Modeling and Simulation of a Reduced-Order Single-Phase PQ Inverter Using the Dynamic Phasor Method

Modeling Lyapunov Control-Based Selective Harmonic Compensated Single-Phase Inverter in the Dynamic Phasor Domain

“…Then, the averaged and DP models of the power stage are presented. In the process of deriving the DP model, the fundamental, third, fifth, and seventh harmonics are assumed to be dominant in the AC side whereas the DC source dynamics and switching harmonics are both neglected [19].…”

“…The nonlinear load is a singlephase DBR feeding an LCR (inductive-capacitive-resistive) load. The DBR is assumed to be working in the continuous conduction mode (CCM) [19]. The distorted current drawn by the nonlinear load is prevented from distorting the gridforming inverter's output voltage by adopting a Lyapunovfunction-based control strategy.…”

“…where 𝐷 𝑠𝑛 = (sin(𝑛𝛿/2))/𝜋𝑛, is amplitude of the switching function, 𝛿 is the conduction angle of the diode switch in radians, and 𝜗 is the phase angle of the monopolar switching function relative to the reference voltage/current. Assuming that 𝜗 = 0 and 𝛿 = 𝜋 (i.e., CCM mode) result in 𝑆 = The equations governing the DBR operations in the DP domain are given by [19]:…”

“…For the simulation result, the step change is performed at 𝑡 = 0.3 s. Before the step change (i.e., when 𝑅 𝑜 = 37.5 Ω), notice that there is a notch in the 𝑣 𝑑 waveforms obtained from the experimental test rig and the SW model. This is because the DBR is not strictly operating in the CCM mode (see [19]). As the DP model has been developed under the assumption of CCM operation, it is unable to capture that notch.…”

“…-by-4 matrix in (75) is the Jacobian matrix, 𝐴. The characteristic equation of the closed-loop system is[19]: det(𝑠𝐼 − 𝐴) = 𝐸 4 𝑠 4 + 𝐸 3 𝑠 3 + 𝐸 2 𝑠 2 + 𝐸 1 𝑠 + 𝐸 0 (76)…”