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All-pass-filter-based active damping for VSCs with LCL filters connected to weak grids

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Figure

Fig. 1.Electrical diagram of a VSC connected to a weak grid via afilter. The controlled variable is LCL i2(t).
Fig. 3.Nichols chart ofmargin is(dashed) P(ejωts), when (solid) φg ≈ 80 deg, and when φg ≈ 0 deg
Fig. 5 shows the phase of D(value that givesd′(ejωts) (fs = 10 kHz) for′ ∈ (0, 1). The phase for a given resonance frequency ωrfr in Hertz) can be modified by changing d′
Fig. 6. (left) Phase response of Dand′(z) designed with two points (φ1 for ωand1 φ2 for ω2)
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