{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T07:08:36Z","timestamp":1781766516720,"version":"3.54.5"},"reference-count":67,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T00:00:00Z","timestamp":1761091200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfeicoamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["001"],"award-info":[{"award-number":["001"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2015\/24245-8"],"award-info":[{"award-number":["2015\/24245-8"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Poorly damped low-frequency oscillation modes can destabilize power systems in the event of contingencies. Advances in the widespread use of phasor measurement units (PMUs) in power systems have led to the development of wide-area damping controllers (WADCs) capable of ensuring good damping ratios for these oscillation modes. However, cyberattacks or communication failures affect PMU data and can cause WADC malfunctions. Poor WADC operation can even destabilize the power system. Therefore, this paper proposes the design of a WADC robust to communication failures through a multi-objective optimization model requiring high damping ratios for the closed-loop system and the existence of a symmetric and positive defined matrix to guarantee the stability of the system. Bio-inspired algorithms can solve this proposed multi-objective optimization model, and the stellar oscillation optimizer proved to be a bio-inspired algorithm with an excellent ability to reach an optimal solution. Case studies show that defining the limiting values of the WADC time constants and the existence of this symmetric, positive-definite matrix are beneficial for good system dynamic performance.<\/jats:p>","DOI":"10.3390\/sym17111781","type":"journal-article","created":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T08:41:08Z","timestamp":1761122468000},"page":"1781","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Multi-Objective Approach for Wide-Area Damping Control Design"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5285-103X","authenticated-orcid":false,"given":"Murilo E. C.","family":"Bento","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Federal University of Rio de Janeiro, Rio de Janeiro 21941-909, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18064","DOI":"10.1109\/ACCESS.2020.2968586","article-title":"Power System Resilience: Current Practices, Challenges, and Future Directions","volume":"8","author":"Bhusal","year":"2020","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Xiong, L., Huang, S., Li, P., Wang, Z., Khan, M.W., and Niu, T. (2025). Hidden Markov Jump System Based Robust Control of Inverter-Fed Power Systems with Asynchronous Sliding Mode Observer. IEEE Trans. Ind. Electron., 1\u201313.","DOI":"10.1109\/TIE.2025.3579102"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Huang, S., Wang, L., Xiong, L., Zhou, Y., Gao, F., Huang, W., Li, Y., Guo, H., and Wang, F. (2025). Hierarchical Robustness Strategy Combining Model-Free Prediction and Fixed-Time Control for Islanded AC Microgrids. IEEE Trans. Smart Grid, 1.","DOI":"10.1109\/TSG.2025.3591597"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"110843","DOI":"10.1016\/j.ijepes.2025.110843","article-title":"The LCC type DC grids forming method and fault ride-through strategy based on fault current limiters","volume":"170","author":"Liu","year":"2025","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1109\/TPWRS.2024.3402233","article-title":"Distributed Predefined-Time Control for Power System with Time Delay and Input Saturation","volume":"40","author":"Huang","year":"2025","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Song, R., Huang, S., Xiong, L., Zhou, Y., Li, T., Tan, P., and Sun, Z. (2024). Takagi\u2013Sugeno Fuzzy Parallel Distributed Compensation Control for Low-Frequency Oscillation Suppression in Wind Energy-Penetrated Power Systems. Electronics, 13.","DOI":"10.3390\/electronics13193795"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ban, C., Huang, S., Xiong, L., Zhou, Y., Wang, Q., Song, R., Wang, L., and Li, F. (2024). Distributed Model Predictive Control Based on Bus Voltage Derivative and SoC Dynamic Model for Shipboard DC Microgrids. Electronics, 13.","DOI":"10.3390\/electronics13142880"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Rogers, G., Elliott, R.T., Trudnowski, D.J., Wilches-Bernal, F., Osipov, D., and Chow, J.H. (2025). Power System Oscillations: An Introduction to Oscillation Analysis and Control, Springer Nature.","DOI":"10.1007\/978-3-031-80581-3"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1016\/j.ijepes.2012.04.025","article-title":"Robust and optimal adjustment of Power System Stabilizers through Linear Matrix Inequalities","volume":"42","author":"Zanetta","year":"2012","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1109\/TEC.2002.801992","article-title":"Optimal design of power-system stabilizers using particle swarm optimization","volume":"17","author":"Abido","year":"2002","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1007\/s40313-017-0351-x","article-title":"Design of Coordinated Decentralized Damping Controllers for Power Systems Considering Uncertainties","volume":"29","author":"Bento","year":"2018","journal-title":"J. Control Autom. Electr. