In this article, a fuzzy logic based power system stabilizer (FPSS) is designed by tuning its input–output scaling factors. Two input signals to FPSS are considered as change of speed and change in power, and the output signal is considered as a correcting voltage signal. The normalizing factors of these signals are considered as the optimization problem with minimization of integral of square error in singlemachine and multimachine power systems. These factors are optimally determined with bat algorithm (BA) and considered as scaling factors of FPSS. The performance of power system with such a designed BA based FPSS (BAFPSS) is compared to that of response with FPSS, Harmony Search Algorithm based FPSS (HSAFPSS) and Particle Swarm Optimization based FPSS (PSOFPSS). The systems considered are singlemachine connected to infinitebus, twoarea 4machine 10bus and IEEE New England 10machine 39bus power systems for evaluating the performance of BAFPSS. The comparison is carried out in terms of the integral of timeweighted absolute error (ITAE), integral of absolute error (IAE) and integral of square error (ISE) of speed response for systems with FPSS, HSAFPSS and BAFPSS. The superior performance of systems with BAFPSS is established considering eight plant conditions of each system, which represents the wide range of operating conditions.
Bat algorithm (BA) ; Fuzzy logic controller (FLC) ; Fuzzy logic based power system stabilizer (FPSS) ; Harmony search algorithm (HSA) ; Input–output scaling factors ; Particle swarm optimization (PSO) ; Performance indices (PIs) ; Power system stabilizer (PSS)
A^{0} Loudness of sound
A System matrix
B Input matrix
D_{i} Damping coefficient for the generator
ε Elite percentage
 Equivalent excitation voltage of the generator
 Internal voltage behind the daxis transient reactance
 Maximum frequency
 Minimum frequency
i generator
 AVR gain of the generator
 HeffronPhillip constants
K_{p} Scaling factor for Δp signal
K_{u} Scaling factor for Δu signal
K_{ω} Scaling factor for Δω signal
M_{i} Machine inertia coefficient for the generator
N Number of generators
 Number of PSS
 Active power
Δp Change in power
r Pulse rate
 AVR timeconstant of the generator
 daxis opencircuit transient timeconstant of the gen
 Mechanical torque of the generator
U Input variable vector
Δu Change in PSS output signal
Δω Change in speed
Δω_{i} Change in speed for the generator
ω_{0} Synchronous speed of the generator
X State variable vector
X_{l} Transmission line reactance
U_{i} PSS output signal of the generator
Modern electric power systems (EPSs) are complex, interconnected and susceptible to low frequency oscillations (LFOs) in the frequency range of 0.2 Hz–3.0 Hz. Power system stabilizers (PSSs) have been commonly used to damp out these LFOs. The changes in loading conditions, operating conditions and some sort of disturbance are main causes to develop LFOs in EPSs. Conventional power system stabilizers (CPSSs) consisting of leadlag networks are generally used PSS for damping out these oscillations because of simple structure and easy installation. The design of CPSS is based on linear control theory and involves the linearized dynamic model with a specific operatic condition of EPS. These controllers give degraded performance with varying operating conditions and sometime unable to maintain stability of EPS on a higher degree of loading conditions [1] and [2] .
The wide range of operating conditions for real EPS has motivated researchers to develop different methods to design PSS with improved performances and this resulted to the application of adaptive and robust control to design PSS. The basic idea behind the adaptive technique is to estimate the dynamic model with resting uncertainties in the system online based on measured signals. The erroneous estimation of states and the uncertainty may lead to design of PSS with degraded performance. In online transient stability assessment, some selected contingencies need to be evaluated as fast as possible before occurrence of a fault or a disturbance in the system. Therefore, the computational time is very critical. H∞ optimization technique is used to design robust PSS, but it gives the PSS order as high as that of the plant, which increases the complexity to the system and reduces its applicability [3] .
In early phase of optimization, CPSS parameters have been tuned using gradient based optimization technique. It requires the computation of sensitivity and eigenvectors at the end iteration, which resulted with heavy computational burden and slow convergence rate. The heuristic based optimization techniques are employed to tune the parameters of CPSS and proportional integral derivative (PID) based PSS. Among these are Tabu search algorithm [1] , real coded genetic algorithm (RCGA) [4] , genetic algorithm [3] , particle swarm optimization (PSO) [4] and [5] , and breeder genetic algorithm [6] . Bacteria foraging algorithm [3] , simulated annealing [7] , differential evolution [1] and strength pareto evolutionary algorithms [8] have been used successfully to tune the CPSS parameters. However, genetic and simulated annealing algorithms have the tendency of revisiting the suboptimal solutions and thus the designed CPSS may give deteriorated performance. These optimization techniques fail with an epistatic objective function, which have closely related to multimodel problems and the higher number of variables [9] .
To mitigate these limitations, an artificial intelligence based methods of PSS design, such as artificial neural networks (ANNs) [10] , fuzzy logic [11] , [12] , [13] and [14] , adaptive fuzzy [15] , neurofuzzy [16] and [17] , and interval type2 [18] and [19] , have been reported in literature. In the case of ANN, the gradient algorithm is being used to learn its parameters using either input/output [20] parameters or online data from different operating points in a power system network.
