Automatic generation control (AGC) also known as load frequency control plays a vital role in interconnected power system for frequency regulation. Electric vehicles (EVs) with battery as the storage device can participate in frequency regulation service. In practice, a large number of EVs are aggregated as a single unit called EV aggregator for participation in frequency regulation service in AGC system. Participation of EV aggregators in AGC system for frequency regulation will be encouraged in near future because EVs have less environmental pollution than the conventional vehicles. However, participation of EV aggregators in AGC system may introduce time delay which degrades the dynamic performance of the power system and even may lead to system instability. Further, generation rate constraint (GRC) and governor dead band (GDB) of synchronous generator introduce nonlinearity in the system, which adversely affects its dynamic performance. Hence, selection of an appropriate control strategy is essential for performance enrichment of the power system. In this work, a PID-fuzzy-PID (PID-FPID) controller optimally designed by hybridizing particle swarm optimization (PSO) and modified sine cosine algorithm (MSCA) is proposed and a novel attempt is made to improve the frequency stability of a two-equal-area interconnected thermal power system with GDB and GRC incorporating an EV aggregators with time-varying delay in each area. Integral time absolute error has been chosen as the objective function to optimally design the controller parameters. Dynamic performance of the system is also investigated with proportional-integral-derivative (PID) controller optimally designed by PSO, sine cosine algorithm (SCA), MSCA, and hybrid PSO-MSCA. The efficacy and supremacy of the proposed hybrid PSO-MSCA-based PID-FPID control strategy is established by contrasting the results with the others. Finally, the robustness of the proposed control strategy is validated by (i) including two EV aggregators with time-varying delay in each area, (ii) applying a large disturbance of 0.4 p.u. in area-1, and (iii) applying a random load in area-1.