Estimation of Power System Inertia Using Nonlinear Koopman Modes

We report a new approach to estimating power system inertia directly from time-series data on power system dynamics. The approach is based on the so-called Koopman Mode Decomposition (KMD) of such dynamic data, which is a nonlinear generalization of linear modal decomposition through spectral analysis of the Koopman operator for nonlinear dynamical systems. The KMD-based approach is thus applicable to dynamic data that evolve in nonlinear regime of power system characteristics. Its effectiveness is numerically evaluated with transient stability simulations of the IEEE New England test system.Comment: 10 pages, 4 figures, conferenc

Adaptive Parameter Estimation of Power System Dynamic Models Using Modal Information

Knowledge of the parameter values of the dynamic generator models is of paramount importance for creating accurate models for power system dynamics studies. Traditionally, power systems consists of a relatively limited numbers of large power stations and the values of generator parameters were provided by manufacturers and validated by utilities. Recently however, with the increasing penetration of distributed generation, the accuracy of these models and parameters cannot be guaranteed. This thesis addresses the above concerns by developing a methodology to estimate the parameter values of a power system dynamic model online, employing dynamic system modes, i.e. modal frequencies and damping. The dynamic modes are extracted from real-time measurements. The aim of the proposed methodology is to minimise the differences between the observed and modelled modes of oscillation. It should be emphasised that the proposed methodology does not aim to develop the dynamic model itself but rather modify its parameter using WAMS measurements. The developed methodology is general and can be used to identify any generator parameters., However, thesis concentrates on the estimation of generator inertia constants. The results suggest that the proposed methodology can estimate inertias and replicate the dynamic behaviour of the power system accurately, through the inclusion of pseudo-measurements in the optimisation process. The pseudo-measurements not only improves the accuracy of the parameter estimation but also the robustness of it. Observability, a problem when there are fewer numbers of measurements than the numbers of parameters to be estimated, has also been successfully tackled. It has been shown that the damping measurements do not influence the accuracy and robustness of generator inertia estimation significantly

Estimation of oscillations and frequency responses of power systems via optimal vector fitting

Orientador: Prof. Dr. Gustavo Henrique da Costa OliveiraCoorientador: Prof. Dr. Rôman KuiavaTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia Elétrica. Defesa : Curitiba, 19/06/2019Inclui referências: p. 123-129Área de concentração: Sistemas de EnergiaResumo: A identificacao de sistemas esta presente em diversas areas da engenharia onde um modelo matematico preciso e exigido. Diferentes tipos de algoritmos de estimacao tem sido usados para identificar sistemas lineares invariantes no tempo. Contudo, o caso particular que considera a utilizacao dos chamados metodos iterativos Vector Fitting (VF) tem atraido atencao significativa da comunidade cientifica, especialmente durante as ultimas duas decadas. Neste contexto, esta tese aborda o problema de formulacao de algoritmos VF para ambos os dominios, do tempo e da frequencia. No dominio do tempo, algoritmos VF sao aqui desenvolvidos dentro de um contexto ringdown, de modo que dinamicas oscilatorias (assim como dinamicas puramente exponenciais) de sistemas de potencia possam ser efetivamente estimadas atraves de conjuntos de dados transitorios extraidos desses sistemas. Neste sentido, tambem e apresentada uma abordagem multisinal para estimar simultaneamente multiplos sinais transitorios possivelmente distribuidos em diferentes localizacoes do sistema de potencia que esta sendo modelado. Por outro lado, no ambito do dominio da frequencia, esta tese apresenta um metodo VF que pode ser aplicado na estimacao de modelos formados por bases de funcoes racionais (BFRs) definidas tanto no tempo continuo como no tempo discreto. Em ambos os contextos do tempo e da frequencia, formulacoes VF alternativas baseadas em variaveis instrumentais (VI) sao tambem vastamente investigadas neste trabalho. Solucoes convergidas fornecidas por essas formulacoes VF baseadas em VI sao provadamente otimos locais de suas funcoes objetivo nao-lineares correspondentes, sendo essa importante propriedade de otimalidade local independente da natureza do ruido que corrompe os dados de estimacao. Exemplos numericos apresentados neste trabalho focam em dados de resposta em frequencia extraidos de transformadores de potencia e de potencial indutivo reais assim como em conjuntos de dados transitorios extraidos do sistema de potencia interconectado Brasileiro e do sistema de interconexao leste norte americano. Palavras-chave: identificacao de sistemas. vector fitting. analise ringdown. estimacao de respostas em frequencia. variaveis instrumentaisAbstract: System identification appears in several areas of engineering where a accurate mathematical model is required. Many different types of estimating algorithms have been used for identifying linear time-invariant systems. Nonetheless, the particular case of using the so-called iterative Vector Fitting (VF) algorithms has been drawing significant attention from scientific community, especially during the last two decades. In this context, this thesis addresses the problem of formulating VF algorithms for both time- and frequencydomain system identification. When it comes to time-domain, VF algorithms are here developed within a ringdown context, so that oscillatory (as well as purely exponential) dynamics of power systems can be effectively estimated through transient (ringdown) data sets extracted from these systems. In this sense, it is also presented a multi-signal approach for simultaneously estimating multiple transient signals possibly distributed over different locations of the power system under modeling. On the other hand, when it comes to frequency-domain, this thesis presents a unifying VF method which can be similarly applied for estimating models formed either by continuous- or discrete-time rational basis functions (RBFs). In both time- and frequency-domain contexts, alternative VF formulations based on instrumental variables (IV) are also intensively investigated throughout this thesis. Converged solutions provided by these IV-based VF formulations are proved to be local optimums of their corresponding nonlinear objective functions, being this important optimality property independent on the nature of the noise that corrupts estimation data. Numerical examples presented in this work focus on frequency response data extracted from actual power and potential transformers as well as on transient data sets extracted from the Brazilian Interconnected Power (BIP) system and from the North American Eastern Interconnection (NAEI) system. Keywords: system identification. vector fitting. ringdown analysis. frequency response estimation. instrumental variables