Fuzzy logic controllers (FLCs) can cope with those that naturally have lots of vagueness or uncertainty in their behavior. These do not require a mathematical model of the controlled process. These have rigidity and robustness as their profound and interesting characteristics in comparison to other methods. The properly designed fuzzy logic based PSS works similar to PD or PID based PSS [21] . Development of an equivalence between the scaling factor of a fuzzy controller and linear PID controller coefficients is reported in [22] . The selection of scaling factors, appropriate membership function, number of linguistic variables and the corresponding rule table are the major requirement in designing PSS based on FLC. The detail on linguistic variables and selection of membership function is well reported in [23] . Based on an organized approach, a standardized rule table is proposed in [24] . The optimization of scaling factors using particle swarm optimization is reported in [5] . The harmony search algorithm (HSA) is proposed by Geem et al in 2001 [25] , and is inspired by the process of the improvisation used by musicians to achieve harmony. The HS algorithm [26] is a metaheuristic optimization algorithm that is similar to the PSO [27] and GA [28] . It has been implemented extensively in the fields of engineering optimization in [26] . It became an alternative to other heuristic algorithms like PSO [27] and simulated annealing (SA) [7] . It is a derivative free, metaheuristic optimization (which does not use trialanderror), inspired by the way musicians improvise new harmonies [29] , and it uses higherlevel techniques to solve problems efficiently [2] .
In the field of optimization, much of algorithms are floating with unique properties. Some are useful to one application, while others are not so. The bat algorithm reported by Yang (2010) is metaheuristic in nature [30] . It is based on the echolocation based behavior of micro bats [31] . It was established by considering benchmark functions that the behavior is superior to PSO and GA [32] . It has also reported that the application of GA and PSO is inappropriate with multimodel problems. The frequencytuning and automatic zooming are out of the main features of the bat algorithm.
Particle swarm optimization (PSO) and Firefly algorithm (FA) generate an efficient codebook, but undergo instability in convergence when particle velocity is high and with the nonavailability of brighter fireflies in the search space, respectively. The application of Bat Algorithm (BA) on the initial solution of LindeBuzoGray (LBG) is presented in [33] . It produces an efficient codebook with less computational time and results due to its automatic zooming feature using adjustable pulse emission rate and loudness of bats [33] . The design of fuzzy proportional derivative controller and fuzzy proportional derivative integral controller for speed control of brushless direct current drive has been presented in [34] . The problem of controller design is considered as an optimization using nature inspired optimization algorithms such as particle swarm, cuckoo search, and bat algorithms [34] . A Firefly Algorithm (FA) optimized fuzzy PID controller is proposed for Automatic Generation Control (AGC) of multiarea multisource power system in [35] .
In [5] , the scaling factors associated with two inputs and one output are optimized by PSO for singlemachine infinitebus (SMIB) and twoarea 4machine 10bus power system. These scaling factors (input–output) have been further optimized using harmony search algorithm in [2] . The performance of the HSAFPSS has been compared and was found better as compared to PSOFPSS for both power systems. In this paper, bat algorithm (BA) has been used to optimize scaling factors of FPSSs for SMIB, 4machine and IEEE New England 10machine 39bus power systems. The performance of the proposed BAFPSS is to be compared to the PSOFPSS [5] and HSAFPSS [2] for the threepower systems. The performance evaluation is carried out in terms of ITAE, IAE and ISE in each case of a controller as well as a power system under study.
In the organization of this paper, the problem formulation is considered by introducing test power systems, and an objective function used for optimization of scaling factors in Section 2.2 . The bat algorithm used to determine optimal set of input–output scaling factors is mentioned in Section 3 . Optimization of scaling factors of FPSSs for all threepower systems using bat algorithm is carried out in Section 4 . The optimal set of scaling factors for SMIB power system using bat algorithm and performance comparison with BAFPSS, with HSAFPSS, PSOFPSS [5] and with FPSS (without scaling factors) is discussed in Section 4.1 . It is repeated for 4machine power system in Section 4.2 . The process of optimal parameters for 10machine power system is determined using harmony search, as well as bat algorithm in Section 4.3 . The detail on harmony search is not given and considered as in [2] with same initializing parameters. The nonlinear timedomain simulation is carried out on this power system using BAFPSS and HSAFPSS and compared with FPSS (without scaling factors) in this section. Lastly, Section 5 concludes.
The aim of this paper is to utilize the superior performance of Bat algorithm for tuning input and output scaling factors of FPSS in connection with power systems; therefore, the EPS elements such as generators, excitation system and PSS must be modeled. To complete the tuning process, an objective function to obtain satisfactory results is necessary and should be defined. Accordingly, the system model and an objective function used in PSS parameter tuning process for SMIB, and multimachine power systems, should be elaborated.
The power system is a multicomponent system. The equivalent of system can be represented by using differential equations. Assuming that the vector of states and the vector of inputs are represented by X and U , respectively, then the power system may be represented as in Eqn. (1) .

