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Cascading failure causes a major risk to society currently. And dynamic thermal rating (DTR) technique is a cost-effective approach to mitigate the risk by exploiting potential transmission capability. From the perspectives of service life and Braess paradox, it is important and challenging to jointly optimize the DTR placement and its operation schedule for changing system state, which is a two-stage combinatorial problem with only discrete variables, suffering from no approximation guarantee and dimension curse in traditional solving algorithms. Thus, the present work proposes a novel two-stage submodular optimization (TSSO) of DTR for risk mitigation considering placement and operation schedule. Specifically, it optimizes DTR placement with proper redundancy in first stage, and then determines the corresponding DTR operation for each system state in second stage. Under the condition of the Markov and submodular features in sub-function of risk mitigation, the submodularity of total objective function of TSSO can be proven for the first time. Based on this, a state-of-the-art efficient solving algorithm is developed that can provide a better approximation guarantee than previous studies by coordinating the separate curvature and error form. The performance of the proposed optimization model is verified by case results.

PV-PQ switching of generator buses when hitting reactive power limits is an important factor in voltage stability. This article establishes the formulation and convexification of voltage stability constrained optimal power flow (VSC-OPF) considering PV-PQ switching that co-optimizes generation dispatch and bus type profile. The conventional power flow Jacobian is intractable to be adopted since it has a variable size under PV-PQ switching. To solve this issue, a big-M-parameterized constant-size power flow Jacobian is constructed which explicitly considers PV-PQ switching. It is proved that this new Jacobian has the same minimum eigenvalue as the conventional Jacobian, which enables us to propose a more tractable VSC-OPF by enforcing a lower bound for the constant-size Jacobian minimum eigenvalue. Further, a linear approximation of the voltage stability constraint is constructed by combining smoothing, relaxation and eigen-sensitivity techniques. Finally, we establish an semi-definite programming formulation for VSC-OPF considering PV-PQ switching, which can be efficiently solved by outer linearization algorithm. The proposed formulation and convexification techniques are extendable to include more general PV-PQ switching actions triggered by hitting the capability curve of converter-interfaced generators. The proposed method is verified via numerical tests on the IEEE 118-bus system. Comparing to the VSC-OPF under a predefined bus type profile, our method finds out the optimal bus type profile that helps to achieve a lower-cost solution and higher precision in voltage stability assessment.

This article proposes a novel method for analytically assessing the value of renewable forecasting accuracy in power system operation. Different from previous assessment methods where renewable forecasting accuracy is perturbed numerically, the proposed method directly derives sensitivity formulae of the operation model with respect to (w.r.t.) renewable forecasting error distribution change. Compared with conventional analytical sensitivity methods dealing with only deterministic parameters, deriving such sensitivity formulae is challenging and necessitates the closed-form expression of forecasting error distribution parameters in the operation model. To tackle this challenge, we propose to model and reformulate the two-stage stochastic unit commitment for wind-penetrated power systems based on the Point Estimate Method (PEM). Then, leveraging the explicitly expressed wind power statistical moments in the PEM-based model, the sensitivity formulae of expected operation costs w.r.t. both global and nodal wind power forecasting error distribution change are derived. The proposed method provides to assess the value of renewable forecasting accuracy and identify critical nodes with uncertain injections that are most influential on system operation without exhausting numerical simulations. Case studies on modified IEEE systems verify the effectiveness of the proposed method.

In this letter, we analytically investigate the sensitivity of stability index to its dependent variables in general power systems. Firstly, we give a small-signal model, the stability index is defined as the solution to a semidefinite program (SDP) based on the related Lyapunov equation. In case of stability, the stability index also characterizes the convergence rate of the system after disturbances. Then, by leveraging the duality of SDP, we deduce an analytical formula of the stability sensitivity to any entries of the system Jacobian matrix in terms of the SDP primal and dual variables. Unlike the traditional numerical perturbation method, the proposed sensitivity evaluation method is more accurate with a much lower computational burden. This letter applies a modified microgrid for comparative case studies. The results reveal the significant improvements on the accuracy and computational efficiency of stability sensitivity evaluation.

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.

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.