Design of a proportional-integral-derivative controller for an automatic ...

IEEE/CAA JOURNAL OF AUTOMATICA SINICA

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Design of a Proportional-Integral-Derivative Controller for an Automatic Generation Control of Multi-area Power Thermal Systems Using Firefly Algorithm K. Jagatheesan, Student Member, IEEE, B. Anand, Fellow, IEEE, Sourav Samanta, Nilanjan Dey, Amira S. Ashour, Valentina E. Balas, Senior Member of IEEE

Abstract—Essentially, it is significant to supply the consumer with reliable and sufficient power. Since, power quality is measured by the consistency in frequency and power flow between control areas. Thus, in a power system operation and control, Automatic Generation Control (AGC) plays a crucial role. In this paper, multi-area (Five areas: area 1, area 2, area 3, area 4 and area 5) reheat thermal power systems are considered with Proportional-Integral-Derivative (PID) controller as a supplementary controller. Each area in the investigated power system is equipped with appropriate governor unit, turbine with reheater unit, generator and speed regulator unit. The PID controller parameters are optimized by considering nature bio-inspired Firefly Algorithm (FFA). The experimental results demonstrated the comparison of the proposed system performance (FFA-PID) with optimized PID controller based Genetic Algorithm (GA) (GAPID) and Particle Swarm Optimization (PSO) technique (PSOPID) for the same investigated power system. The results proved the efficiency of employing the Integral Time Absolute Error (ITAE) cost function with one percent Step Load Perturbation (1% SLP) in area 1. The proposed system based FFA achieved the least settling time compared to using the GA or the PSO algorithms, while, it attained good results with respect to the peak overshoot/ undershoot. In addition, the FFA performance is improved with the increased number of iterations which outperformed the other optimization algorithms based controller. Index Terms—Automatic Generation Control (AGC), FireThis article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. This manuscript was recommended by Associate Editor Chengdong Li. Citation: K. Jagatheesan, B. Anand, S. Samanta, N. Dey, A. S. Ashour, V. E. Balas, “Design of a proportional-integral-derivative controller for an automatic generation control of multi-area power thermal systems using firefly algorithm,” IEEE/CAA Journal of Automatica Sinica, pp. 1−14, 2017. DOI: 10.1109/JAS.2017.7510436. K. Jagatheesan is with the Department of Electrical & Electronics Engg., Mahendra Institute of Engg. & Tech., Namakkal, Tamilnadu, INDIA (e-mail: [email protected]). B. Anand is with the Department of Electrical & Electronics Engg., Hindusthan College of Engg. & Tech., Coimbatore, Tamilnadu, INDIA (email: b anand [email protected]). S. Samanta is with the Department of Computer Science & Engineering, University Institute of Technology, BU, Burdwan, West Bengal, INDIA (email: [email protected]). N. Dey is with the Department of Information Technology, Techno India College of Technology, Kolkata, INDIA (e-mail: [email protected]). A. S. Ashour is with the Department of Electronics and Electrical Communications Engineering, Faculty of Engineering, Tanta University, EGYPT (e-mail:[email protected]). V. E. Balas is with the Faculty of Engineering, Aurel Vlaicu University of Arad, ROMANIA (e-mail:[email protected]).

fly algorithm, Genetic Algorithm (GA), Proportional-IntegralDerivative (PID) controller, Particle Swarm Optimization (PSO).

I. I NTRODUCTION

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UE to modern technologies escalation, industries are modernized and automated, which require power supplies of high quality. The power supply quality is deliberated by stability in the system frequency and voltage profile across the generator terminals. The single power system provides good quality of power, when load disturbance/demand occurs within the specified limit [1]. However, during large load demand condition, system stability, power quality and system performance are affected. In order to overcome these limitations, power generating units are interconnected through the tie-line. During normal loading conditions each power generating unit carries its own load. Thus, when sudden load occurs in any one of the interconnected power systems, it shares the power between the control areas through tie-line to maintain system stability [2]. The interconnection of the power system increases the size and complexity. The primary control of the power system is achieved by speed governor, but the control action provided by the governor is not sufficient to match the generation with load demand [3]. The aforementioned issue with the power system is solved by implementing proper secondary/supplementary controller. From the literature, it is found that many supplementary controllers are successfully designed and implemented in a Load-frequency control (LFC)\AGC crisis of single/multi area power system. Kothari et al.. discussed the AGC of two area thermal power system with Generation Rate Constraint (GRC) and integral controller [4]. While, the AGC of two area power system with governor dead band and integral controller was conducted in [5]. With optimal controller, the AGC of two area hydrothermal power system was mentioned in [6]. Then, the AGC of two area reheat thermal power system using Proportional Integral (PI) controller was discussed in [7]. Das et al.. [8] proposed the AGC of two area reheat thermal power system with Variable Structure Controller (VSC). Tripathy et al.. [9] suggested an AGC of two area reheat thermal power system by considering boiler dynamics and Super Magnetic Energy Storage (SMES) unit.