( 1) 
A nonlinear power system can be linearized by considering small perturbation around an operating point. It is easy to design PSS to such linearized model of power system [9] and [36] . The EPS represented by Eqn. (1) may be shown by state equations as in Eqn. (2) .

( 2) 
The infinitebus of the SMIB power system can be considered by Thevenins equavalent of the large and complex power system. The components and interconnections of the SMIB power system are shown in Fig. 1 . The inadequate damping of the generator is the main cause of small signal oscillations. The PSS may be connected to excitation system to add extradamping of the generator as elaborated in [9] . The pioneer work on the design of appropriate PSS is presented in [37] .

Fig. 1. Line diagram of singlemachine infinitebus power system.

In system representation by Eqn. (2) , A is the system matrix of an order as 4 × 4 and is given by δf /δX , while B is the input matrix with order 4 × 1 and is given by δf /δU . The order of state vector is 4 × 1; the order is 1 × 1. Here, the wellknown HeffronPhillip linearized model is considered for fabricating the model in MATLAB 2011b as in [2] and [9] . The SMIB power system dynamics in terms of differential equations are considered as in [38] .
The 2nd system considered is twoarea 4machine 10bus power system [2] . The linediagram of the system is shown in Fig. 2 . The development of the smallsignal model of multimachine power system is well explained in [38] . It can be represented by a large number of differential and algebraic equations. The general representation of HeffronPhilip model for multimachine power systems is shown in Fig. 3 . Consider N as the number of generators of multimachine power system, with the number of power system stabilizer connected in decentralized manner to the generators. The state model can be represented as in Eqn. (2) , where A is the system matrix with order 4N × 4N (16 × 16) and is given by δf /δX , while B is the input matrix with order (16 × 4) and is given by δf δU . The order of state vector ΔX is 4N × 1 (16 × 1), and the order of ΔU is (4 × 1). Here, the wellknown HeffronPhillip linearized model is used to represent the large multimachine power system as in [2] and [39] and the system dynamics is given in [38] and [40] .

Fig. 2. Line diagram of twoarea 4machine 10bus power system.


Fig. 3. General representation of HeffronPhilip model for multimachine power systems.

The state equations to the power system, consisting of N , the number of generators, and , the number of power system stabilizers, can be written as in Eqn. (2) . In this case, A is the system matrix of the order 4N × 4N (40 × 40) and B is the input matrix with the order (40 × 10). The order of state vector ΔX is 4N × 1 (40 × 1), and the order of ΔU is (10 × 1). Here, the wellknown HeffronPhillip linearized model is used to represent the large multimachine power system, as in Fig. 3 , and the singleline diagram of IEEE 39bus power system is shown in Fig. 4 .

Fig. 4. Line diagram of IEEE New England 10machine 39bus power systems.

The scheme of input–output scaling factors of FPSS is considered as presented in [2] . The input signals to the FPSS are considered as change in speed (Δω ) and change in power (Δp ) with associated scaling factors as K_{ω} and K_{p} , respectively. The output signal of FPSS is considered as change in correction voltage (Δu ) and the scaling factor as K_{u}[2] . In this paper, these scaling factors are determined using bat algorithm. The problem of tuning scaling factors is considered as an optimization with minimization of integral squared error (ISE) of change in speed signal as a fitness function.
As an objective function, the ISE based cost function is represented for SMIB, fourmachine and tenmachine power system by Eqns. (3) , (4) and (5) , respectively. The connections of scaling factors of FPSS are shown in Fig. 5 , where the change in speed is subjected to minimize using the bat algorithm to obtain optimal set of input–output scaling factors.

( 3) 

( 4) 

( 5) 

Fig. 5. Representation of HeffronPhilip model for SMIB power system with input–output scaling factors of FPSS.

The parameter bounds for SMIB power system are as in Eqn. (6)[2] .

( 6) 

( 7) 
Eqn. (7) includes parameter bounds for both multimachine power systems [2] . The i stands for generator in the multimachine power system and refers to simulation time during optimization process and specified as 100 seconds. In the case of IEEE 10machine power system, the value of i is 09, because generator is considered as slack without controller at this generator. Considering one of the above objectives corresponding to the system under investigation, the proposed approach employs the bat algorithm with parameter bounds to solve this optimization problem for an optimal set of input–output scaling factors of FPSS.
This algorithm is based on the echolocation behavior produced by natural bats in locating their prey. The pulse generated by microbats lasts for 8–10 seconds, with frequency range of 25–150 kHz and with associated wave length of 2–14 mm. Necessary assumptions are required to be considered during development of the echolocation characteristics of microbats [9] and [41] .
In optimization problems, an objective function is represented by minimization of F (r ) and subjected to x_{r} ∈ X_{r} , . In initialization step of the bat algorithm, the bat population is generated with velocity v_{r} and position x_{r} for . The pulse frequency is selected in the range . Pulse rate and the loudness are set as above, while the search loop is set to maximum iteration counts as [31] and [42] .
In step 2, the new solutions are generated by considering the following equations of frequency, velocity and position. For bat, the new position and velocity at time step t are represented by and , respectively [43] .

( 8) 

( 9) 

( 10) 
where β represents the uniform distribution in the range β ∈ [0, 1]. The value represents the best location in the search step for n bats.
In step 3, the local search is applied for the generation of the new solutions using local random walk behavior as described by the following Eqn. (11) . The ε is selected in the range of [−1, 1] with average value of loudness A^{t} at time t .

( 11) 
In step 4, the loop operation for generation of the new solutions is considered. On advancement of iterations, the loudness and the rate of pulse emission have to be updated by Eqns. (9) and (10) . The rate of pulse emission is increased when shortening the path to prey.

( 12) 

( 13) 
where α and γ represent the constant values in the range of 0 ≤ α ≤ 1 and 0 < γ . The process behaves like the cooling factor of a cooling schedule in the simulated annealing [44] . The generally selected value of these constants is 0.9 in the literature [45] .
In the last step 5, the stopping criterion is checked as the maximum count of iterations is reached and termination of computation is executed. Otherwise, go to steps 3–4 to repeat the process. The tuning scheme of input–output scaling factors is shown in Fig. 6 , where the speed deviation is minimized using bat algorithm to decide optimal set of parameters. As the connection of scaling factors is already shown in Fig. 5 , Δp is left open intentionally to save space.

