This paper offers an in-depth investigation into various quantitative assessment methods used to quantify the supply regulation capacity in new types of power systems under different conditions. As new forms of energy, including renewables, are increasingly becoming the predominant sources of power systems, the traditional systems are undergoing transformative modifications to efficiently address the issue of power generation and consumption fluctuations. In this regard, this paper proposes an original framework that combines advanced statistical methods and machine learning. The primary purpose of the framework is to identify the level of resilience and flexible adaptability of new power systems. The paper presents the results of the simulations and real-world applications of the proposed measurement methods in enhancing power supply reliability and efficiency in all conditions. The implications based on the results will be beneficial to policymakers and other specialists who are making decisions involving designing and optimizing modern power systems. Furthermore, the paper aims to contribute to the existing discussion by providing further insights into the effectiveness of the proposed methods of measurement.