## 2 Theoretical Framework  
### Reliability Indicators  
This paper analyzes _SAIDI_ and _ENS_, two widely used reliability indicators. _SAIDI_ is a standardized metric applied globally, enabling comparisons between distribution systems. It aligns with regulatory requirements, as many countries use it as a reference for assessing the performance of distribution companies and often define annual improvement targets to ensure service reliability. _SAIDI_ quantifies the average duration of power supply interruptions, indicated in minutes or hours per customer [2; 4]:  
\[SAIDI=\left.\left(\sum_{i}U_{i}\cdot N_{i}\right)\right/N_{T}\ [h/yr], \tag{1}\]  
where \(U_{i}\) represents the annual outage time for location \(i\), \(N_{i}\) is the number of customers in location i, and \(N_{T}\) is the total number of customers served.  
_ENS_ represents the total amount of energy not supplied to consumers due to supply interruptions, directly quantifying their impact. While _SAIDI_ reflects the duration of interruptions, _ENS_ quantifies the unserved energy, making it particularly relevant for assessing both the operational and, with certain extensions, the economic consequences of reliability issues. _ENS_ calculates annual energy not supplied to customers in the considered network due to long supply interruptions [4]:  
\[ENS=\sum_{i}U_{i}\cdot P_{ai}\ [kWh/yr]\, \tag{2}\]  
where \(P_{ai}\) is the average load of a customer (in kW) connected to load point \(i\).  
In addition to _SAIDI_ and _ENS_, this paper introduces and analyzes a cost indicator, an economic metric used to quantify the financial impact of power supply interruptions. Economic impact analysis has received significant attention in the literature, with various indicators used to quantify economic effects [4]. Moreover, many studies rely on variable outage cost data, which differ based on consumer type and interruption duration [4; 37; 38; 39]. Additionally, some studies aim to provide highly accurate estimations of these costs [40; 41], requiring extensive input data that are often difficult to obtain.  
This paper performs a reliability assessment and an optimization of investment options that consider both higher and lower available financial resources. When the investment budget is limited, allocating significant time and resources to collecting input data is unjustified. Moreover, such data may not exist in developing countries, as compensation for supply interruptions is either not implemented or is determined through individual agreements between consumers and the DSO. In some cases, the price is typically negotiated individually with industrial and commercial consumers. Regardless of whether a country formally incorporates this aspect, it is preferable and wise to consider the economic effects. This paper proposes a simplified approach based on a fixed unit monetary value of unserved energy per consumer type, which is independent of interruption duration. This method is suitable for developing countries where detailed data on interruption costs by consumer type may not be available. It is also useful for planning small-scale investments while providing a reliable economic assessment.  
The paper analyzes the value of the cost indicator (\(COST\)), which quantifies the economic impact of power supply interruptions by expressing the reliability of the distribution system in monetary terms:  
\[COST=\sum_{i}U_{i}\cdot P_{ai}\cdot c_{i}\ \ \left[EUR/yr\right]\,, \tag{3}\]  
where \(c_{i}\) is the unit monetary value of unserved energy, reflecting the financial impact of supply interruptions per kilowatt-hour [EUR/kWh] of energy not supplied.