Fig. 6. Representation of tuning scheme for input–output scaling factors of FPSS using bat algorithm.

The line diagram and the small signal model of SMIB power system are represented in Figs. 1 and 5 , respectively. The operating conditions of SMIB power system are represented by different sets of active power and transmission line reactance X_{l} as mentioned in Table 1 . The plants are designed to represent operating conditions and weak conditions through heavy loading conditions. Plant6 represents the nominal operating conditions as in [40] .
PS model 


X_{l}  

Plant1  0.50  0.0251  0.20  
Plant2  0.50  0.0505  0.40  
Plant3  0.75  0.0566  0.20  
Plant4  0.75  0.1152  0.40  
Plant5  1.00  0.1010  0.20  
Plant6  1.00  0.2087  0.40  
Plant7  1.10  0.2550  0.40  
Plant8  1.20  0.3068  0.40 
The problem is formulated in MATLAB environment and executed on Intel (R) Core (TM) – 2 Duo CPU T6400 @ 2.00 GHz with 3 GB RAM, 32bit operating system. The SMIB system is equipped with FPSS along with input–output scaling factors. The scheme of optimization is shown in Fig. 6 . The problem of optimization of scaling factors is considered with an ISE based objective function as in Eqn. (3) . The steps of the bat algorithm are shown in Section 3 . In [32] and [42] , the generally opted values of initializing parameters, such as intensity (A ) and pulse rate (r ) are 0.5 and 0.5, respectively. However, the proper initializing parameters for bat algorithm are considered after long efforts and found as A = 0.9 and r = 0.1. The other constraint such as initializing population is selected as n = 25 and the bandwidth are considered as and . The plant (SMIB power system) operating at nominal operating condition (where in X_{l} = 0.4pu and ) is considered for optimal tuning of input–output scaling factors of FPSS. The scaling factors are considered with lower and upper bounds as , , and . The optimization process with bat algorithms is set to terminate with maximum iteration counts as 100. The behavior of bat algorithm in terms of fitness function with iterations is shown in Fig. 7 . The variation of the PID parameters with iteration count is shown in Fig. 8 . The optimal set of parameters obtained using the bat algorithm is enlisted in Table 2 . The scaling factors using PSO in [5] and HSA in [2] for SMIB system are also included in the table for the purpose of comparison.

Fig. 7. Plot of fitness function using bat algorithm in tuning of input–output scaling factor for SMIB power system with nominal operating condition.


Fig. 8. Plot of input–output scaling factors with iteration count for SMIB power system.

Controller  Parameters  Bounds  

Symbol  Values  Lower  Upper  
BAFPSS (Prop.)  K_{ω}  13.2238  0.001  50.0 
K_{p}  3.0358  0.001  10.0  
K_{u}  2.0128  0.001  5.00  
HSAFPSS [2]  K_{ω}  26.3928  0.001  50.0 
K_{p}  5.3353  0.001  10.0  
K_{u}  2.4531  0.001  5.00  
PSOFPSS [5]  K_{ω}  59.80  0.0  70.0 
K_{p}  4.0  0.0  10.0  
K_{u}  1.0  0.0  10.0 
A SIMULINK based block diagram, including all the nonlinear blocks, is generated in MATLAB software. The SMIB power system performance under nonlinear mode is carried out by creating selfclearing fault at time 5 seconds and persistent for 0.1 second with the wide range of operating conditions. The system with unlike combinations of different active power and transmission line reactance as in Table 1 (eight different plants) and system data as in [9] and [38] is considered for nonlinear simulations. Such obtained eightplants (covering wide range of operating conditions) are examined for the speed response with FPSS, HSAFPSS and BAFPSS in this section.
The fuzzy logic based PSS (FPSS) reported in [14] and [46] is considered for comparison purpose. The numbers of linguistic variables are five as LN (large negative), MN (medium negative), Z (zero), MP (medium positive) and LP (large positive). The input signals to FLC have been considered as change in speed (Δw ) and change in power (Δp ), while that of the output signal is considered as correction voltage ( ). The corresponding 25 rules of the rulebase are considered as presented in [46] . The triangular type membership function is considered for both input and output signals. The crisp value is obtained using centroid type defuzzification method.
The SIMULINK model of SMIB system is prepared in the MATLAB software equipped with FPSS, BAFPSS and HSAFPSS controllers. These systems are simulated for all eight plants as created in Table 1 . The comparison of speed response of SMIB system with FPSS, with PSOFPSS [5] , with HSAFPSS [2] and with BAFPSS is carried out for each plant configuration. The comparative response is carried out for 8plant conditions but shown only for plant3, plant6 and plant7 in Fig. 9 , Fig. 10 and Fig. 11 , respectively. However, the response with other plants are not shown because of space limitation. Clearly, the settling time with BAFPSS is better as compared to HSAFPSS [2] , PSOFPSS [5] and greatly improved with respect to FPSS [14] and [46] . The response with HSAFPSS [2] and BAFPSS is comparable but the response with FPSS [46] settles in more than 25 seconds. The closely related responses with HSAFPSS [2] and BAFPSS are to be differentiated by recording performance indices.

Fig. 9. Speed response for Plant3 with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and proposed BAFPSS for SMIB power system.


Fig. 10. Speed response for Plant6 with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and proposed BAFPSS for SMIB power system.


