Inverse Probabilistic Security-Constrained Optimal Power Flow for Reliability Parameter Calibration, Transmission Investment, and Standard Setting

The provision of reliable and cost-effective electricity supply is vital for modern societies. Achieving this balance between reliability and cost can be explored through stochastic optimization models. However, these models are often perceived by practitioners as overly complex, intractable and demanding extensive, often unavailable, reliability data. This paper presents a novel approach: the inverse optimization problem of the probabilistic security-constrained optimal power flow (PSC-OPF). This method enables the determination of missing outage and repair rates of network components, aligning with observed supply continuity levels. By integrating the determined (or calibrated) outage and repair rates into a transmission network expansion planning model, we assess the impacts of network investments on enhancing supply continuity levels. We employ machine learning, decomposition and regularization approaches to manage large-scale instances of stochastic problems. Through a real-world application to the Chilean power system, we demonstrate that our proposed inverse model's calibration leads to more accurate, realistic, and credible results that then can be used to appropriately plan network investments. Our results informed the setting and upgrading of the transmission network reliability standards in Chile, resulting in substantial cost savings and supply continuity enhancements for the electricity consumers.