Sizing capacities of renewable generation, transmission, and energy storage for low-carbon power systems: A distributionally robust optimization approach

To decrease carbon dioxide emission, a high penetration level of renewable energy will be witnessed over the world in the future. By then, energy storage will play an important role in power balancing and peak shaving. This paper considers the capacity sizing problem during the transition to a low-carbon power system: the retirement plan of conventional fossil-fuel generators and the growth of demands are given. The renewable generation capacities at given sites are to be determined in coordination with the upgrade of transmission lines and installation of energy storage units. In order to capture the inaccuracy of empirical probability distributions for uncertain renewable output and load profiles, a novel distributionally robust bi-objective sizing method using Wasserstein-metric-based ambiguity sets is proposed. The total investment cost and expected carbon dioxide emission subject to operating conditions and a load shedding risk constraint are minimized. The distributionally robust shortfall risk of load shedding and the worst-case expectation of carbon dioxide emission are reformulated into computable forms based on calculating the Lipschitz constants. The final problem comes down to solving mixed-integer linear programming problems. The numerical results demonstrate the effectiveness of the proposed method and the necessity of using distributionally robust optimization.