Fig. 11. Speed response for Plant7 with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and proposed BAFPSS for SMIB power system.

To carry out the analysis with clear perceptiveness and completeness about the system response for all the system conditions, three performance indices that reflect the settling time and overshoot are introduced and evaluated as in [2] and [9] . These indices are defined as folowing in Eqns. (14) , (15) and (16) .

( 14) 

( 15) 

( 16) 
where is the simulation time of the system and Δω (t ) represents the instantaneous speed change. To prove superiority of the BAFPSS, the SMIB system is simulated one by one with all four controllers (FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and BAFPSS) and the performance indices (ITAE, IAE and ISE) of speed response are recorded for the simulation time as 40 seconds and enlisted in Table 3 . The closely related responses with HSAFPSS and BAFPSS are well differentiated by distinct values of performance indices. The lower value of performance index (PI) represents the comparatively better performance of the system with reduced settling time and overshoot. In Table 3 , the value of performance indices (PIs) with BAFPSS is lesser as compared to others, resulting to good performance. The value of PIs of system response with PSOFPSS [5] or plant7 and plant8 are higher as compared to that of with BAFPSS. Therefore, the performance of system with PSOFPSS is degraded against the proposed BAFPSS.
PS model  Controllers  ITAE  IAE  ISE 

Plant1  FPSS [46]  0.0140  0.0025  5.1939E06 
PSOFPSS [5]  0.0072  0.0013  3.0359E06  
HSAFPSS [2]  0.0073  0.0013  3.0437E06  
BAFPSS (Prop.)  0.0073  0.0013  2.9941E06  
Plant2  FPSS [46]  0.0221  0.0036  7.0078E06 
PSOFPSS [5]  0.0119  0.0021  3.9812E06  
HSAFPSS [2]  0.0117  0.0039  3.9599E06  
BAFPSS (Prop.)  0.0115  0.0020  3.8997E06  
Plant3  FPSS [46]  0.0259  0.0044  1.4628E06 
PSOFPSS [5]  0.0159  0.0029  9.5283E06  
HSAFPSS [2]  0.0131  0.0024  8.6405E06  
BAFPSS (Prop.)  0.0110  0.0020  6.7405E06  
Plant4  FPSS [46]  0.0453  0.0071  2.2915E05 
PSOFPSS [5]  0.0162  0.0029  1.0369E05  
HSAFPSS [2]  0.0181  0.0032  1.0954E05  
BAFPSS (Prop.)  0.0177  0.0032  1.0785E05  
Plant5  FPSS [46]  0.0529  0.0086  3.9531E05 
PSOFPSS [5]  0.0229  0.0041  1.6368E05  
HSAFPSS [2]  0.0245  0.0044  2.1180E05  
BAFPSS (Prop.)  0.0150  0.0028  1.1477E05  
Plant6  FPSS [46]  0.1364  0.0182  8.1390E05 
PSOFPSS [5]  0.0411  0.0070  3.1181E05  
HSAFPSS [2]  0.0328  0.0057  2.6481E05  
BAFPSS (Prop.)  0.0247  0.0044  1.9924E05  
Plant7  FPSS [46]  0.2791  0.0313  1.5210E04 
PSOFPSS [5]  0.0821  0.0129  6.7567E05  
HSAFPSS [2]  0.0448  0.0077  4.0846E05  
BAFPSS (Prop.)  0.0398  0.0069  3.4579E05  
Plant8  FPSS [46]  0.97088  0.07295  3.7782E04 
PSOFPSS [5]  124.26  7.7840  6.6780  
HSAFPSS [2]  0.0733  0.0120  7.6007E05  
BAFPSS (Prop.)  0.0644  0.0107  6.7486E05 
The singleline diagram of the twoarea fourmachine tenbus power system is shown in Fig. 2 , which is a benchmark power system to study small signal oscillations [40] . The line data, load flow and machine data are considered as in [38] and [40] . The above multimachine system is modeled using SIMULINK Toolbox with machine model 1.0. The test system (fourmachine system) is considered with the wide range of operating conditions of power system and system connection configuration. Here, the different test models are created by changing the active power of generation, distributed load, line outage and fault at different bus location as mentioned in Table 4 .
PS model  Active power  Active load  F/B^{a}  L/O^{b} 

