<p>Electric spring (ES) is an emerging technology for power quality regulation. At present, the modeling of electric springs is mainly based on integer order calculus. However, inductance and capacitance are essentially fractional orders and their order range can be extended to (0,2). This article introduces fractional order inductors and fractional order capacitors and constructs a fractional order electric spring main circuit with richer and more flexible operating characteristics and better performance by increasing the degrees of freedom of the system. Based on the fractional order mathematical model of electric springs, the analysis shows that the additional order variables of the inductance and capacitance significantly affect the dynamic and static characteristics as well as the output ripple characteristics of power springs. Therefore, fractional order power spring circuit systems with different order combinations can be designed according to different application requirements, such as the need for a fast dynamic response and minimizing output ripple. Furthermore, this article adopts a fractional order dual closed-loop controller to enhance the performance of the electric spring system. Compared to traditional integer order controllers, this controller exhibits significant advantages in terms of improving system stability, response speed, and anti-interference capability. This study provides new ideas and methods for the design and control of electric springs, and has important theoretical and practical value.</p>