Controller parameters tuning of water cycle algorithm and its application to load frequency control of multi-area power systems using TD-TI cascade control

Abstract

In this study, a nature-inspired optimization tool called the water cycle algorithm (WCA) and its practical application to efficiently design a cascade controller for two area interconnected power system model is put forward to address the issues in load frequency control (LFC). The cascade control (CC) structure is one of the most effective controllers for improving the performance of a control scheme in power applications, particularly when disturbances occur. In this paper, a well-systematized combination of the WCA and a well-designed cascade tilt-derivative tilt-integral (TD-TI) cascade controller is introduced, and an error performance function, for example, the integral time absolute error, is taken. The proposed WCA-based effective TD-TI, TID, and PID strategy are executed as one broadly two area multi-source model with/without HVDC link under many scenarios to verify the effectiveness of the proposed system under a high-load perturbation and some critical parameters associated with the interconnected power system. Simulation results reveal that the proposed technique provides superior performance to that of newly published schemes such as many objective/PID, TLBO/PID, IPA/TID and IGWO/Fuzzy-PID controllers. The dynamic investigation is also completed with consideration of the random load pattern, which sufficiently reveals the superior performance of the WCA/TD-TI scheme.

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Abbreviations

i :

Subscript associated \({\text{to area}}\) \(\left( {i = 1, 2} \right)\)

f :

Nominal frequency \(\left( {{\text{Hz}}} \right)\)

P R :

Area \({\text{rated}}\) power \(\left( {{\text{MW}}} \right)\)

P L :

Nominal operative load \(\left( {{\text{MW}}} \right)\)

f i :

Frequency deviations \(\left( {{\text{Hz}}} \right)\)

P Li :

Step load change

P tie :

Tie \({\text{ - line deviation}}\) of power \(\left( {{\text{p}}.{\text{u}}.} \right)\)

B i :

Frequency bias \(\left( {{\text{p}}.{\text{u}}.{\text{MW}}/{\text{Hz}}} \right)\)

R i :

Speed regulation \(({\text{Hz}}/{\text{p}}.{\text{u}}.\))

T ti :

Steam turbine \({\text{time constant}}\) \(\left( {\text{s}} \right)\)

T gi :

Speed governor time constant \(\left( {\text{s}} \right)\)

T 12 :

Synchronizing coefficient \(\left( {{\text{p}}.{\text{u}}.} \right)\)

T RSi :

Hydro \({\text{turbine speed governor}}\) reset time \(\left( {\text{s}} \right)\)

T GHi :

Hydro \({\text{turbine speed governor}}\) time constant \(\left( {\text{s}} \right)\)

T RHi :

\({\text{Hydro turbine speed governor transient}} {\text{droop}}\) Time constant (s)

T Wi :

Nominal initial \({\text{time of water in penstock}}\left( {\text{s}} \right)\)

K Ri :

\({\text{Reheat coefficient of steam turbine}}\)

T ri :

\({\text{Reheat time constant of steam turbine }}\left( {\text{s}} \right)\)

K pSi :

\({\text{Power system gain }}\left( {{\text{Hz}}/{\text{p}}.{\text{u}}.} \right)\)

T pSi :

\({\text{Power system time constant }}\left( {\text{s}} \right)\)

K T :

Contribution factors of thermal unit

K H :

Contribution \({\text{factors of}}\) hydro unit

K G :

\({\text{Contribution factors of gas unit}}\)

K DC :

\({\text{HVDC gain of power system }}\left( {{\text{Hz}}/{\text{p}}.{\text{u}}.} \right)\)

T DC :

HVDC time constant \(\left( {\text{s}} \right)\)

b g :

Gas turbine constant of positioner \(\left( {\text{s}} \right)\)

c g :

Gas turbine valve positioner

Y C :

\({\text{Lag time of gas turbine governor }}\left( {\text{s}} \right)\)

X C :

Lead \({\text{time of gas turbine}}\) \({\text{governor }}\left( {\text{s}} \right)\)

T fi :

Gas \({\text{turbine fuel time}}\) constant \(\left( {\text{s}} \right)\)

T CDi :

\({\text{Gas turbine compressor discharge volume\; time constant (s)}}\)

TCRi :

Gas \({\text{turbine combustion reaction}}\;{\text{time delay }}\left( {\text{s}} \right)\)

References

  1. Abdel-Magid YL, Dawoud MM (1995) Genetic algorithms applications in load frequency control

  2. Alhelou HH, Hamedani-Golshan M-E, Zamani R, Heydarian-Forushani E, Siano P (2018) Challenges and opportunities of load frequency control in conventional, modern and future smart power systems: a comprehensive review. Energies 11(10):2497

    Article  Google Scholar 

  3. Ali ES, Abd-Elazim SM (2013) BFOA based design of PID controller for two area load frequency control with nonlinearities. Int J Electr Power Energy Syst 51:224–231

    Article  Google Scholar 

  4. Barisal AK (2015) Comparative performance analysis of teaching learning based optimization for automatic load frequency control of multi-source power systems. Int J Electr Power Energy Syst 66:67–77