Plant1  7, 7, 7.2172, 7  11.59; 15.75  B/No. 3  As in Fig. 2 
Plant2  7, 7, 7.2172, 7  11.59; 15.75  B/No. 4  B/No. 9–10 
Plant3  7.2, 7.1, 7.0, 6.9  11.59; 15.75  B/No. 5  As in Fig. 2 
Plant4  7.2, 7.1, 7.0, 6.9  11.59; 15.75  B/No. 6  B/No. 7–10 
Plant5  7.2, 7.1, 7.0, 6.9  11.99; 15.45  B/No. 7  As in Fig. 2 
Plant6  7.1, 6.9, 7.5, 6.5  11.19; 15.95  B/No. 8  As in Fig. 2 
Plant7  7.1, 6.9, 7.5, 6.5  11.19; 15.95  B/No. 9  B/No. 5–9 
Plant8  5, 8, 6.2172, 8  11.59; 15.75  B/No. 10  As in Fig. 2 
a. Fault location at a particular bus for nonlinear study.
b. System as in in Fig. 2 or with line outage between two buses.
In Table 4 , the configuration of the 4machine power system is considered by varying active power, active load, bus structure and fault at a particular bus of Fig. 2 . In plant1, the bus structure is as in Fig. 2 but a line between bus no. 9 and bus no. 10 is disconnected in plant2 configuration of the system. It can be observed that the nonlinear simulation is considered by creating selfclearing fault at bus no. 3 and bus no. 4 in plant1 and pant2 configuration, respectively. The active power plant1 associated to 4generators is [7, 7, 7.2172] and changed to [7.2, 7.1, 7.0, 6.9] in plant3. The load connected to system are 2 as [11.59 + j2.12; 15.75 + j2.88] in plant1 configuration but only real parts are enlisted in Table 4 because imaginary part remains the same for all plant conditions. In this way, the eight different plants of the system are considered as shown in Table 4 .
The system model referring to plant1 configuration as in Table 4 is equipped with FPSS to all fourmachines (named as Gen1 to Gen4) and subjected to design using the bat algorithm (as described in Section 3 ), with a simple time domain based minimization of ISE as an objective function as in Eqn. (4) with bounds as defined in Eqn. (7) . The speed signal from each generator is sensed and the minimum value of sum of ISE of the error signal is minimized to tune input–output scaling factors of four FPSSs with parameter bounds as 40 ≤ K_{ω} ≤ 70, , and . The initializing parameters for BA are considered the same as in the previous section. The termination criterion of the tuning process is considered as the maximum number of iterations and set as 100. The parameter bounds are selected by using the trialanderror method; therefore, several attempts are required. The optimized scaling factors are shown in Table 5 . The behavior of BA during optimization in terms of fitness function is plotted in Fig. 12 .
Controllers  Generators 


 

PSOFPSS [5]  Gen1  59.8000  4.0000  1.0000  
Gen2  59.8000  4.0000  1.0000  
Gen3  59.8000  4.0000  1.0000  
Gen4  59.8000  4.0000  1.0000  
HSAFPSS [2]  Gen1  61.1017  3.9703  0.7327  
Gen2  60.8977  4.7107  0.5536  
Gen3  57.0917  3.8375  0.6540  
Gen4  60.3711  3.6118  0.5258  
BAFPSS (Prop.)  Gen1  58.6538  4.0109  1.8991  
Gen2  56.0157  4.0016  1.0021  
Gen3  59.3950  6.4531  4.0501  
Gen4  40.0012  7.997  3.9996 

Fig. 12. Fitness function plot for simultaneous tuning of input–output scaling factors of FPSSs for 4machine 10bus power system using bat algorithm.

The twoarea fourmachine tenbus power system is described and the creations of system models based on operating conditions are elaborated in the previous section. The FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and proposed BAFPSS are connected to the system and simulations are carried out for the speed response. In each plant condition as listed in Table 4 is considered with fault location. The disturbance is considered as selfclearing at different buses at 1.0 second and cleared after 0.05 second. As a sample, the speed response of Gen1 to Gen4 for plant3 is compared with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and BAFPSS in Fig. 13 , Fig. 14 , Fig. 15 and Fig. 16 . These graphical representations of the simulation results reveal that the performance of the system with PSOFPSS [5] , HSAFPSS [2] and BAFPSS is greatly improved as compared to FPSS [46] . The responses of the system with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and BAFPSS are closely related, therefore differentiating the associated performance indices was to be carried out in the next section.

Fig. 13. Speed response for Gen1 of Plant3 with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and BAFPSS.


Fig. 14. Speed response for Gen2 of Plant3 with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and BAFPSS.


Fig. 15. Speed response for Gen3 of Plant3 with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and BAFPSS.


Fig. 16. Speed response for Gen4 of Plant3 with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and BAFPSS.

To evaluate the robustness of the proposed BAFPSS, simulation is carried out for all eight plant configurations, which represent the wide range of operating conditions and system configurations. The system is simulated FPSS [46] , PSOFPSS [5] , HASFPSS [2] and BAFPSS for comparison purpose with eight plant conditions. Each time the performance indices (ITAE, IAE and ISE) are recorded and enlisted in Table 6 . Since the system possesses four generators, the PI values in Table 6 are the sum of PIs of four generators. Comparatively lower value of PI refers to better performance. It is clear from this table that the performance of the system is enhanced by using proposed BAFPSS as compared to other controllers.
PS model  Controllers  ITAE  IAE  ISE 

