Very Short-Term Wind Power Prediction Interval Framework via Bi-Level Optimization and Novel Convex Cost Function

N. Safari, S. M. Mazhari, C. Y. Chung

Research output: Journal article publicationJournal articleAcademic researchpeer-review

26 Citations (Scopus)


Substantial challenges in power systems operation and control as a result of the intermittent and stochastic nature of wind power generation can be significantly alleviated by proficient very short-term wind power prediction interval (WPPI) models. In WPPI models, minimization of cost functions is conducted to train prediction engines and consequently tune their parameters. The prevalent cost functions of prediction engines in WPPI models are mainly non-differentiable and non-convex, and therefore the training process becomes problematic. To transcend such a crucial barrier, this paper addresses a new very short-term WPPI framework based on a bi-level formulation and benefiting from a differentiable and convex cost function. The prediction engine is trained by classical global optimization of the cost function in the lower-level problem, while hyperparameters that control the quality of the WPPIs are injected thereto from the upper-level problem. The hyperparameters can be tuned such that the most useful WPPIs are constructed from the lower-level problem depending on the power system operator's preferences. Lessening the need to heuristically tune a large number of prediction engine parameters is the foremost contribution of this work to the WPPI literature. The superior performance of the proposed WPPI is verified in the multistep ahead prediction of real wind power generation data in comparison to well-tailored benchmark models.

Original languageEnglish
Article number8477144
Pages (from-to)1289-1300
Number of pages12
JournalIEEE Transactions on Power Systems
Issue number2
Publication statusPublished - Mar 2019
Externally publishedYes


  • Bi-level optimization
  • convex optimization
  • prediction interval
  • wind power prediction

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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