Identifying Optimal Energy Flow Solvability in Electricity-Gas Integrated Energy Systems

Significant growth in gas-fired generator use has strengthened the interdependence between the electrical power systems and the natural gas systems. It is therefore imperative to analyze both systems jointly as an electricity-gas integrated energy system (IES). However, peak electricity and gas demands, intermittent renewable- resource power generation, and severe contingencies can result in an unsolvable optimal energy flow (OEF). Unsolvable OEF poses a serious threat to IES because a secure operating condition is unavailable without corrective controls. Thereby, this paper proposes three models for identifying OEF solvability. Model I minimizes the square of the energy flow mismatches, and Model II maximizes the loadability. Both Models I and II add slack variables to equality constraints, while Model III relaxes inequality constraints. Meanwhile, bidirectional gas flow models are employed. Based on Models I-III, the OEF feasibility margin and the infeasibility degree are defined. Case studies integrate an IEEE 39-node system and a 48-node gas network for validating the proposed models.