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Pathfinder algorithm optimized fractional order tilt-integral-derivative (FOTID) controller for automatic generation control of multi-source power system

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Abstract

This paper introduces a fractional order tilt-integral-derivative (FOTID) controller which is structurally analogous to fractional order proportional-integral-derivative controller in a power system for solving automatic generation control (AGC) problem. It is optimized by a recent metaheuristic optimizer called pathfinder algorithm (PFA). An interconnected two-area power system model comprising of multi-sources like thermal, hydro and gas generating units including physical constraints namely, governor dead band (GDB) and generation rate constraint (GRC) are taken into consideration for the study. The efficiency of the proposed controller for AGC is shown by comparing it with PFA optimized tilt-integral-derivative (TID) and proportional-integral-derivative (PID) controllers with integral of time multiplied absolute error (ITAE) taken as the objective function. Simulation study supports the claim that the proposed controller provides better dynamic responses as compared to the others. Sensitivity and robust analyses are done to demonstrate the effectiveness of the proposed PFA optimized FOTID controller to a wide variation in system parameters, at different step load and random load disturbances.

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Abbreviations

\(T_{GT}\) :

Thermal unit time constant (speed governor) in s

\(T_{T}\) :

Time constant (steam turbine) in s

\(K_{R}\) :

Constant (reheat steam turbine)

\(T_{R}\) :

Time constant (reheat steam turbine) in s

\(T_{GH}\) :

Hydro turbine time constant (speed governor main servo) in s

\(T_{RS}\) :

Hydro turbine reset time (speed governor) in s

\(T_{RH}\) :

Hydro turbine transient droop (speed governor) in s

\(T_{W}\) :

Nominal starting time (penstock water) in s

\(c_{G}\) :

Gas turbine (valve positioner)

\(b_{G}\) :

Gas turbine constant (valve positioner)

\(X_{G}\) :

Gas turbine Lead time constant (speed governor) in s

\(Y_{G}\) :

Gas turbine Lag time constant (speed governor) in s

\(T_{CR}\) :

Gas turbine Time delay (combustion reaction) in s

\(T_{F}\) :

Time constant (fuel) of gas turbine in s

\(T_{RS}\) :

Gas turbine time constant (compressor discharge volume) in s

\(a_{T}\) :

Participation factor (thermal unit)

\(a_{H}\) :

Participation factor (hydro unit)

\(a_{G}\) :

Participation factor (gas unit)

\(\varDelta P_{D}\) :

Load demand change in p.u. MW

\(K_{PS}\) :

Gain (power system) in Hz/p.u. MW

\(T_{P}\) :

Time constant (power system) in s

\(R_{T}\) :

Regulating parameter of speed governor of thermal unit in Hz/p.u. MW

\(R_{H}\) :

Regulating parameter of speed governor of hydro unit in Hz/p.u. MW

\(R_{G}\) :

Regulating parameter of speed governor of gas unit in Hz/p.u. MW

B :

Frequency bias parameter in p.u. MW/Hz

ACE :

Area control error

\(\varDelta F\) :

Frequency variation in Hz

\(T_{12}\) :

Synchronizing torque coefficient between area-1 and area-2 in p.u. MW/rad

\(\varDelta P_{12}\) :

Power variation in tie-line between area-1 and area-2 in p.u. MW

D :

Number of variables to be optimized

NP :

Population size

\(X_i\) :

Position vector of \(i\)th search agent

\(X_p\) :

Position vector of Pathfinder

k :

Iteration index of the optimization process

itermax :

Maximum number of iterations

\(B\_ITAE\) :

Best fitness value obtained among followers

\(X_{BEST}\) :

Position vector of best follower

References

  • Abdel-Magid Y, Dawoud M (1996) Optimal AGC tuning with genetic algorithms. Electric Power Syst Res 38(3):231–238

    Article  Google Scholar 

  • Abdel-Magid YL, Abido MA (2003) AGC tuning of interconnected reheat thermal systems with particle swarm optimization. In: Proceedings of the 10th IEEE international conference on electronics, circuits and systems, 2003, vol 1. IEEE, pp 376–379 (2003)

  • Al-Hamouz Z, Abdel-Magid Y (1993) Variable structure load frequency controllers for multiarea power systems. Int J Electr Power Energy Syst 15(5):293–300

    Article  Google Scholar 

  • Ali E, Abd-Elazim S (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 

  • Alomoush MI (2010) Load frequency control and automatic generation control using fractional-order controllers. Electr Eng 91(7):357–368

    Article  Google Scholar 

  • Aparanta A, Sahu RK, Pradhan PC (2019) DE optimized 2-DOF tilt integral derivative controller with filter for frequency regulation of interconnected power system. In: International conference on application of robotics in industry using advanced mechanisms. Springer, pp 130–139

