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.
•A Deep-Learning based approach for forced oscillations is proposed.•It has reliable and robust performance in the presence of topology variation.•It significantly restricts the required information.•It is able to reliably detect multiple oscillation sources simultaneously.
Background
The utility of the forced oscillations technique (FOT) in cystic fibrosis (CF) remains uncertain. The aim of this study was to explore the ability of lower‐frequency FOT indices, alone and ...after adjustment for the lung volume, to assess the extent of ventilation inhomogeneity in CF patients with varying disease severity.
Methods
Forty‐five children, adolescents, and adults with CF (age 6.9–27 years) underwent spirometry, FOT, and nitrogen multiple‐breath washout (N2‐MBW) measurements. The respiratory resistance and reactance at 5 Hz (Rrs5 and Xrs5, respectively) were recorded, and a novel FOT index, the specific respiratory conductance (sGrs), was computed as the reciprocal of Rrs5 divided by the functional residual capacity.
Results
The sGrs correlated well with the lung clearance index (LCI) (Spearman's r: –.797), whereas the correlation of Rrs5 and Xrs5 with the LCI, albeit significant, was weaker (r: .643 and –.631, respectively). The sGrs emerged as the most robust predictor of LCI regardless of the severity of lung disease, as reflected by patients' age and lung function measurements. Most importantly, the relationship between sGrs and LCI remained unaffected by lung hyperinflation, as opposed to that of the LCI with the spirometric and standard FOT indices.
Conclusions
In CF patients, the FOT indices at 5 Hz and the novel, volume‐adjusted parameter sGrs, reflect the extent of lung involvement and the underlying ventilation inhomogeneity in a way comparable to N2‐MBW. Future research should explore the role of lower‐frequency FOT in assessing the severity and monitoring the progression of CF lung disease.
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.
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.
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.
This paper studies the problem of locating the sparse set of sources of forcing inputs driving linear systems from noisy measurements when the initial state is unknown. This problem is particularly ...relevant to detecting forced oscillations in electric power networks. We express measurements as an additive model comprising the initial state and inputs grouped over time, both expanded in terms of the basis functions (i.e., impulse response coefficients). Using this model, with probabilistic guarantees, we recover the locations and simultaneously estimate the initial state and forcing inputs using a variant of the group LASSO (linear absolute shrinkage and selection operator) method. Specifically, we provide upper bounds on: (i) the probability that the group LASSO estimator incorrectly identifies the locations and (ii) the <inline-formula><tex-math notation="LaTeX">\ell _{2}</tex-math></inline-formula>-norm of the estimation error. Our bounds depend on the number of measurements, inputs, and sensors; the sensor noise variance; and the minimum singular value of the observability and impulse response matrices. Our theoretical analysis is one of the first to provide a complete treatment for the group LASSO estimator for the left invertible linear systems with delay. Finally, we validate the performance of the estimator on synthetic models and the IEEE 68-bus, 16-machine power system.
The letter discusses the oscillation event of November 29, 2005 in the western American power system when a 20 MW forced oscillation in Alberta led to 200 MW oscillations on the California-Oregon ...Inter-tie lines. Using archived synchrophasor data from the event, this letter shows that the large amplitude tie-line oscillations were caused by a resonance between the forced oscillations and the 0.25 Hz inter-area western system mode. Specifically the letter shows that resonance occurred even though the system mode was well-damped during the event because of the oscillation frequency and location of the forced oscillations.
Forced oscillations may jeopardize the secure operation of power systems. To mitigate forced oscillations, locating the sources is critical. In this paper, leveraging on Sparse Identification of ...Nonlinear Dynamics (SINDy), an online purely data-driven method to locate the forced oscillation is developed. Validations in all simulated cases (in the WECC 179-bus system) and actual oscillation events (in ISO New England system) in the IEEE Task Force test cases library are carried out, which demonstrate that the proposed algorithm, requiring no model information, can accurately locate sources in most cases, even under resonance condition and when the natural modes are poorly damped. The little tuning requirement and low computational cost make the proposed method viable for online application.
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 (e.g., 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.
Over the past several years, great strides have been made in the effort to monitor the small-signal stability of power systems. These efforts focus on estimating electromechanical modes, which are a ...property of the system that dictate how generators in different parts of the system exchange energy. Though the algorithms designed for this task are powerful and important for reliable operation of the power system, they are susceptible to severe bias when forced oscillations are present in the system. Forced oscillations are fundamentally different from electromechanical oscillations in that they are the result of a rogue input to the system, rather than a property of the system itself. To address the presence of forced oscillations, the frequently used AutoRegressive Moving Average (ARMA) model is adapted to include sinusoidal inputs, resulting in the AutoRegressive Moving Average plus Sinusoid (ARMA+S) model. From this model, a new Two-Stage Least Squares algorithm is derived to incorporate the forced oscillations, thereby enabling the simultaneous estimation of the electromechanical modes and the amplitude and phase of the forced oscillations. The method is validated using simulated power system data as well as data obtained from the western North American power system and Eastern Interconnection.
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