Decentralized frequency restoration and stability enhancement for virtual synchronous machines at economic dispatch in islanded microgrid

Embedding incremental cost (IC) function into the primary control layer of dispatchable virtual synchronous machines (VSMs) enables decentralized economic dispatch (ED) within autonomous microgrids ( μ Grids). This integration minimizes generation costs and provides virtual inertia, enhancing frequency stability. However, it introduces persistent frequency deviations due to the decentralized nature of the model, necessitating secondary frequency control methods to address the deviation. Existing decentralized secondary frequency control strategies, while capable of addressing these deviations, fail to maintain the ED objective. In response to this challenge, this paper first proposes a practical control framework based on integral controllers for grid-forming VSMs. The goal is to restore the frequency of an autonomous μ Grid in a decentralized manner while achieving ED. Although the proposed controllers effectively maintain ED, a small, controllable frequency error must be preserved to sustain decentralized ED. Secondly, the paper proposes a dynamic reactive power control loop to enhance μ Grid stability while retaining the dynamic characteristics of VSMs. Comprehensive small-signal stability analyses are conducted under various conditions to verify improvements in the stability margin. The efficacy of the proposed scheme is validated through extensive time-domain simulations and control-in-loop real-time OPAL-RT simulator tested on the IEEE 38-node μ Grid. • Embedding the incremental cost function into the virtual synchronous machines model. • The combination enables online economic dispatch (ED) and virtual inertia provision. • Frequency restoration, online ED, and inertia emulation are achieved simultaneously. • A dynamic outer voltage controller to improve microgrid stability limit is proposed. • Verified via real-time experiment, small signal stability, and sensitivity analysis.