacitor, a three phase voltage convergence is generated by the inverter.
This is synchronized with the a.c supply. The link inductor links this voltage to the a.c supply side. This is the
basic principle of operation of STATCOM [Lauttamus]. The STATCOM connected in distributed system is
called as DSTATCOM. There are many possible configurations of voltage source inverters (VSI) and
consequently many different configurations of DSTATCOM. Many different strategies such as proportional-
Integral controller, sliding mode controller [Hung-chi Tsai] and nonlinear controller have been suggested to
control DSTATCOM. But in DSTATCOM, nonlinear controller is preferred in comparison with linear method
[Yazdani]. In non-linear controller, the generalized averaged method [Sanders] has been used to determine the
nonlinear time invariant continuous model of the system [P. Petitclair]-[Petitclair].This method has been applied
to implement a nonlinear control law based on exact linearization via feedback for STATCOM [J.E.Slotine].This
technique is particularly interesting because it transforms a nonlinear system into a linear one in terms of its
input-output relationship. In the literature [P .Petitclair]-[Petitclair], only q-axis current was regulated, but it
should be noted that unlike other shunt compensators, large energy storage device that have almost constant
voltage, makes DSTATCOM more robust and it also enhances the response speed. Therefore, there are two
control objectives implemented in DSTATCOM. First is q-axis current and the second is capacitor voltage in dc
link[N.C.Sahoo].Fortunately, q-axes current tracks its corresponding reference value perfectly, but capacitor
voltage is not fixed on reference ideally because of the presence of a PI controller between the reference of the d-
axes current and DC link voltage error. In other words, the performance indices (settling time, rise time and over
shoot) have notable values .thus; the optimized and exact determination of PI gains can lead to reduction in
disturbances of system responses.
In this paper, one of the powerful and famous optimization algorithms i.e. genetic algorithm
[S.N.Sivanandam]-[Davis L] is applied to find optimized values of PI gains. single objective function is defined.
The PI coefficients, calculated in these ways, are implemented in controller to demonstrate the improvement of
convergence speed, reduction error, the overshoot in capacitor voltage and other circuit parameters.

Network and Complex Systems
ISSN 2224-610X (Paper) ISSN 2225-0603 (Online
2. Configuration of DSTATCOM
A DSTATCOM consists of a three
network by means of a coupling transformer. in general, the DSTATCOM can be utilized for providing voltage
regulation, power factor correction, harmonics compensation and load levelling.The ability of the DSTATCOM
of supplying effectively extra power allows expanding its compensating actions, reducing transmission losses
and enhancing the operation of the electric gr
considered. It is shown in Fig. (1).
Figure 1. The Representation of DSTATCOM
It consists of:
A voltage inverter, a capacitor C and an inductance L and a resistor RS on the AC s
L represents the leakage inductance of the transformer and line;
RS represents the inverter and transformer conduction losses.
The line voltages are called , ,
The angular velocity of the AC voltage and current vectors is equal to ω. Let us consider a system of reference (d,
q) rotating at the same speed, and let us note α the angle between d
equations are
= +
The model of the AC side in this system of reference is given by equation (1),
The power are expressed by equation (2)
P= ( + ) , Q= (
If α is chosen by zero, the voltage is equal to zero and the reactive power becomes proportional to
To control the reactive power Q, it is sufficient to control
=0 , Q =
By writing the equation (2) for capacitor voltage and sub
eq.(1)
P= C
By applying the Averaged Model used for control, only fundamental harmonics of inverter output voltage is
considered. the influence of all harmonics is ignored.
The control variable is δ the firings angle with reference to the network voltage
this model is used for simulation purpose, but not to choose and tune the controller. A Generalized Averaging
method is used to get a continuous time invariant model of the converter. The averaged equations are:
(Online)
National Conference on Emerging Trends in Electrical, Instrumentation & Communication Engineering
17
A DSTATCOM consists of a three-phase voltage source inverter shunt-connected to the distribution
ion, power factor correction, harmonics compensation and load levelling.The ability of the DSTATCOM
and enhancing the operation of the electric grid. In this paper, a simplified DSTATCOM configuration is
Figure 1. The Representation of DSTATCOM
A voltage inverter, a capacitor C and an inductance L and a resistor RS on the AC side;
L represents the leakage inductance of the transformer and line;
RS represents the inverter and transformer conduction losses.
, , , , are the inverter output voltage and
q) rotating at the same speed, and let us note α the angle between d axis and line voltage vector . The system
(
The model of the AC side in this system of reference is given by equation (1),
The power are expressed by equation (2)
+ )
voltage is equal to zero and the reactive power becomes proportional to
To control the reactive power Q, it is sufficient to control .
By writing the equation (2) for capacitor voltage and substituting equation (4) in the third equation is added to
considered. the influence of all harmonics is ignored.
The control variable is δ the firings angle with reference to the network voltage zero crossing. In this case,
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connected to the distribution
ion, power factor correction, harmonics compensation and load levelling.The ability of the DSTATCOM
id. In this paper, a simplified DSTATCOM configuration is
is the DC voltage.
axis and line voltage vector . The system
(1)
(2)
voltage is equal to zero and the reactive power becomes proportional to
(3)
stituting equation (4) in the third equation is added to
(4)
zero crossing. In this case,

