A Physics-Based Dynamic Model for Boilers: Part 2 — Model Reduction in a Cogeneration Application

2017 ◽  
Author(s):  
Matthew J. Blom ◽  
Michael J. Brear ◽  
Chris G. Manzie ◽  
Ashley P. Wiese
Keyword(s):  
Model Reduction ◽  
Gas Turbine ◽  
Dynamic Model ◽  
Reduction Process ◽  
Singular Perturbation Theory ◽  
Reduced Order Models ◽  
Reduced Order ◽  
One Dimensional ◽  
Time Scale Separation ◽  
Modelling Framework

This paper is the second part of a two part study that develops, validates and integrates a one-dimensional, physics-based, dynamic boiler model. Part 1 of this study [1] extended and validated a particular modelling framework to boilers. This paper uses this framework to first present a higher order model of a gas turbine based cogeneration plant. The significant dynamics of the cogeneration system are then identified, corresponding to states in the gas path, the steam path, the gas turbine shaft, gas turbine wall temperatures and boiler wall temperatures. A model reduction process based on time scale separation and singular perturbation theory is then demonstrated. Three candidate reduced order models are identified using this model reduction process, and the simplest, acceptable dynamic model of this integrated plant is found to require retention of both the gas turbine and boiler wall temperature dynamics. Subsequent analysis of computation times for the original physics-based one-dimensional model and the candidate, reduced order models demonstrates that significantly faster than real time simulation is possible in all cases. Furthermore, with systematic replacement of the algebraic states with feedforward maps in the reduced order models, further computational savings of up to one order of magnitude can be achieved. This combination of model fidelity and computational tractability suggest suggests that the resulting reduced order models may be suitable for use in model based control of cogeneration plants.

Power system stabilizers design using optimal reduced order models. I. Model reduction

1988 ◽  
Vol 3 (4) ◽  
pp. 1670-1675 ◽  
Author(s):  
A. Feliachi ◽  
X. Zhang ◽  
C.S. Sims
Keyword(s):  
Power System ◽  
Model Reduction ◽  
Reduced Order Models ◽  
Power System Stabilizers ◽  
Reduced Order

Academic Blade Geometries for Baseline Comparisons of Industry-Specific Forced Response Predictions

2017 ◽  
Author(s):  
James H. Little ◽  
Jeffrey L. Kauffman ◽  
Matthias Huels
Keyword(s):  
Model Reduction ◽  
Turbine Blades ◽  
Reduction Process ◽  
Forced Response ◽  
Vibration Characteristics ◽  
Contact Dynamics ◽  
Qualitative Behavior ◽  
Friction Damper ◽  
Blade Vibration ◽  
Reduced Order

Predicting the energy dissipation associated with contact of underplatform dampers remains a critical challenge in turbomachinery blade and friction damper design. Typical turbomachinery blade forced vibration response analyses rely on reduced order models and simplified nonlinear codes to predict blade vibration characteristics in a computationally tractable manner. Recent research has focused on both the model reduction process and simulation of the contact dynamics. This paper proposes two academic turbine blade geometries with coupled underplatform dampers as vehicles by which these model reduction and forced response simulation techniques may be compared. The blades correspond to two types of freestanding turbine blades and demonstrate the same qualitative behavior as more complex industry geometries. The blade geometries are fully described here and analyzed using the same procedure as used for an industry-specific blade. Standard results are presented in terms of resonance frequency, amplitude, and damping across a range of aerodynamic excitation. In addition, the predicted blade vibration characteristics are examined under variations in the contact interface: friction coefficient, damper / platform surface roughness, and damper mass, with relative sensitivities to each term generated. Finally, the effect of the number of modes retained in the reduced order model is studied to uncover patterns of convergence as well as to provide additional sets of standard data for comparison with other model reduction and forced response simulation methods.

Model Reduction for Nonlinear Structural Systems Using Balanced Realization Theory

2013 ◽  
Author(s):  
Al Ferri
Keyword(s):  
Model Reduction ◽  
Dry Friction ◽  
Numerical Models ◽  
Contact Stiffness ◽  
Reduced Order Models ◽  
Joint Models ◽  
Reduced Order ◽  
Truncation Techniques ◽  
Modal Truncation

The development of accurate and efficient numerical models for jointed structures is an important and challenging problem. Due to nonlinearities in the joints, notably dry friction, contact stiffness, and impact, joint models are often complicated and computer-intensive. To create practical models, engineers typically combine “lumped joint models” with reduced-order models for the structural members that they connect. However, the model reduction often distorts how the joint behaves and sometimes destroys important qualitative traits. Simple modal truncation is often inadequate to produce reduced-order models because nonlinearities within the joints such as impact and dry friction can depend critically on the high-frequency characteristics of the mating structural elements. This paper examines the issues surrounding the development of accurate, reduced-order models for nonlinear, jointed structures. The concept of “balanced realizations” from control theory are used to create reduced-order models that best capture the input-output characterization of the linear substructures with the smallest model order. The balanced-realizations are seen to produce very favorable results when compared with standard modal truncation techniques.

