The simulation of very high shares of inverter-based resources in power systems has begun to draw into question the validity of phasor domain tools in capturing relevant dynamics. Electromagnetic transient simulators can capture the dynamics of power electronics with substantially smaller time steps, but are computationally expensive. This work contrasts the results of phasor domain and electromagnetic transient tools for simulations on a validated model of the Maui power system operating at very high inverter-based resource shares with near zero voltage forming devices. The results show that the phasor domain tool predicts optimistic stability with fewer voltage forming elements on the network, and loses computational stability before the electromagnetic transient tool. As the electromagnet transient model is of the entire system, and system-wide discrepancies are observed, this case study of a physical power system highlights the potential need for system-wide detailed modeling during periods of very high shares of inverter-based resources and few voltage forming devices.

DC2AC is an automated tool for achieving a converged AC power flow solution from any dispatch, e.g., determined using DC power flow model based optimal power flow. The entire process is free of human interference. It is usually encountered in practice that, even with a DC power flow solution, acquiring the solved AC power flow solution, if exists, sometimes could be a challenging task, especially during the planning stage. It is also difficult to distinguish the unsolvable cases from diverging iterations. Manual adjustments to approach the desired power flow condition has been largely relied on in the past using lots of engineering heuristics. This tool provides a systematic way to first achieve a solvable AC power flow case by modifying the power flow condition, and then try to track the AC power flow solution while gradually removing the adopted changes. If all adopted changes can be completely removed, then the original AC power flow solution is obtained. Otherwise, insights for actionable controls are derived to help operation and planning. Currently, this tool has been implemented in Python using SIEMENS PTI PSS/E as power flow solver, where only adjusting generator terminal voltage set point is considered as an available means to try to turn an unsolved power flow to a solved one. In future, more means should be considered, including the operation of tap-changing transformers, switched shunts and redispatch of active power.

This paper proposes a new system-level application for monitoring out-of-step (OOS) events in power systems. As already known, amplitude-dependent frequency shift is a nonlinear phenomenon of electromechanical oscillations under large disturbances. The frequency shift indicates the system's nearness to instability. This new tool utilizes the Normal Form method to identify the named phenomenon, leading to accelerated OOS detection. The proposed strategy is illustrated and compared to the equal-area criterion method in a single-machine-infinite-bus power system. Extensive tests on IEEE 3- and IEEE 50-machine power systems prove the efficacy and potential of the proposed method for online warnings of instability and ranking of vulnerable system modes.

Ensuring long-term voltage stability is critical for reliable operations of power grids. High share of distributed energy resources (DERs) can create complicated system operation modes that may invalidate the traditional long-term voltage stability analysis based on typical operation modes. To address this challenge, this paper investigates how to compute the shortest path to the voltage stability boundary in the DER aggregated load space with large dispersion. Instead of working in the Euclidean space, we establish the analysis and computations on the algebraic power flow manifold to better capture the curvature change of the shortest path along the direction of losing stability. A modified optimal control framework is presented for obtaining the ground-truth of the smooth shortest path on the manifold. To efficiently and accurately solve for the shortest path, we further leverage the geometric features of the power flow manifold and propose a tri-sectional approximation model that is scalable for large-scale systems. Several numerical examples, up to the 1354-bus system, with different DER penetration levels and high dimensional renewable power injection variations are evaluated. The simulation results demonstrate that the tri-sectional approximation achieves high accuracy and efficiency to approximate the shortest path to the voltage stability boundary.

This article presents what the authors believe to be the first experimental verification of the ability of grid-forming (GFM) inverters to stabilize a transmission electric power system that is otherwise unstable. The experiments described here were performed using power hardware-in-the-loop (PHIL) simulation to connect a megawatt-scale battery inverter to a real-time electromagnetic transient (EMT) simulation of the near-future Maui power system. This allows the dynamic interactions between the inverter and the power system to be observed without putting the real power system at risk. The ability to use the actual inverter hardware removes the need to rely on a computer model approximation of the inverter’s behavior.

In electromagnetic transient (EMT) simulation, 80-97% of the computational time is devoted to solving the network equations. Akey observation is that the sub-matrix representing the interaction between two far-away groups of buses is usually sparse and can be approximated by a low-rank matrix. Based on this observation, we propose a novel low-rank approximation method which permitsO(N logN)-time matrix-vector multiplication for each network solution time step. Comprehensive numerical studies are conducted on a 39-bus system and a 179-bus system from the literature, and large cases created from the two systems. The results demonstrate that the proposed approach is up to 2.8x faster than the state-of-the-art sparseLUfactorization based network solution, without compromising simulation accuracy. Since our low-rank approximation is highly parallelizable, further speedup may be possible.

