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

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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.

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Abbreviations

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

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

References

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  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)

  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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  22. Mirjalili, S., Lewis, A.: The whale optimization algorithm. Adv. Eng. Softw. 95, 51–67 (2016)

    Article  Google Scholar 

  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. 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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  28. Nomura, S., Tsutsui, H., Tsuji-Iio, S., Shimada, R.: Flexible power interconnection with SMES. IEEE Trans. Appl. Supercond. 16(2), 616–619 (2006)

    Article  Google Scholar 

  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. Gopal, M.: Control systems: principles and design, vol. 2. Tata McGraw Hill Pub, New Delhi (2003)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Motilal Nehru National Institute of Technology, Allahabad, India

    Dipayan Guha

  2. Department of Electrical Engineering, Kalyani Government Engineering College, Kalyani, West Bengal, India

    Provas Kumar Roy

  3. Department of Electrical Engineering, National Institute of Technology, Durgapur, West Bengal, India

    Subrata Banerjee

Authors
  1. Dipayan Guha
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  2. Provas Kumar Roy
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  3. Subrata Banerjee
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Corresponding author

Correspondence to Dipayan Guha.

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Appendix

Appendix

Parameters

Value

Parameters

Value

Parameters

Value

Parameters

Value

Nominal values of test system-1

 \( k_{f1} \)

0.35

\( k_{ac} \)

2

\( \omega_{n,i} \)

3.5

\( T_{12} \)

0.214

 \( k_{f2} \)

– 0.1

\( \xi_{i} \)

1.5

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

2.3 Hz/pu MW

\( T_{sg} \)

0.08

 \( apf \)

0.5

\( \Delta P_{D} \)

0.03 \( pu \)

\( {\rm B}_{1} = {\rm B}_{2} \)

0.425 pu MW/Hz

\( T_{t} \)

0.32

 \( K_{ps} \)

102

\( T_{ps} \)

25

\( P_{r} \)

2000 MW

\( \alpha_{12} \)

– 1

Nominal values of test system-2

 \( T_{sg} \)

0.08

\( T_{r} \)

10

\( P_{r} \)

2000 MW

\( \alpha_{12} \)

– 1

 \( T_{t} \)

0.3

\( K_{r} \)

0.3

\( {\rm B}_{1} = {\rm B}_{2} \)

0.425 pu MW/Hz

\( T_{RH} \)

28.75

 \( K_{ps} \)

120

\( T_{ps} \)

20

\( R_{t} = R_{h} = R_{g} \)

2.3 Hz/pu MW

\( T_{GH} \)

0.2

 \( T_{R} \)

5

\( T_{w} \)

1

\( X \)

0.6

\( Y \)

1

 \( c \)

1

\( b \)

0.05

\( T_{CR} \)

0.3

\( T_{F} \)

0.23

 \( T_{CD} \)

0.2

\( T_{12} \)

0.0433

\( K_{th} \)

0.6

\( K_{hy} \)

0.25

 \( K_{g} \)

0.15

\( f \)

60

\( \Delta P_{D} \)

\( 0.01\,pu \)

  

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Guha, D., Roy, P.K. & Banerjee, S. Whale optimization algorithm applied to load frequency control of a mixed power system considering nonlinearities and PLL dynamics. Energy Syst 11, 699–728 (2020). https://doi.org/10.1007/s12667-019-00326-2

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  • DOI: https://doi.org/10.1007/s12667-019-00326-2

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