Pa rticle swarm optimization (PSO) and Internal Model ... · By MATLAB SIMULINK simulation it is shown that the particle swarm optimization -tuned PI controller performs better than

Particle swarm optimization (PSO) and Internal Model Control

(IMC) based tuning technique for PI controller for DVR for

improved dynamic response and power quality

V.Praveen1 and Dr. SNV Ganesh

2

PSCMR College of Engineering and Technology, Vijayawada, India

ABSTRACT

This paper describes the PI controller for voltage regulation, performance of the DVR under

different voltage disturbances. PI controller is difficult to tune for non linear systems; Dynamic

Voltage Restorer (DVR) is series controller which has capability to mitigate the voltage

disturbance by injecting missing voltage in series to the load. DVR comprises of inverter, DC

energy storage and series transformer. The paper also presents modeling of DVR, and controller.

The DVR maintains the voltage at the point of common coupling (PCC) and at the DC link

voltage across the DC link capacitor. For these two purposes, there are two independent

controllers and these controllers are predominantly of PI types. Tuning the PI controller is a

challenging exercise. In this paper, a novel method for tuning the PI controllers using particle

swarm optimization is presented (PSO) and Internal Model Control (IMC). By MATLAB

SIMULINK simulation it is shown that the particle swarm optimization-tuned PI controller

performs better than the Internal Model Control (IMC).technique-tuned PI controller. The circuit

is simulated in matlab/simulink and results are presented to validate the proposed controller.

Keywords: SAG, SWELL, DVR, IMC, PSO.

1. INTRODUCTION

Power quality has always dragged the attention of many researchers. Power quality may be

defined as the ability of electrical network's or the grid's to supply a clean and

stable power supply. Voltage distortions like power system harmonics and voltage are severe

issue; affecting both the utility company and consumers in the same manner. Sensitive

equipments are mostly affected by the nonlinear loads which create voltage and current

harmonics [1–3].

International Journal of Pure and Applied MathematicsVolume 119 No. 16 2018, 1459-1472ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

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Voltage sags can occur at any instant of time, with amplitudes ranging from 10 – 90% and a

duration lasting for half a cycle to one minute [4]. Commercial power literally enables today’s

modern world to function at its busy pace. Power system transmission lines are subjected to

weather conditions such as hurricanes, lightning storms, snow, ice and flooding along with

equipment failure, traffic accidents and major switching operations. In distribution systems, few

causes of voltage disturbances are short circuit faults, lightning strokes, high starting currents of

induction motors, and inrush currents [5]. Voltage disturbances are sags, swells and harmonics.

Voltage sags can be symmetrical or unsymmetrical. Symmetrical sags have equal phase voltages

and the 120 degrees phase relationship. Otherwise, the sag is unsymmetrical. Symmetrical sags

are caused due to a three-phase short-circuit fault. Unsymmetrical sags are caused due to Single

line-to-ground, phase-to-phase, or two phase-to-ground faults due to lightning, animals,

accidents, and other causes, as well as energizing of large transformers.

These voltage disturbances can be minimized by series and shunt compensators. Dynamic

Voltage Restorer (DVR) is a series compensator which is widely used; connected in series to

load and source through a series injecting transformer. DVR minimizes the voltage disturbance

by injecting missing voltage through voltage source converter driven by pwm pulses. However a

good controller is required possessing qualities like dynamic response, stability and steady-state

accuracy [7–14]. Few controllers have been presented earlier in literature studies, such as

feedback and feed-forward [8], double-vector [9], proportional and integral (PI) [10], fuzzy and

adaptive PI-fuzzy controllers [11, 12].

The rest of this paper organized as follows, section 2 presents the modeling of DVR. Section 3

presents the IMC algorithm. The concepts of PSO controller are explained in section 4. Section 5

presents case studies in simulation results of DVR. Finally, the conclusion and discussion are

given in section 6.

2. MODELING OF DVR

With the Thevinin model of the DVR as shown in the fig 1, the thevinin impedance is the

resultant of fixed resistance, which is equivalent to losses in the DVR and fixed reactance, which

is equivalent to reactive elements of the DVR. Modeling of DVR includes the voltage handling

capability, current handling capability and size of energy storage.

