Chaotic-based particle swarm optimization algorithm for optimal PID tuning in automatic voltage regulator systems
DOI:
https://doi.org/10.20998/2074-272X.2021.1.08Keywords:
proportional integral derivative (PID) tuning, chaotic particle swarm optimization (CPSO), robustness analysis, automatic voltage regulator (AVR), transient responseAbstract
Introduction. In an electrical power system, the output of the synchronous generators varies due to disturbances or sudden load changes. These variations in output severely affect power system stability and power quality. The synchronous generator is equipped with an automatic voltage regulator to maintain its terminal voltage at rated voltage. Several control techniques utilized to improve the response of the automatic voltage regulator system, however, proportional integral derivative (PID) controller is the most frequently used controller but its parameters require optimization. Novelty. In this paper, the chaotic sequence based on the logistic map is hybridized with particle swarm optimization to find the optimal parameters of the PID for the automatic voltage regulator system. The logistic map chaotic sequence-based initialization and global best selection enable the algorithm to escape from local minima stagnation and improve its convergence rate resulting in best optimal parameters. Purpose. The main objective of the proposed approach is to improve the transient response of the automatic voltage regulator system by minimizing the maximum overshoot, settling time, rise time, and peak time values of the terminal voltage, and eliminating the steady-state error. Methods. In the process of parameter tuning, the Chaotic particle swarm optimization technique was run several times through the proposed hybrid objective function, which accommodates the advantages of the two most commonly used objective functions with a minimum number of iterations, and an optimal PID gain value was found. The proposed algorithm is compared with current metaheuristic algorithms including conventional particle swarm optimization, improved kidney algorithm, and others. Results. For performance evaluation, the characteristics of the integral of time multiplied squared error and Zwe-Lee Gaing objective functions are combined. Furthermore, the time-domain analysis, frequency-domain analysis, and robustness analysis are carried out to show the better performance of the proposed algorithm. The result shows that automatic voltage regulator tuned with the chaotic particle swarm optimization based PID yield improvement in overshoot, settling time, and function value of 14.41 %, 37.91 %, 1.73 % over recently proposed IKA, and 43.55 %, 44.5 %, 16.67 % over conventional particle swarm optimization algorithms. The improvement in transient response further improves the automatic voltage regulator system stability for electrical power systems.
References
Tu G., Li Y., Xiang J. Analysis, Control and Optimal Placement of Static Synchronous Compensator with/without Battery Energy Storage. Energies, 2019, vol. 12, no. 24, p. 4715. doi: https://doi.org/10.3390/en12244715.
Tang Y., Cui M., Hua C., Li L., Yang Y. Optimum design of fractional order PIλDμ controller for AVR system using chaotic ant swarm. Expert Systems with Applications, 2012, vol. 39, no. 8, pp. 6887-6896. doi: https://doi.org/10.1016/j.eswa.2012.01.007.
Kumar M.S., Mahadevan K. Removal of Moisture Content in Paper Machine Using Soft Computing Techniques. Circuits and Systems, 2016, vol. 07, no. 09, pp. 2542-2550. doi: https://doi.org/10.4236/cs.2016.79220.
Bahgaat N.K., Moustafa Hassan M.A. Swarm Intelligence PID Controller Tuning for AVR System. Studies in Fuzziness and Soft Computing, 2016, pp. 791-804. doi: https://doi.org/10.1007/978-3-319-30340-6_33.
Åström K.J., Hägglund T. Revisiting the Ziegler–Nichols step response method for PID control. Journal of Process Control, 2004, vol. 14, no. 6, pp. 635-650. doi: https://doi.org/10.1016/j.jprocont.2004.01.002.
Wojsznis W.K., Blevins T.L. Evaluating PID adaptive techniques for industrial implementation. In Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002, p. 1151. doi: https://doi.org/10.1109/acc.2002.1023174.
Gaing Z.-L. A Particle Swarm Optimization Approach for Optimum Design of PID Controller in AVR System. IEEE Transactions on Energy Conversion, 2004, vol. 19, no. 2, pp. 384-391. doi: https://doi.org/10.1109/tec.2003.821821.
Ekinci S., Hekimoglu B. Improved Kidney-Inspired Algorithm Approach for Tuning of PID Controller in AVR System. IEEE Access, 2019, vol. 7, pp. 39935-39947. doi: https://doi.org/10.1109/access.2019.2906980.
Sahib M.A. A novel optimal PID plus second order derivative controller for AVR system. Engineering Science and Technology, an International Journal, 2015, vol. 18, no. 2, pp. 194-206. doi: https://doi.org/10.1016/j.jestch.2014.11.006.
Mohanty P.K., Sahu B.K., Panda S. Tuning and Assessment of Proportional–Integral–Derivative Controller for an Automatic Voltage Regulator System Employing Local Unimodal Sampling Algorithm. Electric Power Components and Systems, 2014, vol. 42, no. 9, pp. 959-969. doi: https://doi.org/10.1080/15325008.2014.903546.