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In 2010, Roy et al.. [10] employed an evolutionary computation technique with the AGC of three area power system. In [11], the LFC of interconnected non reheat power system was analyzed with PI controller. In 2012, Gozde et al.. [12] introduced the AGC of interconnected reheat thermal power system with PI and PID controller. In the same year, Daneshfar et al.. [13] employed the genetic algorithm for multi objective design with the LFC problem. Fuzzy Integral Double Derivative (FIDD) controller with the AGC of multiarea hydrothermal power system was presented in [14]. Debbarma et al.. [15] investigated the AGC of multiarea thermal power system under deregulated environment by considering non-integer controller. In [16], the LFC of two area power system was discussed with 2-Degree of Freedom Proportional-Integral-Derivative (2DOF-PID) controller for load frequency control of power system with governor dead-band (GDB) nonlinearity. Padhan and Majhi [17] presented the PID controller with the LFC of single/multi area power system. Shabani et al.. [18] proposed a robust PID controller based on Imperialist competitive algorithm for load frequency control of power systems. The AGC crisis in interconnected power system with PID controller was presented in [19]. Meanwhile, Taher et al.. studied the LFC of the power system with Fractional Order PID controller (FOPID) [20]. From the preceding literatures, it is concluded that several controllers have been designed and implemented to solve the LFC/AGC concern of the power system. Since, proper selection of the controller gain is very crucial for better controlled performance. Recently by the year 2015, many bioinspired algorithms are developed to optimize the controller gain values, such as i) Direct Synthesis (DS) for tuning of PID controller parameters [21], ii) Grey Wolf Optimizer algorithm for tuning of PI and PID controller gain values [22], iii) Self Adaptive Modified Bat Algorithm (SMBA) for tuning of PI controller [23], iv) Cuckoo search(CS) algorithm for tuning of PI controller [24], v) Teaching Learning Based Optimization (TLBO) for tuning of Fuzzy PID controller gain values [25], vi) hybrid Particle Swarm Optimization (PSO) and Pattern Search (PS) (hPSO-PS) optimization for tuning of Fuzzy PI controller [26], vii) Minority Charge carrier Inspired (MCI) algorithm was proposed for tuning of I and PI controller [27], and viii) Modified Harmony Search Algorithm (MHSA) for tuning PID controller parameters [28]. Since, the PID controllers are widely used to control many kinds of systems, these controllers are used generally to improve the system dynamic response as well as to reduce/ eliminate the steady- state error. Thus, for better performance, the optimal selection of the PID parameters is required. In this regard, the parameters selection can be considered an optimization problem, for which optimization algorithms can be used to determine the optimal controller gain/ parameters. Recently, the well-known firefly algorithm is adapted for solving different design problems [29-32]. Therefore, the main idea of the proposed system is to employ the cooperating fireflies optimization algorithm in order to optimize the PID controller parameters for a five area reheat thermal power systems. Additionally, the genetic algorithm (GA) and the PSO are well-established optimization algorithms. Thus, in


this context, the proposed FFA-PID system performance is compared to both GA and PSO- based PID controllers. The rest of the paper is organized as follows. Section 2 describes the proposed system modeling, followed by section 3 that presents the design procedure of the PID controller. Section 4 depicts the proposed bio-inspired algorithm. Then, section 5 provides the simulation result comparisons of the proposed algorithm to other optimization methods. Finally, the conclusion is conducted in section 6. II. F IVE A REA I NTERCONNECTED R EHEAT T HERMAL P OWER S YSTEM The transfer function model of the investigated multi-area interconnected reheat thermal power system was shown in Fig.1. The multi-area power system incorporated five equal reheat thermal power generating units. Each unit consisted of suitable speed governing unit, turbine and generator unit with PID controller. In Fig 1., R1 , R2 , R3 , R4 and R6 are the self regulation parameters for the governor in p.u. Hz; Tg1 , Tg2 , Tg3 , Tg4 and Tg5 represent the speed governor time constants in sec.; Tr1 , Tr2 , Tr3 , Tr4 and Tr5 are the reheat time constants in sec.; Kr1 , Kr2 , Kr3 , Kr4 and Kr5 are the reheater gain; Tt1 , Tt2 , Tt3 , Tt4 , Tt5 are the steam chest time constant in sec.; Tp1 , Tp2 , Tp3 , Tp4 and Tp5 are the power system time constant in sec. (T p = 2H/f ∗ D); Kp1 , Kp2 , Kp3 , Kp4 and Kp5 are the power system gain (Kp = 1/D); B1 , B2 , B3 , B4 and B5 are the frequency bias parameters; delPtie is the incremental tie-line power change; delF1 , delF2 , delF3 , delF4 and delF5 are the incremental frequency deviations in Hz; ACE1 , ACE2 , ACE3 , ACE4 and ACE5 stand for the area control error. In current work, the PID controller is proposed as a secondary controller. The controller input and output are the Area Control Error (ACE) and the control signal (u); respectively. The ACE is defined as the linear combination of the frequency deviation and the tie-line power flow deviation. The area control error for each area is given by: ACE1 = B1 ∆F1 + ∆Ptie1

