# Utilizing Energy Storage for Reliability Solutions in Active Distribution Systems
## 3 Scenario-Based Probabilistic Modeling of Reliability Solutions with ESS  
This section develops a scenario-based stochastic modeling approach for the mitigation of reliability events brought by ESS. ESS could be present at the customer premise, integrated along the main feeder along with other distributed resources, or in a microgrid protecting one or more customer loads (MG1 and MG2 in Figure 3). Such microgrids generally have DGs, storage, and controllable loads necessary to balance voltage and frequency while operating in an isolated mode in case of a fault in the utility supply side. Management and control system of the microgrid has the ability to switch into an isolated mode in a sub-cycle range with the help of fast-acting switch at PCC, thus, preventing damage to sensitive loads [10]. The same switch at PCC [10] would clear any fault within the microgrid. The seamless transfer to the isolated mode and resynchronization with the utility grid helps mitigate voltage sags and momentary/sustained interruptions experienced by microgrid customers. Figure 3: Distributed energy resources (DERs)/microgrids integrated test distribution network. Figure 2: (**a**) Probability distribution function (PDF) of sag duration; (**b**) Sag tolerance curve. DERs integrated along the main feeder (Seg 3 and Seg 4 in Figure 3) generally disconnect as soon as they detect a fault [15]. However, they can be reconnected, and supply load points located on a healthy segment of the network if an islanding operation is permitted. Such provision reduces the sustained outages experienced by customers but cannot reduce the impact of voltage sags and momentary interruptions. Thus, ESS (DERs) present at customer-premise or inside the microgrid is considered to be able to mitigate both short- and long-duration reliability events, whereas the ESS (DERs) integrated along the feeder are considered to mitigate long-duration reliability events only. The developed model incorporates hardware availability, power rating, state of charge (SOC) levels, and discharge duration of ESS. It also considers the intermittency of renewable DG, varying load level, and energy limitation characteristics of ESS and correlation between renewable DG output and the load. Scenario representation (such as using historical time-series data, or through the simulation approach) preserve the intermittency and correlation associated with renewable DG output and load. However, a large set of scenarios decreases computational efficiency, which necessitates the use of scenario-reduction methods. Utilization of appropriate approaches while generating the original scenario set and obtaining a reduced set is necessary to ensure the accuracy along with the computational efficiency. In this paper, the original scenario set is represented by historical time series data of renewable DG output and load demand. The final reduced set is obtained with a backward-scenario reduction method [10], which uses the relative closeness among the scenarios and individual scenario probability to eliminate scenarios. Steps within Algorithm 2 illustrate the probabilistic modeling of reliability event mitigation assessment with ESS. The model developed in Algorithm 2 is integrated into the reliability evaluation framework (developed in Section 2) as described in Algorithm 3, thus completing the scenario-based probabilistic modeling of reliability event mitigation with ESS. 1. Obtain the original scenario set of hourly renewable DG output, e.g., solar photovoltaic (PV) output, wind generator output, and load level using historical data. 2. Divide the original set of scenarios into two groups, one with data from daylight hours and one with data from night hours, to preserve the typical characteristic of PV not being available during nighttime. 3.