Real-time damping estimation for a dominant inter-area mode is important for situational awareness of potential angular instability in power systems. Electromechanical oscillations energized by large disturbances often manifest obvious nonlinearities in measurements on first several swings. Traditional methods based on linear system theory often discard first several swings intentionally to avoid nonlinearity; if not, the estimated damping ratios often vary with the length and starting point of the measuring window. By identifying a nonlinear oscillator to fit a dominant mode, this paper proposes a new measurement-based approach utilizing complete post-disturbance data for robust damping estimation independent of the measuring window. Case studies on the IEEE 9-bus system and a 48-machine Northeast Power Coordinating Council system validate the proposed approach for providing accurate and robust damping estimation compared with existing methods including the Prony's method. Meanwhile, three factors influencing damping estimation in practical applications are also addressed, including measurement noises, limited coverage of PMU measurements, and existence of multiple dominant modes.

This paper proposes single-port equivalent and two-port equivalent network reduction methods to respectively reduce single-port and two-port areas in a large power network. Parameters of the reduced systems are rigorously derived, which guarantees that the electrical quantities at the port(s) remain unchanged over the reduction, including voltage magnitude and phase and active and reactive power injections into the area to be reduced. The proposed techniques are applied to reduce a practical Maui grid, where the total numbers of buses, lines and transformers are respectively reduced from 212, 106 and 108 to 45, 30 and 13. Dynamic behaviors between the full model and the reduced model are compared in detail to illustrate the efficacy and accuracy of the proposed network reduction.

A two-stage machine learning-based approach for creating synthetic phasor measurement unit (PMU) data is proposed in this article. This approach leverages generative adversarial networks (GAN) in data generation and incorporates neural ordinary differential equation (Neural ODE) to guarantee underlying physical meaning. We utilize this approach to synthetically create massive eventful PMU data, which would otherwise be difficult to obtain from the real world due to the critical energy infrastructure information (CEII) protection. To illustrate the utility of such synthetic data for subsequent data-driven methods, we specifically demonstrate the application of using synthetic PMU data for event classification by scaling up the real data set. The addition of the synthetic PMU data to a small set of real PMU data is shown to have improved the event classification accuracy by 2 to 5 percent.

The Frequency-Amplitude (F-A) curve on power system oscillation under a large disturbance characterizes how a natural oscillation mode transitions to nonlinear oscillations with growing amplitudes and decaying frequencies. The existing formulation of the F-A curve is derived by solving elliptical integrals on oscillation of a single-machine-infinite-bus equivalent about the targeted oscillation mode. The formula is in a form of infinite series and needs to sum a large number of terms for satisfactory accuracy. This paper introduces an explicit, approximate expression obtained from the Homotopy Analysis Method on the F-A curve. The proposed F-A curve expression is derived from an SMIB system and verified on the IEEE 3-machine 9-bus system to show how the oscillation frequency of a dominant mode varies with oscillation amplitude under large disturbances.

Nonlinear modal decoupling (NMD) was recently proposed to nonlinearly transform a multi-oscillator system into as many decoupled oscillators as the oscillation modes of interests with the original system. Those decoupled oscillators together provide a fairly accurate approximation of behaviors of the original system in an extended neighborhood of the equilibrium. Each oscillator has just one degree of freedom and hence can easily be analyzed to infer the nonlinear dynamics of the original system associated with one oscillation mode. As the first attempt of applying the NMD methodology to realistic power system models, this paper proposes an NMD-based approach for the early warning of the oscillation mode that may most likely develop into a mode of transient instability. For a multi-machine power system, the approach first derives decoupled nonlinear oscillators by a coordinates transformation, and then applies Lyapunov stability analysis to decoupled oscillators to assess the stability of the original system. For large-scale power grids, the proposed approach can be efficiently applied by conducting NMD regarding only selected modes. Case studies on a 3-machine 9-bus system and an northeast power coordinating council (NPCC) 48-machine 140-bus system show the potentials of the approach in early warning of transient instability for multi-machine systems.

Future distribution systems will be penetrated with massive power electronics (PE) devices.This paper classifies the dynamics of future PE-rich distribution systems into four categories: dynamics introduced by network, dynamics introduced by PE interfaces, dynamics introduced by control of PE interfaces and dynamics introduced by load, generation and battery energy storage system.The purpose of such a categorization is to facilitate the analysis and control design of future distribution grids as well as to investigate the cause of instabilities.As a gridedge technology, a PE interface named Power Electronics Intelligence at the Network Edge (PINE) is used in numerical studies to demonstrate these four categories of dynamics and show how each of them influences the system dynamics and stability.

