_{max}
is the maximum allowed distance of one jump.
The flow chart of the local memetic evolution using the proposed frog leaping rule is illustrated in
Fig. 7
. The new frog leaping rule extends the local search space in each memetic evolution step; as a result it might improve the algorithm in term of convergence rate and solution performance provided that the vector
W_{max}
=[
w_{1,max}
, …,
w_{S,max}
]
^{T}
is appropriately chosen. However, if W
_{max}
 is too large, the frog leaping rule will loss its directional characteristic, and the algorithm will become more or less random search. Hence, choosing a proper maximum uncertainty vector is an issue to be considered for each particular optimization problem.
The MSFLA flowchart
4. Simulation Results
 4.1 Determination of parameters for MSFLA
The proposed MSFLA methodology is programmed in MATLAB running on an Intel w Core TM2 Duo Processor T5300 (1.73 GHz) PC with 1 GB RAM. The effect of MSFLA parameters on average fitness function (among 100 trials) is investigated. The colony size (
N_{C}
) was 100. Hundred independent trials have been made with 100 iterations per trial. The performance of the MSFLA also depends on the number of colonies. The parameters of MSFLA are selected based on the average fitness function, after a number of careful experimentation as following:

NC= 100; Dmax= 0.6, ri= 1.1; C=1.3; r=0.6.
 4.2 Experimental result
The minimum fitness value evaluating process is depicted in
Fig 8
. According to it, the MSFLA is preferred method in terms of convergence. Thei MSFLA provides the correct answers with high accuracy in the initial iterations which makes the responding time of it extremely fast. The system proper values and damping ratio of mechanical modes with three different loading conditions are tabulated in
Table 6
. It is clear that the system with MSFLASVC is suffered from small damping factors (σ = −1.13, −1.37, −1.14) for light, normal, and heavy loading, respectively.
Convergence profile for MSFLA, SPEA and PSO
Mechanical mode andξunder different loading condition and controllers
Mechanical mode and ξ under different loading condition and controllers
The coordinated controller shifts the electromechanical modes to the left of the Splane, and consequently the values of the damping factors are considerably enhanced to −1.21, −1.36, −1.16 for light, normal, and heavy loading respectively. The damping ratios commensurate with coordinated controller are almost bigger than the uncoordinated ones. Thus, the proposed controller improves the damping features of electromechanical modes and system stability. The value of parameters for the different controllers using the MSFLA technique is shown in
Table 7
.
Optimal PSSs and SVCs parameters for different controllers
Optimal PSSs and SVCs parameters for different controllers
 4.3 Light load condition
The vigorous performance of the coordinated controller under disturbance is confirmed by implementing a three phase fault of 6 cycle duration at 1.0 s close to bus 7. The responses of Δω12, Δω23 and Δω13 for light loading condition are depicted in
Figs. 9

11
.
Response of Δω_{12} for light load condition
Response of Δω_{23} for light load condition
Response of Δω_{13} for light load condition
The ability of the proposed coordinated controller for diminishing the settling time and damping power system oscillations are verified in these figures. In addition, the settling time (T
_{s}
) of these oscillations is 1.94, 2.01, and 2.09s for coordinated controller, MSFLAPSS, and MSFLASVC respectively, and consequently the proposed coordinated controller is able to provide significant damping to the system oscillatory modes compared to MSFLAPSS, and MSFLASVC.
Fig. 12
illustrates the response of Δω
_{12}
for different optimization scheme. As it seen from the figure, MSFLA reveals better performance for designing the coordinated controller compared with SPEA and PSO.
Response of Δω_{12} for different optimization techniques
 4.4 Normal load condition
The responses of Δω
_{12}
, Δω
_{23}
and Δω
_{13}
owing to same disturbance for normal loading condition are shown in
Figs. 13

15
. The results reveal that the proposed coordinated controller has a superior ability for damping power system oscillations and intensifies the dynamic stability of power system. The settling time (
T_{s}
) of these oscillations are 1.85, 2.22, and 2.28s for coordinated controller, MSFLAPSS and MSFLASVC, respectively. Hence the designed controller is competent to provide significant damping to the system oscillatory modes and enlarge the power system stability constrain.
Response of Δω_{12} for normal load condition
Response of Δω_{23} for normal load condition
Response of Δω_{13} for normal load condition
Fig. 16
depicts a comparison between different schemes. The more competent and speedy convergence is seen using the proposed MSFLA scheme compared to SPEA and PSO.
Response of Δω_{12} for different optimization techniques
 4.5 Heavy load condition
The responses of Δω
_{12}
, Δω
_{23}
and Δω
_{13}
owing to same disturbance for heavy loading condition are illustrated in
Figs. 17

19
.
Response of Δω_{12} for heavy load condition
Response of Δω_{23} for heavy load condition
Response of Δω_{13} for heavy load condition
The coordinated controller reveals better damping features for low frequency oscillations. The settling times are 1.94, 2.02, and 2.43 s for coordinated controller, MSFLAPSS and MSFLASVC respectively. The supremacy of the simultaneous coordinated IMSFLASVC and MSFLAPSS over the uncoordinated designed controllers is demonstrated. The supremacy of proposed MSFLA in adjusting the coordinated controller in comparison with SPEA and PSO is shown in
Fig. 20
.
Fig. 21
depicts the supremacy of the coordinated controller in diminishing the settling time and damping power system oscillations over the uncoordinated controller in response of Δω
_{12}
.
Response of Δω_{12} for different optimization techniques
Comparison between coordinated and uncoordinated design
5. Conclusion
The subsequent adjustment of PSS and SVC parameters does not undertake the effectiveness of the PSS and SVC with variable load condition. This study is undertaken to propose a robust design technique for the simultaneous coordinated adjusting of the SVC and PSS damping controller in a multimachine power system. The designing problem is converted to an optimization problem in which the speed deviations between generators are associated. The proposed MSFLA scheme is tested on a multimachine power system under various disturbances and compared with PSO and SPEA based tuned PSS and SVC to demonstrate its strong ability. The most obvious findings from this study are as follow:

1. The proposed MSFLA scheme for tuning SVC and PSSs is easy to implementation without additional computational complexity;

2. The convergence rate of high accuracy and speed are notably improved;

3. Power system stability and also power transfer ability are extended via the proposed scheme.
BIO
Mohsen Darbian He received his B.Sc. and M.Sc. degrees both in electrical engineering from Islamic Azad University (Abhar branch) and University of Zanjan, Iran, in 2010 and 2013, respectively. He is a Ph.D student in Electrical Engineering, at University of Zanjan, Iran.
Abolfazl Jalilvand He received B.Sc. in electrical engineering from Shahid Beheshti University, Iran, in 1995; then M.Sc. and Ph.D. degrees from University of Tabriz, Iran, in Power Engineering and Control Engineering in 1998 and 2005, respectively. Currently, he is an Associate Professor at university of Zanjan, Iran.
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