Study of generalized electric spring modeling based on Hamilton’s principle and its stability

The proposed generalized electric spring (G-ES) topology effectively reduces the redundancy caused by the parallel structure of multiple electric springs in a microgrid system. A modeling method for the G-ES is urgently needed to accurately determine the G-ES parameters and to evaluate its transient operation characteristics. The correspondence between Hamilton’s principle in mechanics and electricity is introduced, and the feasibility of Hamilton’s principle under the smart load topology is verified. The modeling method of the G-ES under Hamilton’s principle is discussed, followed by the application of repetitive control strategies on the G-ES. The filter parameters are designed using the normalization method and a simplified parameter design using repetitive controllers was applied. This article introduces the impedance analysis method into the generalized electric spring to analyze its stability under weak network conditions. This work also derives the stability judgment criteria for generalized electric springs. Finally, the feasibility of modeling the G-ES based on the Hamilton’s principle was verified using MATLAB and a DSP hardware system. In addition, the consistency between the G-ES and a single intelligent load was verified under the Hamilton’s modeling principle. The G-ES stability and dynamic performance under this modeling method meet industry requirements.