Flexibility Characterization of Sustainable Power Systems in Demand Space: A Data-Driven Inverse Optimization Approach

The deepening of the penetration of renewable energy is challenging how power system operators cope with their variability and uncertainty. The inherent flexibility of dispathchable assets present in power systems, which is often ill-characterized, is essential in addressing this challenge. Several proposals for explicit flexibility characterization focus on defining a feasible region that secures operations either in generation or uncertainty spaces. The main drawback of these approaches is the difficulty associated with relying solely on visualizing this feasibility region when there are multiple uncertain parameters. Moreover, these approaches focus on system operational constraints and often neglect the impact of inherent couplings (e.g., spatial correlation) of renewable generation and demand. To address these challenges, we propose a novel data-driven inverse optimization framework for flexibility characterization of power systems in the demand space along with its geometric intuition. The approach captures the spatial correlation of multi-site renewable generation and load using polyhedral uncertainty sets. Moreover, the framework projects the uncertainty on the feasibility region of power systems in the demand space, which are also called loadability sets. The proposed inverse optimization scheme, recast as a linear optimization problem, is used to infer system flexibility adequacy from loadability sets as a scalar quantity.