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Procedia Technology 21 (2015) 295 - 302

SMART GRID Technologies, August 6-8, 2015

Design of Controller for Automatic Voltage Regulator using Teaching Learning Based Optimization

V. Rajinikantha* , Suresh Chandra Satapathyb

aDepartment of Electronics and Instrumentation Engineering, St. Joseph's College of Engineering, Chennai 600119, India bDepartment of Computer Science and Engineering, ANITS, Visakhapatnam 531162, India.

Abstract

In this paper, One Degree Of Freedom (1DOF) and Two Degrees Of Freedom (2DOF) Proportional + Integral + Derivative (PID) controller design is proposed and implemented on the Automatic Voltage Regulator (AVR) system using traditional Teaching Learning Based Optimization (TLBO) algorithm. Minimization of a multi-objective function guides the TLBO algorithm's exploration until the process converges with an optimal solution. A simulation study is carried to examine the performance of TLBO assisted controller design procedure for three, four and five dimensional searches. The performance of the proposed method is validated with most successful heuristic procedures, such as Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO) and Firefly Algorithm (FA). The result show that, 1DOF PID controller and PID controller with filter offers smooth reference tracking response and the 2DOF PID controller with the Feed Forward (FF) and Feed Back (FB) structure presents reduced time domain and error values compared to the alternatives.

© 2015 TheAuthors.PublishedbyElsevierLtd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Amrita School of Engineering, Amrita Vishwa Vidyapeetham University Keywords: AVR; PID controller; degrees of freedom; teaching learning based optimization; multi-objective function.

1. Introduction

In recent years, Heuristic Algorithm (HA) supported optimization is emerged as a powerful tool for discovering optimal solutions for a variety of engineering optimization problems [1-5]. In this work, newly developed Teaching Learning Based Optimization (TLBO) technique is adopted to solve the controller design problem. The TLBO was originally developed and implemented by Rao et al. to find most favorable solution for the constrained mechanical

* Corresponding author. Tel.: +91 9380593801. E-mail address:rajinikanthv@ stjosephs.ac.in

2212-0173 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of Amrita School of Engineering, Amrita Vishwa Vidyapeetham University doi: 10. 1016/j .protcy.2015.10.032

design problems [9]. This algorithm is theoretically similar to the teaching-learning scenario existing in the class room [10, 11]. In the proposed work, PID design problem for the Automatic Voltage Regulator (AVR) is addressed. Even though there exists a number of advanced controller structures, PID and enhanced forms of PID controllers are easy to tune and implement [6-8]. Hence, in this paper One Degree Of Freedom (1DOF) PID and Two Degrees Of Freedom (2DOF) PID controllers are designed and implemented on the benchmark AVR system using the traditional TLBO algorithm. The performance of the TLBO is validated using most successful HAs, such as Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO) and Firefly Algorithm (FA).

2. Automatic Voltage Regulator

Benchmark AVR system widely discussed in the literature is considered in this paper [3-5].

2.1 Principle

Detailed theoretical description about the AVR system can be found in [3]. During power generation process, common troubles, such as dissimilarity of load, limit deviation in transmission system, and turbine oscillation may produce oscillatory output in synchronous generator. This category of electro-mechanical fluctuation affects the firmness of power system. Hence, in modern power generating stations, in order to improve the dynamic stability and to assure the power quality, most of the synchronous generators are outfitted with an excitation unit, which is supervised by an AVR and a Power System Stabilizer (PSS) [4, 5]. Fig. 1. Illustrates the block diagram of the AVR system with linearized intermediate units. During closed loop operation, the controller is responsible to maintain stability, robustness and also to support smooth reference tracking performance based on the set value of terminal voltage.

Vref (s)

Controller

10 1 1 s +1

0.1s + 1 0.4s + 1

Amplifier Exciter Generator

Vout (s) —►

0.01s + 1

Sensor

Fig. 1. Block diagram of the AVR system

2.2 Related previous works

Due to its significance, AVR system is widely considered by most of the researchers. Heuristic algorithm based approaches are already applied on the AVR system in the literature [3-5]. Most of the researchers proposed the PID controller design for the AVR system and the performance of the controller is validated for reference tracking response.Fig.1. indicates that, the delay time present in the higher order AVR system is very small and designing a suitable controller requires the following assumptions: (i) the system is linear, (ii) external disturbance acting on the system is negligible and (iii) the sensor part is free from the measurement noise. In the proposed work, traditional and enhanced forms of PID controller is considered to regulate AVR system and the controller design process in done using heuristic algorithms.

