109,128 research outputs found
A cyclic time-dependent Markov process to model daily patterns in wind turbine power production
Wind energy is becoming a top contributor to the renewable energy mix, which
raises potential reliability issues for the grid due to the fluctuating nature
of its source. To achieve adequate reserve commitment and to promote market
participation, it is necessary to provide models that can capture daily
patterns in wind power production. This paper presents a cyclic inhomogeneous
Markov process, which is based on a three-dimensional state-space (wind power,
speed and direction). Each time-dependent transition probability is expressed
as a Bernstein polynomial. The model parameters are estimated by solving a
constrained optimization problem: The objective function combines two maximum
likelihood estimators, one to ensure that the Markov process long-term behavior
reproduces the data accurately and another to capture daily fluctuations. A
convex formulation for the overall optimization problem is presented and its
applicability demonstrated through the analysis of a case-study. The proposed
model is capable of reproducing the diurnal patterns of a three-year dataset
collected from a wind turbine located in a mountainous region in Portugal. In
addition, it is shown how to compute persistence statistics directly from the
Markov process transition matrices. Based on the case-study, the power
production persistence through the daily cycle is analysed and discussed
Convex Combinatorial Optimization
We introduce the convex combinatorial optimization problem, a far reaching
generalization of the standard linear combinatorial optimization problem. We
show that it is strongly polynomial time solvable over any edge-guaranteed
family, and discuss several applications
Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints
This paper presents a trajectory generation method that optimizes a quadratic
cost functional with respect to linear system dynamics and to linear input and
state constraints. The method is based on continuous-time flatness-based
trajectory generation, and the outputs are parameterized using a polynomial
basis. A method to parameterize the constraints is introduced using a result on
polynomial nonpositivity. The resulting parameterized problem remains
linear-quadratic and can be solved using quadratic programming. The problem can
be further simplified to a linear programming problem by linearization around
the unconstrained optimum. The method promises to be computationally efficient
for constrained systems with a high optimization horizon. As application, a
predictive torque controller for a permanent magnet synchronous motor which is
based on real-time optimization is presented.Comment: Proceedings of the American Control Conference (ACC), pp. 1904-1909,
San Francisco, USA, June 29 - July 1, 201
Nonlinear Integer Programming
Research efforts of the past fifty years have led to a development of linear
integer programming as a mature discipline of mathematical optimization. Such a
level of maturity has not been reached when one considers nonlinear systems
subject to integrality requirements for the variables. This chapter is
dedicated to this topic.
The primary goal is a study of a simple version of general nonlinear integer
problems, where all constraints are still linear. Our focus is on the
computational complexity of the problem, which varies significantly with the
type of nonlinear objective function in combination with the underlying
combinatorial structure. Numerous boundary cases of complexity emerge, which
sometimes surprisingly lead even to polynomial time algorithms.
We also cover recent successful approaches for more general classes of
problems. Though no positive theoretical efficiency results are available, nor
are they likely to ever be available, these seem to be the currently most
successful and interesting approaches for solving practical problems.
It is our belief that the study of algorithms motivated by theoretical
considerations and those motivated by our desire to solve practical instances
should and do inform one another. So it is with this viewpoint that we present
the subject, and it is in this direction that we hope to spark further
research.Comment: 57 pages. To appear in: M. J\"unger, T. Liebling, D. Naddef, G.
Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.), 50
Years of Integer Programming 1958--2008: The Early Years and State-of-the-Art
Surveys, Springer-Verlag, 2009, ISBN 354068274
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