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1109\/TPWRS.2003.814848","article-title":"Optimal multiobjective design of robust power system stabilizers using genetic algorithms","volume":"18","author":"Abido","year":"2003","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.ijepes.2014.03.050","article-title":"Robust tuning of power system stabilizer for small signal stability enhancement using metaheuristic bat algorithm","volume":"61","author":"Sambariya","year":"2014","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.ijepes.2014.07.040","article-title":"Coordinated tuning of power system stabilizers using bio-inspired algorithms","volume":"64","author":"Peres","year":"2015","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Hattabi, I., Kheldoun, A., Bradai, R., Khettab, S., Sabo, A., Belkhier, Y., Khosravi, N., and Oubelaid, A. (2024). Enhanced power system stabilizer tuning using marine predator algorithm with comparative analysis and real time validation. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-80154-2"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Pazderin, A., Zicmane, I., Senyuk, M., Gubin, P., Polyakov, I., Mukhlynin, N., Safaraliev, M., and Kamalov, F. (2023). Directions of Application of Phasor Measurement Units for Control and Monitoring of Modern Power Systems: A State-of-the-Art Review. Energies, 16.","DOI":"10.3390\/en16176203"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1109\/TPWRS.2008.926718","article-title":"Design of Wide-Area Damping Controllers for Interarea Oscillations","volume":"23","author":"Zhang","year":"2008","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1109\/TSG.2010.2053726","article-title":"Smart Transmission Grid: Vision and Framework","volume":"1","author":"Li","year":"2010","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.1016\/j.epsr.2010.03.005","article-title":"Optimal PMU placement method for complete topological and numerical observability of power system","volume":"80","author":"Sodhi","year":"2010","journal-title":"Electr. Power Syst. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.rser.2015.12.167","article-title":"A review on wide-area damping control to restrain inter-area low frequency oscillation for large-scale power systems with increasing renewable generation","volume":"57","author":"Zhang","year":"2016","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"107394","DOI":"10.1109\/ACCESS.2024.3438566","article-title":"An Improved Smith Predictor for Wide-Area Damping Control Considering Time-Delays in Power System","volume":"12","author":"Yu","year":"2024","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Bento, M.E.C. (2023). Wide-Area Measurement-Based Two-Level Control Design to Tolerate Permanent Communication Failures. Energies, 16.","DOI":"10.3390\/en16155646"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2389","DOI":"10.1109\/TSG.2021.3050419","article-title":"Scalable Designs for Reinforcement Learning-Based Wide-Area Damping Control","volume":"12","author":"Mukherjee","year":"2021","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1109\/TPWRS.2021.3091940","article-title":"Coordinated Wide-Area Damping Control Using Deep Neural Networks and Reinforcement Learning","volume":"37","author":"Gupta","year":"2022","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.ijepes.2017.07.010","article-title":"A new scheme of WADC for damping inter-area oscillation based on CART technique and Thevenine impedance","volume":"94","author":"Ranjbar","year":"2018","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Bento, M.E.C. (2018, January 12\u201314). An Optimization Approach for the Wide-Area Damping Control Design. Proceedings of the 2018 13th IEEE International Conference on Industry Applications (INDUSCON), Sao Paulo, Brazil.","DOI":"10.1109\/INDUSCON.2018.8627222"},{"key":"ref_27","first-page":"101116","article-title":"An Unscented Transformation based approach for probabilistic design of Wide-Area Damping Controllers","volume":"46","author":"Peres","year":"2025","journal-title":"Sustain. Comput. Inform. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4936","DOI":"10.1109\/TIA.2025.3537060","article-title":"Design of a Decentralized Wide-Area Damping Controller Resilient to Permanent Communication Failures","volume":"61","author":"Bento","year":"2025","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1109\/TSTE.2015.2508558","article-title":"Hierarchical Co-Ordinated Wide Area and Local Controls of DFIG Wind Turbine and PSS for Robust Power Oscillation Damping","volume":"7","author":"Surinkaew","year":"2016","journal-title":"IEEE Trans. Sustain. Energy"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yuan, Y., Sun, Y., and Cheng, L. (2007, January 24\u201328). Design of Delayed-Input Wide-area FACTS Controller Using Genetic Algorithm. Proceedings of the 2007 IEEE Power Engineering Society General Meeting, Tampa, FL, USA.","DOI":"10.1109\/PES.2007.385438"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Bento, M.E.C. (2016, January 20\u201323). Design analysis of wide-area damping controllers using genetic algorithms. Proceedings of the 2016 12th IEEE International Conference on Industry Applications (INDUSCON), Curitiba, Brazil.","DOI":"10.1109\/INDUSCON.2016.7874508"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"154","DOI":"10.3390\/electricity4020010","article-title":"Design of a Wide-Area Power System Stabilizer to Tolerate Multiple Permanent Communication Failures","volume":"4","author":"Bento","year":"2023","journal-title":"Electricity"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"100258","DOI":"10.1016\/j.rico.2023.100258","article-title":"Design of a Wide-Area Power System Stabilizer resilient to permanent communication failures using bio-inspired algorithms","volume":"12","author":"Bento","year":"2023","journal-title":"Results Control Optim."