Analysis and Design of Resonant Current Controllers for Voltage-Source Converters by Means of Nyquist Diagrams and Sensitivity Function

The following two types of resonant controllers are mainly employed to obtain high performance in voltage-source converters: 1) proportional + resonant (PR) and 2) vector proportional + integral (VPI). The analysis and design of PR controllers is usually performed by Bode diagrams and phase-margin criterion. However, this approach presents some limitations when resonant frequencies are higher than the crossover frequency defined by the proportional gain. This condition occurs in selective harmonic control and applications with high reference frequency with respect to the switching frequency, e.g., high-power converters with a low switching frequency. In such cases, additional 0-dB crossings (phase margins) appear; therefore, the usual methods for simple systems are no longer valid. In addition, VPI controllers always present multiple 0-dB crossings in their frequency response. In this paper, the proximity to the instability of PR and VPI controllers is evaluated and optimized through Nyquist diagrams. A systematic method is proposed to obtain the highest stability and avoidance of closed-loop anomalous peaks: it is achieved by the minimization of the inverse of the Nyquist trajectory distance to the critical point, i.e., the sensitivity function. Finally, several experimental tests, including an active power filter that operates at a low switching frequency and compensates harmonics up to the Nyquist frequency, validate the theoretical approach.