Recherche en systemes, automatique et optimisation

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Enabling inter-area reserve exchange through stable benefit allocation mechanisms *

Orcun Karaca

The establishment of a single European day-ahead market has accomplished the integration of the regional day-ahead markets. However, reserve provision and activation remain an exclusive responsibility of regional operators. This limited spatial coordination and the separated structure hinder the efficient utilization of flexible generation and transmission, since their capacities have to be ex-ante allocated between energy and reserves. To promote reserve exchange, recent work proposed a preemptive model that withdraws a portion of the inter-area transmission capacity available from day-ahead energy for reserves by minimizing the expected system cost. This decision-support tool, formulated as a stochastic bilevel program, respects the current architecture but does not suggest area-specific costs that guarantee sufficient benefits for areas to accept the solution. To this end, we formulate a preemptive model in a framework that allows application of game theory methods to obtain a stable benefit allocation, i.e., an outcome immune to coalitional deviations ensuring willingness of areas to coordinate. We show that benefit allocation mechanisms can be formulated either at the day-ahead or the real-time stages, in order to distribute the expected or the scenario-specific benefits, respectively. For both games, the proposed benefits achieve minimal stability violation, while allowing for a tractable computation with limited queries to the bilevel program. Our case studies, based on an illustrative and a more realistic test case, compare our method with well-studied benefit allocations, namely, the Shapley value and nucleolus, and analyze the factors that drive these allocations (e.g., flexibility, network structure, wind correlations). We show that our method performs better in stability and tractability. (c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

PERGAMON-ELSEVIER SCIENCE LTD2022

Chance-Constrained Trajectory Planning With Multimodal Environmental Uncertainty

We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles' uncertain states. Then, we develop a mixed-integer conic approximation to the chance-constrained trajectory planning problem with deterministic linear systems and polyhedral obstacles. When the GMM moments are estimated via finite samples, we develop a tight concentration bound to ensure the chance constraint with a desired confidence. Moreover, to limit the amount of constraint violation, we develop a Conditional Value-at-Risk (CVaR) approach corresponding to the chance constraints and derive a tractable approximation for known and estimated GMM moments. We verify our methods with state-of-the-art trajectory prediction algorithms and autonomous driving datasets.

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Upper bounds for the reach-avoid probability via robust optimization

John Lygeros

We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by restricting attention to the span of Gaussian radial basis functions and imposing structural assumptions on the transition kernel of the stochastic processes as well as the target and safe sets of the reach-avoid problem. In particular, we require the kernel to be written as a Gaussian mixture density with each mean of the distribution being affine in the current state and input and the target and safe sets to be written as intersections of quadratic inequalities. Taking advantage of these structural assumptions, we formulate a recursion of semidefinite programs where each step provides an upper bound to the value function of the reach- avoid problem. The upper bounds provide a performance metric to which any suboptimal control policy can be compared, and can themselves be used to construct suboptimal control policies. We illustrate via numerical examples that even if the resulting bounds are conservative, the associated control policies achieve higher reach-avoid probabilities than heuristic controllers for problems of large state-input space dimensions (more than 20). The results presented in this paper, far exceed the limits of current approximation methods for reach-avoid problems in the specific class of stochastic systems considered.

2015

Enabling inter-area reserve exchange through stable benefit allocation mechanisms *

Orcun Karaca

PERGAMON-ELSEVIER SCIENCE LTD2022