  • Arya Y (2019) Impact of hydrogen aqua electrolyzer-fuel cell units on automatic generation control of power systems with a new optimal fuzzy TIDF-II controller. Renew Energy 139:468–482

    Article  Google Scholar 

  • Dash P, Saikia LC, Sinha N (2016) Flower pollination algorithm optimized PI-PD cascade controller in automatic generation control of a multi-area power system. Int J Electric Power Energy Syst 82:19–28

    Article  Google Scholar 

  • Debbarma S, Saikia LC, Sinha N (2013) AGC of a multi-area thermal system under deregulated environment using a non-integer controller. Electric Power Syst Res 95:175–183

    Article  Google Scholar 

  • Delassi A, Arif S, Mokrani L (2016) A novel tilt integral derivative plus second derivative order for load frequency control problem in power system. In: 8th International conference on modelling, identification and control (ICMIC). IEEE, pp 359–363

  • 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 Gen Transm Distrib 10(12):2915–2923

    Article  Google Scholar 

  • Gozde H, Taplamacioglu MC (2011) Automatic generation control application with craziness based particle swarm optimization in a thermal power system. Int J Electric Power Energy Syst 33(1):8–16

    Article  Google Scholar 

  • Gozde H, Taplamacioglu MC, Kocaarslan I (2012) Comparative performance analysis of artificial bee colony algorithm in automatic generation control for interconnected reheat thermal power system. Int J Electric Power Energy Syst 42(1):167–178

    Article  Google Scholar 

  • Hasan N, Kumar P et al (2012) Sub-optimal automatic generation control of interconnected power system using constrained feedback control strategy. Int J Electric Power Energy Syst 43(1):295–303

    Article  Google Scholar 

  • Hasanien HM (2017) Whale optimisation algorithm for automatic generation control of interconnected modern power systems including renewable energy sources. IET Gen Transm Distrib 12(3):607–614

    Article  Google Scholar 

  • Hossain M, Islam M, Takahashi T, Rabbani M (2008) Fuzzy-based load frequency controller of a single area power system considering governor nonlinearity. Int Energy J 9(2):1

    Google Scholar 

  • Ismayil C, Kumar RS, Sindhu TK (2015) Optimal fractional order PID controller for automatic generation control of two-area power systems. Int Trans Electric Energy Syst 25(12):3329–3348

    Article  Google Scholar 

  • Kirchmayer LK, Kirchmayer LK (1959) Economic control of interconnected systems. Wiley, New York

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

  • Lurie BJ (1994) Three-parameter tunable tilt-integral-derivative (TID) controller (1994). US Patent 5,371,670

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

    Article  Google Scholar 

  • Nanda J, Mishra S, Saikia LC (2009) Maiden application of bacterial foraging-based optimization technique in multiarea automatic generation control. IEEE Trans Power Syst 24(2):602–609

    Article  Google Scholar 

  • Nosratabadi SM, Bornapour M, Gharaei MA (2019) Grasshopper optimization algorithm for optimal load frequency control considering predictive functional modified PID controller in restructured multi-resource multi-area power system with redox flow battery units. Control Eng Pract 89:204–227

    Article  Google Scholar 

  • Padhan S, Sahu RK, Panda S (2014) Application of firefly algorithm for load frequency control of multi-area interconnected power system. Electric Power Compon Syst 42(13):1419–1430

    Article  Google Scholar 

  • Pan I, Das S (2015) Fractional-order load-frequency control of interconnected power systems using chaotic multi-objective optimization. Appl Soft Comput 29:328–344

    Article  Google Scholar 

  • Parmar KS, Majhi S, Kothari D (2012) Load frequency control of a realistic power system with multi-source power generation. Int J Electr Power Energy Syst 42(1):426–433

    Article  Google Scholar 

  • Rahman A, Saikia LC, Sinha N (2015) Load frequency control of a hydro-thermal system under deregulated environment using biogeography-based optimised three-degree-of-freedom integral-derivative controller. IET Gen Transm Distrib 9(15):2284–2293

    Article  Google Scholar 

  • Rahman A, Saikia LC, Sinha N (2016) Automatic generation control of an unequal four-area thermal system using biogeography-based optimised 3DOF-PID controller. IET Gen Transm Distrib 10(16):4118–4129

    Article  Google Scholar 

  • Rehiara AB, Yorino N, Sasaki Y, Zoka Y (2019) A novel adaptive LFC based on MPC method. IEEJ Trans Electr Electron Eng 14:1145-1152

  • Rosyiana Fitri I, Kim JS, Song H (2017) High-gain disturbance observer-based robust load frequency control of power systems with multiple areas. Energies 10(5):595

    Article  Google Scholar 

  • Sahu BK, Pati TK, Nayak JR, Panda S, Kar SK (2016) A novel hybrid LUS-TLBO optimized fuzzy-PID controller for load frequency control of multi-source power system. Int J Electr Power Energy Syst 74:58–69

