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A novel hybrid AGWO-PSO algorithm in mitigation of power network oscillations with STATCOM

  • * Corresponding author: Ramesh Devarapalli

    * Corresponding author: Ramesh Devarapalli 
Abstract Full Text(HTML) Figure(12) / Table(6) Related Papers Cited by
  • The assimilation of flexible AC transmission (FACTS) controllers to the existing power network outweigh the numerous alternatives in enhancing the damping behavior for the inter-area /intra-area system oscillations of a power network. This paper provides a rigorous analysis in damping of oscillations in a power network. It utilizes a shunt connected voltage source converter (VSC) based FACTS device to enhance the system operating characteristics. A comprehensive system mathematical modelling has been developed for demonstrating the system behavior under different loading conditions. A novel hybrid augmented grey wolf optimization-particle swarm optimization (AGWO-PSO) is proposed for the coordinated design of controllers static synchronous compensator (STATCOM) and power system stabilizers (PSSs). A multi-objective function, comprising damping ratio improvement and drifting the real part to the left-hand side of S-plane of the system poles, has been developed to achieve the objective and the effectiveness of the proposed algorithms have been analyzed by monitoring the system performance under different loading conditions. Eigenvalue analysis and damping nature of the system states under perturbation have been presented for the proposed algorithms under different loading conditions, and the performance evaluation of the proposed algorithms have been done by means of time of execution and the convergence characteristics.

    Mathematics Subject Classification: 65k10; 93D15; 93D09; 49M99.


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  • Figure 1.  Schematic of the mathematically modelled System to coordinate STATCOM and PSS controllers

    Figure 2.  Power System Stabilizer block diagram representation

    Figure 3.  Desired location of eigenvalues [9]

    Figure 4.  Governance hierarchy of GWs

    Figure 5.  Regulation vectors adjustment for catching the prey

    Figure 6.  Attacking and searching strategy of GWs

    Figure 7.  (a) 2D representation of F1-F23, (b) Search space, (c) Average fitness obtained over the iterations, (d) box and whisker plot, (e) Convergence curves

    Figure 8.  Convergence characteristics of the proposed optimization algorithms under (a) Light Load, (b) Nominal Load and (c) Heavy Load condition

    Figure 9.  Execution time (in sec.) of proposed heuristic methods under different loading conditions

    Figure 10.  Damping behavior of system states for 10% perturbation under light load with different algorithms

    Figure 11.  Damping behavior of system states for 10% perturbation under light load with different algorithms

    Figure 12.  Damping behavior of system states for 10% perturbation under heavy load with different algorithms

    Table 1.  Application of different meta-heuristic techniques for research problems in the electric power system

    Suggested Algorithm Performance comparison with algorithm Problem solution Considered Test system Ref.
    SCA ZN, DE, ABC, BBO controller parameters of AVR system Sample test system [17]
    SSA MSA, DE, MDE, PSO, TSA OPF problem with voltage stability objective IEEE 57- and 118-bus [15]
    Variant of HSA Other variants of HSA Economic Emission problem 5, 6, 10, 14- test systems [21]
    SSOA GWO, PSO, DE, EP MRCHPED problem three region test system [3]
    SCA ALO, DA Power system oscillation damping 2 machine with STATCOM [10]
    Hybrid PSO-AFSA PSO, AFSA ELD problem 5, 10 Units system [37]
    ALO PSO PSS parameter tuning SMIB with STATCOM [11]
    IA Algorithms from literature Economic Dispatch problem 8 test systems [2]
    HHO modified GWO, WOA, ALO Stabilizers coordination SMIB with STATCOM [6,8]
     | Show Table
    DownLoad: CSV

    Table 2.  Mean, Standard deviation (SD), Best and worst values obtained with different algorithms

