An official website of the United States government
Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments, this paper focuses on chance-constrained optimization, which provides explicit probabilistic guarantees on the feasibility of optimal solutions. Although quite a few methods have been proposed to solve chance-constrained optimization problems, there is a lack of comprehensive review and comparative analysis of the proposed methods. We first review three categories of existing methods to chance-constrained optimization: (1) scenario approach; (2) sample average approximation; and (3) robust optimization based methods. Data-driven methods, which are not constrained by any particular distributions of the underlying uncertainties, are of particular interest. Key results of the analytical reformulation approach for specific distributions are briefly discussed. We then provide a comprehensive review on the applications of chance-constrained optimization in power systems. Finally, this paper provides a critical comparison of existing methods based on numerical simulations, which are conducted on standard power system test cases.
more »
« less
Chance Constraint based design of Input Shapers
The focus of this paper is on the design of input shapers for systems with uncertainties in the parameters of the vibratory modes which need to be attenuated. A probabilistic framework is proposed for the design of the robust input shaper, when the uncertain modal parameters are characterized by probability density functions. A convex chance constrained optimization problem is posed to determine the parameters of input shapers (time-delay filter) which can accommodate the users acceptable risk levels for a prescribed residual energy threshold. Robust input shapers are developed for various compact support distributions to illustrate the ability of the proposed formulation to synthesize input shapers which can satisfy a residual energy threshold with a given risk level. This problem formulation can conceivably reduce the conservative nature of worst case controllers which have to ensure that all realizations of the uncertain system have to satisfy a prescribed performance index. The chance constrained input shaper is designed for a spring-mass-dashpot system with three different distributions for the uncertain spring stiffness. Results provide encouragement for the extension of the proposed approach to multi-dimensional and multi-model uncertainties.
more »
« less
- Award ID(s):
- 1537210
- PAR ID:
- 10113122
- Date Published:
- Journal Name:
- 2017 IEEE Conference on Control Technology and Applications
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
ABSTRACT This paper introduces a novel robust design approach aimed at reducing the sensitivity of a target metric to parameter uncertainties. Using Shapley effects from game theory as a global sensitivity proxy, we analyze a clamped‐free Euler‐Bernoulli beam with two uncertain mass positions. The first case study reduces sensitivity of the second mode frequency to mass location uncertainty and is validated experimentally on a gantry‐suspended beam. In the second case, a robust controller minimizes the Shapley effect of residual energy on mass location uncertainty. Our approach significantly reduces average residual energy compared to traditional Zero Vibration Derivative Input Shapers, as confirmed by experiments.more » « less
-
This article explores various uncertain control co-design (UCCD) problem formulations. While previous work offers formulations that are method-dependent and limited to only a handful of uncertainties (often from one discipline), effective application of UCCD to real-world dynamic systems requires a thorough understanding of uncertainties and how their impact can be captured. Since the first step is defining the UCCD problem of interest, this article aims at addressing some of the limitations of the current literature by identifying possible sources of uncertainties in a general UCCD context and then formalizing ways in which their impact is captured through problem formulation alone (without having to immediately resort to specific solution strategies). We first develop and then discuss a generalized UCCD formulation that can capture uncertainty representations presented in this article. Issues such as the treatment of the objective function, the challenge of the analysis-type equality constraints, and various formulations for inequality constraints are discussed. Then, more specialized problem formulations such as stochastic in expectation, stochastic chance-constrained, probabilistic robust, worst-case robust, fuzzy expected value, and possibilistic chance-constrained UCCD formulations are presented. Key concepts from these formulations, along with insights from closely-related fields, such as robust and stochastic control theory, are discussed, and future research directions are identified.more » « less
-
The focus of this paper is on the design of state constrained controllers which are robust to time invariant uncertain variables. Polynomial Chaos spectral expansion is used to parameterize the uncertain variables, which permits evaluation of the evolution of the uncertain states. The coefficients of the truncated polynomial chaos expansion are determined using the Galerkin projection resulting in a set of deterministic equations. A mapping into Bernstein polynomial space permits determination of bounds on the evolving states. Linear programming is used on the deterministic set of equation with constraints as the predetermined bounds to determine controllers which are robust to the epistemic uncertainties. Numerical examples are used to illustrate the benefit of the proposed technique for the design of rest-to-rest controllers subject to deformation constraints; which are robust to uncertainties in the stiffness coefficient for the benchmark spring-mass system.more » « less
-
Planning safe trajectories for nonlinear dynamical systems subject to model uncertainty and disturbances is challenging. In this work, we present a novel approach to tackle chance-constrained trajectory planning problems with nonconvex constraints, whereby obstacle avoidance chance constraints are reformulated using the signed distance function. We propose a novel sequential convex programming algorithm and prove that under a discrete time problem formulation, it is guaranteed to converge to a solution satisfying first-order optimality conditions. We demonstrate the approach on an uncertain 6 degrees of freedom spacecraft system and show that the solutions satisfy a given set of chance constraints.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