DVR L th L thV V Z I V

International Journal of Pure and Applied Mathematics Special Issue

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Fig 1: Thevenin model of DVR

The load current IL is given by

𝐼𝐿 = 𝑃𝐿 + 𝑗𝑄𝐿

𝑉𝐿 ∗

The voltage injected by the DVR is

0 ( )DVR L th thV V Z V

Where , and are the angles of VDVR, Zth and Vth respectively. Ѳ is the load power factor

angle and is given by

𝜃 = 𝑡𝑎𝑛−1 𝑄𝐿

𝑃𝐿

From the eqn (2), assuming the thevinin impedance is very less (Zth << 1), the voltage injected by

the DVR can be written as

𝑉𝐷𝑉𝑅 = 𝑉𝐿 − 𝑉𝑡ℎ = (1− 𝐾)𝑉𝐿,

Where K indicates the ratio of source voltage to the load voltage

𝐾 =𝑉𝑡ℎ

𝑉𝐿

Apparent power required by the DVR (SDVR) is then calculated in terms of the apparent load

power (SL).

𝑆𝐷𝑉𝑅 = 𝑆𝐿 1− 𝐾

𝑆𝐷𝑉𝑅 = 𝑉𝐷𝑉𝑅 𝐼𝐿∗


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The corresponding active and reactive powers are:

𝑄𝐷𝑉𝑅 = 𝑆𝐿𝑠𝑖𝑛 𝜃𝐿 − 𝐾 sin 𝜃𝑠

𝑃𝐷𝑉𝑅 = 𝑆𝐿𝐶𝑜𝑠 𝜃𝐿 − 𝐾 Cos 𝜃𝑠

Where Cos (ѲL ) and Cos (Ѳs) are the load power factor and source power factor.

cos1

cos

th L

DVR L

L

VP P

3. INTERNAL MODEL CONTROL (IMC) ALGORITHM

Select the plant and obtain the transfer function of the plant ( )pG s .

Chose the process model ( )pG s .

Factorize the process model into minimum phase and non-minimum phase components.

( ) ( ) ( )p p pG s G s G s . This step ensures that ( )q s is stable and causal. However ( )pG s

contains all Non-minimum phase elements (Noninvertible) in the plant model. i.e. all

Right Half Plane (RHP) zeros and time delays. The factor ( )pG s is Minimum Phase and

invertible.

The controller ( )q s is chosen as inverse of minimum phase component. 1( ) ( )pq s G s .

The filter transfer function ( )f s is to make the controller stable, causal and proper. The

controller with filter is given by

1( )( )

1

p

n

G sq s

s

,

The final form for the closed loop transfer functions characterizing the system is

( ) 1 ( ) ( ) ( )ps q s f s G s

( ) ( ) ( ) ( )ps q s f s G s

Filter time constant shall be selected so as to obtain good closed loop performance and

disturbance rejection.


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Internal model control parameter ( )

1 ( ) ( )imc

p

q sG

q s G s

To avoid excessive frequency gain of the controller should not be more than 20 times its low

frequency gain. For controllers that are ratios of polynomials, this criterion can be expressed as

( )20

(0)

q

q

Higher the value of , higher is the robustness of the control system.

Fig 2: closed loop diagram with IMC controller

4. Particle Swarm Optimization (PSO)

Particle swarm optimization is a heuristic search or optimization technique inspired by the co

operative behavior of flocks of birds or schools of fish. With an extremely intricate system of

communication, the birds or fish hereafter termed as particles interact with each other. In

addition to the communication skills, the particles are characterized by a sort of updating the best

of the past performances in the current flight.

In the PSO model used in industrial optimization, each particle is associated with a set of

parameters. The set of parameters associated with each particle is a vector. This vector is of

equal number of elements for all the particles and the size of this vector is equal to the size of the

vector to be optimized in the application. To start with, the elements of the vectors of each

particle are assigned with arbitrary values within the allowable range. With the arbitrary values


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for the vector elements, the performance of each of the vectors is calculated. The PSO technique

is a heuris-tic search technique which is used to locate a particular point in a multi dimensional

space, where this point is ultimately pointed out by all the particles which satisfy the objective to

be reached.

