Recent Developments in Power Flow and Stability Modeling
Power flow and stability analysis have been used for decades, for analyzing both the traditional electric power grids and the new reformed grid infrastructure the so-called smart grids. Recently, both the power flow and stability analysis have entered a new area of research where several research teams all over the world have contributed with radically new modeling approaches. Regarding power flow, efforts are focused on a more dynamical perspective aiming at incorporating differential equations for evaluating branch parameters, rather than nodal ones. As far as stability concerns, new evaluation techniques based on network oscillations properties are introduced. Synchronization and basin stability as a complement to linear stability are utilized to cope with the dynamical nature of electric power grids. This allows us to view power systems as complex networks, so as to take advantage of complex systems properties. In other words, the new power systems viewpoint is in fact a compromise between two major fields of research and technology, namely electrical power engineering and statistical physics. Among others, the following three new approaches seem to offer the most promising results that pave the way to a radically new approach in power grid analysis.
1. ”Distflow” ODE modeling is an outcome of the branch flow model (Wang, Turitsyn, & Chertkov, 2012) which involves the rate of change of power flow in power grid branches (links), unlike the classic nodal power flow.
2. Models capturing the self-synchronization procedures on power grids (Nishikawa & Motter, 2015; Motter, Myers, Anghel, & Nishikawa, 2013; Rohden, Sorge, Witthaut, & Timme, 2014). They are based on the extended 2nd order Kuramoto model of phase coupled oscillators in complex networks. They also incorporate dynamic spectral analysis. Basin stability as an assistance tool for linear stability is also incorporated in this new research field (Menck & Kurths, 2012; Menck, Heitzig, Marwan, & Kurths, 2013).
3. Network oscillation model based on graph wave equations, incorporated in a discrete spectral graph analysis of the power grid, is also recently introduced (Caputo, Knippel, & Simo, 2013). Graph wave equations obtained as an outcome of the linearization of the Kuramoto model, are only tested for very small-scale networks mainly of mechanical nature, leaving the electric power networks for future investigation.
We briefly present specific topics from the above mentioned efforts, elucidate related concepts, understand the impact of certain characteristics of these models and comment on their practical capabilities and possible theoretical extensions. We focus on computational techniques that hopefully leads to more effective and advanced practical solution techniques.