Transonic Aeroelastic Stability Analysis Using a Kriging-Based Schur Complement Formulation

A method is described to allow searches for transonic aeroelastic instability of realistically sized aircraft models in multidimensional parameter spaces when computational fluid dynamics are used to model the aerodynamics. Aeroelastic instability is predicted from a small nonlinear eigenvalue problem. The approximation of the computationally expensive interaction term modeling the fluid response is formulated to allow the automated and blind search for aeroelastic instability. The approximation uses a kriging interpolation of exact numerical samples covering the parameter space. The approach, demonstrated for the Goland wing and the multidisciplinary optimization transport wing, results in stability analyses over whole flight envelopes at an equivalent cost of several steady-state simulations.

The use of Gramian matrices for aeroelastic stability analysis

Most of the established procedures for analysis of aeroelastic flutter in the development of aircraft are based on frequency domain methods. Proposing new methodologies in this field is always a challenge, because the new methods need to be validated by many experimental procedures. With the interest for new flight control systems and nonlinear behavior of aeroelastic structures, other strategies may be necessary to complete the analysis of such systems. If the aeroelastic model can be written in time domain, using state-space formulation, for instance, then many of the tools used in stability analysis of dynamic systems may be used to help providing an insight into the aeroelastic phenomenon. In this respect, this paper presents a discussion on the use of Gramian matrices to determine conditions of aeroelastic flutter. The main goal of this work is to introduce how observability gramian matrix can be used to identify the system instability. To explain the approach, the theory is outlined and simulations are carried out on two benchmark problems. Results are compared with classical methods to validate the approach and a reduction of computational time is obtained for the second example. © 2013 Douglas Domingues Bueno et al.

Aeroelastic stability analysis using linear matrix inequalities

The present work describes an alternative methodology for identification of aeroelastic stability in a range of varying parameters. Analysis is performed in time domain based on Lyapunov stability and solved by convex optimization algorithms. The theory is outlined and simulations are carried out on a benchmark system to illustrate the method. The classical methodology with the analysis of the system's eigenvalues is presented for comparing the results and validating the approach. The aeroelastic model is represented in state space format and the unsteady aerodynamic forces are written in time domain using rational function approximation. The problem is formulated as a polytopic differential inclusion system and the conceptual idea can be used in two different applications. In the first application the method verifies the aeroelastic stability in a range of air density (or its equivalent altitude range). In the second one, the stability is verified for a rage of velocities. These analyses are in contrast to the classical discrete analysis performed at fixed air density/velocity values. It is shown that this method is efficient to identify stability regions in the flight envelope and it offers promise for robust flutter identification.

Aeroelastic stability analysis considering a continuous flight envelope

This paper presents a new methodology to analyze aeroelastic stability in a continuous range of flight envelope with varying parameter of velocity and altitude. The focus of the paper is to demonstrate that linear matrix inequalities can be used to evaluate the aeroelastic stability in a region of flight envelope instead of a single point, like classical methods. The proposed methodology can also be used to study if a system remains stable during an arbitrary motion from one point to another in the flight envelope, i.e., when the problem becomes time-variant. The main idea is to represent the system as a polytopic differential inclusion system using rational function approximation to write the model in time domain. The theory is outlined and simulations are carried out on the benchmark AGARD 445.6 wing to demonstrate the method. The classical pk-method is used for comparing results and validating the approach. It is shown that this method is efficient to identify stability regions in the flight envelope. (C) 2014 Elsevier Ltd. All rights reserved.

Aeroelastic stability of structures: flutter analysis using Computational Fluid Dynamics

Thanks to the increasing slenderness and lightness allowed by new construction techniques and materials, the effects of wind on structures became in the last decades a research field of great importance in Civil Engineering. Thanks to the advances in computers power, the numerical simulation of wind tunnel tests has became a valid complementary activity and an attractive alternative for the future. Due to its flexibility, during the last years, the computational approach gained importance with respect to the traditional experimental investigation. However, still today, the computational approach to fluid-structure interaction problems is not as widely adopted as it could be expected. The main reason for this lies in the difficulties encountered in the numerical simulation of the turbulent, unsteady flow conditions generally encountered around bluff bodies. This thesis aims at providing a guide to the numerical simulation of bridge deck aerodynamic and aeroelastic behaviour describing in detail the simulation strategies and setting guidelines useful for the interpretation of the results.

