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Hybrid energy station (HES) systems coupling diverse energy sectors can facilitate the low-carbon and sustainable transition by integrating massive wind-solar power and energy conversion technologies. With the proliferation of renewable and flexible demand response (DR), different uncertainties are inevitably introduced into energy systems because of external volatile surroundings and internal consumers' mutable behavior. Moreover, the probability distribution function (PDF) of these uncertainties may be unavailable or ambiguous and even affected by decisions. In this work, we propose a hierarchical optimal framework for HES systems, in which the energy hub plant determines the schedules of generation and trade in different markets (upper-level) and users minimize energy expense by managing facilities operations considering decision-dependent uncertainties (lower-level). A scheme of energy transaction options is also provided under the bounded rationality of user sides. To tackle problems with uncertain PDFs, a tailored chance-constrained distributionally robust method is implemented. In the process, the correlation DR operation pattern and analytic pricing formulation are derived incorporating the property of users. Case studies with comparison tests validate the efficacy of the proposed model in handling uncertainties and pursuing economic profits.

The grid integration of renewable energy sources necessitates using energy storage systems (ESSs) to provide more flexibility and controllability. This article proposes a frequency stability-constrained battery energy storage system (BESS) sizing model for microgrids formulated as a mixed-integer linear programming (MILP) problem and decomposed using Benders decomposition. The optimal size of BESS is determined as a trade-off between minimizing the operating costs or maximizing the benefits and the high investment costs of BESS. Both the grid-connected and stand-alone operating modes are modeled for the microgrid along with the corresponding generation contingencies. The microgrid scheduling optimization model is built for cost-benefit analysis considering unit commitment and frequency stability (FS) constraints. The transient frequency dynamics are considered using an accurate time-domain model based on the discretized swing equation. The proposed method ensures frequency stability criteria, such as frequency nadir/overshoot, rate of change of frequency (RoCoF), and steady-state frequency, are within their allowable ranges following generation contingencies. Simulation results based on a medium-voltage microgrid test case with historical data of load, PV generation, and market price verify the effectiveness of the proposed method.