Abstract
The open communication network in the secondary loop of the load frequency control (LFC) scheme introduces the time delay while transmitting the control signals. The communication time delays (CTDs) affect the load frequency control (LFC) system’s performance, leading to system instability. This paper proposes a robust method for analysis using a graphical technique for proportional integral derivative (PID)-based LFC systems considering CTD for single-area and multi-area. Moreover, the LFC system with CTD is expressed by its transfer function. Then, stability regions are plotted using the stability boundary locus method to compute the set of stabilized PID controller parameters for the LFC systems having delays. The notable features of the proposed approach are determined using frequency response, maximum sensitivity, and \({\mathcal {H}}_{\infty }\) criteria in the presence of CTD. The communication time delay is assumed to be additive uncertainty weight. Finally, stability regions are depicted in the controller parameter spaces. Finally, case studies are carried out for LFC systems considering CTD of a single-area and three-area isolated power systems. Simulation results as stability regions have demonstrated as \((k_p,~k_i),~(k_p,~k_d), \text {and}\, (k_d,~k_i)\) planes for LFC system with the delay of a single-area and three-area isolated power system. These results illustrate the effectiveness of the proposed method for LFC system with CTD and provide robust performance.
Similar content being viewed by others
Data availability
All relevant data that support the outcomes of the manuscript have been provided.
References
Ranjan M, Shankar R (2022) A literature survey on load frequency control considering renewable energy integration in power system: Recent trends and future prospects. J Energy Storage 45:103717. https://doi.org/10.1016/j.est.2021.103717
Phuong DT, Pham et al (2022) Exponential stabilization via tracking convergent rate in load frequency control of multi-area power systems with diverse communication delays. Int J Dyn Control 10(1):107–121. https://doi.org/10.1007/s40435-021-00815-2
Luo H, Hiskens IA, Hu Z (2020) Stability analysis of load frequency control systems with sampling and transmission delay. IEEE Trans Power Syst 35(5):3603–3615. https://doi.org/10.1109/TPWRS.2020.2980883
Luo J (2023) Designing optimized PID controller using improved bacterial foraging optimization algorithm for robust frequency control of islanded microgrid. Int J Dyn Control 11(3):1432–1443. https://doi.org/10.1007/s40435-022-01045-w
Sahu RK, Panda S et al (2014) A novel hybrid DEPS optimized fuzzy PI/PID controller for load frequency control of multi-area interconnected power systems. J Process Control 24(10):1596–1608. https://doi.org/10.1016/j.jprocont.2014.08.006
Tan W (2009) Unified tuning of PID load frequency controller for power systems via IMC. IEEE Trans Power Syst 25(1):341–350. https://doi.org/10.1016/j.isatra.2012.02.004
Dong L, Zhang Y et al (2012) A robust decentralized load frequency controller for interconnected power systems. ISA Trans 51(3):410–419. https://doi.org/10.1016/j.isatra.2012.02.004
Khodabakhshian A, Edrisi M (2008) A new robust PID load frequency controller. Control Eng Pract 16(9):1069–1080. https://doi.org/10.1016/j.conengprac.2007.12.003
Li Y, Ang KH et al (2006) PID control system analysis and design. IEEE Control Syst Mag 26(1):32–41. https://doi.org/10.1109/MCS.2006.1580152
Pradhan JK, Ghosh A (2015) Multi-input and multi-output proportional-integral-derivative controller design via linear quadratic regulator?linear matrix inequality approach. IET Control Theory Appl 9(14):2140–2145. https://doi.org/10.1049/iet-cta.2015.0012
Anwar MN, Pan S (2015) A new PID load frequency controller design method in frequency domain through direct synthesis approach. Int J Electr Power Energy Syst 67:560–569. https://doi.org/10.1016/j.ijepes.2014.12.024
Saxena S, Hote YV (2016) Decentralized PID load frequency control for perturbed multi-area power systems. Int J Electr Power Energy Syst 81:405–415. https://doi.org/10.1016/j.ijepes.2016.02.041
Singh VP, Kishor N et al (2017) Improved load frequency control of power system using LMI based PID approach. J Frank Inst 354(15):6805–6830. https://doi.org/10.1016/j.jfranklin.2017.08.031
Jiang L, Yao W et al (2011) Delay-dependent stability for load frequency control with constant and time-varying delays. IEEE Trans Power Syst 27(2):932–941. https://doi.org/10.1109/TPWRS.2011.2172821
Khalil A, Peng AS (2018) Delay margin computation for load frequency control system with plug-in electric vehicles. Int J Power Energy Syst 38(3):1–17. https://doi.org/10.2316/journal.203.2018.3.203-0060
Bevrani H, Hiyama T (2008) Robust decentralized PI based LFC design for time delay power systems. Energy Convers Manag 49(2):193–204. https://doi.org/10.1016/j.enconman.2007.06.021
Thangaiah JM, Parthasarathy R (2017) Delay? Dependent stability analysis of power system considering communication delays. Int Trans Electr Energy Syst 27(3):e2260. https://doi.org/10.1002/etep.2260