PEAK-TO-PEAK DYNAMICS: A CRITICAL SURVEY

2000 ◽  
Vol 10 (08) ◽  
pp. 1805-1819 ◽  
Author(s):  
MATTEO CANDATEN ◽  
SERGIO RINALDI
Keyword(s):  
Chaotic Systems ◽  
Deterministic Chaos ◽  
Critical Survey ◽  
Reduced Order Models ◽  
Order Model ◽  
Output Variable ◽  
Piecewise Constant ◽  
Reduced Order ◽  
One Dimensional ◽  
Continuous Time System

This paper is devoted to the study of a particular form of deterministic chaos, here called peak-to-peak dynamics (PPD). When a continuous-time system of order n has PPD, the amplitude and the time of occurrence of the next peak of its output variable can be predicted from information concerning at most two previous peaks. In other words, n differential equations can be substituted by a reduced order model, if attention is restricted to the peaks of the variable of concern. The observation of the output peaks is equivalent to the observation of the system on a Poincaré section. This is why the existence of PPD is simply related to the dimension of the attractor. The usefulness of peak-to-peak analysis for the retrieval of one-dimensional dynamics within the attractor and for the estimate of the first Liapunov exponent is demonstrated through examples. Particular attention is devoted to the possibility of exploiting the PPD reduced order models for forecasting the next peak and for the regularization of the dynamics of chaotic systems by means of piecewise constant controls.

scholarly journals Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Imran ◽  
Abdul Ghafoor ◽  
Victor Sreeram
Keyword(s):  
Frequency Response ◽  
Model Reduction ◽  
Discrete Time ◽  
Error Bounds ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Discrete Time Systems ◽  
Weighted Model ◽  
Time Systems

Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole frequency range. However, certain applications (like controller reduction) require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack of stability of reduced order models (for two sided weighting case) and frequency response error bounds. A new frequency weighted technique for balanced model reduction for discrete time systems is proposed. The proposed technique guarantees stable reduced order models even for the case when two sided weightings are present. Efficient technique for frequency weighted Gramians is also proposed. Results are compared with other existing frequency weighted model reduction techniques for discrete time systems. Moreover, the proposed technique yields frequency response error bounds.

A Direct Approach to Order Reduction of Nonlinear Systems Subjected to External Periodic Excitations

2008 ◽  
Vol 3 (3) ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
State Space ◽  
Invariant Manifold ◽  
Large Scale ◽  
Reduction Process ◽  
Order Reduction ◽  
The State ◽  
Reduced Order Models ◽  
External Excitation ◽  
Reduced Order

In this work, the basic problem of order reduction of nonlinear systems subjected to an external periodic excitation is considered. This problem deserves special attention because modes that interact (linearly or nonlinearly) with external excitation dominate the response. These dominant modes are identified and chosen as the “master” modes to be retained in the reduction process. The simplest idea could be to use a linear approach such as the Guyan reduction and choose those modes whose natural frequencies are close to that of external excitation as the master modes. However, this technique does not guarantee accurate results when nonlinear interactions are strong and a nonlinear approach must be adopted. Recently, the invariant manifold technique has been extended to forced problems by “augmenting” the state space, i.e., forcing is treated as an additional state and an invariant manifold is constructed. However, this process does not provide a clear picture of possible resonances and conditions under which an order reduction is possible. In a direct innovative approach suggested here, a nonlinear time-dependent relationship between the dominant and nondominant states is assumed and the dimension of the state space remains the same. This methodology not only yields accurate reduced order models but also explains the consequences of various primary and secondary resonances present in the system. One obtains various reducibility conditions in a closed form, which show interactions among eigenvalues, nonlinearities and the external excitation. One can also recover all “resonance conditions” obtained via perturbation or averaging techniques. The “linear” as well as the “extended invariant manifold” techniques are applied to some typical problems and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control of large-scale externally excited nonlinear systems.

scholarly journals Model reduction for a power grid model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jing Li ◽  
Panos Stinis
Keyword(s):  
Model Reduction ◽  
Long Memory ◽  
Power Grid ◽  
The State ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Grid Model ◽  
Reduction Techniques ◽  
Short Memory ◽  
Better Than

<p style='text-indent:20px;'>We examine the complexity of constructing reduced order models for subsets of the variables needed to represent the state of the power grid. In particular, we apply model reduction techniques to the DeMarco-Zheng power grid model. We show that due to the oscillating nature of the solutions and the absence of timescale separation between resolved and unresolved variables, the construction of accurate reduced models becomes highly non-trivial because one has to account for long memory effects. In addition, we show that a reduced model that includes even a short memory is drastically better than a memoryless model.</p>

scholarly journals Input–output measures for model reduction and closed-loop control: application to global modes

2011 ◽  
Vol 685 ◽  
pp. 23-53 ◽  
Author(s):  
Alexandre Barbagallo ◽  
Denis Sipp ◽  
Peter J. Schmid
Keyword(s):  
Feedback Control ◽  
Model Reduction ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Reduction Process ◽  
Open Loop ◽  
Input Output ◽  
Control Applications ◽  
Reduced Order ◽  
Global Modes

AbstractFeedback control applications for flows with a large number of degrees of freedom require the reduction of the full flow model to a system with significantly fewer degrees of freedom. This model-reduction process is accomplished by Galerkin projections using a reduction basis composed of modal structures that ideally preserve the input–output behaviour between actuators and sensors and ultimately result in a stabilized compensated system. In this study, global modes are critically assessed as to their suitability as a reduction basis, and the globally unstable, two-dimensional flow over an open cavity is used as a test case. Four criteria are introduced to select from the global spectrum the modes that are included in the reduction basis. Based on these criteria, four reduced-order models are tested by computing open-loop (transfer function) and closed-loop (stability) characteristics. Even though weak global instabilities can be suppressed, the concept of reduced-order compensators based on global modes does not demonstrate sufficient robustness to be recommended as a suitable choice for model reduction in feedback control applications. The investigation also reveals a compelling link between frequency-restricted input–output measures of open-loop behaviour and closed-loop performance, which suggests the departure from mathematically motivated ${\mathscr{H}}_{\infty } $-measures for model reduction toward more physically based norms; a particular frequency-restricted input–output measure is proposed in this study which more accurately predicts the closed-loop behaviour of the reduced-order model and yields a stable compensated system with a markedly reduced number of degrees of freedom.

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