Design of power system controllers by nonsmooth, nonconvex optimization

Dotta, Daniel; Silva, Aguinaldo S. e; Decker, Ildemar C.

doi:10.1109/pes.2009.5275366

Cited by 21 publications

(9 citation statements)

References 32 publications

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“…Recently published applications of hifoo include design of teleoperations for minimally invasive surgery [11], design of an aircraft nose landing gear steering system [41], design of an aircraft controller for improved gust alleviation and passenger comfort [50], robust controller design for a proton exchange membrane fuel cell system [49], design of power systems controllers [12] and design of winding systems for elastic web materials [21].…”

Section: Softwarementioning

confidence: 99%

Nonsmooth optimization via quasi-Newton methods

2012

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We investigate the behavior of quasi-Newton algorithms applied to minimize a nonsmooth function f , not necessarily convex. We introduce an inexact line search that generates a sequence of nested intervals containing a set of points of nonzero measure that satisfy the Armijo and Wolfe conditions if f is absolutely continuous along the line. Furthermore, the line search is guaranteed to terminate if f is semi-algebraic. It seems quite difficult to establish a convergence theorem for quasi-Newton methods applied to such general classes of functions, so we give a careful analysis of a special but illuminating case, the Euclidean norm, in one variable using the inexact line search and in two variables assuming that the line search is exact. In practice, we find that when f is locally Lipschitz and semi-algebraic with bounded sublevel sets, the BFGS (Broyden-Fletcher-Goldfarb-Shanno) method with the inexact line search almost always generates sequences whose cluster points are Clarke stationary and with function values converging R-linearly to a Clarke stationary value. We give references documenting the successful use of BFGS in a variety of nonsmooth applications, particularly the design of low-order controllers for linear dynamical systems. We conclude with a challenging open question.

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Section: Softwarementioning

confidence: 99%

Nonsmooth optimization via quasi-Newton methods

2012

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“…Besides that, researches have been carried out in fault location and control applications [10,11]. The LVPMS and the HVPMS have allowed the comparison of measurements acquired at the distribution level and at high voltage.…”

Section: Resultsmentioning

confidence: 99%

Experience and applications of phasor measurements to the Brazilian interconnected power system

Decker

Silva

Agostini

et al. 2010

Int Trans Elec Energy Syst

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SUMMARYIn this paper, applications of phasor measurements to the Brazilian interconnected power system (BIPS) are presented. Two prototypes, the low voltage phasor measurement system (LVPMS), with phasor measurement units (PMUs) installed in nine universities throughout Brazil and the high voltage phasor measurement system (HVPMS), with PMUs installed in four substations in a transmission utility in Southern Brazil, are the first installations in the country. These experimental prototypes have been a rich source of experience on the use of syncronized phasor measurements. Line parameter estimation, detection of oscillation modes, disturbance analysis, and system wide model validation have been the main applications. The LVPMS measurements are acquired at outlet voltage while the HVPMS measurements are acquired at 525 kV substations. The monitoring and analysis of several events in the BIPS have shown that both systems can provide relevant and comparable information on the BIPS dynamics.

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“…Then, since for all k we have 14) and → 0 imply that the cluster point x is stationary for φ ρ * . Moreover, by the construction of the parameter update step 4 in Algorithm 2.1 and the discussion in the second paragraph of section 2.2, we have the existence of an infinite subsequence of iterations K yielding the remainder of the result for part (a) of the theorem.…”

Section: It Follows That With |ρ − ρ| ≤ ζ the Constructed Set T Abovementioning

confidence: 94%

“…For instance, in a collection of recent papers [7,8,30], an algorithm known as gradient sampling (GS) was developed and analyzed for the minimization of locally Lipschitz f . The GS method is interesting theoretically in that convergence guarantees hold with probability one, but it is also widely applicable and robust and has been used to solve a variety of interesting problems [6,14,19,20,42]. It is worthwhile to note that GS does not require the user to compute subgradients as the iterates and sample points remain in the open dense set D f ⊂ R n over which f is continuously differentiable.…”

Section: Introductionmentioning

confidence: 99%

A Sequential Quadratic Programming Algorithm for Nonconvex, Nonsmooth Constrained Optimization

Curtis¹,

Overton²

2012

SIAM J. Optim.

111

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Abstract.We consider optimization problems with objective and constraint functions that may be nonconvex and nonsmooth. Problems of this type arise in important applications, many having solutions at points of nondifferentiability of the problem functions. We present a line search algorithm for situations when the objective and constraint functions are locally Lipschitz and continuously differentiable on open dense subsets of R n . Our method is based on a sequential quadratic programming (SQP) algorithm that uses an 1 penalty to regularize the constraints. A process of gradient sampling (GS) is employed to make the search direction computation effective in nonsmooth regions. We prove that our SQP-GS method is globally convergent to stationary points with probability one and illustrate its performance with a MATLAB implementation.

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Design of power system controllers by nonsmooth, nonconvex optimization

Cited by 21 publications

References 32 publications

Nonsmooth optimization via quasi-Newton methods

Nonsmooth optimization via quasi-Newton methods

Experience and applications of phasor measurements to the Brazilian interconnected power system

A Sequential Quadratic Programming Algorithm for Nonconvex, Nonsmooth Constrained Optimization

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