<p>With the growing penetration of renewable energy sources (RESs), power system operation faces increased uncertainty, making probabilistic optimal power flow (POPF) essential for secure and cost-effective decision-making. Many existing POPF approaches rely on parametric distribution assumptions and approximation techniques, which can reduce accuracy—especially under non-Gaussian uncertainties—and may lead to high computational cost. This paper proposes a non-parametric POPF (N-POPF) framework that represents uncertainty using quantiles, thereby avoiding explicit assumptions about input probability distributions. To solve the resulting N-POPF efficiently, we develop a Quantile Regression Forest (QRF)-based method that learns an inverse power flow mapping and combines critical-region (CR) partitioning with a discrete integration procedure to compute probabilistic outputs. The proposed approach is evaluated on the IEEE 24-bus, IEEE 118-bus, and modified IEEE 300-bus test systems and is compared with common benchmark methods. The results demonstrate that the proposed QRF-based N-POPF provides accurate quantile estimates while maintaining favorable computational performance, supporting its applicability to power system operation studies with significant renewable integration.</p>

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Cost-effective power system operation with nonparametric Probabilistic optimal power flow and quantile regression forests method

  • Chengfu Sun,
  • Chengyu Zhang

摘要

With the growing penetration of renewable energy sources (RESs), power system operation faces increased uncertainty, making probabilistic optimal power flow (POPF) essential for secure and cost-effective decision-making. Many existing POPF approaches rely on parametric distribution assumptions and approximation techniques, which can reduce accuracy—especially under non-Gaussian uncertainties—and may lead to high computational cost. This paper proposes a non-parametric POPF (N-POPF) framework that represents uncertainty using quantiles, thereby avoiding explicit assumptions about input probability distributions. To solve the resulting N-POPF efficiently, we develop a Quantile Regression Forest (QRF)-based method that learns an inverse power flow mapping and combines critical-region (CR) partitioning with a discrete integration procedure to compute probabilistic outputs. The proposed approach is evaluated on the IEEE 24-bus, IEEE 118-bus, and modified IEEE 300-bus test systems and is compared with common benchmark methods. The results demonstrate that the proposed QRF-based N-POPF provides accurate quantile estimates while maintaining favorable computational performance, supporting its applicability to power system operation studies with significant renewable integration.