54 research outputs found
Opportunities for Price Manipulation by Aggregators in Electricity Markets
Aggregators are playing an increasingly crucial role for integrating renewable generation into power systems. However, the intermittent nature of renewable generation makes market interactions of aggregators difficult to monitor and regulate, raising concerns about potential market manipulations. In this paper, we address this issue by quantifying the profit an aggregator can obtain through strategic curtailment of generation in an electricity market. We show that, while the problem of maximizing the benefit from curtailment is hard in general, efficient algorithms exist when the topology of the network is radial (acyclic). Further, we highlight that significant increases in profit can be obtained through strategic curtailment in practical settings
PowerModels.jl: An Open-Source Framework for Exploring Power Flow Formulations
In recent years, the power system research community has seen an explosion of
novel methods for formulating and solving power network optimization problems.
These emerging methods range from new power flow approximations, which go
beyond the traditional DC power flow by capturing reactive power, to convex
relaxations, which provide solution quality and runtime performance guarantees.
Unfortunately, the sophistication of these emerging methods often presents a
significant barrier to evaluating them on a wide variety of power system
optimization applications. To address this issue, this work proposes
PowerModels, an open-source platform for comparing power flow formulations.
From its inception, PowerModels was designed to streamline the process of
evaluating different power flow formulations on shared optimization problem
specifications. This work provides a brief introduction to the design of
PowerModels, validates its implementation, and demonstrates its effectiveness
with a proof-of-concept study analyzing five different formulations of the
Optimal Power Flow problem
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
Sparse Inverse Covariance Estimation for Chordal Structures
In this paper, we consider the Graphical Lasso (GL), a popular optimization
problem for learning the sparse representations of high-dimensional datasets,
which is well-known to be computationally expensive for large-scale problems.
Recently, we have shown that the sparsity pattern of the optimal solution of GL
is equivalent to the one obtained from simply thresholding the sample
covariance matrix, for sparse graphs under different conditions. We have also
derived a closed-form solution that is optimal when the thresholded sample
covariance matrix has an acyclic structure. As a major generalization of the
previous result, in this paper we derive a closed-form solution for the GL for
graphs with chordal structures. We show that the GL and thresholding
equivalence conditions can significantly be simplified and are expected to hold
for high-dimensional problems if the thresholded sample covariance matrix has a
chordal structure. We then show that the GL and thresholding equivalence is
enough to reduce the GL to a maximum determinant matrix completion problem and
drive a recursive closed-form solution for the GL when the thresholded sample
covariance matrix has a chordal structure. For large-scale problems with up to
450 million variables, the proposed method can solve the GL problem in less
than 2 minutes, while the state-of-the-art methods converge in more than 2
hours
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