(1)

ACE2 = B2 ∆F2 + ∆Ptie2

(2)


(3)


(4)


(5)

where, ACE1 , ACE2 , ACE3 , ACE4 and ACE5 are the area control error of areas 1 till 5; respectively. ∆F1 , ∆F2 , ∆F3 , ∆F4 and∆F5 are the frequency deviation in areas 1 till 5; respectively, ∆Ptie is the tie-line power deviation for the corresponding area.

JAGATHEESAN et al.: DESIGN OF A PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROLLER FOR AN AUTOMATIC GENERATION CONTROL OF · · ·

Z III. P ROPORTIONAL -I NTEGRAL -D ERIVATIVE (PID) C ONTROLLER

U4 = KP 4 ACE4 + Ki4

Nowadays, it is most common in all industries to use the significant features of the PID controller for simple construction and easy implementation. Thus, the transfer function of the PID controller is given by:

U5 = K5 ACE5 + Ki5

KD S µ ¶ 1 = KP 1 + + TD S Ti S

Z

GP ID (s) = KP + KI S +

(6)

where, Kp is the Proportional Gain, Ki is the Integral Gain, Kd is the Derivative gain, Ti is the Integral action time and Td is the derivative action time. The PID controller consists of three modes, namely the Proportional, Integral and derivative modes. Based on the input of the PID controller, it generates appropriate control output signal to keep the power system response within the specified limit. The expression for the generated control signal is given by: Z dACE1 (7) U1 = KP 1 ACE1 + Ki1 ACE1 dt + Kd1 dt Z dACE2 U2 = KP 2 ACE2 + Ki2 ACE2 dt + Kd2 (8) dt Z dACE3 U3 = KP 3 ACE3 + Ki3 ACE3 dt + Kd3 (9) dt

Fig. 1.

ACE4 dt + Kd4 ACE5 dt + Kd5

dACE4 dt

dACE5 dt

3

(10) (11)

In the current study, the parameters of the PID controller’s gain values are optimized by using three different bio-inspired optimization algorithms, namely the Genetic Algorithm (GA), the Particle Swarm Optimization (PSO) and the Firefly Algorithm (FFA). The controller’s proper design is based on suitable selection of its objective function. The objective function is defined based on the required specification and constraints as well as the closed loop response of entire system output with time domain specification. The output of the time domain specification analysis is the peak overshoot, undershoot, settling time and steady state error. The different cost functions that can be involved are the Integral Square Error (ISE), Integral Time Square Error (ITSE), Integral Absolute Error (ITAE) and Integral Time Absolute Error (ITAE). Based on the literature, it is evident that the ITAE based objective function provides more superior performance compared to other objective functions [26, 33]. Thus, the ITAE objective function is used in the proposed system using the following expression. Z∞ J = t|e(t)|dt (12) 0

This objective function is to be considered with the optimization algorithms.

Five area interconnected reheat thermal power system ( where, “Gover” refers to the governor

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IV. F IREFLY A LGORITHM The Firefly Algorithm (FFA) [33−37] is a bio-inspired meta-heuristic search algorithm inspired by the behavior of fireflies. Meta-heuristics do not assure that the global optimal solution can ever be achieved, though such global optimality can be found in many cases in practice. Almost all the metaheuristics use some form of stochastic components. Their power comes from their attempt to emulate the best features in nature, biological systems that have specially evolved by natural selection, over millions of years. There are significant attributes of meta-heuristic algorithms, though the selection of the best fit and environmental adaptability are very important. From the algorithm behavior point of view, intensification and diversification are the two key components. Intensification tends to explore local regions around the region of the existing best solutions, selecting the best solutions or candidates. In contrast, miscellany tries to explore the search space more competently by generating solutions with higher diversity. In traditional gradient-based methods, gradient of the function to be optimized has vital information for rapid finding and optimization of the solutions for a specific problem. Though, in the case of dealing contrary to the necessary conditions to the relevance of these methods (highly nonlinear, not differentiable, non-smooth, non-convex problems) face complexities on convergence and often getting trapped in local optima. The Firefly optimization algorithm can remarkably improve the technique of the global search and local optimization ability. The FFA (non-gradient based) is a simple objective function based evolutionary technique that can produce an effective result when dealing with highly nonlinear dynamic optimization problems having quite a few limitations. Like all other well tested meta-heuristic algorithms for optimization, FFA can also find an optimal solution to a problem by iteratively making an effort to enhance a candidate solution considering a specified measure of the solution quality. A nature stimulated meta-heuristic algorithm was developed by Xin-She Yang in 2007, namely Firefly Algorithm (FFA), which is based on the ?ashing patterns and behavior of fireflies [34, 37−40]. This modern meta-heuristic algorithm uses three idealized rules as stated below: • •

•

Fireflies are unisexual. They move towards more appealing and brighter fireflies irrespective of their sex. Attractiveness is proportional to brightness. Brightness is inversely proportional to the distance amongst fireflies. For any two ?ashing fireflies, the less bright moves towards the brighter one. A firefly moves randomly, if there is no brighter ?re?y than the particular one. The landscape of the objective function determines the brightness of a ?re?y. In most of the problem domain, the objective function value is proportional to the brightness.

