Optimal operation of multi-energy carriers considering energy hubs in unbalanced distribution networks under uncertainty

This article presents a two-stage stochastic programming model to address the dispatching scheduling problem in an energy hub, considering an unbalanced active low-voltage (LV) network. A three-phase version of the second-order cone relaxation of DistFlow AC optimal power flow (AC-OPF) is employed to incorporate unbalanced network constraints, while the objective minimizes the Local Energy Community (LEC) operational cost. The model results have been validated using OpenDSS, encompassing energy losses, voltage levels, and active/reactive power. Likewise, a comparative analysis between the three-phase model and the traditional single-phase model, using a modified version of the IEEE European LV Test Feeder as a case study, reveals interesting differences, such that the single-phase model underestimates voltage limits during photovoltaic (PV) system operation and overestimates energy purchased from the main grid, compared with the three-phase model. Similarly, the comparison results reveal that discrepancies between the single and three-phase models intensify as the power injected from PV systems rises. This notably impacts the total energy purchased from the grid, battery operation, and the satisfaction of thermal consumption through electricity. Finally, while the three-phase model offers valuable insights into security levels for voltage and grid energy purchase, its longer computational time makes it more suitable for strategic use rather than daily operational frameworks.