From Optimization-Based Machine Learning to Interpretable Security Rules for Operation

Various supervised machine learning approaches have been used in the past to assess the power system security (also known as reliability). This is typically done by training a classifier on a large number of operating points whose postfault status (stable or unstable) has been determined via time-domain simulations. The output of this training process can be expressed as a security rule that is used online to classify an operating point. A critical, and little-studied aspect of these approaches is the interpretability of the rules produced. The lack of interpretability is a well-known issue of some machine learning approaches, especially when dealing with difficult classification problems. In the case of the security assessment of the power system, which is a complex mission-critical task, interpretability is a key requirement for the adoption and deployment by operators of these approaches. In this paper, for the first time, we explore the tradeoff between predictive accuracy and interpretability in the context of power system security assessment. We begin by demonstrating how decision trees (DTs) can be used to learn data-driven security rules and use the tree depth as a measure for interpretability. We leverage disjunctive programming to formulate novel training methods, capable of learning high-quality DTs while still maintaining interpretability. In particular, we propose two new approaches: 1) optimal classification trees is proposed for training DTs of low-depth and 2) greedy optimization-based tree is proposed for training DTs of intermediate depth, where the increased computational burden is managed by exploiting the nested tree structure. We also demonstrate that the ability to generate high-quality interpretable rules can actually translate to impressive benefits in terms of training requirements. Through case studies on the IEEE 68-bus system, we demonstrate that the proposed methods can produce DTs of higher quality compared to the state-of-the-art approach classification and regression tree approach, also if the DT was trained on a significant smaller database, resulting in computational savings of 80%. Given that generating a large training database is a practical bottleneck in these data-driven approaches, this is a significant breakthrough for real-world application.