Adaptive robust framework for microgrid-integrated generation and network planning under uncertainty☆ ☆

With the proliferation of renewable energy resources and amplifying load demand, the capacity expansion planning problem becomes more challenging, primarily due to uncertainties. This paper employs adaptive robust optimization to address the expansion planning problem for transmission line networks and microgridbased generation units. The key objective is to determine optimal expansion planning decisions that minimize the net system planning cost by anticipating the worst possible realization of long- and short-term uncertainties over the planning horizon from the perspective of a central planner. To model long-term uncertainties associated with future stochastic power generation capacity and power consumption, a cardinality-constraint uncertainty set is formulated. Short-term uncertainties in stochastic power capacity and electricity demand are represented by a set of representative hourly operating conditions. The proposed formulation is structured as a three-level mixed-integer optimization problem under uncertainty, which is subsequently recast into a bi-level optimization problem by amalgamating the second-level objective function with the dual of the third-level optimization problem. This resulting formulation is effectively solved through a tailored column-and-constraint generation algorithm. Numerical analysis has been conducted on the IEEE 24-bus and South Brazilian 46-bus Test systems to demonstrate the proposed model's capacity and efficacy in expansion planning across diverse operational conditions.