Structure-Preserving Model Order Reduction for Nonlinear DAE Models of Power Networks

This paper deals with the joint reduction of the number of dynamic and algebraic states of a nonlinear differential-algebraic equation (NDAE) model of a power network. The dynamic states depict the internal states of generators, loads, renewables, whereas the algebraic ones define network states such as voltages and phase angles. In the current literature of power system model order reduction (MOR), the algebraic constraints are usually neglected and the power network is commonly modeled via a set of ordinary differential equations (ODEs) instead of NDAEs. Thus, reduction is usually carried out for the dynamic states only and the algebraic variables are kept intact. This leaves a significant part of the system's size and complexity <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unreduced</i>. This paper addresses this aforementioned limitation by jointly reducing both dynamic and algebraic variables. As compared to the literature the proposed MOR techniques are endowed with the following features: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i)</i> no system linearization is required, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ii)</i> require no transformation to an equivalent or approximate ODE representation, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(iii)</i> guarantee that the reduced order model to be NDAE-structured and thus preserves the differential-algebraic structure of original power system model, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(iv)</i> can seamlessly reduce both dynamic and algebraic variables while maintaining high accuracy. Case studies performed on a 2000-bus power system reveal that the proposed MOR techniques are able to reduce system order while maintaining accuracy.