=
The nonlinear control law is based on the theory of exact linearization via feedback.
In DSTATCOM system, because of the compensating the reactive power and eliminating the undesired
internal dynamic, Q and are chosen as output control variable. Consequently, the modulation index (m) and
δ are chosen as two control inputs variables. Two prop
(v1 and v2) and an external PI controller is chosen to regulate dc link voltage.
Considering the Iq channel, the equivalent close
=
Where λ determines the response speed of reactive power.
Figure 2. The detail structure of DSTATCO
3. GENETIC ALGORITHM
GAs is adaptive heuristic search algorithms based on the evolutionary ideas of natural selection and
genetics. As such they represent an intelligent exploitation of a random search used to solve optimization
problems. although randomized, Gas are by no means random; instead they exploit historical information to
direct the search into the region of better performance within the search space GAs are not function
approximation techniques, but they are simple and pow
methods(learning mechanisms),which have been inspired by the Darwinian evolution of a population, crossover
and mutations in a selective environment where the fittest survive. Genetic algorithm combines the art
survival of the fittest with genetic operators abstracted from nature to form a very robust mechanism that is
suitable for a variety of optimization problems. In other words, we can describe genetic algorithm as a
computational model that solves th
evolution. They are better than conventional algorithms in that they are more robust. Unlike older AI systems,
they do not break easily even if the inputs are changed slightly or in the
In the natural evolution process of organisms, the reproduction of a set of individuals that forms a certain
generation (i.e., population)is such that those individuals with to environmental adaption survive with high
probability. Reproduction that is based on the degree of conformity of an individual in a GA as an artificial
model that imitates the evolution process of such an organism is performed, and the next
is generated through crossover and mutation. The process is carried out by repeating such genetic operations, and
if the individuals of the last generation that fulfills end conditions can be found, the semi
be determined. The flow of the basic operation of the GA show
1.1 Initialization: An initial population is created from a random selection of solutions (which are analogous to
chromosomes).A population is a collection of individuals. a population consists of a number of individuals being
tested, the phenotype parameters defining the i
and every problem, the population size will depend on the complexity of the problem.
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+
The nonlinear control law is based on the theory of exact linearization via feedback.
tem, because of the compensating the reactive power and eliminating the undesired
are chosen as output control variable. Consequently, the modulation index (m) and
δ are chosen as two control inputs variables. Two proportional controllers are chosen to construct the new inputs
(v1 and v2) and an external PI controller is chosen to regulate dc link voltage.
Considering the Iq channel, the equivalent close-loop transfer function can be described as
Where λ determines the response speed of reactive power.
Figure 2. The detail structure of DSTATCOM controller
lems. although randomized, Gas are by no means random; instead they exploit historical information to
approximation techniques, but they are simple and powerful general purpose stochastic optimization
and mutations in a selective environment where the fittest survive. Genetic algorithm combines the art
computational model that solves the optimization problems by imitating genetic processes & the theory of
they do not break easily even if the inputs are changed slightly or in the presence of reasonable noise.
model that imitates the evolution process of such an organism is performed, and the next
mutation. The process is carried out by repeating such genetic operations, and
if the individuals of the last generation that fulfills end conditions can be found, the semi
be determined. The flow of the basic operation of the GA shown in Fig.3 is explained below.
: An initial population is created from a random selection of solutions (which are analogous to
tested, the phenotype parameters defining the individuals and some information about the search space. For each
and every problem, the population size will depend on the complexity of the problem.
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(5)
tem, because of the compensating the reactive power and eliminating the undesired
are chosen as output control variable. Consequently, the modulation index (m) and
ortional controllers are chosen to construct the new inputs
loop transfer function can be described as
(6)
lems. although randomized, Gas are by no means random; instead they exploit historical information to
erful general purpose stochastic optimization
and mutations in a selective environment where the fittest survive. Genetic algorithm combines the artificial
e optimization problems by imitating genetic processes & the theory of
presence of reasonable noise.
model that imitates the evolution process of such an organism is performed, and the next-generation population
mutation. The process is carried out by repeating such genetic operations, and
if the individuals of the last generation that fulfills end conditions can be found, the semi-optimal solution may
n in Fig.3 is explained below.
: An initial population is created from a random selection of solutions (which are analogous to
ndividuals and some information about the search space. For each

