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Loop Gain Modeling of a Single-Phase PFC for Online Small-Signal Stability Monitoring

Year: 2023 | Author: Qing Lin | Paper: H5.8
Control loop for single phase PFC
Fig.1.Linear dynamics of a single-phase PFC.
  A loop gain with sufficient margin usually indicates a good design in terms of small-signal stability. Power factor correction (PFC) converters are designed with a proper loop gain before being installed in the field. However, the converter's actual loop gain will change after being connected to different source impedances, which reflects the system's stability condition. Based on the virtual d-q frame modeling concept, his paper proposes a voltage loop-gain model of a PFC converter for both a single-phase and a three-phase system. By comparing with the results of the traditional quasi-static approximation method, which treats the system as a DC system, the proposed model is much more accurate in analyzing a single-phase system; moreover, the traditional approach cannot even be used to analyze a three-phase system. The proposed model can help to apply loop-gain-based stability monitoring of an AC system and guide system operation because it can instruct the understanding of the system conditions' impact on the PFC loop gain. Simulation and experimental measurement results are carried out to verify the proposed model.

  The basic idea of virtual d-q frame modeling for both a single-phase and a three-phase system is to create virtual frames by phase shifting the original systems, and transforming the artificial three-phase-balanced system to another rotating frame, in which the system's operating points are time-invariant, so linearization and small-signal analysis are achievable. Fig. 1 shows the small-signal model of a single-phase PFC when considering the source dynamics ZT, including any source impedance or other PFC converters. ZT can be derived based on the system configuration and parameters, and works with either a single-phase system or a three-phase-four-wire system. Then the PFC voltage open-loop gain can be derived as follows:
PFC voltage open-loop gain derivation
Fig. 2. PFC voltage open-loop gain


  The conventional quasi-static approximation for modeling or measuring a PFC's voltage loop gain is done by approximating the PFC converter's dynamics as that of a DC-DC converter. The input voltage of the DC circuit is frozen to be the same as the RMS value of the AC input voltage of the original circuit. Fig. 2 (a) shows the simulation and modeling results for a single-phase system. The proposed model is much more accurate than the quasi-static approximation. Fig. 2 (b) shows the simulation and modeling results for a three-phase-four-wire system. The results of the proposed model closely match those obtained by simulation.
Loop gain plots
Fig. 3. Loop-gain modeling results and simulation results of a single-phase and a three-phase-four-wire system.

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