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Bento, M.E.C. (2021, January 26\u201330). Design of a Resilient Wide-Area Damping Controller Using African Vultures Optimization Algorithm. Proceedings of the 2021 31st Australasian Universities Power Engineering Conference (AUPEC), Perth, Australia.","DOI":"10.1109\/AUPEC52110.2021.9597758"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1007\/s00202-024-02572-9","article-title":"Design of a resilient wide-area damping controller using time delays","volume":"107","author":"Bento","year":"2025","journal-title":"Electr. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"938","DOI":"10.1016\/j.ifacol.2022.04.154","article-title":"Resilient Wide-Area Damping Controller Design Using Crow Search Algorithm","volume":"55","author":"Bento","year":"2022","journal-title":"IFAC-PapersOnLine"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4292","DOI":"10.1109\/TPWRS.2013.2261828","article-title":"Design of Wide-Area Power System Damping Controllers Resilient to Communication Failures","volume":"28","author":"Zhang","year":"2013","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"91909","DOI":"10.1109\/ACCESS.2024.3421515","article-title":"Detection and Correction Matrix-Based Wide Area Damping Controller Design to Tolerate All Kinds of Communication Failures","volume":"12","author":"Naguru","year":"2024","journal-title":"IEEE Access"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1109\/JAS.2020.1003066","article-title":"Unified Smith predictor based H wide-area damping controller to improve the control resiliency to communication failure","volume":"7","author":"Sarkar","year":"2020","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3918","DOI":"10.1109\/TPWRS.2020.2978426","article-title":"Fixed Low-Order Wide-Area Damping Controller Considering Time Delays and Power System Operation Uncertainties","volume":"35","author":"Bento","year":"2020","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"4238","DOI":"10.1109\/TSG.2021.3068390","article-title":"Resilient Wide-Area Damping Control for Inter-Area Oscillations to Tolerate Deception Attacks","volume":"12","author":"Yao","year":"2021","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3438","DOI":"10.1109\/TSG.2021.3055222","article-title":"Wide-Area Damping Control Resilience Towards Cyber-Attacks: A Dynamic Loop Approach","volume":"12","author":"Patel","year":"2021","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2189","DOI":"10.1109\/TPWRS.2014.2300502","article-title":"Wide-Area Control Resiliency Using Redundant Communication Paths","volume":"29","author":"Zhang","year":"2014","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1356","DOI":"10.1109\/JSYST.2020.2985165","article-title":"Markov Game for Securing Wide-Area Damping Control Against False Data Injection Attacks","volume":"15","author":"Liu","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"4831","DOI":"10.1109\/JSYST.2020.3020425","article-title":"Resilient Adaptive Wide-Area Damping Control to Mitigate False Data Injection Attacks","volume":"15","author":"Zhao","year":"2021","journal-title":"IEEE Syst. J."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"111448","DOI":"10.1016\/j.epsr.2025.111448","article-title":"Wide-Area damping control enhanced by non-invasive data verification against false data injection attacks","volume":"242","author":"Sun","year":"2025","journal-title":"Electr. Power Syst. Res."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Vavdareh, M.B., Ghafouri, M., and Ameli, A. (2024, January 17\u201320). Developing Multi-Agent Wide Area Damping Controller to Mitigate False Data Injection Attacks. Proceedings of the 2024 IEEE International Conference on Environment and Electrical Engineering and 2024 IEEE Industrial and Commercial Power Systems Europe (EEEIC\/I&CPS Europe), Rome, Italy.","DOI":"10.1109\/EEEIC\/ICPSEurope61470.2024.10751289"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Kumar, K., Saini, P., Prakash, A., Parida, S.K., and Al Jaafari, K. (2024, January 14\u201316). Detection and Mitigation of False Data Injection Attacks in Wide-Area Damping Controller Using Random Forest Classifier. Proceedings of the 2024 23rd National Power Systems Conference (NPSC), Indore, India.","DOI":"10.1109\/NPSC61626.2024.10987052"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Saini, A., and Bhui, P. (2025). Securing Wide-Area Damping Controller Against Cyber Attacks using Semi-Supervised Generative Adversarial Network and Support Vector Machine-Based