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

Abstract

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.

Simulating swing dynamics of a power system model using nonlinear model order reduction

“…A mathematical model to describe the transient dynamics of an alternator is depicted by the swing equation. It involves a second order differential equation representing the alternator node or bus that originates from the rotor dynamics of the alternator and algebraic equation associated with load buses (Malik et al, 2016). The focus of this work revolves around the most common characteristic of power systems, i.e.…”

“…g i' = 0. The transient state of the power system is described by rotor dynamics of i th alternator in the following form (Malik et al, 2016),…”

“…All the nodes are considered as generator or alternator (or PV) nodes. Equation ( 2) can be formulated in matrix form (Malik et al, 2016) as follows:…”

“…The data used for the study is given in Table I, which are in per unit values (Susuki et al (2011), Malik et al (2016).…”

Automated scheme for linearisation points selection in TPWL method applied to non‐linear circuits

“…TPWL and its variants have been implemented to diverse application areas. TPWL is applied to the power grid simulation to tackle the problem of approximating the non‐linear term in swing models [5]. Model‐order reduction of an inverter chain circuit is performed by combining proper orthogonal decomposition (POD) and TPWL [6].…”