scholarly journals State relevance for model order reduction applied to a microgrid

2021 ◽  
Author(s):  
Andrés Tomás-Martín ◽  
Aurelio García-Cerrada ◽  
Lukas Sigrist ◽  
Sauro Yagüe ◽  
Jorge Suárez-Porras
Keyword(s):  
Power Systems ◽  
Model Order Reduction ◽  
Ad Hoc ◽  
Stability Limit ◽  
Order Reduction ◽  
Original System ◽  
Reduced Model ◽  
State Variables ◽  
Nonlinear Simulation ◽  
Model Order

This paper presents a systematic model order reduction (MOR) algorithm based on state relevance applied to an islanded microgrid with electronic power generation. MOR of such islanded microgrids may not benefit, a priori, from the well-established time-scale separation usually applied to conventional power systems, and a systematic MOR is still an open issue. The proposed algorithm uses a balanced realization of the linear system, where state variables may not have physical meaning, to obtain the states' energies. It then calculates the relevance of the original system states from those energy values. The newly proposed ``state-relevance coefficient'' should help to choose which states to consider in a reduced model in each study case. Detailed nonlinear simulation results show that the proposed algorithm is able to find the relevant states to include in the reduced model systematically, even in operation points near the stability limit, where ad-hoc MOR techniques are likely to fail. The performance of the algorithm is illustrated in a system with grid-forming converters in various scenarios but can be easily applied to other systems.

State relevance for model order reduction applied to a microgrid

2021 ◽  
Author(s):  
Andrés Tomás-Martín ◽  
Aurelio García-Cerrada ◽  
Lukas Sigrist ◽  
Sauro Yagüe ◽  
Jorge Suárez-Porras
Keyword(s):  
Power Systems ◽  
Model Order Reduction ◽  
Ad Hoc ◽  
Stability Limit ◽  
Order Reduction ◽  
Original System ◽  
Reduced Model ◽  
State Variables ◽  
Nonlinear Simulation ◽  
Model Order

This paper presents a systematic model order reduction (MOR) algorithm based on state relevance applied to an islanded microgrid with electronic power generation. MOR of such islanded microgrids may not benefit, a priori, from the well-established time-scale separation usually applied to conventional power systems, and a systematic MOR is still an open issue. The proposed algorithm uses a balanced realization of the linear system, where state variables may not have physical meaning, to obtain the states' energies. It then calculates the relevance of the original system states from those energy values. The newly proposed ``state-relevance coefficient'' should help to choose which states to consider in a reduced model in each study case. Detailed nonlinear simulation results show that the proposed algorithm is able to find the relevant states to include in the reduced model systematically, even in operation points near the stability limit, where ad-hoc MOR techniques are likely to fail. The performance of the algorithm is illustrated in a system with grid-forming converters in various scenarios but can be easily applied to other systems.

A Hybrid Approach for Model Order Reduction and Controller Design of Large-Scale Power Systems

2021 ◽  
pp. 211-226
Author(s):  
Rishabh Singhal ◽  
Yashonidhi Srivastava ◽  
Shini Agarwal ◽  
Abhimanyu Kumar ◽  
Souvik Ganguli
Keyword(s):  
Power Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Controller Design ◽  
Hybrid Approach ◽  
Order Reduction ◽  
Model Order

Substructure Preservation Sylvester-based Model Order Reduction with Application to Power Systems

2014 ◽  
Vol 42 (9) ◽  
pp. 914-926 ◽  
Author(s):  
Othman M. K. Alsmadi ◽  
Saleh S. Saraireh ◽  
Zaer S. Abo-Hammour ◽  
Ali H. Al-Marzouq
Keyword(s):  
Power Systems ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Model Order

scholarly journals Reduced Order Controller Design for Symmetric, Non-Symmetric and Unstable Systems Using Extended Cross-Gramian

Machines ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 48 ◽  
Author(s):  
Azhar ◽  
Zulfiqar ◽  
Liaquat ◽  
Kumar
Keyword(s):  
Model Order Reduction ◽  
Controller Design ◽  
Order Reduction ◽  
Original System ◽  
Computational Effort ◽  
Model Order ◽  
Unstable Systems ◽  
Reduced Order ◽  
The Cross ◽  
Symmetric Systems

In model order reduction and system theory, the cross-gramian is widely applicable. The cross-gramian based model order reduction techniques have the advantage over conventional balanced truncation that it is computationally less complex, while providing a unique relationship with the Hankel singular values of the original system at the same time. This basic property of cross-gramian holds true for all symmetric systems. However, for non-square and non-symmetric dynamical systems, the standard cross-gramian does not satisfy this property. Hence, alternate approaches need to be developed for its evaluation. In this paper, a generalized frequency-weighted cross-gramian-based controller reduction algorithm is presented, which is applicable to both symmetric and non-symmetric systems. The proposed algorithm is also applicable to unstable systems even if they have poles of opposite polarities and equal magnitudes. The proposed technique produces an accurate approximation of the reduced order model in the desired frequency region with a reduced computational effort. A lower order controller can be designed using the proposed technique, which ensures closed-loop stability and performance with the original full order plant. Numerical examples provide evidence of the efficacy of the proposed technique.