    Article  Google Scholar 

  5. Behera A, Panigrahi TK, Ray PK, Sahoo AK (2019) A novel cascaded PID controller for automatic generation control analysis with renewable sources. IEEE/CAA J Autom Sin 6(6):1438–1451

    Article  Google Scholar 

  6. Bevrani H (2014) Robust power system frequency control

  7. Chatterjee K (2011) Design of dual mode PI controller for load frequency control. Int J Emerg Electr Power Syst 11(4)

  8. Crowe J et al (2005) PID control: new identification and design methods. Springer, Berlin

    Google Scholar 

  9. Daneshfar F, Bevrani H, Mansoori F (2011) Bayesian networks design of load-frequency control based on GA. In: The 2nd International Conference on Control, Instrumentation and Automation, 2011, pp 315–319

  10. Dash P, Saikia LC, Sinha N (2015) Automatic generation control of multi area thermal system using Bat algorithm optimized PD-PID cascade controller. Int J Electr Power Energy Syst 68:364–372. https://doi.org/10.1016/j.ijepes.2014.12.063

    Article  Google Scholar 

  11. Elgerd OI (1982) Electric energy systems theory: an introduction

  12. El-Hameed MA, El-Fergany AA (2016) Water cycle algorithm-based load frequency controller for interconnected power systems comprising non-linearity. IET Gener Transm Distrib 10(15):3950–3961

    Article  Google Scholar 

  13. Eskandar H, Sadollah A, Bahreininejad A, Hamdi M (2012) Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110:151–166

    Article  Google Scholar 

  14. Fini MH, Yousefi GR, Alhelou HH (2016) Comparative study on the performance of many-objective and single-objective optimisation algorithms in tuning load frequency controllers of multi-area power systems. IET Gener Transm Distrib 10(12):2915–2923

    Article  Google Scholar 

  15. Franks RG, Worley CW (1956) Quantitative analysis of cascade control. Ind Eng Chem 48(6):1074–1079

    Article  Google Scholar 

  16. Gautam SK, Goyal N (2010) Improved particle swarm optimization based load frequency control in a single area power system. In: 2010 Annual IEEE India Conference (INDICON), 2010, pp 1–4

  17. Guha D, Roy PK, Banerjee S (2018) Maiden application of SSA-optimised CC-TID controller for load frequency control of power systems. IET Gener Transm Distrib 13(7):1110–1120

    Article  Google Scholar 

  18. Hosseini SH, Etemadi AH (2008) Adaptive neuro-fuzzy inference system based automatic generation control. Electr Power Syst Res 78(7):1230–1239

    Article  Google Scholar 

  19. Jain T, Nigam MJ (2008) Optimization of PD-PI controller using swarm intelligence. Int J Comput Cogn 6(4):55–59

    Google Scholar 

  20. Jeng J-C, Liao S-J (2013) A simultaneous tuning method for cascade control systems based on direct use of plant data. Ind Eng Chem Res 52(47):16820–16831

    Article  Google Scholar 

  21. Johnson MA, Moradi MH (2005) PID control. Springer, Berlin

    Google Scholar 

  22. Kumari S, Shankar G (2018) Novel application of integral-tilt-derivative controller for performance evaluation of load frequency control of interconnected power system. IET Gener Transm Distrib 12(14):3550–3560

    Article  Google Scholar 

  23. Kumari S, Shankar G (2019) Maiden application of cascade tilt-integral–tilt-derivative controller for performance analysis of load frequency control of interconnected multi-source power system. IET Gener Transm Distrib 13(23):5326–5338

    Article  Google Scholar 

  24. Kundur P, Balu NJ, Lauby MG (1994) Power system stability and control, vol 7. McGraw-hill, New York

    Google Scholar 

  25. Lee KA, Yee H, Teo CY (1991) Self-tuning algorithm for automatic generation control in an interconnected power system. Electr Power Syst Res 20(2):157–165

    Article  Google Scholar 

  26. Lee Y, Park S, Lee M (1998) PID controller tuning to obtain desired closed loop responses for cascade control systems. Ind Eng Chem Res 37(5):1859–1865

    Article  Google Scholar 

  27. Magdy G, Mohamed EA, Shabib G, Elbaset AA, Mitani Y (2018) SMES based a new PID controller for frequency stability of a real hybrid power system considering high wind power penetration. IET Renew Power Gener 12(11):1304–1313

    Article  Google Scholar 

  28. Mohanty P, Sahu RK (2019) Differential evolution optimized cascade tilt-integral-tilt-integral-derivative controller for frequency regulation of interconnected power system. In: International Conference on Application of Robotics in Industry using Advanced Mechanisms, 2019, pp 104–111

  29. Mohanty B, Panda S, Hota PK (2014) Controller parameters tuning of differential evolution algorithm and its application to load frequency control of multi-source power system. Int J Electr power energy Syst 54:77–85

    Article  Google Scholar 

  30. Sadollah A, Eskandar H, Lee HM, Yoo DG, Kim JH (2016) Water cycle algorithm: a detailed standard code. SoftwareX 5:37–43