Gozde H., Taplamacioglu M.C. Comparative performance analysis of artificial bee colony algorithm for automatic voltage regulator (AVR) system. Journal of the Franklin Institute, 2011, vol. 348, no. 8, pp. 1927-1946. doi: https://doi.org/10.1016/j.jfranklin.2011.05.012.
Ekinci S., Hekimoglu B., Kaya S. Tuning of PID Controller for AVR System Using Salp Swarm Algorithm. 2018 International Conference on Artificial Intelligence and Data Processing (IDAP), Sep. 2018. doi: https://doi.org/10.1109/idap.2018.8620809.
Demiroren A., Hekimoglu B., Ekinci S., Kaya S. Artificial Electric Field Algorithm for Determining Controller Parameters in AVR system. 2019 International Artificial Intelligence and Data Processing Symposium (IDAP), Sep. 2019. doi: https://doi.org/10.1109/idap.2019.8875972.
Ekinci S., Hekimoglu B., Eker E. Optimum Design of PID Controller in AVR System Using Harris Hawks Optimization. 2019 3rd International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT), Oct. 2019. doi: https://doi.org/10.1109/ismsit.2019.8932941.
Hekimoğlu B. Sine-cosine algorithm-based optimization for automatic voltage regulator system. Transactions of the Institute of Measurement and Control, 2018, vol. 41, no. 6, pp. 1761-1771. doi: https://doi.org/10.1177/0142331218811453.
Mosaad A.M., Attia M.A., Abdelaziz A.Y. Whale optimization algorithm to tune PID and PIDA controllers on AVR system. Ain Shams Engineering Journal, 2019, vol. 10, no. 4, pp. 755-767. doi: https://doi.org/10.1016/j.asej.2019.07.004.
Tavazoei M.S. Notes on integral performance indices in fractional-order control systems. Journal of Process Control, 2010, vol. 20, no. 3, pp. 285-291. doi: https://doi.org/10.1016/j.jprocont.2009.09.005.
Gozde H., Taplamacioglu M.C. Comparative performance analysis of artificial bee colony algorithm for automatic voltage regulator (AVR) system. Journal of the Franklin Institute, 2011, vol. 348, no. 8, pp. 1927-1946. doi: https://doi.org/10.1016/j.jfranklin.2011.05.012.
Aydiner E. Chaotic universe model. Scientific Reports, 2018, vol. 8, no. 1, p. 721. doi: https://doi.org/10.1038/s41598-017-18681-4.
Dos Santos Coelho L. Tuning of PID controller for an automatic regulator voltage system using chaotic optimization approach. Chaos, Solitons & Fractals, 2009, vol. 39, no. 4, pp. 1504-1514. doi: https://doi.org/10.1016/j.chaos.2007.06.018.
Abdullah A.H., Enayatifa R, Lee M. A Hybrid Genetic Algorithm and chaotic function model for image encryption. Journal of Electronics and Communication, 2012, vol. 66, pp. 806-816. doi: https://doi.org/10.1016/j.aeue.2012.01.015.
Çelik E., Rafet D. Performance enhancement of automatic voltage regulator by modified cost function and symbiotic organisms search algorithm. Engineering Science and Technology, an International Journal, 2018, vol. 21 no. 5, pp. 1104-1111. doi: https://doi.org/10.1016/j.jestch.2018.08.006.
George R.G., Hasanien H.M., Badr M.A., Elgendy M.A. A Comparative Study among Different Algorithms Investigating Optimum Design of PID Controller in Automatic Voltage Regulator. 2018 53rd International Universities Power Engineering Conference (UPEC), Glasgow, 2018, pp. 1-6. doi: https://doi.org/10.1109/UPEC.2018.8541870.
Çelik E. Incorporation of stochastic fractal search algorithm into efficient design of PID controller for an automatic voltage regulator system. Neural Computing and Applications, 2018, vol. 30, no. 6, pp. 1991-2002. doi: https://doi.org/10.1007/s00521-017-3335-7.
Odili J.B., Mohmad Kahar M.N., Noraziah A. Parameters-tuning of PID controller for automatic voltage regulators using the African buffalo optimization. PLoS One, 2017, vol. 12, no. 4, p. e0175901. doi: https://doi.org/10.1371/journal.pone.0175901.
Bingul Z., Karahan O. A novel performance criterion approach to optimum design of PID controller using cuckoo search algorithm for AVR system. Journal of the Franklin Institute, 2018, vol. 355, no. 13, pp. 5534-5559. doi: https://doi.org/10.1016/j.jfranklin.2018.05.056.
Kansit S., Assawinchaichote W. Optimization of PID controller based on PSOGSA for an automatic voltage regulator system. Procedia Computer Science, 2016, vol. 86, pp. 87-90. doi: https://doi.org/10.1016/j.procs.2016.05.022.
