This paper proposes a novel mathematical approach to deal with cyberattacks impacting on modernized microgrid's tertiary control. Modernized microgrids use many entities based on voltage-source converters to form the fully integrated power and energy system. Having such a power and energy system for modernized microgrids necessitates engineers considering cybersecurity and addressing its effects from the beginning of designing and building systems. Using innovative mathematical tools based on information gap decision theory (also known as IGDT), this paper incorporates the data integrity attacks into tertiary controls of the fully integrated power and energy system of modernized microgrids. The proposed methodology [named cyberattack-tolerant tertiary control (CT 2 C) herein] is able to effectively find the most susceptible points of cyberattack in modernized microgrids when both severe and negligible uncertainties caused by cyberattacks take place. They are able to include both severe data integrity attacks and negligible ones (or undetectable attacks). Here, the most vulnerable points of cyberattack cause the most impactful changes in the tertiary control's principal objective, which is minimizing the operating cost of the whole modernized microgrids. In this regard, this paper describes a hypothesis, and in supporting that, comparative simulation results are given. The outcomes generated by the General Algebraic Modeling System (commonly known as GAMS) environment are able to provide researchers and engineers with appropriate maps for sensitive points of cyberattack. Using the proposed CT 2 C, investments in modernized microgrids cybersecurity will be more accurate and, more importantly, mathematically optimized. Finally, potential ways to implement the proposed methodology are elaborated.Index Terms-Cyberattack (CA), fully integrated power and energy system (FIPES), information gap decision theory (IGDT), modernized microgrid (MMG), operating cost (OC), points of cyberattack (PoCA), tertiary control.