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Whale optimization algorithm applied to load frequency control of a mixed power system considering nonlinearities and PLL dynamics

  • Dipayan GuhaEmail author
  • Provas Kumar Roy
  • Subrata Banerjee
Original Paper
  • 11 Downloads

Abstract

In this work, an attempt has been made to implement a nature-inspired stochastic evolutionary algorithm, namely whale optimization algorithm (WOA) for exploring optimum and practical solutions of load frequency control (LFC) problem in power system. The proposed WOA mimics the ‘bubble-net feeding’ strategy of ‘humpback whales’ in the oceans. The optimization technique is individually applied to a two-area thermal power plant and two-area hydro-thermal-gas power plant with AC–DC tie-line for fine-tuning of the controller parameters. The study further houses the consequences of frequency measurement and the dynamics of a phase-locked loop (PLL) with power system nonlinearities. To establish the efficacy of WOA, the obtained results are compared with results of success history based adaptive differential evolution (SHADE), krill herd algorithm (KHA), and some other well-known control algorithms. Finally, statistical analysis is performed to affirm robustness of the proposed WOA in LFC area.

Keywords

Load frequency control Whale optimization algorithm Phase-locked loop Transient responses Statistical analysis 

List of symbols

\( \xi ,\omega_{n} \)

Damping ratio and natural frequency of oscillation in rad/s

\( apf \)

Area participation factor

\( pu \)

Per unit

\( B_{1} ,B_{2} \)

Frequency bias constant of area-1 and 2, respectively

\( \dim \)

Number of control variable

\( G_{sg} \left( s \right),G_{t} \left( s \right),G_{ps} \left( s \right) \)

T.F. of governor, turbine and power system, respectively

J

Fitness function

\( K_{ps} \)

Gain of power system

\( k_{p} ,k_{i} ,k_{d} \)

Proportional, integral, and derivative gain, respectively

\( K_{ac} \)

Gain of AC tie-line

\( k_{f,m} ,k_{f,n} \)

Frequency control gain of area-m and area-n, respectively \( \left( {m \ne n} \right) \)

\( k_{pd} \)

Gain of phase detector

\( k_{vco} \)

Gain of voltage control oscillator (VCO)

\( n_{p} \)

Population size

\( R_{1} ,R_{2} \)

Speed regulation parameter of speed governor of area-1 and 2, respectively

\( T_{i} \)

Integral time constant in seconds

\( T_{d} \)

Time delay in seconds

\( T_{DC} \)

Time constant of HVDC line in seconds

\( T_{sg} \)

Time constant of speed governor in seconds

\( T_{t} \)

Time constant of steam turbine in seconds

\( T_{ps} \)

Time constant of power system itself in seconds

\( T_{12} \)

Synchronizing time constant of AC tie-line in seconds

\( \Delta P_{tie} \)

Tie-line power deviation in \( pu \)

\( \Delta P_{DC} \)

Power modulated by HVDC in \( pu \)

\( \Delta P_{D} \)

Load disturbance in \( pu \)

\( \Delta f_{1} ,\Delta f_{2} \)