    $\textbf{Functions}$ $\textbf{PSO}$ $\textbf{MFO}$ $\textbf{GWO}$ $\textbf{AGWO}$ $\textbf{AGWOPSO}$
    $\textbf{F1: Sphere}$ Mean 1.21E-27 1.26E-25 1.81E-05 2.74E-25 9.59E-06
    SD 1.40E-27 2.17E-25 8.12E-06 5.90E-25 4.67E-06
    Best 7.00E-30 2.04E-27 6.75E-06 7.01E-27 3.26E-06
    Worst 5.18E-27 1.11E-24 3.63E-05 3.01E-24 2.08E-05
    $\textbf{F2: Schwefel 2.22}$ Mean 1.18E-16 1.45E-15 1.63E-03 1.76E-15 1.09E-03
    SD 7.79E-17 1.51E-15 5.46E-04 1.15E-15 2.13E-04
    Best 1.10E-17 2.02E-16 9.45E-04 4.12E-16 7.33E-04
    Worst 3.57E-16 6.04E-15 3.83E-03 6.38E-15 1.52E-03
    $\textbf{F3: Schwefel 1.2}$ Mean 1.30E-05 2.32E-04 4.84E-01 1.49E-05 1.42E-01
    SD 3.68E-05 5.55E-04 5.71E-01 2.35E-05 1.12E-01
    Best 2.15E-09 3.43E-07 2.36E-02 7.99E-09 8.57E-03
    Worst 1.79E-04 2.46E-03 3.25E+00 9.74E-05 4.45E-01
    $\textbf{F4: Schwefel 2.21}$ Mean 1.15E-06 2.19E-06 3.30E-01 1.93E-06 1.90E-01
    SD 1.09E-06 2.82E-06 1.09E-01 1.18E-06 4.73E-02
    Best 1.29E-07 3.03E-07 1.62E-01 1.66E-07 1.11E-01
    Worst 4.80E-06 1.54E-05 5.45E-01 4.72E-06 2.78E-01
    $\textbf{F5: Rosenbrock}$ Mean 2.95E+01 2.95E+01 3.11E+01 2.97E+01 3.85E+01
    SD 7.79E-01 8.06E-01 6.25E-01 9.26E-01 2.14E+01
    Best 2.84E+01 2.81E+01 2.97E+01 2.78E+01 2.89E+01
    Worst 3.14E+01 3.14E+01 3.18E+01 3.14E+01 1.03E+02
    $\textbf{F6: Step}$ Mean 8.33E-01 8.07E-01 4.48E+00 1.15E+00 5.20E+00
    SD 4.07E-01 4.69E-01 5.37E-01 5.07E-01 6.25E-01
    Best 6.19E-05 2.74E-07 3.58E+00 2.55E-01 3.86E+00
    Worst 1.64E+00 1.82E+00 5.23E+00 2.46E+00 6.31E+00
    $\textbf{F7: Quartic}$ Mean 1.67E-03 2.11E-03 3.53E-02 2.60E-03 2.93E-02
    SD 9.55E-04 1.27E-03 9.30E-03 8.54E-04 8.34E-03
    Best 3.43E-04 8.07E-04 2.13E-02 1.11E-03 1.39E-02
    Worst 4.54E-03 6.70E-03 6.09E-02 4.59E-03 5.91E-02
    $\textbf{F8: Schwefel}$ Mean -6.58E+03 -6.33E+03 -5.72E+03 -1.24E+04 -1.25E+04
    SD 1.15E+03 1.23E+03 1.09E+03 8.64E+02 1.05E+03
    Best -8.55E+03 -8.26E+03 -7.71E+03 -1.37E+04 -1.35E+04
    Worst -3.34E+03 -3.64E+03 -2.28E+03 -9.89E+03 -7.61E+03
    $\textbf{F9: Rastrigin}$ Mean 2.20E+00 3.31E+00 5.81E+01 5.17E+00 4.07E+01
    SD 3.09E+00 4.75E+00 4.16E+01 5.68E+00 1.12E+01
    Best 6.20E-14 6.20E-14 3.21E+01 6.20E-14 2.11E+01
    Worst 1.24E+01 1.63E+01 2.69E+02 1.78E+01 7.27E+01
    $\textbf{F10: Ackley}$ Mean 1.15E-13 2.24E-13 3.78E+00 2.62E-13 3.73E+00
    SD 1.95E-14 6.46E-14 1.01E-01 6.88E-14 8.85E-02
    Best 8.24E-14 1.25E-13 3.35E+00 1.52E-13 3.50E+00
    Worst 1.56E-13 3.77E-13 3.90E+00 4.23E-13 3.85E+00
    $\textbf{F11: Griewank}$ Mean 4.34E-03 3.58E-03 9.42E-03 6.42E-03 6.74E-03
    SD 8.26E-03 7.71E-03 1.17E-02 1.10E-02 1.05E-02
    Best 0.00E+00 0.00E+00 1.25E-05 0.00E+00 5.45E-06
    Worst 2.52E-02 2.78E-02 2.65E-02 4.36E-02 2.68E-02
    $\textbf{F12: Penalized}$ Mean 4.72E-02 3.70E-02 4.97E+00 6.52E-02 5.02E+00
    SD 2.32E-02 1.44E-02 1.38E+00 3.38E-02 1.45E+00