3. PID Controller

Based on the structure and number of initial parameters to be tuned, PID is classified as One Degree Of Freedom

(1DOF) controller, Two Degrees Of Freedom (2DOF) controller and Three Degrees Of Freedom (3DOF) controller [6-8]. In the proposed work, the major aim is to support the reference tracking operation and the considered AVR system is an open-loop stable system. Hence, 1DOF and 2DOF PID structures are considered.

3.1 One DOF structure

One Degree Of Freedom (DOF) PID structure is a commonly used controller structure as given in eqn. (1) and the number of control parameters to be tuner is three, such as Kp, K and Kd [8].

C(s) = Kp +-L + Kds (1)

1DOF PID some time offers larger overshoot (Mp) and larger settling time (ts) due to the proportional and derivative kick. This drawback can be reduced with 2DOF PID structures.

3.2 Two DOF structure

2DOF controllers are enhanced forms of the traditional 1DOF PID controller. A detailed analysis on the existing 2DOF PID structures is available in [6]. Fig. 2 shows the 2DOF PID structures considered in this work such as (a) PID controller with prefilter, (b) PID with Feed-Forward structure and (c) PID with Feed-Back structure and the corresponding mathematical expressions are presented in Eqn. (2) - (6).

(a) PID controller with prefilter

(b) PID with Feed-Forward structure

(c) PID with Feed-Back structure

Fig. 2. 2DOF PID structures

F(s) =

Tfs + 1

C1( s ) = Kp + + Kds

C2(s) = Kp a + pKds

C3(s) = Kp(1 -a) + -L + (1 -P)Kds 1 s

C4(s) = Kp a + pKds (6)

Eqn. (3) and eqn. (4) shows that, inner loop controller is a traditional PID and outer loop has a PD structure with weighting parameters a and fi. Similarly, eqn. (5) shows the PID structure with weighting parameters and eqn. (6) shows the PD controller with a and f.

4. Teaching Learning Based Optimization

TLBO is formulated by imitating the teaching-learning system existing in the classroom scenario and its pseudo code is depicted in Fig. 3. Comparable to other heuristic algorithms, the TLBO also employs a population based approach to obtain the universal solution through the search. A comprehensive explanation about the TLBO can be

found in the recent literature [12,13]. In the proposed work, traditional TLBO is considered to tune the PID controllers for a benchmark AVR system. The TLBO has two essential stages, such as teacher stage and learner stage as shown below:

START;

Initialize algorithm parameters, such as number of learners (N), parameters to be optimized (D), Maximum number of iteration (Miter) and objective function (Jmin) ; Randomly initialize 'N' learners for x: (i = 1, 2, ... n); Evaluate the performance and select the best solution f(xbest); WHILE iter = 1:Miter;

%TEACHER STAGE % Use f(xbest) as teacher;

Sort based on f(x), select other teachers based on : f(x)s = f(xbest) - rand for f(x)s = 2,3, . . . , T; FOR i = 1:n

Calculate TlF = round[ 1 + rand(0,1){2 - 1}] ;

xnew = x + rand( O,1)[ xteacher ~ ( TF xmean )]; %Calculate objective function for f(x'nw)% If f(x'nw) < f(xi), then x' = x'new; End If % End of TEACHER STAGE % %STUDENT STAGE %

Arbitrarily Select the learner x', such that j ^ i;

If 0) < f(xj), then xintw,=xi+rand(0,1)(xi-xj); Else xinew=xi+rand(0,1)(x' - x'); End If

If x'„„ is better than x', then x'= x'new; End If % End of STUDENT STAGE % End FOR

Set k = k+1; End WHILE

Record the controller valus, Jmin, and performance measures;

4.1. Other Heuristic Algorithms in this Study

In this paper, heuristic algorithms such as Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO) and Firefly Algorithm (FA) are considered to validate the performance of TLBO.

4.1.1 Particle Swarm Optimization

PSO is a well known heuristic technique, developed by modeling the group activities in flock of birds [8]. Due to its high computational capability, it is widely considered by the researches to solve constrained and unconstrained optimization problem. In this work, PSO with the following mathematical expression is considered:

where Wt is inertia weight ( chosen as 0.8), R1 and R2 are random values [0,1], C1 and C2 is allotted as 2.1 and 1.8 correspondingly.

