Optimization of TCSC with Multi Objective Genetic Algorithm for improving Stability of Single Machine Infinite Bus System

Optimization of TCSC with Multi Objective Genetic Algorithm for improving Stability of Single Machine Infinite Bus System

Optimization of TCSC with Multi Objective Genetic Algorithm for improving Stability of Single Machine Infinite Bus System.

Balasubramanyam Chiranjeevi K.B Batlanki Sai Surya

Dept. Of ECE, University of Massachusetts Lowell, Massachusetts, USA.

Dept. Of Scientific Instrumentation, Ernst-Abbe Fachhochschule Jena, Germany,

1. INTRODUCTION

   the damping of power system oscillations, TCSC based controller is utilized along with PSS thus improving power system stability. The TCSC controller is designed by two methods i.e., the conventional and proposed GA. These controllers are designed on linearized Phillips-Heffron model of Single Machine Infinite Bus (SMIB) [3, 4] power system and implemented on the same system. The performance of the controllers is compared.

   The paper is organised as follows, in the following section the functioning of TCSC is explained. The third section gives the details about modelling of SMIB system followed by damping controller in the fourth section. The fifth section gives a general picture on Genetic Algorithm (GA) [5-10]. The sixth section depicts the implementation of GA in designing of controller. The results are displayed on the seventh section followed by conclusion.

2. FUNCTIONING OF TCSC

   TCSC is an important FACTS device which makes it possible to vary the apparent impedance of a specific transmission line. TCSC consists of three components capacitor bank C bypass inductor L and bidirectional thyristors SCR1 and SCR2 as shown in Fig.1 [7, 8].

   FACTS devices [1] are installed in power system to

   In Fig.1 IC

   and IL represents instantaneous values of

   increase the power transfer capacity, to enhance continuous control over the voltage profile and/or to damp power system oscillations. They have the ability to control power rapidly, increase stability margins, minimize losses, work within the thermal limits range and as well as damping the power system

   oscillations. TCSC [1] is one of the FACTS devices

   the capacitor bank and inductor respectively IS is the instantaneous current of the controlled transmission line, V is the instantaneous voltage across the TCSC. The firing angle ( ) of the thyristors is controlled to

   adjust the TCSC reactance. The TCSC can be controlled to work in capacitive zone. The equation of

   which are used to improve the stability of the system. But the main challenge is in accurate tuning of its controller. One of the methods to design the TCSC

   reactance which is function of equation (1).

   X 2

   ( ) is represented by

   o sin( )

   controller is by phase compensation method [2]. In this method the controller is designed at one

   X TCSC

   ( ) X C

   X

   X

   C

   C

   • X L

   particular operating point and may not be robust.

   Genetic Algorithm (GA) [3, 4] is a popular method

   4X 2

   cos 2 ( 2 ) (Ktan

   ( K

   2 ) tan( 2 ))

   C

   C

   for solving optimisation problems in different fields of application. GA is utilised to design the parameters

   X C X L

   K 2 1

   (1)

   of the controller. It has the ability to obtain a near-

   where,

   XC =Nominal reactance of the fixed capacitor

   optimal solution and is quite robust. The objective of the method used in this paper is to reduce the oscillations in less time with short peaks, to increase

   C. X L = Inductive reactance of inductor L connected in parallel with C.

   • 2( ) =Conduction angle of TCSC controller.

     b

     K XC =Compensation ratio.

     [K1 K 2Eq K p D]/ M

     XL Eq [K3Eq K 4 Kq E fd ] / Tdo

     E fd [KA (K5 K6Eq Kv U pss )

     • E fd ] / TA

   (2)

   Fig.1 TCSC circuit diagram

3. MODELLING OF SMIB

   The linearized system given by state equation (2) is used for eigenvalue analysis for observing the stability of the system. Further the TCSC controller parameters are designed based on the linearized system to increase the damping of lightly damped eigenvalues.

4. MODELLING TCSC CONTROLLERS

   Fig. 2 shows the SMIB power system with the FACTS device TCSC included in between the 2nd

   The TCSC controller shown in Fig. 4. The controller block has a gain block followed by a washout block

   and 3rd bus. VT and VB are the generator terminal

   and two lead lag blocks as shown in the Fig. 4.The

   voltage and infinite bus voltage respectively, XT and

   PSS is also of the same structure. The PSS damps out

   the oscillations at the generator side. For the PSS

   X Line represent the transformer and transmission line

   input for the controller is rotor speed deviation

   respectively, X TCSC is the reactance of TCSC given

   and the output is VPSS which is to be given to the

   by Equation (1). The non-linear model given in [3],

   [4] has been linearized. The linearized Phillips- Heffron model has been established and given in equation (2). The block diagram of Phillips-Heffron model is shown in Fig.3.

   excitation of the generator. Whereas the input for the TCSC Controller is rotor speed deviation and the output modulates which is the control input signal of TCSC.

