Small-Signal Stability-Constrained Source–Storage Capacity Optimization for Islanded Microgrids
Keywords:
islanded microgrid, capacity optimization, grid-forming storage, small-signal stability, surrogate modelingAbstract
Islanded microgrid planning is usually settled on cost and energy adequacy, with converter stability examined only after photovoltaic and battery ratings have been fixed. That sequence can admit a low-cost design whose dominant modes are poorly damped. This paper places the stability test inside the capacity search. The decision vector contains photovoltaic rating, battery converter power, battery energy, two droop coefficients, and virtual inertia. Each candidate is first evaluated by chronological hourly dispatch and then by a capacity-dependent small-signal model. Feasibility requires a loss-of-power-supply probability below 0.5%, a spectral abscissa no greater than −0.60 s−1, and a minimum oscillatory-mode damping ratio above 8%. In the 8760-h study, designs selected only by cost or reliability fail at least one dynamic requirement, whereas the joint formulation identifies 89 candidates that satisfy all three limits. The selected design has a spectral abscissa of −0.632 s−1 and a minimum damping ratio of 0.421. A polynomial surrogate is used only to screen candidates; all reported designs are checked with the state matrix. Stress maps, modal participation, monthly energy accounting, and the annual state-of-charge duration curve show which constraint becomes active and why.
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