State-Space Modeling Techniques of Emerging Grid-Connected Converters

Abstract

In modern power electronics-based power systems, accurate modeling is necessary inorder to analyze stability and the interaction between the different elements, which are connected toit. State space modeling seems a valid approach to study the modes of a certain system and theircorrelation with its states. Unfortunately, this approach may require complicated calculations andit is difficult to model advanced or emerging control techniques for grid-tied converters, such ascascaded controllers (e.g., voltage and current) and virtual synchronous generators (VSGs). Moreover,this approach does not allow an easy reconfiguration of the modeled system by adding, removing ofmodifying certain elements. To solve such problems, this paper presents a step-by-step approach tothe converter modeling based on the Component Connection Method (CCM). The CCM is explainedin detail and a practical example is given, by modeling one exemplary VSG model available inthe literature. The obtained model is finally validated experimentally to demonstrate the practicalaccuracy of such approach.

The Sensitivity of Grid-Connected Synchronverters With Respect to Measurement Errors

“…To find the equilibrium points of the model ( 18), we set u = 0 andż = 0 in (18). The following result, taken from [16,Sect.…”

“…4], concerns mainly the equation that must be satisfied by the active power P at an equilibrium point. Proposition 3.1: Consider the model (18), with u = 0. We assume that R, L, J, m, D p , D q ,V, ω g , ω n , v set > 0 and the real parameters T m and Q set are given.…”

“…Thus, if the system was at equilibrium before this rotation by π, then it must be again at equilibrium. Remark 3.4: There is an exceptional infinite set of equilibrium points of the system (18), which corresponds to the parameters T m and Q set chosen such that…”

“…The set of equilibrium points of (18) where i e f > 0 can be parametrized by the corresponding powers (P, Q), and then it is a two-dimensional manifold diffeomorphic to R 2 \ {M}. Remark 3.5: The real system can never reach an equilibrium point with the property i e f ≤ 0.…”

“…We consider the output of the system (18) to be the grid currents (in dq coordinates), y = [i d i q ] . We linearize this system near the stable equilibrium point, to explore the small signal behavior of the dq currents as a result of the measurement errors.…”