   Fig. 4 Block Diagram of Controller.

   The gain block determines the damping level; the

   Fig.2 SMIB Power system with TCSC.

   phase compensation block

   compensates the lag

   between the input and output where as the washout block acts as a high pass filter to allow signals of only high frequencies. The PSS and TCSC controller are designed using phase compensation technique [2].

   The value of

   Tw (the washout filter time constant) is

   chosen in the range of 10 to 20s. The reasonable choice of is between 0.1 and 0.3. The alternate

   method i.e, GA is used for designing controller. This paper adopts GA from [5-12] for optimizing the controller parameters.

5. REVIEW OF GENETIC ALGORITHM

   Genetic algorithms (GA) are computerised search and optimization algorithm based on mechanics of nature.(e.g.: nature of selection, survival of the fittest)

   and natural genetics. GA are good at taking large

   Fig. 3 Phillips-Heffron model of SMIB system with TCSC and PSS.

   search spaces and then analysing them for optimal combinations of solutions which are very difficult to be computed by hand.

   There are two important aspects of GA wiz.,

   • Defining the objective function

   • Applying the genetic operators to obtain the required optimization.

6. OPTIMIZATION OF OBJECTIVE

   FUNCTION:

   The term optimization is to improve or find the best

   For the given optimization function we need to

   possible output for a given

   system at particular

   determine chromosome size, population size, type of genetic operator, condition for convergence, crossover probability and points, mutation probability and point.

   1. Chromosome representation:

      Chromosome representation scheme determines how the problem is structured in GA and also the operators which are used. Each individual or chromosome id

      instant. In SMIB system the oscillations are chosen to be observed in generator angle Pe and rotor speed

      . Since the oscillations have to be damped, the objective function is taken which is a functon of the system parameters and controller parameters. The objective function can be formulated as minimization of the fitness function given by FIT .

      i.e., FIT ( f , f ) where,

      made up of a sequence of genes. Each chromosome 1 2

      can be represented in binary, decimal, floating, t1

      integer values, etc formats. In general binary coded chromosome structures are chosen for higher accuracy.

   2. Selection Function:

      The selection of individuals in the population is very important when GA is used. The selection function

      f1 Pe (t, X )2 dt

      0

      t1

      f 2 ( (t, X ))2 dt

      0

      (3)

      (4)

      determines the individuals which survive and move

      Here ' X ' represents the TCSC parameters which

      on to next generation. A probabilistic selection is

      should be minimised, t1 is the time range of

      performed based upon the individuals fitness such

      simulation. X Represents T1 , T2 , KC which are TCSC

      that only the best individuals have the chances of

      parameters and T3 T1; T4 T2 . Since the fitness

      being selected. Out of the all available selection

      function and the system generator parameters are

      processes, Roulette wheel selection is applied in this

      dependent on T , T , K , the change in values of

      paper.

   3. Operators of GA:

   1 2 C

   these parameters is reflected in control of oscillations.

   The two basic operators of GA i.e, cross over and

   f1 Measures the change

   in electrical power

   mutation are used to produce the new solutions based on existing solutions in population. Crossover takes two individuals to be parents and produces two new individuals while mutation alters one individual to produce single new solution. in this paper uniform crossover and uniform mutation methods are chosen as GA operators.

   Fig. 5 Flow chart explaining GA

   oscillations, f 2 measures the rotor oscillations in spspeeeedd.. MMiininimmiisasatiotionn ooff FFIITT changes the system performance by damping the oscillations. For minimizing the FIT function we are adopting Genetic algorithm method which is fast and has a wide range of application. The parameters used in GA are given in Table 1 and 2.

