Improving QC Relaxations of OPF Problems via Voltage Magnitude Difference Constraints and Envelopes for Trilinear Monomials

AC optimal power flow (AC~OPF) is a challenging non-convex optimization problem that plays a crucial role in power system operation and control. Recently developed convex relaxation techniques provide new insights regarding the global optimality of AC~OPF solutions. The quadratic convex (QC) relaxation is one promising approach that constructs convex envelopes around the trigonometric and product terms in the polar representation of the power flow equations. This paper proposes two methods for tightening the QC relaxation. The first method introduces new variables that represent the voltage magnitude differences between connected buses. Using "bound tightening" techniques, the bounds on the voltage magnitude difference variables can be significantly smaller than the bounds on the voltage magnitudes themselves, so constraints based on voltage magnitude differences can tighten the relaxation. Second, rather than a potentially weaker "nested McCormick" formulation, this paper applies "Meyer and Floudas" envelopes that yield the convex hull of the trilinear monomials formed by the product of the voltage magnitudes and trignometric terms in the polar form of the power flow equations. Comparison to a state-of-the-art QC implementation demonstrates the advantages of these improvements via smaller optimality gaps.Comment: 8 pages, 1 figur

The Mystery of Moral Perception

_ Source: _Page Count 24 Accounts of non-naturalist moral perception have been advertised as an empiricist-friendly epistemological alternative to moral rationalism. I argue that these accounts of moral perception conceal a core commitment of rationalism—to substantive a priori justification—and embody its most objectionable feature—namely, “mysteriousness.” Thus, accounts of non-naturalist moral perception do not amount to an interesting alternative to moral rationalis

Emergent Universality and Quantum Critical Points in Multi-Orbital Anderson Models

We apply a joint Renormalised Perturbation Theory and Numerical Renormalisation Group approach to the study of an n-orbital Anderson Model with a Hund's Rule Coupling. We apply the same methods to the analysis of a two-impurity Anderson model, and find the emergence of a single renormalised energy scale on the approach to two types of quantum critical point, such that it is possible to characterise the low energy physics in terms of this energy scale alone.Open Acces

Optimal Placement and Control of Unified Power Flow Control Devices Using Evolutionary Computing and Sequential Quadratic Programming

A crucial factor effecting modern power systems today is power flow control. An effective means for controlling and improving power flow is by installing fast reacting devices such as a unified power flow controller (UPFC). For maximum positive impact of this device on the power grid, it should be installed at an optimal location and employ an optimal realtime control algorithm. This paper proposes the combination of an evolutionary algorithm (EA) to find the optimal location and sequential quadratic programming (SQP) to optimize the UPFC control settings. Simulations are conducted using the classic IEEE 118 bus test system. For comparison purposes, results for the combination of a greedy placement heuristic (H) and the SQP control algorithm are provided as well. The EA+SQP combination is shown to outperform the H+SQP approach