577 research outputs found
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
Recent Advances in Computational Methods for the Power Flow Equations
The power flow equations are at the core of most of the computations for
designing and operating electric power systems. The power flow equations are a
system of multivariate nonlinear equations which relate the power injections
and voltages in a power system. A plethora of methods have been devised to
solve these equations, starting from Newton-based methods to homotopy
continuation and other optimization-based methods. While many of these methods
often efficiently find a high-voltage, stable solution due to its large basin
of attraction, most of the methods struggle to find low-voltage solutions which
play significant role in certain stability-related computations. While we do
not claim to have exhausted the existing literature on all related methods,
this tutorial paper introduces some of the recent advances in methods for
solving power flow equations to the wider power systems community as well as
bringing attention from the computational mathematics and optimization
communities to the power systems problems. After briefly reviewing some of the
traditional computational methods used to solve the power flow equations, we
focus on three emerging methods: the numerical polynomial homotopy continuation
method, Groebner basis techniques, and moment/sum-of-squares relaxations using
semidefinite programming. In passing, we also emphasize the importance of an
upper bound on the number of solutions of the power flow equations and review
the current status of research in this direction.Comment: 13 pages, 2 figures. Submitted to the Tutorial Session at IEEE 2016
American Control Conferenc
Inexact Convex Relaxations for AC Optimal Power Flow: Towards AC Feasibility
Convex relaxations of AC optimal power flow (AC-OPF) problems have attracted
significant interest as in several instances they provably yield the global
optimum to the original non-convex problem. If, however, the relaxation is
inexact, the obtained solution is not AC-feasible. The quality of the obtained
solution is essential for several practical applications of AC-OPF, but
detailed analyses are lacking in existing literature. This paper aims to cover
this gap. We provide an in-depth investigation of the solution characteristics
when convex relaxations are inexact, we assess the most promising AC
feasibility recovery methods for large-scale systems, and we propose two new
metrics that lead to a better understanding of the quality of the identified
solutions. We perform a comprehensive assessment on 96 different test cases,
ranging from 14 to 3120 buses, and we show the following: (i) Despite an
optimality gap of less than 1%, several test cases still exhibit substantial
distances to both AC feasibility and local optimality and the newly proposed
metrics characterize these deviations. (ii) Penalization methods fail to
recover an AC-feasible solution in 15 out of 45 cases, and using the proposed
metrics, we show that most failed test instances exhibit substantial distances
to both AC-feasibility and local optimality. For failed test instances with
small distances, we show how our proposed metrics inform a fine-tuning of
penalty weights to obtain AC-feasible solutions. (iii) The computational
benefits of warm-starting non-convex solvers have significant variation, but a
computational speedup exists in over 75% of the cases
Revealing attributes of supportive healing environments in interior design: staff perceptions in healthcare design
2013 Spring.Includes bibliographical references.People seeking healthcare anticipate an environment supportive of healing and wellness in acute and ambulatory facilities. Such environments synthesize psychological, social, and physical components shown to effect perceptions of healing (McCullough, 2010). "Well-designed physical environments... foster wellness, whereas poorly designed environments... make people frustrated and thereby contribute to the possibility of illness" (Dilani, 2001, p. 34). Wellness factors need to be clearly identified in designing healthcare facilities, becoming an integral part of the therapeutic process (Dilani, 2001). By observing actual healthcare environments, evidence-informed (Nussbaumer, 2009) design strategies can enlighten stress-free environments by emphasizing strategic opportunities to impact the design of healthy facilities (Ulrich, 2000). The purpose of this research study was to closely examine attributes and factors contributing to a healing environment from the perspective of healthcare staff in a campus ambulatory healthcare setting. The study sought to identify attributes critical to the process of designing healing environments and to examine the presence of a hierarchy of healing attributes to support healthcare designers in their problem-solving and design intentions. Data were collected using an e-survey to the population of healthcare staff, with a response rate of 41% (N = 57). Study findings confirm Dilani (2000) and Ulrich's (1991) theoretical framework but suggest duplicity in the initial conceptual model incorporating these attributes and factors, as derived from their research findings. As a result a revised conceptual model was developed, which needs to be tested in future research
A Sufficient Condition for Power Flow Insolvability with Applications to Voltage Stability Margins
For the nonlinear power flow problem specified with standard PQ, PV, and
slack bus equality constraints, we present a sufficient condition under which
the specified set of nonlinear algebraic equations has no solution. This
sufficient condition is constructed in a framework of an associated feasible,
convex optimization problem. The objective employed in this optimization
problem yields a measure of distance (in a parameter set) to the power flow
solution boundary. In practical terms, this distance is closely related to
quantities that previous authors have proposed as voltage stability margins. A
typical margin is expressed in terms of the parameters of system loading
(injected powers); here we additionally introduce a new margin in terms of the
parameters of regulated bus voltages.Comment: 12 pages, 7 figure
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
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