Stability Analysis and Control of Nonlinear Power System Oscillations

This work investigates the nonlinear oscillatory behaviors of multi-machine power systems. New model-based and measurement-based approaches are proposed for stability analysis and control of nonlinear oscillations. For stability analysis, a recently proposed model-based nonlinear oscillation analysis method, nonlinear modal decoupling (NMD), is investigated on its ability in capturing the stability information of a multi-machine power system. From the differential-equation model of the power system, the NMD inversely constructs a set of 1-degree-of-freedom nonlinear oscillators, referred to as decoupled oscillators or subsystems, with each one corresponding to an oscillation mode of the original system. It is shown that retaining high order polynomial terms in the differential equation of each decoupled oscillator can make it more accurately represent the nonlinear modal dynamics and conditions of stability regarding the corresponding oscillation mode. For power system analysis, keeping the polynomial terms up to the 3rd-order during the decoupling is acceptable for the purpose of approximating assessment for transient stability. A transient stability analysis approach is proposed to apply the NMD for early warning of transient instability caused by inter-area oscillations. This new approach simplifies the real-time monitoring of the whole power system to the monitoring of only a few critical modes by checking the dynamics of the corresponding decoupled oscillators and their stability boundaries. Thus, when a critical oscillation mode is going to evolve into a mode of instability, this approach can provide early warning to the power system operator. For stability control, a direct damping feedback control method is proposed to control the damping ratio of a target dominant mode to closely follow a pre-set value by utilizing power converter-interfaced energy resources, e.g. battery-based energy storage devices. The direct damping feedback controller is designed to consist of a proportional-integral controller, a low-pass filter and a power system module that includes a reduced single-oscillator power system equivalent on the target oscillation mode and its measurement-based damping estimation algorithm. The parameters of the PI controller are optimized by considering the trade-off between the requirements of robustness and control performance. The power system module is represented by a transfer function based on the zeroth-order parametric resonance phenomenon. By identifying a nonlinear oscillator to fit dynamics of the target mode under both small and large disturbances, the measurement-based real-time damping estimation algorithm provides a feedback signal to the direct damping feedback controller. Numerical studies on the 48-machine Northeast Power Coordinating Council system validate the effectiveness of the proposed damping control method

New Analysis Framework for Transient Stability Evaluation of DC Microgrids

Because of the low inertia of dc microgrids, system state variables are easily changed acutely after being disturbed. Hence, dc microgrids meet the serious transient stability issues especially for some stressed states. But the transient stability analysis is a very challenging problem since the dc microgrid system is high-order and nonlinear. To offer a new and more effective analysis framework, this paper proposes a nonlinear decoupling method to evaluate the transient stability of dc microgrids. The proposed nonlinear decoupling method takes full consideration of the nonlinearity of the dc microgrid system and approximately transforms the original nonlinear system into a series of decoupled first-order quadratic or second-order quadratic systems. For these decoupled low-order quadratic systems, their dynamics and stability can be analyzed easily, then the transient stability of the original system can be reflected indirectly. Also, the nonlinear decoupling based analysis framework can be extended to other power electronics dominated power systems to evaluate their transient stability. The accuracy of the proposed analysis method has been validated through related case studies

Wavelet-Based High-Order Adaptive Modeling of Lossy Interconnects

Abstract—This paper presents a numerical-modeling strategy for simulation of fast transients in lossy electrical interconnects. The proposed algorithm makes use of wavelet representations of voltages and currents along the structure, with the aim of reducing the computational complexity of standard time-domain solvers. A special weak procedure for the implementation of possibly dynamic and nonlinear boundary conditions allows to preserve stability as well as a high approximation order, thus leading to very accurate schemes. On the other hand, the wavelet expansion allows the computation of the solution by using few significant coefficients which are automatically determined at each time step. A dynamically refinable mesh is then used to perform a sparse time-stepping. Several numerical results illustrate the high efficiency of the proposed algorithm, which has been tuned and optimized for best performance in fast digital applications typically found on modern PCB structures. Index Terms—Finite difference methods, time-domain analysis, transmission lines, wavelet transforms. I

Dynamics and stability of wind turbine generators

Synchronous and induction generators are considered. A comparison is made between wind turbines, steam, and hydro units. The unusual phenomena associated with wind turbines are emphasized. The general control requirements are discussed, as well as various schemes for torsional damping such as speed sensitive stabilizer and blade pitch control. Integration between adjacent wind turbines in a wind farm is also considered

Double-Mode Stellar Pulsations

The status of the hydrodynamical modelling of nonlinear multi-mode stellar pulsations is discussed. The hydrodynamical modelling of steady double-mode (DM) pulsations has been a long-standing quest that is finally being concluded. Recent progress has been made thanks to the introduction of turbulent convection in the numerical hydrodynamical codes which provide detailed results for individual models. An overview of the modal selection problem in the HR diagram can be obtained in the form of bifurcation diagrams with the help of simple nonresonant amplitude equations that capture the DM phenomenon.Comment: 34 pages, to appear as a chapter in Nonlinear Stellar Pulsation in the Astrophysics and Space Science Library (ASSL), Editors: M. Takeuti & D. Sasselov (prints double column with pstops '2:[email protected](22.0cm,-2cm)[email protected](22.0cm,11.0cm)' in.ps out.ps