# Description of the modelling details This section provides a description of the modelling procedures implemented across the Pharoes suite of tools—**CERES**, **KAIROS**, and **FIDES**. Our approach aims to achieve sufficient **technical transparency**, **mathematical rigor**, and **system realism**, ensuring users understand the assumptions, simplifications, and advanced techniques embedded in each solution without overcomplicating the descriptions with excessively complex formulations. --- ## {doc}`Long-term system expansion using decomposition` CERES applies Benders decomposition to solve the long-term power system expansion planning problem using a Least-Cost Planning (LCP) framework. This approach separates the investment (master) problem from the operational (subproblem) model, which covers hourly dispatch across multiple scenarios and years. The decomposition allows high-resolution operational modeling with scalable investment optimization. --- ## {doc}`Randomized outage and scenario generator with variance reduction` FIDES performs high-fidelity reliability analysis of power systems using Monte Carlo simulation. To increase computational efficiency and statistical coverage, it employs Latin Hypercube Sampling (LHS) to generate representative outage schedules for power system assets that deliver reduced variance converging in less number of iterations. These schedules are based on customized probability distributions for time between failures (TBF) and time to recover (TTR), capturing the stochastic nature of outages across generation, storage, and transmission components. --- ## {doc}`Thermal and renewable generation` KAIROS models thermal and renewable power generation with high fidelity, capturing operational and physical constraints that govern real-world generator behavior. These constraints play a critical role in producing realistic and implementable unit commitment and dispatch schedules, particularly in systems with high renewable penetration, tight reserve margins, or strong technical requirements. --- ## {doc}`Hydropower generation ` Hydropower modeling in KAIROS captures the essential operational and environmental aspects of reservoir and run-of-river systems. This includes accurate representation of power-water conversions, pumping operations, reservoir balances, and physical limitations of both storage and waterways. These formulations ensure realistic dispatch, planning, and reliability analysis involving hydroelectric resources. --- ## {doc}`Power demand and flexible consumers ` KAIROS models short-term flexibility sources on the demand side (DSM) to simulate operational responses over sub-hourly to daily horizons. These mechanisms allow modeling of load shifting and flexible demand behavior. The following constraints ensure that these technologies are correctly represented in the optimization problem. --- ## {doc}`Power flows characterization ` KAIROS models short-term flexibility sources on the demand side (DSM) to simulate operational responses over sub-hourly to daily horizons. These mechanisms allow modeling of load shifting and flexible demand behavior. The following constraints ensure that these technologies are correctly represented in the optimization problem. --- ## {doc}`Storage characterization ` KAIROS supports accurate modeling of electricity storage systems, incorporating key operational constraints and temporal dynamics. These constraints are essential for representing short- and long-duration storage assets in unit commitment, dispatch optimization, and energy planning models. The formulation includes energy balance equations, operational limits, and power flow restrictions. --- ## {doc}`Input data schema ` This section describes the input data structure, format, and units used in our suite of solutions. Our tools are designed to ensure flexibility, interoperability, and transparency, enabling users to integrate diverse datasets efficiently while maintaining high computational performance. ---