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Optimal Transmission Switching (OTS) problems minimize operational costs while treating both the transmission line energization statuses and generator setpoints as decision variables. The combination of nonlinearities from an AC power flow model and discrete variables associated with line statuses makes AC-OTS a computationally challenging Mixed-Integer Nonlinear Program (MINLP). To address these challenges, the DC power flow approximation is often used to obtain a DC-OTS formulation expressed as a Mixed-Integer Linear Program (MILP). However, this approximation often leads to suboptimal or infeasible switching decisions when evaluated with an AC power flow model. This paper proposes an enhanced DC-OTS formulation that leverages techniques for training machine learning models to optimize the DC power flow model's parameters. By optimally selecting parameter values that align flows in the DC power flow model with apparent power flows—incorporating both real and reactive components—from AC Optimal Power Flow (OPF) solutions, our method more accurately captures line congestion behavior. Integrating these optimized parameters into the DC-OTS formulation significantly improves the accuracy of switching decisions and reduces discrepancies between DC-OTS and AC-OTS solutions. We compare our optimized DC-OTS model against traditional OTS approaches, including DC-OTS, Linear Programming AC (LPAC)-OTS, and Quadratic Convex (QC)-OTS. Numeric results show that switching decisions from our model yield better performance when evaluated using an AC power flow model, with up to 44% cost reductions in some cases. 

The inherent nonlinearity of the power flow equations poses significant challenges in accurately modeling power systems, particularly when employing linearized approximations. Although power flow linearizations provide computational efficiency, they can fail to fully capture nonlinear behavior across diverse operating conditions. To improve approximation accuracy, we propose conservative piecewise linear approximations (CPLA) of the power flow equations, which are designed to consistently over- or under-estimate the quantity of interest, ensuring conservative behavior in optimization. The flexibility provided by piecewise linear functions can yield improved accuracy relative to standard linear approximations. However, applying CPLA across all dimensions of the power flow equations could introduce significant computational complexity, especially for large-scale optimization problems. In this paper, we propose a strategy that selectively targets dimensions exhibiting significant nonlinearities. Using a second-order sensitivity analysis, we identify the directions where the power flow equations exhibit the most significant curvature and tailor the CPLAs to improve accuracy in these specific directions. This approach reduces the computational burden while maintaining high accuracy, making it particularly well-suited for mixed-integer programming problems involving the power flow equations. 

To model reactive power limited generators within power flow problems, PV-PQ switching fixes generator voltages when reactive power outputs are within limits but allows the voltages to vary with a constant reactive power injection when limits are reached. Power flow algorithms often use heuristics that iteratively modify the generators’ PV versus PQ representation as the algorithm executes. The convergence behavior and speed of power flow algorithms with these heuristics significantly depend on their initialization. To improve computational performance, we propose an approach for using neural networks to initialize PV-PQ switching heuristics. After offline training where the neural networks learn the power flow solution’s PV vs. PQ generator statuses across varying load demands, the neural networks are deployed to initialize power flow algorithms in online applications. Numerical results demonstrate the effectiveness of this approach with speedup factors of 1.55× to 4.32× over the nominal generator PV-PQ status initialization. 

This study introduces a mixed-integer linear programming (MILP) model, effectively co-optimizing patrolling, damage assessment, fault isolation, repair, and load re-energization processes. The model is designed to solve a vital operational conundrum: deciding between further network exploration to obtain more comprehensive data or addressing the repair of already identified faults. As information on the fault location and repair timelines becomes available, the model allows for dynamic adaptation of crew dispatch decisions. In addition, this study proposes a conservative power flow constraint set that considers two network loading scenarios within the final network configuration. This approach results in the determination of an upper and a lower bound for node voltage levels and an upper bound for power line flows. To underscore the practicality and scalability of the proposed model, we have demonstrated its application using IEEE 123-node and 8500-node test systems, where it delivered promising results. 

Machine learning models have been developed for a wide variety of power system applications. The accuracy of a machine learning model strongly depends on the selection of training data. In many settings where real data are limited or unavailable, machine learning models are trained using synthetic data sampled via different strategies. Using the task of approximating the voltage magnitudes associated with specified complex power injections as an illustrative application, this paper compares the performance of neural networks trained on four different sampling strategies: (i) correlated loads at fixed power factor, (ii) correlated loads at varying power factor, (iii) uncor-related loads at fixed power factor, and (iv) uncorrelated loads at varying power factor. A new sampling strategy that combines these four strategies into one training dataset is also introduced and assessed. Results from transmission and distribution test cases of varying sizes show that these strategies for creating synthetic training data yield varied neural network accuracy. The accuracy differences across the various strategies vary by up to a factor of four. While none of the first four strategies outperform the others across all test cases, neural networks trained with the combined dataset perform the best overall, maintaining a high accuracy and low error spreads. 

