Frequency domain analysis of three phase linear current regulators

TLDR

Stationary‑frame linear PI current regulators are inadequate for AC systems due to steady‑state errors, while synchronous‑frame regulators eliminate these errors by operating on DC signals in a rotating reference but at the cost of complex transformations. This study introduces a Laplace‑domain modulation technique to compare stationary and synchronous‑frame PI regulators and to design a new stationary‑frame resonant regulator that achieves zero steady‑state error without complex transformations. The authors model the stationary‑to‑rotating and rotating‑to‑stationary transformations as frequency‑domain modulation processes, enabling a unified comparison of PI regulators and the synthesis of the resonant regulator. The new resonant regulator performs equivalently to the synchronous‑frame PI regulator.

Abstract

Stationary frame linear PI current regulators are conventionally regarded as unsatisfactory for AC systems because they cannot eliminate steady state errors. Consequently, synchronous frame regulators are perceived to be superior, since they achieve zero steady state error by acting on DC signals in a rotating frame of reference. However, a synchronous frame regulator is more complex, and requires in particular a way of transforming a measured stationary frame AC current (or error) to rotating frame DC quantities, and transforming the resultant control action back to the stationary frame for implementation. This paper presents a technique for interpreting the stationary/rotating frame transformations as modulation processes in the Laplace domain which move the control function from one part of the frequency spectrum to another. The technique is used to compare stationary and synchronous frame PI regulators on a common basis to better understand the advantages of a synchronous frame regulator, and then to develop a new form of stationary frame resonant regulator which achieves zero steady state error without requiring the complex transformations of a synchronous frame regulator. The performance of this new regulator is evaluated and found to be equivalent to that of the synchronous frame PI regulator.