Fractional order CES control for frequency regulation in deregulated realistic power systems with integrating RESs

One efficient solution to aid automatic generation control (AGC) in frequency regulation (FR) of competitive power systems integrated with renewables is to offer supplementary controllers for fast-response storage, such as capacitive energy storage (CES). Former CES models have not been presented exclusively for the CES dynamics or have fixed parameters, leading to a failure to contribute actively to the FR issue. Accordingly, the loss of an effective control approach established on the exclusive CES model represents a significant gap that warrants further investigation. To effectively contribute to the FR issue in a hybrid energy system, a maiden control approach based upon non-integer order controllers (NOCs) is offered for application in the exclusive dynamics of CES. A two-area liberal hybrid energy system incorporating photovoltaic, wind, gas, reheat thermal, and hydro plants with intrinsic nonlinearities, including generation rate constraints, communication time delays (CTDs), governor dead bands, and boiler dynamics, is considered to attain a realistic vision and reliable outputs. A CES-AGC concurrent design approach is regarded as performance-reinforcing. Accordingly, the integral of time-weighted squared error (ITSE) index is minimized using metaheuristic algorithms. The numerical analyses and time-domain simulations under an utterly liberal scenario demonstrate that the offered fractional order proportional integral derivative (FOPID)-based CES-AGC strategy is the most effective control strategy for suppressing deviations in area frequency and tie-line error power responses. Employing the proposed FOPID-based CES-AGC achieves a significant improvement in the damping criteria through a substantial reduction of nearly 17 to 13.8 times in peak magnitude (MP) of ΔF1, 2.2 to 2.4 times in MP of ΔF2, 22 to 1.7 times in ITSE, 9.5 to 1.8 times in ISE, and an increase of nearly 8 to 3.7 times in the minimum damping ratio (ζmin) compared to the lead-lag-based CES-AGC and PID-based CES-AGC, in order. Meanwhile, the FOPID-based CES-AGC outperforms the tilt integral derivative (TID)-based CES-AGC in the damping metrics associated with the FR issue. Moreover, by employing the proposed TID-based CES-AGC, a significant improvement in stability measures is obtained via a considerable reduction of closely 4.3 to 3.5 times in MP of ΔF1, 1.3 to 1.5 times in MP of ΔF2, 17 to 1.3 times in ITSE, 7.9 to 1.5 times in ISE, and an increase of approximately 5.6 to 2.6 times in the ζmin when compared with the lead-lag-based CES-AGC and PID-based CES-AGC counterparts, respectively. Additional numerical analyses and time-domain simulations, under various contract violation scenarios, indicate that employing the offered control strategy based on the NOCs has substantially confined the oscillations. Furthermore, the resiliency of the presented NOCs-based control approach is evaluated by determining the system’s maximum tolerable CTD. It is demonstrated that even with considering the maximum tolerable CTD, here 3 s, a remarkable damping performance can be achieved if it is taken into account in the tuning of the proposed controllers. Sensitivity analyses reveal that the NOCs-based CES-AGC is robust against ± 20 % and ± 25 % changes in the system loading and the synchronizing coefficient parameter, respectively.