### Contributions and the Paper Structure  
According to an aforementioned literature survey, it is needed to develop an adaptive and scalable protection coordination (ASPC) approach for OCRs in the DG-integrated DN to improve the reliability of protection system. The ASPC approach for OCRs has two main performance stages: (i) Stage I-increasing the reliability of fault-current calculation results and selecting tripping and pick-up current thresholds for the OCRs; and (ii) Stage II-applying the optimization algorithms to calculate the coefficients and Time-Dial-Setting (TDS) multiplier for the inverse-time OC functions in the OCR. More clearly, Stage I finds the min-max confidence interval of fault currents for each different fault type (e.g., 3 ph-G fault, 2 ph-G fault, 1 ph-G fault, and ph-ph fault) which is the basis for properly selecting tripping and pick-up thresholds of definite-time and inverse-time OC functions in the same OCR. Stage II uses three common optimization algorithms, Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), and Genetic Algorithm (GA) to determine the coefficients and TDS multiplier for the inverse-time OC functions. The objective function of the ASPC approach for the OCRs is formulated by three certain constraints consisting of Coordination Time Interval (CTI), relay operating time and TDS multiplier. Novel contributions and assumptions related to the ASPC system of the OC relays are briefly shown as follows:  
* Increasing the reliability of fault-current calculation results: According to the literature survey, either nominal bus-voltage values or voltage values calculated right after some pre-determined cycles are commonly considered as the reference voltages for the power-flow analysis and fault-current calculation. However, the use of nominal bus-voltage values could lead to inaccurate calculations of power flows and fault currents in the distribution network, which can result in the protection miscoordination of OCRs. Therefore, this study will propose a novel statistical data-filtering method to determine a min-max confidence interval of load power \([P_{\text{load\_min}},P_{\text{load\_max}}]\) and load current \([I_{\text{load\_min}},I_{\text{load\_max}}]\) at each load bus in the DN, as referred in Sections of Forecasting a Min-Max Confidence Interval of Load Power at Each Load Bus and Calculating a Min-Max Confidence Interval of Load Current at Each Load Bus, respectively. Next, a current-injection-based power-flow (CIBPF) analysis method is used to calculate the min-max confidence interval of bus voltage at any \(i\)-th bus on the DN, \([V_{i\_min},V_{i\_max}]\) instead of using either the nominal bus-voltage values or the voltage values calculated right after some pre-determined cycles from the power-flow analysis, as referred to Section of The Current-Injection-Based Power Flow Analysis. Based on the confidence intervals of bus-voltages in the distribution network, an adaptable fault analysis technique depicted in Section of An Adaptable Fault Analysis Technique is proposed to calculate the min-max confidence intervals of fault currents contributed by different DG units and fault current contributed by the utility which are used for effectively selecting tripping and pick-up thresholds of definite-time and inverse-time OC functions in the same OCR. In other words, instead of using a fixed fault-current value for each fault type with the unconsidered reliability, this paper has contributed an adaptable fault analysis technique to calculate the min-max confidence interval of fault current. The maximum and minimum confidence thresholds of fault current are then used to select tripping and pick-up thresholds of definite-time and inverse-time OC functions, respectively. * Propose to use both definite-time and inverse-time protection functions in the same OCR to protect a DG-based distribution network.