   TABLE 1: PARAMETERS USED IN GA:

   Parameter	Value/Type
   Maximum Generations	1000
   Population size	100
   Type of Selection	Normal
   Type of Crossover	Equal crossover (Pc=0.9)
   Type of Mutation	Non uniform (Pm=0.1)
   Termination Method	Convergence

   TABLE 2:

   BOUNDARIES OF UNKNOWN VARIABLES, OPTIMIZATION PARAMETERS:

   Parameters	Gain (Kp)	Time constant (T1 ) (T2)
   Minimum Range	1	0	0
   Maximum Range	10	2	2
   Obtained Parameters	2.4144	1.4854	0.0419

7. RESULTS: VIII. CONCLUSION

The power system defined by

equation (2) is

The problem of bringing

the system back to

simulated in Matlab with the system data and controller parameters given in the Appendix. The oscillations are created by giving in a three phase fault at the generator bus. The different controllers are

placed in the system for respective cases and their

synchronism in the shortest duration of time has been successfully achieved with the help of TCSC controller. The controller is designed by phase compensation and GA methods. The primary

performance is observed in Figs. 6-8. From these

objective of this paper is to improve the stability of

figures it is clear that by using Genetic Algorithm technique for controlling the TCSC is more effective and damps out the oscillations in the rotor speed and

the system while reducing the overshooting of the oscillations at the earliest possible. This paper proves

the contribution of improved method of GA termed as

electrical power much earlier compared to the conventional phase compensation technique. This is

due to the optimal tuning of TCSC while the other

the multiobjective GA to meet the pre defined target. The response of SMIB power system with PSS,

methods are poor in performance due to the multi objective function GA method is more robust. On the other hand the due to the operational sequence of GA, the initial shooing of the oscillations is also

TCSC using phase compensation and genetic algorithm techniques are compared. The inclusion of TCSC controller along with PSS in the SMIB system

improves its stability. The implementation of GA to

significantly damped for the given conditions compared to the conventional phase compensation method.

Fig.6 Response of electrical power to three phase fault

design TCSC controller for dynamic stability showed significantly improved results by damping oscillations in minimum time possible compared to the conventional phase compensation based TCSC controller.

IX. FUTURE RESEARCH:

Advanced research can be implemented where the complexity of computation of the parameters could be decreased there by making it feasible for the user to narrow down the controller parameters reducing the duration of calculations and ensuring the correctness of the results. The new Evolutionary algorithms could

be applied to observe the response of TCSC

parameters and the system stability in the long run.

REFERENCES:

Fig.7 Response of rotor speed to three phase fault

1. N. G. Hingorani and L. Gyugyi, Understanding FACTS: Concepts and Technology of Flexible AC Transmission System. IEEE Press. 2000.

2. H.F.Wang, F.J.Swift, FACTS- Based stabilizer designed by the phase compensation method part I on single machine power systems, Advances in power system control, operation and management, 1997. APSCOM-97, Fourth international conference on 11- 14 Nov 1997.

3. Richard C. Dorf, Modern Control Systems,

   Addison-Wesley Publishing Company, 1992

4. P. Kundur, Power System Stability and Control. Mc Graw-Hill, New York, 1994, ch. 12.

5. D.E.Goldberg Genetic algorithm in search

   Fig.8 Response of rotor speed with different controllers to three phase fault

   optimization and machine learning Addison-Wesley Publications (1989)

6. D.P.Kothari, J.S.Dhillon, Text book on Power System Optimization by Eastern Economy Edition, PHI Learning Pvt.Limited.

7. Sidharatha Panda, R. N. Patel, N. P. Padhy, Power System Stability Improvement by TCSC Controller Employing a Multi- Objective Genetic Algorithm Approach, International Journal of Electrical and Computer Engineering 1:8 2006

8. Sadegh Shajari, Md. Reza Norouzi, Ali Abedini, Kiarash Ahi, " Coordinate Control Of TCSC Based GA Controller with PSS for Stability Improving in Single Machine system", Environment and Electrical Engineering (EEEIC), 2011 10th International Conference

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APPENDIX:

System data: All data are in p.u

Generator: H = 4.0 s, D = 0,

X d =1.0,

X q =0.6;

X d =0.3,

Tdo =5.044, f =50, Ra =0,

Qe =0.303,

Pe =1.0, o =60.620. K A =200, TA =0.04 s.

Transmission line and Transformer:

( X L

= 0.7, XT

= 0.1) = 0. 0 + j0.8.

TCSC Controller:

X TCSCo =0.245, o =156.040,

XC =0.21, X L =0.0525.

PSS controller Parameters:

K PSS =7.0521, TW =10,

T1 =0.2875, T2 =0.1272.(phase compensation method) TCSC controller Parameters: KC =0.4077, TW =10, T1 =1.4510, T2 =0.0202.(phase compensation method)

KC =2.4144, TW =10, T1 =1.4854, T2 =0.0419

(GA based method)