Dissipating Energy Flow Research Articles

A data-driven online approach for detection and localization of forced oscillation in wind turbine integrated power system

This article introduces an innovative approach for online detection and localization of forced oscillation (FO) in power systems with significant integration of wind turbine generation (WTG). The synergistic combination of Multichannel Prony analysis with Periodogram and dissipating energy flow (DEF) approach is proposed in this paper to overcome the challenges inherent in detecting FO amidst the complexities introduced by WTG integration. An adaptive version of multichannel Prony analysis is proposed in this paper that dynamically estimates Prony’s system order via the recursive process. It estimates the frequency and damping ratio of all oscillatory modes, which is used to identify low damping modes that are potentially attributed to FO. Leveraging this information, the proposed method enhances both FO detection and source localization capabilities. The proposed method is verified on measurements taken from IEEE benchmark 4-machine, 11-bus system and 10-machine, 39-bus system with high wind energy penetration. Comprehensive testing demonstrates the proposed approach’s effectiveness across various FO scenarios, including governor valve malfunction, exciter malfunction, and cyclic loads. Furthermore, the methodology is evaluated under resonant conditions and scenarios involving the simultaneous identification of multiple disturbances.

A Cross-Power Spectral Density Method for Locating Oscillation Sources Using Synchrophasor Measurements

This paper proposes a new measurement-based approach for locating the sources of forced or poorly damped oscillations in a power system. The approach is based on the concept of cross-correlation in the frequency domain known as cross-power spectral density (CPSD). CPSDs of synchronized voltage magnitude and voltage angle versus active power and reactive power signals obtained by phasor measurement units (PMUs) are computed using fast Fourier transform. The largest positive imaginary part of a CPSD is used as an indicator of the oscillation source. The type of an oscillation source is determined by comparing the spectral densities of active and reactive power. In addition, preprocessing of the signals is performed via variational mode decomposition for extracting the dynamic component of the signals. The proposed approach was able to successfully identify all submitted test cases in the IEEE-NASPI Oscillation Source Location Contest. Several case studies presented in this paper highlight the advantages of the proposed approach compared to the state-of-the-art dissipating energy flow method.

QFS-CNN for sub-synchronous oscillation source location based on dissipating energy flow

Sub-synchronous oscillation (SSO) caused by large-scale renewable energy generations can threaten the safe and reliable operation of power systems. In this paper, a dissipating energy-based quaternion feature set convolutional neural network (QFS-CNN) method is proposed to locate the SSO sources quickly and accurately, providing the foundation for isolation of the SSO sources from power systems in time. Firstly, aiming at the difficulty in feature extraction of SSO sources due to the poor observability of power system, a temporal and spatial feature extraction method based on oscillation energy is proposed to characterize the SSO sources information in the form of images with limited measurement data. The temporal and spatial feature images are extracted based on the variation of oscillation energy in time and the direction of energy flow power in space, respectively. Then, the correlation between the oscillation energy and the SSO sources location can be revealed by the feature images with less calculation and storage space. Secondly, a QFS-CNN method based on temporal and spatial feature images for SSO sources location is proposed to address the insufficient labeled data of SSO. The QFS data augmentation technique increases the feature set via meaningful recombination of the existing labeled feature images. Then, the augmentative feature set is used to ensure the model training accuracy of QFS-CNN to improve the location accuracy of SSO sources. Finally, the proposed method is demonstrated and evaluated by a modified IEEE 39-bus wind power generation system. Simulation results show that the method has high accuracy and stronger anti-noise ability in the case of poor system observability and few sample data.

