Inertia-Aware Microgrid Investment Planning Using Tractable Decomposition Algorithms

The integration of the frequency dynamics into Micro-Grid (MG) investment and operational planning problems is vital in ensuring the security of the system in the post-contingency states. However, the task of including transient security constraints in MG planning problems is non-trivial. This is due to the highly non-linear and non-convex nature of the analytical closed form of the frequency metrics (e.g., frequency nadir) and power flow constraints. To handle this issue, this paper presents two algorithms for decomposing the MG investment planning problem into multiple levels to enhance computational tractability and optimality. Furthermore, the sensitivity of the decisions made at each level is captured by corresponding dual cutting planes to model feasible secure regions. This, in turn, ensures both the optimal determination and placement of inertia services and accelerates the convergence of the proposed decomposition algorithms. The efficient and effective performance of the proposed algorithms is tested and verified on an 18-bus Low Voltage (LV) network and a 30-bus Medium Voltage (MV) network under various operating scenarios.