This paper presents an algorithm for restoring AC power flow feasibility from solutions to simplified optimal power flow (OPF) problems, including convex relaxations, power flow approximations, and machine learning (ML) models. The proposed algorithm employs a state estimation-based post-processing technique in which voltage phasors, power injections, and line flows from solutions to relaxed, approximated, or ML-based OPF problems are treated similarly to noisy measurements in a state estimation algorithm. The algorithm leverages information from various quantities to obtain feasible voltage phasors and power injections that satisfy the AC power flow equations. Weight and bias parameters are computed offline using an adaptive stochastic gradient descent method. By automatically learning the trustworthiness of various outputs from simplified OPF problems, these parameters inform the online computations of the state estimation-based algorithm to both recover feasible solutions and characterize the performance of power flow approximations, relaxations, and ML models. Furthermore, the proposed algorithm can simultaneously utilize combined solutions from different relaxations, approximations, and ML models to enhance performance. Case studies demonstrate the effectiveness and scalability of the proposed algorithm, with solutions that are both AC power flow feasible and much closer to the true AC OPF solutions than alternative methods, often by several orders of magnitude in the squared two-norm loss function. 

The power flow equations are central to many problems in power system planning, analysis, and control. However, their inherent non-linearity and non-convexity present substantial challenges during problem-solving processes, especially for optimization problems. Accordingly, linear approximations are commonly employed to streamline computations, although this can often entail compromises in accuracy and feasibility. This paper proposes an approach termed Conservative Bias Linear Approximations (CBLA) for addressing these limitations. By minimizing approximation errors across a specified operating range while incorporating conservativeness (over- or under-estimating quantities of interest), CBLA strikes a balance between accuracy and tractability by maintaining linear constraints. By allowing users to design loss functions tailored to the specific approximated function, the bias approximation approach significantly enhances approximation accuracy. We illustrate the effectiveness of our proposed approach through several test cases. 

The ongoing electrification of the transportation fleet will increase the load on the electric power grid. Since both the transportation network and the power grid already experience periods of significant stress, joint analyses of both infrastructures will most likely be necessary to ensure acceptable operation in the future. To enable such analyses, this article presents an open-source testbed that jointly simulates high-fidelity models of both the electric distribution system and the transportation network. The testbed utilizes two open-source simulators, OpenDSS to simulate the electric distribution system and the microscopic traffic simulator SUMO to simulate the traffic dynamics. Electric vehicle charging links the electric distribution system and the transportation network models at vehicle locations determined using publicly available parcel data. Leveraging high-fidelity synthetic electric distribution system data from the SMART-DS project and transportation system data from OpenStreetMap, this testbed models the city of Greensboro, NC down to the household level. Moreover, the methodology and the supporting scripts released with the testbed allow adaption to other areas where high-fidelity geolocated OpenDSS datasets are available. After describing the components and usage of the testbed, we exemplify applications enabled by the testbed via two scenarios modeling the extreme stresses encountered during evacuations. 

This paper presents an algorithm to optimize the parameters of power systems equivalents to enhance the accuracy of the DC power flow approximation in reduced networks. Based on a zonal division of the network, the algorithm produces a reduced power system equivalent that captures inter-zonal flows with aggregated buses and equivalent transmission lines. The algorithm refines coefficient and bias parameters for the DC power flow model of the reduced network, aiming to minimize discrepancies between inter-zonal flows in DC and AC power flow results. Using optimization methods like Broyden-Fletcher-Goldfarb-Shanno (BFGS), Limited-memory BFGS (L-BFGS), and Truncated Newton Conjugate-Gradient (TNC) in an offline training phase, these parameters boost the accuracy of online DC power flow computations. In contrast to existing network equivalencing methods, the proposed algorithm optimizes accuracy over a specified range of operation as opposed to only considering a single nominal point. Numerical tests demonstrate substantial accuracy improvements over traditional equivalencing and approximation methods.