Nonuniform Damping Research Articles

On the Destabilizing Mechanism of Nonuniform Damping in Grid-Forming Converters Penetrated Multi-Machine System

On the Destabilizing Mechanism of Nonuniform Damping in Grid-Forming Converters Penetrated Multi-Machine System

Reasponse-spectra method for assessing seismic resistance of structures possibilities and prospects of usage

The issues of using the response-spectra method for calculating the seismic resistance of structures are considered. The physical meaning of the coefficients included in the normative calculation formulas of the response-spectra technique is analyzed, ways of refining these coefficients are indicated. In particular, the dependence of the peak ground acceleration on the design accelerogram period is noted. The issue of obtaining the displacement spectra on the base of the normative spectral curve is considered. It is noted that with the correct setting of the normative coefficients, calculation by the response-spectra method gives more reliable values of the calculated factors. Dynamic calculating of structures over time are only needed for substantially non-linear systems and, possibly, heavily damped systems with non-uniform damping. Single calculation of the structure according to an accelerogram only disorientate the designer. The refined version of the linear spectral technique presented in the paper should be considered as the main method for assessing the seismic resistance of buildings and structures.

Seismic Response Analysis of Shear Buildings Using Waves

Abstract A method of using waves instead of modes for analyzing the seismic response of buildings is presented. Instead of using the general procedure of response spectra to quantify the seismic hazard of a building a wave response function is used. An important aspect of this approach is that the wave model can describe building response using only four parameters namely, the stiffness, wave speed, time delay, and normalized distance and are shown to be enough to describe the full building response. The method presented is limited to responses due to ground motions from earthquakes and the building response to be predominately in shear. The wave analysis method proposed can be used for variable structure stiffness with uniform and non-uniform damping cases. Comparison using response spectra for a typical shear building is presented and discussed. The strength of the wave function approach is that it provides more information about the response of the specific shear buildings than the response spectra approach. As one of the findings from the analysis using waves is that the maximum strain in a shear building with variable stiffness and non-zero damping is related to the maximum velocity of the ground motion and not the maximum acceleration.

Data-Driven Estimation of Frequency Response From Ambient Synchrophasor Measurements

With the wide deployment of synchrophasor technology, measurement-based dynamic modeling and studies have been becoming increasingly useful for real-time grid operations. This paper considers the problem of estimating the power system frequency response from ambient synchrophasor measurements. Specifically, we develop the analytical conditions for establishing the equivalence between the cross correlation of ambient generator speed data and the system frequency response between any two locations. Our conditions, relying on uniformly damped and equally excited oscillation modes, extend earlier work on electromechanical wave propagation modeling to nonhomogeneous power networks. Numerical results suggest that the validity of the cross correlation approach would hold for more realistic conditions such as nonuniform damping and high-order generator model. Its practical value is further corroborated by real-data results, which closely match with the actual propagation time of electromechanical waves recorded during the 2008 Florida blackout in the Eastern Interconnection system.

Influence of Soil Conditions on the Dynamic Characteristics of Residential Construction

The dynamic characteristics are examined of buildings constructed on soft soil in Ashkhabad. The frequency spectrum and damping are evaluated with respect to soil conditions. It is determined that for buildings up to 5 stories high, damping is strongly nonuniform. Modal first-mode damping is 3-4 times greater than for the rest. For high-rise buildings, modal damping values were close, which was the result of pivoting foundation vibrations and exposure to Rayleigh surface waves. Calculation programs that do not consider nonuniform damping are proposed to be used to assess damping in the first approximation.

Behavior Analysis of the Nonuniform Damping and Screening System in the HTS Generator

The damping and screening system (DSS) is a key structure of the hybrid high-temperature superconducting generator. In this paper, an analytical method was introduced to analyze the performance of the DSS with different time constants on both the d-axis and the q-axis of the generator. First, the distribution of the eddy currents in the DSS was analyzed, and the calculation of the equivalent resistance, inductance, and time constant of the DSS was considered. Then, to analyze the performance of the nonuniform DSS (NDSS), a splitting method was introduced. Using the new method, parameters of the damping part, screening part, and supplementing part of the NDSS were calculated, respectively. At last, the screening and damping performances of the NDSS were evaluated. The finite-element method was also employed to verify the analytical results. An experimental platform was built up to test the screening ratio and verify the simulating results.

Experimental investigation of zero phase shift effects for Coriolis flowmeters due to pipe imperfections

Theoretical investigations of a single, straight, vibrating, fluid-conveying pipe have resulted in simple analytical expressions for the approximate prediction of the spatial shift in vibration phase. The expressions have lead to hypotheses for real Coriolis flowmeters (CFMs). To test these, the flexural vibrations of two bent, parallel, non-fluid-conveying pipes are studied experimentally, employing an industrial CFM. Special attention has been paid on the phase shift in the case of zero mass flow, i.e. the zero shift, caused by various imperfections to the “perfect” CFM, i.e. non-uniform pipe damping and mass, and on ambient temperature changes. Experimental observations confirm the hypothesis that asymmetry in the axial distribution of damping will induce zero shifts similar to the phase shifts due to fluid flow. Axially symmetrically distributed damping was observed to influence phase shift at an order of magnitude smaller than the primary effect of mass flow, while small added mass and ambient temperature changes induced zero shifts two orders of magnitude smaller than the phase shifts due to mass flow. The order of magnitude of the induced zero shifts indicates that non-uniform damping, added mass as well as temperature changes could be causes contributing to a time-varying measured zero shift, as observed with some commercial CFMs. The conducted experimental tests of the theoretically based hypotheses have shown that simple mathematical models and approximate analysis allow general conclusions, that may provide a direct insight, and help increasing the benefit of time consuming numerical simulations and laboratory experiments.