Synthetic Minority Oversampling Technique. J. Mod. Power Syst. Clean Energy, 1\u201313.","DOI":"10.1109\/ISGT59692.2024.10454173"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1763","DOI":"10.35833\/MPCE.2024.000946","article-title":"Non-intrusive Hybrid Two-stage Detection of Dynamic Attacks in Wide-area Damping Controller Using Autoencoder and Unscented Kalman Filter with Unknown Input Estimation","volume":"13","author":"Saini","year":"2025","journal-title":"J. Mod. Power Syst. Clean Energy"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2326","DOI":"10.1109\/TSG.2022.3215785","article-title":"Resilient Wide-Area Damping Control to Mitigate Strong Cyber Attack: A Multiple-Controller Switching Approach","volume":"14","author":"Zhao","year":"2023","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1109\/JETCAS.2022.3151645","article-title":"Incomplete Information Stochastic Game Theoretic Vulnerability Management for Wide-Area Damping Control Against Cyber Attacks","volume":"12","author":"Li","year":"2022","journal-title":"IEEE J. Emerg. Sel. Top. Circuits Syst."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Yao, W., and Wen, J. (2023, January 15\u201318). Resilient Wide-Area Damping Control to Mitigate Sparse Attack Using Robust Subspace Tracking. Proceedings of the 2023 IEEE 7th Conference on Energy Internet and Energy System Integration (EI2), Hangzhou, China.","DOI":"10.1109\/EI259745.2023.10513294"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"2331","DOI":"10.1109\/TSG.2022.3146375","article-title":"Quantifying Resilience of Wide-Area Damping Control Against Cyber Attack Based on Switching System Theory","volume":"13","author":"Zhao","year":"2022","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Bento, M.E.C., Dotta, D., and Ramos, R.A. (2016, January 17\u201321). Performance analysis of Wide-Area Damping Control Design methods. Proceedings of the 2016 IEEE Power and Energy Society General Meeting (PESGM), Boston, MA, USA.","DOI":"10.1109\/PESGM.2016.7741334"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"392","DOI":"10.1016\/j.ijepes.2016.04.026","article-title":"Robust hierarchized controllers using wide area measurements in power systems","volume":"83","year":"2016","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1007\/s10586-024-04976-5","article-title":"Stellar oscillation optimizer: A nature-inspired metaheuristic optimization algorithm","volume":"28","author":"Rodan","year":"2025","journal-title":"Clust. Comput."},{"key":"ref_58","unstructured":"Kennedy, J., and Eberhart, R. (December, January 27). Particle swarm optimization. Proceedings of the ICNN\u201995-International Conference on Neural Networks, Perth, Australia."},{"key":"ref_59","unstructured":"Canizares, C., Fernandes, T., Geraldi, E., Gerin-Lajoie, L., Gibbard, M., Hiskens, I., Kersulis, J., Kuiava, R., Lima, L., and DeMarco, F. (2015). Benchmark Systems for Small-Signal Stability Analysis and Control. Power & Energy Society Technical Report PES-TR18, IEEE. Available online: https:\/\/resourcecenter.ieee-pes.org\/publications\/technical-reports\/pestr18."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Liu, S., Liu, X.P., and El Saddik, A. (2013, January 24\u201327). Denial-of-Service (dos) attacks on load frequency control in smart grids. Proceedings of the 2013 IEEE PES Innovative Smart Grid Technologies Conference (ISGT), Washington, DC, USA.","DOI":"10.1109\/ISGT.2013.6497846"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611970777"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1080\/10556789908805766","article-title":"Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones","volume":"11","author":"Sturm","year":"1999","journal-title":"Optim. Methods Softw."},{"key":"ref_63","unstructured":"Lofberg, J. (2004, January 2\u20134). YALMIP: A toolbox for modeling and optimization in MATLAB. Proceedings of the 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), Taipei, Taiwan. CACSD-04."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Liu, F., Gao, C., and Liu, L. (2024). SK-PSO: A Particle Swarm Optimization Framework with SOM and K-Means for Inverse Kinematics of Manipulators. Symmetry, 16.","DOI":"10.3390\/sym16121667"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1109\/TPWRS.2016.2561263","article-title":"Benchmark Models for the Analysis and Control of Small-Signal Oscillatory Dynamics in Power Systems","volume":"32","author":"Canizares","year":"2017","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_66","unstructured":"MATLAB (2025, August 01). Mathworks Inc.. Available online: https:\/\/www.mathworks.com\/products\/matlab.html."},{"key":"ref_67","unstructured":"CEPEL (2025, August 01). ANATEM User\u2019s Manual. Available online: https:\/\/see.cepel.br\/manual\/anatem\/."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1781\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T04:22:00Z","timestamp":1761279720000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1781"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,22]]},"references-count":67,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111781"],"URL":"https:\/\/doi.org\/10.3390\/sym17111781","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,22]]}}}