he frequency of the power system faces challenges with the growing share of renewable energy and the decreasing inertia. It’s urgent to allocate fast demand response resources for frequency regulation. In this paper, the feasibility that inverter air conditions, energy storage and electric vehicles provide frequency regulation reserve is analyzed. A frequency constrained combined economic dispatching model (FCCED) considering the above fast demand response resources is established to uniformly allocate the frequency regulation reserve between generators and loads. Then, a data-driven method based on the high dimensional model representation (HDMR) is proposed to convert the above high-order, nonlinear and implicit frequency security constraint to a low-order and explicit constraint. As a result, the proposed FCCED model can be solved easily. Finally, the modified IEEE 30-bus system validates the effectiveness of the proposed method. It is explained that the proposed frequency security constraint ensures that the abnormal frequency of the system under unbalanced power is within the constraint. And fast demand response resources have an important positive effect on improving the frequency toughness of the system. This work is supported by the National Science and Technology Innovation 2030 Project (No. 2021ZD0112700).