Distributionally Robust Optimization for Generation Expansion Planning Considering Virtual Inertia from Wind Farms

High penetration of renewable energy generation imposes two significant challenges to power systems: the stability problem caused by low inertia and the reliability problem caused by generation uncertainties. Although these challenges have been widely recognized, their impacts on the optimal generation capacity mix have not been explicitly revealed and quantified. Luckily, with advanced converter control strategies, renewable generators may also provide the so-called virtual inertia similar to conventional inertia provided by thermal generators. This paper proposes a novel distributionally-robust-optimization-based generation expansion planning model considering the virtual inertia support from wind farms. The proposed model minimizes the generation expansion cost under uncertainty while maximizing the probability with which the system can fully absorb renewable energy generation. The constraints include expansion limits, unit commitment constraints, frequency requirements, virtual inertia provision, and distributionally robust joint chance constraints. The proposed formulation is recast into a mixed-integer second-order conic model and solved efficiently via commercial solvers. Case studies are carried on a 9-bus system and the IEEE 118-bus system to demonstrate the validity and scalability of the proposed method and highlight the importance of incorporating inertia response services