The two most significant issues in the firefly algorithm are: 1) Light intensity variation; and 2) Formulation of attractiveness. The firefly’s attractiveness is proportional to the light intensity seen by adjacent fireflies. A monotonically decreasing function, namely the attractiveness function β(r) with the

distance r (r is the distance between two adjacent fireflies) can be represented as the following generalized form: m

β(r) = β0 e−γr ,

m≥1

(13)

where, β0 denotes the maximum attractiveness at r = 0. γ is a fixed light absorption coefficient, which controls the decrease in the light intensity. Although, γ ∈ [0, ∞] but still in practice the value of γ is determined by the characteristic length of the system to be optimized which normally ranges within 0.1 to 10 [40]. In addition, the characteristic distance Γ is the distance over which the attractiveness changes significantly. For a given characteristic length scale in an optimization problem, the parameter γ can be typically initialized by the following value:

γ=

1 Γm 20

(14)

For fixed γ, the characteristic distance will be: Γ = γ −1 → 1 as m → α. The distance between any two fireflies i and j at xi and xj can be computed by the following equation: v u d uX rij = ||xi − xj || = t (xi,k − xj,k )2

(15)

k=1

Where, xi,k is the k th component of the spatial coordinate xi of ith firefly and d denotes the number of dimensions. A firefly i gets attracted to another more appealing (brighter) fireflyj where the relation between the new and old position of firefly iis determined by: 2

xt+1 = xti + β0 e−γrij (xtj − xti ) + αεti i

(16)

Where, the 2nd term in eq. (16) is due to attraction. The 3rd term is randomization with α being the randomization parameter, and εti is a vector of random numbers drawn from a Gaussian distribution or uniform distribution at time t.

A. Firefly Algorithm The main objective of this paper is to use the FFA to optimize the PID control parameters of five reheat thermal power systems. The basic steps of the FFA [34−36] can be summarized by the following pseudo code:


Begin Definethe objective functionf (x) : x = (kpn , kin , kdn )T n=1,2. . . 5 (Eq.12). Generate initial population of fireflies yi ,( i= 1 ,2. . . ..s) Light intensity Ipidvali at xi is determined by f (xi ) (Eq. 12). Define light absorption coefficient γ while ( t < MaxGeneration ) for i= 1 to s all s fireflies for j = 1 to i all s fireflies if Ipidvali < Ipidvalj Move firefly i towards j; end if Attractiveness varies with distance rij via exp [−γ × rij ] Evaluate new solutions and update light intensity end for j end for i Rank the fireflies and find current best. end while Post process on the best so far results and visualization End

solid lines indicate the response of the GA based PID controller equipped power system; the dash-dotted line show the response of the PSO based PID controller equipped power system and the solid bold line illustrates the response of the FFA based PID controller power system.

Fig. 2.

The frequency deviation of area 1 for 100 iterations

Fig. 3.


Fig. 4.


Fig. 5.


V. S IMULATION R ESULTS AND D ISCUSSIONS Extensive efforts were directed to the optimization problems as well as PI controllers and load frequency control [41−52]. It is known that, during normal operation of the power system, it carries its own load and keeps the system parameters within the limit. However, when sudden disturbance occurs in the power system, it affects the system parameters. In order to overcome this problem, it is required to use controllers. In power system, the primary control loop is considered speed regulator and the secondary controller is considered supplementary controller. In the current work, the PID controller is equipped as a secondary controller to generate appropriate control signal based on the error signal developed by the power system. The control signal generated by the controller is used by the power system as a reference signal. The error signal is linear combination of the system frequency error and tie-line power flow error between connected areas. Consequently, this work investigated multi-area reheat thermal power system which has been developed and implemented using Matlab/Simulink environment. The designed power system is simulated by considering one percent Step Load Perturbation (1% SLP) in area 1 and PID controller to measure the proposed algorithm superiority. The optimization algorithms for tuning controller parameters are written as a separate Matlab file and stored. The simulation results are carried out for two different scenarios: (a) Simulation performed for 100 iterations, (b) Simulation performed for 150 iterations. In these scenarios the gain values of the controller parameters are optimized by considering the GA, PSO and FFA algorithms. A. Scenario (a) with 100 Iterations The simulation is performed by considering 100 iterations and responses of the under investigation power system is shown in the Figs (2−16). In these mentioned figures, the

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Fig. 6.

