This paper concerns the application of reduced order modeling techniques to power grid simulation. Swing dynamics is a complex non-linear phenomenon due to which model order reduction of these problems is intricate. A multi point linearization based model reduction technique trajectory piece-wise linearization (TPWL) method is adopted to address the problem of approximating the nonlinear term in swing models. The method combines proper orthogonal decomposition with TPWL in order to build a suitable reduced order model that can accurately predict the swing dynamics. The method consists of two stages, an offline stage where model reduction and selection of linearization points is performed and an online stage where the reduced order multi-point linear simulation is performed. An improvement of the strategy for point selection is also proposed. The TPWL method for a swing dynamics model shows that the method provides accurate reduced order models for non-linear transient problems.

/pdf/reduced-order-modeling-for-transient-simulation-of-power-42x2jixpk5.pdf

Reduced order modeling for transient simulation of power systems using trajectory piece-wise linear approximation

Finite-time balanced truncation for linear systems via shifted Legendre polynomials

Model reduction for linear and nonlinear magneto‐quasistatic equations

The proper generalized decomposition (PGD) is a model order reduction method which allows to reduce the computational time of a numerical problem by seeking for a separated representation of the solution. The PGD has been already applied to study an electrical machine but at standstill without accounting the motion of the rotor. In this paper, we propose a method to account for the rotation in the PGD approach in order to build an efficient metamodel of an electrical machine. Then, the machine metamodel will be coupled to its electrical and mechanical environment in order to obtain accurate results with an acceptable computational time on a full simulation.

/pdf/proper-generalized-decomposition-applied-on-a-rotating-4n0jxtcio9.pdf

Proper Generalized Decomposition Applied on a Rotating Electrical Machine

The proper orthogonal decomposition (POD) approach is applied to a linear finite element (FE) model of a squirrel cage induction machine. In order to obtain a reduced model valid on the whole operating range, snapshots are extracted from the simulation of typical tests, such as at the locked rotor and the synchronous speed. Then, the reduced model of the induction machine is used to simulate different operating points with variable rotation speed, and the results are compared to the full FE model to show the effectiveness of the proposed approach.

/pdf/model-order-reduction-applied-to-a-linear-finite-element-58upx315mo.pdf

Model Order Reduction Applied to a Linear Finite Element Model of a Squirrel Cage Induction Machine Based on POD Approach

Model order reduction (MOR) methods are more and more applied on many different fields of physics in order to reduce the number of unknowns and thus the computational time of large-scale systems. However, their application is quite recent in the field of computational electromagnetics. In the case of electrical machine, the numerical model has to take into account the nonlinear behaviour of ferromagnetic materials, motion of the rotor, circuit equations and mechanical coupling. In this context, we propose to apply the proper orthogonal decomposition combined with the (Discrete) empirical interpolation method in order to reduce the computation time required to study the start-up of an electrical machine until it reaches the steady state. An empirical offline/online approach based on electrical engineering is proposed in order to build an efficient reduced model accurate on the whole operating range. Finally, a 2D example of a synchronous machine is studied with a reduced model deduced from the proposed approach.

/pdf/transient-simulation-of-an-electrical-rotating-machine-ibxtwba4fb.pdf

Transient simulation of an electrical rotating machine achieved through model order reduction

Model order reduction (MOR) methods are applied in different areas of physics in order to reduce the computational time of large scale systems. It has been an active field of research for many years, in mechanics especially, but it is quite recent for magnetoquasi-static problems. Although the most famous method, the proper orthogonal decomposition (POD) has been applied for modeling many electromagnetic devices, this method can lack accuracy for low-order magnitude output quantities, like flux associated with a probe in regions where the field is low. However, the balanced POD (BPOD) is an MOR method, which takes into account these output quantities in its reduced model to render them accurately. Even if the BPOD may lead to unstable reduced systems, this can be overcome by a stabilization procedure. Therefore, the POD and the stabilized BPOD will be compared on a 3-D linear magnetoquasi-static field problem.

/pdf/balanced-proper-orthogonal-decomposition-applied-to-25yssfp0sd.pdf

Balanced Proper Orthogonal Decomposition Applied to Magnetoquasi-Static Problems Through a Stabilization Methodology

In the field of electrical machines, the finite element method provides accurate results but requires a high computational cost to perform, with sometimes weeks of computations. Therefore, model order reduction methods such as the proper orthogonal decomposition combined with the discrete empirical interpolation method are able to speed up the solution of the finite element problem. To use the obtained results for predictive computations, an error estimator is required. However, the different estimators found in the literature do not apply to our problem. Therefore, a simple error indicator that can be applied to a wide range of problems is proposed in this paper.

B. Goursaud

Papers

Transient simulation of an electrical rotating machine achieved through model order reduction

Proper Generalized Decomposition Applied on a Rotating Electrical Machine

Balanced Proper Orthogonal Decomposition Applied to Magnetoquasi-Static Problems Through a Stabilization Methodology

Model Order Reduction Applied to a Linear Finite Element Model of a Squirrel Cage Induction Machine Based on POD Approach

Robust model order reduction of an electrical machine at startup through reduction error estimation