    Best 7.19E-03 1.39E-02 2.08E+00 1.11E-05 2.43E+00
    Worst 1.29E-01 7.27E-02 8.08E+00 1.24E-01 8.91E+00
    $\textbf{F13: Penalize 2}$ Mean 7.08E-01 6.16E-01 3.52E+00 7.88E-01 2.28E+00
    SD 2.93E-01 2.06E-01 5.98E-01 2.66E-01 7.11E-01
    Best 2.17E-01 1.02E-01 2.35E+00 3.38E-01 9.85E-01
    Worst 1.37E+00 9.03E-01 4.91E+00 1.43E+00 3.37E+00
    $\textbf{F14: Foxholes}$ Mean 6.63E+00 7.34E+00 1.11E+01 6.73E+00 1.37E+01
    SD 5.22E+00 5.43E+00 4.50E+00 5.56E+00 6.05E+00
    Best 1.09E+00 1.09E+00 2.17E+00 1.09E+00 1.09E+00
    Worst 1.38E+01 1.38E+01 2.00E+01 1.38E+01 2.50E+01
    $\textbf{F15: Kowalik}$ Mean 6.26E-03 5.54E-03 2.32E-03 4.38E-04 1.53E-03
    SD 9.79E-03 9.36E-03 5.66E-03 3.21E-04 6.23E-03
    Best 3.36E-04 3.36E-04 3.35E-04 3.36E-04 3.35E-04
    Worst 2.22E-02 2.22E-02 2.29E-02 1.74E-03 3.45E-02
    $\textbf{F16: Six-hump }\; \textbf{Camel-Back}$ Mean -1.13E+00 -1.13E+00 -1.12E+00 -1.13E+00 -1.12E+00
    SD 3.15E-08 9.19E-12 8.76E-03 4.23E-08 8.76E-03
    Best -1.13E+00 -1.13E+00 -1.13E+00 -1.13E+00 -1.13E+00
    Worst -1.13E+00 -1.13E+00 -1.09E+00 -1.13E+00 -1.09E+00
    $\textbf{F17: Branin}$ Mean 4.34E-01 4.34E-01 5.22E-01 4.34E-01 4.34E-01
    SD 4.68E-06 3.05E-04 4.82E-01 1.62E-06 3.12E-07
    Best 4.34E-01 4.34E-01 4.34E-01 4.34E-01 4.34E-01
    Worst 4.34E-01 4.35E-01 3.07E+00 4.34E-01 4.34E-01
    $\textbf{F18: Goldstein-Price}$ Mean 3.27E+00 3.27E+00 4.26E+00 3.27E+00 1.41E+01
    SD 7.76E-05 5.59E-05 5.38E+00 6.06E-05 1.44E+01
    Best 3.27E+00 3.27E+00 3.27E+00 3.27E+00 3.27E+00
    Worst 3.27E+00 3.27E+00 3.27E+01 3.27E+00 3.27E+01
    $\textbf{F19: Hartman 3}$ Mean -4.21E+00 -4.21E+00 -4.21E+00 -4.21E+00 -4.21E+00
    SD 2.19E-03 2.30E-03 6.26E-04 4.28E-05 7.99E-06
    Best -4.21E+00 -4.21E+00 -4.21E+00 -4.21E+00 -4.21E+00
    Worst -4.21E+00 -4.21E+00 -4.21E+00 -4.21E+00 -4.21E+00
    $\textbf{F20: Hartman 6}$ Mean -3.53E+00 -3.57E+00 -3.59E+00 -3.62E+00 -3.62E+00
    SD 9.68E-02 6.93E-02 6.05E-02 2.38E-02 3.29E-02
    Best -3.62E+00 -3.62E+00 -3.62E+00 -3.62E+00 -3.62E+00
    Worst -3.37E+00 -3.42E+00 -3.49E+00 -3.49E+00 -3.49E+00
    $\textbf{F21: Shekel5}$ Mean -1.02E+01 -1.03E+01 -7.45E+00 -9.52E+00 -5.84E+00
    SD 2.10E+00 1.91E+00 4.00E+00 2.67E+00 3.43E+00
    Best -1.11E+01 -1.11E+01 -1.11E+01 -1.11E+01 -1.11E+01
    Worst -5.52E+00 -5.52E+00 -2.87E+00 -2.93E+00 -1.48E+00
    $\textbf{F22: Shekel7}$ Mean -1.13E+01 -1.14E+01 -7.49E+00 -1.00E+01 -5.89E+00
    SD 9.28E-04 2.21E-07 4.20E+00 2.48E+00 3.30E+00
    Best -1.14E+01 -1.14E+01 -1.14E+01 -1.14E+01 -1.14E+01
    Worst -1.13E+01 -1.14E+01 -3.00E+00 -5.55E+00 -1.53E+00
    $\textbf{F23: Shekel10}$ Mean -1.11E+01 -1.13E+01 -8.14E+00 -1.03E+01 -7.10E+00
    SD 1.50E+00 1.07E+00 4.20E+00 2.51E+00 4.02E+00
    Best -1.15E+01 -1.15E+01 -1.15E+01 -1.15E+01 -1.15E+01
    Worst -5.60E+00 -5.65E+00 -2.64E+00 -4.09E+00 -1.86E+00
     | Show Table
    DownLoad: CSV