Transonic Aeroelastic Stability Predictions Under the Influence of Structural Variability

Flutter prediction as currently practiced is almost always deterministic in nature, based on a single structural model that is assumed to represent a fleet of aircraft. However, it is also recognized that there can be significant structural variability, even for different flights of the same aircraft. The safety factor used for flutter clearance is in part meant to account for this variability. Simulation tools can, however, represent the consequences of structural variability in the flutter predictions, providing extra information that could be useful in planning physical tests and assessing risk. The main problem arising for this type of calculation when using high-fidelity tools based on computational fluid dynamics is the computational cost. The current paper uses an eigenvalue-based stability method together with Euler-level aerodynamics and different methods for propagating structural variability to stability predictions. The propagation methods are Monte Carlo, perturbation, and interval analysis. The feasibility of this type of analysis is demonstrated. Results are presented for the Goland wing and a generic fighter configuration.

How Structural Model Variability Influences Transonic Aeroelastic Stability

This paper considers the ways in which structural model parameter variability can influence aeroelastic stability. Previous work on formulating the stability calculation (with the Euler equations providing the aerodynamic predictions) is exploited to use Monte Carlo, interval, and perturbation calculations to allow this question to be investigated. Three routes are identified. The first involves variable normal-mode frequencies only. The second involves normal-mode frequencies and shapes. Finally, the third, in addition to normal-mode frequencies and shapes, also includes their influence on the static equilibrium. Previous work has suggested only considering the first route, which allows significant gains in computational efficiency if reduced-order models can be built for the aerodynamics. However, results in the current paper show that neglecting the mode-shape variation can give misleading results for the flutter-onset prediction, complicating the development of reduced aerodynamic models for variability analysis.

Stability analysis and control of multiple converter based autonomous microgrid

In this paper, the stability of an autonomous microgrid with multiple distributed generators (DG) is studied through eigenvalue analysis. It is assumed that all the DGs are connected through Voltage Source Converter (VSC) and all connected loads are passive. The VSCs are controlled by state feedback controller to achieve desired voltage and current outputs that are decided by a droop controller. The state space models of each of the converters with its associated feedback are derived. These are then connected with the state space models of the droop, network and loads to form a homogeneous model, through which the eigenvalues are evaluated. The system stability is then investigated as a function of the droop controller real and reac-tive power coefficients. These observations are then verified through simulation studies using PSCAD/EMTDC. It will be shown that the simulation results closely agree with stability be-havior predicted by the eigenvalue analysis.

Power system stability analysis based on descriptive study of electrical indices

In a power network, when a propagation energy wave caused by a disturbance hits a weak link, a reflection is appeared and some of energy is transferred across the link. In this work, an analytical descriptive methodology is proposed to study the dynamical stability of a large scale power system. For this purpose, the measured electrical indices (angle, or voltage/frequency) following a fault in different points among the network are used, and the behaviors of the propagated waves through the lines, nodes and buses are studied. This work addresses a new tool for power system stability analysis based on a descriptive study of electrical measurements. The proposed methodology is also useful to detect the contingency condition and synthesis of an effective emergency control scheme.

Stability analysis based on birfurcation theory of the DSTATCOM operating in current control mode

This paper presents the stability analysis for a distribution static compensator (DSTATCOM) that operates in current control mode based on bifurcation theory. Bifurcations delimit the operating zones of nonlinear circuits and, hence, the capability to compute these bifurcations is of important interest for practical design. A control design for the DSTATCOM is proposed. Along with this control, a suitable mathematical representation of the DSTATCOM is proposed to carry out the bifurcation analysis efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the point of common coupling. In addition, the stability regions in the control gain space, as well as the contour lines for different Floquet multipliers are computed. It is demonstrated through bifurcation analysis that the loss of stability in the DSTATCOM is due to the emergence of a Neimark bifurcation. The observations are verified through simulation studies.

