電力系統における非線形動的現象とその応用-Hopf分岐解析とカオス動揺解析を中心として-

The authors analyze interarea mode phenomena in stressed power systems, following large disturbances. It is shown that the interarea mode phenomenon could occur as a result of a nonlinear interaction of the natural modes of oscillation in the system. A technique for determining the interaction is developed and the machines participating in the interaction are identified. A procedure for predicting the onset of the interarea mode is presented. The technique was tested on two realistic sample test systems: a 50 generator system and a 126 generator system. The results of this analysis indicate that the procedure can detect the onset of the interarea mode phenomenon and also detect the machines which participate in the interacting natural modes of oscillation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Phasor measurement based on IEC 61850-9-2 and Kalman–Filtering

Yenilenebilir enerji kaynaklarının hızlı gelişimi, dağıtık üretim tesislerinin entegrasyonu ve dijitalleşmedeki ilerlemeler dünya genelindeki güç sistemlerinde karmaşık bir değişime neden olmaktadır. Güç sistemlerinin karmaşıklığı hem lisans hem de lisansüstü öğrencilerinin güç sistemleri ile ilgili çalışmalarını sıkıcı, zor ve zaman alıcı hale getirmektedir. Bununla birlikte, simülasyon araçlarının kullanılması, güç sistemleri çalışmalarıyla ilgili hesaplama işlemlerini büyük ölçüde basitleştirmiştir. Yalnızca güç sisteminin mevcut çalışma koşulları altında çalışmasını değil, aynı zamanda gelecekteki genişlemelerin planını ve tasarımını da değerlendirmek için güç akışı çalışmaları giderek daha gerekli hale gelmektedir. Bu makale, öğrencilerin güç sistemlerindeki karmaşık olayları daha iyi anlamalarına yardımcı olmak için gelişmiş görselleştirme teknikleri kullanan PowerWorld Simülatör ile güç akışı analizinin bir incelemesini sunmaktadır. Bu amaçla, Stevenson’ın 5 baralı güç sisteminin güç akışı analizi Newton-Raphson, Gauss-Seidel ve Hızlı Ayrık metotları ile incelenmiştir. Simülasyon sonuçları hem görsel olarak hem de tablo olarak verilmiştir. Sonuç olarak, PowerWorld Simülatör ile öğrencilerin geleneksel çözümlere ek olarak güç sistemi analiz problemlerini daha iyi anlayacağı görülmüştür.

Autoparametric Vibrations of a Nonlinear System with a Pendulum and Magnetorheological Damping, by Jerzy Warminski and Krzysztof Kecik: Introduction to Autoparametric Vibrations. - Model of the Nonlinear Oscillator with an Attached Pendulum. - Approximate Analytical Solutions and Their Stability. - Regular and Chaotic Dynamics Near the Main Parametric Resonance. - Experimental Setup of the System with Active MR Damper. - Dynamics of an Autoparametric System with MR Damper. - Influence of a Nonlinear System's Suspension on the InstabilityRegions. - Conclusions and Remarks. - References. - On the Dynamics of Pedestrians-Induced Lateral Vibrations of Footbridges, by Stefano Lenci and Laura Marcheggiani: Introduction and Literature Review. - A Continuous-Time Model: the SAMEO Model. - A Discrete-Time Model. - Conclusions. - References. - Applications for Shape Memory Alloys in Structural and Machine Dynamics, by Matthew P. Cartmell, Arkadiusz J. Z ak and Olga A. Ganilova: Review of the Literature and Introduction. - Modelling of the Shape Memory Effect. - Dynamics of Composite Beams and Plates with Integrated SMA Elements. - Applications to Flexible Rotors. - Antagonistic Actuation Control of Vibration in Plates. - Conclusions. - References. - Theoretical and Experimental Nonlinear Vibrations of Sagged Elastic Cables, by Giuseppe Rega: Introduction. - Cable Modelling and Theoretical Analysis. - Nonlinear Phenomena in Forced Dynamic Response. - Experimental Characterisation of Cable Nonlinear Dynamics. - Further Developments and Research Topics. - References. - Engineering Applications of Non-Smooth Dynamics, by Marian Wiercigroch and Ekaterina Pavlovskaia Non-Smooth Dynamical Systems in Engineering Dynamics. - Drifting Oscillator as an Effective Model of Vibro-Impact Moling. - Nonlinear Dynamics Caused by Fatigue Crack Growth. - Regular and Chaotic Dynamics of a Rotor System with a Bearing Clearance. - Conclusions. - References.

Chaotic oscillation is an undesirable phenomenon in power system and it can destroy the stability of power system. The objective of this paper is to propose variable speed synergetic control to eliminate chattering phenomenon in sliding-mode control and avoid undesirable phenomena when suppressing chaotic oscillation in power system. The prominent advantage of proposed control scheme is that it can adjust convergence speed according to the system response thus avoiding undesirable phenomena in the control process. Simulation results show that our control scheme avoids undesirable phenomena in the control process and speeds up convergence rate.

36 - Electromagnetic Transients

With the increasing usage of power electronic devices that contribute to harmonic distortion in power systems, analysis of harmonic components has become important for maintaining power quality. Moreover, time-synchronized point-on-wave measurements are of growing interest for analyzing dynamic phenomena in power systems, where synchrophasors that report a magnitude and angle of the estimated fundamental component of a signal are insufficient. This paper proposes a new method for estimating harmonic content by applying quadrature demodulation iteratively to estimate a synchrophasor for each harmonic component of a power system signal. We first apply the method to simulated signals to verify its accuracy, then we demonstrate its effectiveness at reconstructing a signal from data measured from real power distribution systems.