1.2. Reproduction: The degree of conformity of each object is calculated and an individual is reproduced
fixed rule depending on the degree of conformity. Here, some individuals with a low degree of conformity will
be screened, while individuals with a high degree of conformity will increase.
1.3. Crossover: New individuals are generated by the method
1.4. Mutation: This is performed by an operation determined by the installed mutation probability or mutation,
and a new individual is generated.
1.5. End judging: If end condition is fulfilled, the best individua
otherwise return to 2.
1.6 objective function
ITAE criterion, i.e., integral time absolute error is widely adopted to evaluate the dynamic performance of
the control system. The index ITAE is expresse
=
Where the upper limit T is a finite time chosen so that the integral approaches a steady
chosen as the setting time Ts.
For the DSTATCOM system, the adopted object
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: The degree of conformity of each object is calculated and an individual is reproduced
be screened, while individuals with a high degree of conformity will increase.
: New individuals are generated by the method of the intersection that has been set up.
: This is performed by an operation determined by the installed mutation probability or mutation,
: If end condition is fulfilled, the best individual thus obtained is the semi
the control system. The index ITAE is expressed in (7)
(7)
Where the upper limit T is a finite time chosen so that the integral approaches a steady-state value and is usually
For the DSTATCOM system, the adopted objective function is:
(8)
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: The degree of conformity of each object is calculated and an individual is reproduced under a
of the intersection that has been set up.
: This is performed by an operation determined by the installed mutation probability or mutation,
l thus obtained is the semi-optimal solution,
state value and is usually

Where
=
Is a performance index corresponding to the No. i objective.
objective. is the error between the real valu
the weighted factor corresponding to the No. j controlled variable .Vector Z=[
system parameters ,i.e., PI parameters.
For the DSTATCOM objective function, the objective function deduced by (7) is expressed in:
(
(
Z=
The Eq. (10) is used when the goal is controlling the
individually regulated.
4. SIMULATION RESULTS
The system parameters of DSTATCOM are as
C=6000(µF), F=50 Hz, Rs=.28 (Ώ),L=.0013 (H),
=110 rms(L-L) (V) =200 (V),Initial voltage=200v.
The normal solution for determination of PI gains is trial and error method. Many pairs should be tested. Best of
them are selected. Here a set of pairs are tested and finally PI are given as
certain of optimized PI gains, GA as a powerful, famous and applicable method is applied. In this paper the
objective function defined focuses on capacitor voltage to regulate it independently. The objective function leads
to =617.9668 and =39.1076 .the above obtained PI co
overshoot is very small and voltage is fixed on 200v.Thus, if the objective is controlling
very effective and should be chosen.
0
199.3
199.4
199.5
199.6
199.7
199.8
199.9
200
200.1
Capacitorvoltage(V)
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Is a performance index corresponding to the No. i objective. is a weighted factor corresponding to the
is the error between the real value of the No. j controlled variable and its desired value.
the weighted factor corresponding to the No. j controlled variable .Vector Z=[
system parameters ,i.e., PI parameters.
ction, the objective function deduced by (7) is expressed in:
The Eq. (10) is used when the goal is controlling the and .Instead, the Eq.(11) is used when
The system parameters of DSTATCOM are as follows:
C=6000(µF), F=50 Hz, Rs=.28 (Ώ),L=.0013 (H),
=200 (V),Initial voltage=200v.
ted. Here a set of pairs are tested and finally PI are given as =2 and
on capacitor voltage to regulate it independently. The objective function leads
=39.1076 .the above obtained PI co-efficient are implemented to DSTATCOM. The
overshoot is very small and voltage is fixed on 200v.Thus, if the objective is controlling
very effective and should be chosen.
500 1000 1500 2000 2500
Time(s)
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(9)
is a weighted factor corresponding to the
e of the No. j controlled variable and its desired value. is
] is the control
ction, the objective function deduced by (7) is expressed in:
(10)
(11)
.Instead, the Eq.(11) is used when is
=2 and =90.due to being
on capacitor voltage to regulate it independently. The objective function leads
efficient are implemented to DSTATCOM. The
only, this method is

Figure 4 the Capacitor voltage response to PI gain at
Figure 5. Modulation index response to PI gain at
0
0.44
0.445
0.45
0.455
0.46
0.465
0.47
0.475
0.48
Modulationindex(M)
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4 the Capacitor voltage response to PI gain at =2 and =90
Figure 5. Modulation index response to PI gain at =2 and =90
500 1000 1500 2000 2500
Time(s)
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=90
=90
2500

