This chapter presents advanced mathematical models and programming tools for optimizing the composition and operational modes of energy systems amid the rapid expansion of renewable energy capacities, with a specific focus on Ukraine. The study introduces dynamic models for cyclic development, incorporating economic and technological indicators with discrete stochastic variables, and illustrates the technological evolution via logistic curves. Key indicators such as the Levelized Cost of Electricity (LCOE) and the Levelized Avoided Cost of Electricity (LACE) are utilized to evaluate the economic competitiveness of various energy generation technologies. Methodologies for economic-technological forecasting and optimal energy system functioning are explored, providing scenarios for the Integrated Power System (IPS) of Ukraine until 2040. The models address the minimization of inconsistency between energy supply and consumption, considering constraints and optimization criteria for various power plants and storage units. Implemented in the MathProg language through SolverStudio, the models assess generation, storage, and import/export modes, evaluating operational constraints to optimize cost and system stability. The study demonstrates significant potential for reducing electricity production costs while enhancing the stability and robustness of the Ukrainian power system. Overall, this research contributes valuable insights into energy system optimization and the sustainable management of energy resources.