The relay coordination problem is of dire importance as it is critical to isolate the faulty portion in a timely way and thus ensure electrical network security and reliability. Meanwhile a relay protection optimization problem is highly constraint and complicated problem to be addressed. To fulfill this purpose, Harris Hawk Optimization (HHO) is adapted to solve the optimization problem for Directional Over-current Relays (DOCRs) and numerical relays. As it is inspired by the intelligent and collegial chasing and preying behavior of hawks for capturing the prey, it shows quite an impressive result for finding the global optimum values. Two decision variables; Time Dial Settings (TDS) and Plug Settings (PS) are chosen as the decision variables for minimization of overall operating time of relays. The proposed algorithm is implemented on three IEEE test systems. In comparison to other state-of-the-art nature inspired and traditional algorithms, the results demonstrate the superiority of HHO.

Efficient coordination of directional overcurrent relays (DOCRs) is vital for maintaining the stability and reliability of electrical power systems (EPSs). The task of optimizing DOCR coordination in complex power networks is modeled as an optimization problem. This study aims to enhance the performance of protection systems by minimizing the cumulative operating time of DOCRs. This is achieved by effectively synchronizing primary and backup relays while ensuring that coordination time intervals (CTIs) remain within predefined limits (0.2 to 0.5 s). A novel optimization strategy, the fractional-order derivative war optimizer (FODWO), is proposed to address this challenge. This innovative approach integrates the principles of fractional calculus (FC) into the conventional war optimization (WO) algorithm, significantly improving its optimization properties. The incorporation of fractional-order derivatives (FODs) enhances the algorithm’s ability to navigate complex optimization landscapes, avoiding local minima and achieving globally optimal solutions more efficiently. This leads to the reduced cumulative operating time of DOCRs and improved reliability of the protection system. The FODWO method was rigorously tested on standard EPSs, including IEEE three, eight, and fifteen bus systems, as well as on eleven benchmark optimization functions, encompassing unimodal and multimodal problems. The comparative analysis demonstrates that incorporating fractional-order derivatives (FODs) into the WO enhances its efficiency, enabling it to achieve globally optimal solutions and reduce the cumulative operating time of DOCRs by 3%, 6%, and 3% in the case of a three, eight, and fifteen bus system, respectively, compared to the traditional WO algorithm. To validate the effectiveness of FODWO, comprehensive statistical analyses were conducted, including box plots, quantile–quantile (QQ) plots, the empirical cumulative distribution function (ECDF), and minimal fitness evolution across simulations. These analyses confirm the robustness, reliability, and consistency of the FODWO approach. Comparative evaluations reveal that FODWO outperforms other state-of-the-art nature-inspired algorithms and traditional optimization methods, making it a highly effective tool for DOCR coordination in EPSs.

In electrical power systems, ensuring a reliable, precise, and efficient relay strategy is crucial for safe and trustworthy operation, especially in multi-loop distribution systems. Overcurrent relays (OCRs) have emerged as effective solutions for these challenges. This study focuses on optimizing the coordination of OCRs to minimize the overall operational time of main relays, thereby reducing power outages. The optimization problem is addressed by adjusting the time multiplier setting (TMS) using the War Strategy Optimization (WSO) algorithm, which efficiently solves this constrained problem. This algorithm mimics ancient warfare strategies of attack and defense to solve complex optimization problems efficiently. The results show that WSO provides superior performance in minimizing total operating time and achieving global optimum solutions with reduced computational effort, outperforming traditional optimization methods (i.e., SM, HPSO, GA, RTO, and JAYA). The proposed algorithm shows a net time gains of 7.77 s, 2.57 s, and 0.8484 s when compared to GA, RTO, and JAYA respectively. This robust protection coordination ensures better reliability and efficiency in multi-loop power systems.

In electrical power systems, directional overcurrent relay (DOCR) coordination is assumed to be an essential component of the system for protection purposes. To diminish and reduce power losses, the coordination between these relays ought to be kept at an ideal value to minimalize the overall operating time of all primary-relay shortcoming situations. The coordination of DOCR is a complex and profoundly compelling nonlinear problem. The objective function is to minimalize the overall total operating time of all essential relays to minimize inordinate breakdown and interference. Coordination is performed using the marine predator algorithm (MPA), inspired by a widespread foraging strategy, namely Lévy and Brownian movements, to search for global optimal solutions in order to resolve the DOCRs coordination issue. The results acquired from MPA are equated with other state-of-the-art algorithms, and it was observed that the proposed algorithm outperforms other algorithms.

The remarkable progress of power electronic converters (PEC) technology has led to their increased penetration in distributed energy systems (DES). Particularly, the direct current (dc) nanogrid-based DES embody a variety of sources and loads, connected through a central dc bus. Therefore, PECs are required to be employed as an interface. It would facilitate incorporation of the renewable energy sources and battery storage system into dc nanogrids. However, it is more challenging as the integration of multiple modules may cause instabilities in the overall system dynamics. Future dc nanogrids are envisioned to deploy ready-to-use commercial PEC, for which designers have no insight into their dynamic behavior. Furthermore, the high variability of the operating conditions constitute a new paradigm in dc nanogrids. It exacerbates the dynamic analysis using traditional techniques. Therefore, the current work proposes behavioral modeling to perform system level analysis of a dc nanogrid-based DES. It relies only on the data acquired via measurements performed at the input–output terminals only. To verify the accuracy of the model, large signal disturbances are applied. The matching of results for the switch model and its behavioral model verifies the effectiveness of the proposed model.