Dynamic model reduction: An overview of available techniques with application to power systems

Abstract This article presents a comparison between two different methods to perform model reduction of an Electrical Power System (EPS). The first is the well-known Kron Reduction Method (KRM) that is used to remove the interior nodes (also known as internal, passive, or load nodes) of an EPS. This method computes the Schur complement of the primitive admittance matrix of an EPS to obtain a reduced model that preserves the information of the system as seen from to the generation nodes. Since the primitive admittance matrix is equivalent to the Laplacian of a graph that represents the interconnections between the nodes of an EPS, this procedure is also significant from the perspective of graph theory. On the other hand, the second procedure based on Power Transfer Distribution Factors (PTDF) uses approximations of DC power flows to define regions to be reduced within the system. In this study, both techniques were applied to obtain reduced-order models of two test beds: a 14-node IEEE system and the Colombian power system (1116 buses), in order to test scalability. In analyzing the reduction of the test beds, the characteristics of each method were classified and compiled in order to know its advantages depending on the type of application. Finally, it was found that the PTDF technique is more robust in terms of the definition of power transfer in congestion zones, while the KRM method may be more accurate.

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Linearization threshold condition and stability analysis of a stochastic dynamic model of one-machine infinite-bus (OMIB) power systems

Protection and Control of Modern Power Systems ◽

10.1186/s41601-021-00198-8 ◽

2021 ◽

Vol 6 (1) ◽

Author(s):

Lijuan Li ◽

Yongdong Chen ◽

Bin Zhou ◽

Hongliang Liu ◽

Yongfei Liu

Keyword(s):

Power Systems ◽

Power System ◽

Dynamic Model ◽

Threshold Model ◽

Security Evaluation ◽

Stochastic Dynamic ◽

Threshold Condition ◽

Stochastic Excitation ◽

Predictor Corrector ◽

One Machine

AbstractWith the increase in the proportion of multiple renewable energy sources, power electronics equipment and new loads, power systems are gradually evolving towards the integration of multi-energy, multi-network and multi-subject affected by more stochastic excitation with greater intensity. There is a problem of establishing an effective stochastic dynamic model and algorithm under different stochastic excitation intensities. A Milstein-Euler predictor-corrector method for a nonlinear and linearized stochastic dynamic model of a power system is constructed to numerically discretize the models. The optimal threshold model of stochastic excitation intensity for linearizing the nonlinear stochastic dynamic model is proposed to obtain the corresponding linearization threshold condition. The simulation results of one-machine infinite-bus (OMIB) systems show the correctness and rationality of the predictor-corrector method and the linearization threshold condition for the power system stochastic dynamic model. This study provides a reference for stochastic modelling and efficient simulation of power systems with multiple stochastic excitations and has important application value for stability judgment and security evaluation.

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Model reduction in power systems using a structure-preserving balanced truncation approach

Electric Power Systems Research ◽

10.1016/j.epsr.2019.106002 ◽

2019 ◽

Vol 177 ◽

pp. 106002

Author(s):

Johnny Leung ◽

Michel Kinnaert ◽

Jean-Claude Maun ◽

Fortunato Villella

Keyword(s):

Power Systems ◽

Model Reduction ◽

Balanced Truncation ◽

Structure Preserving

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

Volume 6: Ceramics; Controls, Diagnostics and Instrumentation; Education; Manufacturing Materials and Metallurgy ◽

10.1115/gt2017-63546 ◽

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.

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