Sonmez S, Ayasun S (2018) Computation of PI controllers ensuring desired gain and phase margins for two-area load frequency control system with communication time delays. Electr Power Compon Syst 46(8):938–947. https://doi.org/10.1080/15325008.2018.1509914
Yu X, Tomsovic K (2004) Application of linear matrix inequalities for load frequency control with communication delays. IEEE Trans Power Syst 19(3):1508–1515. https://doi.org/10.1109/TPWRS.2004.831670
Dey R, Ghosh S, Ray G, Rakshit A (2012) \({\cal{H} }_{\infty }\)-load frequency control of interconnected power systems with communication delays. Int J Electr Power Energy Syst 42(1):672–684. https://doi.org/10.1016/j.ijepes.2012.03.035
Prasad S, Purwar S et al (2015) On design of a non-linear sliding mode load frequency control of interconnected power system with communication time delay. In: 2015 IEEE conference on control applications (CCA) IEEE, pp 1546–1551. https://doi.org/10.1109/CCA.2015.7320830
Zhao X, Ma Z et al (2022) Robust LFC of power systems with wind power under packet losses and communication delays. IEEE J Emerg Sel Top Circuits Syst 12(1):135–148. https://doi.org/10.1109/JETCAS.2022.3141108
Mary TJ, Rangarajan P (2016) Design of robust controller for LFC of interconnected power system considering communication delays. Circuits Syst 7(6):794–804. https://doi.org/10.4236/cs.2016.76068
Tang X, Fu X, Sun X (2019) Periodic motion for an oblique impact system with single degree of freedom. J Vib Test Syst Dyn 3(1):71–89. https://doi.org/10.5890/JVTSD.2019.03.006
Emami T (2009) A bridge from stability to robust performance design of PID controllers in the frequency domain. Dissertation, Wichita State University
Tan N, Kaya I et al (2006) Computation of stabilizing PI and PID controllers using the stability boundary locus. Energy Convers Manag 47(18–19):3045–3058. https://doi.org/10.1016/j.enconman.2006.03.022
Veeramachaneni SR, Watkins JM (2013) Weighted sensitivity design of PID controllers for time-delay systems with a Smith predictor. In: 2013 IEEE international conference on control applications (CCA), pp 802–807. IEEE. 978-1-4799-1559-0/13/31
Gogoi M, Emami T, Watkins JM (2010) Robust stability design of pi controllers for a non-reheat steam generator unit. In: Dynamic systems and control conference, vol 44182, pp 507–513. https://doi.org/10.1115/DSCC2010-4107
Sonmez S, Ayasun S (2015) Stability region in the parameter space of PI controller for a single-area load frequency control system with time delay. IEEE Trans Power Syst 31(1):829–830. https://doi.org/10.1109/TPWRS.2015.2412678
Naveed A, Sonmez S et al (2019) Stability regions in the parameter space of PI Controller for LFC System with EVs aggregator and incommensurate time delays. In: 2019 \(1^{st}\) global power, energy and communication conference (GPECOM), pp 461–466. https://doi.org/10.1109/GPECOM.2019.8778591
Ozyetkin MM (2018) A simple tuning method of fractional order PI\(\lambda \)-PD\(\mu \) controllers for time delay systems. ISA Trans 74:77–87. https://doi.org/10.1016/j.isatra.2018.01.021
Sharma J, Hote YV, Prasad R (2019) PID controller design for interval load frequency control system with communication time delay. Control Eng Pract 89:154–168. https://doi.org/10.1016/j.conengprac.2019.05.016
Sonmez S (2019) Computation of stability regions for load frequency control systems including incommensurate time delays. Turk J Electr Eng Comput Sci 27(6):4596–4607. https://doi.org/10.3906/elk-1904-6
Saxena S, Hote YV (2018) PI controller based load frequency control approach for single-area power system having communication delay. IFAC-PapersOnLine 51(4):622–626. https://doi.org/10.1016/j.ifacol.2018.06.165
Jain S, Hote YV (2020) Design of generalized active disturbance rejection control for delayed systems: an application to load frequency control. Int J Control 94:3146–3160. https://doi.org/10.1016/j.ijepes.2021.107166
Kumar M, Hote YV (2021) Maximum sensitivity-constrained coefficient diagram method-based PIDA controller design: application for load frequency control of an isolated microgrid. Electr Eng 103(5):2415–2429. https://doi.org/10.1007/s40998-019-00246-y
Funding
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
Author information
Authors and Affiliations
Contributions
Equal contributions were made by all authors to this work. This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors
Corresponding author
Ethics declarations
Conflict of interest
The corresponding author declares that there is no Conflict of interest/ Conflict of interest.
Ethics approval
Authors confirm that the work done in the manuscript has not been published partly or fully, and it is not under consideration for possible publication in any other journal.
Consent for publication
Authors give their consent for the publication of the manuscript provided the later gets accepted.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sharma, P., Neeli, S. Computation of stability boundary locus of robust PID controller for time delayed LFC system. Int. J. Dynam. Control 12, 1455–1465 (2024). https://doi.org/10.1007/s40435-023-01276-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40435-023-01276-5