Computationally Efficient Data-Driven Joint Chance Constraints for Power Systems Scheduling

Although data-driven nonparametric Joint Chance Constraints (JCCs) may lead to more reliable decision-making than individual chance constraints, their computational complexity is a major bottleneck. This paper presents computationally efficient data-driven nonparametric joint chance-constrained prog...

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Bibliographic Details
Published inIEEE transactions on power systems Vol. 38; no. 3; pp. 2858 - 2867
Main Authors Wu, Chutian, Kargarian, Amin
Format Journal Article
LanguageEnglish
Published New York IEEE 01.05.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Approximation
Computational efficiency
Computational modeling
Constraint modelling
data-driven
Decision making
Indexes
joint chance constraint
Kernel
Kernel function
Kernel functions
linear relaxation
Linearization
Optimization
Parameter uncertainty
Power system optimization
Programming
Renewable energy sources
Scheduling
Systems management
Tightness
Transmission lines
Uncertainty
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Summary:Although data-driven nonparametric Joint Chance Constraints (JCCs) may lead to more reliable decision-making than individual chance constraints, their computational complexity is a major bottleneck. This paper presents computationally efficient data-driven nonparametric joint chance-constrained programming for multi-interval power systems management. Reserve and transmission line constraints are modeled as data-driven JCCs. Piecewise uniform kernel functions incorporate historical data of uncertain parameters into optimization. Data-driven nonparametric JCCs are modeled as a product of integrated kernel functions. Two approaches are proposed to linearize data-driven nonparametric JCCs. i) The noncontinuous kernel function is linearized with Special Ordered Sets of type 1 (SOS1) variables. ii) A tight convex envelope of multilinear monomial terms, which appear due to the product of kernel functions, is approximated by an optimization subproblem making the scheduling problem bi-level optimization. The continuity and linearity of the lower-level convex envelope approximation subproblem allow replacing it with optimality conditions to form a single-level scheduling problem. Simulation results show the tightness of the proposed linearization approaches and the computational efficiency of data-driven JCC programming.
ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2022.3195127