Chatterjee S., Mukherjee V. PID controller for automatic voltage regulator using teaching–learning based optimization technique. International Journal of Electrical Power & Energy Systems, 2016, vol. 77, pp. 418-429. doi: https://doi.org/10.1016/j.ijepes.2015.11.010.
Guvenc U., Yigit T., Isik A.H, , Akkaya I. Performance analysis of biogeography-based optimization for automatic voltage regulator system. Turkish Journal of Electrical Engineering and Computer Sciences, 2016, vol. 24, no. 3, pp. 1150-1162. doi: https://doi.org/10.3906/elk-1311-111.
Tang Y., Cui M., Hua C., Li L., Yang Y. Optimum design of fractional order PIλDμ controller for AVR system using chaotic ant swarm. Expert Systems with Applications, 2012, vol. 39, no. 8, pp. 6887-6896. doi: https://doi.org/10.1016/j.eswa.2012.01.007.
Gozde H., Taplamacıoğlu M.C. Comparative performance analysis of artificial bee colony algorithm for automatic voltage regulator (AVR) system. Journal of the Franklin Institute, 2011, vol. 348, no. 8, pp. 1927-1946. doi: https://doi.org/10.1016/j.jfranklin.2011.05.012.
Taherkhani M., Safabakhsh R. A novel stability-based adaptive inertia weight for particle swarm optimization. Applied Soft Computing, 2016, vol. 38, pp. 281-295. doi: https://doi.org/10.1016/j.asoc.2015.10.004.
Cao L., Xu L., Goodman E.D. A guiding evolutionary algorithm with greedy strategy for global optimization problems. Computational Intelligence and Neuroscience, 2016. doi: https://doi.org/10.1155/2016/2565809.
Liu Z., Murakami T., Kawamura S., Yoshida H. Parallel Implementation of Chaos Neural Networks for an Embedded GPU. 2019 IEEE 10th International Conference on Awareness Science and Technology (iCAST), Morioka, Japan, 2019, pp. 1-6. doi: https://doi.org/10.1109/ICAwST.2019.8923383.
Huang L., Ding S., Yu S., Wang J., Lu K. Chaos-enhanced Cuckoo search optimization algorithms for global optimization. Applied Mathematical Modelling, 2016, vol. 40, no. 5, pp. 3860-3875. doi: https://doi.org/10.1016/j.apm.2015.10.052.
Wang X., Sun H. A chaotic image encryption algorithm based on improved Joseph traversal and cyclic shift function. Optics & Laser Technology, 2020, vol. 122, p. 105854. doi: https://doi.org/10.1016/j.optlastec.2019.105854.
Tubishat M., Idris N., Shuib L., Abushariah M.A.M., Mirjalili S. Improved Salp Swarm Algorithm based on opposition based learning and novel local search algorithm for feature selection. Expert Systems with Applications, 2020, vol. 145, pp. 113122. doi: https://doi.org/10.1016/j.eswa.2019.113122.
Petrovic M., Vuković N., Mitić M., Miljković Z. Integration of process planning and scheduling using chaotic particle swarm optimization algorithm. Expert Systems with Applications, 2016, vol. 64, pp. 569-588. doi: https://doi.org/10.1016/j.eswa.2016.08.019.
Shadravan S., Naji H.R., Bardsiri V.K. The Sailfish Optimizer: A novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems. Engineering Applications of Artificial Intelligence, 2019, vol. 80, pp. 20-34. doi: https://doi.org/10.1016/j.engappai.2019.01.001.
Luo Y., Yu J., Lai W., Liu L. A novel chaotic image encryption algorithm based on improved baker map and logistic map. Multimedia Tools and Applications, 2019, vol. 78, no. 15, pp. 22023-22043. doi: https://doi.org/10.1007/s11042-019-7453-3.
Sato Y., Son D.T., Lamb J.S.W., Rasmussen M. Dynamical characterization of stochastic bifurcations in a random logistic map. ArXiv, 2018, pp. 1811-03994. Available at: https://arxiv.org/pdf/1811.03994.pdf (accessed on 11 May 2020).
Liu B., Wang L., Jin Y.-H., Tang F., Huang D.-X. Improved particle swarm optimization combined with chaos. Chaos, Solitons & Fractals. 2005, vol. 25, no. 5, pp. 1261-1271. doi: https://doi.org/10.1016/j.chaos.2004.11.095.
Kumar A., Kumar V. A novel interval type-2 fractional order fuzzy PID controller: design, performance evaluation, and its optimal time domain tuning. ISA Transactions, 2017, vol. 68, pp. 251-275. doi: https://doi.org/10.1016/j.isatra.2017.03.022.
Zheng W., Luo Y., Wang X., Pi Y., Chen Y. Fractional order PIλDμ controller design for satisfying time and frequency domain specifications simultaneously. ISA Transactions, 2017, vol. 68, pp. 212-222. doi: https://doi.org/10.1016/j.isatra.2017.02.016.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 N. Anwar , A. Hanif , M.U. Ali , A. Zafar
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.