## 5 Conclusions  
The protection coordination of OCRs becomes more complicated when a distribution network allows high penetration of DGs. Therefore, this paper has proposed an adaptive and scalable protection coordination (ASPC) system for the OCRs in the DG-based DN with two main performance stages. The first stage is to improve the reliability of fault-current calculation results through determining the min-max confidence interval of fault current for each different fault type including 3 ph-G, 2 ph-G, ph-ph, and 1 ph-G faults. The maximum and minimum confidence thresholds of fault current are used to select tripping and pick-up thresholds of definite-time and inverse-time OC functions in the same OCR, respectively. This contribution is to increase the scalability of the relay protection coordination system. In addition, the proposed ASPC approach for the OCRs has high adaptability to different fault current contributions from IBDGs and RBDGs and the available 'on-grid' and 'off-grid' operation modes for these DG units. The second stage is to calculate the \(A\), \(B\), and \(C\) certain coefficients and the Time-Dial-Setting (TDS) multiplier for the inverse-time OC functions in the OCR. Three common algorithms, GSA, hybrid PSO-GSA and GA, have been used to find the optimal setting parameters of the OCRs that are satisfied with all coordination constraint conditions. Moreover, the relay coordination results have shown an effective protection combination of the definite-time OC functions (50P and 50G) and the inverse-time OC functions (51P and 51G) in the same OCR to get the adaptable and scalable DN protection system. A real 22 kV DG-integrated distribution network has been simulated by ETAP software to analyze the min-max fault-current values of each fault type. In other words, this real 22 kV DN is used as a test-bed to validate the relay coordination results obtained by the ASPC system. The relay coordination results also show the visibility and superiority of the GSA because it has the fast computation time and the highest stability in comparison with the hybrid PSO-GSA and the GA. The tripping time difference between the desired one and the calculated one of the GSA is also the lowest. Last but not least, it could be interesting that this study has presented the protection coordination results of the related OCRs corresponding to all possible FISR plans of the DG-contained DN after a typical fault is cleared.  
[PERSON], T.P.N., and H.N. contribute conceptualization, methodology, and writing--review and editing of the paper. P.D.L. contributes investigation, data collection and analysis, software, and writing--original draft preparation of the paper. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Ministry of Education and Training (MOET) and Vietnamese-German University (VGU), a grant number of B2020-VGU-01 and an issued number of 103/QP-BGDDT by 21 st February 2020.  
Not applicable.  
The authors sincerely thank to the Ministry of Education and Training (MOET), Vietnamese-German University (VGU), and Ho Chi Minh City Power Corporation for data supply, administrative and technical support in this research paper.  
The authors declare no conflict of interest.