Sparse Vector Methods

Integration of geomagnetic disturbance modeling into the power flow: A methodology for large-scale system studies

“…Rather it is to demonstrate that these values can be quickly determined and visualized, with the calculations need to taking on the order of one second. (11) in which the only non-zeros in ∆ ∆ ∆ ∆I would be equal and opposite values at the positions for buses m and n, and the only desired values in ∆ ∆ ∆ ∆V are at the positions for buses j and k. Sparse vector methods could be used for fast computation of such sensitivities [12].…”

Voltage security enhancement using energy based sensitivities

“…For illustrative purposes, the sensitivity equations for changes in generator real power output ( M W ) is examined in the following example. This example will consider the influence of M W output on a generator's peak Mvar capacity, denoted below as Q(Pcj)limit With x = [a, IVIIT the sensitivity of energy with respect to generator real power output at bus j is given by Note that (11) can be quite efficienrly calculated since the terms a19/axu and a19/axs depend only upon first neighbors of generator j, and the terms aXu/aPGj, aXs/aPGj, ax'/aQ(PGj),i,it, and axS/aQ(PGj)limit can be determined using sparse vector methods [20]. As noted above, the last term is included to account for the variation in the unit's reactive power limits with respect to changes in real power output.…”

An efficient ordering algorithm to improve sparse vector methods

“…More recently, Sparse Vector techniques were introduced to speed up a number of important power system problems [2]. Two kinds of papers can be found in the literature related with these topics: Basic developments and applications.…”

“…Other recent papers related to applications deal with the following problems: Parallel Inversion of Sparse Matrices [4), Fault Analysis [5) and Linear Contingency Analysis [6]. The first kind of papers are devoted to the development of algorithms and basic concepts that permit to get better performances when these techniques are applied to particular problems [2,[7][8][9]. This paper falls under presents a new ordering application.…”

“…The leftmost column indicates the order in which the nodes have been eliminated. For both problems formerly interesting to introduce, moreover, following [2]. mentioned it is other concepts, First of all, non-zero element singleton is an follows: a singleton is a vector with only one (e.g.…”