A Comprehensive Electric Spring Modeling in a Synchronous Reference Frame

Electric Spring (ES) is one of the most promising technologies to stabilize the supply voltage of the critical loads of a user. Different versions and evolutions of ES have been proposed, whose novelties mostly stand in their circuital architecture and steady-state behavior. Nevertheless, a dynamic model of a single-phase user load equipped with ES have not been investigated yet for loads of resistive-inductive type. In this paper such a modeling is performed, disregarding its control strategy and if it whether exchanges only reactive or both active and reactive power. The obtained model has the peculiarity of being universal for a user load equipped with ES and the possibility of being applied for the development of any control strategy. At first, the time-domain equations relevant to the circuit are derived to achieve the state-space model. Subsequently, the equations that uses the dq components of the circuit quantities in a synchronous reference frame are derived, obtaining the state-space model in dq. The verification of such a modeling is performed through comparison of its outputs with those from the circuital simulation in the Simulink/Matlab environment of the whole circuit. As final step, the convenience of the state-space model is discussed for different ES control strategies.