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Determining contingency aware dispatch decisions by solving a security-constrained optimal power flow (SCOPF) is challenging for real-world power systems, as the high problem dimensionality often leads to impractical computational requirements. This problem becomes more severe when the SCOPF has to be solved not only for a single instance, but for multiple periods, e.g. in the context of electricity market analyses. This paper proposes an algorithm that identifies the minimal set of constraints that exactly define the space of feasible nodal injections for a given network and contingency scenarios. By internalizing the technical limits of the nodal injections and enforcing a minimal worst-case impact of contingencies to line flows, computational effort can be further improved. The case study applies and analyzes the methods on the IEEE 118 and A&M 2000 bus systems, as well as the German and European transmission systems. In all tested cases the proposed algorithm identifies at least 95% of the network and security constraints as redundant, leading to significant SCOPF solve time reductions. Scalability and practical implementation are explicitly discussed. The code and input data of the case study is published supplementary to the paper under an open-source license. [ABSTRACT FROM AUTHOR]

As a result of many factors, including the European Union's aim to increase the share of electrical energy from renewable sources, the number of distributed-generation (DG) devices in Europe is significantly increasing. Increasing numbers of DG units may cause problems with power quality (PQ). In this paper, a PQ-management algorithm is presented that reduces or even solves this problem in low-voltage grids. This algorithm will be implemented as one of several software modules in a system for distributed power operation and PQ management in low-voltage grids. PQ management in this context means maintaining PQ within prescribed limits by optimizing the control of generators, storage units, and controllable loads. Significant advantages of the presented approach are that the algorithm is universal and that it adapts its control variables automatically. Therefore, a detailed analysis of the grid in advance is not necessary. Furthermore, local PQ control of distributed resources can work autonomously and continuously without triggering by external signals, which is advantageous in the case of loss of communications. Various simulations to validate the effectiveness and stable operation of the algorithm were performed and results presented that show a marked improvement in PQ. [ABSTRACT FROM AUTHOR]

In the sparse polynomial multiplication problem, one is asked to multiply two sparse polynomials $f$ and $g$ in time that is proportional to the size of the input plus the size of the output. The polynomials are given via lists, $F$ and $G$ , of their coefficients. Cole and Hariharan (STOC 02) have given a nearly optimal algorithm when the coefficients are positive, and Arnold and Roche (ISSAC 15) devised an algorithm running in time proportional to the “structural sparsity” of the product, i.e. the set $\mathrm {supp}(F) + \mathrm {supp}(G)$. The latter algorithm is particularly efficient when there are not “too many cancellations” of coefficients in the product. In this work we give a clean, nearly optimal algorithm for the sparse polynomial multiplication problem. [ABSTRACT FROM AUTHOR]