    Table 3.  Wilcoxon paired signed ranks test for the test system

    Algorithm p-value $ +/-/\backsim $
    Light Load
    (Pe1=Pe2=0.3& Qe1=Qe2=0.1)
    AGWO-PSO Versus MFO 1.7344e-06 +
    AGWO-PSO Versus GWO 1.7344e-06 +
    AGWO-PSO Versus PSO 1.7344e-06 +
    AGWO-PSO Versus AGWO 1.7344e-06 +
    Nominal Load
    (Pe1=Pe2=0.8& Qe1=Qe2=0.6)
    AGWO-PSO Versus MFO 1.7344e-06 +
    AGWO-PSO Versus GWO 1.7344e-06 +
    AGWO-PSO Versus PSO 1.7344e-06 +
    AGWO-PSO Versus AGWO 1.7344e-06 +
    Heavy Load
    (Pe1=Pe2=1.3& Qe1=Qe2=1.0)
    AGWO-PSO Versus MFO 1.7344e-06 +
    AGWO-PSO Versus GWO 1.7344e-06 +
    AGWO-PSO Versus PSO 1.7344e-06 +
    AGWO-PSO Versus AGWO 7.7122e-04 +
     | Show Table
    DownLoad: CSV

    Table 4.  Tuned parameters of controller parameters with the proposed metaheuristic optimization algorithms

    T11 T21 K1 T12 T22 K2 me de TOE Jmin
    Light Load MFO 2 0.353621 17.1851 0.896599 2 50 0.877263 0 21.1012 20634.638
    Pe1=Pe2=0.3 & GWO 1.99226 0.631084 20.0048 2 0.408557 7.68251 1 0.553048 19.8576 19744.427
    PSO 1.99616 0.531169 17.1061 1.99706 0.376092 7.67036 0.93685 0.471697 22.568 19790.2423
    AGWO 2 0.814356 20.0335 0.223326 0.349201 0.145617 1 0.606624 20.511 19749.174
    Qe1=Qe2=0.1 AGWO-PSO 1.91829 0.315199 16.476 2 0.367394 7.72613 0.759916 0 21.5609 19657.1023
    Nominal Load MFO 2 0.34587 6.5268 2 0.23173 4.0409 0.71636 1 25.2134 20069.6872
    Pe1=Pe2=0.8 & GWO 2 0.20802 4.8299 2 0.18249 4.344 1 0.00080834 21.9609 19897.141
    PSO 2 0.34586 6.5267 2 0.23173 4.0409 0.71631 0.99996 23.2164 19918.5198
    AGWO 2 0.30786 5.9268 2 0.22043 2.9841 0.71539 1 20.9591 19457.3614
    Qe1=Qe2=0.6 AGWO-PSO 2 0.21304 5.271 2 0.20313 5.4271 1 0 20.5927 19425.0108
    Heavy Load MFO 2 0.12956 3.698 2 0.1436 5.036 1 0 21.3626 20880.619
    Pe1=Pe2=1.3 & GWO 2 0.12949 3.7016 2 0.14394 5.0545 1 0.00074374 20.4907 20388.983
    PSO 0.709342 0.168539 19.6737 0.69435 0.174195 19.1828 0.235767 0 22.1254 20396.0086
    AGWO 2 0.13122 3.7291 2 0.13306 4.9783 1 0 20.5043 20387.3276
    Qe1=Qe2=1.0 AGWO-PSO 2 0.12329 3.5156 2 0.14564 5.9558 1 0 22.1768 20387.1437
     | Show Table
    DownLoad: CSV

    Table 5.  ANOVA test for the test system under different loading conditions

     | Show Table
    DownLoad: CSV

    Table 6.  System Eigenvalues & Damping ratios under various loading conditions with the proposed optimization algorithms

     | Show Table
    DownLoad: CSV
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