Decentralized stability rules for microgrids

Transient Safety Filter Design for Grid-Forming Inverters

“…the invariance of the domain D i [c i ] is guaranteed under bounded disturbances, x j ∈ D j [c j ] , from the neighbors. Note that, for polynomial barrier functions that are quadratic or higher order polynomials, we have ∇B i (0) = 0 , i.e., by construction, the semi-algebraic set (11) leads to sector-like bounds on the control input.…”

Distributed Small-Signal Stability Conditions for Inverter-Based Unbalanced Microgrids

“…Identification of parametric stability conditions for inverterbased microgrids in terms of the droop gains has generated some interest recently [9]- [14]. In [9], the authors used a lossless microgrid model to draw the similarity between droopcontrolled inverters and Kuramoto oscillators, and prescribed droop gain values for frequency synchronization and desirable power sharing.…”

“…A main drawback in the above two works is the assumption of a lossless microgrid, which is invalid in low-to-medium voltage systems with non-negligible line resistance-to-reactance ratios. This assumption has been relaxed in [11]- [14], where the authors derived stability conditions on the droop coefficients for a (lossy) microgrid, which are verifiable locally at each inverter node. In [11], the authors derive closed-form distributed stability conditions involving droop gains and line parameters.…”

“…A sum-of-squares optimization method was used in [12] to compute robust distributed stability certificates on the inverter droop gains, under bounded and time-varying uncertainties. A computational method using the dissipativity approach was proposed in [14] to estimate stability certificates in different frequency regions. The aforementioned works, with the exception of [11], use the conventional quasi-static phasor models, while a dynamic phasor-based modeling approach ( [24]- [26]) is often better suited to capture the electromagnetic transient effects in the stability of microgrids.…”

“…Many of the existing analytical methods used to obtain closed form estimates of the stability regions, on the other hand, suffer from various modeling assumptions that do not hold in practice (e.g. the works of [9]- [14], as discussed in Sec. I-A).…”