Chance-constrained DC Optimal Power Flow with Non-Gaussian Distributed Uncertainties

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Abstract
Chance-constrained programming (CCP) is a promising approach to handle uncertainties in optimal power flow (OPF). However, conventional CCP usually assumes that uncertainties follow Gaussian distributions, which may not match reality. A few papers employed the Gaussian mixture model (GMM) to extend CCP to cases with non-Gaussian uncertainties, but they are only appropriate for cases with uncertainties on the right-hand side but not applicable to DC OPF that containing left-hand side uncertainties. To address this, we develop a tractable GMM-based chance-constrained DC OPF model. In this model, we not only leverage GMM to capture the probability characteristics of non-Gaussian distributed uncertainties, but also develop a linearization technique to reformulate the chance constraints with non-Gaussian distributed uncertainties on the lefthand side into tractable forms. A mathematical proof is further provided to demonstrate that the corresponding reformulation is a safe approximation of the original problem, which guarantees the feasibility of solutions.
Funding Information
  • Science and Technology Development Fund (SKL-IOTSC(UM)-2021-2023,0137/2019/A3,0003/2020/AKP)

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