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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. 

Faults on power lines and other electric equipment are known to cause wildfire ignitions. To mitigate the threat of wildfire ignitions from electric power infrastructure, many utilities preemptively de-energize power lines, which may result in power shutoffs. Data regarding wildfire ignition risks are key inputs for effective planning of power line de-energizations. However, there are multiple ways to formulate risk metrics that spatially aggregate wildfire risk map data, and there are different ways of leveraging this data to make decisions. The key contribution of this paper is to define and compare the results of employing six metrics for quantifying the wildfire ignition risks of power lines from risk maps, considering both threshold- and optimization-based methods for planning power line de-energizations. The numeric results use the California Test System (CATS), a large-scale synthetic grid model with power line corridors accurately representing California infrastructure, in combination with real Wildland Fire Potential Index data for a full year. This is the first application of optimal power shutoff planning on such a large and realistic test case. Our results show that the choice of risk metric significantly impacts the lines that are de-energized and the resulting load shed. We find that the optimization-based method results in significantly less load shed than the threshold-based method while achieving the same risk reduction. 

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. 

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. 

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 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. 

Combinatorial distribution system optimization problems, such as scheduling electric vehicle (EV) charging during evacuations, present significant computational challenges. These challenges stem from the large numbers of constraints, continuous variables, and discrete variables, coupled with the unbalanced nature of distribution systems. In response to the escalating frequency of extreme events impacting electric power systems, this paper introduces a method that integrates sample-based conservative linear power flow approximations (CLAs) into an optimization framework. In particular, this integration aims to ameliorate the aforementioned challenges of distribution system optimization in the context of efficiently minimizing the charging time required for EVs in urban evacuation scenarios.