Fig. 7.

Fig. 8.

Fig. 9.

Fig. 10.


Fig. 11.

Tie-line power flow from area 5 for 100 iterations


Fig. 12.

Area control error of area 1 for 100 iterations

Fig. 13.


Fig. 14.


Fig. 15.






Fig. 16.


From the previous figures responses, it is clearly shown that the FFA algorithm optimized PID controller equipped power

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system achieved the least damping oscillations with the fastest settled response, in addition to the minimal overshoot peak. Thus, it provided a superior controlled performance response compared to using the GA and PSO based PID controller equipped power system. It obvious that the frequency deviation of area 1 has the maximum undershoot peak compared to the other areas. While, it has the minimal overshoot peak compared to the other areas. With respect to the tie-line power flow, it is illustrated that area 1 has negative undershoot peak, while the other areas have positive values. The numerical value comparisons of settling time, peak overshoot and undershoot are given in the Table I along with a statistical bar chart comparisons of the peak overshoot,

TABLE I C OMPARISON VALUES OF S ETTLING T IME , P EAK OVER S HOOT AND P PEAK U NDER S HOOT FOR 100 I TERATIONS

delF1 delF2 delF3 delF4 delF5 delPtie1 delPtie2 delPtie3 delPtie4 delPtie5 ACE1 ACE2 ACE3 ACE4 ACE5

GA 19.12 21.09 22.17 21.09 23.86 25.83 19.2 24.76 17.42 23.25 17.84 26.63 17.19 24.33 17.19

Settling Time PSO 16.97 16.3 20.01 18.92 20.86 24.83 16.75 24.59 16.36 21.70 16.33 22.7 16.54 23.23 16.33

FFA 14.55 12.94 16.12 16.12 15.67 24.53 14.52 24.05 13.94 18.92 13.53 21.8 14.55 22.77 13.79

GA 0.00146 0.00068 0.0001 0.0005 0.00056 0.0004 0.0005 0.0018 0.0006 0.0018 0.00071 0.00063 0.0006 0.00089 0.0006

Peak overshoot PSO 0.0015 0.0003 0.00001 0.00045 0.00048 0.0003 0.00042 0.0018 0.00044 0.0017 0.00042 0.00065 0.00042 0.00078 0.00042

FFA 0.0014 0.00029 0.00014 0.0005 0.00012 0.0004 0.00038 0.0019 0.00038 0.0019 0.00038 0.00075 0.00038 0.00085 0.00038

GA 0.0107 0.0048 0.0053 0.006 0.0052 0.0076 0.005 0.00007 0.0048 0.00013 0.0048 0.00092 0.0048 0.0019 0.0048

Peak undershoot PSO 0.0103 0.0049 0.0052 0.0055 0.0051 0.0072 0.0047 0.00005 0.0047 0.00008 0.0047 0.00099 0.0049 0.0015 0.0047

FFA 0.011 0.0059 0.0052 0.0053 0.0056 0.0078 0.0059 0.00001 0.0059 0.00017 0.0056 0.0015 0.0059 0.0017 0.0056

undershoot and settling times using 100 iterations.

B. Scenario (b) with 150 Iterations

Fig. 19.

Fig. 17.

Frequency deviation of area 1 for 150 iterations

Fig. 18.



In this scenario, the gain values of the controller parameters are optimized by considering GA, PSO and FFA algorithms with 150 iterations. The response of the investigated power system is shown in the Figs. (17−31).

Fig. 20.


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Fig. 21.


Fig. 22.


Fig. 23.


Fig. 24.


Fig. 25.


Fig. 26.


Fig. 27.


Fig. 28.


Fig. 29.


Fig. 30.



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Figures 17−31 established that the power system response with FFA based PID controller achieved superior performance compared to PSO and GA based PID controller performance in terms of minimal settling time with lesser damping oscillations and peak over and under shoot values. The numerical value comparisons of the settling time, peak overshoot and undershoot are given in the Table II along with statistical bar chart comparisons of the peak overshoot, undershoot and settling times using 150 iterations. Fig. 31.


TABLE II C OMPARISON VALUES OF S ETTLING T IME , P EAK OVER S HOOT AND P EAK U NDER S HOOT FOR 150 I TERATIONS

delF1 delF2 delF3 delF4 delF5 delPtie1 delPtie2 delPtie3 delPtie4 delPtie5 ACE1 ACE2 ACE3 ACE4 ACE5

GA 15.48 14.82 23.62 14.62 20.86 24.32 18.3 27.55 22.36 19.78 21.84 21.53 26.9 25.81 18.87

Settling Time PSO 14.62 14.2 11.16 13.83 16.37 23.2 17.23 26.01 20.23 25.81 21.74 20.38 22.82 25.01 23.89