Intrinsic Damping: Modeling Techniques for Engineering Systems

Mathematical models for capturing the effects of intrinsic damping are based upon a multitude of simplifying assumptions. In this work, common equivalent linear models are reviewed, and their implementations for modeling energy dissipation on the system and material scales are compared in simple, representative examples. It is shown that several independent methodologies result in approximately the same predicted responses for systems with uniform dissipative characteristics if certain assumptions are made regarding the frequency dependence of intrinsic damping. However, these assumptions result in divergences of predicted responses when extended to composite systems with nonuniform dissipative characteristics. As no analytical or validated numerical solutions for the dynamic response of composite systems with nonuniform dissipative characteristics exist, it is unclear as to which methodologies most closely predict composite system behavior. Further work in developing models to capture nonuniform intrinsic damping characteristics must be performed to generate a fully robust means for capturing energy dissipation across all levels of complexity in engineering systems.

The role of damping on energy and power in vibrating systems

The role of damping with respect to energy and energy flow in vibrating mechanical systems was examined with the aim of establishing some general relationships. The link between the energy flow and the system energy is considered from both the local and global points of view. Locally, the mean intensity divergence is shown to be strictly proportional to the product of internal damping and potential energy density at a given point, while the imaginary value of complex divergence is proportional to the mean Lagrangian energy density. Globally, the mean value of the total vibratory power input to a structure is proportional to the volume integral of the product between the loss factor and the potential energy density. If the damping is uniformly distributed within a structure, this integral reduces to the product between the (constant) loss factor and the total potential energy. The global potential and kinetic energies can be obtained from the known complex input power to the structure and the known loss factor. In the case of non-uniform damping, the simple power–energy relationships are shown to hold fairly well where potential energy is involved, but could break down if kinetic energy is used instead. Several examples are given to illustrate the theoretical findings.

Modal oscillation control in internally patternedNi80Fe20thin film microstructures

The broadband magnetization dynamics (MD) of lithographic, polycrystalline thin film ferromagnetic ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ elements is studied experimentally using time-resolved scanning Kerr microscopy and numerically via micromagnetic simulation. The spatiotemporal evolution of the polar component of magnetization in response to a small out-of-plane transient magnetic pulse is imaged in the presence of a weak in-plane static bias field. In a uniform square platelet the spatial response is strongly controlled by the nonuniform static magnetization distribution associated with the closure domains transverse to the bias field direction. A circular pinhole is patterned in the center of a square platelet to show that the spatial pattern of magnetization oscillation response also depends sensitively on weaker variations of the static magnetization. The Landau Lifshitz Gilbert model reproduces the observed modal oscillation symmetry and reveals in detail that the observation of spatially nonuniform damping in the experiment is a result of conversion of energy into shorter wavelength modes in the vicinity of the domain boundaries.

A new Lyapunov function for interconnected power systems

A Lyapunov function is constructed for a general n-machine power system with nonzero transfer conductance. The theory of dissipative dynamic systems and its modifications are used. The Lyapunov function construction procedure calls for checking positive definiteness of a sparse matrix. Results are reported only for the case of nonuniform damping, which is more complex than the uniformly damped system. The procedure is iterative and is guaranteed to converge for uniform damping but may fail to converge for a very lightly nonuniformly damped system with strong interconnections. The Lyapunov function is a quadratic term plus a weighted sum of integrals, a form not reported before. This is an extension of a previously reported quadratic Lyapunov function.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

New decomposition-aggregation approach applied to power system with speed governor

A new decomposition-aggregation approach is developed to perform transient stability analysis of an N-machine power system with a speed governor. The system decomposition is performed so that every subsystem includes four machines, instead of only two or three machines as considered in other work. The system model is derived and decomposed into (N − 1)/3 11th-order interconnected subsystems considering transfer conductances, nonuniform mechanical damping, electromagnetic damping and speed governor action. Each of these subsystems is decomposed into a free subsystem containing 12 nonlinearities and interconnections. A square aggregation matrix of order (N − 1)/3 is obtained instead of orders N and (N + 1)/2 for the pair-wise and triple-wise decompositions, respectively. The approach is applied to a 10-machine power system and an estimate for the system asymptotic stability domain is determined. System transient stability computations are carried out considering a three-phase short circuit fault, with successful reclosure, near a system bus or a sudden loss of one of the system loads. The approach is used to determine a reclosure time for the faulted line and a reconnection time for the lost load required for the system to regain its prefault (normal) conditions. The approach developed is suitable and can be easily used for stability analysis of power systems (the number of machines may be more than 10). The developed approach can also reduce the conservativeness of the decomposition-aggregation method.