Methodology for characterizing electric power system response and locating the energized capacitor banks using conventional power quality data

textA relatively small harmonic current with frequencies near or at the power system parallel resonant frequencies could excite the power system into a resonance condition. While a capacitor bank is not the root cause of the condition, it facilitates and helps cause the problem. This is because when the capacitor bank is energized, the system resonant frequency could shift closer to existing harmonic frequencies produced by nonlinear loads. Therefore, the objective of this dissertation is to quantify the power system characteristics corresponding to the parallel resonant frequencies and system damping. Additionally, since a capacitor bank actively facilitates the resonance condition, the relative or exact location of the involved bank must be determined. This dissertation first presents a practical and accurate methodology to estimate system parallel resonant frequencies by performing spectral analysis of the voltage and current transient data immediately after the capacitor bank switching. The proposed method is also robust in that the accuracy of the resulting estimates is not affected by prevalent harmonics in the system. This dissertation provides two efficient algorithms for estimating the system damping parameters using the Hilbert and analytic wavelet transforms. These algorithms take advantage of the principle of an asymptotic or weaklymodulated signal, for which the signal phase varies much more rapidly than the amplitude. The zero-input voltage response or free response of the capacitor bank energizing can be categorized into these asymptotic signals, and one can assign a unique time-varying amplitude with the system damping information and phase pair by building analytic signals. System model reduction theory also allows us to interpret or quantify this damping as an effective X/R ratio. This dissertation defines two fundamental signatures of shunt capacitor bank energizing. It demonstrates that these two signatures can be utilized to accurately determine the relative location of an energized capacitor bank whether it is upstream or downstream from the monitoring location. This dissertation also presents an efficient and accurate methodology for finding the exact location of an energized capacitor bank. Once a PQ monitor is found to be upstream from the capacitor bank by the relative location finding algorithm, the proposed algorithm can further determine the exact location of the switched capacitor bank by estimating the distance between the PQ monitor and the energized capacitor bank. Thus, one can pinpoint the energized capacitor bank causing the resonance.Electrical and Computer Engineerin

Synchronized Measurements Processing Methodology as a Tool for Monitoring Power System Oscillations

Monitoring, protection and control of the electrical power system require the design and implementation of specific applications that are based on analytical methods for the processing of synchronized measurements. Therefore, it is necessary to select the adequate type of mathematical analysis that best suits the requirements of a particular application. This paper describes analytical methods used for the processing of synchronized measured electrical quantities for detection and analysis of the variety of oscillations. The oscillatory phenomena of active power and frequency as a case study of one disturbance in the power system are analyzed. The results of processing the actual synchronized measurements for that case study are presented afterwards. Different data processing methods (spectral analysis methods) are compared, and finally, a recommendation for appropriate methods for processing synchronized measurements in application for recognition, processing and alarming of oscillations of active power is given

Generalized Participation Factors on Nonlinear Power System Oscillations

This work investigates the linear and nonlinear participation factors in power system oscillations, introducing novel model-based and measurement-based approaches for stability analysis. From the measurement perspective, this research proposes a method for estimating participation factors from generator response measurements under diverse disturbances. The devised technique computes extended participation factors that align precisely with model-based factors, given that the measured responses satisfy an ideally symmetric condition. The symmetric condition is further relaxed by identifying a coordinate transformation from the original measurement space to an optimally symmetric space, thereby achieving the ideal estimation of participation factors from measurements alone. The effectiveness of the proposed approach is demonstrated comprehensively on a two-area system before being tested on a 48-machine power system from the Northeast Power Coordinating Council (NPCC). Given that measurement-based PFs often necessitate considerable data and a black-box system model, the study also proposes response-based PFs for system application, including Electromagnetic Transients (EMT) simulations. Additionally, this research introduces an Extended Prony Analysis method for measurement-based modal analysis. Drawing upon normal form theory, it juxtaposes analyses on transient and post-transient waveforms, distinguishing resonance modes triggered by near-resonance conditions from natural modes. This method provides more precise modal properties than traditional Prony Analysis, particularly in the case of near-resonance disturbances. From the model-based perspective, this research scrutinizes the limitations of existing nonlinear PFs, advocating for Time-Variant Nonlinear Participation Factor (TNPF). The relationships between PFs and NPFs are examined in detail from three aspects: perturbation amplitude, time dimension, and nonlinear mode. Additionally, the uniqueness of linear and nonlinear PFs is proven by introducing scaling factors. To bridge the discontinuity between linear and nonlinear PFs, two steps are taken: introducing a time decaying factor to address perturbation amplitude and time dimension, and defining a nonlinear mode via convolution, considering the influence from resonances. The resulting TNPF is presented, with its efficacy demonstrated through a case study

Measurement-based analysis of the dynamic performance of microgrids using system identification techniques

The dynamic performance of microgrids is of crucial importance, due to the increased complexity introduced by the combined effect of inverter interfaced and rotating distributed generation. This paper presents a methodology for the investigation of the dynamic behavior of microgrids based on measurements using Prony analysis and state-space black-box modeling techniques. Both methods are compared and evaluated using real operating conditions data obtained by a laboratory microgrid system. The recorded responses and the calculated system eigenvalues are used to analyze the system dynamics and interactions among the distributed generation units. The proposed methodology can be applied to any real-world microgrid configuration, taking advantage of the future smart grid technologies and features