Daily Papers

State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power system dynamics, primarily because of limitations in encoding the grid topology and sparse measurements. This paper proposes a physics-informed graphical learning state estimation method to address these limitations by leveraging both domain physical knowledge and a graph neural network (GNN). We employ a GNN architecture that can handle the graph-structured data of power systems more effectively than traditional data-driven methods. The physics-based knowledge is constructed from the branch current formulation, making the approach adaptable to both transmission and distribution systems. The validation results of three IEEE test systems show that the proposed method can achieve lower mean square error more than 20% than the conventional methods.

We study a kinematical consequence of the Hopf-algebraic momentum composition law in κ-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues P_μ are nonlinearly related to the ordered-plane-wave labels p_μ. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one real auxiliary preimage, the branch-sensitive quantity P_+equiv P_0+P_4=κe^{p_0/κ} enters the coproduct and resolves the branches in two-particle states. Imposing the vanishing total-momentum constraint therefore gives branch-dependent κ-deformed back-to-back momentum correlations. In a single-branch regime this is just a deformed correlated product, while in a multibranch regime a state specified only by P_μ can be expanded into distinct auxiliary branches. If P_μ are taken as the directly meaningful momenta, the physical content is the resulting deformed correlation pattern. If the auxiliary variables p_μ are assigned operational meaning, the same constrained state can be interpreted as a superposition over different auxiliary branches. We also compare this structure with standard regular self-adjoint nonrelativistic minimal-length models and find no analogous smooth local two-real-branch inversion on their physical domains.

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger Bridge Matching, effectively learn mappings between two distributions by modeling a single stochastic path. However, these methods are inherently limited to unimodal transitions and cannot capture branched or divergent evolution from a common origin to multiple distinct outcomes. To address this, we introduce Branched Schr\"odinger Bridge Matching (BranchSBM), a novel framework that learns branched Schr\"odinger bridges. BranchSBM parameterizes multiple time-dependent velocity fields and growth processes, enabling the representation of population-level divergence into multiple terminal distributions. We show that BranchSBM is not only more expressive but also essential for tasks involving multi-path surface navigation, modeling cell fate bifurcations from homogeneous progenitor states, and simulating diverging cellular responses to perturbations.

Model predictive control (MPC)-based energy management systems (EMS) are essential for ensuring optimal, secure, and stable operation in microgrids with high penetrations of distributed energy resources. However, due to the high computational cost for the decision-making, the conventional MPC-based EMS typically adopts a simplified integrated-bus power balance model. While this simplification is effective for small networks, large-scale systems require a more detailed branch flow model to account for the increased impact of grid power losses and security constraints. This work proposes an efficient and reliable MPC-based EMS that incorporates power-loss effects and grid-security constraints. %, while adaptively shaping the battery power profile in response to online renewable inputs, achieving reduced operational costs. It enhances system reliability, reduces operational costs, and shows strong potential for online implementation due to its reduced computational effort. Specifically, a second-order cone program (SOCP) branch flow relaxation is integrated into the constraint set, yielding a convex formulation that guarantees globally optimal solutions with high computational efficiency. Owing to the radial topology of the microgrid, this relaxation is practically tight, ensuring equivalence to the original problem. Building on this foundation, an online demand response (DR) module is designed to further reduce the operation cost through peak shaving. To the best of our knowledge, no prior MPC-EMS framework has simultaneously modeled losses and security constraints while coordinating flexible loads within a unified architecture. The developed framework enables secure operation with effective peak shaving and reduced total cost. The effectiveness of the proposed method is validated on 10-bus, 18-bus, and 33-bus systems.

Access to realistic transmission grid models is essential for power systems research, yet detailed network data in the United States remains restricted under critical-infrastructure regulations. We present a pipeline that constructs complete, OPF-solvable transmission network models entirely from publicly available data. The five-stage pipeline (1) extracts power infrastructure from OpenStreetMap via a local Overpass API instance, (2) reconstructs bus-branch topology through voltage inference, line merging, and transformer detection, (3) estimates electrical parameters using voltage-class lookup tables calibrated with U.S. Energy Information Administration (EIA) plant-level data, (4) allocates hourly demand from EIA-930 to individual buses using US Census population as a spatial proxy, and (5) solves both DC and AC optimal power flow using PowerModels.jl with a progressive relaxation strategy that automatically loosens constraints on imprecise models. We validate the pipeline on all 48 contiguous US states and six multi-state regions, including the full Western (5,076 buses) and Eastern (21,697 buses) Interconnections. Of the 48 single-state models, 42 (88%) converge at the strictest relaxation level for AC-OPF at peak hour and 44 (92%) off-peak. Dispatch costs (median $22/MWh) and system losses (median 1.0%) are consistent with real wholesale-market outcomes. The pipeline relies exclusively on open data sources, enabling reproducible grid analysis without proprietary data. All 54 models (48 single-state and 6 multi-state) are publicly released at https://github.com/microsoft/GridSFM.

Machine Learning (ML) techniques for Optimal Power Flow (OPF) problems have recently garnered significant attention, reflecting a broader trend of leveraging ML to approximate and/or accelerate the resolution of complex optimization problems. These developments are necessitated by the increased volatility and scale in energy production for modern and future grids. However, progress in ML for OPF is hindered by the lack of standardized datasets and evaluation metrics, from generating and solving OPF instances, to training and benchmarking machine learning models. To address this challenge, this paper introduces PGLearn, a comprehensive suite of standardized datasets and evaluation tools for ML and OPF. PGLearn provides datasets that are representative of real-life operating conditions, by explicitly capturing both global and local variability in the data generation, and by, for the first time, including time series data for several large-scale systems. In addition, it supports multiple OPF formulations, including AC, DC, and second-order cone formulations. Standardized datasets are made publicly available to democratize access to this field, reduce the burden of data generation, and enable the fair comparison of various methodologies. PGLearn also includes a robust toolkit for training, evaluating, and benchmarking machine learning models for OPF, with the goal of standardizing performance evaluation across the field. By promoting open, standardized datasets and evaluation metrics, PGLearn aims at democratizing and accelerating research and innovation in machine learning applications for optimal power flow problems. Datasets are available for download at https://www.huggingface.co/PGLearn.

A general approach is formulated to describe spontaneous surface current distribution in a chiral p-wave superconductor. We use the quasiclassical Eilenberger formalism in the Ricatti parametrization to describe various types of the superconductor surface, including arbitrary roughness and metallic behaviour of the surface layer. We calculate angle resolved distributions of the spontaneous surface currents and formulate the conditions of their observability. We argue that local measurements of these currents by muSR technique may provide an information on the underlying pairing symmetry in the bulk superconductor.