# Utilizing Energy Storage for Reliability Solutions in Active Distribution Systems
## 2 Quantification of Reliability Events  
This section illustrates different reliability events and their causes and presents a framework to assess the reliability of the distribution network. Upon the occurrence of a fault in the network, root mean square voltage magnitude drops below the nominal voltage, thus leading to voltage sag. Both temporary and permanent faults cause the voltage sag until the responsible protection device operates [14]. The severity of voltage sag depends on fault location, fault impedance, fault-clearing time, sensitivity of customer equipment/process, moment of occurrence of sag event, etc. A momentary interruption occurs due to a brief loss of continuity of supply resulting from opening and closing of a protective device for a short duration (usually, the duration of 1-5 min is taken). Multiple interruptions caused by the recloser operating sequence is designated as one momentary interruption event in this work. The permanent fault, besides the temporary fault, can lead to a momentary interruption due to the service restoration with an automatic switching [2]. The momentary interruption introduced by DERs due to the restoration of supply with the islanded operation with automatic switching [15] is also considered in this work. The sustained interruption is defined as any interruption event, other than the momentary interruption. It should be noted that the temporary failure might cause sustained interruption as well. For instance, if a temporary failure causes a fuse to operate, customers downstream the fuse would experience sustained interruption until the fuse is replaced [2]. It should be noted that depending on the nature of the contingency and protection settings different load points experience different reliability events. Voltage sags, momentary interruptions, and sustained interruptions resulting from both temporary and permanent failures are considered in this work. Sometimes, one reliability event experienced by the customer evolves to another one upon the sequence of protection device operations. It is illustrated with an example of a permanent fault on L4 in Figure 1. It causes R2 to operate in order to clear the fault; therefore, LP3 and LP4 experience a momentary interruption during recloser operation. It should be noted that before R2 actuates, all load points in the network experience voltage sag. However, after a preset number of operations, R2 lock-opens resulting in sustained interruptions for LP3 and LP4 until the repair is done. In these situations of the temporally evolving reliability events, the final reliability event due to a contingency is assigned to the load point. Such practices result in a better estimation of customer reliability profile and associated financial losses. Reliability evaluation frameworks are mostly based on failure mode and effect analysis (FEMA) using the contingency enumeration technique. This paper adopts the same approach. Steps illustrated in Algorithm 1 quantifies different reliability events for load points and the system. The frequency and duration of reliability events and the associated customer damage cost are utilized to quantify the reliability profile. \(F_{l,DSE}\) denotes the expected frequency of equipment/processes disruption due to voltage sag for a load point. Expected frequency of momentary and sustained interruptions experienced by a load point is represented by \(F_{l,MI}\) and \(F_{l,SI}\), respectively. These frequency indices are expressed in terms of occurrence/year. Expected annual outage time (also called unavailability) associated with a sustained interruption for a load point is represented by \(U_{l,SI}\) and measured in hr/yr. \(D_{l,DSE}\), \(D_{l,MI}\), and \(D_{l,SI}\) provide the estimation of average annual customer damage cost (k$/yr) due to disruptive voltage sags, momentary interruptions, and sustained interruptions, respectively. The damage cost is a function of customer category, outage duration, and average demand of a customer.