Fig.3. Pseudo code for TLBO algorithm

Vi(t +1) = WtVit + CiRi(Pt - Sj) + C2R2(Gt - St ) Xi (t + 1) = xt +Vi (t + 1)

4.1.2 Bacterial Foraging Optimization

BFO is developed by mimicking the foraging scheme of E.coli bacteria. In this paper, the enhanced BFO discuss ed in [8] is considered.The algorithm values are assigned as: Number of E.Coli bacteria = N

Nc= —; Ns=Nre ~ Ned ~ N ;Nr= N; Ped= | Ned I; d^t = Watt = — ; and hKp= Wrep = Nc (9)

c 2 3 4 r 2 d ^ N + Nr) att att N p rep N

4.1.3 Firefly Algorithm

FA is originally discussed by Yang [14]. This technique employs a mathematical representation of the firefly, searching for a mate in the search universe and details of FA can be found in [15 - 17]. The association of an attracted firefly towards a mate can be expressed as:

Xj+1 = Xt + p0e 7 diJ ( Xtj - Xt ) + a1 (rand - Vi) (10)

t t+1 df- t t where Xi is early location; Xi is updated location; fi0e 11 ( X - - Xi ) is attraction among fireflies; f0 is

preliminary attractiveness; y is absorption coefficient; a1 is randomization operator and rand is random number [0,1]. In this paper, the following values are chosen for FA parameters: a1= 0.15; f0 = 0.1and y = 1.

5. Result and Discussions

In this paper, simulation study is performed and implemented using Matlab R2010a software. The following objective function is considered to guide the heuristic search:

Jmin = Wj Mp + W2 .ts + W3 .ITAE + W4 .ITSE (11)

where the weights W1 and W2 are chosen as '2' and the W3 and W4 are chosen as '5' (preference is given to the

minimization of ITAE and ITSE), Mp is overshoot, ts is the settling time, ITAE and ITSE are integral time absolute

error and integral time squared error respectively. The HA assisted exploration is initiated with a search limit for the

1DOF and 2DOF controller parameters are assigned as follows:

For controller parameters: 0 < Kp < 0.5; 0 < K < 0.5; and 0 < Kd < 0.5.

For filter time constant: 0 < Tf < 0.1;

For weighting parameters: 0 < a <1 and 0 < p < 1.

In order to perform a fair estimation, all the considered heuristic procedures are assigned with the similar preliminary algorithm parameters as specified below:

Population size (N) is 20; Criterion to terminate the search is Jmin , maximum number of iteration is assigned as100 and simulation time is allocated as 5sec. The controller tuning practice is repeated 10 times for each algorithm with each PID structure and the best Jmin acquired between the trials are selected as the most favorable solution. Firstly, 1DOF PID design procedure is executed with TLBO using a three dimensional search (Kp, K;, Kd). Later, similar tuning procedure is repeated on the AVR system using other heuristic methods, such as PSO, BFO and FA. For PID with prefilter (FPID) a four dimensional search is considered (jf, Kp, K;, Kd) and the obtained PID values are presented in Table 1. During this search, the following filter values are attained: TfpLBO = 0.0516; TfPSO = 0.0637; Tf BFO = 0.0741 and Tf FA = 0.0816. For Feed-forward type 2DOF PID (FFPID) a five dimensional search is proposed (a, fi, Kp, Ki, Kd) and the optimal values are shown in Table 1. Similar controller parameters are chosen to analyze the performance using the FBPID controller. Initially, the heuristic algorithm designed 1DOF PID controller is considered to support the reference tracking performance of the AVR system. During the simulation study, it is

assumed that, the system is free from external disturbances. Fig .4(a) presents the value of the terminal voltage with respect to the simulation time and the corresponding performance measure values are recorded in Table 2. From this table, it is noted that, the TLBO offers smaller Mp and ITAE values compared with alternatives. The FA tuned PID results in better Jmin, ts and ITSE compared with TLBO, PSO and BFO.

