Moment-Based Relaxation of the Optimal Power Flow Problem

The optimal power flow (OPF) problem minimizes power system operating cost subject to both engineering and network constraints. With the potential to find global solutions, significant research interest has focused on convex relaxations of the non-convex AC OPF problem. This paper investigates ``moment-based'' relaxations of the OPF problem developed from the theory of polynomial optimization problems. At the cost of increased computational requirements, moment-based relaxations are generally tighter than the semidefinite relaxation employed in previous research, thus resulting in global solutions for a broader class of OPF problems. Exploration of the feasible space for test systems illustrates the effectiveness of the moment-based relaxation.Comment: 7 pages, 4 figures. Abstract accepted, full paper in revie

Supply-side effects of strong energy price hikes in German industry and transportation

The paper studies the short-term effects of energy price hikes on the supply of industrial goods and transport services including the repercussions on remuneration of input factors. While industry had suffered more strongly from the oil price shock of the late 1970s compared with the one of the early 1970s and the 2004-08 upsurge, evidence is reverse for transportation. Regarding the impact on the income distribution, both sectors share the pattern that in the recent episode rising energy costs were more than compensated by falling unit labor costs while in the 1970s cost structures had been strained by expansive wage policy in addition to the oil price shocks. --Energy prices,supply of goods and services,income distribution

Solution of Optimal Power Flow Problems using Moment Relaxations Augmented with Objective Function Penalization

The optimal power flow (OPF) problem minimizes the operating cost of an electric power system. Applications of convex relaxation techniques to the non-convex OPF problem have been of recent interest, including work using the Lasserre hierarchy of "moment" relaxations to globally solve many OPF problems. By preprocessing the network model to eliminate low-impedance lines, this paper demonstrates the capability of the moment relaxations to globally solve large OPF problems that minimize active power losses for portions of several European power systems. Large problems with more general objective functions have thus far been computationally intractable for current formulations of the moment relaxations. To overcome this limitation, this paper proposes the combination of an objective function penalization with the moment relaxations. This combination yields feasible points with objective function values that are close to the global optimum of several large OPF problems. Compared to an existing penalization method, the combination of penalization and the moment relaxations eliminates the need to specify one of the penalty parameters and solves a broader class of problems.Comment: 8 pages, 1 figure, to appear in IEEE 54th Annual Conference on Decision and Control (CDC), 15-18 December 201

Grid-Aware versus Grid-Agnostic Distribution System Control: A Method for Certifying Engineering Constraint Satisfaction

Growing penetrations of distributed energy resources (DERs) in distribution systems have motivated the design of controllers that leverage DER capabilities to achieve system-wide objectives. These controllers may be either grid-agnostic or grid-aware, depending on whether distribution network constraints are considered. Grid-agnostic controllers have the benefit of not requiring network models or system measurements, but may cause dangerous constraint violations. Rather than develop a specific controller, this paper considers the potential impacts of DER controllers with respect to network constraint violations. Specifically, this paper develops an optimization-based method to rigorously certify when any grid-agnostic controller can be applied without concern regarding network constraint violations, or, conversely, when grid-aware control may be needed to maintain distribution grid security. The proposed method uses convex optimization techniques to bound the impacts of load variability, given a subset of buses with voltage measurements and control. The method either provides a certificate for secure operation or identifies potentially critical constraints and the need for additional controllability. Numerical tests illustrate the ability to certify secure operation for different ranges of variability

Moyal Quantum Mechanics: The Semiclassical Heisenberg Dynamics

The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\hbar$. Its semiclassical expansion `coefficients,' acting on symbols that represent observables, are simple, globally defined differential operators constructed in terms of the classical flow. Two methods of constructing this expansion are discussed. The first introduces a cluster-graph expansion for the symbol of an exponentiated operator, which extends Groenewold's formula for the Weyl product of symbols. This Poisson bracket based cluster expansion determines the Jacobi equations for the semiclassical expansion of `quantum trajectories.' Their Green function solutions construct the regular $\hbar\downarrow0$ asymptotic series for the Heisenberg--Weyl evolution map. The second method directly substitutes such a series into the Moyal equation of motion and determines the $\hbar$ coefficients recursively. The Heisenberg--Weyl description of evolution involves no essential singularity in $\hbar$, no Hamilton--Jacobi equation to solve for the action, and no multiple trajectories, caustics or Maslov indices.Comment: 50, MANIT-94-0

Flight Testing of the Gulfstream Quiet Spike(TradeMark) on a NASA F-15B

Gulfstream Aerospace has long been interested in the development of an economically viable supersonic business jet (SBJ). A design requirement for such an aircraft is the ability for unrestricted supersonic flight over land. Although independent studies continue to substantiate that a market for a SBJ exists, regulatory and public acceptance challenges still remain for supersonic operation over land. The largest technical barrier to achieving this goal is sonic boom attenuation. Gulfstream's attention has been focused on fundamental research into sonic boom suppression for several years. This research was conducted in partnership with the NASA Aeronautics Research Mission Directorate (ARMD) supersonic airframe cruise efficiency technical challenge. The Quiet Spike, a multi-stage telescopic nose boom and a Gulfstream-patented design (references 1 and 2), was developed to address the sonic boom attenuation challenge and validate the technical feasibility of a morphing fuselage. The Quiet Spike Flight Test Program represents a major step into supersonic technology development for sonic boom suppression. The Gulfstream Aerospace Quiet Spike was designed to reduce the sonic boom signature of the forward fuselage for an aircraft flying at supersonic speeds. In 2004, the Quiet Spike Flight Test Program was conceived by Gulfstream and NASA to demonstrate the feasibility of sonic boom mitigation and centered on the structural and mechanical viability of the translating test article design. Research testing of the Quiet Spike consisted of numerous ground and flight operations. Each step in the process had unique objectives, and involved numerous test team members from the NASA Dryden Flight Research Center (DFRC) and Gulfstream Aerospace. Flight testing of the Quiet Spike was conducted at the NASA Dryden Flight Research Center on an F-15B aircraft from August, 2006, to February, 2007. During this period, the Quiet Spike was flown at supersonic speeds up to Mach 1.8 at the maximum design dynamic pressure of 685 pounds per square foot. Extension and retraction tests were conducted at speeds up to Mach 1.4. The design of the Quiet Spike to shape the forward shock wave environment of the aircraft was confirmed during near-field shock wave probing at Mach 1.4. Thirty-two flights were performed without incident and all project objectives were achieved. The success of the Quiet Spike Flight Test Program represents an important step towards developing commercial aircraft capable of supersonic flight over land within the continental United States and in international airspace