Scenario-Based Economic Dispatch With Tunable Risk Levels in High-Renewable Power Systems

Modarresi, Mohammad Sadegh; Xie, Le; Campi, Marco C.; Garatti, Simone; Carè, Algo; Thatte, Anupam A.

doi:10.1109/pesgm41954.2020.9281572

Cited by 15 publications

(29 citation statements)

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“…By the complementary slackness conditions ( 22) and ( 23) and the first sub-case in (25), it follows that ν B = 0. Moreover, since x B = 0 and ν B = 0, it follows from (23) that…”

Section: B Preliminary Results Based On Duality Analysismentioning

confidence: 98%

On the sensitivity of linear resource sharing problems to the arrival of new agents

Falsone¹,

Margellos²,

Zizzo³

et al. 2021

Preprint

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We consider a multi-agent optimal resource sharing problem that is represented by a linear program. The amount of resource to be shared is fixed, and agents belong to a population that is characterized probabilistically so as to allow heterogeneity among the agents. In this paper, we provide a characterization of the probability that the arrival of a new agent affects the resource share of other agents, which means that accommodating the new agent request at the detriment of the other agents allocation provides some payoff. This probability represents a sensitivity index for the optimal solution of a linear programming resource sharing problem when a new agent shows up, and it is of fundamental importance for a correct and profitable operation of the multi-agent system. Our developments build on the equivalence between the resource sharing problem and certain dual reformulations which can be interpreted as scenario programs with the number of scenarios corresponding to the number of agents in the primal problem. The recent "wait-and-judge" scenario approach is then used to obtain the sought sensitivity index. Our theoretical findings are demonstrated through a numerical example on optimal cargo aircraft loading.

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“…By the complementary slackness conditions ( 22) and ( 23) and the first sub-case in (25), it follows that ν B = 0. Moreover, since x B = 0 and ν B = 0, it follows from (23) that…”

Section: B Preliminary Results Based On Duality Analysismentioning

confidence: 98%

On the sensitivity of linear resource sharing problems to the arrival of new agents

Falsone¹,

Margellos²,

Zizzo³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this section, we define the look-ahead economic dispatch (LAED) problem. Our formulation is inspired by a similar structure in [31]. The objective of the LAED problem is to minimize the total cost of generation over a time-horizon of length T , while satisfying operational constraints and the forecasted power demand in an appropriate sense in the presence of uncertain power generation from renewable (solar and wind) energy sources (RESs).…”

Section: Look-ahead Economic Dispatch Under Uncertaintymentioning

confidence: 99%

“…denotes the vector of power injections at the nodes. We refer the reader to [31], [38], [39] for analytical and [40] for numerical approaches to compute PTDF matrices.…”

Section: Look-ahead Economic Dispatch Under Uncertaintymentioning

confidence: 99%

“…As a result, we resort to empirical analysis of constraint violation as opposed relying on finite sample guarantees which hold under the assumption that samples are i.i.d., according to a true distribution. Similarly, the guarantees provided under the scenario approach [31] are not necessarily applicable.…”

Section: Distributionally Robust Dispatch With Historical Datamentioning

confidence: 99%

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Wasserstein Distributionally Robust Look-Ahead Economic Dispatch

Poolla

Hota

Bolognani

et al. 2021

IEEE Trans. Power Syst.

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We consider the problem of look-ahead economic dispatch (LAED) with uncertain renewable energy generation. The goal of this problem is to minimize the cost of conventional energy generation subject to uncertain operational constraints. The risk of violating these constraints must be below a given threshold for a family of probability distributions with characteristics similar to observed past data or predictions. We present two data-driven approaches based on two novel mathematical reformulations of this distributionally robust decision problem. The first one is a tractable convex program in which the uncertain constraints are defined via the distributionally robust conditional-value-at-risk. The second one is a scalable robust optimization program that yields an approximate distributionally robust chance-constrained LAED. Numerical experiments on the IEEE 39-bus system with real solar production data and forecasts illustrate the effectiveness of these approaches. We discuss how system operators should tune these techniques in order to seek the desired robustness-performance trade-off and we compare their computational scalability.

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“…Modaressi et al [48] solved a look-ahead real-time economic dispatch in a 2000-bus synthetic grid using the scenario approach. However, the scenario approach demands the convexity of the uncertain problem, so it is not directly applied for unit-commitment problems [49].…”

Section: Scenario Approachmentioning

confidence: 99%

A Scenario Approach for Chance-Constrained Short-Term Scheduling With Affine Rules

Machado¹

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Scenario-Based Economic Dispatch With Tunable Risk Levels in High-Renewable Power Systems

Cited by 15 publications

References 0 publications

On the sensitivity of linear resource sharing problems to the arrival of new agents

On the sensitivity of linear resource sharing problems to the arrival of new agents

Wasserstein Distributionally Robust Look-Ahead Economic Dispatch

A Scenario Approach for Chance-Constrained Short-Term Scheduling With Affine Rules

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