Heating, ventilation and air-conditioning (HVAC) systems constitute the majority of the demands in modern power systems for aggregated buildings. However, HVAC integrated with renewable energy sources (RES) face notable issues, such as uneven demand–supply balance, frequency oscillation and significant drop in system inertia owing to sudden disturbances in nearby generation for a longer period. To overcome these challenges, load frequency control (LFC) is implemented to regulate the frequency, maintain zero steady-state error between the generation and demand, reduce frequency deviations and balance the active power flow with neighboring control areas at a specified value. In view of this, the present paper investigates LFC with a proposed centralized single control strategy for a micro-grid (µG) system consisting of RESs and critical load of a HVAC system. The proposed control strategy includes a newly developed cascaded two-degree-of-freedom (2-DOF) proportional integral (PI) and proportional derivative filter (PDF) controller optimized with a very recent meta-heuristic algorithm—a modified crow search algorithm (mCSA)—after experimenting with the number of performance indices (PICs). The superiority of both the proposed optimization algorithm and the proposed controller is arrived at after comparison with similar other algorithms and similar controllers, respectively. Compared to conventional control schemes, the proposed scheme significantly reduces the frequency deviations, improving by 27.22% from the initial value and reducing the performance index criteria (ƞISE) control error to 0.000057. Furthermore, the demand response (DR) is implemented by an energy storage device (ESD), which validates the suitability of the proposed control strategy for the µG system and helps overcome the challenges associated with variable RESs inputs and load demand. Additionally, the improved robustness of the proposed controller for this application is demonstrated through sensitivity analysis with ±20% μG coefficient variation.