Plant1  FPSS [46]  0.0763  0.0231  4.5996E05 
PSOFPSS [5]  0.0308  0.0128  4.0754E05  
HSAFPSS [2]  0.0356  0.0135  4.2913E05  
BAFPSS (Prop.)  0.0285  0.0133  3.9055E05  
Plant2  FPSS [46]  0.1823  0.0473  1.4331E04 
PSOFPSS [5]  0.0828  0.0322  1.6105E04  
HSAFPSS [2]  0.0846  0.0354  1.8268E04  
BAFPSS (Prop.)  0.0775  0.0302  1.4252E04  
Plant3  FPSS [46]  0.0596  0.0169  1.4331E04 
PSOFPSS [5]  0.0191  0.0053  8.3550E06  
HSAFPSS [2]  0.0169  0.0050  7.4998E06  
BAFPSS (Prop.)  0.0155  0.0046  6.4506E06  
Plant4  FPSS [46]  0.0497  0.0132  1.1295E05 
PSOFPSS [5]  0.0301  0.0062  9.0234E06  
HSAFPSS [2]  0.0262  0.0059  8.2087E06  
BAFPSS (Prop.)  0.0183  0.0055  7.6245E06  
Plant5  FPSS [46]  0.0625  0.0167  1.7306E05 
PSOFPSS [5]  0.0224  0.0052  6.5374E06  
HSAFPSS [2]  0.0280  0.0064  7.6419E06  
BAFPSS (Prop.)  0.0171  0.0048  5.7325E06  
Plant6  FPSS [46]  0.0362  0.0111  1.0156E05 
PSOFPSS [5]  0.0206  0.0050  6.1350E06  
HSAFPSS [2]  0.0270  0.0058  6.7488E06  
BAFPSS (Prop.)  0.0132  0.0046  5.8600E06  
Plant7  FPSS [46]  0.0613  0.0149  9.2326E06 
PSOFPSS [5]  0.0320  0.0038  1.7054E06  
HSAFPSS [2]  0.0309  0.0037  1.7049E06  
BAFPSS (Prop.)  0.0195  0.0036  1.6846E06  
Plant8  FPSS [46]  0.0428  0.0111  6.8407E06 
PSOFPSS [5]  0.0082  0.0021  1.2035E06  
HSAFPSS [2]  0.0168  0.0037  2.0258E06  
BAFPSS (Prop.)  0.0094  0.0027  1.5931E06 
The IEEE 39bus power system is configured with different sets of active power and active load connected to the system shown in Fig. 4 . It has 10 generators and 19 loads connected as in [38] . The active power assigned to plant1 (base case) are as [5.519816, 10.0, 6.5, 5.08, 6.32, 6.5, 5.6, 5.4, 8.3, 2.5]. The load assigned to plant1 (basecase) for bus nos. [1, 2, 13, 14, 17, 18, 21, 23, 24, 25, 26, 27, 28, 29, 30, 32, 35, 36, 38] = [(0.092 + j0.046), (11.04 + j2.5), (3.22 + j0.024), (5.0 + j1.84), (2.3380 + j0.8400), (5.22 + j1.76), (2.74 + j1.15), (2.745 + j0.8466), (3.086 + j0.922), (2.24 + j0.472), (1.39 + j0.17), (2.81 + j0.755), (2.06 + j0.276), (2.835 + j0.269), (6.28 + j1.030), (.075 + j0.88), (3.20 + j1.53), (3.294 + j0.323), (1.58 + j0.30)]. To generate 8plant configurations, the different sets of active power of generators and active load are considered. These system plants are shown in Table 7 . The last column of Table 7 refers to the selfclearing fault at a bus for nonlinear behavior of system.
Power system model  Active power^{a}  Active load^{b}  Fault at bus 

Plant1  Base case  Base case  Bus16 
Plant2  3,5  2,13,27,28  Bus13 
Plant3  1,2,3,4  17,24  Bus11 
Plant4  7,8  27,28,30,32  Bus9 
Plant5  2,7  30,35,36,38  Bus7 
Plant6  1,3,9,10  24–27,30,35,36  Bus17 
Plant7  1,4,5,6  13,25,30,35  Bus19 
Plant8  4,5,6,7  18,21,27,28,36,38  Bus21 
a. Active power of the generators is changed w.r.t. base case.
b. The connected load to the buses is changed w.r.t. base case.
The creation of experimental plants for IEEE New England tenmachine thirty ninebus power system is well explained in the previous section. The required machine data, load flow data, transformer data and line data for the system configuration are considered as presented in [38] and [40] . The system model referring to plant1 configuration as in Table 7 is equipped with FPSS at all ninemachines (named as Gen1 to Gen9) except Gen10, which is considered as the slack and subjected to controller design using harmony search algorithm (as described in [2] ) and the bat algorithm in Section 3 , with parameter bounds as , , and . With the initializing parameters as above for BA and as in [2] for HSA; the systems are simulated for an iteration count as 200. The fitness function variation for 200 iterations with HSA and BA is shown in Fig. 17 . The optimal values of scaling factors with bat and harmony search algorithm are mentioned in Table 8 .

Fig. 17. Fitness function plot for simultaneous tuning of input–output scaling factors of FPSSs for 10machine 39bus power system using bat algorithm.

Controllers  Generators 


 

HSAFPSS  Gen1  10.0000  9.7770  9.9991  
Gen2  56.8062  6.8892  9.9382  
Gen3  10.0899  9.9099  10.000  
Gen4  59.8892  5.8811  10.000  
Gen5  55.5804  8.9766  9.7362  
Gen6  59.5663  9.8928  10.000  
Gen7  60.0000  6.5596  8.9733  
Gen8  52.9681  9.0131  8.7615  
Gen9  56.4434  7.9649  6.4976  
BAFPSS  Gen1  19.6546  4.7485  3.0247  
Gen2  59.7079  8.4225  4.8785  
Gen3  13.1155  8.4256  3.9920  
Gen4  59.4908  7.1621  3.1274  
Gen5  25.9536  2.9191  4.6584  
Gen6  17.4769  4.2649  4.8460  
Gen7  44.3857  9.0319  3.6861  
Gen8  45.5560  4.6530  3.9345  
Gen9  27.4008  7.8812  4.7202 
The 9generators of the system are equipped controllers, and simulation is carried out for the speed response from the system. The system is equipped with FPSS [47] and [48] , HSAFPSS and BAFPSS and graphical comparison is recorded. The response from the system with all controllers and for all generators is impossible because of space constraint. The response of plant5 for Gen1, Gen3, Gen5, Gen8 and Gen9 is shown in Fig. 18 , Fig. 19 , Fig. 20 , Fig. 21 and Fig. 22 . The improved performance from the system with the bat algorithm can be observed with reduced settling time and overshoot as compared to others. The graphical representation of the response due to these controllers is quite clear to interpret best performance with BAFPSS and worst as with FPSS [47] and [48] . It can be seen that the overshoot as well as the settling time with BAFPSS is greatly improved as compared to that of FPSS [47] and [48] . However, the response with BAFPSS is closely related to that of HSAFPSS; therefore, the performance indices based analysis is needed to differentiate the degree of performance.

