Accurate High Frequency Modelling of the Input Admittance of PWM Grid-Connected VSCs

Abstract

This paper addresses high frequency admittance modelling of current-controlled voltage source converters (VSCs). Recent studies have shown that harmonic instability may also occur at frequencies above the Nyquist frequency. To form an accurate multiple-frequency model in this frequency range, sidebands that originate from modulation and sampling must be examined. In this paper, an accurate small-signal model is developed taking into account an adequate digital pulse-width modulator (DPWM) representation, which allows to predict dependence of the frequency response on the steady-state DC (SSDC) operating point. It is shown that, when center-pulse sampling is implemented, PWM sidebands do not create additional loops leaving only sampling sidebands to be considered. Using the same approach as for SS-DC operation, a model which accurately represents admittance measurements during sinusoidal AC (S-AC) operation is developed. Its basis is a novel DPWM model suitable for S-AC regime, which allows to predict dependence of the VSC’s input admittance on the grid voltage magnitude. Experimental and simulated admittance measurements, performed on a single-phase two-level VSC during various SS-DC and S-AC regimes, show an excellent match with the proposed models up to twice the sampling frequency

Passivation of Grid-Following VSCs: A Comparison Between Active Damping and Multi-sampled PWM

“…where m is the modulating waveform, equal to v i,r after one step delay, and d is the continuous-time duty-cycle of x, used in averaged modeling [5]. From (2), it is clear that digitallycontrolled VSCs exhibit operating point dependency, which is often overlooked when using delay or ZOH models for the DPWM, due to its limited impact at low and medium frequencies [45]. However, in [45], it is shown that this nonlinearity may yield significant impacts in the high frequency range.…”

“…From (2), it is clear that digitallycontrolled VSCs exhibit operating point dependency, which is often overlooked when using delay or ZOH models for the DPWM, due to its limited impact at low and medium frequencies [45]. However, in [45], it is shown that this nonlinearity may yield significant impacts in the high frequency range. For D = 0.5, DPWM model reduces to a pure time delay e −s Ts 2 .…”

“…Some mismatch is seen close to f s . Using the analytical approach from [45], where sampling sidebands are taken into account, near-perfect match is obtained up to 2f s . Note the existence of two nonpassive zones, where phase drops below −90 degrees.…”

“…The admittance Y i in(6) is the so-called single-frequency model[8],[45]. For digitally controlled VSCs, sampling and PWM create sideband components that can be taken into account using multi-frequency modeling[8].…”

Passivation of Grid-Following VSCs: A Comparison Between Active Damping and Multi-sampled PWM

“…Note that these measurements were conducted, and the results were found to be somewhere in between dc results for all operating points in the sinusoidal ac range. More considerations on this can be found in [42], [45].…”