Abstract
Small-signal modeling of converters interfacing with ac power systems is difficult as they involve time-periodic quantities in the steady-state and their linearized dynamics result in a linear time-periodic (LTP) system. This paper presents signal-flow graphs for LTP systems to complement the harmonic linearization method and simplify the modeling process. The proposed graphs visually describe the flow of small-signal perturbation through converters and frequency cross-coupling among different variables. Since complex PLL structures are most difficult to model in a converter control system, the paper demonstrates modeling using signal-flow graphs for two single-phase PLLs: SOGI-PLL and Park-PLL. The developed loop-gain models accurately predict the phase-lag introduced by orthogonal signal generator block in these PLLs, which limits the maximum bandwidth for which a PLL can be designed. Automated modeling using a signal-flow graph solver is also presented.
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