Insights Into Dissipating Energy-Based Source/Sink Characterization of TCSC and STATCOM for Low-Frequency Oscillations

Determination of the sources of oscillations in the power system helps operators take appropriate preventive actions. In recent years, the dissipating energy flow (DEF) method has emerged as a promising tool for the online localization of low-frequency oscillation sources. In literature, the mathematical foundation of the DEF method is well-studied for networks with synchronous generators. In this paper, we extend the analysis to flexible AC transmission systems (FACTS). We derive the DEF-expressions for a thyristor controlled series capacitor (TCSC) and a static synchronous compensator (STATCOM) operating with conventional control strategies. Specifically, TCSC with both fixed and variable compensation, and STATCOM in grid-following mode with dc-link voltage and ac voltage-reactive power droop control are considered. Analyzing their respective DEFs, we obtain the conditions for which these FACTS devices could appear as the sources of low-frequency oscillations. Our findings are structured into propositions and are supported through numerical case studies on IEEE test systems.

Forced Oscillation Identification and Filtering From Multi-Channel Time-Frequency Representation

Location of non-stationary forced oscillation (FO) sources can be a challenging task, especially under resonance condition with natural system modes. In this case, the magnitudes of the oscillations could be greater in places distant from the source and the oscillation spreads over a large region of the power system. Detection, frequency identification and filtering of FO oscillatory components constitutes an initial and critical step for the application of oscillation source location (OSL) methods. Specifically, this step has a major impact on the performance of the OSL method, such as the Dissipating Energy Flow (DEF) method. In this paper we develop a systematic methodology for detection, identification and filtering of non-stationary FO based on multi-channel time-frequency (TF) representation (TFR). We compare three TF approaches applied together with the DEF method: short-time Fourier transform (STFT), STFT-based synchrosqueezing transform (FSST) and second order FSST (FSST2). We have used simulated signals and real world PMU data to show that the proposed method provides a systematic framework for the identification and filtering of power systems non-stationary forced oscillations.

Transformer-based deep learning model for forced oscillation localization

Accurately locating Forced Oscillations (FOs) source(s) in a large-scale power system is a challenging task, and an important aspect of power system operation. In this paper, a complementary use of Deep Learning (DL)-based and Dissipating Energy Flow (DEF)-based methods are proposed to localize forced oscillation source(s) using data from Phasor Measurement Units (PMUs), by tracing the forced oscillations source(s) on the branch level in the power system network. The robustness, effectiveness and speed of the proposed approach is demonstrated in a WECC 240-bus test system, with high renewable integration in the system. Several simulated cases were tested, including non-gaussian noise, partially observable system, and operational topology variations in the system which correspond to real-world challenges. Timely localization of forced oscillation at an early stage provides the opportunity for taking remedial reaction. The results show that without the information of system operational topology, the proposed method can achieve high localization accuracy in only 0.33 s.

DSE-assisted DEF strategy for locating forced oscillations in synchronous generators

We present a new methodology to identify if forced oscillation (FO) sources are located in excitation systems or turbine governors. In this context, we propose to harness the information that dynamic state estimation (DSE) provides to be able to apply a dissipating energy flow (DEF) method. Measurements from phasor measurement units (PMUs) are used to estimate the internal states of different generators connected to the same bus. Using these estimations, we compute energy functions for the mechanical control loop and for the excitation control loop to determine where the FO was originated. Simulated signals from the IEEE-NASPI Oscillation Source Location (OSL) Contest are used to show that our proposal provides an online systematic methodology for identification and location of power systems forced oscillations, even when current measurements of the generator causing the FO are missing.

Complex Dissipating Energy Flow Method for Forced Oscillation Source Location

In this letter we propose an extension of the Dissipating Energy Flow (DEF) method for locating sources of forced oscillations (FOs), based on an energy function constructed by the complex integral approach, which we call Complex DEF (CDEF). To trace sources of FO, we study the scalar projection of CDEF in a specific direction on the complex plane. We show by simulated cases that this alternative has a good performance in cases where the original DEF fails.