Besides, each particle over a number of iterations may exhibit different performances in each

iteration and by considering the past and the present iteration, the certain combination of the

elements of the vector for a particular iteration might stand the best performing vector pertaining

to that particular particle. This particular vector is the personal best of the said particle. All the

particles are updated with the best vector that gives the best results.

Based on the vector of the personal best of each particle and based on the vector of the

globally best performing particle, a velocity is estimated and this velocity is added up

respectively with the updated best performing vector of each particle. Thus, at the end of each

iteration, the vectors of all the particles are updated and the performance evaluated with

Equations given below.

𝑣𝑑𝑖 = 𝑤 𝐺 ∗ 𝑣𝑑

𝑖 + 𝑐1 ∗ 𝑟𝑎𝑛𝑑2𝑖𝑑 ∗ 𝑝𝑏𝑒𝑠𝑡𝑖

𝑑 − 𝑋𝑖𝑑 + 𝑐2 ∗ 𝑟𝑎𝑛𝑑2𝑖

𝑑 ∗ 𝑔𝑏𝑒𝑠𝑡𝑖𝑑 − 𝑋𝑖

𝑑

𝑋𝑖𝑑=𝑋𝑖

𝑑 + 𝑉𝑖𝑑

As the iterative process is under process, the elements of the vector of each particle are

modified little by little and they all move toward the common goal from different directions to

ultimately meet at the unique point. At this unique, the elements of the vectors of all the particles

will be the same and all the particles show up almost the same performance with respect to the

objective function.

The elements of the vector of all particles will be the same at the point of convergence and that

is the required solution.

Particle Swarm Optimization for obtaining Filter Time constant :

1. Initialize the position Randomly and velocity of the particles: Xi(0) and Vi(0)

2. The fitness function for the particle iX Is to be Evaluated

3. Position of the particle becomes particle’s best ( bestp ) and global best ( bestg ).

4. for i = 1 to number of particles

5. Evaluate the fitness:= fi , 1

1if

error


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6. Compare the particle’s value with bestp for each particle. If the current value is better

than the bestp value, than set this value as the bestp and current particle’s position, iX as

ip

7. the particle that has the best fitness value want to be Identified. The value of its fitness

function is identified as bestg and its position as gp .

8. For all particles Update the position and velocities

9. ( ) ( 1) ( )i i iX t X t v t and

10. 1 1 2 2( ) ( 1) . ( ( 1) . ( ( 1)i i i i g iv t v t rand p X t rand p X t

11. Using equations (1) Adapt velocity of the particle

12. Update the position of the particle;

13. increase i

14. Repeat steps 2-12 until a stopping criterion is met (either maximum number of iterations

or sufficiently good fitness value)

Fig. 3. Typical PI controller.

SIMULATION DIAGRAM AND RESULT

Test system as shown in the fig is composed of a 0.415 kV, 50 Hz generation system feeding

two transmission lines through a three-winding transformer connected in Yg/D/D, 0.415/11/11

kV. Such transmission lines feed two distribution networks through two transformers connected

in D/Yg, 11/0.415 kV. Bus-A represents the unhealthy feeder in which different faults will occur

at point X, while bus-B represents the adjacent feeder connected to sensitive loads. Multiple


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voltage sags, swells are created in the system ate various time periods. The DVR is simulated to

be in operation only for the duration of the fault. The test system parameters are shown in table.

Fig 4: Simulation diagram for DG system with DVR under different fault conditions.

Table-1: System and DVR parameters

Case I: multiple Voltage sag created by three phase to ground fault for 2.5 cycles at different

time periods for IMC.

