Voltage collapse analysis in a graph theoretical framework

Interaction Graphs for Cascading Failure Analysis in Power Grids: A Survey

“…These include: (1) methods that define the interactions based on changes in the power flow due to changes in physical attributes of components caused by outage conditions [43][44][45][46][47] and (2) methods that define the interactions among components during normal or non-outage operating conditions [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]78]. The category of defining interactions during non-outage operating conditions is classified into two sub-categories: (i) impedance-based methods, which define interactions by considering a single impedance measure among the components connected over multiple paths [48][49][50][51][52][53][54][55][56][57][58][59] and (ii) sensitivities in components' states due to changes in voltage magnitudes and voltage phase angles [60][61][62][63]78]. This novel taxonomy is used to classify twenty-one detailed research studies, including conference and journal publications, in the electric distance-based category into various subcategories.…”

“…The seminal work of electrical distances by Lagonotte et al in [78] focuses on using the Jacobian sub-matrix (J QV ), also known as the voltage sensitivity matrix ∂V/∂Q, to find the electric distance between buses. Similarly, the study in [60] also uses the voltage sensitivity matrix. In both studies, the matrix of maximum attenuations is found, which consists of columns of voltage sensitivity matrix divided by the diagonal values.…”

“…The study in [61] also uses the voltage sensitivity matrix to find electric distance between buses, but instead of finding matrix of attenuations, the study applies the sensitivity matrix to Klein resistance distance formulation. Note that studies in [60,61] analyze risk of cascading failures by studying the voltage collapse phenomenon, which is a sequential process during which large parts of the power grid may suffer due to low voltages [95]. Similarly, the studies in [62] and [63] apply the Jacobian sub-matrix J Pθ or the sensitivity matrix ∂P/∂θ to Klein resistance distance and find electrical distances between buses.…”

Interaction Graphs for Cascading Failure Analysis in Power Grids: A Survey

“…Inverse Admittance [29], [30], [31], [32], [33], [34], [35] Resistance Distance [36], [37], [38] Weighted Impedance [39] Sensitivity-based Outage Induced [40], [41], [42], [43], [44] Non-outage Induced [45], [46], [47], [48], [33], [51] (historical and real data or simulation data) for extracting and characterizing interactions among the components of the system. We further define five sub-categories for data-driven interaction graphs based on the method used for analyzing the data.…”

“…We define two sub-categories for power physics-based interaction graphs based on the electrical properties utilized for creating the graphs. These include (1) physics and structurebased methods, which define interactions by replacing multiple paths between components by a single distinct equivalent path using impedance values [29]- [35], effective resistances [36]- [38], or weighted impedance [39], and (2) methods that define the interactions based on changes in power flow due to outage in transmission lines [40]- [44] or sensitivities in components' states due to changes in voltage magnitudes [45]- [48], [51]. We will discuss these methods in detail in Section III.…”