Nonlinear model order reduction for the fast solution of induction heating problems in time-domain

2017 ◽  
Vol 36 (2) ◽  
pp. 469-475 ◽  
Author(s):  
Lorenzo Codecasa ◽  
Federico Moro ◽  
Piergiorgio Alotto
Keyword(s):  
Induction Heating ◽  
Model Order Reduction ◽  
Computing Time ◽  
Computational Cost ◽  
Order Reduction ◽  
Reduced Model ◽  
Problem Solution ◽  
Model Order ◽  
Content Type ◽  
Time Harmonic

Purpose This paper aims to propose a fast and accurate simulation of large-scale induction heating problems by using nonlinear reduced-order models. Design/methodology/approach A projection space for model order reduction (MOR) is quickly generated from the first kernels of Volterra’s series to the problem solution. The nonlinear reduced model can be solved with time-harmonic phasor approximation, as the nonlinear quadratic structure of the full problem is preserved by the projection. Findings The solution of induction heating problems is still computationally expensive, even with a time-harmonic eddy current approximation. Numerical results show that the construction of the nonlinear reduced model has a computational cost which is orders of magnitude smaller than that required for the solution of the full problem. Research limitations/implications Only linear magnetic materials are considered in the present formulation. Practical implications The proposed MOR approach is suitable for the solution of industrial problems with a computing time which is orders of magnitude smaller than that required for the full unreduced problem, solved by traditional discretization methods such as finite element method. Originality/value The most common technique for MOR is the proper orthogonal decomposition. It requires solving the full nonlinear problem several times. The present MOR approach can be built directly at a negligible computational cost instead. From the reduced model, magnetic and temperature fields can be accurately reconstructed in whole time and space domains.

An Automated Model-Order Reduction Method for Automatic Transmissions

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Vanja Ranogajec ◽  
Joško Deur
Keyword(s):  
State Space ◽  
Model Order Reduction ◽  
Reduction Method ◽  
State Space Model ◽  
Order Reduction ◽  
Torque Converter ◽  
State Variables ◽  
Model Order ◽  
Automatic Transmissions ◽  
Order Reduction Method

New generation of torque converter automatic transmissions (AT) includes a large number of gears for improved fuel economy and vehicle performance, which leads to exponentially increasing number of shift types and shift events. In order to facilitate various numerical/simulation analyses of AT dynamics, shift control optimization, and control strategy design, a full-order AT model is usually reduced by eliminating state variables related to locked clutches in particular gears or shifts. The paper proposes an automated model-order reduction method for an arbitrary, user-specified clutch state, and demonstrates its application on an example of ten-speed AT. The method is based on determining the locked-clutch torque variables and their substitution into the full-order state-space model input vector, as well as finding a linear relation between the reduced-order and full-order model state-space variables.

Model Order Reduction for Design of Torsional Disk Couplings

2014 ◽  
Author(s):  
Alex Francis ◽  
Ilya Avdeev
Keyword(s):  
Power Systems ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Element Model ◽  
Torsional Stiffness ◽  
Normal Operation ◽  
Operating Characteristics ◽  
Modeling Framework ◽  
Model Order ◽  
Operation Speed

Torsional couplings are used to transmit power between various rotating components of power systems while allowing for relatively small misalignments that may otherwise lead to equipment failure. When selecting a proper coupling type and size, one has to consider three important conditions: (1) maximum load applied to the coupling, (2) maximum operation speed and (3) amount of misalignment allowable for normal operation. There are many types of flexible couplings that use various materials for the flexible element of the coupling on the market today. Design of the coupling and the materials used for the flexible elements determine the coupling’s operating characteristics. In this project, we study metal disk couplings. Benefits of this type of coupling include: ease of replacement or repair, clear visual feedback of element failure, and the absence of a need for lubrication. The torsional stiffness of a coupling is a major factor relative to the amount of misalignment allowable. Currently, flexible couplings are tested by manufacturers to experimentally determine the torsional stiffness; a process which requires expensive equipment and more importantly employee time to set-up and run. The torsional coupling lumped characteristics, such as torsional- and flexural stiffness, as well as natural frequencies are important for design of the entire power system and have to be as precise as possible. In this work, we have developed an accurate modeling framework for determining these parameters based on a full 3-D finite element model and model-order reduction procedure. Developed methodology was validated by available experimental data from one of the leading manufacturers of torsional couplings.

scholarly journals Application of the Craig-Bampton model order reduction method to a composite structure: MACco, COMAC, COMAC-S and eCOMAC

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Humberto Peredo Fuentes ◽  
Manfred Zehn
Keyword(s):  
Composite Structure ◽  
Model Order Reduction ◽  
Reduction Method ◽  
Order Reduction ◽  
Element Model ◽  
Reduced Model ◽  
Full Model ◽  
Slight Improvement ◽  
Model Order ◽  
Order Reduction Method

Abstract The Craig-Bampton model order reduction (CBMOR) method based on the Rayleigh-Ritz approach was applied in a previous work to simulate dynamic behavior of a composite structure (CFRP) using the modal assurance criteria (MAC) and cross orthogonality (XOR) to validate the correlation. Different coordinate modal assurance criteria are applied to complement and verify the eigenfrequencies and eigenvectors obtained of the full and reduced models using substructures (super-elements). An improvement is observed per paired mode-sensor with the MAC per coordinates criterion (MACco) in a CFRP once the stiffness parameters are updated in the full model applying a mix-numerical experimental technique (MNET) using a design of experiments (DOE). The coordinate modal assurance criteria (COMAC) and the scaleCOMAC (COMACS) results of the full models display the best results respect to the reduced model. Furthermore, slight improvement of the enhanced COMAC (eCOMAC) results are observed in the reduced model despite having lower MAC performance. This approach complements the results of the previous work using several COMAC techniques, and demostrates the feasibility to achieve low COMACs results in the reduced finite element model once the stiffness parameters of the full element model are updated. The example was prepared and solved with MSC/NASTRAN SOL103 and SDTools-MATLAB for comparative purposes.

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