Fig. 18. Speed response of Gen1 for plant5 of 10machine 39bus power system with FPSS [47] and [48] , HSAFPSS and BAFPSS.


Fig. 19. Speed response of Gen3 for plant5 of 10machine 39bus power system with FPSS [47] and [48] , HSAFPSS and BAFPSS.


Fig. 20. Speed response of Gen5 for plant5 of 10machine 39bus power system with FPSS [47] and [48] , HSAFPSS and BAFPSS.


Fig. 21. Speed response of Gen8 for plant5 with of 10machine 39bus power system FPSS [47] and [48] , HSAFPSS and BAFPSS.


Fig. 22. Speed response of Gen9 for plant5 with of 10machine 39bus power system FPSS [47] and [48] , HSAFPSS and BAFPSS.

To evaluate the robustness of the proposed BAFPSS, simulation is carried out for all eight plant configurations, which represent the wide range of operating conditions and system configurations. The system is simulated with FPSS and with HSAFPSS for comparison purpose with eight plant conditions. Each time the performance indices (ITAE, IAE and ISE) are recorded and enlisted in Table 9 . Since the system possesses ten generators, the PI values in Table 9 are the sum of PIs of ten generators. Comparatively lower value of PI refers to better performance. It is clear from this table that the performance of the system is enhanced by using proposed BAFPSS as compared to performance with FPSS and with HASFPSS.
PS model  Controllers  ITAE  IAE  ISE 

Plant1  FPSS [47] and [48]  0.0236  0.0122  8.3233E06 
HSAFPSS  0.0104  0.0064  5.8288E06  
BAFPSS  0.0099  0.0063  5.3339E06  
Plant2  FPSS [47] and [48]  0.0339  0.0149  8.4324E06 
HSAFPSS  0.0097  0.0056  3.1842E06  
BAFPSS  0.0080  0.0051  3.0877E06  
Plant3  FPSS [47] and [48]  0.0115  0.0063  1.5598E06 
HSAFPSS  0.0021  0.0022  5.5395E07  
BAFPSS  0.0017  0.0019  5.0791E07  
Plant4  FPSS [47] and [48]  0.0185  0.0104  1.0332E05 
HSAFPSS  0.0066  0.0048  6.3518E06  
BAFPSS  0.0063  0.0048  5.6729E06  
Plant5  FPSS [47] and [48]  0.0132  0.0086  7.0048E06 
HSAFPSS  0.0082  0.0056  6.3767E06  
BAFPSS  0.0079  0.0054  5.7404E06  
Plant6  FPSS [47] and [48]  0.0204  0.0107  5.8676E06 
HSAFPSS  0.0081  0.0052  3.4451E06  
BAFPSS  0.0076  0.0049  3.6366E06  
Plant7  FPSS [47] and [48]  0.0120  0.0066  1.9293E06 
HSAFPSS  0.0030  0.0025  8.0286E07  
BAFPSS  0.0027  0.0023  7.7544E07  
Plant8  FPSS [47] and [48]  0.0291  0.0135  8.2817E06 
HSAFPSS  0.0084  0.0056  4.3251E06  
BAFPSS  0.0075  0.0052  4.3215E06 
In this paper, the application of the bat algorithm is used to tune the input–output scaling factors of fuzzy logic based power system stabilizer for three systems such as singlemachine infinitebus power system (SMIB), twoarea fourmachine tenbus power system and IEEE New England tenmachine thirty ninebus power systems.
The SMIB power system is equipped with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and proposed BAFPSS. The system is simulated for eight plant conditions, and consequently the speed response from the system for different plants is compared. The performance indices with BAFPSS are greatly improved as compared to others.
The twoarea fourmachine tenbus power system is simulated for speed response comparison with FPSS [46] , PSOFPSS [5] , HSAFPSS [2] and proposed BAFPSS. The simulation study is revealed that speed response with BAFPSS is much better as compared to others. The superiority of the proposed controller (BAFPSS) proved in terms of performance indices.
In case of IEEE tenmachine power system only FPSS [47] and [48] is available; therefore, the harmony search and bat algorithms are considered to optimize the input–output scaling factors. The system responses with FPSS [47] and [48] , with HSAFPSS and with BAFPSS are compared and found that the BAFPSS appeared with superior performance. The speed response is compared graphically as a sample for plant5 and superior performance with BAFPSS is validated over eight plant conditions using performance indices.
The strong aspect of the bat algorithm is its quick start property and the strength to optimize in global space. The harmony search is able to optimize system globally but after a prolonged number of iterations.
This research was supported by All India Council for Technical Education , New Delhi, India in the name of D. K. Sambariya. The author is grateful to the University College of Engineering, Rajasthan Technical University, Kota, for sponsoring him under Quality Improvement Programme. He also thanks his colleagues for sharing the responsibility at the parent institute during the stay at Roorkee.
Published on 10/04/17
Licence: Other
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