Subsynchronous Oscillation Analysis Using Multisynchrosqueezing Transform and Dissipating Energy Flow Method

With a high proportion of new energy and power electronic equipment connected to the modern power system, a new type of subsynchronous oscillation (SSO) is triggered, which affects the safe and stable operation of the system. Accurate analysis and identification of the SSO source becomes the key to studying this problem. This article presents a novel method to analyze SSOs. First, multisynchrosqueezing transform is applied to the signal to get the concentrated time–frequency analysis results. Then, the ridge tracking method is utilized to identify and reconstruct the subsynchronous component signals. The method of dissipating energy flow is applied to locate the source and sink of the SSO in the subsynchronous component signals. The performances of the proposed method are verified using electromagnetic transient simulations in a three-wind farms system and a modified IEEE 10-generator 39-bus New England power system.

Very Low-Frequency Oscillation Source Localization on Ireland's Power System

This paper presents an approach for studying Very Low-Frequency Oscillations (VLFOs) between 0.03 and 0.08 Hz that have been observed on Irelands All-Island transmission system. Previous work by Ireland's TSO has found that the occurrence of the VLFO is linked to the generation dispatch of synchronous machines with governor control. This study verifies previous research by Ireland's TSO and analyses sensitivities such as inertia, system frequency and online generator status that causes an increase in VLF mode magnitude. This paper's results are based on 1-second resolution system frequency, metered generation and power system metric data from 1/1/2018 to 1/10/2020. This analysis demonstrates that the VLF oscillatory mode's stability is highly correlated if governors that consistently provide positive damping torque to the VLF mode are not synchronized. The findings from the study are demonstrated on several events on the Irish system using PMU data. The governor-based dissipating energy flow method is used to validate the relationships found from the generator status and system frequency case study.

Non-Stationary Power System Forced Oscillation Analysis Using Synchrosqueezing Transform

Non-stationary forced oscillations (FOs) have been observed in power system operations. However, most detection methods assume that the frequency of FOs is stationary. In this paper, we present a methodology for the analysis of non-stationary FOs. Firstly, Fourier synchrosqueezing transform (FSST) is used to provide a concentrated time-frequency representation of the signals that allows identification and retrieval of non-stationary signal components. To continue, the Dissipating Energy Flow (DEF) method is applied to the extracted components to locate the source of forced oscillations. The methodology is tested using simulated as well as real PMU data. The results show that the proposed FSST-based signal decomposition provides a systematic framework for the application of DEF Method to non-stationary FOs.

ISO New England Experience in Locating the Source of Oscillations Online

The article describes the experience of a successful online implementation of the Dissipating Energy Flow method for locating the source of oscillations in the Oscillation Source Locating (OSL) application. The OSL is a key component of the online oscillation management at ISO New England and in operation since September 2017. The article includes analysis of 1000+ actual oscillatory events processed by the OSL demonstrating the efficiency of the process in locating the source of oscillations.

A Passivity Interpretation of Energy-Based Forced Oscillation Source Location Methods

This paper develops a systematic framework for analyzing how low frequency forced oscillations propagate in electric power systems. Using this framework, the paper shows how to mathematically justify the so-called Dissipating Energy Flow (DEF) forced oscillation source location technique. The DEF's specific deficiencies are pinpointed, and its underlying energy function is analyzed via incremental passivity theory. This analysis is then used to prove that there exists no passivity transformation (i.e. quadratic energy function) which can simultaneously render all components of a lossy classical power system passive. The paper goes on to develop a simulation-free algorithm for predicting the performance of the DEF method in a generalized power system, and it analyzes the passivity of three non-classical load and generation components. The proposed propagation framework and performance algorithm are both tested and illustrated on the IEEE 39-bus New England system and the WECC 179-bus system.

Dissipating energy flow method for locating the source of sustained oscillations

The modification of an energy-based approach called the dissipating energy flow (DEF) method is proposed, which uses data from phasor measurement units (PMUs) to trace the source of poorly damped natural and forced oscillations in power systems. The original energy-based approach (Chen et al., 2013) assumes the ability to determine steady-state values of variables measured by PMU during the transient process and that prevents the reliable use of the original method with actual PMU data. PMU data processing, proposed in the DEF method, is a key step in converting the energy-based method into a robust and automated tool for use with actual PMU data. The effectiveness of the proposed DEF method is demonstrated by testing multiple simulated cases of sustained oscillations, including both poorly damped natural and forced oscillations and more than 30 actual events in ISO New England (ISO-NE) and two events in Western Electricity Coordination Council (WECC) systems. The study also demonstrates the potential for using the DEF method to estimate the contribution of any generator to the damping of a specific oscillation mode.

