This paper investigates the critical challenge of simultaneously managing electrical energy supply and inertia services in modern power systems. With the increasing share of renewable energy sources and the reduction of mechanical inertia resulting from the replacement of traditional generators, the frequency stability of the grid is compromised. Acknowledging the necessity of new mechanisms, this research offers a comprehensive framework to address this issue.The main problem studied is the modeling of power system operation under the influence of renewable energy sources, considering the concurrent needs for energy and inertia. This model is formulated as a constrained optimization problem, aiming to determine the optimal operational schedule of controllable resources to maximize economic performance and grid stability, while adhering to technical constraints.The primary method employed is the use of mathematical programming and optimization analysis to derive pricing mechanisms. The power system operation problem is modeled, considering the constraint of providing minimum inertia, and Karush-Kuhn-Tucker (KKT) optimality conditions are used for sensitivity analysis and extraction of economic prices. By analyzing the dual variables corresponding to the power balance constraint and the minimum inertia provision constraint, analytical formulas for energy price and the comprehensive price of network inertia services are derived.The extracted prices not only reflect the costs of energy production but also the economic value of inertia services.These results indicate that creating a market for inertia services can provide the necessary incentives for investment in inertia-providing technologies (such as ES) and significantly contribute to enhancing grid stability. The validity of the results is confirmed through simulations on a representative network with a significant share of renewable energy sources and comparison with data. This research provides practical solutions for improving the performance of power systems with a high penetration of renewable energy sources and increasing the stability of the electricity grid.