A framework based on mixed-integer models to support the operation of active distribution systems with invisible ders. Uma metodologia baseada em modelos de programação inteira mista para apoiar a operação de sistemas de distribuição ativos com ders invisíveis

Abstract

The modernization of electric power systems, marked by the widespread deployment of Distributed Energy Resources (DERs), is transforming traditional distribution networks into dynamic, actively managed systems. However, a major operational challenge persists: the limited visibility of unmonitored DERs, hereon referred to as invisible DERs. While critical to future grid flexibility, these resources introduce uncertainty that hampers system observability, operational decision-making, and resilience. This research proposes a novel methodological framework based on mixed-integer optimization models to support the operation of active distribution systems under limited DER observability. The approach focuses on developing equivalent aggregate models for invisible DERs, enabling system operators to infer critical network states—such as voltage magnitudes and branch power flows—using sparse or incomplete measurement data. By formulating the problem as a convex Mixed-Integer Nonlinear Programming (MINLP) task, the methodology allows for strategically placing and sizing equivalent aggregate DER models that best replicate observed system behavior in steady-state. The research introduces a linearized model variant, including Mixed-Integer Linear Programming (MILP) formulation using McCormick relaxations to enhance computational tractability without compromising estimation accuracy. Furthermore, hybrid DER models combining technologies such as photovoltaic generation and battery storage are incorporated to better capture the steady-state behavior of modern distribution networks with invisible hybrid DERs. Comprehensive case studies demonstrate that the proposed framework can accurately estimate unobserved system states even under reduced number of metered buses, achieving low average errors while significantly reducing solution times through linearization techniques. The integration with OpenDSS enables the validation of the implementation in an industry-standard tool of equivalent feeder models with aggregate DER models representing innumerable invisible resources with high numerical accuracy and reduced solution times. Overall, this work advances the state-of-the-art by providing a scalable, data-efficient modeling approach that empowers distribution system operators to maintain reliable and efficient grid operations despite the growing presence of invisible DERs.