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The global experience on wind farm development reveals that the wind power uncertainty is affected by large-scale wind farm sizes due to the spatial smoothing effect. The dependence on wind farm sizes features the wind power uncertainty as decision-dependent uncertainty (DDU) during the wind farm expansion process. This paper proposes a stochastic expansion planning model for large-scale wind farms considering the DDU and addresses the coupling relationship between expansion decisions and DDU. Specifically, to explore how the structural features of the expansion model change with DDU in different forms, the proposed expansion model with DDU is established based on Point Estimate Method (PEM). Via the explicit expression between decisions and decision-dependent statistical moments of uncertain parameters in the PEM-based model, an in-depth discussion of model features is implemented. An iterative solution method with convergence analysis is proposed based on the explored model features to tackle the DDU. Besides, a modified Benders decomposition method is adopted in each iteration for the PEM-based two-stage optimization model potentially containing both min-min and min-max terms. The effects of DDU on wind farm expansion schemes are analyzed. Case studies verify the proposed expansion model and the solution method.

A sandstorm is one of the extreme weather events causing extensive damage to overhead transmission lines (OTLs). Due to potential postsandstorm insulator flashover, OTLs face high failure probabilities, and implementing in-time maintenance on OTLs is crucial to mitigate postsandstorm losses. Aiming at determining an optimal maintenance sequence of targeted OTLs, this article proposes a decision-dependent stochastic approach for the joint operation and maintenance of OTLs. First, considering the inherent dependency of the uncertain availability of OTLs on maintenance decisions, the multiperiod maintenance process of OTLs is modeled as a stochastic process with decision-dependent uncertainty (DDU). Second, a two-stage stochastic model with DDU is formulated, where the maintenance sequence and unit commitment decisions are made in the first stage and the second stage comprises scenariowise operation. Then, to tackle the coupling relation between decisions and DDU, a unique modeling transformation technique is adopted to convert the established decision-dependent stochastic model into a computationally efficient form. Case studies verify the effectiveness of the proposed method for postsandstorm maintenance scheduling.

Cascading failure poses a significant risk to society. One approach to mitigate failure risk is through dynamic thermal rating (DTR) sensor, placed in transmission lines to achieve both risk mitigation and investment postponement of new lines. Sensor placement, as the basis of DTR analysis, is intrinsically a combinatorial optimization problem, while traditional solving methods cannot provide optimality guarantee and suffer easily from dimensionality curse. Besides, the risk mitigation may result in Braess paradox, a counterintuitive phenomenon that line update inversely increases failure risk. This paper proposes a submodular optimization-based DTR placement model for risk mitigation considering Braess paradox. First, a model based on Markov probability and important sampling weight techniques is utilized to efficiently quantify the failure risk before and after DTR placement. Then the risk model is applied to analytically reveal the Braess paradox condition which can invalidate the submodular formulation. For this invalidation issue, a novel submodular optimization approach is established to reformulate the risk mitigation model containing estimation error. Finally, a computationally efficient solving algorithm is designed to address this nonmonotone submodular optimization, which provides a provable approximation guarantee. The benefits brough from DTR and performance of the proposed algorithms are verified by case results.

The global experience on wind farm development reveals that due to the spatial correlation, the prediction error of wind power is related to the scale of wind farms. This evidence indicates that the uncertainty features of wind power output from large-scale wind farms are not fixed but dependent on expansion decisions. The decision-dependent uncertainty (DDU) will alter the traditional optimization process and pose solution challenges. This article proposes a coordinated planning model for large-scale wind farms and energy storage considering DDU. First, a DDU model, which quantifies the relationship between wind power prediction errors and the wind farm size, is established based on historical data. The proposed DDU model for a single wind farm is extended to multiple wind farms with their spatial correlation captured by a Gaussian Mixture Model. Then, tackling the coupling relationship between decisions and uncertainty, an affine function-based solution method for the stochastic model with decision-dependent probability distributions is proposed. The constructed affine function maps planning decisions to decision-dependent wind power scenario sets via linear transformation. The difference between the planning model with and without the DDU in wind power is compared and discussed. Case studies verify the proposed model and solution method.