    Article  Google Scholar 

  • Sahu RK, Panda S, Biswal A, Sekhar GC (2016) 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 

  • Sahu RK, Panda S, Rout UK, Sahoo DK (2016) 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 

  • Sahu RK, Panda S, Sekhar GC (2015) 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

    Article  Google Scholar 

  • Sahu RK, Sekhar GC, Priyadarshani S (2019) Differential evolution algorithm tuned tilt integral derivative controller with filter controller for automatic generation control. Evol Intell 1:1–16

    Google Scholar 

  • Saikia LC, Mishra S, Sinha N, Nanda J (2011) Automatic generation control of a multi area hydrothermal system using reinforced learning neural network controller. Int J Electr Power Energy Syst 33(4):1101–1108

    Article  Google Scholar 

  • Saikia LC, Nanda J, Mishra S (2011) Performance comparison of several classical controllers in AGC for multi-area interconnected thermal system. Int J Electr Power Energy Syst 33(3):394–401

    Article  Google Scholar 

  • Saikia LC, Sinha N (2016) Automatic generation control of a multi-area system using ant lion optimizer algorithm based PID plus second order derivative controller. Int J Electr Power Energy Syst 80:52–63

    Article  Google Scholar 

  • Saikia LC, Sinha N, Nanda J (2013) Maiden application of bacterial foraging based fuzzy IDD controller in AGC of a multi-area hydrothermal system. Int J Electr Power Energy Syst 45(1):98–106

    Article  Google Scholar 

  • Sharma Y, Saikia LC (2015) Automatic generation control of a multi-area ST-thermal power system using grey wolf optimizer algorithm based classical controllers. Int J Electr Power Energy Syst 73:853–862

    Article  Google Scholar 

  • Tripathy S, Hope G, Malik O (1982) Optimisation of load-frequency control parameters for power systems with reheat steam turbines and governor deadband nonlinearity. In: IEE Proceedings C (Generation, Transmission and Distribution), vol 129. IET, pp 10–16

  • Yapici H, Cetinkaya N (2019) A new meta-heuristic optimizer: pathfinder algorithm. Appl Soft Comput 78:545–568

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Electrical Engineering, National Institute of Technology, Rourkela, Odisha, 769008, India

    Sonali Priyadarshani, K. R. Subhashini & J. K. Satapathy

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  1. Sonali Priyadarshani
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  2. K. R. Subhashini
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  3. J. K. Satapathy
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Correspondence to Sonali Priyadarshani.

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Appendix

Appendix

The nominative parameters of power system model taken for the study are as follows: \(P_R\)= 2000 MW (rating); \(P_L= 1840\) MW (nominal loading); \(F= 60\) Hz; \(B_1= B_2=B= 0.4312\) p.u. MW/Hz; \(R_{T1}= R_{T2}= R_T=R_{H1}= R_{H2}= R_H=R_{G1}= R_{G2}=R_G= 2.4\)  Hz/p.u. MW; \(T_{GT1}= T_{GT2}= T_{GT}=0.08\) s; \(T_{T1}= T_{T2}=T_{T}= 0.3\) s; \(K_{R1}= K_{R2}=K_{R}= 0.3; T_{R1}= T_{R2}= T_{R}=10 s; K_{PS1}= K_{PS2}= K_{PS}= 68.9566\) Hz/p.u. MW; \(T_{P1}= T_{P2}= T_{P}=11.49\) s; \(T_{12}= 0.0433\) p.u. MW/rad; \(T_{W1}= T_{W2}= T_{W}=1\) s; \(T_{RS1}= T_{RS2}= T_{RS}=5\) s; \(T_{RH1}= T_{RH2}= T_{RH}=28.75\) s; \(T_{GH1}= T_{GH2}=T_{GH}= 0.2\) s; \(X_{G1}= X_{G2}= X_{G}=0.6\) s; \(Y_{G1}= Y_{G2}= Y_{G}=1\) s; \(c_{G1}= c_{G2}= c_{G}= 1\); \(b_{G1}= b_{G2}=b_{G}= 0.05\) s; \(T_{F1}= T_{F2}= T_{F}=0.23\) s; \(T_{CR1}= T_{CR2}=T_{CR}= 0.01\) s; \(T_{CD1}= T_{CD2}= T_{CD}=0.2\) s; \(a_{T1}= a_{T2}=a_{T}= 0.543478; a_{H1}= a_{H2}=a_{H}= 0.326084; a_{G1}= a_{G2}=a_{G}= 0.130438; a_{12}= -1\)

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Priyadarshani, S., Subhashini, K.R. & Satapathy, J.K. Pathfinder algorithm optimized fractional order tilt-integral-derivative (FOTID) controller for automatic generation control of multi-source power system. Microsyst Technol 27, 23–35 (2021). https://doi.org/10.1007/s00542-020-04897-4

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