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To facilitate effective decarbonization of the electric power sector, this paper introduces the generic Carbon-aware Optimal Power Flow (C-OPF) method for power system decision-making that considers demand-side carbon accounting and emission management. Built upon the classic optimal power flow (OPF) model, the C-OPF method incorporates carbon emission flow equations and constraints, as well as carbon-related objectives, to jointly optimize power flow and carbon flow. In particular, this paper establishes the feasibility and solution uniqueness of the carbon emission flow equations, and proposes modeling and linearization techniques to address the issues of undetermined power flow directions and bilinear terms in the C-OPF model. Additionally, two novel carbon emission models, together with the carbon accounting schemes, for energy storage systems are developed and integrated into the C-OPF model. Numerical simulations demonstrate the characteristics and effectiveness of the C-OPF method, in comparison with OPF solutions.

Grid regulators and participants are paying increasing attention to Dynamic Line Ratings (DLR) as a new approach to address transmission system bottlenecks. In this paper, a thorough comparison of DLR, Ambient Adjusted Ratings (AAR), and the traditional Static Line Ratings (SLR) are conducted on a synthetic ERCOT grid. Estimates of DLR and AAR are calculated using an equation based on heat balance physics, along with high-resolution weather data of temperature and wind velocities. A constraint generation method for contingency screening is developed for solving security-constrained optimal power flow. Numerical results suggest that employing DLR could double the benefits compared to those of AAR relative to SLR, in terms of system costs, renewable curtailment, and emissions., Comment: 6 pages, 8 figures

Classical primal-dual algorithms attempt to solve $\max_{\mu}\min_{x} \mathcal{L}(x,\mu)$ by alternatively minimizing over the primal variable $x$ through primal descent and maximizing the dual variable $\mu$ through dual ascent. However, when $\mathcal{L}(x,\mu)$ is highly nonconvex with complex constraints in $x$, the minimization over $x$ may not achieve global optimality, and hence the dual ascent step loses its valid intuition. This observation motivates us to propose a new class of primal-dual algorithms for nonconvex constrained optimization with the key feature to reverse dual ascent to a conceptually new dual descent, in a sense, elevating the dual variable to the same status as the primal variable. Surprisingly, this new dual scheme achieves some best iteration complexities for solving nonconvex optimization problems. In particular, when the dual descent step is scaled by a fractional constant, we name it scaled dual descent (SDD), otherwise, unscaled dual descent (UDD). For nonconvex multiblock optimization with nonlinear equality constraints, we propose SDD-ADMM and show that it finds an $\epsilon$-stationary solution in $\mathcal{O}(\epsilon^{-4})$ iterations. The complexity is further improved to $\mathcal{O}(\epsilon^{-3})$ and $\mathcal{O}(\epsilon^{-2})$ under proper conditions. We also propose UDD-ALM, combining UDD with ALM, for weakly convex minimization over affine constraints. We show that UDD-ALM finds an $\epsilon$-stationary solution in $\mathcal{O}(\epsilon^{-2})$ iterations. These complexity bounds for both algorithms either achieve or improve the best-known results in the ADMM and ALM literature. Moreover, SDD-ADMM addresses a long-standing limitation of existing ADMM frameworks.

Modeling and predicting solar events, particularly the solar ramping event, is critical for improving situational awareness for solar power generation systems. It has been acknowledged that weather conditions such as temperature, humidity, and cloud density can significantly impact the emergence and position of solar ramping events. As a result, modeling these events with complex spatio-temporal correlations is highly challenging. To tackle the question, we adopt a novel spatio-temporal categorical point process model, which intuitively and effectively addresses correlation and interaction among ramping events. We demonstrate the interpretability and predictive power of our model on extensive real-data experiments.

It is well-known that optimizing network topology by switching on and off transmission lines improves the efficiency of power delivery in electrical networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that the U.S. should "encourage, as appropriate, the deployment of advanced transmission technologies" including "optimized transmission line configurations". As such, many authors have studied the problem of determining an optimal set of transmission lines to switch off to minimize the cost of meeting a given power demand under the direct current (DC) model of power flow. This problem is known in the literature as the Direct-Current Optimal Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on heuristic algorithms for generating quality solutions or on the application of DC-OTS to crucial operational and strategic problems such as contingency correction, real-time dispatch, and transmission expansion. The mathematical theory of the DC-OTS problem is less well-developed. In this work, we formally establish that DC-OTS is NP-Hard, even if the power network is a series-parallel graph with at most one load/demand pair. Inspired by Kirchoff's Voltage Law, we give a cycle-based formulation for DC-OTS, and we use the new formulation to build a cycle-induced relaxation. We characterize the convex hull of the cycle-induced relaxation, and the characterization provides strong valid inequalities that can be used in a cutting-plane approach to solve the DC-OTS. We give details of a practical implementation, and we show promising computational results on standard benchmark instances.

The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today's power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. Motivated by this, we present a new framework using adaptive robust optimization for the economic dispatch of power systems with high level of wind penetration. In particular, we propose an adaptive robust optimization model for multi-period economic dispatch, and introduce the concept of dynamic uncertainty sets and methods to construct such sets to model temporal and spatial correlations of uncertainty. We also develop a simulation platform which combines the proposed robust economic dispatch model with statistical prediction tools in a rolling horizon framework. We have conducted extensive computational experiments on this platform using real wind data. The results are promising and demonstrate the benefits of our approach in terms of cost and reliability over existing robust optimization models as well as recent look-ahead dispatch models., Comment: Accepted for publication at IEEE Transactions on Power Systems