Impact of grid partitioning algorithms on combined distributed AC optimal power flow and parallel dynamic power grid simulationn

The complexity of most power grid simulation algorithms scales with the network size, which corresponds to the number of buses and branches in the grid. Parallel and distributed computing is one approach that can be used to achieve improved scalability. However, the efficiency of these algorithms requires an optimal grid partitioning strategy. To obtain the requisite power grid partitionings, the authors first apply several graph theory based partitioning algorithms, such as the Karlsruhe fast flow partitioner (KaFFPa), spectral clustering, and METIS. The goal of this study is an examination and evaluation of the impact of grid partitioning on power system problems. To this end, the computational performance of AC optimal power flow (OPF) and dynamic power grid simulation are tested. The partitioned OPF-problem is solved using the augmented Lagrangian based alternating direction inexact Newton method, whose solution is the basis for the initialisation step in the partitioned dynamic simulation problem. The computational performance of the partitioned systems in the implemented parallel and distributed algorithms is tested using various IEEE standard benchmark test networks. KaFFPa not only outperforms other partitioning algorithms for the AC OPF problem, but also for dynamic power grid simulation with respect to computational speed and scalability

Bounded-degree factors of lacunary multivariate polynomials

In this paper, we present a new method for computing bounded-degree factors of lacunary multivariate polynomials. In particular for polynomials over number fields, we give a new algorithm that takes as input a multivariate polynomial f in lacunary representation and a degree bound d and computes the irreducible factors of degree at most d of f in time polynomial in the lacunary size of f and in d. Our algorithm, which is valid for any field of zero characteristic, is based on a new gap theorem that enables reducing the problem to several instances of (a) the univariate case and (b) low-degree multivariate factorization. The reduction algorithms we propose are elementary in that they only manipulate the exponent vectors of the input polynomial. The proof of correctness and the complexity bounds rely on the Newton polytope of the polynomial, where the underlying valued field consists of Puiseux series in a single variable.Comment: 31 pages; Long version of arXiv:1401.4720 with simplified proof