FFA 14.12 14.12 18.16 13.6 16.44 23.1 20.8 25.81 21.03 24.32 20.8 19.38 21.3 24.12 18.16

GA 0.0017 0.00051 0.00032 0.0012 0.00069 0.00014 0.002 0.0021 0.0023 0.0024 0.0008 0.0007 0.00073 0.00088 0.00095

Peak overshoot PSO 0.0014 0.00074 0.00079 0.00068 0.00082 0.000016 0.0021 0.0021 0.0021 0.002 0.00047 0.00084 0.0008 0.00083 0.00071

Statistical calculations are carried out to check the supremacy of proposed FFA optimization technique. A comparison of PID controllers performance designed on the basis of three different optimization techniques, namely FFA-PID, GA-PID and PSO-PID with respect to the average values of the settling time is illustrated in Figs. 32-39. Figure 32 illustrates the bar chart of the peak overshoots using 100 iterations based PID controller performance with GA, PSO and FFA optimization algorithms.

Bar chart comparisons of peak overshoots using 100 iterations

Figure 32 established that in terms of the delF1, delF2, delF5, delPtie2, delPtie4, ACE1, ACE3 and ACE5 values,

GA 0.0117 0.0061 0.0062 0.0067 0.0071 0.0089 0.00009 0.000045 0.000079 0.0000016 0.011 0.0012 0.0012 0.0019 0.0022

Peak undershoot PSO 0.0114 0.0063 0.0062 0.0064 0.0058 0.0085 0.000032 0.000056 0.000047 0.00002 0.0111 0.0018 0.0015 0.0017 0.0011

FFA -0.009 0.0052 0.0044 0.0049 0.0051 0.0069 0.00007 0.0000056 0.000016 0.00002 0.0091 0.0014 0.00071 0.0012 0.0014

the proposed FFA based controller has effectively reduced the peak overshoot compared to the other optimization algorithms. Figure 33 illustrates the bar chart comparison with respect to the peak undershoots using 100 iterations based PID controller performance with GA, PSO and FFA optimization algorithms.

Fig. 33.

Fig. 32.

FFA 0.0011 0.00048 0.00023 0.00049 0.00047 0.00011 0.0017 0.0015 0.0017 0.0017 0.0001 0.00075 0.00057 0.0007 0.00073

Bar chart comparisons of peak undershoots using 100 iterations

Figure 33 depicted that in terms of the delF3, delF4 and delPtie3, the proposed FFA based controller has effectively reduced the peak undershoot compared to the other GA-PID and PSO-PID approaches. Figure 34 illustrates the bar chart comparison of the settling time using 100 iterations based PID controller performance with GA, PSO and FFA optimization

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techniques.

Fig. 36.

Bar chart comparisons of peak undershoot for 150 iterations

Fig. 34. Bar chart comparisons of settling time for 100 iterations

Figure 34 indicated that in terms of the delF1, delF2, delF3, delF4, delF5, delPtie1, delPtie2, delPtie3, delPtie4, delPtie5, ACE, ACE2, ACE3, ACE4 and ACE5, the proposed FFA based controller provided the fastest settled response compared to other optimization techniques based controller for the same investigated power system.

Figure 36 illustrates the superiority of the proposed FFAPID controller system with the delF1, delF2, delF3, delF4, delF5, delPtie1, delPtie3, delPtie4, delPtie5, ACE1, ACE3 and ACE4, where it effectively reduces the peak undershoot. Figure 37 demonstrates the bar chart comparison of the settling time using 150 iterations based PID controller performance with GA, PSO and FFA algorithm techniques.

Meanwhile, the comparison values in Table 2 are statistically illustrated for 150 iterations in Figs 35−37. Figure 35 illustrates the bar chart comparisons of peak overshoots for 150 iterations based PID controller performance with GA, PSO and FFA algorithm techniques.

Fig. 37.

Fig. 35.

Bar chart comparisons of peak overshoot for 150 iterations

Figure 35 depicts that with respect to the delF1, delF2, delF3, delF4, delF5, delPtie2, delPtie3, delPtie4, delPtie5, ACE1, ACE3 and ACE4, the proposed FFA based controller has effectively reduced the peak overshoot. Figure 36 demonstrates the bar chart comparison of the peak undershoots using 150 iterations based PID controller performance with GA, PSO and FFA algorithm techniques.

Bar chart comparisons of settling time for 150 iterations

Figure 37 clearly depicts that in delF1, delF2, delF4, delPtie1, delPtie3, ACE1, ACE2, ACE3, ACE4 and ACE5, the proposed FFA based controller provided fast settled response compared to other optimization techniques based controller performance in the same investigated power system.

Generally, a comparison chart of the percentage improvement of the Firefly Algorithm based PID controller performance over GA and PSO optimized PID controllers’ response for the same investigated power system for 100 iterations is shown in Fig. 38.