Stability and security assessment of a class of systems governed by LaGrange's equation with application to multi-machine power systems

In recent studies, it has been verified heuristically and experimentally (via simulations) that instability in power systems due to a fault occurs when one machine or a group of machines, called the critical group, loses synchronism with the remaining machines. Using energy functions associated with a critical group (rather than system-wide energy functions), transient stability results which are less conservative than other existing results, have recently been obtained. The existence and identity of a critical group is ascertained in these studies by off-line simulations. In the present paper, we first establish some general stability results for a large class of dynamical systems (which are arrived at via a Lagrange formulation). We then show how multi-machine power systems with nonuniform damping are special cases of this class of dynamical systems. Next, we show that our stability results can be used to establish analytically the existence and the identity of the critical group of machines in a power system due to a given fault. Furthermore, we also show that our stability results can be used to obtain an estimate of the domain of attraction of an asymptotically stable equilibrium of a power system. The results presented herein can potentially be used on-line to determine which machines belong to a critical group, and to use this information for corrective action (e.g., shedding of the critical generators or fast valving for these generators.) As such, our results have potential applications in fault diagnosis and security assessment of certain classes of dynamical systems in general and of power systems in particular. The applicability of the present results is explored by means of a specific example (a 162-bus, 17-generator model of the power network of the State of Iowa). Certain limitations of the present results are recognized and avenues for further research are identified.

Instability of parametric dynamic systems with non-uniform damping

A unified way of looking at parametric and combination resonances in systems with periodic coefficients and different amounts of damping in the various modes of vibration is presented. The stability boundaries of the coupled Mathieu equations are determined by the harmonic balance method, Fourier series with periods 2 T and T being assumed. The basic characteristics of the solution are discussed and the method is applied to multiple-degree-of-freedom dynamic systems. The destabilizing effect on the combination resonances is obtained by the present method.

On the attractivity of imbedded systems

A new approach designed to aid in the construction of Liapunov functions is proposed. It is based on the notion of partial properties. A given dynamic system is imbedded into an augmented system whose attractivity with respect to a part of variables is deduced by means of an auxiliary function. This leads to an exact procedure for computation of attractivity region estimates for dynamic systems. An important feature of the method is the great reduction of conservativeness of the region estimate in the case of the overlapping decomposition of large-scale systems. When applied to a multimachine power system with non-uniform damping and transfer conductances, the method gives an enlarged estimate of the region of transient stability.

Decomposition and Stability of Multimachine Power Systems

An m-machine model with nonuniform damping and transfer conductances is pair-wise decomposed into m-1 interconnected subsystems each containing the speed of the reference machine as a common part. The overlapping decomposition leads to a Lur’e-Postnikov type of subsystem stability analysis and a vector Liapunov function application to computations of stability region estimates for the overall m-machine model. The proposed decomposition stability analysis should be judged satisfactory to the extent that the conservativeness of the obtained estimates are outweighed by their computational simplicity and the structural insight the approach can provide in transient stability analysis of multimachine power systems.

Derivation of completely controllable and completely observable state models for multimachine power system stability studies†

The object of the present paper is to develop state models for multimachine power system stability studies which are completely controllable and completely observable. They are necessary for any stability studies based on the second method of Lyapunov. Starting from the definition of the degree of a rational function matrix, the minimal realizations for a two- and three-machine power system with uniform and nonuniform damping are obtained and are shown to be completely controllable and completely observable. A generalization for an H-machine power system follows as a natural consequence. Further, the present work provides the theoretical basis for the proper choice of state variables, i.e. relative rotor angles instead of absolute rotor angles as state variables.

Impulsive Motion of Elasto-Plastic Shear Buildings

The method of normal modes is applied to the analysis of elasto-plastic shear buildings subjected to impulsive loads, foundation uplift, and nonuniform viscous damping. Interaction of foundation ro...

Frequency Response Fluctuations in Rooms. II. An Approximate Theory

Irregularities in the steady-state frequency response of rooms arise from the normal mode structure, and depend on the frequency spacing, the damping, and the relative excitation of the normal modes. A first approximation theory of transmission irregularity, Φ, has been developed on a simplified model. Uniformly spaced normal modes, equally excited and equally damped, are added to yield an average ratio of maximum to minimum response. The influence of non-uniform spacing is introduced in the form of a frequency spacing index, ψ, which has been calculated for certain cases. The influences of non-uniform excitation and non-uniform damping are introduced formally but explicit evaluation has been made only for certain simple conditions. The resulting equation has the form Φ = A V ν2 log[1 + Bψν4a2] db/c.p.s. where A and B are constants, V is volume of room, a is the room absorption factor (reducing to Σαs for Sabine conditions). There is a region of maximum roughness (irregularity per c.p.s.) at a frequency of the order of 104(T/V)12, where T is reverberation time and V is volume. Well above this region, Φ diminishes inversely with ν2 and A2. This result is compared with experimental data.