Figure 6. d-axis current response to PI gain at
Figure 7. q-axis current response to PI gain at
Figure 8. The phase difference response to PI gain at
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
d-axisCurrent(A)
0
0
5
10
15
q-axiscurrent(A)
0
-12
-10
-8
-6
-4
-2
0
phasedifference(deg)
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axis current response to PI gain at =2 and =90
axis current response to PI gain at =2 and =90
Figure 8. The phase difference response to PI gain at =2 and =90
500 1000 1500 2000 2500
Time(s)
500 1000 1500 2000 2500
Time(s)
500 1000 1500 2000 2500
Time(s)
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=90
=90
2500
2500
2500

23
Figure 9. The capacitor voltage response to optimized PI gain
Figure 10. Modulation index response to optimized PI gain
Figure11. d-axis current response to optimized PI gain
0 500 1000 1500 2000 2500
199.65
199.7
199.75
199.8
199.85
199.9
199.95
200
Time(s)
Capacitorvoltage(v)
0 500 1000 1500 2000 2500
0.45
0.455
0.46
0.465
0.47
0.475
0.48
Time(s)
Modulationindex(M)
0 500 1000 1500 2000 2500
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Time(s)
d-axisCurrent(A)

24
Figure12. q-axis current response to optimized PI gain
Figure13. The phase difference response to optimized PI gain
5. CONCLUSION
The nonlinear control method of the DSTATCOM which is based on the exact linearization via feedback uses
one proportional-integral controller. Normal way to calculate modulation index, capacitor voltage, phase
difference and DC link voltage coefficients is using trial and error method. In this paper, genetic algorithm with
single type of objective function is suggested. Using this method leads to a better regulation of DC link voltage
and other circuit parameters. Actually the time of reaching to steady state value, the fluctuations and overshoot
decrease.
6. REFERENCES
[1] N. G. Hingorani and L. Gyugyi, Understanding FACTS, Concepts and Technology of Flexible AC
Transmission Systems.New York: IEEE Press, 1999, 0-7803-3455-8
[2] S. Iyer, A. Ghosh and A. Joshi, Inverter topologies for DSTATCOM applications-a simulations study, Electr.
Power Syst. Res. 75 (2005) (August (3)), pp. 161–170 (Elsevier)
[3] Lauttamus, P.; Tuusa, H.; "Comparison of Five Conversion Conference, 2-5 April 2007 Page(s):659-666
Hung-Chi Tsai; Chia-Chi Chu; "Nonlinear STATCOM Controller using Passivity APCCAS, 4-7 Dec. 2006
Page(s):1996-1999
[4] Yazdani, A.; Crow, M.L.; Guo,enhancement" IEEE Power and Energy Society General Meeting Century, 20-
24 July 2008 Page(s):1-6
[5] Sanders, S.R.; Noworolski, J.M.; Liu, X.Z.; Verghese, G.C.; "Generalized averaging method for power
conversion circuits"IEEE Transaction on Power Electronics, Vol. 6,April 1991 page(s):251-259
[6] P. Petitclair, S. Bacha, and J. P. Rognon, “Averaged modeling and nonlinear control of an ASVC (advanced
static VAr compensator),” in Proc. IEEE/PESC’96 Annu.. Meeting, Jun. 1996, pp.753-758
[7] Petitclair,, P..Bacha, S. Ferrieux,, J-P. ”Optimized linearization via feedback control law for a STATCOM”
In IEEE industry Applications Conference Volume 2,5-9 Oct.1997 page(s):880-885.
[8] J.E.Slotine and W.Li. Applied nonlinear control.Prentice Hall,New Jersey,1991
0 500 1000 1500 2000 2500
0
5
10
15
Time(s)
q-axisCurrent(A)
0 500 1000 1500 2000 2500
-12
-10
-8
-6
-4
-2
0
Time(s)
phasedifference(Deg)

25
[9] N.C.Sahoo, B.K.Panigrahi,, P.K.Dash and G.Panda, Application of a multivariable feedback linearization
scheme for STATCOM control,Electric Power Syst.Res. 62(2002) (No.1),pp.81-91
[10] S.N. Sivanandam, S.N. Deepa, PRINCIPLES OF SOFT COMPUTING, Second edition page(s):385-401
[11] Goldberg D.E., GENETIC ALGORITHM IN SEARCH, OPTIMIZATION AND MACHINE LEARNING,
MA: AddisonWesley, 1989
[12] Davis.L., HANDBOOK OF GENETIC ALGORITHM, New York: Van Nostrand,1991

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