Computing Essential Sets for Convex and Non-convex Scenario Problems: Theory and Application

Geng, Xinbo; Xie, Le; Modarresi, Mohammad Sadegh

doi:10.48550/arxiv.1910.07672

Cited by 1 publication

(6 citation statements)

References 48 publications

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“…The original scenario approach theory [15,17,18,23] only applies to single-stage optimization problems. There is a lack of known results of multi-stage scenario approach.…”

Section: Probabilistic Guarantees Via the Scenario Approachmentioning

confidence: 99%

“…After converting the scenariobased two-stage robust optimization as the single-stage scenario program, Theorem 1 is essentially Theorem 1 of [15], Theorem 2 is from Theorem 2 of [17], and Theorem 3 is a direct corollary of Theorem 1 in [18]. The relatively completely recourse assumption is necessary to meet the feasibility assumption in [15,17,18,23] (see Assumption 2 in Appendix A.1).…”

Section: Probabilistic Guarantees Via the Scenario Approachmentioning

confidence: 99%

“…Although Theorems 1, 2 and 3 hold for any invariant set, the tightest guarantee is achieved for the essential set, i.e., the invariant set with minimal cardinality [23]. In general, finding essential sets is a combinatorial problem, which could be computationally intractable for non-convex scenario problems (4)).…”

Section: Probabilistic Guarantees Via the Scenario Approachmentioning

confidence: 99%

“…This simple construction of uncertainty set is closely related with the scenario approach theory [15,16,17,18]. The scenario approach has been recently introduced to the energy systems problems, e.g., resource adequacy and security assessment [19], economic dispatch [20], demand response scheduling [21], and unit commitment [22,23] .…”

Section: Introductionmentioning

confidence: 99%

“…For the convex case in Theorem 1,[23] shows that the essential set is the set of support scenarios as in[15]. For non-convex case, an essential set is the minimal support-subsample in[18].…”

mentioning

confidence: 97%

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Two-stage Robust Energy Storage Planning with Probabilistic Guarantees: A Data-driven Approach

Yan¹,

Geng²,

Bie³

et al. 2021

Preprint

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In conventional planning decision making, shorter-term (e.g., hourly) variations are not explicitly accounted for. However, given the deepening penetration of variable resources, it is becoming imperative to consider such shorter-term variation in the longer-term planning exercise. This paper addresses a central challenge of jointly considering such shorter-term and longer-term uncertainties in power system planning with increasing penetration of renewable and storage resources. By leveraging the abundant operational observation data, we propose a scenario-based robust planning framework that provides rigorous guarantees on the future operation risk of planning decisions considering a broad range of operational conditions, such as renewable generation fluctuations and load variations. By connecting two-stage robust optimization with the scenario approach theory, we show that with a carefully chosen number of scenarios, the operational risk level of the robust solution can be adaptive to the risk preference set by planners. The theoretical guarantees hold true for any distributions, and the proposed approach is scalable towards real-world power grids. Furthermore, the column-and-constraint generation algorithm is used to solve the two-stage robust planning problem and tighten theoretical guarantees. We substantiate this framework through a planning problem of energy storage in a power grid with deep renewable penetration. Case studies are performed on large-scale test systems (modified IEEE 118-bus system) to illustrate the theoretical bounds as well as the scalability of the proposed algorithm.

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“…The original scenario approach theory [15,17,18,23] only applies to single-stage optimization problems. There is a lack of known results of multi-stage scenario approach.…”

Section: Probabilistic Guarantees Via the Scenario Approachmentioning

confidence: 99%