Frequency deviation of area-1 and 2, respectively, in Hz

Notes

References

  1. 1.
    Chon, N.: Some aspects of tie-line bias control on interconnected powers. Am. Inst. Electr. Eng. Trans. 75, 1415–1436 (1957)Google Scholar
  2. 2.
    Elgerd, O.I., Fosha, C.E.: Optimum megawatt-frequency control of multi-area electric energy systems. IEEE Trans. Power Appar. Syst. 89(4), 556–563 (1970)CrossRefGoogle Scholar
  3. 3.
    Sahu, R.K., Panda, S., Sekhar, G.T.C.: A novel hybrid PSO-PS optimized fuzzy PI controller for AGC in multi area interconnected power systems. Int. J. Electr. Power Energy Syst. 64, 880–893 (2015)CrossRefGoogle Scholar
  4. 4.
    Prakash, S., Sinha, S.K.: Neuro-fuzzy computational technique to control load frequency in hydro-thermal interconnected power system. J. Inst. Eng. India Ser. B 96(3), 273–282 (2015)CrossRefGoogle Scholar
  5. 5.
    Prakash, S., Sinha, S.K.: Simulation based neuro-fuzzy hybrid intelligent PI control approach in four-area load frequency control of interconnected power system. Appl. Soft Comput. 23, 152–164 (2014)CrossRefGoogle Scholar
  6. 6.
    Sabahi, K., Ghaemi, S., Pezeshki, S.: Application of type-2 fuzzy logic system for load frequency control using feedback error learning approaches. Appl. Soft Comput. 21, 1–11 (2014)CrossRefGoogle Scholar
  7. 7.
    Mohanty, B.: TLBO optimized sliding mode controller for multi-area multi-source nonlinear interconnected AGC system. Int. J. Electr. Power Energy Syst. 73, 872–881 (2015)CrossRefGoogle Scholar
  8. 8.
    Guha, D., Roy, P.K., Banerjee, S.: Load frequency control of interconnected power system using grey wolf optimization. Swarm Evol. Comput. 27, 97–115 (2016)CrossRefGoogle Scholar
  9. 9.
    Shiva, C.K., Shankar, G., Mukherjee, V.: Automatic generation control of power system using a novel quasi-oppositional harmony search algorithm. Int. J. Electr. Power Energy Syst. 73, 787–804 (2015)CrossRefGoogle Scholar
  10. 10.
    Guha, D., Roy, P.K., Banerjee, S.: Study of differential search algorithm based automatic generation control of an interconnected thermal-thermal system with governor dead band. Appl. Soft Comput. 52, 160–175 (2017)CrossRefGoogle Scholar
  11. 11.
    Guha, D., Roy, P.K., Banerjee, S.: Quasi-oppositional symbiotic organism search algorithm applied to load frequency control. Swarm Evol. Comput. 33, 46–67 (2017)CrossRefGoogle Scholar
  12. 12.
    Pradhan, P.C., Sahu, R.K., Panda, S.: Firefly algorithm optimized fuzzy PID controller for AGC of multi-area multi-source power systems with UPFC and SMES. Eng. Sci. Tech. Int. J 19, 338–354 (2016)CrossRefGoogle Scholar
  13. 13.
    Abd-Elazim, S.M., Ali, E.S.: Load frequency controller design via BAT algorithm for nonlinear interconnected power system. Int. J. Electr. Power Energy Syst. 77, 166–177 (2016)CrossRefGoogle Scholar
  14. 14.
    Routh, U.K., Sahu, R.K., Panda, S.: Design and analysis of differential evolution algorithm based automatic generation control for interconnected power system. Ain Shams Eng. J. 4, 409–421 (2013)CrossRefGoogle Scholar
  15. 15.
    Tanabe, R., Fukunaga, A.: Success-history based parameter adaptation for differential evolution. In: Proc. of 2013 IEEE Congress on Evolut Comput June 20–23; Cancun, Mexico, 71–78 (2013)Google Scholar
  16. 16.
    Guha D, Roy PK, Banerjee S. Application of krill herd algorithm for optimum design of load frequency controller for multi-area power system network with generation rate constraint. In: Proc of the 4th Int Conf on frontiers in intelligent computing: theory and applications (FICTA); 404:245–257 (2015)Google Scholar
  17. 17.
    Guha, D., Roy, P.K., Banerjee, S.: Krill herd algorithm for automatic generation control with flexible AC transmission system controller including superconducting magnetic energy storage units. J. Eng. IET 2016(5), 147–161 (2016)Google Scholar
  18. 18.
    Shabani, H., Vahidi, B., Ebrahimpour, M.: A robust PID controller based on imperialist competitive algorithm for load-frequency control of power systems. ISA Trans. 52(1), 88–95 (2012)CrossRefGoogle Scholar
  19. 19.
    Ibraheem, Nizamuddin, Bhatti, T.S.: AGC of two area power system interconnected by AC/DC links with diverse sources in each area. Int. J. Electr. Power Energy Syst. 55, 297–304 (2014)CrossRefGoogle Scholar
  20. 20.
    Rakhshani, E., Rodriguez, P.: Inertia emulation in AC/DC interconnected power systems using derivative technique considering frequency measurement effects. IEEE Trans on Power Syst, 1–12 (2016)Google Scholar
  21. 21.
    Rakhshani, E., Remon, D., Rodriguez, P.: Effects of PLL and frequency measurements on LFC problem in multi-area HVDC interconnected systems. Int. J. Electr. Power Energy Syst. 81, 140–152 (2016)CrossRefGoogle Scholar
  22. 22.
    Mirjalili, S., Lewis, A.: The whale optimization algorithm. Adv. Eng. Softw. 95, 51–67 (2016)CrossRefGoogle Scholar
  23. 23.
    Bhatt, R., Parmar, G., Gupta, R.: Whale optimized PID controllers for LFC of two area interconnected thermal power plants. ICTACT J. Microelectr. 3(4), 467–472 (2018)Google Scholar
  24. 24.
    Sivalingam, R., Chinnamuthu, S., Dash, S.S.: A modified whale optimization algorithm-based adaptive fuzzy logic PID controller for load frequency control of autonomous power generation systems. Automatika J. Control, Meas., Electr., Comput. Commun. 58(4), 410–421 (2018)Google Scholar
  25. 25.
    Hasanien, H.M.: Whale optimisation algorithm for automatic generation control of interconnected modern power systems including renewable energy sources. IET Gener. Trans. Distrib. 12(3), 607–614 (2018)CrossRefGoogle Scholar
  26. 26.
    Guha, D., Roy, P.K., Banerjee, S.: Oppositional biogeography-based optimisation applied to SMES and TCSC-based load frequency control with generation rate constraints and time delay. Int. J. Power Energy Convers. 7(4), 391–423 (2016)CrossRefGoogle Scholar
  27. 27.
    Zhang, Z.D.Y., Chen, Z., Li, P., Ni, Y., Shi, L.: Integrated emergency frequency control method for interconnected AC/DC power systems using centre of inertia signals. IET Gener. Trans. Distrib. 6(6), 584–592 (2012)CrossRefGoogle Scholar
  28. 28.
    Nomura, S., Tsutsui, H., Tsuji-Iio, S., Shimada, R.: Flexible power interconnection with SMES. IEEE Trans. Appl. Supercond. 16(2), 616–619 (2006)CrossRefGoogle Scholar
  29. 29.
    Tripathy, S.C., Hope, G.S., Malik, O.P.: Optimisation of load-frequency control parameters for power systems with reheat steam turbines and governor dead band nonlinearity. IEEE Proc. 129(1), 10–16 (1982)Google Scholar
  30. 30.
    Gopal, M.: Control systems: principles and design, vol. 2. Tata McGraw Hill Pub, New Delhi (2003)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringMotilal Nehru National Institute of TechnologyAllahabadIndia
  2. 2.Department of Electrical EngineeringKalyani Government Engineering CollegeKalyaniIndia
  3. 3.Department of Electrical EngineeringNational Institute of TechnologyDurgapurIndia

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