Modeling, stability analysis and control of microgrid

With the increase in the level of global warming, renewable energy based distributed generators (DGs) will increasingly play a dominant role in electricity production. Distributed generation based on solar energy (photovoltaic and solar thermal), wind, biomass, mini-hydro along with use of fuel cells and micro turbines will gain considerable momentum in the near future. A microgrid consists of clusters of load and distributed generators that operate as a single controllable system. The interconnection of the DG to the utility/grid through power electronic converters has raised concern about safe operation and protection of the equipments. Many innovative control techniques have been used for enhancing the stability of microgrid as for proper load sharing. The most common method is the use of droop characteristics for decentralized load sharing. Parallel converters have been controlled to deliver desired real power (and reactive power) to the system. Local signals are used as feedback to control converters, since in a real system, the distance between the converters may make the inter-communication impractical. The real and reactive power sharing can be achieved by controlling two independent quantities, frequency and fundamental voltage magnitude. In this thesis, an angle droop controller is proposed to share power amongst converter interfaced DGs in a microgrid. As the angle of the output voltage can be changed instantaneously in a voltage source converter (VSC), controlling the angle to control the real power is always beneficial for quick attainment of steady state. Thus in converter based DGs, load sharing can be performed by drooping the converter output voltage magnitude and its angle instead of frequency. The angle control results in much lesser frequency variation compared to that with frequency droop. An enhanced frequency droop controller is proposed for better dynamic response and smooth transition between grid connected and islanded modes of operation. A modular controller structure with modified control loop is proposed for better load sharing between the parallel connected converters in a distributed generation system. Moreover, a method for smooth transition between grid connected and islanded modes is proposed. Power quality enhanced operation of a microgrid in presence of unbalanced and non-linear loads is also addressed in which the DGs act as compensators. The compensator can perform load balancing, harmonic compensation and reactive power control while supplying real power to the grid A frequency and voltage isolation technique between microgrid and utility is proposed by using a back-to-back converter. As utility and microgrid are totally isolated, the voltage or frequency fluctuations in the utility side do not affect the microgrid loads and vice versa. Another advantage of this scheme is that a bidirectional regulated power flow can be achieved by the back-to-back converter structure. For accurate load sharing, the droop gains have to be high, which has the potential of making the system unstable. Therefore the choice of droop gains is often a tradeoff between power sharing and stability. To improve this situation, a supplementary droop controller is proposed. A small signal model of the system is developed, based on which the parameters of the supplementary controller are designed. Two methods are proposed for load sharing in an autonomous microgrid in rural network with high R/X ratio lines. The first method proposes power sharing without any communication between the DGs. The feedback quantities and the gain matrixes are transformed with a transformation matrix based on the line R/X ratio. The second method involves minimal communication among the DGs. The converter output voltage angle reference is modified based on the active and reactive power flow in the line connected at point of common coupling (PCC). It is shown that a more economical and proper power sharing solution is possible with the web based communication of the power flow quantities. All the proposed methods are verified through PSCAD simulations. The converters are modeled with IGBT switches and anti parallel diodes with associated snubber circuits. All the rotating machines are modeled in detail including their dynamics.

Small-signal stability analysis of a DFIG-based wind power system under different modes of operation

This paper focuses on the super/subsynchronous operation of the doubly fed induction generator (DFIG) system. The impact of a damping controller on the different modes of operation for the DFIG-based wind generation system is investigated. The coordinated tuning of the damping controller to enhance the damping of the oscillatory modes using bacteria foraging technique is presented. The results from eigenvalue analysis are presented to elucidate the effectiveness of the tuned damping controller in the DFIG system. The robustness issue of the damping controller is also investigated.