*2.2. Modeling for System Reliability*

Often in the literature, the terms *security* of electricity supply, power system *reliability*, and power system adequacy are used interchangeably. Heylen et al. [32], in their comprehensive review of reliability indicators, provided a classification where system reliability is composed of system adequacy and system security. System adequacy refers to the ability of the supply to meet the demand in regular circumstances. System security refers to the ability of the system to accommodate disturbances. Many different indicators exist in both categories and, often, they are related to each other to different extents.

Peter and Wagner [19] utilize a commonly used approach with respect to the measure of system reliability in their hybrid model. The reliability measure *expected energy unserved* (EEU) characterizes the overall system reliability. It is, essentially, the expected load level

that cannot be served over a time span and is defined based on *loss of load probability* (LOLP), a common system adequacy indicator. The contribution of individual technologies to the system reliability or their *capacity value* can be defined via *equivalent firm capacity* (EFC), where the term 'firm' refers to only the amount of capacity that actually contributes to electricity generation. Thus, the capacity of an individual technology is practically a share of its overall installed capacity that contributes to the decrease in the loss of load probability and, thus, improves system reliability.

System reliability is a system-level issue and, thus, should be studied by system-level models. The reliability of electricity supply depends on all power plants, storage solutions, and demand flexibility available in the system, and all of these actors should be taken into account. Typically, long-term energy system optimization models have been used for this matter. In such models, the evolution of the power-generation technology mix can be traced, and its reliability can be assessed, usually on a year-by-year basis and sometimes while taking into account seasonal, weekly, or day/night variations in the supply and demand. However, with the increasing share of renewable energy sources, in which the power output varies from hour to hour and from day to day, a necessity for integrating more fine resolutions into those models arose [20]. Operational power system models match the supply and demand on an hourly basis and are commonly utilized by system operators to balance the system. Such models, however, do not have room for new investments and long-term technology mix evolution [33]. Thus, policymakers call for hybrid models that are able to combine short-term power variations and long-term technology development [34].

A handful of studies attempted to integrate the finer details of operational power system models into long-term energy system models [19,35]. Peter and Wagner [19] specifically focused their modeling efforts on accounting for the complementarity of renewable energy. The operational detail of the model allows for capturing the temporal and spatial heterogeneity of renewable energy power generation. When available in the region, the anti-correlation of wind speeds is translated into a reliability value for the energy system. The more nonsynchronous the power-generation profiles of wind farms, the larger their overall contribution to the energy system adequacy and the less backup capacity needed to support such a system. The authors estimate that such a wise investment approach into renewable energy would allow for avoiding 66 GW of unnecessary backup capacities at an annual cost of 3.8 billion euros by 2050 in Europe [19].

Methodologically wise, energy system models and operational power system models are often simulation-based and often embody analytical and hybrid approaches [20,36]. Critical design decisions in these models include the scope and resolution of temporal, technical, and spatial representation [20].
