When several grid-forming battery energy storage systems (BESS) operate in the same low-inertia network, the virtual inertia and damping of each unit affect not only the system frequency but also local rates of change of frequency (RoCoF) and the damping of oscillatory modes in which the converters participate. Tuning each unit independently, or splitting a system-wide requirement uniformly or by rating, ignores these network effects. This paper formulates the coordinated selection of the virtual inertia H_v and damping D_v of multiple virtual synchronous machines (VSMs) as a constrained optimization problem. The objective is the total storage burden, defined as the converter headroom plus the sustained power share. The constraints are the bus-level RoCoF for every single-bus contingency, the centre-of-inertia (COI) nadir, the minimum damping ratio of electromechanical modes and the converter ratings. The problem is solved by sequential quadratic programming on an exactly discretized linear model of a Kron-reduced network, and a scenario-based robust variant covers a tie-line outage, a 20 % inertia reduction and a 25 % larger disturbance. On a two-area test system with four grid-forming BESS, coordination reduced the storage burden by 8.6 % and the sustained reserve by 29 % relative to the best uniform allocation. A network-agnostic COI-based design violated the damping limit (ζ = 0.047 against 0.10). Nominal designs, whether coordinated or not, failed at least two of the four stress scenarios, whereas the robust coordinated design satisfied all of them at 6.2 % lower burden than a robust uniform design. Modal analysis showed that the critical 1.98 Hz mode is controllable only from two of the four units, which explains the non-uniform optimum.
Coordinated Virtual Inertia and Damping Optimization of Multiple Grid-Forming Battery Energy Storage Systems
DOI:
Abstract
References
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