    Article  Google Scholar 

  31. Sahoo BP, Panda S (2018) Improved grey wolf optimization technique for fuzzy aided PID controller design for power system frequency control. Sustain Energy Grids Networks 16:278–299

    Article  Google Scholar 

  32. Sahu RK, Gorripotu TS, Panda S (2015) A hybrid DE–PS algorithm for load frequency control under deregulated power system with UPFC and RFB. Ain Shams Eng J 6(3):893–911

    Article  Google Scholar 

  33. Sahu RK, Panda S, Rout UK, Sahoo DK (2016a) Teaching learning based optimization algorithm for automatic generation control of power system using 2-DOF PID controller. Int J Electr Power Energy Syst 77:287–301

    Article  Google Scholar 

  34. Sahu RK, Panda S, Biswal A, Sekhar GTC (2016b) Design and analysis of tilt integral derivative controller with filter for load frequency control of multi-area interconnected power systems. ISA Trans 61:251–264

    Article  Google Scholar 

  35. Shayeghi H, Shayanfar HA, Jalili A (2009) LFC design of a deregulated power system with TCPS using PSO. Int J Electr Electron Eng 3(10):632–640

    Google Scholar 

  36. Shoults RR, Ibarra JAJ (1993) Multi-area adaptive LFC developed for a comprehensive AGC simulator. IEEE Trans Power Syst 8(2):541–547

    Article  Google Scholar 

  37. Simhadri KS, Mohanty B, Panda SK (2019) Comparative performance analysis of 2DOF state feedback controller for automatic generation control using whale optimization algorithm. Optim Control Appl Methods 40(1):24–42

    MathSciNet  Article  Google Scholar 

  38. Talaq J, Al-Basri F (1999) Adaptive fuzzy gain scheduling for load frequency control. IEEE Trans Power Syst 14(1):145–150

    Article  Google Scholar 

  39. Tan W (2009) Unified tuning of PID load frequency controller for power systems via IMC. IEEE Trans Power Syst 25(1):341–350

    Article  Google Scholar 

  40. Topno PN, Chanana S (2018) Load frequency control of a two-area multi-source power system using a tilt integral derivative controller. J Vib Control 24(1):110–125

    MathSciNet  Article  Google Scholar 

  41. Vrdoljak K, Perić N, Šepac D (2010) Optimal distribution of load-frequency control signal to hydro power plants. In: 2010 IEEE International Symposium on Industrial Electronics, 2010, pp 286–291

  42. Yousef H (2015) Adaptive fuzzy logic load frequency control of multi-area power system. Int J Electr Power Energy Syst 68:384–395

    Article  Google Scholar 

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Correspondence to Mohamed Barakat.

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Appendix A (Mohanty et al. 2014)

Appendix A (Mohanty et al. 2014)

\({\text{P}}_{{{\text{rt}}}} = 2000{\text{ MW}};\;{\text{P}}_{{\text{L}}} = 1840{\text{ MW}}; \;B_{1} = B_{2} = 0.4312 \;{\text{p}}.{\text{u}}.{\text{ MW}}/{\text{H}}_{{\text{Z}}}\); \(R_{1} = R_{2} = R_{3} = 2.4{\text{ H}}_{Z} /{\text{p}}.{\text{u}}.\); \(T_{sg1} = T_{sg2} = 0.08{\text{ s}}\);

\(T_{t1} = T_{t2} = 0.3 s\); \(K_{r1} = K_{r2} = 0.3; \) \(T_{r1} = T_{r2} = 10 s; \) \(K_{PS1} = K_{PS2} = 68.9566{\text{ H}}_{Z} /{\text{p}}.{\text{u}}\); \(T_{PS1} = T_{PS2} = 11.49 {\text{ s}}\);

\(T_{12} = 0.0433 {\text{p}}.{\text{u}}.;{ }a_{12} = - 1; \) \(T_{w1} = T_{w2} = 1{\text{ s}}; \) \(T_{RS1} = T_{RS2} = 5 {\text{ s}}\); \(T_{RH1} = T_{RH2} = 78.75 {\text{ s}}\); \(T_{GH1} = T_{GH2} = 0.2 {\text{ s}}\); \(X_{C} = 0.6 s\); \(Y_{C} = 1 {\text{s}};\) \(c_{g} = 1 s;\) \(b_{g} = 0.05 s;\) \(T_{F1} = T_{F2} = 0.23 {\text{s}}\); \(T_{CD1} = T_{CD2} = 0.2 {\text{s}}\); \(T_{CR1} = T_{CR2} = 0.01 {\text{s}}\);

\(K_{T} = 0.543478\); \(K_{H} = 0.326084\); \(K_{G} = 0.130438\); \(K_{DC} = 1\); \(T_{DC} = 0.2 s\);

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Barakat, M., Donkol, A., Hamed, H.F.A. et al. Controller parameters tuning of water cycle algorithm and its application to load frequency control of multi-area power systems using TD-TI cascade control. Evolving Systems (2021). https://doi.org/10.1007/s12530-020-09363-0

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Keywords

  • Interconnected power system
  • Load frequency control
  • Cascade control
  • Water cycle algorithm
  • And TID controller