Fluctuation corrections to thermodynamic functions: Finite-size effects

The explicit thermodynamic functions, in particular, the specific heat of a spin system interacting with a spin bath which exerts finite dissipation on the system are determined. We show that the specific heat is a sum of the products of a thermal equilibration factor that carries the temperature dependence and a dynamical correction factor, characteristic of the dissipative energy flow under steady state from the system. The variation of specific heat with temperature is accompanied by an abrupt transition that depends on these dynamical factors characteristic of the finite system size.

Picosecond dynamics of n-hexane solvated trans-stilbene

In this article, we report studies of the time- and frequency-resolved picosecond dynamics of trans-stilbene solvated with one n-hexane molecule in a van der Waals complex. Excitations are made to several overtones of a low-frequency intermolecular vibration and to combination bands of these overtones with the symmetric in-plane ethylene bend mode ν25 in the S1 state of two distinct conformers, A and C, of these complexes. A Franck-Condon analysis of these spectra allows a characterization of the potential for this intermolecular mode in the ground and excited electronic state of both conformers. From the time-resolved dynamics of the A-isomer, the three different types of IVR behavior in the cluster, as in the bare molecule, are identified and studied. Single exponential fluorescence decays are observed at low excess energies, showing no IVR on the time scale of the lifetime of the molecule. At intermediate energies, between 220 and 260 cm−1, quantum-beat modulated decay profiles indicate restricted IVR dynamics. At higher excess energies IVR becomes dissipative and biexponential decays are observed. The decrease in the lowest excess energy at which dissipative IVR behavior sets in, from 1200 cm−1 in the bare t-stilbene molecule to less than 300 cm−1 in the complex, is attributed to a large increase in the density of vibrational states of the complex due to the six low-frequency intermolecular vibrations of the cluster. A similar study of the C-isomer reveals that the IVR dynamics become even more accelerated. Excitation of the stilbene mode ν25 at 200 cm−1 leads to dissipative energy flow from the stilbene molecule into the cluster vibrations within tens of picoseconds, becoming faster for higher excess energies. The results present a nice example of the significant impact that low-frequency “solvent-like” cluster vibrations have on the dynamics of vibrational energy redistribution and the coherent transfer of vibrational energy between the solute and the cluster modes.

A classical description of relaxation of interacting pairs of unlike spins: Extension to T1 ϱ, T2, and T1 ϱoff, including contact interactions

A novel derivation of the equations that describe the spin-lattice magnetic relaxation of nuclear spin moments, in liquids, resulting from magnetic dipolar interactions with neighboring paramagnetic ions, the Solomon-Bloembergen-Morgan equations was previously presented (S. H. Koenig, J. Magn. Reson. 31, 1 (1978)). The derivation involves a computation of the dissipative energy flow from the nuclear spins to the lattice rather than a computation of the lattice-produced fluctuations of the local field at the nuclear spins. Two advantages accrue: (1) the spectral densities that enter into the relaxation expressions can be directly related to well-defined absorption transitions and relaxation processes of the paramagnetic ions, clarifying the physical processes that produce relaxation, and (2) the derivation can be readily generalized to paramagnetic ions with arbitrary spin Hamiltonian, and to deviations of their susceptibility from Curie law behavior. The derivation is extended to include relaxation in liquids in the rotating frame: the on resonance T 1 ϱ which reduces to T 2 for small amplitude radiofrequency fields; and the off resonance T 1 ϱoff , which reduces to T 1. The results, which are given for contact as well as dipolar interactions, also describe relaxation of 13C and 15N nuclei by protons under conditions of proton-decoupling, a situation becoming increasingly important in the study of biological macromolecules by high-resolution NMR spectroscopy.