## 1 Introduction
Given its significance in reliability assessment, _ENS_ has been widely used as a key indicator in studies focused on network optimization, distributed energy resource integration, and system reconfiguration. An approach proposed in [22] focuses on optimally placing micro-phasor measurement units (uPMUs) to improve distribution system reliability. It determines the optimal number and placement of uPMUs, with reliability evaluation based on _SAIDI_ and _ENS_. The optimal allocation of photovoltaic (PV) and battery energy storage (BES) systems in distribution networks is proposed in [23]. The aim is to minimize energy losses and _ENS_ under normal conditions while mitigating load interruptions during emergencies, considering practical constraints that include the associated costs of PV and BES. A study in [24] addresses distribution network reconfiguration (DNR) alongside the placement and sizing of distributed generators (DGs). Reliability improvement is a key objective achieved through _ENS_ reduction for end-users. The reliability of rural distribution systems with integrated microgrids (MGs) has been analyzed in [25], considering different penetration levels of renewable and nonrenewable distributed generation and the rated energy storage power, with _ENS_ serving as the key reliability indicator. Research in [26] examines the impact of control techniques on DG placement and sizing, considering technical, economic, and reliability factors. One aim was to minimize the _ENS_ parameter and reduce the costs associated with the optimal installation of DG units. The integration of renewable energy sources into microgrids in the mining sector has been analyzed in [27], considering energy cost, emissions, and reliability. Reliability was assessed using the _ENS_ indicator. Several studies have addressed reliability improvement by focusing on cost minimization during problem-solving. The approach for determining the optimal number, type, and location of automation devices installed in the network and identifying the new locationsof existing devices has been presented in [28]. The problem is addressed by minimizing the costs related to new devices or the relocation of existing ones to achieve the target values of reliability indices. The study in [29] focuses on selecting protective devices strategically distributed in distribution networks. The selection process is based on minimizing the total cost of reliability, considering the costs related to equipment installation and the expected customer interruption costs. The study also indirectly includes a constrained budget for reliability improvement, achieved by defining the available quantity of fuses and switches for installation. The paper in [30] proposes a multi-criteria decision-making approach for the optimal placement of switches and protective devices in distribution networks to generate possible solutions with varying investment and reliability levels. These solutions are evaluated based on the distribution operator's preferences using a multiple-criteria decision-making strategy. A method for optimizing the placement of reclosers and sectionalizers while ensuring protection coordination is proposed in [31]. The approach minimizes \(\mathit{ENS}\) and quantifies the financial benefits for distribution companies resulting from reduced unserved energy. In [32], the proposed model determines the optimal allocation of manual switches, remote-controlled switches (RCSs), and field circuit breakers (FCBs) to minimize costs and \(\mathit{EENS}\) in the objective function while also considering the possibility of malfunctions in RCSs and FCBs. While numerous studies have investigated strategies for improving reliability indicators, the economic feasibility of these improvements remains largely unaddressed. Some studies assess reliability improvements without considering the cost of implementation.