Fig 5: Load voltage depicting multiple sags

Discrete,Ts = 5e-005 s.

powergui

a b c

load1

A

B

C

A

B

C

A

B

C

A

B

C

a

b

c

A

B

C

a

b

c

A

B

C

a

b

c

A

B

C

a

b

c

A

B

C

A

B

C

A

B

C

A

B

C

A a B b C c

A

B

C

Conn1

Conn3

Conn2

Conn5

Conn7

Conn8

Conn9

Conn4

Conn6

Vabcb1

Vabcb

Vabca

A

B

C

a

b

c

A

B

C

a

b

c

A

B

C

a

b

c

0 0.05 0.1 0.15 0.2 0.25 0.3

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (secs)

mag

(pu)

Parameter value

Line resistance (Ω) 1.0

Line inductance (mH) 5.0

Line frequency (Hz) 50

Load phase voltage(V) 230

Load power per phase(W) 0.5HP

Injection transformer turns ratio 1:1

Saw-tooth carrier wave frequency (Hz) 2000

DC supply voltage (V) 400

Filter series inductance (mH) 20

Filter series resistance (Ω) 1

Filter shunt capacitance (µF) 20

Filter Inductance(mH) 3


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Fig 6: Load voltage after DVR compensation

First sag occurs at 0.1 and lasts for 2.5 cycles and second sag occurs at 0.2 and last for 2.5

cycles. The voltage sag reduces the load voltage to 0.5pu without DVR. The fig 5 shows the load

voltage with sag. The DVR is operated during the sag and the compensated load voltages are

shown in fig 6.

*Case II: Multiple voltage swells created by adding capacitive loads at various time periods in

the system for IMC.

Fig 7: Load voltage without compensation

Fig 8: Load voltage after compensation

Fig 7 depicts the load voltage without compensation. The load voltage raises to 15pu which I

very dangerous to the load. Swells are created at different time periods namely at 0.1 and 0.2,

each lasting for 2.5 cycles. With DVR, the load voltage comes to normal voltage; during swell

0 0.05 0.1 0.15 0.2 0.25 0.3

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (secs)

Mag

(pu)

0 0.05 0.1 0.15 0.2 0.25 0.3-1.5

-1

-0.5

0

0.5

1

1.5

Time (secs)

mag

(pu)

0 0.05 0.1 0.15 0.2 0.25 0.3-1.5

-1

-0.5

0

0.5

1

1.5

Time (secs)

mag

(pu)


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conditions, the DVR injects voltage at 180deg out of phase to bring load voltage to normal. Fig 8

shows the load voltage after compensation.

*Case I: Voltage sag created by three phase to ground fault at different time periods for PSO.

Fig 9: Load voltage depicting sag


Figure 9 shows the voltage sag. The simulation results of single area system under single

line – ground fault shows from this result that it is observed that the sag appears in the system

between the time 0.3 to 0.7 sec, so that the dynamic voltage restorer compensate these voltage

problems as shown in Figure 10.

*Case II: Voltage Swell created by adding capacitive loads at various time periods in the system

for PSO.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time(s)

ma

g(p

u)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time(s)

ma

g(p

u)


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Fig 11: Load voltage depicting swell


Fig 11 depicts the load voltage without compensation. The load voltage raises to 15pu which I

very dangerous to the load. Swells are created at different time periods .With DVR, the load

voltage comes to normal voltage; during swell conditions, the DVR injects voltage at 180deg out

of phase to bring load voltage to normal. Fig 12 shows the load voltage after compensation.

THD VALUES FOR IMC AND PSO:

Fig 13: THD value for IMC Fig 14: THD value for PSO

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

time(s)

ma

g(p

u)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1.5

-1

-0.5

0

0.5

1

1.5

time(s)

ma

g(p

u)


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Figure 13 and 14 shows the outputs of the total harmonic with dynamic voltage

restorer by considering IMC and PSO. Out of these controllers the PSO get good THD as

compared with the IMC.