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It is established from the above results that with increasing number of iterations, the settling time using the FFA is slightly increased, while it is decreasing both the peak overshoot and undershoot efficiently. With 150 iterations, the FFA settling time, peak overshoot and undershoot values are superior to those obtained using GA and PSO. Consequently, the preceding results depicted the superiority of the PID-FFA over the PID-GA and the PID-PSO. Since, the Differential Evolution (DE) is a popular optimization method, thus it is recommended to compare the proposed system performance using FFA-PID to the DE-PID controller performance. Fig. 38. Bar chart comparisons of the improvement percentage (y-axis) for proposed FFA over GA and PSO for 100 iterations

It is clearly shown that the overall performance of the proposed system for all areas is improved compared to GA and PSO optimization techniques. Additionally, Fig. 39 demonstrates comparison chart of the percentage improvement of Firefly Algorithm based PID controller performance over GA and PSO optimized PID controllers’ response for the same investigated power system for 150 iterations.

Fig. 39. Bar chart comparisons of the improvement percentage (y-axis) for proposed FFA over GA and PSO for 150 iterations

Figure 39 establishes that in all areas the performance of the proposed controlled system is improved compared to GA and PSO optimization techniques except the responses of delF3, delPtie2, delPtie4, delPtie5 for the investigated power system. Furthermore, a computational time comparison is done between the proposed FFA-PID controller and the GA-PID and PSO-PID controllers as shown in Table III. TABLE III C OMPARISON VALUES OF THE C OMPUTATIONAL T IME OF THE T HREE A LGORITHMS Iteration 100 150

Execution Time (min.) GA PSO FA 12.4235 42.3184 4.1594 15.2182 61.4776 6.2194

Table III proves that the computational time using the proposed FFA-PID is superior to the ones obtained with the GA-PID and the PSO-PID as shown in the above table when using 100 or 150 iterations.

VI. C ONCLUSION The proposed work studied and developed an Automatic Generation Control (AGC) of five area interconnected equal reheat thermal power system by considering ProportionalIntegral-Derivative (PID) controller. The controller parameters, namely the Proportional gain (kp ), Integral gain (Ki ) and Derivative gain (Kd ) are tuned by using nature bioinspired Firefly Algorithm (FFA) considering one percent Step Load Perturbation (1% SLP) in area 1. The performance of proposed algorithm was compared to both the Genetic Algorithm (GA) and the Particle Swarm Optimization (PSO) technique based PID controller response. The superiority of the proposed algorithms was tested with changing the number of iterations of each algorithm. Finally, the simulation result obviously demonstrated that the FF algorithm tuned PID controller gained superiority (lesser damping oscillations, minimal settling time with less peak overshoot/ undershoot values) compared to using the GA and PSO tuned controller performance. It is established that the FFA performance is improved with increasing the number of iterations. However, the proposed approach required to solve the tradeoff between increasing the number of iterations which lead to the increase in the settling time with decreasing the peak overshoot and undershoot. Appendix Nominal parameters of the five area interconnected reheat thermal power system are: R1 = R2 = R3 = R4 = R5 = 2.4 p.u.−1 HzM W ; Tg1 = Tg2 = Tg3 = Tg4 = Tg5 = 0.2s; T r1 = T r2 = T r3 = T r4 = T r5 = 1 s; Kr1 = Kr2 = Kr3 = Kr4 = Kr5 = 0.333; Tt1 = Tt2 = Tt3 = Tt4 = Tt5 = 0.3s; Tp1 = Tp2 = Tp3 = Tp4 = Tp5 = 20s; T12 = T13 = T14 = T15 = T23 = T24 = T25 = T34 = T35 = T45 = 0.0707 M W rad−1 ; Kp1 = Kp2 = Kp3 = Kp4 = Kp5 = 20s; B1 = B2 , B3 = B4 = B5 = 0.425.

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K. Jagatheesan received his B.E degree in Electrical Engineering in 2009 from Hindusthan College of Engineering and Technology, Coimbatore, Tamil Nadu, India and M.E. degree in Applied Electronics in 2012 from Paavai College of Engineering, Namakkal, Tamil Nadu, INDIA. He is currently working towards the Ph.D. degree with the faculty of Information & Communication Engineering, Anna University Chennai, Chennai, India. His area of interest includes Advanced Control System, Electrical Machines and Power system modeling and control and he has published more than 15 papers in National/International journals and conferences. He is an Associate Member of UACEE, Member of SCIEI, IACSIT, IAENG, ISRD and Graduate Student Member of IEEE.

B. Anand received his B.E degree in Electrical and Electronic Engineering in 2001 from Government College of Engineering, Tirunelveli and M.E. degree in Power Systems Engineering from Annamalai University in 2002 and Ph.D. degree in Electrical Engineering from Anna University, Chennai in 2011. Since 2003, he has been with the Department of Electrical and Electronic Engineering, Hindusthan College of Engineering and Technology, Coimbatore, Tamilnadu, INDIA. Currently, he is an Associate Professor. His research interests are in Power System Control, Optimization, and application of computational intelligence to power system problems and he published more than 45 papers in National/International journals and conferences. He is member of IEEE, SSI and ISTE.

