Evaluation of Delays-based Stability of LFC Systems in the Presence of Electric ‎Vehicles Aggregator

Document Type : Research paper


Department of Electrical Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran


In the integrated electrical systems, frequency control service considering the electric vehicle (EV) aggregators could lead to time-varying delay in load frequency control (LFC) schemes. These delays influence the LFC system efficiency, and in some situations, the lack of a clear choice of a control strategy considering the time-varying delays causes power system instability. Thus, this paper illustrates different time-varying delays based on the stability of an LFC system in the EV aggregators presence. The LFC's delay-dependent stability study is executed for finding the stability region and, stability criteria is suggested using the linear matrix inequality (LMI) method and Lyapunov-Krasovskii theory. Also, Wirtinger-based improved inequality and bounding lemma are applied to compute the greatest allowable delay in the LFC system, including the EV aggregators.


[1]  Y. Zheng et al., “Integrating plug-in electric vehicles into power grids: A comprehensive review on power interaction mode, scheduling methodology and mathematical foundation”, Renew. Sustain. Energy Rev., vol. 112, pp. 424-439, 2019.
[2]  A. Safari, F. Babaei, M. Farrokhifar, “A load frequency control using a PSO-based ANN for micro-grids in the presence of electric vehicles”, Int. J. Ambient Energy., Vol. 42, pp. 688-700,  2021.
[3]  D. Aravindh et al., “Design of observer-based non-fragile load frequency control for power systems with electric vehicles”, ISA Trans, vol. 91, pp. 21-31, 2019.
[4]  K. Tan, V. Ramachandaramurthy, J. Yong, “Integration of electric vehicles in smart grid: A review on vehicle to grid technologies and optimization techniques”, Renew. Sustain. Energy Rev., vol. 53, pp. 720-732, 2016.
[5]  H. Liu et al., “Decentralized vehicle-to-grid control for primary frequency regulation considering charging demands”, IEEE Trans. Power Syst., vol. 28, pp. 3480-89, 2013.
[6]  J. Pillai, B. Bak-Jensen, “Integration of vehicle-to-grid in the western Danish power system”, IEEE Trans. Sustain. Energy., vol. 2, pp. 12-19, 2010.
[7]  M. Galus, S. Koch, G. Andersson, “Provision of load frequency control by PHEVs, controllable loads, and a cogeneration unit”, IEEE Trans. Ind. Electron., vol. 58, pp. 4568-82, 2010.
[8]  M. Sarker, Y. Dvorkin, M. Ortega-Vazquez, “Optimal participation of an electric vehicle aggregator in day-ahead energy and reserve markets”, IEEE Trans. Power Syst., vol. 31, pp. 3506-15, 2015.
[9]  M. Vayá, G. Andersson, “Optimal bidding strategy of a plug-in electric vehicle aggregator in day-ahead electricity markets under uncertainty”, IEEE Trans. Power Syst., vol. 30, pp. 2375-85, 2014.
[10]  K. Ko, S. Han, D. Sung, “A new mileage payment for EV aggregators with varying delays in frequency regulation service”, IEEE Trans. Smart Grid., vol. 9, pp. 2616-24, 2016.
[11]  A. Molisch, “Wireless communications”, John Wiley & Sons, 2012.
[12]  C. Zhang et al., “Delay-dependent robust load frequency control for time delay power systems”, IEEE Trans. Power Syst., vol. 28, pp. 2192-2201, 2013.
[13]  Ş. Sönmez, S. Ayasun, C. Nwankpa, “An exact method for computing delay margin for stability of load frequency control systems with constant communication delays”, IEEE Trans. Power Syst., vol. 31, pp. 370-7, 2015.