CONCLUSIONS

In this paper, particle swarm optimization has been proposed for optimally tuning the

controllers associated with the DVR. The performance parameters of the DVR with PI

controllers tuned by the IMC method and the proposed tuning method using the PSO technique

are compared. The results reveal that PSO-tuned PI controllers have some definite edge over the

IMC tuning method. The proposed method has been validated using the MATLAB/SIMULINK

environment. The results confirm that the proposed idea of tuning the PI controller for the

distributed DVR with Kp and Ki values as suggested by the PSO-based tuning algorithm is far

superior than the IMC tuning method.

REFERENCES

[1] Jayaprakash P, Member, Singh B, Kothari D P, Chandra A, Al-Haddad K, “Control of Reduced-Rating

Dynamic Voltage Restorer with a Battery Energy Storage System” at IEEE TRANSACTIONS ON INDUSTRY

APPLICATIONS, VOL.50, and Issue 2, MARCH/APRIL 2014, pp-1295-1303

[2] Choi S S, Wang T X and Vilathgamuwa D M, “A series compensator with fault current limiting function,”

IEEE Transactions on Power Delivery volume 20, no.3, pp.2248–2256, Jul.2005.

[3] Deliveryfino B, Fornari F, and Procopio R, “An effective SSC control scheme for voltage sag compensation,”

IEEE Transactions .Power Delivery. vol.20, no.3, pp.2100–2107, Jul.2005.

[4] Badrkhani F Ajaei, Afsharnia S, Kahrobaeian A, and Farhangi S, “A fast and effective control scheme for the

dynamic voltage restorer,” IEEE Transactions. Power Delivery, vol.26, no.4, pp.2398–2406, Oct.2011.

[5] Roncero Sánchez, Acha E, Ortega Calderon J E, Feliu V, and García A, “A versatile control scheme for a

dynamic voltage re-storer for power-quality improvement,” IEEE Transactions. Power Delivery, vol.24, no.1,

pp.277–

[6] Weixing, Ooi B T, "Optimal Acquisition and Aggregation of Offshore wind Power by Multiterminal Voltage-

Source HVDC," IEEE Transactions. Power Delivery, vol.18, pp.201–206.

[7] Boonchiam P and Mithulananthan N, “Understanding of Dynamic Voltage Restorers through MATLAB

Simulation,” Thammast Int.J.Sc.Tech., Vol.11, No.3.

[8] Vilathgamuwa D M, Perera M A A D R, and Choi S S, “Performance improvement of the dynamic voltage

restorer with closed-loop load voltage and current-mode control,” IEEE Transactions.Power.Electron.vol.17,

no.5, pp.824–834.

[9] Weimers, L."A New Technology for a Better Environment," Power Engineering Review, IEEE, vol.18, issue 8,

PP 1560-1563.


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[10] Schettler F., Huang H., and Christl N."HVDC Transmission systems using voltage source converters – design

and applications," IEEE Power Engineering Society Summer Meeting, July 2000, pp 715-720.

[11] Jeong J, Han B “Development of Line-Interactive Dynamic Voltage Restorer with Hybrid Sag Detection” IEEE

Transactions, Volume 3 July 2010.

[12] Bae B, Jeong J “Novel Sag Detection Method for Line-Interactive Dynamic Voltage Restorer” IEEE

Transactions on power Delivery, vol.25, Issue 2, April 2010 pp-1210-1211.

[13] K. A. Siddartha, N. Manikanta Babu, Y. Suresh, M. Varun Mohan “Enhanced Performance of a DVR using

Mixed Cascaded Multilevel Inverter” INDJST Journal, Volume 8, Supplementary 2, January 2015”.

[14] D. Deepak Chowdary, G. V. Nagesh Kumar “Restoration of Single Phase Distribution System Voltage under

Fault Conditions with DVR Using Sliding Mode Control” INDJST Journal, Volume 1, Issue 5, October 2008.

[15] Farid Rezvani, Babak Mozafari, Faramarz Faghihi "Power Quality Analysis for Photovoltaic System

Considering Unbalanced Voltage" INDJST Journal, Volume 8, Issue 14, July 2015.


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Documents

Pa rticle swarm optimization (PSO) and Internal Model ... · By MATLAB SIMULINK simulation it is shown that the particle swarm optimization -tuned PI controller performs better than