Using Effective Generator Impedance for Forced Oscillation Source Location

Locating the sources of forced low-frequency oscillations in power systems is an important problem. A number of proposed methods demonstrate their practical usefulness, but many of them rely on strong modeling assumptions and provide poor performance in certain cases for reasons still not well understood. This paper proposes a systematic method for locating the source of a forced oscillation by considering a generator's response to fluctuations of its terminal voltages and currents. It is shown that a generator can be represented as an effective admittance matrix with respect to low-frequency oscillations, and an explicit form for this matrix, for various generator models, is derived. Furthermore, it is shown that a source generator, in addition to its effective admittance, is characterized by the presence of an effective current source thus giving a natural qualitative distinction between source and nonsource generators. Detailed descriptions are given of a source detection procedure based on this developed representation, and the method's effectiveness is confirmed by simulations on the recommended testbeds (eg. WECC 179-bus system). This method is free of strong modeling assumptions and is also shown to be robust in the presence of measurement noise and generator parameter uncertainty.Comment: 13 page

A Parallelized, Adam-Based Solver for Reserve and Security Constrained AC Unit Commitment

Power system optimization problems which include the nonlinear AC power flow equations require powerful and robust numerical solution algorithms. Within this sub-field of nonlinear optimization, interior point methods have come to dominate the solver landscape. Over the last decade, however, a number of efficient numerical optimizers have emerged from the field of Machine Learning (ML). One algorithm in particular, Adam, has become the optimizer-of-choice for a massive percentage of ML training problems (including, e.g., the training of GPT-3), solving some of the largest unconstrained optimization problems ever conceived of. Inspired by such progress, this paper designs a parallelized Adam-based numerical solver to overcome one of the most challenging power system optimization problems: security and reserve constrained AC Unit Commitment. The resulting solver, termed quasiGrad, recently competed in the third ARPA-E Grid Optimization (GO3) competition. In the day-ahead market clearing category (with systems ranging from 3 to 23,643 buses over 48 time periods), quasiGrad's aggregated market surplus scores were within 5% of the winningest market surplus scores. The quasiGrad solver is now released as an open-source Julia package: quasiGrad.jl. The internal gradient-based solver (Adam) can easily be substituted for other ML-inspired solvers (e.g., AdaGrad, AdaDelta, RMSProp, etc.). Test results from large experiments are provided

Scalable Bilevel Optimization for Generating Maximally Representative OPF Datasets

New generations of power systems, containing high shares of renewable energy resources, require improved data-driven tools which can swiftly adapt to changes in system operation. Many of these tools, such as ones using machine learning, rely on high-quality training datasets to construct probabilistic models. Such models should be able to accurately represent the system when operating at its limits (i.e., operating with a high degree of ``active constraints"). However, generating training datasets that accurately represent the many possible combinations of these active constraints is a particularly challenging task, especially within the realm of nonlinear AC Optimal Power Flow (OPF), since most active constraints cannot be enforced explicitly. Using bilevel optimization, this paper introduces a data collection routine that sequentially solves for OPF solutions which are ``optimally far" from previously acquired voltage, power, and load profile data points. The routine, termed RAMBO, samples critical data close to a system's boundaries much more effectively than a random sampling benchmark. Simulated test results are collected on the 30-, 57-, and 118-bus PGLib test cases

Optimization-Based Exploration of the Feasible Power Flow Space for Rapid Data Collection

This paper provides a systematic investigation into the various nonlinear objective functions which can be used to explore the feasible space associated with the optimal power flow problem. A total of 40 nonlinear objective functions are tested, and their results are compared to the data generated by a novel exhaustive rejection sampling routine. The Hausdorff distance, which is a min-max set dissimilarity metric, is then used to assess how well each nonlinear objective function performed (i.e., how well the tested objective functions were able to explore the non-convex power flow space). Exhaustive test results were collected from five PGLib test-cases and systematically analyzed

Towards Optimal Kron-based Reduction Of Networks (Opti-KRON) for the Electric Power Grid

For fast timescales or long prediction horizons, the AC optimal power flow (OPF) problem becomes a computational challenge for large-scale, realistic AC networks. To overcome this challenge, this paper presents a novel network reduction methodology that leverages an efficient mixed-integer linear programming (MILP) formulation of a Kron-based reduction that is optimal in the sense that it balances the degree of the reduction with resulting modeling errors in the reduced network. The method takes as inputs the full AC network and a pre-computed library of AC load flow data and uses the graph Laplacian to constraint nodal reductions to only be feasible for neighbors of non-reduced nodes. This results in a highly effective MILP formulation which is embedded within an iterative scheme to successively improve the Kron-based network reduction until convergence. The resulting optimal network reduction is, thus, grounded in the physics of the full network. The accuracy of the network reduction methodology is then explored for a 100+ node medium-voltage radial distribution feeder example across a wide range of operating conditions. It is finally shown that a network reduction of 25-85% can be achieved within seconds and with worst-case voltage magnitude deviation errors within any super node cluster of less than 0.01pu. These results illustrate that the proposed optimization-based approach to Kron reduction of networks is viable for larger networks and suitable for use within various power system applications

GPU-Accelerated Verification of Machine Learning Models for Power Systems

Computational tools for rigorously verifying the performance of large-scale machine learning (ML) models have progressed significantly in recent years. The most successful solvers employ highly specialized, GPU-accelerated branch and bound routines. Such tools are crucial for the successful deployment of machine learning applications in safety-critical systems, such as power systems. Despite their successes, however, barriers prevent out-of-the-box application of these routines to power system problems. This paper addresses this issue in two key ways. First, for the first time to our knowledge, we enable the simultaneous verification of multiple verification problems (e.g., checking for the violation of all line flow constraints simultaneously and not by solving individual verification problems). For that, we introduce an exact transformation that converts the "worst-case" violation across a set of potential violations to a series of ReLU-based layers that augment the original neural network. This allows verifiers to interpret them directly. Second, power system ML models often must be verified to satisfy power flow constraints. We propose a dualization procedure which encodes linear equality and inequality constraints directly into the verification problem; and in a manner which is mathematically consistent with the specialized verification tools. To demonstrate these innovations, we verify problems associated with data-driven security constrained DC-OPF solvers. We build and test our first set of innovations using the $\alpha,\beta$-CROWN solver, and we benchmark against Gurobi 10.0. Our contributions achieve a speedup that can exceed 100x and allow higher degrees of verification flexibility

Emission-Aware Optimization of Gas Networks: Input-Convex Neural Network Approach

Gas network planning optimization under emission constraints prioritizes gas supply with the least CO$_2$ intensity. As this problem includes complex physical laws of gas flow, standard optimization solvers cannot guarantee convergence to a feasible solution. To address this issue, we develop an input-convex neural network (ICNN) aided optimization routine which incorporates a set of trained ICNNs approximating the gas flow equations with high precision. Numerical tests on the Belgium gas network demonstrate that the ICNN-aided optimization dominates non-convex and relaxation-based solvers, with larger optimality gains pertaining to stricter emission targets. Moreover, whenever the non-convex solver fails, the ICNN-aided optimization provides a feasible solution to network planning