*1.2. Literature Review*

Metaheuristic techniques such as genetic algorithm (GA) have been applied successfully for reducing the tripping time of relays and avoiding miscoordination problems [5]. For miscoordination problems that are associated with both discrete- and continuous-time multiplier settings, in ref. [6], the particle swarm optimization (PSO) algorithm proved its effectiveness to deal with complex coordination problems. In addition, hybrid techniques have been established to improve metaheuristic techniques. For instance, a hybrid particle swarm optimization and moth–flame optimization (PSOMFO), which is a combination between the PSO and MFO to improve their achievement, and the outcomes proved its effectiveness compared to PSO and MFO algorithms individually [7]. In ref. [8], the authors proposed a hybrid gravitational search algorithm and sequential quadratic programming (GSA–SQP) algorithm that introduces a robust high-quality solution to solving the OCR coordination problem. It is effective due to it taking the pros of both GSA and SQP techniques; it has been tested and evaluated on various test systems. Secondly, some papers proposed and considered the effect of the new or reduced constraints on solving the OCR coordination problem. For the distribution system with a combination of the DGs in ref. [9], the study relieved about 43% of burdensome constraints from the process of coordination optimization compared to the two standards. A considerable number of constraints is an optimization problem; the inactive inequality constraints in the OCR coordination problem have been detected and removed by using a new proposed index. It is defined as a ratio for each OCR pair. The given results illustrate that the proposed index detected and removed more than 90% of unused constraints [10].

Dual-setting directional overcurrent relays (DOCRs) can operate in both directions which are forward and reverse; it is another solution that has been introduced for overcoming challenges relating to the MGs' protection systems. In ref. [11], a new coordination scheme using dual-setting DOCRs has been proposed to determine two optimum pairs of settings for each relay in connected and disconnected DGs. The obtained results appear to

demonstrate the effectiveness of the proposed approach and reduce the overall operation time (OT) by roughly 50% compared to the traditional coordination scheme that utilizes the DOCRs with a pair of settings. A novel protection scheme for dual-setting DOCRs in MGs with DGs has been introduced in ref. [12]. This scheme uses a dual-protection setting in the main and backup operation topologies in one relay. Two strategy cases of one-point and three-point have been executed by the optimization. During utilization of the three-point coordination strategy, the total OT has been reduced by 57% compared with the conventional dual-setting method. The proposed method proves its applicability for both grid-connecting and islanding modes and improves the system's reliability by eliminating the demand for communication between relays. One of the suggestions made by many authors to contribute to preventing the miscoordinations is modifying the objective function. Multiple modifications in the objective function for DOCRs for meshed networks have been suggested by Alam et al. in ref. [13]; it minimized the OT for main and backup relays simultaneously. In ref. [14], a novel objective function is proposed to direct the settings of the OCRs towards optimal solutions suitably. The proposed approach showed a significant reduction in the OT of relays and avoided miscoordinations among them.

Investigation of alternative methods to standard protection schemes has required a considerable amount of effort by researchers by employing NSCs, which will be taken into consideration in this literature. There is limited literature on designing OCR coordination schemes based on NSCs for a power network equipped with DGs. For example, a hybrid application uses an inverse-time characteristic and a definite-time characteristic in parallel with the absence of the DG units has been proposed in ref. [15]. This novel hybrid NSC entails no complexity or additional cost, whereas the problem of dynamic coordination has appeared in these hybrid NSCs which require careful application. Thus, they can lead to miscoordination and less flexibility. In addition to the fault current characteristic, there are some NSCs based on the fault voltage that have been proposed and applied [16,17]. The authors in ref. [16] added per-unit voltage to measure the IEC standard characteristics (SCs) to reduce the overall OTs of the relays. In ref. [4], a significant reduction in the total OT of the OCRs has been achieved by employing the fault voltage natural logarithm function in the denominator of the characteristic equation. However, this logarithm function had a limited effect on the obtained characteristic. In another study [18], a new scheme excluded the time multiple setting (TMS) and utilized fault voltage in the numerator as a logarithm function. The relay OTs are not raised when the location of the relay moves to the source due to TMS elimination. To achieve lower OTs in comparison with SCs, an NSC-based algorithm function has been introduced in ref. [19]. However, the major disadvantage of NSCs in refs. [4,16,18] is the inability of applying the approaches within existing industrial OCRs. In addition, the new requirements of measuring the fault voltage beside the fault current will increase the problem's complexity.

To mitigate and avoid the limitations in the SCs such as the inverse time–current characteristics of MG systems, a new NSC based on adding the auxiliary variable to the conventional OCR OT equation is presented by ref. [20], which aims to achieve a fast protection scheme based on well-defined time–current characteristics (TCCs). All of these auxiliary variables are measured as coordination constraints; however, it is inapplicable in existing industrial OCRs. Therefore, a piece-wise linear (PWL) characteristic has been proposed in ref. [21] to preserve the coordination time interval (CTI) between the primary and the backup relay pairs for the entire range of the fault current. The successive straight lines were joined together to formulate the new characteristic curve and a tabular format is used to adjust the curve for the existing industrial relays. For obtaining the optimal coordination of OCRs in meshed networks, the piece-wise linear characteristic (PWLC) has been evolved as a novel method [22]. It used variables coefficients, namely A and B, of the PWLCs of the OCRs for adjusting purposes and obtaining a more flexible TCC with the normally inverse (NI) standard; however, the proposed method was not tested by changing the location and the size of the DGs to evaluate their effect on the performance of the proposed approach. There are some researchers who have considered the SCs' constant parameters as variable set points, which is another NSC format [23,24]. This NSC format aims to develop flexible TCCs by creating necessary CTI for the range of the entire fault current between the primary/backup pairs of the relay. To improve the selectivity and sensitivity in the OCR coordination and avoid the NI standard curve disadvantages, an optimal coordination scheme based on nonstandard time–current characteristics is presented in refs. [25,26]. However, the nonstandard time–current characteristics are created by using the logarithmic function and constant coefficients, which lead to significantly minimizing the overall operational time on maximum fault currents, but it showed limited behavior on minimum fault currents. Table 1 shows an overview of the literature review that has been introduced above.


**Table 1.** A Literature Review Comparison Analysis for Protection of Radial and Meshed Networks.
