A Chance-Constrained Decentralized Operation of Multi-Area Integrated Electricity–Natural Gas Systems With Variable Wind and Solar Energy

Time-efficient Joint Chance-constrained Optimal Power Flow with a Learning-based Robust Approximation

“…( 10)-( 11), the uncertainty ω from the wind power affects the power injections on each bus. Based on the power flow model ( 6)- (7), this uncertainty further propagates to the square of the bus voltage U t , branch power flows P t and Q t . Thus, the impacts of this uncertainty must be considered in the OPF model; otherwise, the obtained OPF solutions may be infeasible for ( 8)- (9).…”

“…Reference [6] combined the CC-OPF with the Gaussian mixture model to handle constraints with non-Gaussian uncertainties. In [7], a CC-OPF model was presented to coordinate natural gas systems with power systems. However, most of them, including [4]- [7], used individual chance constraints (ICCs) to describe the probabilistic satisfaction requirement of the power flow constraints under uncertainties, which can not effectively ensure the joint satisfaction of critical constraints of the entire system with a pre-determined probability [8].…”

A two-stage approach for a mixed-integer economic dispatch game in integrated electrical and gas distribution systems

“…Several works, e.g., [5]- [14], study the interdependent operation of an integrated electrical and gas system (IEGS), particularly in determining optimal operating points for the generators. In these papers, the economic dispatch problem is posed as an optimization program where the main objective is to minimize the operational cost of the whole network, which includes electrical and gas production costs, subject to physical and operational constraints.…”

“…In these papers, the economic dispatch problem is posed as an optimization program where the main objective is to minimize the operational cost of the whole network, which includes electrical and gas production costs, subject to physical and operational constraints. Differently from [5]- [14], where a common objective is considered, when DGs are owned by different independent entities (prosumers), the operations of these DGs depend on several individual objectives. In the latter case, to compute optimal operating points of its DG, each prosumer must solve its own economic dispatch problem.…”

“…In Section IV, we show the performance of our algorithm via numerical simulations of a benchmark 33-bus-20-node distribution network. In the preliminary work [26], we show that our two-stage method without the refining iterations obtains solutions with better gas-flow approximation than those of the state-of-the-art method in [11] for the economic dispatch problem of multi-area IEGSs [8], [11], [14], which is an optimization problem with a common and separable cost function, instead of a noncooperative game.…”