A Matrix-Based Multifrequency Output Impedance Model for Beat Frequency Oscillation Analysis in Distributed Power Systems

Harmonic Stability in Power Electronic-Based Power Systems: Concept, Modeling, and Analysis

“…A similar harmonic instability phenomenon has also been seen in the dc systems, where the interconnected dc-dc converters with different switching frequencies can interact with each other, resulting in beat frequency oscillations [39]. The other case is the negative damping added above the Nyquist frequency by the ACC loop with the reduced time delay [15], and the negative damping may destabilize the LC resonance frequency above the Nyquist frequency.…”

Investigation of the sideband effect for the LCL-type grid-connected inverter with high LCL resonance frequency

“…Compared with the harmonic spectrum of PWM modulation in DC system, the harmonic spectrum of sinusoidal PWM modulation in AC system is much more complicated when the reference modulating waveform contains both the fundamental and perturbation components. Moreover, when the digital control is employed, the sampling and hold (S&H) procedure also introduces sideband components [11]. Therefore, when the sampling frequency is different from the switching (carrier-) frequency, the output of the digital sinusoidal PWM modulator will contain multiple sideband harmonics.…”

“…Therefore, ZOH model may lose much of the essential dynamics digital SPWM modulator. In order to fully describe the high-nonlinearity of PWM modulation, multi-frequency model has been developed in the dc system both for the analog control [10] and digital control [11]. Yet, both the multi-frequency model and the impedance matrix are established at the dc steady-state operating point, which is not readily used for the paralleled inverters, due to the timevarying operating point with the sinusoidal fundamental waveform.…”

Generalised average modelling of grid‐connected three‐phase VSC with closed‐loop vector control and regular‐sampled modulation

“…In order to consider the switching process and investigate the harmonic dynamics of the power converters, extended harmonic domain (EHD) [6–10], harmonic state‐space (HSS) [11–15], and generalised averaging method (GAM), also named as the multifrequency averaging method [16–23], models have been introduced. The EHD models can consider the high‐order harmonic interactions of the power converters, and have been used to address the issues such as the steady‐state analysis and design of passive components for VSCs [9], and the optimal design of distributed generation units [10].…”

“…However, the existing EHD models mainly concentrate on the open‐loop circuits and the control dynamics of the converters have been overlooked [14]. Based on the linear time‐periodic (LTP) system theory [23] and the harmonic transfer function concept, the HSS model can be constructed in the frequency domain to investigate the harmonic stability issues for complex power electronics systems, like the cross‐coupling dynamics caused by the harmonic interactions between paralleled closed‐loop three‐phase grid‐connected converters [12], the sideband effect of the PWM modulation [13], and the asymmetrical controller behaviours [14]. However, the HSS models are linearised small‐signal models in the frequency domain, which are good tools for optimal controller design and harmonic interaction analysis, but are unsuitable for power system‐level studies, in which large‐signal models must be considered.…”