This paper proposes a new analytical probabilistic power flow (PPF) approach for power systems with high penetration of distributed energy resources. The approach solves probability distributions of system variables about operating conditions. Unlike existing analytical PPF algorithms in literature, this new approach preserves nonlinearities of ac power flow equations and retain more accurate tail effects of the probability distributions. The approach first employs a multidimensional holomorphic embedding method to obtain an analytical nonlinear ac power flow solution for concerned outputs such as bus voltages and line flows. The embedded symbolic variables in the analytical solution are the inputs such as power injections. Then, the approach derives cumulants of the outputs by a generalized cumulant method, and recovers their distributions by Gram-Charlier expansions. This PPF approach can accept both parametric and nonparametric distributions of random inputs and their covariances. Case studies on the IEEE 30-bus system validate the effectiveness of the proposed approach.

This paper proposes an efficient scheme to reduce computational redundancy and speed up the dynamic simulation in online transient stability assessment of power systems. The paper first analyzes the mechanism of generating redundant computations in a traditional scheme that multiple combinations of operating points and faults lead to identical fault-cleared state, and then shows that the probability of redundancy will grow with the increase of diversified operating conditions in smart grid. The proposed scheme offline constructs a unique set of sampling points using sparse grid in the state space about the fault-cleared states and simulates the post-fault dynamic responses on those sampling points. In the online stage, the real-time post-fault trajectory can be recovered from the trajectories on the sampling points whenever the true fault-cleared state is obtained. The case study on IEEE 39-bus system shows great potential of the proposed approach.

The recently proposed Nonlinear Modal Decoupling (NMD) approach provides a new way to study stability of large non-linear multi-oscillator systems such as multi-machine power systems. The approach finds a coordinate transformation to decouple the mathematical model of the original system into as many decoupled nonlinear oscillators as the system’s oscillation modes of interests so that individual decoupled one-degree-of-freedom oscillators can be easily analyzed to infer nonlinear modal dynamics and stability of the original system. By applying NMD to the IEEE 3-machine 9-bus power system, this paper studies the consistency between the stability boundaries obtained respectively from the original system and decoupled oscillators, which are the regions of attraction about a stable equilibrium. The paper proposes an approach to improve accuracy of the stability boundary estimated from the decoupled oscillators.

The recently proposed Nonlinear Modal Decoupling (NMD) approach provides a new way for the stability analysis of large non-linear multi-oscillator systems such as power systems. NMD inversely constructs as many decoupled nonlinear oscillators as the system's oscillation modes so that individual decoupled oscillators can be easily analyzed to infer dynamics and stability of the original system. This paper presents a theoretical investigation of the consistency of the stability information between the decoupled system and the original system in terms of equilibrium points. A procedure for the approximation of closest unstable equilibrium point via nonlinear modal decoupling is proposed. The IEEE 9-bus power system is used to test the performance of this procedure.

Small signal analysis is a special case of analytical approaches using 1st-order Taylor expansion of power system differential equations. High-order Taylor expansions (TEs) can lead to better analytical approaches for stability analysis by considering higher-order nonlinearities, e.g. normal form, modal series and nonlinear modal decoupling. This paper presents fundamental studies on how accurate transient stability analysis results can be obtained from the high-order TEs compared to that based on the original system. Analytical investigations are conducted on single-machine-infinite-bus power systems. Observations are summarized from there and verified on two multi-machine power systems by extensive simulations.

This paper concerns with the production of synthetic phasor measurement unit (PMU) data for research and education purposes. Due to the confidentiality of real PMU data and no public access to the real power systems infrastructure information, the lack of credible realistic data becomes a growing concern. Instead of constructing synthetic power grids and then producing synthetic PMU measurement data by time simulations, we propose a model-free approach to directly generate synthetic PMU data. we train the generative adversarial network (GAN) with real PMU data, which can be used to generate synthetic PMU data capturing the system dynamic behaviors. To validate the sequential generation by GAN to mimic PMU data, we theoretically analyze GAN's capacity of learning system dynamics. Further by evaluating the synthetic PMU data by a proposed quantitative method, we verify GAN's potential to synthesize realistic samples and meanwhile realize that GAN model in this paper still has room to improve. Moreover it is the first time that such generative model is applied to synthesize PMU data.

This paper proposes a method for estimating the transient stability margin of a multi-machine system regarding a single dominant oscillation mode under a disturbance. The nonlinear modal dynamics of the system regarding a dominant mode before it develops to an instability mode is characterized using an equivalent nonlinear oscillator that is modeled by a second order nonlinear differential equation and identifiable from measurements of the post-disturbance trajectory. With reasonable selection for the formulation of this oscillator, the unstable equilibrium points estimated directly by this equation can give conservative transient stability margin regarding that dominant mode. Case studies on the IEEE 9-bus and New England 39-bus power systems validate the proposed method.