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Sourav Samanta is an Assistant Professor in the Department of Computer Science in University Institute of Technology, The University of Burdwan, West Bengal, INDIA. He also holds an honorary position of Visiting Scientist at Global Biomedical Technologies Inc., CA, USA. He completed his MTech in Computer Science and Engineering from JIS College of Engineering, Kalyani, West Bengal and BE in Information Technology from University Institute of Technology, Burdwan, West Bengal respectively. He has approximately four years academic experience. He is working with researchers from five different countries. His research area includes bio inspired computing, quantum computing, reversible computing etc. He has about 25 research papers published in national and international journals on image processing & analysis. He is a regular reviewer of various international journals.

Nilanjan Dey is an Asst. Professor in the Department of Information Technology in Techno India College of Technology, Rajarhat, Kolkata, INDIA. He holds an honorary position of Visiting Scientist at Global Biomedical Technologies Inc., CA, USA and Research Scientist of Laboratory of Applied Mathematical Modeling in Human Physiology, Territorial Organization-of-gientifig and Engineering Unions, BULGARIA. He is the Editor-in-Chief of International Journal of Ambient Computing, Intelligence (IGI Global), US, International Journal of Rough Sets and Data Analysis (IGI Global), US and the International Journal of Synthetic Emotions (IJSE), (IGI Global), US Series Editor of Advances in Geospatial Technologies (AGT) Book Series, (IGI Global), US, Executive Editor of International Journal of Image Mining (IJIM), Inderscience, Regional Editor-Asia of International Journal of Intelligent Engineering Informatics (IJIEI), Inderscience and Associated Editor of International Journal of Service Science, Management, Engineering, and Technology, IGI Global. His research interests include: Medical Imaging, Soft computing, Data mining, Machine learning, Rough set, Mathematical Modeling and Computer Simulation, Modeling of Biomedical Systems, Robotics and Systems, Information Hiding, Security, Computer Aided Diagnosis, Atherosclerosis. He has authored 8 books and published 150 international conferences and journal papers. He is a life member of IE, UACEE, ISOC, etc.

Amira S. Ashour is Assistant Professor and Vice Chair of Computer Engineering Department, Computers and Information Technology College, Taif University, KSA. She has been the vice chair of Computer Science Department, CIT college, Taif University, KSA, for 5 years. She is a Lecturer of Electronics and Electrical Communications Engineering, Faculty of Engineering, Tanta University, Egypt. She received her PhD in Smart Antenna (2005) in the Electronics and Electrical Communications Engineering, Tanta University, Egypt. She had her Masters in Enhancement of Electromagnetic Non-Destructive Evaluation Performance using Advanced Signal Processing Techniques in Faculty of Engineering, Egypt, 2000. She is the Editor-in-Chief of the International Journal of Synthetic Emotions (IJSE), (IGI Global), US, an Associate Editor for the International Journal of Rough Sets and Data Analysis (IJRSDA), IGI Global, US as well as the International Journal of Ambient Computing and Intelligence (IJACI), IGI Global, US. She is an Editorial Board Member of the International Journal of Image Mining (IJIM), Inderscience. Moreover, she is in the editorial review board of the International Journal of System Dynamics Applications (IJSDA), IGI Global, US. She has authored 3 books and several international publications. Her research interests include: image processing, medical imaging, Biomedical Systems, machine learning, smart antenna and adaptive antenna arrays.

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Valentina E. Balas is currently Professor in the Department of Automatics and Applied Software at the Faculty of Engineering, University “Aurel Vlaicu” Arad, ROMANIA. She holds a Ph.D. in Applied Electronics and Telecommunications from Polytechnic University of Timisoara since 2003. She is author of more than 170 research papers in refereed journals and International Conferences. Her research interests are in Intelligent Systems, Fuzzy Control, Soft Computing, Smart Sensors, Information Fusion, Modeling and Simulation. She is Editorin Chief of International Journal of Advanced Intelligence Paradigms (IJAIP), member of Editorial Boards for national and international journals, serves


as reviewer for many international journals and conferences and is evaluator expert for national and international projects. She has participated in many international conferences as General Chair, Organizer, Session Chair and member of International Program Committee. She was mentor for many student teams in Microsoft (Imagine Cup), Google and IEEE competitions in the last six years. She has a great experience in research projects. She is member of EUSFLAT, ACM and a Senior Member IEEE, member in TC Emergent Technologies (IEEE CIS) and member in TC – Soft Computing (IEEE SMCS). Dr. Balas is Vice-president (Awards) of IFSA International Fuzzy Systems Association Council and Joint Secretary of the Governing Council of Forum for Interdisciplinary Mathematics (FIM), Multidisciplinary Academic Body, INDIA. She is a Senior Member of IEEE.