Table 1. Optimal controller parameters

PID Kp Ki Kd a ß

TLBO 0.1986 0.1217 0.2683 - -

1DOF PSO 0.1836 0.1311 0.2088 - -

BFO 0.1889 0.1263 0.1862 - -

FA 0.1958 0.1261 0.2107 - -

TLBO 0.2026 0.1257 0.3174 - -

2DOF (FPID) PSO BFO 0.2003 0.1995 0.1247 0.1295 0.3579 0.3347 - -

FA 0.2102 0.1301 0.3257 - -

TLBO 0.4019 0.3382 0.0161 0.3914 0.0214

2DOF (FF) PSO 0.3904 0.3188 0.0186 0.4018 0.0311

BFO 0.4038 0.3122 0.0206 0.3882 0.0177

FA 0.3986 0.3117 0.0218 0.4170 0.0184

(a) Reference tracking with 1DOF PID (b) Reference tracking with FPID

(c) AVR response with 2DOF PID (FB) (d) AVR response with 2DOF PID (FF)

Fig. 4. Reference tracking response of AVR with various controllers

Time (sec) (a) Reference tracking response

Time (sec) (b) Controller output

Fig. 5. AVR's response with TLBO tuned controllers

From Table 1 and Table 2, the observation is that, the controller values obtained for 1DOF PID with TLBO, BFO, PSO and FA and the corresponding performance measure values are approximately similar. Hence, the performance of the considered algorithms on the 1DOF PID is identical. Fig. 4(b) depicts the reference tracking response of AVR with FPID controller. This controller offers smooth response compared with the 1DOF PID. Table 1 denotes that, the controller value provided by the considered heuristic methods is approximately similar. Table 2 shows that, PSO offers better Mp and ITAE values and FA offers improved Jmin, ts and ITSE. Fig .4(c) and Fig . 4(d) shows the set point tracking performance of AVR for FBPID structure and FFPID structure respectively. As discussed earlier, the controller parameters obtained with FBPID is implemented using FFPID structure. Hence, both the 2DOF PID configuration offers identical performance measures as shown in Table 2. The 2DOF PID designed using TLBO offers negligible Mp with better Jmin, ts, ITAE and ITSE values compared with PSO, BFO and FA.

A comparative study is also carried to evaluate the performance of 1DOF and 2DOF PID structures. Fig . 5(a) and Fig. 5(b) shows the AVR terminal voltage and corresponding controller output for the PIDs designed using TLBO. From these figures, it can be observed that, the FPID shows sluggish reference tracking response and fluctuating controller output compared with other controller structures. The FBPID and FFPID structures present enhanced reference tracking with better controller output compared with other PIDs. From this study, it is verified that, even though the number of controller parameters to be tuned is large, the 2DOF PID structure offers better setpoint tracking response and enced controller output compared with traditional PID and FPID controllers.

Table 2. Minimized objective function values

PID Method Jmin Mp ts ITAE ITSE

TLBO 6.5787 0.0126 1.6015 0.4469 0.2232

1DOF PSO 6.8963 0.0472 1.5007 0.5249 0.2352

BFO 6.6788 0.0424 1.4825 0.4980 0.2278

FA 6.5577 0.0361 1.4825 0.4827 0.2214

TLBO 7.4911 0.0216 1.7382 0.5160 0.2783

2DOF (FPID) PSO 7.6572 0.0000 1.8806 0.4934 0.2858

BFO 7.6532 0.0216 1.7780 0.5258 0.2850

FA 7.2895 0.0249 1.6411 0.5189 0.2726

TLBO 6.5833 0.0236 1.7243 0.4313 0.1862

2DOF (FF) PSO 6.8609 0.0000 1.8187 0.4416 0.2031

BFO 6.8617 0.0000 1.7281 0.4787 0.2024

FA 7.0679 0.0000 1.7262 0.5041 0.2190

TLBO 6.6271 0.0241 1.7252 0.4391 0.1866

2DOF (FB) PSO 6.9119 0.0000 1.8187 0.4530 0.2019

BFO 6.9137 0.0000 1.7281 0.4898 0.2017

FA 7.1189 0.0000 1.7262 0.5152 0.2181

5. Conclusion

In this paper, traditional TLBO based 1DOF and 2DOF PID controller design is proposed for a benchmark AVR system and its performance is validated with PSO, BFO and FA. The simulation study shows that, the controller parameters obtained with the considered heuristic algorithms are approximately similar and all the algorithms shows approximately similar Jmin value, time domain values and error values with the traditional PID and FPID controllers. In addition, the proposed study depicts that, the performance of 2DOF PID is better than PID and FPID structures. The FFPID and FBPID designed with traditional TLBO offers better performance measure values compared with the 2DOF PID controller designed using PSO, BFO and FA.

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