A method based on a Lure Lyapunov function is developed to analyse subsynchronous resonance (SSR) phenomena in power systems. An improved Lure Lyapunov function used to analyse the stability of a power system including the turbine-generator (T-G) shaft is presented first. Then, a standard Lure control model for a power system with a T-G shaft is obtained. The stability of such nonlinear systems at the equilibrium points is discussed in detail. The stable operation region of the system is discussed with the proposed method. The effectiveness of the proposed method is verified by a case study. This study has shown potential benefits and the validity of the Lyapunov direct method in the subsynchronous resonance analysis. Compared with the conventional analysis method, such as eigenvalue and frequency scanning techniques, the proposed method is based on the original nonlinear system. Error, that may be introduced by linearisation, is avoided completely. Moreover, the stable operation region of power systems can be obtained by the proposed method.

International audience

Electromagnetic transient study on flexible control processes of ferroresonance

Only qualitative aspects on the skin effect in conductors are properly described in the technical literature on power systems applications. Although the qualitative analysis is an important issue, it is not sufficient for a full approach and proper understanding of this electromagnetic phenomenon in power systems, more specifically in power transmission systems. The present work intends to provide a quantitative analysis of the skin effect on conductors based exclusively on the Maxwell Equations, whereby both physical and mathematical treatments of the phenomenon are properly analysed. This approach contrasts with the traditional one that uses a complex formulation based on both the differential Maxwell equations and potential concepts. Finally, a discussion on the application of the Poynting theorem on the external surface of the cylindrical conductor is presented in order to evaluate not only the resistance, but also the inductance as a function of the frequency, which is not properly discussed in the technical literature on power systems.

A dicone moving on a pair of cylindrical rails can be considered as a simplified model of a railway wheelset. Taking into account the non-linear friction laws of rolling contact, the equations of motion for this non-linear mechanical system result in a set of differential-algebraic equations. Previous simulations performed with the differential-algebraic solver DASSL, [2], and experiments, [7], indicated non-linear phenomena such as limit-cycles, bifurcations as well as chaotic behaviour. In this paper the non-linear phenomena are investigated in more detail with the aid of special in-house software and the path-following algorithm PATH [10]. We apply Poincare sections and Poincare maps to describe the structure of periodic, quasiperiodic and chaotic motions. The analyses show that part of the chaotic behaviour of the non-linear system can be fully understood as a non-linear iterative process. The resulting stretching and folding processes are illustrated by series of Poincare sections.

This article considers the nonlinear dynamic model formulated as the system of differential and operator equations. This system is assumed to enjoy an equilibrium point. The Cauchy problem with the initial condition with respect to one of the desired functions is formulated. The second function controls the corresponding nonlinear dynamic process. The sufficient conditions of the global classical solution’s existence and stabilisation at infinity to the equilibrium point are formulated. The solution can be constructed by the method of successive approximations. If the conditions of the main theorem are not satisfied, then several solutions may exist. Some solutions can blow-up in a finite time, while others stabilise to an equilibrium point. The special case of considered dynamic models are differential-algebraic equations which model various nonlinear phenomena in circuit analysis, power systems, chemical processes and many other processes.

The increasing complexity of power systems and the need for analyses that ensure the safe and reliable operation of the system have led to the development and use of software tools that simulate system behaviour. In this context, Electromagnetic transient (EMT) studies are essential for understanding high-frequency phenomena in power systems, most often occurring during switching operations and atmospheric discharge.This paper discusses the application of SCAD/EMTDC, one of the leading software tools for EMT studies. It provides an example of modelling and energization of an overhead transmission line, with a focus on overvoltages and inrush currents that occur in the process. A detailed explanation of line modelling using the frequency-dependent model in PSCAD/EMTDC will be provided, as this level of detail is necessary for studies involving frequencies higher than the system’s fundamental frequency. Since switching overvoltages depend on the instantaneous voltage values in each phase, energization will be performed at different time instants within a single cycle to capture the worst-case overvoltage scenario. The simulation results will be analysed and compared with official technical recommendations for grid connection. Additionally, the study will provide insights into potential issues arising from switching operations and propose mitigation measures to reduce overvoltage stresses.

The onset of Partial Discharge (PD) activity within an insulation system is often an important signature of degradation. Changes in the PD pattern aid assessment of the insulation degradation level. High voltage transients such as lightning and switching impulses are inevitable phenomena in power systems. They can impose electrical stresses on the insulation system of power components such as power transformers and their bushings which may lead to their failure. After the arrival of a transient the AC PD pattern may change, in a way that is influenced by the type of PD source. In this paper, the effect of HV impulses on the change of surface and cavity discharges of oil-impregnated paper has been investigated. With resemblance to the real situation, insulation samples have been subjected to an impulse voltage superimposed on the AC voltage. The behavior of PDs before and after the impulse for different defects and moisture content levels in oil-impregnated paper has been studied. The results show a distinctive behavior of PD due to the impulse for each defect and insulation condition, either by change in the PD rate and magnitude or by causing PD inception or extinction. Recording the voltage signals and associated PD measurements during and after the incident of high voltage transients can be used for assessing the insulation condition of power transformers and their bushings and interpretation of the recorded signals can be used for online diagnostics.