198 research outputs found
On trivial line bundles on toric DM stacks of dim
We study line bundles on smooth toric DM stacks
of arbitrary dimension. A sufficient condition
is given for when infinitely many line bundles on
have trivial cohomology. In dimension three, the
sufficient condition is also a necessary condition in the case that
has no more than one pair of collinear rays.Comment: 16 pages, 6 figures. Reference added. arXiv admin note: text overlap
with arXiv:1812.0175
Fano varieties with conjecturally largest Fano index
For Fano varieties of various singularities such as canonical and terminal,
we construct examples with large Fano index. By low-dimensional evidence, we
conjecture that our examples have the largest Fano index for all dimensions.Comment: 13 page
Optimization of Battery Energy Storage to Improve Power System Oscillation Damping
A placement problem for multiple Battery Energy Storage System (BESS) units
is formulated towards power system transient voltage stability enhancement in
this paper. The problem is solved by the Cross-Entropy (CE) optimization
method. A simulation-based approach is adopted to incorporate higher-order
dynamics and nonlinearities of generators and loads. The objective is to
maximize the voltage stability index, which is setup based on certain
grid-codes. Formulations of the optimization problem are then discussed.
Finally, the proposed approach is implemented in MATLAB/DIgSILENT and tested on
the New England 39-Bus system. Results indicate that installing BESS units at
the optimized location can alleviate transient voltage instability issue
compared with the original system with no BESS. The CE placement algorithm is
also compared with the classic PSO (Particle Swarm Optimization) method, and
its superiority is demonstrated in terms of a faster convergence rate with
matched solution qualities.Comment: This paper has been accepted by IEEE Transactions on Sustainable
Energy and now still in online-publication phase, IEEE Transactions on
Sustainable Energy. 201
Online Voltage Stability Assessment for Load Areas Based on the Holomorphic Embedding Method
This paper proposes an online steady-state voltage stability assessment
scheme to evaluate the proximity to voltage collapse at each bus of a load
area. Using a non-iterative holomorphic embedding method (HEM) with a proposed
physical germ solution, an accurate loading limit at each load bus can be
calculated based on online state estimation on the entire load area and a
measurement-based equivalent for the external system. The HEM employs a power
series to calculate an accurate Power-Voltage (P-V) curve at each load bus and
accordingly evaluates the voltage stability margin considering load variations
in the next period. An adaptive two-stage Pade approximants method is proposed
to improve the convergence of the power series for accurate determination of
the nose point on the P-V curve with moderate computational burden. The
proposed method is illustrated in detail on a 4-bus test system and then
demonstrated on a load area of the Northeast Power Coordinating Council (NPCC)
48-geneartor, 140-bus power system.Comment: Revised and Submitted to IEEE Transaction on Power System
Calabi-Yau varieties of large index
Call a projective variety Calabi-Yau if its canonical divisor is -linearly equivalent to zero. The smallest positive integer with
linearly equivalent to zero is called the index of . We construct Calabi-Yau
varieties with the largest known index in high dimensions. In our examples, the
index grows doubly exponentially with dimension. We conjecture that our
examples have the largest possible index, with supporting evidence in low
dimensions. The examples are obtained by mirror symmetry from our Calabi-Yau
varieties with an ample Weil divisor of small volume. We also give examples for
several related problems, including Calabi-Yau varieties with large orbifold
Betti numbers or small minimal log discrepancy.Comment: 31 pages, 3 figures; v2: Theorem 3.1 due to Jihao Li
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