[14]  R. Zhang et al., “New approaches to stability analysis for time-varying delay systems”, J. Franklin Inst., vol. 356, pp. 4174-89, 2019.
[15]  C. Duan et al., “Structure-exploiting delay-dependent stability analysis applied to power system load frequency control”, IEEE Trans. Power Syst., vol. 32, pp. 4528-40, 2017.
[16]  K. Ramakrishnan, G. Ray, “Stability criteria for nonlinearly perturbed load frequency systems with time-delay”, IEEE J. Emerging Sel. Top. Circuits Syst., vol.  5, pp. 383-92, 2015.
[17]  A. Khalil et al., “The impact of the time delay on the load frequency control system in microgrid with plug-in-electric vehicles”, Sustain. Cities Soc.., vol. 35, pp. 365-77, 2017.
[18]  S. Sönmez, S. Ayasun, “Stability region in the parameter space of PI controller for a single-area load frequency control system with time delay”, IEEE Trans. Power Syst., vol. 31, pp.  829-30, 2015.
[19]  C. Zhang et al., “Further results on delay-dependent stability of multi-area load frequency control”, IEEE Trans. Power Syst., vol. 28, pp. 4465-74, 2013.
[20]  V. Çelik, M. Özdemir, G. Bayrak, “The effects on stability region of the fractional-order PI controller for one-area time-delayed load–frequency control systems”, Trans. Inst. Meas. Control., vol. 39, pp. 1509-21, 2017.
[21]  P. Ojaghi, M. Rahmani, “LMI-based robust predictive load frequency control for power systems with communication delays”, IEEE Trans. Power Syst., vol. 32, pp. 4091-100. 2017.
[22]  F. Yang et al., “Auxiliary-function-based double integral inequality approach to stability analysis of load frequency control systems with interval time-varying delay”, IET Control Theory Appl., Vol. 12, pp. 601-12, 2017.
[23]  L. Jin et al., “Delay-dependent stability analysis of multi-area load frequency control with enhanced accuracy and computation efficiency”, IEEE Trans. Power Syst., vol. 34, pp. 3687-96 2019.
[24]  K. Ko, D. Sung, “The effect of EV aggregators with time-varying delays on the stability of a load frequency control system”, IEEE Trans. Power Syst., vol. 33, pp. 669-80, 2017.
[25]  Y. Rebours et al., “A survey of frequency and voltage control ancillary services-Part I: Technical features”, IEEE Trans. Power Syst., vol. 22, pp. 350-57, 2007.
[26]  M. Khooban, T. Niknam, “A new intelligent online fuzzy tuning approach for multi-area load frequency control: self adaptive modified bat algorithm”, Int. J. Electr. Power Energy Syst., vol. 71, pp. 254-261, 2015.
[27]  F. Babaei et al., “SSA based Fractional-Order PID Controller for LFC Systems in the Presence of Delayed EV aggregators”, IET Electr. Syst., vol. 10, pp. 259-67, 2020.
[28]  R. Dey, G. Ray, V. Balas, “Stability and stabilization of linear and fuzzy time-delay systems: a linear matrix inequality approach”, Springer, 2017. 
[29]  F. Zheng, Q. Wang, T. Lee, “On the design of multivariable PID controllers via LMI approach”, Automatica., Vol. 38, pp. 517-26, 2002.
[30]  V. Suplin, E. Fridman, U. Shaked, “H/sub/splinfin/control of linear uncertain time-delay systems-a projection approach”, IEEE Trans. Autom. Control.,  vol. 51, pp. 680-85, 2006.
[31]  N. Chowdary, M. Chidambaram, “Robust controller design for first order plus time delay systems using kharitonov theorem”, IFAC Proc. Vol., vol. 47, pp. 184-91, 2014.
[32]  A. Seuret, F. Gouaisbaut, “Wirtinger-based integral inequality: application to time-delay systems”, Automatica, vol. 49, pp. 2860-66, 2009.
[33]  P. Park, J. Ko, C. Jeong, “Reciprocally convex approach to stability of systems with time-varying delays”, Automatica., vol. 47, pp. 235-38, 2011.